%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX188+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 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 : Tue May 5 05:34:39 PM UTC 2026
% Result : Theorem 142.60s 101.32s
% Output : CNFRefutation 154.41s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_67)
% Comments :
%------------------------------------------------------------------------------
fof(goal_054,conjecture,
? [X6] : opt(d(X6)) = opt(x(n(s(s(z))),x(x2,x2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_054) ).
fof(axiom_024,axiom,
! [X11,X12] :
( X11 != n(proj1N(X11))
=> ( X11 != y(proj12(X11),proj22(X11))
=> fail32(X11,X12) = fail4(X11,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
fof(axiom_023,axiom,
! [X11,X12] : fail4(X11,X12) = y(opt(X11),opt(X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_023) ).
fof(axiom_025,axiom,
! [X12,X13] :
( X12 != n(proj1N(X12))
=> fail32(n(X13),X12) = fail4(n(X13),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_025) ).
fof(axiom_016,axiom,
! [X6,X7,X8] :
( x(X7,X8) != X6
=> fail2(x(X7,X8),X6) = opt(x(X7,x(X8,X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_016) ).
fof(axiom_027,axiom,
! [X12,X15,X16] : fail32(y(X15,X16),X12) = opt(y(X15,y(X16,X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
fof(axiom_041,axiom,
! [X22,X23] : d(y(X22,X23)) = x(y(d(X22),X23),y(X22,d(X23))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_041) ).
fof(axiom_033,axiom,
! [X12,X18] : fail12(n(s(s(X18))),X12) = fail22(n(s(s(X18))),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_033) ).
fof(axiom_029,axiom,
! [X11,X17] : fail22(X11,n(s(s(X17)))) = fail32(X11,n(s(s(X17)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
fof(axiom_052,axiom,
! [X12,X25] : opt(y(n(s(X25)),X12)) = fail3(n(s(X25)),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_052) ).
fof(axiom_049,axiom,
! [X6,X4] : opt(x(n(s(X4)),X6)) = fail(n(s(X4)),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_049) ).
fof(axiom_015,axiom,
! [X5,X6] :
( X5 != X6
=> ( X5 != x(proj1(X5),proj2(X5))
=> fail2(X5,X6) = x(opt(X5),opt(X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_015) ).
fof(axiom_014,axiom,
! [X5,X6] :
( X5 = X6
=> fail2(X5,X6) = y(n(s(s(z))),opt(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_014) ).
fof(axiom_037,axiom,
! [X11,X19] : fail3(X11,n(s(X19))) = fail12(X11,n(s(X19))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_037) ).
fof(axiom_021,axiom,
! [X5,X2] : fail(X5,n(s(X2))) = fail1(X5,n(s(X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_021) ).
fof(axiom_047,axiom,
! [X1] :
( X1 != x(proj1(X1),proj2(X1))
=> ( X1 != y(proj12(X1),proj22(X1))
=> opt(X1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_047) ).
fof(axiom_045,axiom,
! [X5,X24] : mulNat(s(X24),X5) = addNat(X5,mulNat(X24,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_045) ).
fof(axiom_026,axiom,
! [X13,X14] : fail32(n(X13),n(X14)) = n(mulNat(X13,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
fof(axiom_019,axiom,
! [X9,X10] : fail1(n(X9),n(X10)) = n(addNat(X9,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
fof(axiom_040,axiom,
! [X20,X21] : d(x(X20,X21)) = x(d(X20),d(X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_040) ).
fof(axiom_051,axiom,
! [X11,X12] :
( X11 != n(proj1N(X11))
=> opt(y(X11,X12)) = fail3(X11,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_051) ).
fof(axiom_048,axiom,
! [X5,X6] :
( X5 != n(proj1N(X5))
=> opt(x(X5,X6)) = fail(X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_048) ).
fof(axiom_018,axiom,
! [X6,X9] :
( X6 != n(proj1N(X6))
=> fail1(n(X9),X6) = fail2(n(X9),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_018) ).
fof(axiom_043,axiom,
! [X5,X24] : addNat(s(X24),X5) = s(addNat(X24,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_043) ).
fof(axiom_011,axiom,
! [X1,X2,X3,X4] : x(X1,X2) != y(X3,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
fof(axiom_036,axiom,
! [X11,X12] :
( X12 != n(proj1N(X12))
=> fail3(X11,X12) = fail12(X11,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_036) ).
fof(axiom_032,axiom,
! [X11,X12] :
( X11 != n(proj1N(X11))
=> fail12(X11,X12) = fail22(X11,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_032) ).
fof(axiom_028,axiom,
! [X11,X12] :
( X12 != n(proj1N(X12))
=> fail22(X11,X12) = fail32(X11,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_028) ).
fof(axiom_020,axiom,
! [X5,X6] :
( X6 != n(proj1N(X6))
=> fail(X5,X6) = fail1(X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
fof(axiom_017,axiom,
! [X5,X6] :
( X5 != n(proj1N(X5))
=> fail1(X5,X6) = fail2(X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_017) ).
fof(axiom_053,axiom,
! [X12] : opt(y(n(z),X12)) = n(z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_053) ).
fof(axiom_050,axiom,
! [X6] : opt(x(n(z),X6)) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_050) ).
fof(axiom_035,axiom,
! [X12] : fail12(n(z),X12) = fail22(n(z),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_035) ).
fof(axiom_031,axiom,
! [X11] : fail22(X11,n(z)) = fail32(X11,n(z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_031) ).
fof(axiom_007,axiom,
! [X1,X2] : proj22(y(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
fof(axiom_006,axiom,
! [X1,X2] : proj12(y(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
fof(axiom_005,axiom,
! [X1,X2] : proj2(x(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
fof(axiom_004,axiom,
! [X1,X2] : proj1(x(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
fof(axiom_009,axiom,
! [X1,X2,X3] : n(X1) != y(X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
fof(axiom_008,axiom,
! [X1,X2,X3] : n(X1) != x(X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_008) ).
fof(axiom_034,axiom,
! [X12] : fail12(n(s(z)),X12) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_034) ).
fof(axiom_030,axiom,
! [X11] : fail22(X11,n(s(z))) = X11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_030) ).
fof(axiom_013,axiom,
! [X1,X2] : y(X1,X2) != x2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_013) ).
fof(axiom_012,axiom,
! [X1,X2] : x(X1,X2) != x2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
fof(axiom_038,axiom,
! [X11] : fail3(X11,n(z)) = n(z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_038) ).
fof(axiom_022,axiom,
! [X5] : fail(X5,n(z)) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
fof(axiom_044,axiom,
! [X5] : addNat(z,X5) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_044) ).
fof(axiom_039,axiom,
! [X5] : d(n(X5)) = n(z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_039) ).
fof(axiom_046,axiom,
! [X5] : mulNat(z,X5) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_046) ).
fof(axiom_003,axiom,
! [X1] : proj1N(n(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
fof(axiom_001,axiom,
! [X1] : proj1S(s(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
fof(axiom_010,axiom,
! [X1] : n(X1) != x2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
fof(axiom_002,axiom,
! [X1] : s(X1) != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
fof(axiom_042,axiom,
d(x2) = n(s(z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_042) ).
fof(i_0_54,negated_conjecture,
~ ? [X6] : opt(d(X6)) = opt(x(n(s(s(z))),x(x2,x2))),
inference(assume_negation,[status(cth)],[goal_054]) ).
fof(i_0_55,plain,
! [X167,X168] :
( X167 = n(proj1N(X167))
| X167 = y(proj12(X167),proj22(X167))
| fail32(X167,X168) = fail4(X167,X168) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_024])]) ).
fof(i_0_56,plain,
! [X165,X166] : fail4(X165,X166) = y(opt(X165),opt(X166)),
inference(variable_rename,[status(thm)],[axiom_023]) ).
fof(i_0_57,plain,
! [X169,X170] :
( X169 = n(proj1N(X169))
| fail32(n(X170),X169) = fail4(n(X170),X169) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_025])]) ).
fof(i_0_58,negated_conjecture,
! [X215] : opt(d(X215)) != opt(x(n(s(s(z))),x(x2,x2))),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_54])]) ).
fof(i_0_59,plain,
! [X151,X152,X153] :
( x(X152,X153) = X151
| fail2(x(X152,X153),X151) = opt(x(X152,x(X153,X151))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_016])]) ).
fof(i_0_60,plain,
! [X173,X174,X175] : fail32(y(X174,X175),X173) = opt(y(X174,y(X175,X173))),
inference(variable_rename,[status(thm)],[axiom_027]) ).
fof(i_0_61,plain,
! [X196,X197] : d(y(X196,X197)) = x(y(d(X196),X197),y(X196,d(X197))),
inference(variable_rename,[status(thm)],[axiom_041]) ).
fof(i_0_62,plain,
! [X184,X185] : fail12(n(s(s(X185))),X184) = fail22(n(s(s(X185))),X184),
inference(variable_rename,[status(thm)],[axiom_033]) ).
fof(i_0_63,plain,
! [X178,X179] : fail22(X178,n(s(s(X179)))) = fail32(X178,n(s(s(X179)))),
inference(variable_rename,[status(thm)],[axiom_029]) ).
fof(i_0_64,plain,
! [X212,X213] : opt(y(n(s(X213)),X212)) = fail3(n(s(X213)),X212),
inference(variable_rename,[status(thm)],[axiom_052]) ).
fof(i_0_65,plain,
! [X207,X208] : opt(x(n(s(X208)),X207)) = fail(n(s(X208)),X207),
inference(variable_rename,[status(thm)],[axiom_049]) ).
cnf(i_0_66,plain,
( X1 = n(proj1N(X1))
| X1 = y(proj12(X1),proj22(X1))
| fail32(X1,X2) = fail4(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]) ).
cnf(i_0_67,plain,
fail4(X1,X2) = y(opt(X1),opt(X2)),
inference(split_conjunct,[status(thm)],[i_0_56]) ).
fof(i_0_68,plain,
! [X149,X150] :
( X149 = X150
| X149 = x(proj1(X149),proj2(X149))
| fail2(X149,X150) = x(opt(X149),opt(X150)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_015])]) ).
cnf(i_0_69,plain,
( X1 = n(proj1N(X1))
| fail32(n(X2),X1) = fail4(n(X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_57]) ).
fof(i_0_70,plain,
! [X147,X148] :
( X147 != X148
| fail2(X147,X148) = y(n(s(s(z))),opt(X147)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_014])]) ).
fof(i_0_71,plain,
! [X190,X191] : fail3(X190,n(s(X191))) = fail12(X190,n(s(X191))),
inference(variable_rename,[status(thm)],[axiom_037]) ).
fof(i_0_72,plain,
! [X162,X163] : fail(X162,n(s(X163))) = fail1(X162,n(s(X163))),
inference(variable_rename,[status(thm)],[axiom_021]) ).
fof(i_0_73,plain,
! [X204] :
( X204 = x(proj1(X204),proj2(X204))
| X204 = y(proj12(X204),proj22(X204))
| opt(X204) = X204 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_047])]) ).
fof(i_0_74,plain,
! [X201,X202] : mulNat(s(X202),X201) = addNat(X201,mulNat(X202,X201)),
inference(variable_rename,[status(thm)],[axiom_045]) ).
fof(i_0_75,plain,
! [X171,X172] : fail32(n(X171),n(X172)) = n(mulNat(X171,X172)),
inference(variable_rename,[status(thm)],[axiom_026]) ).
fof(i_0_76,plain,
! [X158,X159] : fail1(n(X158),n(X159)) = n(addNat(X158,X159)),
inference(variable_rename,[status(thm)],[axiom_019]) ).
fof(i_0_77,plain,
! [X194,X195] : d(x(X194,X195)) = x(d(X194),d(X195)),
inference(variable_rename,[status(thm)],[axiom_040]) ).
fof(i_0_78,plain,
! [X210,X211] :
( X210 = n(proj1N(X210))
| opt(y(X210,X211)) = fail3(X210,X211) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_051])]) ).
fof(i_0_79,plain,
! [X205,X206] :
( X205 = n(proj1N(X205))
| opt(x(X205,X206)) = fail(X205,X206) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_048])]) ).
fof(i_0_80,plain,
! [X156,X157] :
( X156 = n(proj1N(X156))
| fail1(n(X157),X156) = fail2(n(X157),X156) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_018])]) ).
fof(i_0_81,plain,
! [X198,X199] : addNat(s(X199),X198) = s(addNat(X199,X198)),
inference(variable_rename,[status(thm)],[axiom_043]) ).
fof(i_0_82,plain,
! [X139,X140,X141,X142] : x(X139,X140) != y(X141,X142),
inference(variable_rename,[status(thm)],[axiom_011]) ).
fof(i_0_83,plain,
! [X188,X189] :
( X189 = n(proj1N(X189))
| fail3(X188,X189) = fail12(X188,X189) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_036])]) ).
fof(i_0_84,plain,
! [X182,X183] :
( X182 = n(proj1N(X182))
| fail12(X182,X183) = fail22(X182,X183) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_032])]) ).
fof(i_0_85,plain,
! [X176,X177] :
( X177 = n(proj1N(X177))
| fail22(X176,X177) = fail32(X176,X177) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_028])]) ).
fof(i_0_86,plain,
! [X160,X161] :
( X161 = n(proj1N(X161))
| fail(X160,X161) = fail1(X160,X161) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_020])]) ).
fof(i_0_87,plain,
! [X154,X155] :
( X154 = n(proj1N(X154))
| fail1(X154,X155) = fail2(X154,X155) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_017])]) ).
fof(i_0_88,plain,
! [X214] : opt(y(n(z),X214)) = n(z),
inference(variable_rename,[status(thm)],[axiom_053]) ).
fof(i_0_89,plain,
! [X209] : opt(x(n(z),X209)) = X209,
inference(variable_rename,[status(thm)],[axiom_050]) ).
fof(i_0_90,plain,
! [X187] : fail12(n(z),X187) = fail22(n(z),X187),
inference(variable_rename,[status(thm)],[axiom_035]) ).
fof(i_0_91,plain,
! [X181] : fail22(X181,n(z)) = fail32(X181,n(z)),
inference(variable_rename,[status(thm)],[axiom_031]) ).
fof(i_0_92,plain,
! [X130,X131] : proj22(y(X130,X131)) = X131,
inference(variable_rename,[status(thm)],[axiom_007]) ).
fof(i_0_93,plain,
! [X128,X129] : proj12(y(X128,X129)) = X128,
inference(variable_rename,[status(thm)],[axiom_006]) ).
fof(i_0_94,plain,
! [X126,X127] : proj2(x(X126,X127)) = X127,
inference(variable_rename,[status(thm)],[axiom_005]) ).
fof(i_0_95,plain,
! [X124,X125] : proj1(x(X124,X125)) = X124,
inference(variable_rename,[status(thm)],[axiom_004]) ).
fof(i_0_96,plain,
! [X135,X136,X137] : n(X135) != y(X136,X137),
inference(variable_rename,[status(thm)],[axiom_009]) ).
fof(i_0_97,plain,
! [X132,X133,X134] : n(X132) != x(X133,X134),
inference(variable_rename,[status(thm)],[axiom_008]) ).
fof(i_0_98,plain,
! [X186] : fail12(n(s(z)),X186) = X186,
inference(variable_rename,[status(thm)],[axiom_034]) ).
fof(i_0_99,plain,
! [X180] : fail22(X180,n(s(z))) = X180,
inference(variable_rename,[status(thm)],[axiom_030]) ).
fof(i_0_100,plain,
! [X145,X146] : y(X145,X146) != x2,
inference(variable_rename,[status(thm)],[axiom_013]) ).
fof(i_0_101,plain,
! [X143,X144] : x(X143,X144) != x2,
inference(variable_rename,[status(thm)],[axiom_012]) ).
fof(i_0_102,plain,
! [X192] : fail3(X192,n(z)) = n(z),
inference(variable_rename,[status(thm)],[axiom_038]) ).
fof(i_0_103,plain,
! [X164] : fail(X164,n(z)) = X164,
inference(variable_rename,[status(thm)],[axiom_022]) ).
fof(i_0_104,plain,
! [X200] : addNat(z,X200) = X200,
inference(variable_rename,[status(thm)],[axiom_044]) ).
fof(i_0_105,plain,
! [X193] : d(n(X193)) = n(z),
inference(variable_rename,[status(thm)],[axiom_039]) ).
fof(i_0_106,plain,
! [X203] : mulNat(z,X203) = z,
inference(variable_rename,[status(thm)],[axiom_046]) ).
fof(i_0_107,plain,
! [X123] : proj1N(n(X123)) = X123,
inference(variable_rename,[status(thm)],[axiom_003]) ).
fof(i_0_108,plain,
! [X121] : proj1S(s(X121)) = X121,
inference(variable_rename,[status(thm)],[axiom_001]) ).
fof(i_0_109,plain,
! [X138] : n(X138) != x2,
inference(variable_rename,[status(thm)],[axiom_010]) ).
fof(i_0_110,plain,
! [X122] : s(X122) != z,
inference(variable_rename,[status(thm)],[axiom_002]) ).
cnf(i_0_111,negated_conjecture,
opt(d(X1)) != opt(x(n(s(s(z))),x(x2,x2))),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_112,plain,
( x(X1,X2) = X3
| fail2(x(X1,X2),X3) = opt(x(X1,x(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_113,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_114,plain,
d(y(X1,X2)) = x(y(d(X1),X2),y(X1,d(X2))),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_115,plain,
fail12(n(s(s(X1))),X2) = fail22(n(s(s(X1))),X2),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_116,plain,
fail22(X1,n(s(s(X2)))) = fail32(X1,n(s(s(X2)))),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_117,plain,
opt(y(n(s(X1)),X2)) = fail3(n(s(X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_118,plain,
opt(x(n(s(X1)),X2)) = fail(n(s(X1)),X2),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_119,plain,
( X1 = n(proj1N(X1))
| X1 = y(proj12(X1),proj22(X1))
| fail32(X1,X2) = y(opt(X1),opt(X2)) ),
inference(rw,[status(thm)],[i_0_66,c_0_67]),
[final] ).
cnf(i_0_120,plain,
( X1 = X2
| X1 = x(proj1(X1),proj2(X1))
| fail2(X1,X2) = x(opt(X1),opt(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_121,plain,
( X1 = n(proj1N(X1))
| fail32(n(X2),X1) = y(opt(n(X2)),opt(X1)) ),
inference(rw,[status(thm)],[i_0_69,c_0_67]),
[final] ).
cnf(i_0_122,plain,
( fail2(X1,X2) = y(n(s(s(z))),opt(X1))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_123,plain,
fail3(X1,n(s(X2))) = fail12(X1,n(s(X2))),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_124,plain,
fail(X1,n(s(X2))) = fail1(X1,n(s(X2))),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_125,plain,
( X1 = x(proj1(X1),proj2(X1))
| X1 = y(proj12(X1),proj22(X1))
| opt(X1) = X1 ),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_126,plain,
mulNat(s(X1),X2) = addNat(X2,mulNat(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_127,plain,
fail32(n(X1),n(X2)) = n(mulNat(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_128,plain,
fail1(n(X1),n(X2)) = n(addNat(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_129,plain,
d(x(X1,X2)) = x(d(X1),d(X2)),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_130,plain,
( X1 = n(proj1N(X1))
| opt(y(X1,X2)) = fail3(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_131,plain,
( X1 = n(proj1N(X1))
| opt(x(X1,X2)) = fail(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_132,plain,
( X1 = n(proj1N(X1))
| fail1(n(X2),X1) = fail2(n(X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_133,plain,
addNat(s(X1),X2) = s(addNat(X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_134,plain,
x(X1,X2) != y(X3,X4),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_135,plain,
( X1 = n(proj1N(X1))
| fail3(X2,X1) = fail12(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_136,plain,
( X1 = n(proj1N(X1))
| fail12(X1,X2) = fail22(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_137,plain,
( X1 = n(proj1N(X1))
| fail22(X2,X1) = fail32(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_138,plain,
( X1 = n(proj1N(X1))
| fail(X2,X1) = fail1(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_139,plain,
( X1 = n(proj1N(X1))
| fail1(X1,X2) = fail2(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_140,plain,
opt(y(n(z),X1)) = n(z),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_141,plain,
opt(x(n(z),X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_142,plain,
fail12(n(z),X1) = fail22(n(z),X1),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_143,plain,
fail22(X1,n(z)) = fail32(X1,n(z)),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_144,plain,
proj22(y(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_92]),
[final] ).
cnf(i_0_145,plain,
proj12(y(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_146,plain,
proj2(x(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[i_0_94]),
[final] ).
cnf(i_0_147,plain,
proj1(x(X1,X2)) = X1,
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_148,plain,
n(X1) != y(X2,X3),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_149,plain,
n(X1) != x(X2,X3),
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_150,plain,
fail12(n(s(z)),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_98]),
[final] ).
cnf(i_0_151,plain,
fail22(X1,n(s(z))) = X1,
inference(split_conjunct,[status(thm)],[i_0_99]),
[final] ).
cnf(i_0_152,plain,
y(X1,X2) != x2,
inference(split_conjunct,[status(thm)],[i_0_100]),
[final] ).
cnf(i_0_153,plain,
x(X1,X2) != x2,
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_154,plain,
fail3(X1,n(z)) = n(z),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_155,plain,
fail(X1,n(z)) = X1,
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_156,plain,
addNat(z,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_157,plain,
d(n(X1)) = n(z),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_158,plain,
mulNat(z,X1) = z,
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_159,plain,
proj1N(n(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_160,plain,
proj1S(s(X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_161,plain,
d(x2) = n(s(z)),
inference(split_conjunct,[status(thm)],[axiom_042]),
[final] ).
cnf(i_0_162,plain,
n(X1) != x2,
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_163,plain,
s(X1) != z,
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_164,axiom,
X1 = X1 ).
cnf(i_0_165,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_166,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_167,axiom,
( X1 != X2
| opt(X1) = opt(X2) ) ).
cnf(i_0_168,axiom,
( X1 != X2
| fail22(X1,X3) = fail22(X2,X3) ) ).
cnf(i_0_169,axiom,
( X1 != X2
| fail22(X3,X1) = fail22(X3,X2) ) ).
cnf(i_0_170,axiom,
( X1 != X2
| fail3(X1,X3) = fail3(X2,X3) ) ).
cnf(i_0_171,axiom,
( X1 != X2
| fail3(X3,X1) = fail3(X3,X2) ) ).
cnf(i_0_172,axiom,
( X1 != X2
| fail(X1,X3) = fail(X2,X3) ) ).
cnf(i_0_173,axiom,
( X1 != X2
| fail(X3,X1) = fail(X3,X2) ) ).
cnf(i_0_174,axiom,
( X1 != X2
| proj1N(X1) = proj1N(X2) ) ).
cnf(i_0_175,axiom,
( X1 != X2
| proj12(X1) = proj12(X2) ) ).
cnf(i_0_176,axiom,
( X1 != X2
| proj22(X1) = proj22(X2) ) ).
cnf(i_0_177,axiom,
( X1 != X2
| proj1(X1) = proj1(X2) ) ).
cnf(i_0_178,axiom,
( X1 != X2
| proj2(X1) = proj2(X2) ) ).
cnf(i_0_179,axiom,
( X1 != X2
| fail1(X1,X3) = fail1(X2,X3) ) ).
cnf(i_0_180,axiom,
( X1 != X2
| fail1(X3,X1) = fail1(X3,X2) ) ).
cnf(i_0_181,axiom,
( X1 != X2
| mulNat(X1,X3) = mulNat(X2,X3) ) ).
cnf(i_0_182,axiom,
( X1 != X2
| mulNat(X3,X1) = mulNat(X3,X2) ) ).
cnf(i_0_183,axiom,
( X1 != X2
| d(X1) = d(X2) ) ).
cnf(i_0_184,axiom,
( X1 != X2
| addNat(X1,X3) = addNat(X2,X3) ) ).
cnf(i_0_185,axiom,
( X1 != X2
| addNat(X3,X1) = addNat(X3,X2) ) ).
cnf(i_0_186,axiom,
( X1 != X2
| proj1S(X1) = proj1S(X2) ) ).
cnf(i_0_187,axiom,
( X1 != X2
| x(X1,X3) = x(X2,X3) ) ).
cnf(i_0_188,axiom,
( X1 != X2
| x(X3,X1) = x(X3,X2) ) ).
cnf(i_0_189,axiom,
( X1 != X2
| n(X1) = n(X2) ) ).
cnf(i_0_190,axiom,
( X1 != X2
| s(X1) = s(X2) ) ).
cnf(i_0_191,axiom,
( X1 != X2
| fail2(X1,X3) = fail2(X2,X3) ) ).
cnf(i_0_192,axiom,
( X1 != X2
| fail2(X3,X1) = fail2(X3,X2) ) ).
cnf(i_0_193,axiom,
( X1 != X2
| fail32(X1,X3) = fail32(X2,X3) ) ).
cnf(i_0_194,axiom,
( X1 != X2
| fail32(X3,X1) = fail32(X3,X2) ) ).
cnf(i_0_195,axiom,
( X1 != X2
| y(X1,X3) = y(X2,X3) ) ).
cnf(i_0_196,axiom,
( X1 != X2
| y(X3,X1) = y(X3,X2) ) ).
cnf(i_0_197,axiom,
( X1 != X2
| fail12(X1,X3) = fail12(X2,X3) ) ).
cnf(i_0_198,axiom,
( X1 != X2
| fail12(X3,X1) = fail12(X3,X2) ) ).
cnf(i_0_199,plain,
fail2(X1,X1) = y(n(s(s(z))),opt(X1)),
inference(equality_inference,[],[122]) ).
cnf(i_0_203,plain,
x(X1,X2) != y(X3,X4),
inference(rename_variables,[],[i_0_134]) ).
cnf(i_0_205,plain,
n(X1) != y(X2,X3),
inference(rename_variables,[],[i_0_148]) ).
cnf(i_0_206,plain,
n(X1) != x(X2,X3),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_209,plain,
x(X1,X2) != y(X3,X4),
inference(rename_variables,[],[i_0_134]) ).
cnf(i_0_214,plain,
addNat(z,X1) = X1,
inference(rename_variables,[],[i_0_156]) ).
cnf(i_0_216,plain,
n(X1) != y(X2,X3),
inference(rename_variables,[],[i_0_148]) ).
cnf(i_0_219,plain,
x(X1,X2) != y(X3,X4),
inference(rename_variables,[],[i_0_134]) ).
cnf(i_0_223,plain,
proj1N(n(X1)) = X1,
inference(rename_variables,[],[i_0_159]) ).
cnf(i_0_229,plain,
proj1S(s(X1)) = X1,
inference(rename_variables,[],[i_0_160]) ).
cnf(i_0_232,plain,
proj22(y(X1,X2)) = X2,
inference(rename_variables,[],[i_0_144]) ).
cnf(i_0_239,plain,
n(addNat(X1,X2)) = fail1(n(X1),n(X2)),
inference(scs_inference,[],[i_0_128,i_0_165]) ).
cnf(i_0_240,plain,
proj12(y(fail1(n(X1),n(X2)),X3)) = n(addNat(X1,X2)),
inference(scs_inference,[],[i_0_128,i_0_145,i_0_165,i_0_166]) ).
cnf(i_0_241,plain,
proj12(y(X1,X2)) = X1,
inference(rename_variables,[],[i_0_145]) ).
cnf(i_0_248,plain,
x(d(X1),d(X2)) = d(x(X1,X2)),
inference(scs_inference,[],[i_0_129,i_0_165]) ).
cnf(i_0_249,plain,
n(X1) != d(x(X2,X3)),
inference(scs_inference,[],[i_0_129,i_0_149,i_0_165,i_0_166]) ).
cnf(i_0_250,plain,
n(X1) != x(X2,X3),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_251,plain,
s(addNat(X1,X2)) = addNat(s(X1),X2),
inference(scs_inference,[],[i_0_133,i_0_165]) ).
cnf(i_0_253,plain,
addNat(s(X1),X2) = s(addNat(X1,X2)),
inference(rename_variables,[],[i_0_133]) ).
cnf(i_0_257,plain,
fail(X1,n(z)) = X1,
inference(rename_variables,[],[i_0_155]) ).
cnf(i_0_258,plain,
X1 = proj2(x(X2,X1)),
inference(scs_inference,[],[i_0_146,i_0_165]) ).
cnf(i_0_259,plain,
s(X1) != mulNat(z,X2),
inference(scs_inference,[],[i_0_163,i_0_146,i_0_158,i_0_165,i_0_166]) ).
cnf(i_0_260,plain,
X1 = proj1(x(X1,X2)),
inference(scs_inference,[],[i_0_147,i_0_165]) ).
cnf(i_0_268,plain,
opt(x(n(z),X1)) = X1,
inference(rename_variables,[],[i_0_141]) ).
cnf(i_0_271,plain,
n(X1) != x(X2,X3),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_272,plain,
fail22(n(z),X1) = fail12(n(z),X1),
inference(scs_inference,[],[i_0_142,i_0_165]) ).
cnf(i_0_279,plain,
fail32(X1,n(z)) = fail22(X1,n(z)),
inference(scs_inference,[],[i_0_143,i_0_165]) ).
cnf(i_0_282,plain,
n(z) = d(n(X1)),
inference(scs_inference,[],[i_0_157,i_0_165]) ).
cnf(i_0_288,plain,
fail12(n(s(z)),X1) = X1,
inference(rename_variables,[],[i_0_150]) ).
cnf(i_0_291,plain,
fail22(X1,n(s(z))) = X1,
inference(rename_variables,[],[i_0_151]) ).
cnf(i_0_309,plain,
n(z) = fail3(X1,n(z)),
inference(scs_inference,[],[i_0_154,i_0_165]) ).
cnf(i_0_318,plain,
n(s(z)) = d(X1),
inference(scs_inference,[],[i_0_161,i_0_165]) ).
cnf(i_0_320,plain,
x(y(d(X1),X2),y(X1,d(X2))) = d(y(X1,X2)),
inference(scs_inference,[],[i_0_114,i_0_165]) ).
cnf(i_0_322,plain,
opt(y(X1,y(X2,X3))) = fail32(y(X1,X2),X3),
inference(scs_inference,[],[i_0_113,i_0_165]) ).
cnf(i_0_324,plain,
addNat(z,X1) = X1,
inference(rename_variables,[],[i_0_156]) ).
cnf(i_0_327,plain,
proj1N(n(X1)) = X1,
inference(rename_variables,[],[i_0_159]) ).
cnf(i_0_331,plain,
fail12(X1,n(s(X2))) = fail3(X1,n(s(X2))),
inference(scs_inference,[],[i_0_123,i_0_165]) ).
cnf(i_0_334,plain,
fail1(X1,n(s(X2))) = fail(X1,n(s(X2))),
inference(scs_inference,[],[i_0_124,i_0_165]) ).
cnf(i_0_361,plain,
proj1S(s(X1)) = X1,
inference(rename_variables,[],[i_0_160]) ).
cnf(i_0_367,plain,
proj22(y(X1,X2)) = X2,
inference(rename_variables,[],[i_0_144]) ).
cnf(i_0_373,plain,
proj12(y(X1,X2)) = X1,
inference(rename_variables,[],[i_0_145]) ).
cnf(i_0_383,plain,
n(z) = opt(y(n(z),X1)),
inference(scs_inference,[],[i_0_140,i_0_165]) ).
cnf(i_0_385,plain,
proj2(x(X1,X2)) = X2,
inference(rename_variables,[],[i_0_146]) ).
cnf(i_0_421,plain,
fail22(n(s(s(X1))),X2) = fail12(n(s(s(X1))),X2),
inference(scs_inference,[],[i_0_115,i_0_165]) ).
cnf(i_0_430,plain,
proj1(x(X1,X2)) = X1,
inference(rename_variables,[],[i_0_147]) ).
cnf(i_0_433,plain,
fail(X1,n(z)) = X1,
inference(rename_variables,[],[i_0_155]) ).
cnf(i_0_441,plain,
fail32(X1,n(s(s(X2)))) = fail22(X1,n(s(s(X2)))),
inference(scs_inference,[],[i_0_116,i_0_165]) ).
cnf(i_0_471,plain,
fail3(n(s(X1)),X2) = opt(y(n(s(X1)),X2)),
inference(scs_inference,[],[i_0_117,i_0_165]) ).
cnf(i_0_484,plain,
fail(n(s(X1)),X2) = opt(x(n(s(X1)),X2)),
inference(scs_inference,[],[i_0_118,i_0_165]) ).
cnf(i_0_487,plain,
addNat(X1,mulNat(X2,X1)) = mulNat(s(X2),X1),
inference(scs_inference,[],[i_0_126,i_0_165]) ).
cnf(i_0_490,plain,
n(mulNat(X1,X2)) = fail32(n(X1),n(X2)),
inference(scs_inference,[],[i_0_127,i_0_165]) ).
cnf(i_0_501,plain,
z = mulNat(z,X1),
inference(scs_inference,[],[i_0_158,i_0_165]) ).
cnf(i_0_529,plain,
X1 = opt(x(n(z),X1)),
inference(scs_inference,[],[i_0_141,i_0_165]) ).
cnf(i_0_534,plain,
fail12(n(s(z)),X1) = X1,
inference(rename_variables,[],[i_0_150]) ).
cnf(i_0_543,plain,
fail22(X1,n(s(z))) = X1,
inference(rename_variables,[],[i_0_151]) ).
cnf(i_0_557,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_566,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_580,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_593,plain,
X1 = addNat(z,X1),
inference(scs_inference,[],[i_0_156,i_0_165]) ).
cnf(i_0_607,plain,
X1 = proj1N(n(X1)),
inference(scs_inference,[],[i_0_159,i_0_165]) ).
cnf(i_0_619,plain,
X1 = proj1S(s(X1)),
inference(scs_inference,[],[i_0_160,i_0_165]) ).
cnf(i_0_622,plain,
X1 = proj22(y(X2,X1)),
inference(scs_inference,[],[i_0_144,i_0_165]) ).
cnf(i_0_630,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_634,plain,
X1 = proj12(y(X1,X2)),
inference(scs_inference,[],[i_0_145,i_0_165]) ).
cnf(i_0_637,plain,
X1 = fail(X1,n(z)),
inference(scs_inference,[],[i_0_155,i_0_165]) ).
cnf(i_0_646,plain,
X1 = fail12(n(s(z)),X1),
inference(scs_inference,[],[i_0_150,i_0_165]) ).
cnf(i_0_652,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_670,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_692,plain,
X1 = fail22(X1,n(s(z))),
inference(scs_inference,[],[i_0_151,i_0_165]) ).
cnf(i_0_715,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_816,plain,
proj2(x(X1,X2)) = X2,
inference(rename_variables,[],[i_0_146]) ).
cnf(i_0_819,plain,
proj1(x(X1,X2)) = X1,
inference(rename_variables,[],[i_0_147]) ).
cnf(i_0_822,plain,
fail3(X1,n(z)) = n(z),
inference(rename_variables,[],[i_0_154]) ).
cnf(i_0_825,plain,
fail(X1,n(s(X2))) = fail1(X1,n(s(X2))),
inference(rename_variables,[],[i_0_124]) ).
cnf(i_0_827,plain,
fail32(y(n(s(X1)),X2),X3) = fail3(n(s(X1)),y(X2,X3)),
inference(scs_inference,[],[i_0_113,i_0_117,i_0_166]) ).
cnf(i_0_828,plain,
opt(y(n(s(X1)),X2)) = fail3(n(s(X1)),X2),
inference(rename_variables,[],[i_0_117]) ).
cnf(i_0_829,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_830,plain,
fail3(n(s(X1)),y(X2,X3)) = fail32(y(n(s(X1)),X2),X3),
inference(scs_inference,[],[i_0_113,i_0_117,i_0_166,i_0_165]) ).
cnf(i_0_838,plain,
fail32(n(X1),n(X2)) = n(mulNat(X1,X2)),
inference(rename_variables,[],[i_0_127]) ).
cnf(i_0_857,plain,
n(X1) != d(y(X2,X3)),
inference(scs_inference,[],[i_0_114,i_0_149,i_0_166]) ).
cnf(i_0_858,plain,
n(X1) != x(X2,X3),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_875,plain,
opt(d(X1)) != addNat(z,opt(x(n(s(s(z))),x(X2,X2)))),
inference(scs_inference,[],[i_0_111,i_0_156,i_0_166]) ).
cnf(i_0_876,plain,
addNat(z,X1) = X1,
inference(rename_variables,[],[i_0_156]) ).
cnf(i_0_878,plain,
fail32(n(X1),n(X2)) = n(mulNat(X1,X2)),
inference(rename_variables,[],[i_0_127]) ).
cnf(i_0_894,plain,
n(X1) != y(X2,X3),
inference(rename_variables,[],[i_0_148]) ).
cnf(i_0_936,plain,
n(X1) != x(X2,X3),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_1561,plain,
x(X1,X2) != y(X3,X4),
inference(rename_variables,[],[i_0_134]) ).
cnf(i_0_1715,plain,
n(X1) != x(X2,X3),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_1868,plain,
n(X1) != X2,
inference(rename_variables,[],[i_0_162]) ).
cnf(i_0_1869,plain,
n(X1) != x(X2,X3),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_2059,plain,
y(X1,X2) != X3,
inference(rename_variables,[],[i_0_152]) ).
cnf(i_0_2948,plain,
opt(x(n(s(X1)),X2)) = fail(n(s(X1)),X2),
inference(rename_variables,[],[i_0_118]) ).
cnf(i_0_3026,plain,
opt(x(n(s(X1)),X2)) = fail(n(s(X1)),X2),
inference(rename_variables,[],[i_0_118]) ).
cnf(i_0_3072,plain,
x(X1,X2) != y(X3,X4),
inference(rename_variables,[],[i_0_134]) ).
cnf(i_0_3191,plain,
fail2(fail32(y(X1,X2),X3),opt(y(X1,y(X2,X3)))) = y(n(s(s(z))),opt(fail32(y(X1,X2),X3))),
inference(scs_inference,[],[i_0_113,i_0_122]) ).
cnf(i_0_3193,plain,
fail22(fail32(y(X1,X2),X3),X4) = fail22(opt(y(X1,y(X2,X3))),X4),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168]) ).
cnf(i_0_3194,plain,
fail22(X1,fail32(y(X2,X3),X4)) = fail22(X1,opt(y(X2,y(X3,X4)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169]) ).
cnf(i_0_3195,plain,
fail3(fail32(y(X1,X2),X3),X4) = fail3(opt(y(X1,y(X2,X3))),X4),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170]) ).
cnf(i_0_3196,plain,
fail3(X1,fail32(y(X2,X3),X4)) = fail3(X1,opt(y(X2,y(X3,X4)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171]) ).
cnf(i_0_3197,plain,
fail(fail32(y(X1,X2),X3),X4) = fail(opt(y(X1,y(X2,X3))),X4),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172]) ).
cnf(i_0_3198,plain,
fail(X1,fail32(y(X2,X3),X4)) = fail(X1,opt(y(X2,y(X3,X4)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173]) ).
cnf(i_0_3199,plain,
proj1N(fail32(y(X1,X2),X3)) = proj1N(opt(y(X1,y(X2,X3)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174]) ).
cnf(i_0_3200,plain,
proj12(fail32(y(X1,X2),X3)) = proj12(opt(y(X1,y(X2,X3)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175]) ).
cnf(i_0_3201,plain,
proj22(fail32(y(X1,X2),X3)) = proj22(opt(y(X1,y(X2,X3)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176]) ).
cnf(i_0_3202,plain,
proj1(fail32(y(X1,X2),X3)) = proj1(opt(y(X1,y(X2,X3)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177]) ).
cnf(i_0_3203,plain,
proj2(fail32(y(X1,X2),X3)) = proj2(opt(y(X1,y(X2,X3)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178]) ).
cnf(i_0_3204,plain,
fail1(fail32(y(X1,X2),X3),X4) = fail1(opt(y(X1,y(X2,X3))),X4),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179]) ).
cnf(i_0_3205,plain,
fail1(X1,fail32(y(X2,X3),X4)) = fail1(X1,opt(y(X2,y(X3,X4)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180]) ).
cnf(i_0_3206,plain,
mulNat(fail32(y(X1,X2),X3),X4) = mulNat(opt(y(X1,y(X2,X3))),X4),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181]) ).
cnf(i_0_3207,plain,
mulNat(X1,fail32(y(X2,X3),X4)) = mulNat(X1,opt(y(X2,y(X3,X4)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182]) ).
cnf(i_0_3208,plain,
addNat(fail32(y(X1,X2),X3),X4) = addNat(opt(y(X1,y(X2,X3))),X4),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184]) ).
cnf(i_0_3209,plain,
addNat(X1,fail32(y(X2,X3),X4)) = addNat(X1,opt(y(X2,y(X3,X4)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184,i_0_185]) ).
cnf(i_0_3210,plain,
proj1S(fail32(y(X1,X2),X3)) = proj1S(opt(y(X1,y(X2,X3)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184,i_0_185,i_0_186]) ).
cnf(i_0_3211,plain,
x(fail32(y(X1,X2),X3),X4) = x(opt(y(X1,y(X2,X3))),X4),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184,i_0_185,i_0_186,i_0_187]) ).
cnf(i_0_3212,plain,
x(X1,fail32(y(X2,X3),X4)) = x(X1,opt(y(X2,y(X3,X4)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188]) ).
cnf(i_0_3213,plain,
n(fail32(y(X1,X2),X3)) = n(opt(y(X1,y(X2,X3)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189]) ).
cnf(i_0_3214,plain,
s(fail32(y(X1,X2),X3)) = s(opt(y(X1,y(X2,X3)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190]) ).
cnf(i_0_3215,plain,
fail2(fail32(y(X1,X2),X3),X4) = fail2(opt(y(X1,y(X2,X3))),X4),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191]) ).
cnf(i_0_3216,plain,
fail2(X1,fail32(y(X2,X3),X4)) = fail2(X1,opt(y(X2,y(X3,X4)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192]) ).
cnf(i_0_3217,plain,
fail32(fail32(y(X1,X2),X3),X4) = fail32(opt(y(X1,y(X2,X3))),X4),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193]) ).
cnf(i_0_3218,plain,
fail32(X1,fail32(y(X2,X3),X4)) = fail32(X1,opt(y(X2,y(X3,X4)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194]) ).
cnf(i_0_3219,plain,
y(fail32(y(X1,X2),X3),X4) = y(opt(y(X1,y(X2,X3))),X4),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195]) ).
cnf(i_0_3220,plain,
y(X1,fail32(y(X2,X3),X4)) = y(X1,opt(y(X2,y(X3,X4)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196]) ).
cnf(i_0_3221,plain,
fail12(fail32(y(X1,X2),X3),X4) = fail12(opt(y(X1,y(X2,X3))),X4),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196,i_0_197]) ).
cnf(i_0_3222,plain,
fail12(X1,fail32(y(X2,X3),X4)) = fail12(X1,opt(y(X2,y(X3,X4)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196,i_0_197,i_0_198]) ).
cnf(i_0_3223,plain,
d(fail32(y(X1,X2),X3)) = d(opt(y(X1,y(X2,X3)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196,i_0_197,i_0_198,i_0_183]) ).
cnf(i_0_3224,plain,
opt(fail32(y(X1,X2),X3)) = opt(opt(y(X1,y(X2,X3)))),
inference(scs_inference,[],[i_0_113,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196,i_0_197,i_0_198,i_0_183,i_0_167]) ).
cnf(i_0_200,plain,
y(n(s(s(z))),opt(X1)) = fail2(X1,X1),
inference(scs_inference,[],[i_0_199,i_0_165]) ).
cnf(i_0_201,plain,
d(X1) != x(n(s(s(z))),x(X2,X2)),
inference(scs_inference,[],[i_0_111,i_0_199,i_0_165,i_0_167]) ).
cnf(i_0_202,plain,
x(X1,X2) != fail2(X3,X3),
inference(scs_inference,[],[i_0_111,i_0_199,i_0_134,i_0_165,i_0_167,i_0_166]) ).
cnf(i_0_204,plain,
opt(n(X1)) = n(X1),
inference(scs_inference,[],[i_0_111,i_0_199,i_0_134,i_0_148,i_0_149,i_0_165,i_0_167,i_0_166,i_0_125]) ).
cnf(i_0_242,plain,
n(addNat(X1,X2)) = proj12(y(fail1(n(X1),n(X2)),X3)),
inference(scs_inference,[],[i_0_240,i_0_165]) ).
cnf(i_0_261,plain,
n(addNat(X1,X2)) = proj2(x(X3,fail1(n(X1),n(X2)))),
inference(scs_inference,[],[i_0_239,i_0_258,i_0_147,i_0_165,i_0_166]) ).
cnf(i_0_262,plain,
X1 = proj2(x(X2,X1)),
inference(rename_variables,[],[i_0_258]) ).
cnf(i_0_265,plain,
X1 = proj1(x(X1,X2)),
inference(rename_variables,[],[i_0_260]) ).
cnf(i_0_275,plain,
X1 = proj1(x(X1,X2)),
inference(rename_variables,[],[i_0_260]) ).
cnf(i_0_283,plain,
fail32(n(z),n(z)) = fail12(n(z),n(z)),
inference(scs_inference,[],[i_0_272,i_0_279,i_0_157,i_0_165,i_0_166]) ).
cnf(i_0_284,plain,
fail22(n(z),X1) = fail12(n(z),X1),
inference(rename_variables,[],[i_0_272]) ).
cnf(i_0_285,plain,
fail32(X1,n(z)) = fail22(X1,n(z)),
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_296,plain,
fail22(n(z),X1) = fail12(n(z),X1),
inference(rename_variables,[],[i_0_272]) ).
cnf(i_0_302,plain,
X1 = proj2(x(X2,X1)),
inference(rename_variables,[],[i_0_258]) ).
cnf(i_0_323,plain,
addNat(z,x(y(d(X1),X2),y(X1,d(X2)))) = d(y(X1,X2)),
inference(scs_inference,[],[i_0_320,i_0_113,i_0_156,i_0_165,i_0_166]) ).
cnf(i_0_335,plain,
fail22(n(z),n(s(X1))) = fail3(n(z),n(s(X1))),
inference(scs_inference,[],[i_0_331,i_0_272,i_0_124,i_0_165,i_0_166]) ).
cnf(i_0_336,plain,
fail12(X1,n(s(X2))) = fail3(X1,n(s(X2))),
inference(rename_variables,[],[i_0_331]) ).
cnf(i_0_337,plain,
fail22(n(z),X1) = fail12(n(z),X1),
inference(rename_variables,[],[i_0_272]) ).
cnf(i_0_340,plain,
fail1(X1,n(s(X2))) = fail(X1,n(s(X2))),
inference(rename_variables,[],[i_0_334]) ).
cnf(i_0_341,plain,
n(addNat(X1,X2)) = fail1(n(X1),n(X2)),
inference(rename_variables,[],[i_0_239]) ).
cnf(i_0_352,plain,
fail1(X1,n(s(X2))) = fail(X1,n(s(X2))),
inference(rename_variables,[],[i_0_334]) ).
cnf(i_0_384,plain,
proj2(x(X1,opt(y(X2,y(X3,X4))))) = fail32(y(X2,X3),X4),
inference(scs_inference,[],[i_0_322,i_0_140,i_0_146,i_0_165,i_0_166]) ).
cnf(i_0_389,plain,
n(z) = opt(y(n(z),X1)),
inference(rename_variables,[],[i_0_383]) ).
cnf(i_0_426,plain,
fail22(n(s(s(X1))),X2) = fail12(n(s(s(X1))),X2),
inference(rename_variables,[],[i_0_421]) ).
cnf(i_0_427,plain,
fail32(X1,n(z)) = fail22(X1,n(z)),
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_436,plain,
fail12(X1,n(s(X2))) = fail3(X1,n(s(X2))),
inference(rename_variables,[],[i_0_331]) ).
cnf(i_0_437,plain,
fail22(n(s(s(X1))),X2) = fail12(n(s(s(X1))),X2),
inference(rename_variables,[],[i_0_421]) ).
cnf(i_0_447,plain,
fail32(X1,n(s(s(X2)))) = fail22(X1,n(s(s(X2)))),
inference(rename_variables,[],[i_0_441]) ).
cnf(i_0_475,plain,
fail3(n(s(X1)),X2) = opt(y(n(s(X1)),X2)),
inference(rename_variables,[],[i_0_471]) ).
cnf(i_0_482,plain,
fail3(n(s(X1)),X2) = opt(y(n(s(X1)),X2)),
inference(rename_variables,[],[i_0_471]) ).
cnf(i_0_488,plain,
opt(d(X1)) != fail(n(s(s(z))),x(X2,X2)),
inference(scs_inference,[],[i_0_111,i_0_484,i_0_126,i_0_165,i_0_166]) ).
cnf(i_0_489,plain,
fail(n(s(X1)),X2) = opt(x(n(s(X1)),X2)),
inference(rename_variables,[],[i_0_484]) ).
cnf(i_0_491,plain,
s(addNat(X1,mulNat(X2,s(X1)))) = mulNat(s(X2),s(X1)),
inference(scs_inference,[],[i_0_487,i_0_251,i_0_127,i_0_165,i_0_166]) ).
cnf(i_0_492,plain,
addNat(X1,mulNat(X2,X1)) = mulNat(s(X2),X1),
inference(rename_variables,[],[i_0_487]) ).
cnf(i_0_493,plain,
s(addNat(X1,X2)) = addNat(s(X1),X2),
inference(rename_variables,[],[i_0_251]) ).
cnf(i_0_503,plain,
n(mulNat(X1,X2)) = fail32(n(X1),n(X2)),
inference(rename_variables,[],[i_0_490]) ).
cnf(i_0_531,plain,
X1 = proj2(x(X2,X1)),
inference(rename_variables,[],[i_0_258]) ).
cnf(i_0_549,plain,
fail32(X1,n(z)) = fail22(X1,n(z)),
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_599,plain,
X1 = addNat(z,X1),
inference(rename_variables,[],[i_0_593]) ).
cnf(i_0_606,plain,
s(X1) != mulNat(z,X2),
inference(rename_variables,[],[i_0_259]) ).
cnf(i_0_608,plain,
mulNat(X1,z) = mulNat(s(X1),z),
inference(scs_inference,[],[i_0_487,i_0_593,i_0_159,i_0_165,i_0_166]) ).
cnf(i_0_609,plain,
addNat(X1,mulNat(X2,X1)) = mulNat(s(X2),X1),
inference(rename_variables,[],[i_0_487]) ).
cnf(i_0_610,plain,
X1 = addNat(z,X1),
inference(rename_variables,[],[i_0_593]) ).
cnf(i_0_614,plain,
z = mulNat(z,X1),
inference(rename_variables,[],[i_0_501]) ).
cnf(i_0_618,plain,
s(X1) != mulNat(z,X2),
inference(rename_variables,[],[i_0_259]) ).
cnf(i_0_627,plain,
X1 = proj22(y(X2,X1)),
inference(rename_variables,[],[i_0_622]) ).
cnf(i_0_636,plain,
X1 = proj1S(s(X1)),
inference(rename_variables,[],[i_0_619]) ).
cnf(i_0_638,plain,
fail32(y(X1,X2),X3) = proj12(y(opt(y(X1,y(X2,X3))),X4)),
inference(scs_inference,[],[i_0_113,i_0_634,i_0_155,i_0_165,i_0_166]) ).
cnf(i_0_639,plain,
X1 = proj12(y(X1,X2)),
inference(rename_variables,[],[i_0_634]) ).
cnf(i_0_645,plain,
X1 = fail(X1,n(z)),
inference(rename_variables,[],[i_0_637]) ).
cnf(i_0_657,plain,
X1 = fail12(n(s(z)),X1),
inference(rename_variables,[],[i_0_646]) ).
cnf(i_0_697,plain,
X1 = fail22(X1,n(s(z))),
inference(rename_variables,[],[i_0_692]) ).
cnf(i_0_711,plain,
X1 = fail12(n(s(z)),X1),
inference(rename_variables,[],[i_0_646]) ).
cnf(i_0_721,plain,
addNat(X1,mulNat(X2,X1)) = mulNat(s(X2),X1),
inference(rename_variables,[],[i_0_487]) ).
cnf(i_0_815,plain,
proj2(x(X1,x(y(d(X2),X3),y(X2,d(X3))))) = d(y(X2,X3)),
inference(scs_inference,[],[i_0_320,i_0_146,i_0_166]) ).
cnf(i_0_817,plain,
d(y(X1,X2)) = proj2(x(X3,x(y(d(X1),X2),y(X1,d(X2))))),
inference(scs_inference,[],[i_0_320,i_0_146,i_0_166,i_0_165]) ).
cnf(i_0_818,plain,
proj1(x(x(y(d(X1),X2),y(X1,d(X2))),X3)) = d(y(X1,X2)),
inference(scs_inference,[],[i_0_320,i_0_147,i_0_166]) ).
cnf(i_0_820,plain,
d(y(X1,X2)) = proj1(x(x(y(d(X1),X2),y(X1,d(X2))),X3)),
inference(scs_inference,[],[i_0_320,i_0_147,i_0_166,i_0_165]) ).
cnf(i_0_843,plain,
n(mulNat(X1,z)) = fail22(n(X1),n(z)),
inference(scs_inference,[],[i_0_490,i_0_279,i_0_166]) ).
cnf(i_0_844,plain,
fail32(X1,n(z)) = fail22(X1,n(z)),
inference(rename_variables,[],[i_0_279]) ).
cnf(i_0_845,plain,
n(mulNat(X1,X2)) = fail32(n(X1),n(X2)),
inference(rename_variables,[],[i_0_490]) ).
cnf(i_0_846,plain,
fail22(n(X1),n(z)) = n(mulNat(X1,z)),
inference(scs_inference,[],[i_0_490,i_0_279,i_0_166,i_0_165]) ).
cnf(i_0_883,plain,
d(y(X1,X2)) = proj1N(n(x(y(d(X1),X2),y(X1,d(X2))))),
inference(scs_inference,[],[i_0_114,i_0_607,i_0_166]) ).
cnf(i_0_884,plain,
X1 = proj1N(n(X1)),
inference(rename_variables,[],[i_0_607]) ).
cnf(i_0_885,plain,
proj1N(n(x(y(d(X1),X2),y(X1,d(X2))))) = d(y(X1,X2)),
inference(scs_inference,[],[i_0_114,i_0_607,i_0_166,i_0_165]) ).
cnf(i_0_888,plain,
d(y(X1,X2)) = proj22(y(X3,x(y(d(X1),X2),y(X1,d(X2))))),
inference(scs_inference,[],[i_0_114,i_0_622,i_0_166]) ).
cnf(i_0_889,plain,
X1 = proj22(y(X2,X1)),
inference(rename_variables,[],[i_0_622]) ).
cnf(i_0_890,plain,
proj22(y(X1,x(y(d(X2),X3),y(X2,d(X3))))) = d(y(X2,X3)),
inference(scs_inference,[],[i_0_114,i_0_622,i_0_166,i_0_165]) ).
cnf(i_0_893,plain,
n(X1) != fail2(X2,X2),
inference(scs_inference,[],[i_0_148,i_0_199,i_0_166]) ).
cnf(i_0_933,plain,
X1 = opt(x(n(z),X1)),
inference(rename_variables,[],[i_0_529]) ).
cnf(i_0_1014,plain,
X1 = proj1N(n(X1)),
inference(rename_variables,[],[i_0_607]) ).
cnf(i_0_1054,plain,
X1 = proj1S(s(X1)),
inference(rename_variables,[],[i_0_619]) ).
cnf(i_0_1091,plain,
X1 = proj12(y(X1,X2)),
inference(rename_variables,[],[i_0_634]) ).
cnf(i_0_1171,plain,
X1 = fail(X1,n(z)),
inference(rename_variables,[],[i_0_637]) ).
cnf(i_0_1246,plain,
X1 = opt(x(n(z),X1)),
inference(rename_variables,[],[i_0_529]) ).
cnf(i_0_1327,plain,
X1 = fail22(X1,n(s(z))),
inference(rename_variables,[],[i_0_692]) ).
cnf(i_0_1402,plain,
X1 = addNat(z,X1),
inference(rename_variables,[],[i_0_593]) ).
cnf(i_0_1637,plain,
X1 = proj1N(n(X1)),
inference(rename_variables,[],[i_0_607]) ).
cnf(i_0_1712,plain,
X1 = proj1S(s(X1)),
inference(rename_variables,[],[i_0_619]) ).
cnf(i_0_1753,plain,
X1 = proj1(x(X1,X2)),
inference(rename_variables,[],[i_0_260]) ).
cnf(i_0_1790,plain,
X1 = proj22(y(X2,X1)),
inference(rename_variables,[],[i_0_622]) ).
cnf(i_0_1827,plain,
X1 = proj12(y(X1,X2)),
inference(rename_variables,[],[i_0_634]) ).
cnf(i_0_1907,plain,
X1 = fail(X1,n(z)),
inference(rename_variables,[],[i_0_637]) ).
cnf(i_0_1944,plain,
X1 = opt(x(n(z),X1)),
inference(rename_variables,[],[i_0_529]) ).
cnf(i_0_2019,plain,
X1 = fail12(n(s(z)),X1),
inference(rename_variables,[],[i_0_646]) ).
cnf(i_0_2133,plain,
X1 = fail22(X1,n(s(z))),
inference(rename_variables,[],[i_0_692]) ).
cnf(i_0_2173,plain,
X1 = addNat(z,X1),
inference(rename_variables,[],[i_0_593]) ).
cnf(i_0_2213,plain,
X1 = proj1N(n(X1)),
inference(rename_variables,[],[i_0_607]) ).
cnf(i_0_2288,plain,
X1 = proj1S(s(X1)),
inference(rename_variables,[],[i_0_619]) ).
cnf(i_0_2325,plain,
X1 = proj2(x(X2,X1)),
inference(rename_variables,[],[i_0_258]) ).
cnf(i_0_2365,plain,
X1 = proj1(x(X1,X2)),
inference(rename_variables,[],[i_0_260]) ).
cnf(i_0_2515,plain,
X1 = proj22(y(X2,X1)),
inference(rename_variables,[],[i_0_622]) ).
cnf(i_0_2707,plain,
X1 = proj12(y(X1,X2)),
inference(rename_variables,[],[i_0_634]) ).
cnf(i_0_2865,plain,
X1 = fail(X1,n(z)),
inference(rename_variables,[],[i_0_637]) ).
cnf(i_0_2906,plain,
X1 = opt(x(n(z),X1)),
inference(rename_variables,[],[i_0_529]) ).
cnf(i_0_3109,plain,
X1 = fail12(n(s(z)),X1),
inference(rename_variables,[],[i_0_646]) ).
cnf(i_0_3186,plain,
X1 = fail22(X1,n(s(z))),
inference(rename_variables,[],[i_0_692]) ).
cnf(i_0_3263,plain,
X1 = addNat(z,X1),
inference(rename_variables,[],[i_0_593]) ).
cnf(i_0_212,plain,
n(X1) = opt(n(X1)),
inference(scs_inference,[],[i_0_204,i_0_165]) ).
cnf(i_0_213,plain,
addNat(z,opt(n(X1))) = n(X1),
inference(scs_inference,[],[i_0_204,i_0_156,i_0_165,i_0_166]) ).
cnf(i_0_247,plain,
n(addNat(X1,X2)) = proj12(y(fail1(n(X1),n(X2)),X3)),
inference(rename_variables,[],[i_0_242]) ).
cnf(i_0_263,plain,
proj2(x(X1,fail1(n(X2),n(X3)))) = n(addNat(X2,X3)),
inference(scs_inference,[],[i_0_261,i_0_165]) ).
cnf(i_0_264,plain,
x(d(X1),d(X2)) = proj1(x(d(x(X1,X2)),X3)),
inference(scs_inference,[],[i_0_248,i_0_260,i_0_261,i_0_165,i_0_166]) ).
cnf(i_0_286,plain,
fail12(n(z),n(z)) = fail32(n(z),n(z)),
inference(scs_inference,[],[i_0_283,i_0_165]) ).
cnf(i_0_287,plain,
fail12(n(s(z)),fail32(n(z),n(z))) = fail12(n(z),n(z)),
inference(scs_inference,[],[i_0_283,i_0_150,i_0_165,i_0_166]) ).
cnf(i_0_305,plain,
n(addNat(X1,X2)) = proj12(y(fail1(n(X1),n(X2)),X3)),
inference(rename_variables,[],[i_0_242]) ).
cnf(i_0_308,plain,
n(addNat(X1,X2)) = proj2(x(X3,fail1(n(X1),n(X2)))),
inference(rename_variables,[],[i_0_261]) ).
cnf(i_0_325,plain,
d(y(X1,X2)) = addNat(z,x(y(d(X1),X2),y(X1,d(X2)))),
inference(scs_inference,[],[i_0_323,i_0_165]) ).
cnf(i_0_326,plain,
proj1N(n(opt(y(X1,y(X2,X3))))) = fail32(y(X1,X2),X3),
inference(scs_inference,[],[i_0_322,i_0_323,i_0_159,i_0_165,i_0_166]) ).
cnf(i_0_338,plain,
fail3(n(z),n(s(X1))) = fail22(n(z),n(s(X1))),
inference(scs_inference,[],[i_0_335,i_0_165]) ).
cnf(i_0_339,plain,
n(addNat(X1,s(X2))) = fail(n(X1),n(s(X2))),
inference(scs_inference,[],[i_0_334,i_0_335,i_0_239,i_0_165,i_0_166]) ).
cnf(i_0_370,plain,
n(addNat(X1,X2)) = proj12(y(fail1(n(X1),n(X2)),X3)),
inference(rename_variables,[],[i_0_242]) ).
cnf(i_0_386,plain,
fail32(y(X1,X2),X3) = proj2(x(X4,opt(y(X1,y(X2,X3))))),
inference(scs_inference,[],[i_0_384,i_0_165]) ).
cnf(i_0_446,plain,
fail22(n(z),n(s(X1))) = fail3(n(z),n(s(X1))),
inference(rename_variables,[],[i_0_335]) ).
cnf(i_0_494,plain,
mulNat(s(X1),s(X2)) = s(addNat(X2,mulNat(X1,s(X2)))),
inference(scs_inference,[],[i_0_491,i_0_165]) ).
cnf(i_0_496,plain,
s(addNat(X1,mulNat(X2,s(X1)))) = mulNat(s(X2),s(X1)),
inference(rename_variables,[],[i_0_491]) ).
cnf(i_0_554,plain,
proj2(x(X1,opt(y(X2,y(X3,X4))))) = fail32(y(X2,X3),X4),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_611,plain,
mulNat(s(X1),z) = mulNat(X1,z),
inference(scs_inference,[],[i_0_608,i_0_165]) ).
cnf(i_0_612,plain,
z = mulNat(s(z),z),
inference(scs_inference,[],[i_0_608,i_0_501,i_0_165,i_0_166]) ).
cnf(i_0_613,plain,
mulNat(X1,z) = mulNat(s(X1),z),
inference(rename_variables,[],[i_0_608]) ).
cnf(i_0_640,plain,
proj12(y(opt(y(X1,y(X2,X3))),X4)) = fail32(y(X1,X2),X3),
inference(scs_inference,[],[i_0_638,i_0_165]) ).
cnf(i_0_642,plain,
fail32(y(X1,X2),X3) = proj12(y(opt(y(X1,y(X2,X3))),X4)),
inference(rename_variables,[],[i_0_638]) ).
cnf(i_0_808,plain,
proj2(x(X1,opt(y(X2,y(X3,X4))))) = fail32(y(X2,X3),X4),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_859,plain,
n(X1) != proj2(x(X2,x(y(d(X3),X4),y(X3,d(X4))))),
inference(scs_inference,[],[i_0_815,i_0_857,i_0_166]) ).
cnf(i_0_860,plain,
proj2(x(X1,x(y(d(X2),X3),y(X2,d(X3))))) = d(y(X2,X3)),
inference(rename_variables,[],[i_0_815]) ).
cnf(i_0_861,plain,
n(X1) != proj1(x(x(y(d(X2),X3),y(X2,d(X3))),X4)),
inference(scs_inference,[],[i_0_818,i_0_857,i_0_166]) ).
cnf(i_0_862,plain,
proj1(x(x(y(d(X1),X2),y(X1,d(X2))),X3)) = d(y(X1,X2)),
inference(rename_variables,[],[i_0_818]) ).
cnf(i_0_873,plain,
n(X1) != addNat(z,x(y(d(X2),X3),y(X2,d(X3)))),
inference(scs_inference,[],[i_0_323,i_0_857,i_0_166]) ).
cnf(i_0_874,plain,
addNat(z,x(y(d(X1),X2),y(X1,d(X2)))) = d(y(X1,X2)),
inference(rename_variables,[],[i_0_323]) ).
cnf(i_0_886,plain,
n(X1) != proj1N(n(x(y(d(X2),X3),y(X2,d(X3))))),
inference(scs_inference,[],[i_0_885,i_0_857,i_0_166]) ).
cnf(i_0_887,plain,
proj1N(n(x(y(d(X1),X2),y(X1,d(X2))))) = d(y(X1,X2)),
inference(rename_variables,[],[i_0_885]) ).
cnf(i_0_891,plain,
n(X1) != proj22(y(X2,x(y(d(X3),X4),y(X3,d(X4))))),
inference(scs_inference,[],[i_0_890,i_0_857,i_0_166]) ).
cnf(i_0_892,plain,
proj22(y(X1,x(y(d(X2),X3),y(X2,d(X3))))) = d(y(X2,X3)),
inference(rename_variables,[],[i_0_890]) ).
cnf(i_0_935,plain,
n(X1) != fail2(X2,X2),
inference(rename_variables,[],[i_0_893]) ).
cnf(i_0_1055,plain,
fail2(n(mulNat(X1,z)),fail22(n(X1),n(z))) = y(n(s(s(z))),opt(n(mulNat(X1,z)))),
inference(scs_inference,[],[i_0_843,i_0_122]) ).
cnf(i_0_1057,plain,
fail22(n(mulNat(X1,z)),X2) = fail22(fail22(n(X1),n(z)),X2),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168]) ).
cnf(i_0_1058,plain,
fail22(X1,n(mulNat(X2,z))) = fail22(X1,fail22(n(X2),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169]) ).
cnf(i_0_1059,plain,
fail3(n(mulNat(X1,z)),X2) = fail3(fail22(n(X1),n(z)),X2),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170]) ).
cnf(i_0_1060,plain,
fail3(X1,n(mulNat(X2,z))) = fail3(X1,fail22(n(X2),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171]) ).
cnf(i_0_1061,plain,
fail(n(mulNat(X1,z)),X2) = fail(fail22(n(X1),n(z)),X2),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172]) ).
cnf(i_0_1062,plain,
fail(X1,n(mulNat(X2,z))) = fail(X1,fail22(n(X2),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173]) ).
cnf(i_0_1063,plain,
proj1N(n(mulNat(X1,z))) = proj1N(fail22(n(X1),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174]) ).
cnf(i_0_1064,plain,
proj12(n(mulNat(X1,z))) = proj12(fail22(n(X1),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175]) ).
cnf(i_0_1065,plain,
proj22(n(mulNat(X1,z))) = proj22(fail22(n(X1),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176]) ).
cnf(i_0_1066,plain,
proj1(n(mulNat(X1,z))) = proj1(fail22(n(X1),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177]) ).
cnf(i_0_1067,plain,
proj2(n(mulNat(X1,z))) = proj2(fail22(n(X1),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178]) ).
cnf(i_0_1068,plain,
fail1(n(mulNat(X1,z)),X2) = fail1(fail22(n(X1),n(z)),X2),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179]) ).
cnf(i_0_1069,plain,
fail1(X1,n(mulNat(X2,z))) = fail1(X1,fail22(n(X2),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180]) ).
cnf(i_0_1070,plain,
mulNat(n(mulNat(X1,z)),X2) = mulNat(fail22(n(X1),n(z)),X2),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181]) ).
cnf(i_0_1071,plain,
mulNat(X1,n(mulNat(X2,z))) = mulNat(X1,fail22(n(X2),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182]) ).
cnf(i_0_1072,plain,
d(n(mulNat(X1,z))) = d(fail22(n(X1),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183]) ).
cnf(i_0_1073,plain,
addNat(n(mulNat(X1,z)),X2) = addNat(fail22(n(X1),n(z)),X2),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184]) ).
cnf(i_0_1074,plain,
addNat(X1,n(mulNat(X2,z))) = addNat(X1,fail22(n(X2),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185]) ).
cnf(i_0_1075,plain,
proj1S(n(mulNat(X1,z))) = proj1S(fail22(n(X1),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186]) ).
cnf(i_0_1076,plain,
x(n(mulNat(X1,z)),X2) = x(fail22(n(X1),n(z)),X2),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187]) ).
cnf(i_0_1077,plain,
x(X1,n(mulNat(X2,z))) = x(X1,fail22(n(X2),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188]) ).
cnf(i_0_1078,plain,
n(n(mulNat(X1,z))) = n(fail22(n(X1),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189]) ).
cnf(i_0_1079,plain,
s(n(mulNat(X1,z))) = s(fail22(n(X1),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190]) ).
cnf(i_0_1080,plain,
fail2(n(mulNat(X1,z)),X2) = fail2(fail22(n(X1),n(z)),X2),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191]) ).
cnf(i_0_1081,plain,
fail2(X1,n(mulNat(X2,z))) = fail2(X1,fail22(n(X2),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192]) ).
cnf(i_0_1082,plain,
fail32(n(mulNat(X1,z)),X2) = fail32(fail22(n(X1),n(z)),X2),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193]) ).
cnf(i_0_1083,plain,
fail32(X1,n(mulNat(X2,z))) = fail32(X1,fail22(n(X2),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194]) ).
cnf(i_0_1084,plain,
y(n(mulNat(X1,z)),X2) = y(fail22(n(X1),n(z)),X2),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195]) ).
cnf(i_0_1085,plain,
y(X1,n(mulNat(X2,z))) = y(X1,fail22(n(X2),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196]) ).
cnf(i_0_1086,plain,
fail12(n(mulNat(X1,z)),X2) = fail12(fail22(n(X1),n(z)),X2),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196,i_0_197]) ).
cnf(i_0_1087,plain,
fail12(X1,n(mulNat(X2,z))) = fail12(X1,fail22(n(X2),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196,i_0_197,i_0_198]) ).
cnf(i_0_1088,plain,
opt(n(mulNat(X1,z))) = opt(fail22(n(X1),n(z))),
inference(scs_inference,[],[i_0_843,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196,i_0_197,i_0_198,i_0_167]) ).
cnf(i_0_221,plain,
n(X1) = addNat(z,opt(n(X1))),
inference(scs_inference,[],[i_0_213,i_0_165]) ).
cnf(i_0_222,plain,
proj1N(n(addNat(z,opt(n(X1))))) = n(X1),
inference(scs_inference,[],[i_0_213,i_0_159,i_0_165,i_0_166]) ).
cnf(i_0_226,plain,
n(X1) = opt(n(X1)),
inference(rename_variables,[],[i_0_212]) ).
cnf(i_0_243,plain,
proj12(y(fail1(n(X1),n(X2)),X3)) = opt(n(addNat(X1,X2))),
inference(scs_inference,[],[i_0_240,i_0_212,i_0_165,i_0_166]) ).
cnf(i_0_244,plain,
n(X1) = opt(n(X1)),
inference(rename_variables,[],[i_0_212]) ).
cnf(i_0_266,plain,
proj1(x(d(x(X1,X2)),X3)) = x(d(X1),d(X2)),
inference(scs_inference,[],[i_0_264,i_0_165]) ).
cnf(i_0_267,plain,
opt(x(n(z),x(d(X1),d(X2)))) = proj1(x(d(x(X1,X2)),X3)),
inference(scs_inference,[],[i_0_264,i_0_141,i_0_165,i_0_166]) ).
cnf(i_0_289,plain,
fail12(n(z),n(z)) = fail12(n(s(z)),fail32(n(z),n(z))),
inference(scs_inference,[],[i_0_287,i_0_165]) ).
cnf(i_0_290,plain,
fail22(fail12(n(s(z)),fail32(n(z),n(z))),n(s(z))) = fail12(n(z),n(z)),
inference(scs_inference,[],[i_0_287,i_0_151,i_0_165,i_0_166]) ).
cnf(i_0_314,plain,
addNat(z,opt(n(X1))) = n(X1),
inference(rename_variables,[],[i_0_213]) ).
cnf(i_0_328,plain,
fail32(y(X1,X2),X3) = proj1N(n(opt(y(X1,y(X2,X3))))),
inference(scs_inference,[],[i_0_326,i_0_165]) ).
cnf(i_0_329,plain,
x(y(d(X1),X2),y(X1,d(X2))) = addNat(z,x(y(d(X1),X2),y(X1,d(X2)))),
inference(scs_inference,[],[i_0_326,i_0_325,i_0_320,i_0_165,i_0_166]) ).
cnf(i_0_330,plain,
d(y(X1,X2)) = addNat(z,x(y(d(X1),X2),y(X1,d(X2)))),
inference(rename_variables,[],[i_0_325]) ).
cnf(i_0_342,plain,
fail(n(X1),n(s(X2))) = n(addNat(X1,s(X2))),
inference(scs_inference,[],[i_0_339,i_0_165]) ).
cnf(i_0_343,plain,
proj2(x(X1,fail1(n(X2),n(s(X3))))) = fail(n(X2),n(s(X3))),
inference(scs_inference,[],[i_0_339,i_0_263,i_0_165,i_0_166]) ).
cnf(i_0_344,plain,
n(addNat(X1,s(X2))) = fail(n(X1),n(s(X2))),
inference(rename_variables,[],[i_0_339]) ).
cnf(i_0_345,plain,
proj2(x(X1,fail1(n(X2),n(X3)))) = n(addNat(X2,X3)),
inference(rename_variables,[],[i_0_263]) ).
cnf(i_0_358,plain,
addNat(z,opt(n(X1))) = n(X1),
inference(rename_variables,[],[i_0_213]) ).
cnf(i_0_364,plain,
n(X1) = opt(n(X1)),
inference(rename_variables,[],[i_0_212]) ).
cnf(i_0_376,plain,
n(X1) = opt(n(X1)),
inference(rename_variables,[],[i_0_212]) ).
cnf(i_0_392,plain,
proj1N(n(opt(y(X1,y(X2,X3))))) = fail32(y(X1,X2),X3),
inference(rename_variables,[],[i_0_326]) ).
cnf(i_0_407,plain,
fail32(y(X1,X2),X3) = proj2(x(X4,opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_386]) ).
cnf(i_0_615,plain,
mulNat(s(z),z) = z,
inference(scs_inference,[],[i_0_612,i_0_165]) ).
cnf(i_0_616,plain,
s(X1) != mulNat(s(z),z),
inference(scs_inference,[],[i_0_611,i_0_612,i_0_259,i_0_165,i_0_166]) ).
cnf(i_0_617,plain,
mulNat(s(X1),z) = mulNat(X1,z),
inference(rename_variables,[],[i_0_611]) ).
cnf(i_0_649,plain,
proj12(y(opt(y(X1,y(X2,X3))),X4)) = fail32(y(X1,X2),X3),
inference(rename_variables,[],[i_0_640]) ).
cnf(i_0_688,plain,
proj12(y(opt(y(X1,y(X2,X3))),X4)) = fail32(y(X1,X2),X3),
inference(rename_variables,[],[i_0_640]) ).
cnf(i_0_691,plain,
mulNat(s(X1),z) = mulNat(X1,z),
inference(rename_variables,[],[i_0_611]) ).
cnf(i_0_763,plain,
fail32(y(X1,X2),X3) = proj2(x(X4,opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_386]) ).
cnf(i_0_800,plain,
proj1N(n(opt(y(X1,y(X2,X3))))) = fail32(y(X1,X2),X3),
inference(rename_variables,[],[i_0_326]) ).
cnf(i_0_881,plain,
fail3(n(z),n(s(X1))) = fail22(n(z),n(s(X1))),
inference(rename_variables,[],[i_0_338]) ).
cnf(i_0_224,plain,
n(X1) = proj1N(n(addNat(z,opt(n(X1))))),
inference(scs_inference,[],[i_0_222,i_0_165]) ).
cnf(i_0_225,plain,
proj1N(n(addNat(z,opt(n(X1))))) = opt(n(X1)),
inference(scs_inference,[],[i_0_212,i_0_222,i_0_165,i_0_166]) ).
cnf(i_0_235,plain,
n(X1) = addNat(z,opt(n(X1))),
inference(rename_variables,[],[i_0_221]) ).
cnf(i_0_245,plain,
opt(n(addNat(X1,X2))) = proj12(y(fail1(n(X1),n(X2)),X3)),
inference(scs_inference,[],[i_0_243,i_0_165]) ).
cnf(i_0_246,plain,
proj12(y(fail1(n(X1),n(X2)),X3)) = proj12(y(fail1(n(X1),n(X2)),X4)),
inference(scs_inference,[],[i_0_243,i_0_242,i_0_240,i_0_165,i_0_166]) ).
cnf(i_0_269,plain,
proj1(x(d(x(X1,X2)),X3)) = opt(x(n(z),x(d(X1),d(X2)))),
inference(scs_inference,[],[i_0_267,i_0_165]) ).
cnf(i_0_270,plain,
n(X1) != proj1(x(d(x(X2,X3)),X4)),
inference(scs_inference,[],[i_0_266,i_0_267,i_0_149,i_0_165,i_0_166]) ).
cnf(i_0_292,plain,
fail12(n(z),n(z)) = fail22(fail12(n(s(z)),fail32(n(z),n(z))),n(s(z))),
inference(scs_inference,[],[i_0_290,i_0_165]) ).
cnf(i_0_293,plain,
fail22(fail12(n(s(z)),fail32(n(z),n(z))),n(s(z))) = fail32(n(z),n(z)),
inference(scs_inference,[],[i_0_290,i_0_286,i_0_165,i_0_166]) ).
cnf(i_0_299,plain,
proj1N(n(addNat(z,opt(n(X1))))) = n(X1),
inference(rename_variables,[],[i_0_222]) ).
cnf(i_0_332,plain,
opt(y(X1,y(X2,X3))) = proj1N(n(opt(y(X1,y(X2,X3))))),
inference(scs_inference,[],[i_0_328,i_0_322,i_0_123,i_0_165,i_0_166]) ).
cnf(i_0_333,plain,
fail32(y(X1,X2),X3) = proj1N(n(opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_346,plain,
fail(n(X1),n(s(X2))) = proj2(x(X3,fail1(n(X1),n(s(X2))))),
inference(scs_inference,[],[i_0_343,i_0_165]) ).
cnf(i_0_347,plain,
fail(n(X1),n(s(X2))) = addNat(z,opt(n(addNat(X1,s(X2))))),
inference(scs_inference,[],[i_0_342,i_0_343,i_0_221,i_0_165,i_0_166]) ).
cnf(i_0_348,plain,
n(X1) = addNat(z,opt(n(X1))),
inference(rename_variables,[],[i_0_221]) ).
cnf(i_0_355,plain,
proj1N(n(addNat(z,opt(n(X1))))) = n(X1),
inference(rename_variables,[],[i_0_222]) ).
cnf(i_0_379,plain,
n(X1) = addNat(z,opt(n(X1))),
inference(rename_variables,[],[i_0_221]) ).
cnf(i_0_401,plain,
fail32(y(X1,X2),X3) = proj1N(n(opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_831,plain,
fail3(n(s(X1)),y(X2,X3)) = proj1N(n(opt(y(n(s(X1)),y(X2,X3))))),
inference(scs_inference,[],[i_0_830,i_0_328,i_0_166]) ).
cnf(i_0_832,plain,
fail32(y(X1,X2),X3) = proj1N(n(opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_328]) ).
cnf(i_0_833,plain,
proj1N(n(opt(y(n(s(X1)),y(X2,X3))))) = fail3(n(s(X1)),y(X2,X3)),
inference(scs_inference,[],[i_0_830,i_0_328,i_0_166,i_0_165]) ).
cnf(i_0_895,plain,
fail22(mulNat(s(z),z),X1) = fail22(z,X1),
inference(scs_inference,[],[i_0_615,i_0_168]) ).
cnf(i_0_896,plain,
fail22(X1,mulNat(s(z),z)) = fail22(X1,z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169]) ).
cnf(i_0_897,plain,
fail3(mulNat(s(z),z),X1) = fail3(z,X1),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170]) ).
cnf(i_0_898,plain,
fail3(X1,mulNat(s(z),z)) = fail3(X1,z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171]) ).
cnf(i_0_899,plain,
fail(mulNat(s(z),z),X1) = fail(z,X1),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172]) ).
cnf(i_0_900,plain,
fail(X1,mulNat(s(z),z)) = fail(X1,z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173]) ).
cnf(i_0_901,plain,
proj1N(mulNat(s(z),z)) = proj1N(z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174]) ).
cnf(i_0_902,plain,
proj12(mulNat(s(z),z)) = proj12(z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175]) ).
cnf(i_0_903,plain,
proj22(mulNat(s(z),z)) = proj22(z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176]) ).
cnf(i_0_904,plain,
proj1(mulNat(s(z),z)) = proj1(z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177]) ).
cnf(i_0_905,plain,
proj2(mulNat(s(z),z)) = proj2(z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178]) ).
cnf(i_0_906,plain,
fail1(mulNat(s(z),z),X1) = fail1(z,X1),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179]) ).
cnf(i_0_907,plain,
fail1(X1,mulNat(s(z),z)) = fail1(X1,z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180]) ).
cnf(i_0_908,plain,
mulNat(mulNat(s(z),z),X1) = mulNat(z,X1),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181]) ).
cnf(i_0_909,plain,
mulNat(X1,mulNat(s(z),z)) = mulNat(X1,z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182]) ).
cnf(i_0_910,plain,
d(mulNat(s(z),z)) = d(z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183]) ).
cnf(i_0_911,plain,
addNat(mulNat(s(z),z),X1) = addNat(z,X1),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184]) ).
cnf(i_0_912,plain,
addNat(X1,mulNat(s(z),z)) = addNat(X1,z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185]) ).
cnf(i_0_913,plain,
proj1S(mulNat(s(z),z)) = proj1S(z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186]) ).
cnf(i_0_914,plain,
x(mulNat(s(z),z),X1) = x(z,X1),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187]) ).
cnf(i_0_915,plain,
x(X1,mulNat(s(z),z)) = x(X1,z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188]) ).
cnf(i_0_916,plain,
n(mulNat(s(z),z)) = n(z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189]) ).
cnf(i_0_917,plain,
s(mulNat(s(z),z)) = s(z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190]) ).
cnf(i_0_918,plain,
fail2(mulNat(s(z),z),X1) = fail2(z,X1),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191]) ).
cnf(i_0_919,plain,
fail2(X1,mulNat(s(z),z)) = fail2(X1,z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192]) ).
cnf(i_0_920,plain,
fail32(mulNat(s(z),z),X1) = fail32(z,X1),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193]) ).
cnf(i_0_921,plain,
fail32(X1,mulNat(s(z),z)) = fail32(X1,z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194]) ).
cnf(i_0_922,plain,
y(mulNat(s(z),z),X1) = y(z,X1),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195]) ).
cnf(i_0_923,plain,
y(X1,mulNat(s(z),z)) = y(X1,z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196]) ).
cnf(i_0_924,plain,
fail12(mulNat(s(z),z),X1) = fail12(z,X1),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196,i_0_197]) ).
cnf(i_0_925,plain,
fail12(X1,mulNat(s(z),z)) = fail12(X1,z),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196,i_0_197,i_0_198]) ).
cnf(i_0_926,plain,
fail2(mulNat(s(z),z),z) = y(n(s(s(z))),opt(mulNat(s(z),z))),
inference(scs_inference,[],[i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196,i_0_197,i_0_198,i_0_122]) ).
cnf(i_0_928,plain,
fail2(x(X1,X2),fail2(X3,X3)) = opt(x(X1,x(X2,fail2(X3,X3)))),
inference(scs_inference,[],[i_0_202,i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196,i_0_197,i_0_198,i_0_122,i_0_112]) ).
cnf(i_0_930,plain,
opt(mulNat(s(z),z)) = opt(z),
inference(scs_inference,[],[i_0_202,i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196,i_0_197,i_0_198,i_0_122,i_0_112,i_0_167]) ).
cnf(i_0_931,plain,
opt(x(n(s(s(z))),x(X1,X1))) != opt(d(X2)),
inference(scs_inference,[],[i_0_111,i_0_202,i_0_615,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196,i_0_197,i_0_198,i_0_122,i_0_112,i_0_167,i_0_165]) ).
cnf(i_0_932,plain,
opt(x(n(z),opt(d(X1)))) != opt(x(n(s(s(z))),x(X2,X2))),
inference(scs_inference,[],[i_0_111,i_0_202,i_0_615,i_0_529,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196,i_0_197,i_0_198,i_0_122,i_0_112,i_0_167,i_0_165,i_0_166]) ).
cnf(i_0_934,plain,
fail2(n(X1),fail2(X2,X2)) = x(opt(n(X1)),opt(fail2(X2,X2))),
inference(scs_inference,[],[i_0_111,i_0_893,i_0_202,i_0_615,i_0_529,i_0_149,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191,i_0_192,i_0_193,i_0_194,i_0_195,i_0_196,i_0_197,i_0_198,i_0_122,i_0_112,i_0_167,i_0_165,i_0_166,i_0_120]) ).
cnf(i_0_227,plain,
opt(n(X1)) = proj1N(n(addNat(z,opt(n(X1))))),
inference(scs_inference,[],[i_0_225,i_0_165]) ).
cnf(i_0_228,plain,
proj1S(s(mulNat(s(X1),X2))) = addNat(X2,mulNat(X1,X2)),
inference(scs_inference,[],[i_0_225,i_0_126,i_0_160,i_0_165,i_0_166]) ).
cnf(i_0_273,plain,
d(x(X1,X2)) = opt(x(n(z),x(d(X1),d(X2)))),
inference(scs_inference,[],[i_0_269,i_0_260,i_0_142,i_0_165,i_0_166]) ).
cnf(i_0_274,plain,
proj1(x(d(x(X1,X2)),X3)) = opt(x(n(z),x(d(X1),d(X2)))),
inference(rename_variables,[],[i_0_269]) ).
cnf(i_0_294,plain,
fail32(n(z),n(z)) = fail22(fail12(n(s(z)),fail32(n(z),n(z))),n(s(z))),
inference(scs_inference,[],[i_0_293,i_0_165]) ).
cnf(i_0_295,plain,
fail22(n(z),n(z)) = fail22(fail12(n(s(z)),fail32(n(z),n(z))),n(s(z))),
inference(scs_inference,[],[i_0_293,i_0_292,i_0_272,i_0_165,i_0_166]) ).
cnf(i_0_319,plain,
fail12(n(s(z)),fail32(n(z),n(z))) = fail22(fail12(n(s(z)),fail32(n(z),n(z))),n(s(z))),
inference(scs_inference,[],[i_0_292,i_0_287,i_0_161,i_0_165,i_0_166]) ).
cnf(i_0_349,plain,
addNat(z,opt(n(addNat(X1,s(X2))))) = fail(n(X1),n(s(X2))),
inference(scs_inference,[],[i_0_347,i_0_165]) ).
cnf(i_0_350,plain,
fail1(n(X1),n(s(X2))) = addNat(z,opt(n(addNat(X1,s(X2))))),
inference(scs_inference,[],[i_0_347,i_0_334,i_0_165,i_0_166]) ).
cnf(i_0_351,plain,
fail(n(X1),n(s(X2))) = addNat(z,opt(n(addNat(X1,s(X2))))),
inference(rename_variables,[],[i_0_347]) ).
cnf(i_0_387,plain,
n(z) = proj1N(n(opt(y(n(z),y(X1,X2))))),
inference(scs_inference,[],[i_0_384,i_0_332,i_0_383,i_0_165,i_0_166]) ).
cnf(i_0_388,plain,
opt(y(X1,y(X2,X3))) = proj1N(n(opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_332]) ).
cnf(i_0_411,plain,
opt(y(X1,y(X2,X3))) = proj1N(n(opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_332]) ).
cnf(i_0_452,plain,
n(X1) = proj1N(n(addNat(z,opt(n(X1))))),
inference(rename_variables,[],[i_0_224]) ).
cnf(i_0_461,plain,
proj1N(n(addNat(z,opt(n(X1))))) = opt(n(X1)),
inference(rename_variables,[],[i_0_225]) ).
cnf(i_0_1131,plain,
fail22(mulNat(s(z),z),X1) = fail22(z,X1),
inference(rename_variables,[],[i_0_895]) ).
cnf(i_0_1132,plain,
fail22(X1,mulNat(s(z),z)) = fail22(X1,z),
inference(rename_variables,[],[i_0_896]) ).
cnf(i_0_1172,plain,
fail2(fail3(mulNat(s(z),z),X1),fail3(z,X1)) = y(n(s(s(z))),opt(fail3(mulNat(s(z),z),X1))),
inference(scs_inference,[],[i_0_897,i_0_122]) ).
cnf(i_0_1174,plain,
fail22(fail3(mulNat(s(z),z),X1),X2) = fail22(fail3(z,X1),X2),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168]) ).
cnf(i_0_1175,plain,
fail22(X1,fail3(mulNat(s(z),z),X2)) = fail22(X1,fail3(z,X2)),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169]) ).
cnf(i_0_1176,plain,
fail3(fail3(mulNat(s(z),z),X1),X2) = fail3(fail3(z,X1),X2),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170]) ).
cnf(i_0_1177,plain,
fail3(X1,fail3(mulNat(s(z),z),X2)) = fail3(X1,fail3(z,X2)),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171]) ).
cnf(i_0_1178,plain,
fail(fail3(mulNat(s(z),z),X1),X2) = fail(fail3(z,X1),X2),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172]) ).
cnf(i_0_1179,plain,
fail(X1,fail3(mulNat(s(z),z),X2)) = fail(X1,fail3(z,X2)),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173]) ).
cnf(i_0_1180,plain,
proj1N(fail3(mulNat(s(z),z),X1)) = proj1N(fail3(z,X1)),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174]) ).
cnf(i_0_1181,plain,
proj12(fail3(mulNat(s(z),z),X1)) = proj12(fail3(z,X1)),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175]) ).
cnf(i_0_1182,plain,
proj22(fail3(mulNat(s(z),z),X1)) = proj22(fail3(z,X1)),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176]) ).
cnf(i_0_1183,plain,
proj1(fail3(mulNat(s(z),z),X1)) = proj1(fail3(z,X1)),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177]) ).
cnf(i_0_1184,plain,
proj2(fail3(mulNat(s(z),z),X1)) = proj2(fail3(z,X1)),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178]) ).
cnf(i_0_1185,plain,
fail1(fail3(mulNat(s(z),z),X1),X2) = fail1(fail3(z,X1),X2),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179]) ).
cnf(i_0_1186,plain,
fail1(X1,fail3(mulNat(s(z),z),X2)) = fail1(X1,fail3(z,X2)),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180]) ).
cnf(i_0_1187,plain,
mulNat(fail3(mulNat(s(z),z),X1),X2) = mulNat(fail3(z,X1),X2),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181]) ).
cnf(i_0_1188,plain,
mulNat(X1,fail3(mulNat(s(z),z),X2)) = mulNat(X1,fail3(z,X2)),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182]) ).
cnf(i_0_1189,plain,
d(fail3(mulNat(s(z),z),X1)) = d(fail3(z,X1)),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183]) ).
cnf(i_0_1190,plain,
addNat(fail3(mulNat(s(z),z),X1),X2) = addNat(fail3(z,X1),X2),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184]) ).
cnf(i_0_1191,plain,
addNat(X1,fail3(mulNat(s(z),z),X2)) = addNat(X1,fail3(z,X2)),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185]) ).
cnf(i_0_1192,plain,
proj1S(fail3(mulNat(s(z),z),X1)) = proj1S(fail3(z,X1)),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186]) ).
cnf(i_0_1193,plain,
x(fail3(mulNat(s(z),z),X1),X2) = x(fail3(z,X1),X2),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187]) ).
cnf(i_0_1194,plain,
x(X1,fail3(mulNat(s(z),z),X2)) = x(X1,fail3(z,X2)),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188]) ).
cnf(i_0_1195,plain,
n(fail3(mulNat(s(z),z),X1)) = n(fail3(z,X1)),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189]) ).
cnf(i_0_1196,plain,
s(fail3(mulNat(s(z),z),X1)) = s(fail3(z,X1)),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190]) ).
cnf(i_0_1197,plain,
fail2(fail3(mulNat(s(z),z),X1),X2) = fail2(fail3(z,X1),X2),
inference(scs_inference,[],[i_0_897,i_0_122,i_0_168,i_0_169,i_0_170,i_0_171,i_0_172,i_0_173,i_0_174,i_0_175,i_0_176,i_0_177,i_0_178,i_0_179,i_0_180,i_0_181,i_0_182,i_0_183,i_0_184,i_0_185,i_0_186,i_0_187,i_0_188,i_0_189,i_0_190,i_0_191]) ).
cnf(c_0_1870,plain,
n(X1) != X2,
i_0_1868 ).
cnf(c_0_1871,plain,
$false,
inference(er,[status(thm)],[c_0_1870]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX188+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n005.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 07:54:00 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 142.60/101.32 % Version : CSE_E---1.7
% 142.60/101.32 % Problem : theBenchmark.p
% 142.60/101.32 % SZS status Theorem for theBenchmark.p
% 142.60/101.32 % SZS output start CNFRefutation
% See solution above
% 154.41/113.17 % Total time : 100.987s
%------------------------------------------------------------------------------