%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV022-2 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:58 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HWV022-2 : TPTP v9.0.0. Released v2.5.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 17:19:50 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(p_LES_EQU__type, type, (
% 0.20/0.43 p_LES_EQU_: ( $i * $i ) > $o)).
% 0.20/0.43 tff(f_SUB__type, type, (
% 0.20/0.43 f_SUB_: ( $i * $i ) > $i)).
% 0.20/0.43 tff(n1_type, type, (
% 0.20/0.43 n1: $i)).
% 0.20/0.43 tff(fwork_DOTfifo_DOTrtl_DOTfifo__length__type, type, (
% 0.20/0.43 fwork_DOTfifo_DOTrtl_DOTfifo__length_: $i)).
% 0.20/0.43 tff(fwork_DOTfifo_DOTrtl_DOTint__level__type, type, (
% 0.20/0.43 fwork_DOTfifo_DOTrtl_DOTint__level_: $i > $i)).
% 0.20/0.43 tff(t_206_type, type, (
% 0.20/0.43 t_206: $i)).
% 0.20/0.43 tff(f_ADD__type, type, (
% 0.20/0.43 f_ADD_: ( $i * $i ) > $i)).
% 0.20/0.43 tff(n0_type, type, (
% 0.20/0.43 n0: $i)).
% 0.20/0.43 tff(def_89_type, type, (
% 0.20/0.43 def_89: ( $i * $i ) > $o)).
% 0.20/0.43 tff(fwork_DOTfifo_DOTrtl_DOTlevel__type, type, (
% 0.20/0.43 fwork_DOTfifo_DOTrtl_DOTlevel_: $i > $i)).
% 0.20/0.43 tff(p__pred__type, type, (
% 0.20/0.43 p__pred_: $i > $o)).
% 0.20/0.43 tff(fwork_DOTfifo_DOTrtl_DOTrd__type, type, (
% 0.20/0.43 fwork_DOTfifo_DOTrtl_DOTrd_: $i > $i)).
% 0.20/0.43 tff(fwork_DOTfifo_DOTrtl_DOTreset__type, type, (
% 0.20/0.43 fwork_DOTfifo_DOTrtl_DOTreset_: $i > $i)).
% 0.20/0.43 tff(fwork_DOTfifo_DOTrtl_DOTwr__type, type, (
% 0.20/0.43 fwork_DOTfifo_DOTrtl_DOTwr_: $i > $i)).
% 0.20/0.43 tff(1,plain,
% 0.20/0.43 ((n1 = f_ADD_(n0, n1)) <=> (n1 = f_ADD_(n0, n1))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(2,axiom,(n1 = f_ADD_(n0, n1)), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_78')).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (n1 = f_ADD_(n0, n1)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.20/0.43 tff(4,plain,
% 0.20/0.43 (f_ADD_(n0, n1) = n1),
% 0.20/0.43 inference(symmetry,[status(thm)],[3])).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), f_ADD_(n0, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[4])).
% 0.20/0.43 tff(6,plain,
% 0.20/0.43 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), f_ADD_(n0, n1))),
% 0.20/0.43 inference(symmetry,[status(thm)],[5])).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (^[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)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(8,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.43 tff(9,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(10,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')).
% 0.20/0.43 tff(11,plain,
% 0.20/0.43 (![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.43 tff(12,plain,(
% 0.20/0.43 ![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))),
% 0.20/0.43 inference(skolemize,[status(sab)],[11])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 (![T_0: $i] : (fwork_DOTfifo_DOTrtl_DOTlevel_(T_0) = fwork_DOTfifo_DOTrtl_DOTint__level_(T_0))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 ((~![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))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 (fwork_DOTfifo_DOTrtl_DOTlevel_(t_206) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.20/0.43 tff(16,plain,
% 0.20/0.43 (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = fwork_DOTfifo_DOTrtl_DOTlevel_(t_206)),
% 0.20/0.43 inference(symmetry,[status(thm)],[15])).
% 0.20/0.43 tff(17,plain,
% 0.20/0.43 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[16])).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[4])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), f_ADD_(n0, n1))),
% 0.20/0.43 inference(transitivity,[status(thm)],[18, 17, 6])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (def_89(f_ADD_(n0, n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1))) <=> def_89(f_ADD_(n0, n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), f_ADD_(n0, n1)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.43 tff(21,plain,
% 0.20/0.43 (def_89(f_ADD_(n0, n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), f_ADD_(n0, n1))) <=> def_89(f_ADD_(n0, n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1)))),
% 0.20/0.43 inference(symmetry,[status(thm)],[20])).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 ((f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTfifo__length_) <=> (f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(23,axiom,(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTfifo__length_), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_1')).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTfifo__length_),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (fwork_DOTfifo_DOTrtl_DOTfifo__length_ = f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1)),
% 0.20/0.43 inference(symmetry,[status(thm)],[24])).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 (fwork_DOTfifo_DOTrtl_DOTfifo__length_ = f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), f_ADD_(n0, n1))),
% 0.20/0.43 inference(transitivity,[status(thm)],[25, 6])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 (def_89(f_ADD_(n0, n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_) <=> def_89(f_ADD_(n0, n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), f_ADD_(n0, n1)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 (def_89(f_ADD_(n0, n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_) <=> def_89(f_ADD_(n0, n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[27, 21])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 ((~def_89(f_ADD_(n0, n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_)) <=> (~def_89(f_ADD_(n0, n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[28])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_ADD_(n0, n1)) <=> p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), f_ADD_(n0, n1))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), f_ADD_(n0, n1)) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_ADD_(n0, n1))),
% 0.20/0.43 inference(symmetry,[status(thm)],[30])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 ((~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), f_ADD_(n0, n1))) <=> (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_ADD_(n0, n1)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[31])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(n0, n1)) <=> p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), f_ADD_(n0, n1))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[17])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 ((~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(n0, n1))) <=> (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), f_ADD_(n0, n1)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[33])).
% 0.20/0.43 tff(35,assumption,(n0 = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)), introduced(assumption)).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0),
% 0.20/0.43 inference(symmetry,[status(thm)],[35])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) <=> p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), n0)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[25, 36])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), n0) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.20/0.43 inference(symmetry,[status(thm)],[37])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 ((~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), n0)) <=> (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (^[X_81: $i] : refl((~p_LES_EQU_(f_ADD_(X_81, n1), n0)) <=> (~p_LES_EQU_(f_ADD_(X_81, n1), n0)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(41,plain,
% 0.20/0.43 (![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), n0)) <=> ![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), n0))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.43 tff(42,plain,
% 0.20/0.43 (![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), n0)) <=> ![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), n0))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(43,axiom,(![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), n0))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_60')).
% 0.20/0.43 tff(44,plain,
% 0.20/0.43 (![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), n0))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.43 tff(45,plain,(
% 0.20/0.43 ![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), n0))),
% 0.20/0.43 inference(skolemize,[status(sab)],[44])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 (![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), n0))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 ((~![X_81: $i] : (~p_LES_EQU_(f_ADD_(X_81, n1), n0))) | (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), n0))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), n0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[48, 39])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = fwork_DOTfifo_DOTrtl_DOTfifo__length_),
% 0.20/0.43 inference(transitivity,[status(thm)],[17, 24])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 ((~![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)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 (fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[51, 13])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1))),
% 0.20/0.43 inference(symmetry,[status(thm)],[52])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 ((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)) <=> (fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[53, 50])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 ((fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTfifo__length_) <=> (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.20/0.43 inference(symmetry,[status(thm)],[54])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 ((~(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTfifo__length_)) <=> (~(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[55])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 ((~(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_))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(58,axiom,(~(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTfifo__length_)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_5')).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (~(fwork_DOTfifo_DOTrtl_DOTlevel_(f_ADD_(t_206, n1)) = fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (~(fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[59, 56])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) <=> (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(62,axiom,(~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_4')).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))) <=> (~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(65,axiom,(~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_3')).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) <=> p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(68,axiom,(p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','quest_2')).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | 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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | 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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | 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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (^[T_13: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (![T_13: $i] : (((((fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.43 tff(76,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')).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | 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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.44 tff(78,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.20/0.44 tff(79,plain,(
% 0.20/0.44 ![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)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[78])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[80, 70])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (((~![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 ((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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (((~![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))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[83])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 (((~![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)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[84, 82])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 ((~![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)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(T_13)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(T_13, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(f_ADD_(t_206, n1)) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[87, 81, 69, 66, 63])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[88, 60])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[89, 49])).
% 0.20/0.44 tff(91,plain,(~(n0 = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n0) <=> p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), n0)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[17])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), n0) <=> p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n0)),
% 0.20/0.44 inference(symmetry,[status(thm)],[92])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 ((~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), n0)) <=> (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n0))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n0)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[48, 94])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (^[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)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[96])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[99])).
% 0.20/0.44 tff(101,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/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_68')).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.20/0.44 tff(104,plain,(
% 0.20/0.44 ![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))),
% 0.20/0.44 inference(skolemize,[status(sab)],[103])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 (((~![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), n0)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n0) | (n0 = 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_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n0) | (n0 = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 ((~![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), n0)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n0) | (n0 = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 ((~![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), n0)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n0) | (n0 = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0)) | p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), n0) | (n0 = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[108, 105])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0)) | (n0 = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[109, 95])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[110, 91])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (^[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)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[112])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(115,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/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_66')).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.44 tff(117,plain,(
% 0.20/0.44 ![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))),
% 0.20/0.44 inference(skolemize,[status(sab)],[116])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (((~![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_(n0, n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0))) <=> ((~![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_(n0, n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 ((~![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_(n0, n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 ((~![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_(n0, n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 ((~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(n0, n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[121, 118])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1), f_ADD_(n0, n1))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[122, 111])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 (~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), f_ADD_(n0, n1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[123, 34])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_ADD_(n0, n1))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[124, 32])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (^[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)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[126])).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(129,plain,
% 0.20/0.44 (^[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)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.44 tff(131,axiom,(![Y_84: $i, X_83: $i] : (p_LES_EQU_(X_83, Y_84) | (~def_89(Y_84, X_83)))), file('/export/starexec/sandbox/benchmark/Axioms/HWV004-0.ax','axiom_65')).
% 0.20/0.44 tff(132,plain,
% 0.20/0.44 (![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.44 tff(133,plain,
% 0.20/0.44 (![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.20/0.44 tff(134,plain,(
% 0.20/0.44 ![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))),
% 0.20/0.44 inference(skolemize,[status(sab)],[133])).
% 0.20/0.44 tff(135,plain,
% 0.20/0.44 (![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 (((~![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))) | ((~def_89(f_ADD_(n0, n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_ADD_(n0, n1)))) <=> ((~![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))) | (~def_89(f_ADD_(n0, n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_ADD_(n0, n1)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 ((~![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))) | ((~def_89(f_ADD_(n0, n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_ADD_(n0, n1)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 ((~![Y_84: $i, X_83: $i] : ((~def_89(Y_84, X_83)) | p_LES_EQU_(X_83, Y_84))) | (~def_89(f_ADD_(n0, n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_ADD_(n0, n1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 ((~def_89(f_ADD_(n0, n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_ADD_(n0, n1))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[138, 135])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 (~def_89(f_ADD_(n0, n1), fwork_DOTfifo_DOTrtl_DOTfifo__length_)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[139, 125])).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (~def_89(f_ADD_(n0, n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[140, 29])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 (^[Y_84: $i, Z_85: $i] : refl(((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84))) <=> ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 (![Y_84: $i, Z_85: $i] : ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84))) <=> ![Y_84: $i, Z_85: $i] : ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[142])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 (![Y_84: $i, Z_85: $i] : ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84))) <=> ![Y_84: $i, Z_85: $i] : ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 (![Y_84: $i, Z_85: $i, X_83: $i] : ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84))) <=> ![Y_84: $i, Z_85: $i] : ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84)))),
% 0.20/0.45 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 (![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_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84)))),
% 0.20/0.45 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 (![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] : ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[146, 145])).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 (^[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)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 (![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)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[148])).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 (![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] : ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84)))),
% 0.20/0.45 inference(transitivity,[status(thm)],[149, 147])).
% 0.20/0.45 tff(151,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')).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 (![Y_84: $i, Z_85: $i] : ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 (![Y_84: $i, Z_85: $i] : ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[152, 144])).
% 0.20/0.45 tff(154,plain,(
% 0.20/0.45 ![Y_84: $i, Z_85: $i] : ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[153])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 (![Y_84: $i, Z_85: $i] : ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[154, 143])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 (((~![Y_84: $i, Z_85: $i] : ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84)))) | ((f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1)), f_ADD_(n0, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | def_89(f_ADD_(n0, n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1))))) <=> ((~![Y_84: $i, Z_85: $i] : ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84)))) | (f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1)), f_ADD_(n0, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | def_89(f_ADD_(n0, n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 ((~![Y_84: $i, Z_85: $i] : ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84)))) | ((f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1)), f_ADD_(n0, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | def_89(f_ADD_(n0, n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(158,plain,
% 0.20/0.45 ((~![Y_84: $i, Z_85: $i] : ((f_SUB_(f_ADD_(Z_85, Y_84), Y_84) = Z_85) | def_89(Y_84, f_ADD_(Z_85, Y_84)))) | (f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1)), f_ADD_(n0, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | def_89(f_ADD_(n0, n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 ((f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1)), f_ADD_(n0, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) | def_89(f_ADD_(n0, n1), f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[158, 155])).
% 0.20/0.45 tff(160,plain,
% 0.20/0.45 (f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1)), f_ADD_(n0, n1)) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[159, 141])).
% 0.20/0.45 tff(161,plain,
% 0.20/0.45 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1))),
% 0.20/0.45 inference(symmetry,[status(thm)],[18])).
% 0.20/0.45 tff(162,plain,
% 0.20/0.45 (f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1) = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n1)),
% 0.20/0.45 inference(symmetry,[status(thm)],[17])).
% 0.20/0.45 tff(163,plain,
% 0.20/0.45 (fwork_DOTfifo_DOTrtl_DOTfifo__length_ = f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1))),
% 0.20/0.45 inference(transitivity,[status(thm)],[25, 162, 161])).
% 0.20/0.45 tff(164,plain,
% 0.20/0.45 (f_SUB_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n1) = f_SUB_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), f_ADD_(n0, n1)), f_ADD_(n0, n1))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[163, 3])).
% 0.20/0.45 tff(165,plain,
% 0.20/0.45 (f_SUB_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n1) = fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)),
% 0.20/0.45 inference(transitivity,[status(thm)],[164, 160])).
% 0.20/0.45 tff(166,plain,
% 0.20/0.45 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_SUB_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n1)) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[165])).
% 0.20/0.45 tff(167,plain,
% 0.20/0.45 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, fwork_DOTfifo_DOTrtl_DOTint__level_(t_206)) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_SUB_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n1))),
% 0.20/0.45 inference(symmetry,[status(thm)],[166])).
% 0.20/0.45 tff(168,plain,
% 0.20/0.45 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_SUB_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n1))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[89, 167])).
% 0.20/0.45 tff(169,plain,
% 0.20/0.45 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0) <=> p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), n0)),
% 0.20/0.45 inference(monotonicity,[status(thm)],[25])).
% 0.20/0.45 tff(170,plain,
% 0.20/0.45 (p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), n0) <=> p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0)),
% 0.20/0.45 inference(symmetry,[status(thm)],[169])).
% 0.20/0.45 tff(171,plain,
% 0.20/0.45 ((~p_LES_EQU_(f_ADD_(fwork_DOTfifo_DOTrtl_DOTlevel_(t_206), n1), n0)) <=> (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[170])).
% 0.20/0.45 tff(172,plain,
% 0.20/0.45 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[48, 171])).
% 0.20/0.45 tff(173,plain,
% 0.20/0.45 (^[X_82: $i] : refl(((~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, n0)))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(174,plain,
% 0.20/0.45 (![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))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[173])).
% 0.20/0.45 tff(175,plain,
% 0.20/0.45 (![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))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(176,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')).
% 0.20/0.45 tff(177,plain,
% 0.20/0.45 (![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, n0))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.20/0.45 tff(178,plain,(
% 0.20/0.45 ![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, n0))),
% 0.20/0.45 inference(skolemize,[status(sab)],[177])).
% 0.20/0.45 tff(179,plain,
% 0.20/0.45 (![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, n0))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.20/0.45 tff(180,plain,
% 0.20/0.45 (((~![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, n0))) | ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_SUB_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0))) <=> ((~![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, n0))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_SUB_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(181,plain,
% 0.20/0.45 ((~![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, n0))) | ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_SUB_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(182,plain,
% 0.20/0.45 ((~![X_82: $i] : ((~p_LES_EQU_(X_82, f_SUB_(X_82, n1))) | p_LES_EQU_(X_82, n0))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_SUB_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.20/0.46 tff(183,plain,
% 0.20/0.46 ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_SUB_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n1))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n0)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[182, 179])).
% 0.20/0.46 tff(184,plain,
% 0.20/0.46 (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, f_SUB_(fwork_DOTfifo_DOTrtl_DOTfifo__length_, n1))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[183, 172])).
% 0.20/0.46 tff(185,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[184, 168])).
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------