%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : HWV021-2 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : HWV021-2 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.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 17:19:57 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(p_LES_EQU__type, type, (
% 0.20/0.42 p_LES_EQU_: ( $i * $i ) > $o)).
% 0.20/0.42 tff(n0_type, type, (
% 0.20/0.42 n0: $i)).
% 0.20/0.42 tff(fwork_DOTfifo_DOTrtl_DOTint__level__type, type, (
% 0.20/0.42 fwork_DOTfifo_DOTrtl_DOTint__level_: $i > $i)).
% 0.20/0.42 tff(t_206_type, type, (
% 0.20/0.42 t_206: $i)).
% 0.20/0.42 tff(p__pred__type, type, (
% 0.20/0.42 p__pred_: $i > $o)).
% 0.20/0.42 tff(fwork_DOTfifo_DOTrtl_DOTempty__type, type, (
% 0.20/0.42 fwork_DOTfifo_DOTrtl_DOTempty_: $i > $i)).
% 0.20/0.42 tff(fwork_DOTfifo_DOTrtl_DOTwr__type, type, (
% 0.20/0.42 fwork_DOTfifo_DOTrtl_DOTwr_: $i > $i)).
% 0.20/0.42 tff(fwork_DOTfifo_DOTrtl_DOTrd__type, type, (
% 0.20/0.42 fwork_DOTfifo_DOTrtl_DOTrd_: $i > $i)).
% 0.20/0.42 tff(fwork_DOTfifo_DOTrtl_DOTreset__type, type, (
% 0.20/0.42 fwork_DOTfifo_DOTrtl_DOTreset_: $i > $i)).
% 0.20/0.42 tff(fwork_DOTfifo_DOTrtl_DOTrd__error__type, type, (
% 0.20/0.42 fwork_DOTfifo_DOTrtl_DOTrd__error_: $i > $i)).
% 0.20/0.42 tff(f_ADD__type, type, (
% 0.20/0.42 f_ADD_: ( $i * $i ) > $i)).
% 0.20/0.42 tff(n1_type, type, (
% 0.20/0.42 n1: $i)).
% 0.20/0.42 tff(1,assumption,(p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0)), introduced(assumption)).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206))) <=> (~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(3,axiom,(~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_4')).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (~p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (^[T_3: $i] : refl((p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) = n0))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) = n0))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (![T_3: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) = n0))) <=> ![T_3: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) = n0)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (![T_3: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) = n0))) <=> ![T_3: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) = n0)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(8,axiom,(![T_3: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) = n0)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax','axiom_8')).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (![T_3: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) = n0)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.42 tff(10,plain,(
% 0.20/0.42 ![T_3: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) = n0)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[9])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (![T_3: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) = n0)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (((~![T_3: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) = n0)))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0)))) <=> ((~![T_3: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) = n0)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 ((~![T_3: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) = n0)))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 ((~![T_3: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(T_3)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(T_3) = n0)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTempty_(t_206)) | (~(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (~(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[14, 11, 4])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (^[X_103: $i] : refl(((~p_LES_EQU_(X_103, n0)) | (X_103 = n0)) <=> ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0)) <=> ![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0)) <=> ![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(19,axiom,(![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax','axiom_73')).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.42 tff(21,plain,(
% 0.20/0.42 ![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0))),
% 0.20/0.42 inference(skolemize,[status(sab)],[20])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (((~![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0))) | ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0))) <=> ((~![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 ((~![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0))) | ((~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 ((~![X_103: $i] : ((~p_LES_EQU_(X_103, n0)) | (X_103 = n0))) | (~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0)) | (fwork_DOTfifo_DOTrtl_DOTint__level_(t_206) = n0)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[25, 22, 15, 1])).
% 0.20/0.42 tff(27,plain,(~p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206)) <=> p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(29,axiom,(p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_3')).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))) <=> (~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(32,axiom,(~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_2')).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (~p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1))) <=> p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(35,axiom,(p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','quest_1')).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (^[T_13: $i] : refl((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (^[T_13: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))), (((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) <=> (((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))))), rewrite((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))), (((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)))), ((((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))))), rewrite((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))), ((((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (![T_13: $i] : (((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.42 tff(42,axiom,(![T_13: $i] : (((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax','axiom_46')).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.42 tff(45,plain,(
% 0.20/0.42 ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.20/0.42 inference(skolemize,[status(sab)],[44])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 ((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0)) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[48])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[49, 47])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[52, 46, 36, 33, 30])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[53, 27])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (^[T_13: $i] : refl((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (^[T_13: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))), (((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) <=> (((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))))), rewrite((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))), (((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) <=> ((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)))), ((((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))))), rewrite((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))), ((((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (![T_13: $i] : (((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13))) <=> ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.43 tff(60,axiom,(![T_13: $i] : (((((~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13)))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)))), file('/export/starexec/sandbox2/benchmark/Axioms/HWV004-0.ax','axiom_34')).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.43 tff(63,plain,(
% 0.20/0.43 ![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.20/0.43 inference(skolemize,[status(sab)],[62])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 ((p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0)) <=> (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[66])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0))) <=> ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[67, 65])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 ((~![T_13: $i] : (p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(T_13)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(T_13, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(T_13))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(T_13))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(T_13), n0))) | p__pred_(fwork_DOTfifo_DOTrtl_DOTreset_(t_206)) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd_(t_206))) | p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTrd__error_(f_ADD_(t_206, n1)))) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 (p_LES_EQU_(fwork_DOTfifo_DOTrtl_DOTint__level_(t_206), n0) | (~p__pred_(fwork_DOTfifo_DOTrtl_DOTwr_(t_206)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[70, 64, 36, 33, 30])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[71, 54, 27])).
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44 % E exiting
%------------------------------------------------------------------------------