%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWX193+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n024.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 05:34:41 PM UTC 2026
% Result : Theorem 122.27s 80.57s
% Output : CNFRefutation 131.89s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_67)
% Comments :
%------------------------------------------------------------------------------
fof(goal_054,conjecture,
? [X6] : opt(d(X6)) = x(y(x2,y(x2,y(x2,y(x2,x2)))),y(x2,x(y(x2,y(x2,y(x2,x2))),y(x2,x(y(x2,y(x2,x2)),y(x2,x(y(x2,x2),y(x2,x(x2,x2))))))))),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_024) ).
fof(axiom_023,axiom,
! [X11,X12] : fail4(X11,X12) = y(opt(X11),opt(X12)),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_014) ).
fof(axiom_037,axiom,
! [X11,X19] : fail3(X11,n(s(X19))) = fail12(X11,n(s(X19))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_037) ).
fof(axiom_021,axiom,
! [X5,X2] : fail(X5,n(s(X2))) = fail1(X5,n(s(X2))),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_047) ).
fof(axiom_045,axiom,
! [X5,X24] : mulNat(s(X24),X5) = addNat(X5,mulNat(X24,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_045) ).
fof(axiom_026,axiom,
! [X13,X14] : fail32(n(X13),n(X14)) = n(mulNat(X13,X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
fof(axiom_019,axiom,
! [X9,X10] : fail1(n(X9),n(X10)) = n(addNat(X9,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
fof(axiom_040,axiom,
! [X20,X21] : d(x(X20,X21)) = x(d(X20),d(X21)),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
fof(axiom_043,axiom,
! [X5,X24] : addNat(s(X24),X5) = s(addNat(X24,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_043) ).
fof(axiom_011,axiom,
! [X1,X2,X3,X4] : x(X1,X2) != y(X3,X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
fof(axiom_036,axiom,
! [X11,X12] :
( X12 != n(proj1N(X12))
=> fail3(X11,X12) = fail12(X11,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_036) ).
fof(axiom_032,axiom,
! [X11,X12] :
( X11 != n(proj1N(X11))
=> fail12(X11,X12) = fail22(X11,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_032) ).
fof(axiom_028,axiom,
! [X11,X12] :
( X12 != n(proj1N(X12))
=> fail22(X11,X12) = fail32(X11,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_028) ).
fof(axiom_020,axiom,
! [X5,X6] :
( X6 != n(proj1N(X6))
=> fail(X5,X6) = fail1(X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
fof(axiom_017,axiom,
! [X5,X6] :
( X5 != n(proj1N(X5))
=> fail1(X5,X6) = fail2(X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
fof(axiom_053,axiom,
! [X12] : opt(y(n(z),X12)) = n(z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_053) ).
fof(axiom_050,axiom,
! [X6] : opt(x(n(z),X6)) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_050) ).
fof(axiom_035,axiom,
! [X12] : fail12(n(z),X12) = fail22(n(z),X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_035) ).
fof(axiom_031,axiom,
! [X11] : fail22(X11,n(z)) = fail32(X11,n(z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_031) ).
fof(axiom_007,axiom,
! [X1,X2] : proj22(y(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
fof(axiom_006,axiom,
! [X1,X2] : proj12(y(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
fof(axiom_005,axiom,
! [X1,X2] : proj2(x(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
fof(axiom_004,axiom,
! [X1,X2] : proj1(x(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
fof(axiom_009,axiom,
! [X1,X2,X3] : n(X1) != y(X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
fof(axiom_008,axiom,
! [X1,X2,X3] : n(X1) != x(X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
fof(axiom_034,axiom,
! [X12] : fail12(n(s(z)),X12) = X12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_034) ).
fof(axiom_030,axiom,
! [X11] : fail22(X11,n(s(z))) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_030) ).
fof(axiom_013,axiom,
! [X1,X2] : y(X1,X2) != x2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
fof(axiom_012,axiom,
! [X1,X2] : x(X1,X2) != x2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
fof(axiom_038,axiom,
! [X11] : fail3(X11,n(z)) = n(z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_038) ).
fof(axiom_022,axiom,
! [X5] : fail(X5,n(z)) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_022) ).
fof(axiom_044,axiom,
! [X5] : addNat(z,X5) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_044) ).
fof(axiom_039,axiom,
! [X5] : d(n(X5)) = n(z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_039) ).
fof(axiom_046,axiom,
! [X5] : mulNat(z,X5) = z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_046) ).
fof(axiom_003,axiom,
! [X1] : proj1N(n(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
fof(axiom_001,axiom,
! [X1] : proj1S(s(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
fof(axiom_010,axiom,
! [X1] : n(X1) != x2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
fof(axiom_002,axiom,
! [X1] : s(X1) != z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
fof(axiom_042,axiom,
d(x2) = n(s(z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_042) ).
fof(i_0_54,negated_conjecture,
~ ? [X6] : opt(d(X6)) = x(y(x2,y(x2,y(x2,y(x2,x2)))),y(x2,x(y(x2,y(x2,y(x2,x2))),y(x2,x(y(x2,y(x2,x2)),y(x2,x(y(x2,x2),y(x2,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)) != x(y(x2,y(x2,y(x2,y(x2,x2)))),y(x2,x(y(x2,y(x2,y(x2,x2))),y(x2,x(y(x2,y(x2,x2)),y(x2,x(y(x2,x2),y(x2,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)) != x(y(x2,y(x2,y(x2,y(x2,x2)))),y(x2,x(y(x2,y(x2,y(x2,x2))),y(x2,x(y(x2,y(x2,x2)),y(x2,x(y(x2,x2),y(x2,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
| y(X1,X3) = y(X2,X3) ) ).
cnf(i_0_190,axiom,
( X1 != X2
| y(X3,X1) = y(X3,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
| fail12(X1,X3) = fail12(X2,X3) ) ).
cnf(i_0_196,axiom,
( X1 != X2
| fail12(X3,X1) = fail12(X3,X2) ) ).
cnf(i_0_197,axiom,
( X1 != X2
| n(X1) = n(X2) ) ).
cnf(i_0_198,axiom,
( X1 != X2
| s(X1) = s(X2) ) ).
cnf(i_0_199,plain,
fail2(X1,X1) = y(n(s(s(z))),opt(X1)),
inference(equality_inference,[],[122]) ).
cnf(i_0_202,plain,
n(X1) != x(X2,X3),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_205,plain,
x(X1,X2) != y(X3,X4),
inference(rename_variables,[],[i_0_134]) ).
cnf(i_0_207,plain,
n(X1) != y(X2,X3),
inference(rename_variables,[],[i_0_148]) ).
cnf(i_0_208,plain,
n(X1) != x(X2,X3),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_211,plain,
x(X1,X2) != y(X3,X4),
inference(rename_variables,[],[i_0_134]) ).
cnf(i_0_216,plain,
n(X1) != x(X2,X3),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_218,plain,
n(X1) != y(X2,X3),
inference(rename_variables,[],[i_0_148]) ).
cnf(i_0_221,plain,
x(X1,X2) != y(X3,X4),
inference(rename_variables,[],[i_0_134]) ).
cnf(i_0_225,plain,
addNat(z,X1) = X1,
inference(rename_variables,[],[i_0_156]) ).
cnf(i_0_228,plain,
proj1N(n(X1)) = X1,
inference(rename_variables,[],[i_0_159]) ).
cnf(i_0_234,plain,
proj1S(s(X1)) = X1,
inference(rename_variables,[],[i_0_160]) ).
cnf(i_0_237,plain,
proj22(y(X1,X2)) = X2,
inference(rename_variables,[],[i_0_144]) ).
cnf(i_0_240,plain,
proj12(y(X1,X2)) = X1,
inference(rename_variables,[],[i_0_145]) ).
cnf(i_0_241,plain,
n(mulNat(X1,X2)) = fail32(n(X1),n(X2)),
inference(scs_inference,[],[i_0_127,i_0_165]) ).
cnf(i_0_244,plain,
n(addNat(X1,X2)) = fail1(n(X1),n(X2)),
inference(scs_inference,[],[i_0_128,i_0_165]) ).
cnf(i_0_253,plain,
x(d(X1),d(X2)) = d(x(X1,X2)),
inference(scs_inference,[],[i_0_129,i_0_165]) ).
cnf(i_0_258,plain,
proj2(x(X1,X2)) = X2,
inference(rename_variables,[],[i_0_146]) ).
cnf(i_0_261,plain,
proj1(x(X1,X2)) = X1,
inference(rename_variables,[],[i_0_147]) ).
cnf(i_0_264,plain,
fail(X1,n(z)) = X1,
inference(rename_variables,[],[i_0_155]) ).
cnf(i_0_265,plain,
s(addNat(X1,X2)) = addNat(s(X1),X2),
inference(scs_inference,[],[i_0_133,i_0_165]) ).
cnf(i_0_268,plain,
z = mulNat(z,X1),
inference(scs_inference,[],[i_0_158,i_0_165]) ).
cnf(i_0_270,plain,
opt(x(n(z),X1)) = X1,
inference(rename_variables,[],[i_0_141]) ).
cnf(i_0_276,plain,
fail12(n(s(z)),X1) = X1,
inference(rename_variables,[],[i_0_150]) ).
cnf(i_0_279,plain,
n(X1) != x(X2,X3),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_280,plain,
fail22(n(z),X1) = fail12(n(z),X1),
inference(scs_inference,[],[i_0_142,i_0_165]) ).
cnf(i_0_286,plain,
fail32(X1,n(z)) = fail22(X1,n(z)),
inference(scs_inference,[],[i_0_143,i_0_165]) ).
cnf(i_0_289,plain,
n(z) = d(n(X1)),
inference(scs_inference,[],[i_0_157,i_0_165]) ).
cnf(i_0_291,plain,
fail22(X1,n(s(z))) = X1,
inference(rename_variables,[],[i_0_151]) ).
cnf(i_0_295,plain,
n(z) = fail3(X1,n(z)),
inference(scs_inference,[],[i_0_154,i_0_165]) ).
cnf(i_0_300,plain,
addNat(z,X1) = X1,
inference(rename_variables,[],[i_0_156]) ).
cnf(i_0_301,plain,
n(s(z)) = d(X1),
inference(scs_inference,[],[i_0_161,i_0_165]) ).
cnf(i_0_303,plain,
proj1N(n(X1)) = X1,
inference(rename_variables,[],[i_0_159]) ).
cnf(i_0_304,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_307,plain,
opt(y(X1,y(X2,X3))) = fail32(y(X1,X2),X3),
inference(scs_inference,[],[i_0_113,i_0_165]) ).
cnf(i_0_309,plain,
proj1S(s(X1)) = X1,
inference(rename_variables,[],[i_0_160]) ).
cnf(i_0_312,plain,
proj22(y(X1,X2)) = X2,
inference(rename_variables,[],[i_0_144]) ).
cnf(i_0_313,plain,
fail12(X1,n(s(X2))) = fail3(X1,n(s(X2))),
inference(scs_inference,[],[i_0_123,i_0_165]) ).
cnf(i_0_315,plain,
proj12(y(X1,X2)) = X1,
inference(rename_variables,[],[i_0_145]) ).
cnf(i_0_316,plain,
fail1(X1,n(s(X2))) = fail(X1,n(s(X2))),
inference(scs_inference,[],[i_0_124,i_0_165]) ).
cnf(i_0_318,plain,
proj2(x(X1,X2)) = X2,
inference(rename_variables,[],[i_0_146]) ).
cnf(i_0_321,plain,
proj1(x(X1,X2)) = X1,
inference(rename_variables,[],[i_0_147]) ).
cnf(i_0_324,plain,
fail(X1,n(z)) = X1,
inference(rename_variables,[],[i_0_155]) ).
cnf(i_0_325,plain,
n(z) = opt(y(n(z),X1)),
inference(scs_inference,[],[i_0_140,i_0_165]) ).
cnf(i_0_336,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_339,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_350,plain,
fail3(n(s(X1)),X2) = opt(y(n(s(X1)),X2)),
inference(scs_inference,[],[i_0_117,i_0_165]) ).
cnf(i_0_359,plain,
opt(x(n(z),X1)) = X1,
inference(rename_variables,[],[i_0_141]) ).
cnf(i_0_360,plain,
fail(n(s(X1)),X2) = opt(x(n(s(X1)),X2)),
inference(scs_inference,[],[i_0_118,i_0_165]) ).
cnf(i_0_383,plain,
fail12(n(s(z)),X1) = X1,
inference(rename_variables,[],[i_0_150]) ).
cnf(i_0_384,plain,
addNat(X1,mulNat(X2,X1)) = mulNat(s(X2),X1),
inference(scs_inference,[],[i_0_126,i_0_165]) ).
cnf(i_0_399,plain,
fail22(X1,n(s(z))) = X1,
inference(rename_variables,[],[i_0_151]) ).
cnf(i_0_400,plain,
X1 = addNat(z,X1),
inference(scs_inference,[],[i_0_156,i_0_165]) ).
cnf(i_0_402,plain,
addNat(z,X1) = X1,
inference(rename_variables,[],[i_0_156]) ).
cnf(i_0_403,plain,
X1 = proj1N(n(X1)),
inference(scs_inference,[],[i_0_159,i_0_165]) ).
cnf(i_0_415,plain,
X1 = proj1S(s(X1)),
inference(scs_inference,[],[i_0_160,i_0_165]) ).
cnf(i_0_418,plain,
X1 = proj22(y(X2,X1)),
inference(scs_inference,[],[i_0_144,i_0_165]) ).
cnf(i_0_426,plain,
proj12(y(X1,X2)) = X1,
inference(rename_variables,[],[i_0_145]) ).
cnf(i_0_427,plain,
X1 = proj2(x(X2,X1)),
inference(scs_inference,[],[i_0_146,i_0_165]) ).
cnf(i_0_476,plain,
X1 = proj1(x(X1,X2)),
inference(scs_inference,[],[i_0_147,i_0_165]) ).
cnf(i_0_481,plain,
X1 = fail(X1,n(z)),
inference(scs_inference,[],[i_0_155,i_0_165]) ).
cnf(i_0_484,plain,
X1 = opt(x(n(z),X1)),
inference(scs_inference,[],[i_0_141,i_0_165]) ).
cnf(i_0_494,plain,
X1 = fail12(n(s(z)),X1),
inference(scs_inference,[],[i_0_150,i_0_165]) ).
cnf(i_0_498,plain,
X1 = fail22(X1,n(s(z))),
inference(scs_inference,[],[i_0_151,i_0_165]) ).
cnf(i_0_501,plain,
X1 = proj12(y(X1,X2)),
inference(scs_inference,[],[i_0_145,i_0_165]) ).
cnf(i_0_598,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_603,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_606,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_617,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_628,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_637,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_706,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_741,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_779,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_800,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_849,plain,
fail32(y(X1,X2),X3) = opt(y(X1,y(X2,X3))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_892,plain,
n(X1) != d(y(X2,X3)),
inference(scs_inference,[],[i_0_114,i_0_149,i_0_166]) ).
cnf(i_0_893,plain,
n(X1) != x(X2,X3),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_1536,plain,
n(X1) != x(X2,X3),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_2154,plain,
n(X1) != X2,
inference(rename_variables,[],[i_0_162]) ).
cnf(i_0_2155,plain,
n(X1) != x(X2,X3),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_2230,plain,
proj1S(s(X1)) = X1,
inference(rename_variables,[],[i_0_160]) ).
cnf(i_0_2315,plain,
x(X1,X2) != y(X3,X4),
inference(rename_variables,[],[i_0_134]) ).
cnf(i_0_2560,plain,
proj1N(n(X1)) = X1,
inference(rename_variables,[],[i_0_159]) ).
cnf(i_0_2642,plain,
x(X1,X2) != y(X3,X4),
inference(rename_variables,[],[i_0_134]) ).
cnf(i_0_2719,plain,
fail12(n(s(z)),X1) = X1,
inference(rename_variables,[],[i_0_150]) ).
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,
fail2(n(X1),x(proj1(n(X1)),proj2(n(X1)))) = x(opt(n(X1)),opt(x(proj1(n(X1)),proj2(n(X1))))),
inference(scs_inference,[],[i_0_199,i_0_149,i_0_165,i_0_120]) ).
cnf(i_0_204,plain,
x(X1,X2) != fail2(X3,X3),
inference(scs_inference,[],[i_0_199,i_0_134,i_0_149,i_0_165,i_0_120,i_0_166]) ).
cnf(i_0_206,plain,
opt(n(X1)) = n(X1),
inference(scs_inference,[],[i_0_199,i_0_134,i_0_148,i_0_149,i_0_202,i_0_165,i_0_120,i_0_166,i_0_125]) ).
cnf(i_0_269,plain,
opt(x(n(z),s(addNat(X1,X2)))) = addNat(s(X1),X2),
inference(scs_inference,[],[i_0_265,i_0_158,i_0_141,i_0_165,i_0_166]) ).
cnf(i_0_308,plain,
proj1S(s(x(y(d(X1),X2),y(X1,d(X2))))) = d(y(X1,X2)),
inference(scs_inference,[],[i_0_304,i_0_113,i_0_160,i_0_165,i_0_166]) ).
cnf(i_0_317,plain,
proj2(x(X1,opt(y(X2,y(X3,X4))))) = fail32(y(X2,X3),X4),
inference(scs_inference,[],[i_0_307,i_0_124,i_0_146,i_0_165,i_0_166]) ).
cnf(i_0_326,plain,
fail22(n(z),n(s(X1))) = fail3(n(z),n(s(X1))),
inference(scs_inference,[],[i_0_313,i_0_280,i_0_140,i_0_165,i_0_166]) ).
cnf(i_0_327,plain,
fail12(X1,n(s(X2))) = fail3(X1,n(s(X2))),
inference(rename_variables,[],[i_0_313]) ).
cnf(i_0_328,plain,
fail22(n(z),X1) = fail12(n(z),X1),
inference(rename_variables,[],[i_0_280]) ).
cnf(i_0_331,plain,
fail1(X1,n(s(X2))) = fail(X1,n(s(X2))),
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_340,plain,
fail32(n(s(s(X1))),n(z)) = fail12(n(s(s(X1))),n(z)),
inference(scs_inference,[],[i_0_336,i_0_286,i_0_116,i_0_165,i_0_166]) ).
cnf(i_0_341,plain,
fail22(n(s(s(X1))),X2) = fail12(n(s(s(X1))),X2),
inference(rename_variables,[],[i_0_336]) ).
cnf(i_0_342,plain,
fail32(X1,n(z)) = fail22(X1,n(z)),
inference(rename_variables,[],[i_0_286]) ).
cnf(i_0_345,plain,
fail32(X1,n(s(s(X2)))) = fail22(X1,n(s(s(X2)))),
inference(rename_variables,[],[i_0_339]) ).
cnf(i_0_346,plain,
n(mulNat(X1,X2)) = fail32(n(X1),n(X2)),
inference(rename_variables,[],[i_0_241]) ).
cnf(i_0_355,plain,
fail3(n(s(X1)),X2) = opt(y(n(s(X1)),X2)),
inference(rename_variables,[],[i_0_350]) ).
cnf(i_0_356,plain,
n(z) = fail3(X1,n(z)),
inference(rename_variables,[],[i_0_295]) ).
cnf(i_0_365,plain,
fail(n(s(X1)),X2) = opt(x(n(s(X1)),X2)),
inference(rename_variables,[],[i_0_360]) ).
cnf(i_0_366,plain,
fail1(X1,n(s(X2))) = fail(X1,n(s(X2))),
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_374,plain,
fail32(X1,n(s(s(X2)))) = fail22(X1,n(s(s(X2)))),
inference(rename_variables,[],[i_0_339]) ).
cnf(i_0_389,plain,
addNat(X1,mulNat(X2,X1)) = mulNat(s(X2),X1),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_408,plain,
X1 = proj1N(n(X1)),
inference(rename_variables,[],[i_0_403]) ).
cnf(i_0_420,plain,
X1 = proj1S(s(X1)),
inference(rename_variables,[],[i_0_415]) ).
cnf(i_0_423,plain,
X1 = proj22(y(X2,X1)),
inference(rename_variables,[],[i_0_418]) ).
cnf(i_0_429,plain,
X1 = addNat(z,X1),
inference(rename_variables,[],[i_0_400]) ).
cnf(i_0_432,plain,
X1 = proj2(x(X2,X1)),
inference(rename_variables,[],[i_0_427]) ).
cnf(i_0_446,plain,
X1 = proj2(x(X2,X1)),
inference(rename_variables,[],[i_0_427]) ).
cnf(i_0_452,plain,
fail12(X1,n(s(X2))) = fail3(X1,n(s(X2))),
inference(rename_variables,[],[i_0_313]) ).
cnf(i_0_455,plain,
X1 = addNat(z,X1),
inference(rename_variables,[],[i_0_400]) ).
cnf(i_0_459,plain,
fail3(n(s(X1)),X2) = opt(y(n(s(X1)),X2)),
inference(rename_variables,[],[i_0_350]) ).
cnf(i_0_463,plain,
fail22(n(s(s(X1))),X2) = fail12(n(s(s(X1))),X2),
inference(rename_variables,[],[i_0_336]) ).
cnf(i_0_469,plain,
X1 = proj1N(n(X1)),
inference(rename_variables,[],[i_0_403]) ).
cnf(i_0_480,plain,
X1 = proj1(x(X1,X2)),
inference(rename_variables,[],[i_0_476]) ).
cnf(i_0_486,plain,
X1 = fail(X1,n(z)),
inference(rename_variables,[],[i_0_481]) ).
cnf(i_0_489,plain,
X1 = opt(x(n(z),X1)),
inference(rename_variables,[],[i_0_484]) ).
cnf(i_0_500,plain,
X1 = fail12(n(s(z)),X1),
inference(rename_variables,[],[i_0_494]) ).
cnf(i_0_503,plain,
X1 = fail22(X1,n(s(z))),
inference(rename_variables,[],[i_0_498]) ).
cnf(i_0_506,plain,
X1 = proj12(y(X1,X2)),
inference(rename_variables,[],[i_0_501]) ).
cnf(i_0_509,plain,
X1 = proj22(y(X2,X1)),
inference(rename_variables,[],[i_0_418]) ).
cnf(i_0_513,plain,
X1 = proj12(y(X1,X2)),
inference(rename_variables,[],[i_0_501]) ).
cnf(i_0_519,plain,
addNat(X1,mulNat(X2,X1)) = mulNat(s(X2),X1),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_553,plain,
X1 = opt(x(n(z),X1)),
inference(rename_variables,[],[i_0_484]) ).
cnf(i_0_560,plain,
fail32(y(X1,X2),X3) = proj1S(s(opt(y(X1,y(X2,X3))))),
inference(scs_inference,[],[i_0_113,i_0_415,i_0_166]) ).
cnf(i_0_561,plain,
X1 = proj1S(s(X1)),
inference(rename_variables,[],[i_0_415]) ).
cnf(i_0_562,plain,
proj1S(s(opt(y(X1,y(X2,X3))))) = fail32(y(X1,X2),X3),
inference(scs_inference,[],[i_0_113,i_0_415,i_0_166,i_0_165]) ).
cnf(i_0_563,plain,
fail32(y(X1,X2),X3) = fail22(opt(y(X1,y(X2,X3))),n(s(z))),
inference(scs_inference,[],[i_0_113,i_0_498,i_0_166]) ).
cnf(i_0_564,plain,
X1 = fail22(X1,n(s(z))),
inference(rename_variables,[],[i_0_498]) ).
cnf(i_0_565,plain,
fail22(opt(y(X1,y(X2,X3))),n(s(z))) = fail32(y(X1,X2),X3),
inference(scs_inference,[],[i_0_113,i_0_498,i_0_166,i_0_165]) ).
cnf(i_0_579,plain,
fail32(y(X1,X2),X3) = fail(opt(y(X1,y(X2,X3))),n(z)),
inference(scs_inference,[],[i_0_113,i_0_481,i_0_166]) ).
cnf(i_0_580,plain,
X1 = fail(X1,n(z)),
inference(rename_variables,[],[i_0_481]) ).
cnf(i_0_581,plain,
fail(opt(y(X1,y(X2,X3))),n(z)) = fail32(y(X1,X2),X3),
inference(scs_inference,[],[i_0_113,i_0_481,i_0_166,i_0_165]) ).
cnf(i_0_652,plain,
X1 = fail(X1,n(z)),
inference(rename_variables,[],[i_0_481]) ).
cnf(i_0_664,plain,
fail32(X1,n(z)) = fail22(X1,n(z)),
inference(rename_variables,[],[i_0_286]) ).
cnf(i_0_668,plain,
fail22(n(z),X1) = fail12(n(z),X1),
inference(rename_variables,[],[i_0_280]) ).
cnf(i_0_682,plain,
fail(n(s(X1)),X2) = opt(x(n(s(X1)),X2)),
inference(rename_variables,[],[i_0_360]) ).
cnf(i_0_686,plain,
fail32(y(X1,X2),X3) = proj22(y(X4,opt(y(X1,y(X2,X3))))),
inference(scs_inference,[],[i_0_113,i_0_418,i_0_166]) ).
cnf(i_0_687,plain,
X1 = proj22(y(X2,X1)),
inference(rename_variables,[],[i_0_418]) ).
cnf(i_0_688,plain,
proj22(y(X1,opt(y(X2,y(X3,X4))))) = fail32(y(X2,X3),X4),
inference(scs_inference,[],[i_0_113,i_0_418,i_0_166,i_0_165]) ).
cnf(i_0_744,plain,
fail32(y(X1,X2),X3) = proj12(y(opt(y(X1,y(X2,X3))),X4)),
inference(scs_inference,[],[i_0_113,i_0_501,i_0_166]) ).
cnf(i_0_745,plain,
X1 = proj12(y(X1,X2)),
inference(rename_variables,[],[i_0_501]) ).
cnf(i_0_746,plain,
proj12(y(opt(y(X1,y(X2,X3))),X4)) = fail32(y(X1,X2),X3),
inference(scs_inference,[],[i_0_113,i_0_501,i_0_166,i_0_165]) ).
cnf(i_0_754,plain,
fail1(X1,n(s(X2))) = fail(X1,n(s(X2))),
inference(rename_variables,[],[i_0_316]) ).
cnf(i_0_758,plain,
n(addNat(X1,X2)) = fail1(n(X1),n(X2)),
inference(rename_variables,[],[i_0_244]) ).
cnf(i_0_761,plain,
fail22(n(s(s(X1))),X2) = fail12(n(s(s(X1))),X2),
inference(rename_variables,[],[i_0_336]) ).
cnf(i_0_836,plain,
fail32(y(X1,X2),X3) = opt(x(n(z),opt(y(X1,y(X2,X3))))),
inference(scs_inference,[],[i_0_113,i_0_484,i_0_166]) ).
cnf(i_0_837,plain,
X1 = opt(x(n(z),X1)),
inference(rename_variables,[],[i_0_484]) ).
cnf(i_0_838,plain,
opt(x(n(z),opt(y(X1,y(X2,X3))))) = fail32(y(X1,X2),X3),
inference(scs_inference,[],[i_0_113,i_0_484,i_0_166,i_0_165]) ).
cnf(i_0_881,plain,
s(addNat(X1,X2)) = addNat(s(X1),X2),
inference(rename_variables,[],[i_0_265]) ).
cnf(i_0_899,plain,
addNat(X1,mulNat(X2,X1)) = mulNat(s(X2),X1),
inference(rename_variables,[],[i_0_384]) ).
cnf(i_0_902,plain,
X1 = proj12(y(X1,X2)),
inference(rename_variables,[],[i_0_501]) ).
cnf(i_0_907,plain,
d(y(X1,X2)) = proj1N(n(x(y(d(X1),X2),y(X1,d(X2))))),
inference(scs_inference,[],[i_0_114,i_0_403,i_0_166]) ).
cnf(i_0_908,plain,
X1 = proj1N(n(X1)),
inference(rename_variables,[],[i_0_403]) ).
cnf(i_0_909,plain,
proj1N(n(x(y(d(X1),X2),y(X1,d(X2))))) = d(y(X1,X2)),
inference(scs_inference,[],[i_0_114,i_0_403,i_0_166,i_0_165]) ).
cnf(i_0_912,plain,
d(y(X1,X2)) = fail22(x(y(d(X1),X2),y(X1,d(X2))),n(s(z))),
inference(scs_inference,[],[i_0_114,i_0_498,i_0_166]) ).
cnf(i_0_913,plain,
X1 = fail22(X1,n(s(z))),
inference(rename_variables,[],[i_0_498]) ).
cnf(i_0_914,plain,
fail22(x(y(d(X1),X2),y(X1,d(X2))),n(s(z))) = d(y(X1,X2)),
inference(scs_inference,[],[i_0_114,i_0_498,i_0_166,i_0_165]) ).
cnf(i_0_933,plain,
d(y(X1,X2)) = addNat(z,x(y(d(X1),X2),y(X1,d(X2)))),
inference(scs_inference,[],[i_0_114,i_0_400,i_0_166]) ).
cnf(i_0_934,plain,
X1 = addNat(z,X1),
inference(rename_variables,[],[i_0_400]) ).
cnf(i_0_935,plain,
addNat(z,x(y(d(X1),X2),y(X1,d(X2)))) = d(y(X1,X2)),
inference(scs_inference,[],[i_0_114,i_0_400,i_0_166,i_0_165]) ).
cnf(i_0_938,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_418,i_0_166]) ).
cnf(i_0_939,plain,
X1 = proj22(y(X2,X1)),
inference(rename_variables,[],[i_0_418]) ).
cnf(i_0_940,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_418,i_0_166,i_0_165]) ).
cnf(i_0_944,plain,
fail22(n(s(s(X1))),X2) = fail12(n(s(s(X1))),X2),
inference(rename_variables,[],[i_0_336]) ).
cnf(i_0_951,plain,
fail12(X1,n(s(X2))) = fail3(X1,n(s(X2))),
inference(rename_variables,[],[i_0_313]) ).
cnf(i_0_954,plain,
fail3(n(s(X1)),X2) = opt(y(n(s(X1)),X2)),
inference(rename_variables,[],[i_0_350]) ).
cnf(i_0_991,plain,
n(mulNat(X1,X2)) = fail32(n(X1),n(X2)),
inference(rename_variables,[],[i_0_241]) ).
cnf(i_0_1000,plain,
d(y(X1,X2)) = opt(x(n(z),x(y(d(X1),X2),y(X1,d(X2))))),
inference(scs_inference,[],[i_0_114,i_0_484,i_0_166]) ).
cnf(i_0_1001,plain,
X1 = opt(x(n(z),X1)),
inference(rename_variables,[],[i_0_484]) ).
cnf(i_0_1002,plain,
opt(x(n(z),x(y(d(X1),X2),y(X1,d(X2))))) = d(y(X1,X2)),
inference(scs_inference,[],[i_0_114,i_0_484,i_0_166,i_0_165]) ).
cnf(i_0_1014,plain,
d(y(X1,X2)) = fail(x(y(d(X1),X2),y(X1,d(X2))),n(z)),
inference(scs_inference,[],[i_0_114,i_0_481,i_0_166]) ).
cnf(i_0_1015,plain,
X1 = fail(X1,n(z)),
inference(rename_variables,[],[i_0_481]) ).
cnf(i_0_1016,plain,
fail(x(y(d(X1),X2),y(X1,d(X2))),n(z)) = d(y(X1,X2)),
inference(scs_inference,[],[i_0_114,i_0_481,i_0_166,i_0_165]) ).
cnf(i_0_1019,plain,
d(y(X1,X2)) = proj12(y(x(y(d(X1),X2),y(X1,d(X2))),X3)),
inference(scs_inference,[],[i_0_114,i_0_501,i_0_166]) ).
cnf(i_0_1020,plain,
X1 = proj12(y(X1,X2)),
inference(rename_variables,[],[i_0_501]) ).
cnf(i_0_1021,plain,
proj12(y(x(y(d(X1),X2),y(X1,d(X2))),X3)) = d(y(X1,X2)),
inference(scs_inference,[],[i_0_114,i_0_501,i_0_166,i_0_165]) ).
cnf(i_0_1062,plain,
X1 = proj1(x(X1,X2)),
inference(rename_variables,[],[i_0_476]) ).
cnf(i_0_1145,plain,
X1 = fail12(n(s(z)),X1),
inference(rename_variables,[],[i_0_494]) ).
cnf(i_0_1185,plain,
X1 = proj1S(s(X1)),
inference(rename_variables,[],[i_0_415]) ).
cnf(i_0_1222,plain,
X1 = proj2(x(X2,X1)),
inference(rename_variables,[],[i_0_427]) ).
cnf(i_0_1458,plain,
X1 = proj1(x(X1,X2)),
inference(rename_variables,[],[i_0_476]) ).
cnf(i_0_1612,plain,
X1 = fail12(n(s(z)),X1),
inference(rename_variables,[],[i_0_494]) ).
cnf(i_0_1768,plain,
X1 = addNat(z,X1),
inference(rename_variables,[],[i_0_400]) ).
cnf(i_0_1922,plain,
X1 = proj1N(n(X1)),
inference(rename_variables,[],[i_0_403]) ).
cnf(i_0_2038,plain,
X1 = proj1S(s(X1)),
inference(rename_variables,[],[i_0_415]) ).
cnf(i_0_2075,plain,
X1 = proj2(x(X2,X1)),
inference(rename_variables,[],[i_0_427]) ).
cnf(i_0_2112,plain,
X1 = proj1(x(X1,X2)),
inference(rename_variables,[],[i_0_476]) ).
cnf(i_0_2193,plain,
X1 = fail12(n(s(z)),X1),
inference(rename_variables,[],[i_0_494]) ).
cnf(i_0_2269,plain,
X1 = fail22(X1,n(s(z))),
inference(rename_variables,[],[i_0_498]) ).
cnf(i_0_2310,plain,
X1 = addNat(z,X1),
inference(rename_variables,[],[i_0_400]) ).
cnf(i_0_2477,plain,
fail2(X1,X1) = y(n(s(s(z))),opt(X1)),
inference(rename_variables,[],[i_0_199]) ).
cnf(i_0_2793,plain,
X1 = proj1N(n(X1)),
inference(rename_variables,[],[i_0_403]) ).
cnf(i_0_2907,plain,
X1 = proj1S(s(X1)),
inference(rename_variables,[],[i_0_415]) ).
cnf(i_0_2984,plain,
X1 = proj22(y(X2,X1)),
inference(rename_variables,[],[i_0_418]) ).
cnf(i_0_3020,plain,
X1 = proj2(x(X2,X1)),
inference(rename_variables,[],[i_0_427]) ).
cnf(i_0_214,plain,
x(opt(n(X1)),opt(x(proj1(n(X1)),proj2(n(X1))))) = fail2(n(X1),x(proj1(n(X1)),proj2(n(X1)))),
inference(scs_inference,[],[i_0_201,i_0_165]) ).
cnf(i_0_215,plain,
n(X1) != fail2(n(X2),x(proj1(n(X2)),proj2(n(X2)))),
inference(scs_inference,[],[i_0_201,i_0_149,i_0_165,i_0_166]) ).
cnf(i_0_223,plain,
n(X1) = opt(n(X1)),
inference(scs_inference,[],[i_0_206,i_0_165]) ).
cnf(i_0_224,plain,
addNat(z,opt(n(X1))) = n(X1),
inference(scs_inference,[],[i_0_206,i_0_156,i_0_165,i_0_166]) ).
cnf(i_0_271,plain,
addNat(s(X1),X2) = opt(x(n(z),s(addNat(X1,X2)))),
inference(scs_inference,[],[i_0_269,i_0_165]) ).
cnf(i_0_310,plain,
d(y(X1,X2)) = proj1S(s(x(y(d(X1),X2),y(X1,d(X2))))),
inference(scs_inference,[],[i_0_308,i_0_165]) ).
cnf(i_0_311,plain,
proj22(y(X1,proj1S(s(x(y(d(X2),X3),y(X2,d(X3))))))) = d(y(X2,X3)),
inference(scs_inference,[],[i_0_308,i_0_144,i_0_165,i_0_166]) ).
cnf(i_0_319,plain,
fail32(y(X1,X2),X3) = proj2(x(X4,opt(y(X1,y(X2,X3))))),
inference(scs_inference,[],[i_0_317,i_0_165]) ).
cnf(i_0_320,plain,
proj1(x(proj2(x(X1,opt(y(X2,y(X3,X4))))),X5)) = fail32(y(X2,X3),X4),
inference(scs_inference,[],[i_0_317,i_0_147,i_0_165,i_0_166]) ).
cnf(i_0_329,plain,
fail3(n(z),n(s(X1))) = fail22(n(z),n(s(X1))),
inference(scs_inference,[],[i_0_326,i_0_165]) ).
cnf(i_0_343,plain,
fail12(n(s(s(X1))),n(z)) = fail32(n(s(s(X1))),n(z)),
inference(scs_inference,[],[i_0_340,i_0_165]) ).
cnf(i_0_344,plain,
n(mulNat(X1,s(s(X2)))) = fail22(n(X1),n(s(s(X2)))),
inference(scs_inference,[],[i_0_339,i_0_340,i_0_241,i_0_165,i_0_166]) ).
cnf(i_0_518,plain,
opt(x(n(z),s(addNat(X1,mulNat(X2,s(X1)))))) = mulNat(s(X2),s(X1)),
inference(scs_inference,[],[i_0_384,i_0_269,i_0_166]) ).
cnf(i_0_520,plain,
opt(x(n(z),s(addNat(X1,X2)))) = addNat(s(X1),X2),
inference(rename_variables,[],[i_0_269]) ).
cnf(i_0_521,plain,
mulNat(s(X1),s(X2)) = opt(x(n(z),s(addNat(X2,mulNat(X1,s(X2)))))),
inference(scs_inference,[],[i_0_384,i_0_269,i_0_166,i_0_165]) ).
cnf(i_0_566,plain,
proj1S(s(opt(y(X1,y(X2,X3))))) = fail22(opt(y(X1,y(X2,X3))),n(s(z))),
inference(scs_inference,[],[i_0_562,i_0_563,i_0_166]) ).
cnf(i_0_567,plain,
fail32(y(X1,X2),X3) = fail22(opt(y(X1,y(X2,X3))),n(s(z))),
inference(rename_variables,[],[i_0_563]) ).
cnf(i_0_568,plain,
fail22(opt(y(X1,y(X2,X3))),n(s(z))) = proj1S(s(opt(y(X1,y(X2,X3))))),
inference(scs_inference,[],[i_0_562,i_0_563,i_0_166,i_0_165]) ).
cnf(i_0_582,plain,
fail22(opt(y(X1,y(X2,X3))),n(s(z))) = fail(opt(y(X1,y(X2,X3))),n(z)),
inference(scs_inference,[],[i_0_565,i_0_579,i_0_166]) ).
cnf(i_0_583,plain,
fail32(y(X1,X2),X3) = fail(opt(y(X1,y(X2,X3))),n(z)),
inference(rename_variables,[],[i_0_579]) ).
cnf(i_0_584,plain,
fail(opt(y(X1,y(X2,X3))),n(z)) = fail22(opt(y(X1,y(X2,X3))),n(s(z))),
inference(scs_inference,[],[i_0_565,i_0_579,i_0_166,i_0_165]) ).
cnf(i_0_585,plain,
fail(opt(y(X1,y(X2,X3))),n(z)) = proj1S(s(opt(y(X1,y(X2,X3))))),
inference(scs_inference,[],[i_0_560,i_0_581,i_0_166]) ).
cnf(i_0_586,plain,
fail32(y(X1,X2),X3) = proj1S(s(opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_560]) ).
cnf(i_0_587,plain,
proj1S(s(opt(y(X1,y(X2,X3))))) = fail(opt(y(X1,y(X2,X3))),n(z)),
inference(scs_inference,[],[i_0_560,i_0_581,i_0_166,i_0_165]) ).
cnf(i_0_609,plain,
proj1S(s(opt(y(X1,y(X2,X3))))) = fail32(y(X1,X2),X3),
inference(rename_variables,[],[i_0_562]) ).
cnf(i_0_689,plain,
proj22(y(X1,opt(y(X2,y(X3,X4))))) = proj22(y(X5,opt(y(X2,y(X3,X4))))),
inference(scs_inference,[],[i_0_688,i_0_686,i_0_166]) ).
cnf(i_0_690,plain,
fail32(y(X1,X2),X3) = proj22(y(X4,opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_686]) ).
cnf(i_0_691,plain,
proj22(y(X1,opt(y(X2,y(X3,X4))))) = proj1S(s(opt(y(X2,y(X3,X4))))),
inference(scs_inference,[],[i_0_688,i_0_560,i_0_166]) ).
cnf(i_0_692,plain,
fail32(y(X1,X2),X3) = proj1S(s(opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_560]) ).
cnf(i_0_693,plain,
proj1S(s(opt(y(X1,y(X2,X3))))) = proj22(y(X4,opt(y(X1,y(X2,X3))))),
inference(scs_inference,[],[i_0_688,i_0_560,i_0_166,i_0_165]) ).
cnf(i_0_694,plain,
fail22(opt(y(X1,y(X2,X3))),n(s(z))) = proj22(y(X4,opt(y(X1,y(X2,X3))))),
inference(scs_inference,[],[i_0_686,i_0_565,i_0_166]) ).
cnf(i_0_695,plain,
fail32(y(X1,X2),X3) = proj22(y(X4,opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_686]) ).
cnf(i_0_696,plain,
proj22(y(X1,opt(y(X2,y(X3,X4))))) = fail22(opt(y(X2,y(X3,X4))),n(s(z))),
inference(scs_inference,[],[i_0_686,i_0_565,i_0_166,i_0_165]) ).
cnf(i_0_743,plain,
fail32(y(X1,X2),X3) = fail(opt(y(X1,y(X2,X3))),n(z)),
inference(rename_variables,[],[i_0_579]) ).
cnf(i_0_747,plain,
proj12(y(opt(y(X1,y(X2,X3))),X4)) = proj12(y(opt(y(X1,y(X2,X3))),X5)),
inference(scs_inference,[],[i_0_746,i_0_744,i_0_166]) ).
cnf(i_0_748,plain,
fail32(y(X1,X2),X3) = proj12(y(opt(y(X1,y(X2,X3))),X4)),
inference(rename_variables,[],[i_0_744]) ).
cnf(i_0_751,plain,
proj12(y(opt(y(X1,y(X2,X3))),X4)) = fail32(y(X1,X2),X3),
inference(rename_variables,[],[i_0_746]) ).
cnf(i_0_776,plain,
fail32(y(X1,X2),X3) = proj12(y(opt(y(X1,y(X2,X3))),X4)),
inference(rename_variables,[],[i_0_744]) ).
cnf(i_0_806,plain,
fail32(y(X1,X2),X3) = fail22(opt(y(X1,y(X2,X3))),n(s(z))),
inference(rename_variables,[],[i_0_563]) ).
cnf(i_0_810,plain,
fail(opt(y(X1,y(X2,X3))),n(z)) = fail32(y(X1,X2),X3),
inference(rename_variables,[],[i_0_581]) ).
cnf(i_0_815,plain,
fail32(y(X1,X2),X3) = proj12(y(opt(y(X1,y(X2,X3))),X4)),
inference(rename_variables,[],[i_0_744]) ).
cnf(i_0_841,plain,
opt(x(n(z),opt(y(X1,y(X2,X3))))) = fail32(y(X1,X2),X3),
inference(rename_variables,[],[i_0_838]) ).
cnf(i_0_845,plain,
opt(x(n(z),opt(y(X1,y(X2,X3))))) = fail32(y(X1,X2),X3),
inference(rename_variables,[],[i_0_838]) ).
cnf(i_0_852,plain,
fail32(y(X1,X2),X3) = opt(x(n(z),opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_836]) ).
cnf(i_0_896,plain,
n(X1) != proj1S(s(x(y(d(X2),X3),y(X2,d(X3))))),
inference(scs_inference,[],[i_0_308,i_0_892,i_0_166]) ).
cnf(i_0_897,plain,
proj1S(s(x(y(d(X1),X2),y(X1,d(X2))))) = d(y(X1,X2)),
inference(rename_variables,[],[i_0_308]) ).
cnf(i_0_910,plain,
n(X1) != proj1N(n(x(y(d(X2),X3),y(X2,d(X3))))),
inference(scs_inference,[],[i_0_909,i_0_892,i_0_166]) ).
cnf(i_0_911,plain,
proj1N(n(x(y(d(X1),X2),y(X1,d(X2))))) = d(y(X1,X2)),
inference(rename_variables,[],[i_0_909]) ).
cnf(i_0_915,plain,
n(X1) != fail22(x(y(d(X2),X3),y(X2,d(X3))),n(s(z))),
inference(scs_inference,[],[i_0_914,i_0_892,i_0_166]) ).
cnf(i_0_916,plain,
fail22(x(y(d(X1),X2),y(X1,d(X2))),n(s(z))) = d(y(X1,X2)),
inference(rename_variables,[],[i_0_914]) ).
cnf(i_0_936,plain,
n(X1) != addNat(z,x(y(d(X2),X3),y(X2,d(X3)))),
inference(scs_inference,[],[i_0_935,i_0_892,i_0_166]) ).
cnf(i_0_937,plain,
addNat(z,x(y(d(X1),X2),y(X1,d(X2)))) = d(y(X1,X2)),
inference(rename_variables,[],[i_0_935]) ).
cnf(i_0_941,plain,
n(X1) != proj22(y(X2,x(y(d(X3),X4),y(X3,d(X4))))),
inference(scs_inference,[],[i_0_940,i_0_892,i_0_166]) ).
cnf(i_0_942,plain,
proj22(y(X1,x(y(d(X2),X3),y(X2,d(X3))))) = d(y(X2,X3)),
inference(rename_variables,[],[i_0_940]) ).
cnf(i_0_1003,plain,
n(X1) != opt(x(n(z),x(y(d(X2),X3),y(X2,d(X3))))),
inference(scs_inference,[],[i_0_1002,i_0_892,i_0_166]) ).
cnf(i_0_1004,plain,
opt(x(n(z),x(y(d(X1),X2),y(X1,d(X2))))) = d(y(X1,X2)),
inference(rename_variables,[],[i_0_1002]) ).
cnf(i_0_1017,plain,
n(X1) != fail(x(y(d(X2),X3),y(X2,d(X3))),n(z)),
inference(scs_inference,[],[i_0_1016,i_0_892,i_0_166]) ).
cnf(i_0_1018,plain,
fail(x(y(d(X1),X2),y(X1,d(X2))),n(z)) = d(y(X1,X2)),
inference(rename_variables,[],[i_0_1016]) ).
cnf(i_0_1022,plain,
n(X1) != proj12(y(x(y(d(X2),X3),y(X2,d(X3))),X4)),
inference(scs_inference,[],[i_0_1021,i_0_892,i_0_166]) ).
cnf(i_0_1023,plain,
proj12(y(x(y(d(X1),X2),y(X1,d(X2))),X3)) = d(y(X1,X2)),
inference(rename_variables,[],[i_0_1021]) ).
cnf(i_0_226,plain,
n(X1) = addNat(z,opt(n(X1))),
inference(scs_inference,[],[i_0_224,i_0_165]) ).
cnf(i_0_227,plain,
proj1N(n(addNat(z,opt(n(X1))))) = n(X1),
inference(scs_inference,[],[i_0_224,i_0_159,i_0_165,i_0_166]) ).
cnf(i_0_231,plain,
n(X1) = opt(n(X1)),
inference(rename_variables,[],[i_0_223]) ).
cnf(i_0_249,plain,
addNat(z,opt(n(X1))) = n(X1),
inference(rename_variables,[],[i_0_224]) ).
cnf(i_0_287,plain,
s(addNat(X1,X2)) = opt(x(n(z),s(addNat(X1,X2)))),
inference(scs_inference,[],[i_0_271,i_0_265,i_0_143,i_0_165,i_0_166]) ).
cnf(i_0_288,plain,
addNat(s(X1),X2) = opt(x(n(z),s(addNat(X1,X2)))),
inference(rename_variables,[],[i_0_271]) ).
cnf(i_0_314,plain,
proj12(y(proj22(y(X1,proj1S(s(x(y(d(X2),X3),y(X2,d(X3))))))),X4)) = d(y(X2,X3)),
inference(scs_inference,[],[i_0_311,i_0_123,i_0_145,i_0_165,i_0_166]) ).
cnf(i_0_322,plain,
fail32(y(X1,X2),X3) = proj1(x(proj2(x(X4,opt(y(X1,y(X2,X3))))),X5)),
inference(scs_inference,[],[i_0_320,i_0_165]) ).
cnf(i_0_323,plain,
fail(proj1(x(proj2(x(X1,opt(y(X2,y(X3,X4))))),X5)),n(z)) = fail32(y(X2,X3),X4),
inference(scs_inference,[],[i_0_320,i_0_155,i_0_165,i_0_166]) ).
cnf(i_0_335,plain,
d(y(X1,X2)) = proj1S(s(x(y(d(X1),X2),y(X1,d(X2))))),
inference(rename_variables,[],[i_0_310]) ).
cnf(i_0_338,plain,
fail32(y(X1,X2),X3) = proj2(x(X4,opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_347,plain,
fail22(n(X1),n(s(s(X2)))) = n(mulNat(X1,s(s(X2)))),
inference(scs_inference,[],[i_0_344,i_0_165]) ).
cnf(i_0_370,plain,
fail3(n(z),n(s(X1))) = fail22(n(z),n(s(X1))),
inference(rename_variables,[],[i_0_329]) ).
cnf(i_0_404,plain,
addNat(z,opt(n(s(z)))) = d(X1),
inference(scs_inference,[],[i_0_301,i_0_224,i_0_159,i_0_165,i_0_166]) ).
cnf(i_0_405,plain,
addNat(z,opt(n(X1))) = n(X1),
inference(rename_variables,[],[i_0_224]) ).
cnf(i_0_435,plain,
n(X1) = opt(n(X1)),
inference(rename_variables,[],[i_0_223]) ).
cnf(i_0_531,plain,
fail32(y(X1,X2),X3) = proj2(x(X4,opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_613,plain,
fail22(opt(y(X1,y(X2,X3))),n(s(z))) = proj1S(s(opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_568]) ).
cnf(i_0_622,plain,
proj1S(s(opt(y(X1,y(X2,X3))))) = fail22(opt(y(X1,y(X2,X3))),n(s(z))),
inference(rename_variables,[],[i_0_566]) ).
cnf(i_0_631,plain,
fail22(opt(y(X1,y(X2,X3))),n(s(z))) = fail(opt(y(X1,y(X2,X3))),n(z)),
inference(rename_variables,[],[i_0_582]) ).
cnf(i_0_643,plain,
proj1S(s(opt(y(X1,y(X2,X3))))) = fail(opt(y(X1,y(X2,X3))),n(z)),
inference(rename_variables,[],[i_0_587]) ).
cnf(i_0_650,plain,
fail(opt(y(X1,y(X2,X3))),n(z)) = proj1S(s(opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_585]) ).
cnf(i_0_699,plain,
proj22(y(X1,opt(y(X2,y(X3,X4))))) = fail22(opt(y(X2,y(X3,X4))),n(s(z))),
inference(rename_variables,[],[i_0_696]) ).
cnf(i_0_702,plain,
fail22(opt(y(X1,y(X2,X3))),n(s(z))) = proj22(y(X4,opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_694]) ).
cnf(i_0_716,plain,
fail(opt(y(X1,y(X2,X3))),n(z)) = proj22(y(X4,opt(y(X1,y(X2,X3))))),
inference(scs_inference,[],[i_0_584,i_0_694,i_0_166]) ).
cnf(i_0_717,plain,
fail22(opt(y(X1,y(X2,X3))),n(s(z))) = proj22(y(X4,opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_694]) ).
cnf(i_0_718,plain,
proj22(y(X1,opt(y(X2,y(X3,X4))))) = fail(opt(y(X2,y(X3,X4))),n(z)),
inference(scs_inference,[],[i_0_584,i_0_694,i_0_166,i_0_165]) ).
cnf(i_0_728,plain,
proj1S(s(opt(y(X1,y(X2,X3))))) = proj22(y(X4,opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_693]) ).
cnf(i_0_734,plain,
proj22(y(X1,opt(y(X2,y(X3,X4))))) = proj1S(s(opt(y(X2,y(X3,X4))))),
inference(rename_variables,[],[i_0_691]) ).
cnf(i_0_737,plain,
proj1S(s(opt(y(X1,y(X2,X3))))) = fail22(opt(y(X1,y(X2,X3))),n(s(z))),
inference(rename_variables,[],[i_0_566]) ).
cnf(i_0_764,plain,
fail12(n(s(s(X1))),n(z)) = fail32(n(s(s(X1))),n(z)),
inference(rename_variables,[],[i_0_343]) ).
cnf(i_0_796,plain,
fail32(y(X1,X2),X3) = proj2(x(X4,opt(y(X1,y(X2,X3))))),
inference(rename_variables,[],[i_0_319]) ).
cnf(i_0_860,plain,
addNat(s(X1),X2) = opt(x(n(z),s(addNat(X1,X2)))),
inference(rename_variables,[],[i_0_271]) ).
cnf(i_0_874,plain,
mulNat(s(X1),s(X2)) = opt(x(n(z),s(addNat(X2,mulNat(X1,s(X2)))))),
inference(rename_variables,[],[i_0_521]) ).
cnf(i_0_229,plain,
n(X1) = proj1N(n(addNat(z,opt(n(X1))))),
inference(scs_inference,[],[i_0_227,i_0_165]) ).
cnf(i_0_230,plain,
proj1N(n(addNat(z,opt(n(X1))))) = opt(n(X1)),
inference(scs_inference,[],[i_0_223,i_0_227,i_0_165,i_0_166]) ).
cnf(i_0_245,plain,
proj1N(n(addNat(z,opt(n(mulNat(X1,X2)))))) = fail32(n(X1),n(X2)),
inference(scs_inference,[],[i_0_241,i_0_227,i_0_128,i_0_165,i_0_166]) ).
cnf(i_0_246,plain,
proj1N(n(addNat(z,opt(n(X1))))) = n(X1),
inference(rename_variables,[],[i_0_227]) ).
cnf(i_0_254,plain,
proj1N(n(addNat(z,opt(n(addNat(X1,X2)))))) = fail1(n(X1),n(X2)),
inference(scs_inference,[],[i_0_244,i_0_227,i_0_129,i_0_165,i_0_166]) ).
cnf(i_0_255,plain,
proj1N(n(addNat(z,opt(n(X1))))) = n(X1),
inference(rename_variables,[],[i_0_227]) ).
cnf(i_0_290,plain,
fail22(s(addNat(X1,X2)),n(s(z))) = opt(x(n(z),s(addNat(X1,X2)))),
inference(scs_inference,[],[i_0_287,i_0_157,i_0_151,i_0_165,i_0_166]) ).
cnf(i_0_337,plain,
fail(proj1(x(proj2(x(X1,opt(y(X2,y(X3,X4))))),X5)),n(z)) = proj2(x(X6,opt(y(X2,y(X3,X4))))),
inference(scs_inference,[],[i_0_319,i_0_323,i_0_115,i_0_165,i_0_166]) ).
cnf(i_0_348,plain,
proj1N(n(addNat(z,opt(n(mulNat(X1,s(s(X2)))))))) = fail22(n(X1),n(s(s(X2)))),
inference(scs_inference,[],[i_0_344,i_0_227,i_0_165,i_0_166]) ).
cnf(i_0_349,plain,
proj1N(n(addNat(z,opt(n(X1))))) = n(X1),
inference(rename_variables,[],[i_0_227]) ).
cnf(i_0_351,plain,
opt(y(X1,y(X2,X3))) = proj1(x(proj2(x(X4,opt(y(X1,y(X2,X3))))),X5)),
inference(scs_inference,[],[i_0_322,i_0_307,i_0_117,i_0_165,i_0_166]) ).
cnf(i_0_352,plain,
fail32(y(X1,X2),X3) = proj1(x(proj2(x(X4,opt(y(X1,y(X2,X3))))),X5)),
inference(rename_variables,[],[i_0_322]) ).
cnf(i_0_369,plain,
fail22(n(X1),n(s(s(X2)))) = n(mulNat(X1,s(s(X2)))),
inference(rename_variables,[],[i_0_347]) ).
cnf(i_0_393,plain,
n(X1) = addNat(z,opt(n(X1))),
inference(rename_variables,[],[i_0_226]) ).
cnf(i_0_406,plain,
d(X1) = addNat(z,opt(n(s(z)))),
inference(scs_inference,[],[i_0_404,i_0_165]) ).
cnf(i_0_472,plain,
n(X1) = addNat(z,opt(n(X1))),
inference(rename_variables,[],[i_0_226]) ).
cnf(i_0_475,plain,
proj1N(n(addNat(z,opt(n(X1))))) = n(X1),
inference(rename_variables,[],[i_0_227]) ).
cnf(i_0_721,plain,
proj22(y(X1,opt(y(X2,y(X3,X4))))) = fail(opt(y(X2,y(X3,X4))),n(z)),
inference(rename_variables,[],[i_0_718]) ).
cnf(i_0_986,plain,
fail22(n(X1),n(s(s(X2)))) = n(mulNat(X1,s(s(X2)))),
inference(rename_variables,[],[i_0_347]) ).
cnf(i_0_232,plain,
opt(n(X1)) = proj1N(n(addNat(z,opt(n(X1))))),
inference(scs_inference,[],[i_0_230,i_0_165]) ).
cnf(i_0_233,plain,
proj1S(s(mulNat(s(X1),X2))) = addNat(X2,mulNat(X1,X2)),
inference(scs_inference,[],[i_0_230,i_0_126,i_0_160,i_0_165,i_0_166]) ).
cnf(i_0_247,plain,
fail32(n(X1),n(X2)) = proj1N(n(addNat(z,opt(n(mulNat(X1,X2)))))),
inference(scs_inference,[],[i_0_245,i_0_165]) ).
cnf(i_0_248,plain,
addNat(z,opt(n(addNat(X1,X2)))) = fail1(n(X1),n(X2)),
inference(scs_inference,[],[i_0_244,i_0_245,i_0_224,i_0_165,i_0_166]) ).
cnf(i_0_256,plain,
fail1(n(X1),n(X2)) = proj1N(n(addNat(z,opt(n(addNat(X1,X2)))))),
inference(scs_inference,[],[i_0_254,i_0_165]) ).
cnf(i_0_257,plain,
proj2(x(X1,x(d(X2),d(X3)))) = d(x(X2,X3)),
inference(scs_inference,[],[i_0_253,i_0_254,i_0_146,i_0_165,i_0_166]) ).
cnf(i_0_292,plain,
opt(x(n(z),s(addNat(X1,X2)))) = fail22(s(addNat(X1,X2)),n(s(z))),
inference(scs_inference,[],[i_0_290,i_0_165]) ).
cnf(i_0_293,plain,
addNat(z,opt(n(X1))) = proj1N(n(addNat(z,opt(n(X1))))),
inference(scs_inference,[],[i_0_229,i_0_290,i_0_224,i_0_165,i_0_166]) ).
cnf(i_0_294,plain,
n(X1) = proj1N(n(addNat(z,opt(n(X1))))),
inference(rename_variables,[],[i_0_229]) ).
cnf(i_0_330,plain,
proj1N(n(addNat(z,opt(n(addNat(X1,s(X2))))))) = fail(n(X1),n(s(X2))),
inference(scs_inference,[],[i_0_316,i_0_326,i_0_254,i_0_165,i_0_166]) ).
cnf(i_0_332,plain,
proj1N(n(addNat(z,opt(n(addNat(X1,X2)))))) = fail1(n(X1),n(X2)),
inference(rename_variables,[],[i_0_254]) ).
cnf(i_0_353,plain,
proj1(x(proj2(x(X1,opt(y(X2,y(X3,X4))))),X5)) = opt(y(X2,y(X3,X4))),
inference(scs_inference,[],[i_0_351,i_0_165]) ).
cnf(i_0_354,plain,
n(z) = opt(y(n(s(X1)),n(z))),
inference(scs_inference,[],[i_0_350,i_0_351,i_0_295,i_0_165,i_0_166]) ).
cnf(i_0_466,plain,
proj1N(n(addNat(z,opt(n(X1))))) = opt(n(X1)),
inference(rename_variables,[],[i_0_230]) ).
cnf(i_0_541,plain,
opt(y(X1,y(X2,X3))) = proj1(x(proj2(x(X4,opt(y(X1,y(X2,X3))))),X5)),
inference(rename_variables,[],[i_0_351]) ).
cnf(i_0_551,plain,
n(X1) = proj1N(n(addNat(z,opt(n(X1))))),
inference(rename_variables,[],[i_0_229]) ).
cnf(i_0_663,plain,
proj1N(n(addNat(z,opt(n(mulNat(X1,z)))))) = fail22(n(X1),n(z)),
inference(scs_inference,[],[i_0_245,i_0_286,i_0_166]) ).
cnf(i_0_665,plain,
proj1N(n(addNat(z,opt(n(mulNat(X1,X2)))))) = fail32(n(X1),n(X2)),
inference(rename_variables,[],[i_0_245]) ).
cnf(i_0_666,plain,
fail22(n(X1),n(z)) = proj1N(n(addNat(z,opt(n(mulNat(X1,z)))))),
inference(scs_inference,[],[i_0_245,i_0_286,i_0_166,i_0_165]) ).
cnf(i_0_831,plain,
proj1N(n(addNat(z,opt(n(X1))))) = opt(n(X1)),
inference(rename_variables,[],[i_0_230]) ).
cnf(i_0_834,plain,
proj1N(n(addNat(z,opt(n(addNat(X1,X2)))))) = fail1(n(X1),n(X2)),
inference(rename_variables,[],[i_0_254]) ).
cnf(i_0_927,plain,
opt(y(X1,y(X2,X3))) = proj1(x(proj2(x(X4,opt(y(X1,y(X2,X3))))),X5)),
inference(rename_variables,[],[i_0_351]) ).
cnf(i_0_999,plain,
opt(y(X1,y(X2,X3))) = proj1(x(proj2(x(X4,opt(y(X1,y(X2,X3))))),X5)),
inference(rename_variables,[],[i_0_351]) ).
cnf(i_0_235,plain,
addNat(X1,mulNat(X2,X1)) = proj1S(s(mulNat(s(X2),X1))),
inference(scs_inference,[],[i_0_233,i_0_165]) ).
cnf(i_0_236,plain,
proj22(y(X1,proj1S(s(mulNat(s(X2),X3))))) = addNat(X3,mulNat(X2,X3)),
inference(scs_inference,[],[i_0_233,i_0_144,i_0_165,i_0_166]) ).
cnf(i_0_250,plain,
fail1(n(X1),n(X2)) = addNat(z,opt(n(addNat(X1,X2)))),
inference(scs_inference,[],[i_0_248,i_0_165]) ).
cnf(i_0_259,plain,
d(x(X1,X2)) = proj2(x(X3,x(d(X1),d(X2)))),
inference(scs_inference,[],[i_0_257,i_0_165]) ).
cnf(i_0_260,plain,
proj1(x(proj2(x(X1,x(d(X2),d(X3)))),X4)) = d(x(X2,X3)),
inference(scs_inference,[],[i_0_257,i_0_147,i_0_165,i_0_166]) ).
cnf(i_0_296,plain,
addNat(s(X1),X2) = fail22(s(addNat(X1,X2)),n(s(z))),
inference(scs_inference,[],[i_0_292,i_0_271,i_0_154,i_0_165,i_0_166]) ).
cnf(i_0_297,plain,
opt(x(n(z),s(addNat(X1,X2)))) = fail22(s(addNat(X1,X2)),n(s(z))),
inference(rename_variables,[],[i_0_292]) ).
cnf(i_0_333,plain,
fail(n(X1),n(s(X2))) = proj1N(n(addNat(z,opt(n(addNat(X1,s(X2))))))),
inference(scs_inference,[],[i_0_330,i_0_165]) ).
cnf(i_0_357,plain,
opt(y(n(s(X1)),n(z))) = n(z),
inference(scs_inference,[],[i_0_354,i_0_165]) ).
cnf(i_0_361,plain,
opt(n(mulNat(X1,s(s(X2))))) = fail22(n(X1),n(s(s(X2)))),
inference(scs_inference,[],[i_0_348,i_0_232,i_0_118,i_0_165,i_0_166]) ).
cnf(i_0_362,plain,
opt(n(X1)) = proj1N(n(addNat(z,opt(n(X1))))),
inference(rename_variables,[],[i_0_232]) ).
cnf(i_0_377,plain,
fail32(n(X1),n(X2)) = proj1N(n(addNat(z,opt(n(mulNat(X1,X2)))))),
inference(rename_variables,[],[i_0_247]) ).
cnf(i_0_380,plain,
fail1(n(X1),n(X2)) = proj1N(n(addNat(z,opt(n(addNat(X1,X2)))))),
inference(rename_variables,[],[i_0_256]) ).
cnf(i_0_386,plain,
addNat(z,opt(n(X1))) = proj1N(n(addNat(z,opt(n(X1))))),
inference(rename_variables,[],[i_0_293]) ).
cnf(i_0_407,plain,
proj1(x(proj2(x(X1,opt(y(X2,y(X3,X4))))),X5)) = proj1N(n(opt(y(X2,y(X3,X4))))),
inference(scs_inference,[],[i_0_403,i_0_353,i_0_404,i_0_165,i_0_166]) ).
cnf(i_0_497,plain,
proj1(x(proj2(x(X1,opt(y(X2,y(X3,X4))))),X5)) = opt(y(X2,y(X3,X4))),
inference(rename_variables,[],[i_0_353]) ).
cnf(i_0_555,plain,
opt(n(X1)) = proj1N(n(addNat(z,opt(n(X1))))),
inference(rename_variables,[],[i_0_232]) ).
cnf(i_0_558,plain,
fail32(n(X1),n(X2)) = proj1N(n(addNat(z,opt(n(mulNat(X1,X2)))))),
inference(rename_variables,[],[i_0_247]) ).
cnf(i_0_667,plain,
proj1N(n(addNat(z,opt(n(mulNat(z,z)))))) = fail12(n(z),n(z)),
inference(scs_inference,[],[i_0_663,i_0_280,i_0_166]) ).
cnf(i_0_669,plain,
proj1N(n(addNat(z,opt(n(mulNat(X1,z)))))) = fail22(n(X1),n(z)),
inference(rename_variables,[],[i_0_663]) ).
cnf(i_0_670,plain,
fail12(n(z),n(z)) = proj1N(n(addNat(z,opt(n(mulNat(z,z)))))),
inference(scs_inference,[],[i_0_663,i_0_280,i_0_166,i_0_165]) ).
cnf(i_0_753,plain,
addNat(z,opt(n(addNat(X1,s(X2))))) = fail(n(X1),n(s(X2))),
inference(scs_inference,[],[i_0_248,i_0_316,i_0_166]) ).
cnf(i_0_755,plain,
addNat(z,opt(n(addNat(X1,X2)))) = fail1(n(X1),n(X2)),
inference(rename_variables,[],[i_0_248]) ).
cnf(i_0_756,plain,
fail(n(X1),n(s(X2))) = addNat(z,opt(n(addNat(X1,s(X2))))),
inference(scs_inference,[],[i_0_248,i_0_316,i_0_166,i_0_165]) ).
cnf(i_0_859,plain,
proj1S(s(mulNat(s(X1),s(X2)))) = opt(x(n(z),s(addNat(X2,mulNat(X1,s(X2)))))),
inference(scs_inference,[],[i_0_233,i_0_271,i_0_166]) ).
cnf(i_0_861,plain,
proj1S(s(mulNat(s(X1),X2))) = addNat(X2,mulNat(X1,X2)),
inference(rename_variables,[],[i_0_233]) ).
cnf(i_0_862,plain,
opt(x(n(z),s(addNat(X1,mulNat(X2,s(X1)))))) = proj1S(s(mulNat(s(X2),s(X1)))),
inference(scs_inference,[],[i_0_233,i_0_271,i_0_166,i_0_165]) ).
cnf(i_0_997,plain,
fail32(n(X1),n(X2)) = proj1N(n(addNat(z,opt(n(mulNat(X1,X2)))))),
inference(rename_variables,[],[i_0_247]) ).
cnf(i_0_238,plain,
addNat(X1,mulNat(X2,X1)) = proj22(y(X3,proj1S(s(mulNat(s(X2),X1))))),
inference(scs_inference,[],[i_0_236,i_0_165]) ).
cnf(i_0_239,plain,
proj12(y(proj22(y(X1,proj1S(s(mulNat(s(X2),X3))))),X4)) = addNat(X3,mulNat(X2,X3)),
inference(scs_inference,[],[i_0_236,i_0_145,i_0_165,i_0_166]) ).
cnf(i_0_243,plain,
addNat(X1,mulNat(X2,X1)) = proj1S(s(mulNat(s(X2),X1))),
inference(rename_variables,[],[i_0_235]) ).
cnf(i_0_262,plain,
d(x(X1,X2)) = proj1(x(proj2(x(X3,x(d(X1),d(X2)))),X4)),
inference(scs_inference,[],[i_0_260,i_0_165]) ).
cnf(i_0_263,plain,
fail(proj1(x(proj2(x(X1,x(d(X2),d(X3)))),X4)),n(z)) = d(x(X2,X3)),
inference(scs_inference,[],[i_0_260,i_0_155,i_0_165,i_0_166]) ).
cnf(i_0_267,plain,
d(x(X1,X2)) = proj2(x(X3,x(d(X1),d(X2)))),
inference(rename_variables,[],[i_0_259]) ).
cnf(i_0_298,plain,
fail22(s(addNat(X1,X2)),n(s(z))) = addNat(s(X1),X2),
inference(scs_inference,[],[i_0_296,i_0_165]) ).
cnf(i_0_363,plain,
fail22(n(X1),n(s(s(X2)))) = opt(n(mulNat(X1,s(s(X2))))),
inference(scs_inference,[],[i_0_361,i_0_165]) ).
cnf(i_0_364,plain,
fail1(n(s(X1)),n(s(X2))) = opt(x(n(s(X1)),n(s(X2)))),
inference(scs_inference,[],[i_0_360,i_0_361,i_0_316,i_0_165,i_0_166]) ).
cnf(i_0_396,plain,
fail1(n(X1),n(X2)) = addNat(z,opt(n(addNat(X1,X2)))),
inference(rename_variables,[],[i_0_250]) ).
cnf(i_0_409,plain,
proj1N(n(opt(y(X1,y(X2,X3))))) = proj1(x(proj2(x(X4,opt(y(X1,y(X2,X3))))),X5)),
inference(scs_inference,[],[i_0_407,i_0_165]) ).
cnf(i_0_410,plain,
fail32(y(X1,X2),X3) = proj1N(n(opt(y(X1,y(X2,X3))))),
inference(scs_inference,[],[i_0_407,i_0_322,i_0_165,i_0_166]) ).
cnf(i_0_411,plain,
proj1(x(proj2(x(X1,opt(y(X2,y(X3,X4))))),X5)) = proj1N(n(opt(y(X2,y(X3,X4))))),
inference(rename_variables,[],[i_0_407]) ).
cnf(i_0_477,plain,
opt(y(n(s(X1)),n(z))) = d(n(X2)),
inference(scs_inference,[],[i_0_289,i_0_357,i_0_147,i_0_165,i_0_166]) ).
cnf(i_0_523,plain,
addNat(X1,mulNat(X2,X1)) = proj1S(s(mulNat(s(X2),X1))),
inference(rename_variables,[],[i_0_235]) ).
cnf(i_0_527,plain,
d(x(X1,X2)) = proj2(x(X3,x(d(X1),d(X2)))),
inference(rename_variables,[],[i_0_259]) ).
cnf(i_0_592,plain,
fail(n(X1),n(s(X2))) = proj1N(n(addNat(z,opt(n(addNat(X1,s(X2))))))),
inference(rename_variables,[],[i_0_333]) ).
cnf(i_0_595,plain,
fail(n(X1),n(s(X2))) = proj1N(n(addNat(z,opt(n(addNat(X1,s(X2))))))),
inference(rename_variables,[],[i_0_333]) ).
cnf(i_0_684,plain,
opt(y(n(s(X1)),n(z))) = fail3(X2,n(z)),
inference(scs_inference,[],[i_0_295,i_0_357,i_0_166]) ).
cnf(i_0_685,plain,
fail3(X1,n(z)) = opt(y(n(s(X2)),n(z))),
inference(scs_inference,[],[i_0_295,i_0_357,i_0_166,i_0_165]) ).
cnf(i_0_830,plain,
fail12(n(z),n(z)) = opt(n(mulNat(z,z))),
inference(scs_inference,[],[i_0_670,i_0_230,i_0_166]) ).
cnf(i_0_832,plain,
opt(n(mulNat(z,z))) = fail12(n(z),n(z)),
inference(scs_inference,[],[i_0_670,i_0_230,i_0_166,i_0_165]) ).
cnf(c_0_2156,plain,
n(X1) != X2,
i_0_2154 ).
cnf(c_0_2157,plain,
$false,
inference(er,[status(thm)],[c_0_2156]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWX193+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Tue May 5 02:55:56 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 122.27/80.57 % Version : CSE_E---1.7
% 122.27/80.57 % Problem : theBenchmark.p
% 122.27/80.57 % SZS status Theorem for theBenchmark.p
% 122.27/80.57 % SZS output start CNFRefutation
% See solution above
% 131.89/90.16 % Total time : 80.322s
%------------------------------------------------------------------------------