TSTP Solution File: HWV029-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV029-2 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 02:10:45 EDT 2022
% Result : Unsatisfiable 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : HWV029-2 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 22:21:32 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.47 % SZS status Unsatisfiable
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 tff(p_LES_EQU__type, type, (
% 0.21/0.47 p_LES_EQU_: ( $i * $i ) > $o)).
% 0.21/0.47 tff(f__length__type, type, (
% 0.21/0.47 f__length_: $i > $i)).
% 0.21/0.47 tff(f__empty__type, type, (
% 0.21/0.47 f__empty_: $i)).
% 0.21/0.47 tff(fwork_DOTfifo_DOTrtl_DOTfifo__length__type, type, (
% 0.21/0.47 fwork_DOTfifo_DOTrtl_DOTfifo__length_: $i)).
% 0.21/0.47 tff(f_SUB__type, type, (
% 0.21/0.47 f_SUB_: ( $i * $i ) > $i)).
% 0.21/0.47 tff(n1_type, type, (
% 0.21/0.47 n1: $i)).
% 0.21/0.47 tff(f_ADD__type, type, (
% 0.21/0.47 f_ADD_: ( $i * $i ) > $i)).
% 0.21/0.47 tff(n0_type, type, (
% 0.21/0.47 n0: $i)).
% 0.21/0.47 tff(def_89_type, type, (
% 0.21/0.47 def_89: ( $i * $i ) > $o)).
% 0.21/0.47 tff(fwork_DOTfifo_DOTrtl_DOTint__level__type, type, (
% 0.21/0.47 fwork_DOTfifo_DOTrtl_DOTint__level_: $i > $i)).
% 0.21/0.47 tff(t_206_type, type, (
% 0.21/0.47 t_206: $i)).
% 0.21/0.47 tff(p__pred__type, type, (
% 0.21/0.47 p__pred_: $i > $o)).
% 0.21/0.47 tff(fwork_DOTfifo_DOTrtl_DOTrd__type, type, (
% 0.21/0.47 fwork_DOTfifo_DOTrtl_DOTrd_: $i > $i)).
% 0.21/0.47 tff(fwork_DOTfifo_DOTrtl_DOTlevel__type, type, (
% 0.21/0.47 fwork_DOTfifo_DOTrtl_DOTlevel_: $i > $i)).
% 0.21/0.47 tff(fwork_DOTfifo_DOTrtl_DOTwr__type, type, (
% 0.21/0.47 fwork_DOTfifo_DOTrtl_DOTwr_: $i > $i)).
% 0.21/0.47 tff(fwork_DOTfifo_DOTrtl_DOTreset__type, type, (
% 0.21/0.47 fwork_DOTfifo_DOTrtl_DOTreset_: $i > $i)).
% 0.21/0.47 tff(1,plain,
% 0.21/0.47 ((n1 = f_ADD_(n0, n1)) <=> (n1 = f_ADD_(f__length_(f__empty_), n1))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(2,plain,
% 0.21/0.47 ((n1 = f_ADD_(n0, n1)) <=> (n1 = f_ADD_(n0, n1))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(3,axiom,(n1 = f_ADD_(n0, n1)), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_78')).
% 0.21/0.47 tff(4,plain,
% 0.21/0.47 (n1 = f_ADD_(n0, n1)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.21/0.47 tff(5,plain,
% 0.21/0.47 (n1 = f_ADD_(f__length_(f__empty_), n1)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.47 tff(6,plain,
% 0.21/0.47 (f_SUB_(f_ADD_(f__length_(f__empty_), n1), n1) = f_SUB_(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[5])).
% 0.21/0.47 tff(7,plain,
% 0.21/0.47 (f_SUB_(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)) = f_SUB_(f_ADD_(f__length_(f__empty_), n1), n1)),
% 0.21/0.47 inference(symmetry,[status(thm)],[6])).
% 0.21/0.47 tff(8,assumption,(def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1))), introduced(assumption)).
% 0.21/0.47 tff(9,plain,
% 0.21/0.47 (^[Y_84: $i, X_83: $i] : refl(((~(X_83 = Y_84)) | (~def_89(Y_84, X_83))) <=> ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(10,plain,
% 0.21/0.47 (![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83))) <=> ![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.47 tff(11,plain,
% 0.21/0.47 (![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83))) <=> ![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(12,axiom,(![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_64')).
% 0.21/0.47 tff(13,plain,
% 0.21/0.47 (![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.21/0.47 tff(14,plain,(
% 0.21/0.47 ![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[13])).
% 0.21/0.47 tff(15,plain,
% 0.21/0.47 (![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.21/0.47 tff(16,plain,
% 0.21/0.47 (((~![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))) | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)))) <=> ((~![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))) | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(17,plain,
% 0.21/0.47 (($false | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)))) <=> (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(18,plain,
% 0.21/0.47 ((~$true) <=> $false),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(19,plain,
% 0.21/0.47 ((f_ADD_(f__length_(f__empty_), n1) = f_ADD_(f__length_(f__empty_), n1)) <=> $true),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(20,plain,
% 0.21/0.47 ((~(f_ADD_(f__length_(f__empty_), n1) = f_ADD_(f__length_(f__empty_), n1))) <=> (~$true)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[19])).
% 0.21/0.47 tff(21,plain,
% 0.21/0.47 ((~(f_ADD_(f__length_(f__empty_), n1) = f_ADD_(f__length_(f__empty_), n1))) <=> $false),
% 0.21/0.47 inference(transitivity,[status(thm)],[20, 18])).
% 0.21/0.47 tff(22,plain,
% 0.21/0.47 (((~(f_ADD_(f__length_(f__empty_), n1) = f_ADD_(f__length_(f__empty_), n1))) | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)))) <=> ($false | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[21])).
% 0.21/0.47 tff(23,plain,
% 0.21/0.47 (((~(f_ADD_(f__length_(f__empty_), n1) = f_ADD_(f__length_(f__empty_), n1))) | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)))) <=> (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[22, 17])).
% 0.21/0.47 tff(24,plain,
% 0.21/0.47 (((~![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))) | ((~(f_ADD_(f__length_(f__empty_), n1) = f_ADD_(f__length_(f__empty_), n1))) | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1))))) <=> ((~![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))) | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[23])).
% 0.21/0.47 tff(25,plain,
% 0.21/0.47 (((~![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))) | ((~(f_ADD_(f__length_(f__empty_), n1) = f_ADD_(f__length_(f__empty_), n1))) | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1))))) <=> ((~![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))) | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[24, 16])).
% 0.21/0.47 tff(26,plain,
% 0.21/0.47 ((~![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))) | ((~(f_ADD_(f__length_(f__empty_), n1) = f_ADD_(f__length_(f__empty_), n1))) | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(27,plain,
% 0.21/0.47 ((~![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))) | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.47 tff(28,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[27, 15, 8])).
% 0.21/0.47 tff(29,plain,(~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(30,plain,
% 0.21/0.47 (f_ADD_(f__length_(f__empty_), n1) = n1),
% 0.21/0.47 inference(symmetry,[status(thm)],[5])).
% 0.21/0.47 tff(31,plain,
% 0.21/0.47 (f_ADD_(f__length_(f__empty_), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(f__length_(f__empty_), n1)),
% 0.21/0.47 inference(monotonicity,[status(thm)],[30])).
% 0.21/0.47 tff(32,plain,
% 0.21/0.47 (^[Y_84: $i, Z_85: $i, X_83: $i] : refl(((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83))) <=> ((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(33,plain,
% 0.21/0.47 (![Y_84: $i, Z_85: $i, X_83: $i] : ((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83))) <=> ![Y_84: $i, Z_85: $i, X_83: $i] : ((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.47 tff(34,plain,
% 0.21/0.47 (![Y_84: $i, Z_85: $i, X_83: $i] : ((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83))) <=> ![Y_84: $i, Z_85: $i, X_83: $i] : ((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(35,plain,
% 0.21/0.47 (^[Y_84: $i, Z_85: $i, X_83: $i] : trans(monotonicity(rewrite((def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83))) <=> (def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83)))), (((def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83))) | (f_SUB_(X_83, Y_84) = Z_85)) <=> ((def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83))) | (f_SUB_(X_83, Y_84) = Z_85)))), rewrite(((def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83))) | (f_SUB_(X_83, Y_84) = Z_85)) <=> ((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83)))), (((def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83))) | (f_SUB_(X_83, Y_84) = Z_85)) <=> ((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(36,plain,
% 0.21/0.47 (![Y_84: $i, Z_85: $i, X_83: $i] : ((def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83))) | (f_SUB_(X_83, Y_84) = Z_85)) <=> ![Y_84: $i, Z_85: $i, X_83: $i] : ((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.47 tff(37,axiom,(![Y_84: $i, Z_85: $i, X_83: $i] : ((def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83))) | (f_SUB_(X_83, Y_84) = Z_85))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_63')).
% 0.21/0.47 tff(38,plain,
% 0.21/0.47 (![Y_84: $i, Z_85: $i, X_83: $i] : ((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.47 tff(39,plain,
% 0.21/0.47 (![Y_84: $i, Z_85: $i, X_83: $i] : ((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.21/0.47 tff(40,plain,(
% 0.21/0.47 ![Y_84: $i, Z_85: $i, X_83: $i] : ((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[39])).
% 0.21/0.47 tff(41,plain,
% 0.21/0.47 (![Y_84: $i, Z_85: $i, X_83: $i] : ((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.21/0.47 tff(42,plain,
% 0.21/0.47 (((~![Y_84: $i, Z_85: $i, X_83: $i] : ((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83)))) | ((f_SUB_(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)) = f__length_(f__empty_)) | def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)) | (~(f_ADD_(f__length_(f__empty_), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(f__length_(f__empty_), n1))))) <=> ((~![Y_84: $i, Z_85: $i, X_83: $i] : ((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83)))) | (f_SUB_(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)) = f__length_(f__empty_)) | def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)) | (~(f_ADD_(f__length_(f__empty_), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(f__length_(f__empty_), n1))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(43,plain,
% 0.21/0.47 ((~![Y_84: $i, Z_85: $i, X_83: $i] : ((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83)))) | ((f_SUB_(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)) = f__length_(f__empty_)) | def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)) | (~(f_ADD_(f__length_(f__empty_), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(f__length_(f__empty_), n1))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(44,plain,
% 0.21/0.47 ((~![Y_84: $i, Z_85: $i, X_83: $i] : ((f_SUB_(X_83, Y_84) = Z_85) | def_89(Y_84, X_83) | (~(f_ADD_(Z_85, Y_84) = X_83)))) | (f_SUB_(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)) = f__length_(f__empty_)) | def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)) | (~(f_ADD_(f__length_(f__empty_), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(f__length_(f__empty_), n1)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.47 tff(45,plain,
% 0.21/0.47 ((f_SUB_(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)) = f__length_(f__empty_)) | def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[44, 41, 31])).
% 0.21/0.47 tff(46,plain,
% 0.21/0.47 (f_SUB_(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1)) = f__length_(f__empty_)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[45, 29])).
% 0.21/0.48 tff(47,plain,
% 0.21/0.48 (f__length_(f__empty_) = f_SUB_(f_ADD_(f__length_(f__empty_), n1), f_ADD_(f__length_(f__empty_), n1))),
% 0.21/0.48 inference(symmetry,[status(thm)],[46])).
% 0.21/0.48 tff(48,plain,
% 0.21/0.48 (f__length_(f__empty_) = f_SUB_(f_ADD_(f__length_(f__empty_), n1), n1)),
% 0.21/0.48 inference(transitivity,[status(thm)],[47, 7])).
% 0.21/0.48 tff(49,plain,
% 0.21/0.48 (^[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)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(50,plain,
% 0.21/0.48 (![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))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[49])).
% 0.21/0.48 tff(51,plain,
% 0.21/0.48 (![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))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(52,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')).
% 0.21/0.48 tff(53,plain,
% 0.21/0.48 (![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.21/0.48 tff(54,plain,(
% 0.21/0.48 ![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))),
% 0.21/0.48 inference(skolemize,[status(sab)],[53])).
% 0.21/0.48 tff(55,plain,
% 0.21/0.48 (![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.21/0.48 tff(56,plain,
% 0.21/0.48 ((~![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))) | (fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(57,plain,
% 0.21/0.48 (fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.21/0.48 tff(58,plain,
% 0.21/0.48 (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1))),
% 0.21/0.48 inference(symmetry,[status(thm)],[57])).
% 0.21/0.48 tff(59,assumption,(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f__length_(f__empty_)), introduced(assumption)).
% 0.21/0.48 tff(60,plain,
% 0.21/0.48 (fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = f__length_(f__empty_)),
% 0.21/0.48 inference(transitivity,[status(thm)],[57, 59])).
% 0.21/0.48 tff(61,plain,
% 0.21/0.48 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), f__length_(f__empty_)) <=> p_LES_EQU_(f__length_(f__empty_), f_SUB_(f_ADD_(f__length_(f__empty_), n1), n1))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[60, 48])).
% 0.21/0.48 tff(62,plain,
% 0.21/0.48 (p_LES_EQU_(f__length_(f__empty_), f_SUB_(f_ADD_(f__length_(f__empty_), n1), n1)) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), f__length_(f__empty_))),
% 0.21/0.48 inference(symmetry,[status(thm)],[61])).
% 0.21/0.48 tff(63,plain,
% 0.21/0.48 (p_LES_EQU_(f__length_(f__empty_), f__length_(f__empty_)) <=> p_LES_EQU_(f__length_(f__empty_), f_SUB_(f_ADD_(f__length_(f__empty_), n1), n1))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[48])).
% 0.21/0.48 tff(64,plain,
% 0.21/0.48 (p_LES_EQU_(f__length_(f__empty_), f_SUB_(f_ADD_(f__length_(f__empty_), n1), n1)) <=> p_LES_EQU_(f__length_(f__empty_), f__length_(f__empty_))),
% 0.21/0.48 inference(symmetry,[status(thm)],[63])).
% 0.21/0.48 tff(65,plain,
% 0.21/0.48 ((~p_LES_EQU_(f__length_(f__empty_), f_SUB_(f_ADD_(f__length_(f__empty_), n1), n1))) <=> (~p_LES_EQU_(f__length_(f__empty_), f__length_(f__empty_)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[64])).
% 0.21/0.48 tff(66,assumption,(~p_LES_EQU_(f__length_(f__empty_), f_SUB_(f_ADD_(f__length_(f__empty_), n1), n1))), introduced(assumption)).
% 0.21/0.48 tff(67,plain,
% 0.21/0.48 (~p_LES_EQU_(f__length_(f__empty_), f__length_(f__empty_))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.21/0.48 tff(68,plain,
% 0.21/0.48 (^[X_106: $i] : refl(p_LES_EQU_(X_106, X_106) <=> p_LES_EQU_(X_106, X_106))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(69,plain,
% 0.21/0.48 (![X_106: $i] : p_LES_EQU_(X_106, X_106) <=> ![X_106: $i] : p_LES_EQU_(X_106, X_106)),
% 0.21/0.48 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.48 tff(70,plain,
% 0.21/0.48 (![X_106: $i] : p_LES_EQU_(X_106, X_106) <=> ![X_106: $i] : p_LES_EQU_(X_106, X_106)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(71,axiom,(![X_106: $i] : p_LES_EQU_(X_106, X_106)), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_75')).
% 0.21/0.48 tff(72,plain,
% 0.21/0.48 (![X_106: $i] : p_LES_EQU_(X_106, X_106)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.48 tff(73,plain,(
% 0.21/0.48 ![X_106: $i] : p_LES_EQU_(X_106, X_106)),
% 0.21/0.48 inference(skolemize,[status(sab)],[72])).
% 0.21/0.48 tff(74,plain,
% 0.21/0.48 (![X_106: $i] : p_LES_EQU_(X_106, X_106)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.21/0.48 tff(75,plain,
% 0.21/0.48 ((~![X_106: $i] : p_LES_EQU_(X_106, X_106)) | p_LES_EQU_(f__length_(f__empty_), f__length_(f__empty_))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(76,plain,
% 0.21/0.48 (p_LES_EQU_(f__length_(f__empty_), f__length_(f__empty_))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.21/0.48 tff(77,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[76, 67])).
% 0.21/0.48 tff(78,plain,(p_LES_EQU_(f__length_(f__empty_), f_SUB_(f_ADD_(f__length_(f__empty_), n1), n1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(79,plain,
% 0.21/0.48 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), f__length_(f__empty_))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[78, 62])).
% 0.21/0.48 tff(80,plain,
% 0.21/0.48 ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0)) <=> (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f__length_(f__empty_)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(81,plain,
% 0.21/0.48 ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0)) <=> (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(82,axiom,(~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_3')).
% 0.21/0.48 tff(83,plain,
% 0.21/0.48 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.21/0.48 tff(84,plain,
% 0.21/0.48 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f__length_(f__empty_))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[83, 80])).
% 0.21/0.48 tff(85,plain,
% 0.21/0.48 ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_)) <=> (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(86,axiom,(~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_2')).
% 0.21/0.48 tff(87,plain,
% 0.21/0.48 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.48 tff(88,plain,
% 0.21/0.48 (^[X_98: $i, Y_99: $i, Z_100: $i] : refl((p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98))) <=> (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(89,plain,
% 0.21/0.48 (![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98))) <=> ![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[88])).
% 0.21/0.48 tff(90,plain,
% 0.21/0.48 (![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98))) <=> ![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(91,plain,
% 0.21/0.48 (^[X_98: $i, Y_99: $i, Z_100: $i] : rewrite((((~p_LES_EQU_(Z_100, X_98)) | p_LES_EQU_(Y_99, X_98)) | p_LES_EQU_(Z_100, Y_99)) <=> (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(92,plain,
% 0.21/0.48 (![X_98: $i, Y_99: $i, Z_100: $i] : (((~p_LES_EQU_(Z_100, X_98)) | p_LES_EQU_(Y_99, X_98)) | p_LES_EQU_(Z_100, Y_99)) <=> ![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[91])).
% 0.21/0.48 tff(93,axiom,(![X_98: $i, Y_99: $i, Z_100: $i] : (((~p_LES_EQU_(Z_100, X_98)) | p_LES_EQU_(Y_99, X_98)) | p_LES_EQU_(Z_100, Y_99))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_71')).
% 0.21/0.48 tff(94,plain,
% 0.21/0.48 (![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.48 tff(95,plain,
% 0.21/0.48 (![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.21/0.48 tff(96,plain,(
% 0.21/0.48 ![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[95])).
% 0.21/0.48 tff(97,plain,
% 0.21/0.48 (![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.21/0.48 tff(98,plain,
% 0.21/0.48 (((~![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))) | (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f__length_(f__empty_)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), f__length_(f__empty_))))) <=> ((~![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f__length_(f__empty_)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), f__length_(f__empty_))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(99,plain,
% 0.21/0.48 ((~![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))) | (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f__length_(f__empty_)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), f__length_(f__empty_))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(100,plain,
% 0.21/0.48 ((~![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f__length_(f__empty_)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), f__length_(f__empty_)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.21/0.48 tff(101,plain,
% 0.21/0.48 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), f__length_(f__empty_))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[100, 97, 87, 84])).
% 0.21/0.48 tff(102,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[101, 79])).
% 0.21/0.48 tff(103,plain,(~(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f__length_(f__empty_))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(104,plain,
% 0.21/0.48 (^[T_5: $i] : refl(((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = f__length_(f__empty_))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = f__length_(f__empty_))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(105,plain,
% 0.21/0.48 (![T_5: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = f__length_(f__empty_))) <=> ![T_5: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = f__length_(f__empty_)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[104])).
% 0.21/0.48 tff(106,plain,
% 0.21/0.48 (^[T_5: $i] : rewrite(((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = n0)) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = f__length_(f__empty_))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(107,plain,
% 0.21/0.48 (![T_5: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = n0)) <=> ![T_5: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = f__length_(f__empty_)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[106])).
% 0.21/0.48 tff(108,plain,
% 0.21/0.48 (![T_5: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = n0)) <=> ![T_5: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = n0))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(109,plain,
% 0.21/0.48 (^[T_5: $i] : rewrite(((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = n0) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = n0)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(110,plain,
% 0.21/0.48 (![T_5: $i] : ((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = n0) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5)))) <=> ![T_5: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = n0))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[109])).
% 0.21/0.48 tff(111,axiom,(![T_5: $i] : ((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = n0) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_12')).
% 0.21/0.48 tff(112,plain,
% 0.21/0.48 (![T_5: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = n0))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.48 tff(113,plain,
% 0.21/0.48 (![T_5: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = n0))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.21/0.48 tff(114,plain,
% 0.21/0.48 (![T_5: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = f__length_(f__empty_)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[113, 107])).
% 0.21/0.48 tff(115,plain,(
% 0.21/0.48 ![T_5: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = f__length_(f__empty_)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[114])).
% 0.21/0.48 tff(116,plain,
% 0.21/0.48 (![T_5: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = f__length_(f__empty_)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[115, 105])).
% 0.21/0.48 tff(117,plain,
% 0.21/0.48 (((~![T_5: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = f__length_(f__empty_)))) | ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f__length_(f__empty_)))) <=> ((~![T_5: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = f__length_(f__empty_)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f__length_(f__empty_)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(118,plain,
% 0.21/0.48 ((~![T_5: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = f__length_(f__empty_)))) | ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f__length_(f__empty_)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(119,plain,
% 0.21/0.48 ((~![T_5: $i] : ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_5))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_5, n1)) = f__length_(f__empty_)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f__length_(f__empty_))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.48 tff(120,plain,
% 0.21/0.48 ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f__length_(f__empty_))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[119, 116])).
% 0.21/0.48 tff(121,plain,
% 0.21/0.48 (~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[120, 103])).
% 0.21/0.48 tff(122,assumption,(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)), introduced(assumption)).
% 0.21/0.48 tff(123,plain,
% 0.21/0.48 (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))),
% 0.21/0.48 inference(symmetry,[status(thm)],[122])).
% 0.21/0.48 tff(124,plain,
% 0.21/0.48 ((~![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))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(125,plain,
% 0.21/0.48 (fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[124, 55])).
% 0.21/0.48 tff(126,plain,
% 0.21/0.48 (fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1))),
% 0.21/0.48 inference(transitivity,[status(thm)],[125, 123, 58])).
% 0.21/0.48 tff(127,plain,
% 0.21/0.48 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[126])).
% 0.21/0.48 tff(128,plain,
% 0.21/0.48 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.48 inference(symmetry,[status(thm)],[127])).
% 0.21/0.48 tff(129,plain,
% 0.21/0.48 ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_)) <=> (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[128])).
% 0.21/0.48 tff(130,plain,
% 0.21/0.48 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[87, 129])).
% 0.21/0.48 tff(131,plain,
% 0.21/0.48 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(132,axiom,(p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_1')).
% 0.21/0.48 tff(133,plain,
% 0.21/0.48 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.48 tff(134,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[133, 130])).
% 0.21/0.48 tff(135,plain,(~(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(136,assumption,(~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))), introduced(assumption)).
% 0.21/0.48 tff(137,plain,
% 0.21/0.48 (^[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__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))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(138,plain,
% 0.21/0.48 (![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))) <=> ![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)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[137])).
% 0.21/0.48 tff(139,plain,
% 0.21/0.48 (![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))) <=> ![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)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(140,plain,
% 0.21/0.48 (^[T_13: $i] : trans(monotonicity(trans(monotonicity(rewrite(((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = 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)))), ((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = 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__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__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)))), ((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = 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))))), (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = 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__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__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)))), (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = 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)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(141,plain,
% 0.21/0.48 (![T_13: $i] : ((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = 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)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[140])).
% 0.21/0.48 tff(142,axiom,(![T_13: $i] : ((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = 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_51')).
% 0.21/0.48 tff(143,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.21/0.48 tff(144,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.21/0.48 tff(145,plain,(
% 0.21/0.48 ![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)))),
% 0.21/0.48 inference(skolemize,[status(sab)],[144])).
% 0.21/0.48 tff(146,plain,
% 0.21/0.48 (![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)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[145, 138])).
% 0.21/0.48 tff(147,plain,
% 0.21/0.48 (((~![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__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)))) <=> ((~![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__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)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(148,plain,
% 0.21/0.48 ((~![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__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)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(149,plain,
% 0.21/0.48 ((~![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__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))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.21/0.48 tff(150,plain,
% 0.21/0.48 (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))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[149, 146])).
% 0.21/0.48 tff(151,plain,
% 0.21/0.48 (p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[150, 136, 135, 121])).
% 0.21/0.48 tff(152,plain,
% 0.21/0.48 (^[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)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(153,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[152])).
% 0.21/0.48 tff(154,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(155,plain,
% 0.21/0.48 (^[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))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(156,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[155])).
% 0.21/0.48 tff(157,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')).
% 0.21/0.48 tff(158,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.21/0.48 tff(159,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.21/0.48 tff(160,plain,(
% 0.21/0.48 ![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))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[159])).
% 0.21/0.48 tff(161,plain,
% 0.21/0.48 (![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))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[160, 153])).
% 0.21/0.48 tff(162,plain,
% 0.21/0.48 (((~![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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(163,plain,
% 0.21/0.48 ((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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(164,plain,
% 0.21/0.48 (((~![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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[163])).
% 0.21/0.48 tff(165,plain,
% 0.21/0.48 (((~![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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[164, 162])).
% 0.21/0.49 tff(166,plain,
% 0.21/0.49 ((~![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))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(167,plain,
% 0.21/0.49 ((~![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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.21/0.49 tff(168,plain,
% 0.21/0.49 (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(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__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[167, 161])).
% 0.21/0.49 tff(169,plain,
% 0.21/0.49 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[168, 136, 135, 121, 151])).
% 0.21/0.49 tff(170,plain,
% 0.21/0.49 (^[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))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(171,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[170])).
% 0.21/0.49 tff(172,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(173,plain,
% 0.21/0.49 (^[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)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(174,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[173])).
% 0.21/0.49 tff(175,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')).
% 0.21/0.49 tff(176,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.21/0.49 tff(177,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.21/0.49 tff(178,plain,(
% 0.21/0.49 ![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)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[177])).
% 0.21/0.49 tff(179,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[178, 171])).
% 0.21/0.49 tff(180,plain,
% 0.21/0.49 (((~![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))) | 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))) | 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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(181,plain,
% 0.21/0.49 ((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))) | 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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(182,plain,
% 0.21/0.49 (((~![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))) | 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))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[181])).
% 0.21/0.49 tff(183,plain,
% 0.21/0.49 (((~![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))) | 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)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[182, 180])).
% 0.21/0.49 tff(184,plain,
% 0.21/0.49 ((~![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)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(185,plain,
% 0.21/0.49 ((~![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))) | 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))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.21/0.49 tff(186,plain,
% 0.21/0.49 (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_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))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[185, 179])).
% 0.21/0.49 tff(187,plain,
% 0.21/0.49 (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[186, 169, 136, 121, 151])).
% 0.21/0.49 tff(188,plain,
% 0.21/0.49 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))),
% 0.21/0.49 inference(symmetry,[status(thm)],[187])).
% 0.21/0.49 tff(189,plain,
% 0.21/0.49 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1))),
% 0.21/0.49 inference(transitivity,[status(thm)],[188, 58])).
% 0.21/0.49 tff(190,plain,
% 0.21/0.49 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[189])).
% 0.21/0.49 tff(191,plain,
% 0.21/0.49 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) <=> p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.49 inference(symmetry,[status(thm)],[190])).
% 0.21/0.49 tff(192,plain,
% 0.21/0.49 ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_)) <=> (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[191])).
% 0.21/0.49 tff(193,plain,
% 0.21/0.49 (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[87, 192])).
% 0.21/0.49 tff(194,plain,
% 0.21/0.49 (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),
% 0.21/0.49 inference(symmetry,[status(thm)],[125])).
% 0.21/0.49 tff(195,plain,
% 0.21/0.49 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[194])).
% 0.21/0.49 tff(196,plain,
% 0.21/0.49 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.49 inference(symmetry,[status(thm)],[195])).
% 0.21/0.49 tff(197,plain,
% 0.21/0.49 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[133, 196])).
% 0.21/0.49 tff(198,plain,
% 0.21/0.49 (^[Y_95: $i, X_94: $i] : refl(((X_94 = Y_95) | (~p_LES_EQU_(X_94, Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95)) <=> ((X_94 = Y_95) | (~p_LES_EQU_(X_94, Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(199,plain,
% 0.21/0.49 (![Y_95: $i, X_94: $i] : ((X_94 = Y_95) | (~p_LES_EQU_(X_94, Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95)) <=> ![Y_95: $i, X_94: $i] : ((X_94 = Y_95) | (~p_LES_EQU_(X_94, Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[198])).
% 0.21/0.49 tff(200,plain,
% 0.21/0.49 (![Y_95: $i, X_94: $i] : ((X_94 = Y_95) | (~p_LES_EQU_(X_94, Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95)) <=> ![Y_95: $i, X_94: $i] : ((X_94 = Y_95) | (~p_LES_EQU_(X_94, Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(201,plain,
% 0.21/0.49 (^[Y_95: $i, X_94: $i] : rewrite((((~p_LES_EQU_(X_94, Y_95)) | (X_94 = Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95)) <=> ((X_94 = Y_95) | (~p_LES_EQU_(X_94, Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(202,plain,
% 0.21/0.49 (![Y_95: $i, X_94: $i] : (((~p_LES_EQU_(X_94, Y_95)) | (X_94 = Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95)) <=> ![Y_95: $i, X_94: $i] : ((X_94 = Y_95) | (~p_LES_EQU_(X_94, Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[201])).
% 0.21/0.49 tff(203,axiom,(![Y_95: $i, X_94: $i] : (((~p_LES_EQU_(X_94, Y_95)) | (X_94 = Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_69')).
% 0.21/0.49 tff(204,plain,
% 0.21/0.49 (![Y_95: $i, X_94: $i] : ((X_94 = Y_95) | (~p_LES_EQU_(X_94, Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.21/0.49 tff(205,plain,
% 0.21/0.49 (![Y_95: $i, X_94: $i] : ((X_94 = Y_95) | (~p_LES_EQU_(X_94, Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[204, 200])).
% 0.21/0.49 tff(206,plain,(
% 0.21/0.49 ![Y_95: $i, X_94: $i] : ((X_94 = Y_95) | (~p_LES_EQU_(X_94, Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95))),
% 0.21/0.49 inference(skolemize,[status(sab)],[205])).
% 0.21/0.49 tff(207,plain,
% 0.21/0.49 (![Y_95: $i, X_94: $i] : ((X_94 = Y_95) | (~p_LES_EQU_(X_94, Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[206, 199])).
% 0.21/0.49 tff(208,plain,
% 0.21/0.49 (((~![Y_95: $i, X_94: $i] : ((X_94 = Y_95) | (~p_LES_EQU_(X_94, Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95))) | ((fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTfifo__length_) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_))) <=> ((~![Y_95: $i, X_94: $i] : ((X_94 = Y_95) | (~p_LES_EQU_(X_94, Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTfifo__length_) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(209,plain,
% 0.21/0.49 ((~![Y_95: $i, X_94: $i] : ((X_94 = Y_95) | (~p_LES_EQU_(X_94, Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95))) | ((fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTfifo__length_) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(210,plain,
% 0.21/0.49 ((~![Y_95: $i, X_94: $i] : ((X_94 = Y_95) | (~p_LES_EQU_(X_94, Y_95)) | p_LES_EQU_(f_ADD_(X_94, n1), Y_95))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTfifo__length_) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.21/0.49 tff(211,plain,
% 0.21/0.49 ((fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTfifo__length_) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[210, 207])).
% 0.21/0.49 tff(212,plain,
% 0.21/0.49 (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTfifo__length_),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[211, 197, 193])).
% 0.21/0.49 tff(213,plain,
% 0.21/0.49 (fwork_DOTfifo_DOTrtl_DOTfifo__length_ = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),
% 0.21/0.49 inference(symmetry,[status(thm)],[212])).
% 0.21/0.49 tff(214,plain,
% 0.21/0.49 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[213])).
% 0.21/0.49 tff(215,plain,
% 0.21/0.49 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.21/0.49 inference(symmetry,[status(thm)],[214])).
% 0.21/0.49 tff(216,plain,
% 0.21/0.49 ((f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) <=> (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[188])).
% 0.21/0.49 tff(217,plain,
% 0.21/0.49 ((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) <=> (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.21/0.49 inference(symmetry,[status(thm)],[216])).
% 0.21/0.49 tff(218,plain,
% 0.21/0.49 ((~(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))) <=> (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[217])).
% 0.21/0.49 tff(219,plain,
% 0.21/0.49 (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[135, 218])).
% 0.21/0.49 tff(220,plain,
% 0.21/0.49 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[188])).
% 0.21/0.49 tff(221,plain,
% 0.21/0.49 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.21/0.49 inference(symmetry,[status(thm)],[220])).
% 0.21/0.49 tff(222,assumption,(~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)))), introduced(assumption)).
% 0.21/0.49 tff(223,plain,
% 0.21/0.49 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[58])).
% 0.21/0.49 tff(224,plain,
% 0.21/0.49 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.49 inference(symmetry,[status(thm)],[223])).
% 0.21/0.49 tff(225,plain,
% 0.21/0.49 ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_)) <=> (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[224])).
% 0.21/0.49 tff(226,plain,
% 0.21/0.49 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[87, 225])).
% 0.21/0.49 tff(227,plain,
% 0.21/0.49 (((~![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))) | (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)))) <=> ((~![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(228,plain,
% 0.21/0.49 ((p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_))) <=> (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(229,plain,
% 0.21/0.49 (((~![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))) | (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)))) <=> ((~![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))) | (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[228])).
% 0.21/0.49 tff(230,plain,
% 0.21/0.49 (((~![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))) | (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)))) <=> ((~![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[229, 227])).
% 0.21/0.49 tff(231,plain,
% 0.21/0.49 ((~![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))) | (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(232,plain,
% 0.21/0.49 ((~![X_98: $i, Y_99: $i, Z_100: $i] : (p_LES_EQU_(Z_100, Y_99) | p_LES_EQU_(Y_99, X_98) | (~p_LES_EQU_(Z_100, X_98)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.21/0.49 tff(233,plain,
% 0.21/0.49 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTfifo__length_))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[232, 97, 226])).
% 0.21/0.49 tff(234,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[233, 197, 222])).
% 0.21/0.49 tff(235,plain,(p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(236,plain,
% 0.21/0.49 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[235, 221])).
% 0.21/0.49 tff(237,plain,
% 0.21/0.49 (^[Y_102: $i, X_101: $i] : refl((p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102)) <=> (p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102)))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(238,plain,
% 0.21/0.49 (![Y_102: $i, X_101: $i] : (p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102)) <=> ![Y_102: $i, X_101: $i] : (p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[237])).
% 0.21/0.49 tff(239,plain,
% 0.21/0.49 (![Y_102: $i, X_101: $i] : (p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102)) <=> ![Y_102: $i, X_101: $i] : (p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(240,plain,
% 0.21/0.49 (^[Y_102: $i, X_101: $i] : trans(monotonicity(rewrite(((f_ADD_(X_101, n1) = Y_102) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1)))) <=> ((~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102))), ((((f_ADD_(X_101, n1) = Y_102) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1)))) | p_LES_EQU_(Y_102, X_101)) <=> (((~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102)) | p_LES_EQU_(Y_102, X_101)))), rewrite((((~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102)) | p_LES_EQU_(Y_102, X_101)) <=> (p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102))), ((((f_ADD_(X_101, n1) = Y_102) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1)))) | p_LES_EQU_(Y_102, X_101)) <=> (p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(241,plain,
% 0.21/0.49 (![Y_102: $i, X_101: $i] : (((f_ADD_(X_101, n1) = Y_102) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1)))) | p_LES_EQU_(Y_102, X_101)) <=> ![Y_102: $i, X_101: $i] : (p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[240])).
% 0.21/0.49 tff(242,axiom,(![Y_102: $i, X_101: $i] : (((f_ADD_(X_101, n1) = Y_102) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1)))) | p_LES_EQU_(Y_102, X_101))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_72')).
% 0.21/0.49 tff(243,plain,
% 0.21/0.49 (![Y_102: $i, X_101: $i] : (p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.21/0.49 tff(244,plain,
% 0.21/0.49 (![Y_102: $i, X_101: $i] : (p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[243, 239])).
% 0.21/0.50 tff(245,plain,(
% 0.21/0.50 ![Y_102: $i, X_101: $i] : (p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102))),
% 0.21/0.50 inference(skolemize,[status(sab)],[244])).
% 0.21/0.50 tff(246,plain,
% 0.21/0.50 (![Y_102: $i, X_101: $i] : (p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[245, 238])).
% 0.21/0.50 tff(247,plain,
% 0.21/0.50 (((~![Y_102: $i, X_101: $i] : (p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102))) | (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))) | (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))) <=> ((~![Y_102: $i, X_101: $i] : (p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))) | (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(248,plain,
% 0.21/0.50 ((~![Y_102: $i, X_101: $i] : (p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102))) | (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))) | (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(249,plain,
% 0.21/0.50 ((~![Y_102: $i, X_101: $i] : (p_LES_EQU_(Y_102, X_101) | (~p_LES_EQU_(Y_102, f_ADD_(X_101, n1))) | (f_ADD_(X_101, n1) = Y_102))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))) | (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.21/0.50 tff(250,plain,
% 0.21/0.50 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))) | (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[249, 246])).
% 0.21/0.50 tff(251,plain,
% 0.21/0.50 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[250, 236, 219])).
% 0.21/0.50 tff(252,plain,
% 0.21/0.50 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[251, 215])).
% 0.21/0.50 tff(253,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[169, 252])).
% 0.21/0.50 tff(254,plain,(p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(255,assumption,(~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))), introduced(assumption)).
% 0.21/0.50 tff(256,plain,
% 0.21/0.50 (^[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_DOTint__level_(T_13), f__length_(f__empty_)))) <=> (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_DOTint__level_(T_13), f__length_(f__empty_)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(257,plain,
% 0.21/0.50 (![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_DOTint__level_(T_13), f__length_(f__empty_)))) <=> ![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_DOTint__level_(T_13), f__length_(f__empty_))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[256])).
% 0.21/0.50 tff(258,plain,
% 0.21/0.50 (^[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_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_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_DOTint__level_(T_13), f__length_(f__empty_)))))), rewrite((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_DOTint__level_(T_13), f__length_(f__empty_)))) <=> (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_DOTint__level_(T_13), f__length_(f__empty_))))), ((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_DOTint__level_(T_13), n0))) <=> (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_DOTint__level_(T_13), f__length_(f__empty_))))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(259,plain,
% 0.21/0.50 (![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_DOTint__level_(T_13), n0))) <=> ![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_DOTint__level_(T_13), f__length_(f__empty_))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[258])).
% 0.21/0.50 tff(260,plain,
% 0.21/0.50 (![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_DOTint__level_(T_13), n0))) <=> ![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_DOTint__level_(T_13), n0)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(261,plain,
% 0.21/0.50 (^[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_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)))), (((((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_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))))), ((((((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_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_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_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_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)))), ((((((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_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)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(262,plain,
% 0.21/0.50 (![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_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)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[261])).
% 0.21/0.50 tff(263,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_47')).
% 0.21/0.50 tff(264,plain,
% 0.21/0.50 (![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_DOTint__level_(T_13), n0)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.21/0.50 tff(265,plain,
% 0.21/0.50 (![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_DOTint__level_(T_13), n0)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[264, 260])).
% 0.21/0.50 tff(266,plain,
% 0.21/0.50 (![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_DOTint__level_(T_13), f__length_(f__empty_))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[265, 259])).
% 0.21/0.50 tff(267,plain,(
% 0.21/0.50 ![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_DOTint__level_(T_13), f__length_(f__empty_))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[266])).
% 0.21/0.50 tff(268,plain,
% 0.21/0.50 (![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_DOTint__level_(T_13), f__length_(f__empty_))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[267, 257])).
% 0.21/0.50 tff(269,plain,
% 0.21/0.50 (((~![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_DOTint__level_(T_13), f__length_(f__empty_))))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(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__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(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_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), f__length_(f__empty_))))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(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__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(270,plain,
% 0.21/0.50 ((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_DOTint__level_(t_206), f__length_(f__empty_)))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(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__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(271,plain,
% 0.21/0.50 (((~![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_DOTint__level_(T_13), f__length_(f__empty_))))) | (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_DOTint__level_(t_206), f__length_(f__empty_))))) <=> ((~![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_DOTint__level_(T_13), f__length_(f__empty_))))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(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__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[270])).
% 0.21/0.50 tff(272,plain,
% 0.21/0.50 (((~![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_DOTint__level_(T_13), f__length_(f__empty_))))) | (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_DOTint__level_(t_206), f__length_(f__empty_))))) <=> ((~![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_DOTint__level_(T_13), f__length_(f__empty_))))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(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__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[271, 269])).
% 0.21/0.50 tff(273,plain,
% 0.21/0.50 ((~![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_DOTint__level_(T_13), f__length_(f__empty_))))) | (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_DOTint__level_(t_206), f__length_(f__empty_))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(274,plain,
% 0.21/0.50 ((~![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_DOTint__level_(T_13), f__length_(f__empty_))))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(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__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.21/0.50 tff(275,plain,
% 0.21/0.50 (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(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__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[274, 268])).
% 0.21/0.50 tff(276,plain,
% 0.21/0.50 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[275, 255, 121, 135, 254])).
% 0.21/0.50 tff(277,plain,
% 0.21/0.50 (^[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_DOTint__level_(T_13), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTint__level_(T_13), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(278,plain,
% 0.21/0.50 (![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_DOTint__level_(T_13), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTint__level_(T_13), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[277])).
% 0.21/0.50 tff(279,plain,
% 0.21/0.50 (^[T_13: $i] : rewrite((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_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTint__level_(T_13), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(280,plain,
% 0.21/0.50 (![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_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTint__level_(T_13), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[279])).
% 0.21/0.50 tff(281,plain,
% 0.21/0.50 (![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_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(282,plain,
% 0.21/0.50 (^[T_13: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) <=> (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))), ((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))))), rewrite(((p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))), ((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))))), (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))), (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1))))), ((((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))), ((((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(283,plain,
% 0.21/0.50 (![T_13: $i] : (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[282])).
% 0.21/0.50 tff(284,axiom,(![T_13: $i] : (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_43')).
% 0.21/0.50 tff(285,plain,
% 0.21/0.50 (![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_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.21/0.50 tff(286,plain,
% 0.21/0.50 (![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_DOTint__level_(T_13), n0) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[285, 281])).
% 0.21/0.50 tff(287,plain,
% 0.21/0.50 (![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_DOTint__level_(T_13), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[286, 280])).
% 0.21/0.50 tff(288,plain,(
% 0.21/0.50 ![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_DOTint__level_(T_13), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[287])).
% 0.21/0.50 tff(289,plain,
% 0.21/0.50 (![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_DOTint__level_(T_13), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[288, 278])).
% 0.21/0.50 tff(290,plain,
% 0.21/0.50 (((~![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_DOTint__level_(T_13), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTint__level_(t_206), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_SUB_(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_DOTint__level_(T_13), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTint__level_(t_206), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(291,plain,
% 0.21/0.50 ((~![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_DOTint__level_(T_13), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTint__level_(t_206), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(292,plain,
% 0.21/0.50 ((~![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_DOTint__level_(T_13), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_SUB_(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_DOTint__level_(t_206), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.21/0.50 tff(293,plain,
% 0.21/0.50 (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_DOTint__level_(t_206), f__length_(f__empty_)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[292, 289])).
% 0.21/0.50 tff(294,plain,
% 0.21/0.50 (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[293, 276, 121, 254, 255])).
% 0.21/0.50 tff(295,plain,
% 0.21/0.50 (f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))),
% 0.21/0.50 inference(symmetry,[status(thm)],[294])).
% 0.21/0.50 tff(296,plain,
% 0.21/0.50 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[295])).
% 0.21/0.50 tff(297,plain,
% 0.21/0.50 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.21/0.50 inference(symmetry,[status(thm)],[296])).
% 0.21/0.50 tff(298,plain,
% 0.21/0.50 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[235, 297])).
% 0.21/0.50 tff(299,plain,
% 0.21/0.50 (^[X_82: $i] : refl(((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_))) <=> ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(300,plain,
% 0.21/0.50 (![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_))) <=> ![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[299])).
% 0.21/0.50 tff(301,plain,
% 0.21/0.50 (^[X_82: $i] : rewrite(((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, n0)) <=> ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(302,plain,
% 0.21/0.50 (![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, n0)) <=> ![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[301])).
% 0.21/0.50 tff(303,plain,
% 0.21/0.50 (![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, n0)) <=> ![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, n0))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(304,axiom,(![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, n0))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_61')).
% 0.21/0.50 tff(305,plain,
% 0.21/0.50 (![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, n0))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.21/0.50 tff(306,plain,
% 0.21/0.50 (![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[305, 302])).
% 0.21/0.50 tff(307,plain,(
% 0.21/0.50 ![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[306])).
% 0.21/0.50 tff(308,plain,
% 0.21/0.50 (![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[307, 300])).
% 0.21/0.50 tff(309,plain,
% 0.21/0.50 (((~![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_)))) | ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)))) <=> ((~![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_)))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(310,plain,
% 0.21/0.50 ((~![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_)))) | ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(311,plain,
% 0.21/0.50 ((~![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_)))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.21/0.50 tff(312,plain,
% 0.21/0.50 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_SUB_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[311, 308, 276])).
% 0.21/0.51 tff(313,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[312, 298])).
% 0.21/0.51 tff(314,plain,(p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(315,plain,
% 0.21/0.51 (^[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_))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(316,plain,
% 0.21/0.51 (![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_)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[315])).
% 0.21/0.51 tff(317,plain,
% 0.21/0.51 (^[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_)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(318,plain,
% 0.21/0.51 (![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_)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[317])).
% 0.21/0.51 tff(319,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(320,plain,
% 0.21/0.51 (^[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))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(321,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[320])).
% 0.21/0.51 tff(322,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')).
% 0.21/0.51 tff(323,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.21/0.51 tff(324,plain,
% 0.21/0.51 (![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))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[323, 319])).
% 0.21/0.51 tff(325,plain,
% 0.21/0.51 (![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_)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[324, 318])).
% 0.21/0.51 tff(326,plain,(
% 0.21/0.51 ![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_)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[325])).
% 0.21/0.51 tff(327,plain,
% 0.21/0.51 (![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_)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[326, 316])).
% 0.21/0.51 tff(328,plain,
% 0.21/0.51 (((~![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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(329,plain,
% 0.21/0.51 ((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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(330,plain,
% 0.21/0.51 (((~![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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[329])).
% 0.21/0.51 tff(331,plain,
% 0.21/0.51 (((~![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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[330, 328])).
% 0.21/0.51 tff(332,plain,
% 0.21/0.51 ((~![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_)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(333,plain,
% 0.21/0.51 ((~![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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.21/0.51 tff(334,plain,
% 0.21/0.51 (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[333, 327])).
% 0.21/0.51 tff(335,plain,
% 0.21/0.51 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[334, 314, 135, 121, 254])).
% 0.21/0.51 tff(336,plain,
% 0.21/0.51 (^[X_103: $i] : refl(((~p_LES_EQU_(X_103, f__length_(f__empty_))) | (X_103 = f__length_(f__empty_))) <=> ((~p_LES_EQU_(X_103, f__length_(f__empty_))) | (X_103 = f__length_(f__empty_))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(337,plain,
% 0.21/0.51 (![X_103: $i] : ((~p_LES_EQU_(X_103, f__length_(f__empty_))) | (X_103 = f__length_(f__empty_))) <=> ![X_103: $i] : ((~p_LES_EQU_(X_103, f__length_(f__empty_))) | (X_103 = f__length_(f__empty_)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[336])).
% 0.21/0.51 tff(338,plain,
% 0.21/0.51 (^[X_103: $i] : rewrite(((~p_LES_EQU_(X_103, n0)) | (X_103 = n0)) <=> ((~p_LES_EQU_(X_103, f__length_(f__empty_))) | (X_103 = f__length_(f__empty_))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(339,plain,
% 0.21/0.51 (![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0)) <=> ![X_103: $i] : ((~p_LES_EQU_(X_103, f__length_(f__empty_))) | (X_103 = f__length_(f__empty_)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[338])).
% 0.21/0.51 tff(340,plain,
% 0.21/0.51 (![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0)) <=> ![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(341,axiom,(![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_73')).
% 0.21/0.51 tff(342,plain,
% 0.21/0.51 (![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.21/0.51 tff(343,plain,
% 0.21/0.51 (![X_103: $i] : ((~p_LES_EQU_(X_103, f__length_(f__empty_))) | (X_103 = f__length_(f__empty_)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[342, 339])).
% 0.21/0.51 tff(344,plain,(
% 0.21/0.51 ![X_103: $i] : ((~p_LES_EQU_(X_103, f__length_(f__empty_))) | (X_103 = f__length_(f__empty_)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[343])).
% 0.21/0.51 tff(345,plain,
% 0.21/0.51 (![X_103: $i] : ((~p_LES_EQU_(X_103, f__length_(f__empty_))) | (X_103 = f__length_(f__empty_)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[344, 337])).
% 0.21/0.51 tff(346,plain,
% 0.21/0.51 (((~![X_103: $i] : ((~p_LES_EQU_(X_103, f__length_(f__empty_))) | (X_103 = f__length_(f__empty_)))) | ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = f__length_(f__empty_)))) <=> ((~![X_103: $i] : ((~p_LES_EQU_(X_103, f__length_(f__empty_))) | (X_103 = f__length_(f__empty_)))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = f__length_(f__empty_)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(347,plain,
% 0.21/0.51 ((~![X_103: $i] : ((~p_LES_EQU_(X_103, f__length_(f__empty_))) | (X_103 = f__length_(f__empty_)))) | ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = f__length_(f__empty_)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(348,plain,
% 0.21/0.51 ((~![X_103: $i] : ((~p_LES_EQU_(X_103, f__length_(f__empty_))) | (X_103 = f__length_(f__empty_)))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = f__length_(f__empty_))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.21/0.51 tff(349,plain,
% 0.21/0.51 (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = f__length_(f__empty_)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[348, 345, 335])).
% 0.21/0.51 tff(350,plain,
% 0.21/0.51 (^[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_)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(351,plain,
% 0.21/0.51 (![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_))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[350])).
% 0.21/0.51 tff(352,plain,
% 0.21/0.51 (^[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_))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(353,plain,
% 0.21/0.51 (![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_))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[352])).
% 0.21/0.51 tff(354,plain,
% 0.21/0.51 (![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)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(355,plain,
% 0.21/0.51 (^[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)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(356,plain,
% 0.21/0.51 (![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)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[355])).
% 0.21/0.51 tff(357,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')).
% 0.21/0.51 tff(358,plain,
% 0.21/0.51 (![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)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.21/0.51 tff(359,plain,
% 0.21/0.51 (![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)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[358, 354])).
% 0.21/0.51 tff(360,plain,
% 0.21/0.51 (![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_))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[359, 353])).
% 0.21/0.51 tff(361,plain,(
% 0.21/0.51 ![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_))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[360])).
% 0.21/0.51 tff(362,plain,
% 0.21/0.51 (![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_))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[361, 351])).
% 0.21/0.51 tff(363,plain,
% 0.21/0.51 (((~![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_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (~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)))) <=> ((~![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_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (~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)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(364,plain,
% 0.21/0.51 ((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_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (~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)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(365,plain,
% 0.21/0.51 (((~![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_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (~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))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[364])).
% 0.21/0.51 tff(366,plain,
% 0.21/0.51 (((~![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_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (~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)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[365, 363])).
% 0.21/0.51 tff(367,plain,
% 0.21/0.51 ((~![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_))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(368,plain,
% 0.21/0.51 ((~![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_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (~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))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.21/0.52 tff(369,plain,
% 0.21/0.52 (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (~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))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[368, 362])).
% 0.21/0.52 tff(370,plain,
% 0.21/0.52 (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[369, 335, 121, 254, 314])).
% 0.21/0.52 tff(371,plain,
% 0.21/0.52 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))),
% 0.21/0.52 inference(symmetry,[status(thm)],[370])).
% 0.21/0.52 tff(372,plain,
% 0.21/0.52 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1))),
% 0.21/0.52 inference(transitivity,[status(thm)],[371, 58])).
% 0.21/0.52 tff(373,plain,
% 0.21/0.52 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.52 inference(monotonicity,[status(thm)],[372])).
% 0.21/0.52 tff(374,plain,
% 0.21/0.52 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_) <=> p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.52 inference(symmetry,[status(thm)],[373])).
% 0.21/0.52 tff(375,plain,
% 0.21/0.52 ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)), fwork_DOTfifo_DOTrtl_DOTfifo__length_)) <=> (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[374])).
% 0.21/0.52 tff(376,plain,
% 0.21/0.52 (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[87, 375])).
% 0.21/0.52 tff(377,plain,
% 0.21/0.52 (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTfifo__length_),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[211, 197, 376])).
% 0.21/0.52 tff(378,plain,
% 0.21/0.52 (fwork_DOTfifo_DOTrtl_DOTfifo__length_ = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),
% 0.21/0.52 inference(symmetry,[status(thm)],[377])).
% 0.21/0.52 tff(379,plain,
% 0.21/0.52 (fwork_DOTfifo_DOTrtl_DOTfifo__length_ = f__length_(f__empty_)),
% 0.21/0.52 inference(transitivity,[status(thm)],[378, 349])).
% 0.21/0.52 tff(380,plain,
% 0.21/0.52 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f__length_(f__empty_)) <=> p_LES_EQU_(f__length_(f__empty_), f_SUB_(f_ADD_(f__length_(f__empty_), n1), n1))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[379, 48])).
% 0.21/0.52 tff(381,plain,
% 0.21/0.52 (p_LES_EQU_(f__length_(f__empty_), f_SUB_(f_ADD_(f__length_(f__empty_), n1), n1)) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f__length_(f__empty_))),
% 0.21/0.52 inference(symmetry,[status(thm)],[380])).
% 0.21/0.52 tff(382,plain,
% 0.21/0.52 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f__length_(f__empty_))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[78, 381])).
% 0.21/0.52 tff(383,plain,
% 0.21/0.52 ($false),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[84, 382])).
% 0.21/0.52 % SZS output end Proof
%------------------------------------------------------------------------------