TSTP Solution File: HWV022-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : HWV022-2 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 02:10:41 EDT 2022
% Result : Unsatisfiable 0.23s 0.49s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : HWV022-2 : TPTP v8.1.0. Released v2.5.0.
% 0.08/0.15 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.37 % Computer : n007.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Wed Aug 31 21:49:02 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.37 Usage: tptp [options] [-file:]file
% 0.14/0.37 -h, -? prints this message.
% 0.14/0.37 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.37 -m, -model generate model.
% 0.14/0.37 -p, -proof generate proof.
% 0.14/0.37 -c, -core generate unsat core of named formulas.
% 0.14/0.37 -st, -statistics display statistics.
% 0.14/0.37 -t:timeout set timeout (in second).
% 0.14/0.37 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.37 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.37 -<param>:<value> configuration parameter and value.
% 0.14/0.37 -o:<output-file> file to place output in.
% 0.23/0.49 % SZS status Unsatisfiable
% 0.23/0.49 % SZS output start Proof
% 0.23/0.49 tff(f_ADD__type, type, (
% 0.23/0.49 f_ADD_: ( $i * $i ) > $i)).
% 0.23/0.49 tff(n1_type, type, (
% 0.23/0.49 n1: $i)).
% 0.23/0.49 tff(f__length__type, type, (
% 0.23/0.49 f__length_: $i > $i)).
% 0.23/0.49 tff(f__empty__type, type, (
% 0.23/0.49 f__empty_: $i)).
% 0.23/0.49 tff(fwork_DOTfifo_DOTrtl_DOTint__level__type, type, (
% 0.23/0.49 fwork_DOTfifo_DOTrtl_DOTint__level_: $i > $i)).
% 0.23/0.49 tff(t_206_type, type, (
% 0.23/0.49 t_206: $i)).
% 0.23/0.49 tff(p_LES_EQU__type, type, (
% 0.23/0.49 p_LES_EQU_: ( $i * $i ) > $o)).
% 0.23/0.49 tff(def_89_type, type, (
% 0.23/0.49 def_89: ( $i * $i ) > $o)).
% 0.23/0.49 tff(f_SUB__type, type, (
% 0.23/0.49 f_SUB_: ( $i * $i ) > $i)).
% 0.23/0.49 tff(fwork_DOTfifo_DOTrtl_DOTlevel__type, type, (
% 0.23/0.49 fwork_DOTfifo_DOTrtl_DOTlevel_: $i > $i)).
% 0.23/0.49 tff(n0_type, type, (
% 0.23/0.49 n0: $i)).
% 0.23/0.49 tff(fwork_DOTfifo_DOTrtl_DOTfifo__length__type, type, (
% 0.23/0.49 fwork_DOTfifo_DOTrtl_DOTfifo__length_: $i)).
% 0.23/0.49 tff(p__pred__type, type, (
% 0.23/0.49 p__pred_: $i > $o)).
% 0.23/0.49 tff(fwork_DOTfifo_DOTrtl_DOTrd__type, type, (
% 0.23/0.49 fwork_DOTfifo_DOTrtl_DOTrd_: $i > $i)).
% 0.23/0.49 tff(fwork_DOTfifo_DOTrtl_DOTreset__type, type, (
% 0.23/0.49 fwork_DOTfifo_DOTrtl_DOTreset_: $i > $i)).
% 0.23/0.49 tff(fwork_DOTfifo_DOTrtl_DOTwr__type, type, (
% 0.23/0.49 fwork_DOTfifo_DOTrtl_DOTwr_: $i > $i)).
% 0.23/0.49 tff(1,assumption,(f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)), introduced(assumption)).
% 0.23/0.49 tff(2,plain,
% 0.23/0.49 ((n1 = f_ADD_(n0, n1)) <=> (n1 = f_ADD_(f__length_(f__empty_), n1))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(3,plain,
% 0.23/0.49 ((n1 = f_ADD_(n0, n1)) <=> (n1 = f_ADD_(n0, n1))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(4,axiom,(n1 = f_ADD_(n0, n1)), file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax','axiom_78')).
% 0.23/0.49 tff(5,plain,
% 0.23/0.49 (n1 = f_ADD_(n0, n1)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.23/0.49 tff(6,plain,
% 0.23/0.49 (n1 = f_ADD_(f__length_(f__empty_), n1)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.23/0.49 tff(7,plain,
% 0.23/0.49 (^[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)))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(8,plain,
% 0.23/0.49 (![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))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[7])).
% 0.23/0.49 tff(9,plain,
% 0.23/0.49 (![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))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(10,axiom,(![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax','axiom_5')).
% 0.23/0.49 tff(11,plain,
% 0.23/0.49 (![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.23/0.49 tff(12,plain,(
% 0.23/0.49 ![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))),
% 0.23/0.49 inference(skolemize,[status(sab)],[11])).
% 0.23/0.49 tff(13,plain,
% 0.23/0.49 (![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.23/0.49 tff(14,plain,
% 0.23/0.49 ((~![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))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(15,plain,
% 0.23/0.49 (fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.23/0.49 tff(16,plain,
% 0.23/0.49 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[15])).
% 0.23/0.49 tff(17,plain,
% 0.23/0.49 (f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), n1) = f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[16, 6])).
% 0.23/0.49 tff(18,plain,
% 0.23/0.49 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1)),
% 0.23/0.49 inference(symmetry,[status(thm)],[16])).
% 0.23/0.49 tff(19,plain,
% 0.23/0.49 (f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n1) = f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), n1)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[18])).
% 0.23/0.49 tff(20,plain,
% 0.23/0.49 (f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n1) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),
% 0.23/0.49 inference(transitivity,[status(thm)],[19, 17, 1])).
% 0.23/0.49 tff(21,plain,
% 0.23/0.49 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n1)) <=> p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[18, 20])).
% 0.23/0.49 tff(22,plain,
% 0.23/0.49 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) <=> p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n1))),
% 0.23/0.49 inference(symmetry,[status(thm)],[21])).
% 0.23/0.49 tff(23,plain,
% 0.23/0.49 ((~![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)))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(24,plain,
% 0.23/0.49 (fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[23, 13])).
% 0.23/0.49 tff(25,plain,
% 0.23/0.49 ((fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1)) <=> (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[24, 16])).
% 0.23/0.49 tff(26,plain,
% 0.23/0.49 ((~(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1))) <=> (~(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[25])).
% 0.23/0.49 tff(27,plain,
% 0.23/0.49 ((~(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTfifo__length_)) <=> (~(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(28,plain,
% 0.23/0.49 ((~(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTfifo__length_)) <=> (~(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTfifo__length_))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(29,axiom,(~(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTfifo__length_)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_5')).
% 0.23/0.49 tff(30,plain,
% 0.23/0.49 (~(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.23/0.49 tff(31,plain,
% 0.23/0.49 (~(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.23/0.49 tff(32,plain,
% 0.23/0.49 (~(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.23/0.49 tff(33,plain,
% 0.23/0.49 ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) <=> (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(34,axiom,(~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_4')).
% 0.23/0.49 tff(35,plain,
% 0.23/0.49 (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.23/0.49 tff(36,plain,
% 0.23/0.49 ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))) <=> (~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(37,axiom,(~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_3')).
% 0.23/0.49 tff(38,plain,
% 0.23/0.49 (~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.23/0.49 tff(39,plain,
% 0.23/0.49 (p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) <=> p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(40,axiom,(p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_2')).
% 0.23/0.49 tff(41,plain,
% 0.23/0.49 (p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.23/0.49 tff(42,plain,
% 0.23/0.49 (^[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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), 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)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(T_13))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(43,plain,
% 0.23/0.49 (![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)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), 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)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[42])).
% 0.23/0.49 tff(44,plain,
% 0.23/0.49 (^[T_13: $i] : trans(monotonicity(rewrite(p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) <=> p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), 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)) | 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_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), 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))))), 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_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), 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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), 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)) | 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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(45,plain,
% 0.23/0.49 (![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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[44])).
% 0.23/0.49 tff(46,plain,
% 0.23/0.49 (![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)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(47,plain,
% 0.23/0.49 (^[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)))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(48,plain,
% 0.23/0.49 (![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)))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[47])).
% 0.23/0.49 tff(49,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/sandbox2/benchmark/Axioms/HWV004-0.ax','axiom_18')).
% 0.23/0.49 tff(50,plain,
% 0.23/0.49 (![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)))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.23/0.49 tff(51,plain,
% 0.23/0.49 (![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)))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.23/0.49 tff(52,plain,
% 0.23/0.49 (![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)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[51, 45])).
% 0.23/0.49 tff(53,plain,(
% 0.23/0.49 ![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)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))),
% 0.23/0.49 inference(skolemize,[status(sab)],[52])).
% 0.23/0.49 tff(54,plain,
% 0.23/0.49 (![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)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.23/0.49 tff(55,plain,
% 0.23/0.49 (((~![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)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), 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)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), 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)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(56,plain,
% 0.23/0.49 ((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), 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)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(57,plain,
% 0.23/0.49 (((~![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)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), 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)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(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)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), 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))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[56])).
% 0.23/0.49 tff(58,plain,
% 0.23/0.49 (((~![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)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), 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)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(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)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), 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)))),
% 0.23/0.49 inference(transitivity,[status(thm)],[57, 55])).
% 0.23/0.49 tff(59,plain,
% 0.23/0.49 ((~![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)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), 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)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(60,plain,
% 0.23/0.49 ((~![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)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), 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))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.23/0.49 tff(61,plain,
% 0.23/0.49 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), 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))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[60, 54, 41, 38, 35])).
% 0.23/0.49 tff(62,plain,
% 0.23/0.49 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[61, 32])).
% 0.23/0.49 tff(63,plain,
% 0.23/0.49 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n1))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[62, 22])).
% 0.23/0.49 tff(64,plain,
% 0.23/0.49 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_)) <=> p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), f__length_(f__empty_))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[18])).
% 0.23/0.49 tff(65,plain,
% 0.23/0.49 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), f__length_(f__empty_)) <=> p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_))),
% 0.23/0.49 inference(symmetry,[status(thm)],[64])).
% 0.23/0.49 tff(66,plain,
% 0.23/0.49 ((~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), f__length_(f__empty_))) <=> (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_)))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[65])).
% 0.23/0.49 tff(67,plain,
% 0.23/0.49 (^[X_81: $i] : refl((~p_LES_EQU_(f_ADD_(X_81, n1), f__length_(f__empty_))) <=> (~p_LES_EQU_(f_ADD_(X_81, n1), f__length_(f__empty_))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(68,plain,
% 0.23/0.49 (![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), f__length_(f__empty_))) <=> ![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), f__length_(f__empty_)))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[67])).
% 0.23/0.49 tff(69,plain,
% 0.23/0.49 (^[X_81: $i] : rewrite((~p_LES_EQU_(f_ADD_(X_81, n1), n0)) <=> (~p_LES_EQU_(f_ADD_(X_81, n1), f__length_(f__empty_))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(70,plain,
% 0.23/0.49 (![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), n0)) <=> ![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), f__length_(f__empty_)))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[69])).
% 0.23/0.49 tff(71,plain,
% 0.23/0.49 (![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), n0)) <=> ![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), n0))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(72,axiom,(![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), n0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax','axiom_60')).
% 0.23/0.49 tff(73,plain,
% 0.23/0.49 (![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), n0))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.23/0.49 tff(74,plain,
% 0.23/0.49 (![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), f__length_(f__empty_)))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[73, 70])).
% 0.23/0.49 tff(75,plain,(
% 0.23/0.49 ![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), f__length_(f__empty_)))),
% 0.23/0.49 inference(skolemize,[status(sab)],[74])).
% 0.23/0.49 tff(76,plain,
% 0.23/0.49 (![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), f__length_(f__empty_)))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.23/0.49 tff(77,plain,
% 0.23/0.49 ((~![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), f__length_(f__empty_)))) | (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), f__length_(f__empty_)))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(78,plain,
% 0.23/0.49 (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), f__length_(f__empty_))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.23/0.49 tff(79,plain,
% 0.23/0.49 (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[78, 66])).
% 0.23/0.49 tff(80,plain,
% 0.23/0.49 (^[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_))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(81,plain,
% 0.23/0.49 (![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_)))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[80])).
% 0.23/0.49 tff(82,plain,
% 0.23/0.49 (^[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_))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(83,plain,
% 0.23/0.49 (![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_)))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[82])).
% 0.23/0.49 tff(84,plain,
% 0.23/0.49 (![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))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(85,axiom,(![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, n0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax','axiom_61')).
% 0.23/0.49 tff(86,plain,
% 0.23/0.49 (![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, n0))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.23/0.49 tff(87,plain,
% 0.23/0.49 (![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_)))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[86, 83])).
% 0.23/0.49 tff(88,plain,(
% 0.23/0.49 ![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_)))),
% 0.23/0.50 inference(skolemize,[status(sab)],[87])).
% 0.23/0.50 tff(89,plain,
% 0.23/0.50 (![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.23/0.50 tff(90,plain,
% 0.23/0.50 (((~![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_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n1))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), 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_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n1))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(91,plain,
% 0.23/0.50 ((~![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_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n1))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(92,plain,
% 0.23/0.50 ((~![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, f__length_(f__empty_)))) | (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n1))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.23/0.50 tff(93,plain,
% 0.23/0.50 ((~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n1))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[92, 89])).
% 0.23/0.50 tff(94,plain,
% 0.23/0.50 (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n1))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[93, 79])).
% 0.23/0.50 tff(95,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[94, 63])).
% 0.23/0.50 tff(96,plain,(~(f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.50 tff(97,plain,
% 0.23/0.50 (f_ADD_(f__length_(f__empty_), n1) = n1),
% 0.23/0.50 inference(symmetry,[status(thm)],[6])).
% 0.23/0.50 tff(98,plain,
% 0.23/0.50 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[97])).
% 0.23/0.50 tff(99,plain,
% 0.23/0.50 (^[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))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(100,plain,
% 0.23/0.50 (![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)))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[99])).
% 0.23/0.50 tff(101,plain,
% 0.23/0.50 (![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)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(102,plain,
% 0.23/0.50 (^[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)))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(103,plain,
% 0.23/0.50 (![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)))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[102])).
% 0.23/0.50 tff(104,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/sandbox2/benchmark/Axioms/HWV004-0.ax','axiom_63')).
% 0.23/0.50 tff(105,plain,
% 0.23/0.50 (![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)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.23/0.50 tff(106,plain,
% 0.23/0.50 (![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)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.23/0.50 tff(107,plain,(
% 0.23/0.50 ![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)))),
% 0.23/0.50 inference(skolemize,[status(sab)],[106])).
% 0.23/0.50 tff(108,plain,
% 0.23/0.50 (![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)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.23/0.50 tff(109,plain,
% 0.23/0.50 (((~![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)))) | (def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | (f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), 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)))) | def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | (f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(110,plain,
% 0.23/0.50 (((f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)))) <=> (def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | (f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(111,plain,
% 0.23/0.50 (((~![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_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), 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)))) | (def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | (f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[110])).
% 0.23/0.50 tff(112,plain,
% 0.23/0.50 (((~![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_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), 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)))) | def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | (f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[111, 109])).
% 0.23/0.50 tff(113,plain,
% 0.23/0.50 ((~![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_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(114,plain,
% 0.23/0.50 ((~![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)))) | def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | (f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.23/0.50 tff(115,plain,
% 0.23/0.50 (def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) | (f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[114, 108, 98])).
% 0.23/0.50 tff(116,plain,
% 0.23/0.50 (def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[115, 96])).
% 0.23/0.50 tff(117,plain,
% 0.23/0.50 (^[Y_84: $i, X_83: $i] : refl(((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84)) <=> ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84)))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(118,plain,
% 0.23/0.50 (![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84)) <=> ![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[117])).
% 0.23/0.50 tff(119,plain,
% 0.23/0.50 (![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84)) <=> ![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(120,plain,
% 0.23/0.50 (^[Y_84: $i, X_83: $i] : rewrite((p_LES_EQU_(X_83, Y_84) | (~def_89(Y_84, X_83))) <=> ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84)))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(121,plain,
% 0.23/0.50 (![Y_84: $i, X_83: $i] : (p_LES_EQU_(X_83, Y_84) | (~def_89(Y_84, X_83))) <=> ![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[120])).
% 0.23/0.50 tff(122,axiom,(![Y_84: $i, X_83: $i] : (p_LES_EQU_(X_83, Y_84) | (~def_89(Y_84, X_83)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax','axiom_65')).
% 0.23/0.50 tff(123,plain,
% 0.23/0.50 (![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.23/0.50 tff(124,plain,
% 0.23/0.50 (![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.23/0.50 tff(125,plain,(
% 0.23/0.50 ![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))),
% 0.23/0.50 inference(skolemize,[status(sab)],[124])).
% 0.23/0.50 tff(126,plain,
% 0.23/0.50 (![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.23/0.50 tff(127,plain,
% 0.23/0.50 (((~![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))) | ((~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1)))) <=> ((~![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))) | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(128,plain,
% 0.23/0.50 ((~![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))) | ((~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(129,plain,
% 0.23/0.50 ((~![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))) | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.23/0.50 tff(130,plain,
% 0.23/0.50 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[129, 126, 116])).
% 0.23/0.50 tff(131,assumption,(p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1))), introduced(assumption)).
% 0.23/0.50 tff(132,assumption,(~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))), introduced(assumption)).
% 0.23/0.50 tff(133,plain,
% 0.23/0.50 (^[X_90: $i, Y_91: $i] : refl(((~p_LES_EQU_(f_ADD_(Y_91, n1), f_ADD_(X_90, n1))) | p_LES_EQU_(Y_91, X_90)) <=> ((~p_LES_EQU_(f_ADD_(Y_91, n1), f_ADD_(X_90, n1))) | p_LES_EQU_(Y_91, X_90)))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(134,plain,
% 0.23/0.50 (![X_90: $i, Y_91: $i] : ((~p_LES_EQU_(f_ADD_(Y_91, n1), f_ADD_(X_90, n1))) | p_LES_EQU_(Y_91, X_90)) <=> ![X_90: $i, Y_91: $i] : ((~p_LES_EQU_(f_ADD_(Y_91, n1), f_ADD_(X_90, n1))) | p_LES_EQU_(Y_91, X_90))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[133])).
% 0.23/0.50 tff(135,plain,
% 0.23/0.50 (![X_90: $i, Y_91: $i] : ((~p_LES_EQU_(f_ADD_(Y_91, n1), f_ADD_(X_90, n1))) | p_LES_EQU_(Y_91, X_90)) <=> ![X_90: $i, Y_91: $i] : ((~p_LES_EQU_(f_ADD_(Y_91, n1), f_ADD_(X_90, n1))) | p_LES_EQU_(Y_91, X_90))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(136,axiom,(![X_90: $i, Y_91: $i] : ((~p_LES_EQU_(f_ADD_(Y_91, n1), f_ADD_(X_90, n1))) | p_LES_EQU_(Y_91, X_90))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax','axiom_66')).
% 0.23/0.50 tff(137,plain,
% 0.23/0.50 (![X_90: $i, Y_91: $i] : ((~p_LES_EQU_(f_ADD_(Y_91, n1), f_ADD_(X_90, n1))) | p_LES_EQU_(Y_91, X_90))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.23/0.50 tff(138,plain,(
% 0.23/0.50 ![X_90: $i, Y_91: $i] : ((~p_LES_EQU_(f_ADD_(Y_91, n1), f_ADD_(X_90, n1))) | p_LES_EQU_(Y_91, X_90))),
% 0.23/0.50 inference(skolemize,[status(sab)],[137])).
% 0.23/0.50 tff(139,plain,
% 0.23/0.50 (![X_90: $i, Y_91: $i] : ((~p_LES_EQU_(f_ADD_(Y_91, n1), f_ADD_(X_90, n1))) | p_LES_EQU_(Y_91, X_90))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.23/0.50 tff(140,plain,
% 0.23/0.50 (((~![X_90: $i, Y_91: $i] : ((~p_LES_EQU_(f_ADD_(Y_91, n1), f_ADD_(X_90, n1))) | p_LES_EQU_(Y_91, X_90))) | ((~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)))) <=> ((~![X_90: $i, Y_91: $i] : ((~p_LES_EQU_(f_ADD_(Y_91, n1), f_ADD_(X_90, n1))) | p_LES_EQU_(Y_91, X_90))) | (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(141,plain,
% 0.23/0.50 ((~![X_90: $i, Y_91: $i] : ((~p_LES_EQU_(f_ADD_(Y_91, n1), f_ADD_(X_90, n1))) | p_LES_EQU_(Y_91, X_90))) | ((~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(142,plain,
% 0.23/0.50 ((~![X_90: $i, Y_91: $i] : ((~p_LES_EQU_(f_ADD_(Y_91, n1), f_ADD_(X_90, n1))) | p_LES_EQU_(Y_91, X_90))) | (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.23/0.50 tff(143,plain,
% 0.23/0.50 ($false),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[142, 139, 132, 131])).
% 0.23/0.50 tff(144,plain,((~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(f__length_(f__empty_), n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.50 tff(145,plain,
% 0.23/0.50 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[144, 130])).
% 0.23/0.50 tff(146,plain,
% 0.23/0.50 (^[Y_93: $i, X_92: $i] : refl(((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92)) <=> ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92)))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(147,plain,
% 0.23/0.50 (![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92)) <=> ![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[146])).
% 0.23/0.50 tff(148,plain,
% 0.23/0.50 (![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92)) <=> ![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(149,plain,
% 0.23/0.50 (^[Y_93: $i, X_92: $i] : trans(monotonicity(rewrite(((Y_93 = X_92) | (~p_LES_EQU_(X_92, Y_93))) <=> ((~p_LES_EQU_(X_92, Y_93)) | (Y_93 = X_92))), ((((Y_93 = X_92) | (~p_LES_EQU_(X_92, Y_93))) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93)) <=> (((~p_LES_EQU_(X_92, Y_93)) | (Y_93 = X_92)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93)))), rewrite((((~p_LES_EQU_(X_92, Y_93)) | (Y_93 = X_92)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93)) <=> ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))), ((((Y_93 = X_92) | (~p_LES_EQU_(X_92, Y_93))) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93)) <=> ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(150,plain,
% 0.23/0.50 (![Y_93: $i, X_92: $i] : (((Y_93 = X_92) | (~p_LES_EQU_(X_92, Y_93))) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93)) <=> ![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[149])).
% 0.23/0.50 tff(151,axiom,(![Y_93: $i, X_92: $i] : (((Y_93 = X_92) | (~p_LES_EQU_(X_92, Y_93))) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax','axiom_68')).
% 0.23/0.50 tff(152,plain,
% 0.23/0.50 (![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.23/0.50 tff(153,plain,
% 0.23/0.50 (![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.23/0.50 tff(154,plain,(
% 0.23/0.50 ![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))),
% 0.23/0.50 inference(skolemize,[status(sab)],[153])).
% 0.23/0.50 tff(155,plain,
% 0.23/0.50 (![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.23/0.50 tff(156,plain,
% 0.23/0.50 (((~![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))) | (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))) <=> ((~![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(157,plain,
% 0.23/0.50 (((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_)) | (f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))) <=> (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(158,plain,
% 0.23/0.50 (((~![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))) | ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_)) | (f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))) <=> ((~![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))) | (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[157])).
% 0.23/0.50 tff(159,plain,
% 0.23/0.50 (((~![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))) | ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_)) | (f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))) <=> ((~![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.23/0.50 inference(transitivity,[status(thm)],[158, 156])).
% 0.23/0.50 tff(160,plain,
% 0.23/0.50 ((~![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))) | ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_)) | (f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.23/0.50 inference(quant_inst,[status(thm)],[])).
% 0.23/0.50 tff(161,plain,
% 0.23/0.50 ((~![Y_93: $i, X_92: $i] : ((~p_LES_EQU_(X_92, Y_93)) | p_LES_EQU_(f_ADD_(X_92, n1), Y_93) | (Y_93 = X_92))) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.23/0.50 tff(162,plain,
% 0.23/0.50 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f__length_(f__empty_)) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[161, 155])).
% 0.23/0.50 tff(163,plain,
% 0.23/0.50 ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f__length_(f__empty_))) | (f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[162, 79])).
% 0.23/0.50 tff(164,plain,
% 0.23/0.50 (f__length_(f__empty_) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),
% 0.23/0.50 inference(unit_resolution,[status(thm)],[163, 145])).
% 0.23/0.50 tff(165,plain,
% 0.23/0.50 (f_ADD_(f__length_(f__empty_), n1) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[164])).
% 0.23/0.50 tff(166,plain,
% 0.23/0.50 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f_ADD_(f__length_(f__empty_), n1)),
% 0.23/0.50 inference(symmetry,[status(thm)],[165])).
% 0.23/0.50 tff(167,plain,
% 0.23/0.50 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(f__length_(f__empty_), n1)),
% 0.23/0.50 inference(transitivity,[status(thm)],[98, 166])).
% 0.23/0.50 tff(168,plain,
% 0.23/0.50 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(f__length_(f__empty_), n1))),
% 0.23/0.50 inference(symmetry,[status(thm)],[98])).
% 0.23/0.50 tff(169,plain,
% 0.23/0.50 ((f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f_ADD_(f__length_(f__empty_), n1)) <=> (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(f__length_(f__empty_), n1))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[168])).
% 0.23/0.50 tff(170,plain,
% 0.23/0.50 ((~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f_ADD_(f__length_(f__empty_), n1))) <=> (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(f__length_(f__empty_), n1)))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[169])).
% 0.23/0.50 tff(171,plain,
% 0.23/0.50 (^[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))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(172,plain,
% 0.23/0.50 (![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)))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[171])).
% 0.23/0.50 tff(173,plain,
% 0.23/0.50 (![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)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(174,axiom,(![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax','axiom_64')).
% 0.23/0.50 tff(175,plain,
% 0.23/0.50 (![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.23/0.50 tff(176,plain,(
% 0.23/0.50 ![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))),
% 0.23/0.50 inference(skolemize,[status(sab)],[175])).
% 0.23/0.50 tff(177,plain,
% 0.23/0.50 (![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.23/0.50 tff(178,plain,
% 0.23/0.50 (((~![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))) | ((~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f_ADD_(f__length_(f__empty_), n1))) | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))))) <=> ((~![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))) | (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f_ADD_(f__length_(f__empty_), n1))) | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(179,plain,
% 0.23/0.51 ((~![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))) | ((~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f_ADD_(f__length_(f__empty_), n1))) | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))))),
% 0.23/0.51 inference(quant_inst,[status(thm)],[])).
% 0.23/0.51 tff(180,plain,
% 0.23/0.51 ((~![Y_84: $i, X_83: $i] : ((~(X_83 = Y_84)) | (~def_89(Y_84, X_83)))) | (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f_ADD_(f__length_(f__empty_), n1))) | (~def_89(f_ADD_(f__length_(f__empty_), n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.23/0.51 tff(181,plain,
% 0.23/0.51 (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f_ADD_(f__length_(f__empty_), n1))),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[180, 177, 116])).
% 0.23/0.51 tff(182,plain,
% 0.23/0.51 (~(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(f__length_(f__empty_), n1)) = f_ADD_(f__length_(f__empty_), n1))),
% 0.23/0.51 inference(modus_ponens,[status(thm)],[181, 170])).
% 0.23/0.51 tff(183,plain,
% 0.23/0.51 ($false),
% 0.23/0.51 inference(unit_resolution,[status(thm)],[182, 167])).
% 0.23/0.51 % SZS output end Proof
%------------------------------------------------------------------------------