%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG268^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:45:17 AM UTC 2026
% Result : Theorem 5.22s 1.11s
% Output : Refutation 5.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 37
% Syntax : Number of formulae : 298 ( 71 unt; 0 typ; 26 def)
% Number of atoms : 1683 ( 444 equ; 0 cnn)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 3198 ( 274 ~; 424 |; 0 &;2157 @)
% ( 28 <=>; 138 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 212 ( 212 >; 0 *; 0 +; 0 <<)
% Number of symbols : 472 ( 467 usr; 207 con; 0-4 aty)
% ( 171 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 416 ( 6 sgn 172 !; 2 ?; 416 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_6,type,
subst: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
one: term ).
thf(func_def_1,type,
ap: term > term > term ).
thf(func_def_2,type,
lam: term > term ).
thf(func_def_3,type,
sub: term > subst > term ).
thf(func_def_4,type,
id: subst ).
thf(func_def_5,type,
sh: subst ).
thf(func_def_6,type,
push: term > subst > subst ).
thf(func_def_7,type,
comp: subst > subst > subst ).
thf(func_def_8,type,
var: term > $o ).
thf(func_def_9,type,
pushprop_lem1v2: $o ).
thf(func_def_10,type,
pushprop_lem1_gthm: $o ).
thf(func_def_11,type,
axmap: $o ).
thf(func_def_12,type,
pushprop_lem0_gthm: $o ).
thf(func_def_13,type,
shinj: $o ).
thf(func_def_14,type,
hoasinduction_lem1v2: $o ).
thf(func_def_15,type,
hoasinduction_lem1v2_gthm: $o ).
thf(func_def_16,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_17,type,
induction2lem: $o ).
thf(func_def_18,type,
hoasinduction_lem3v2_f: $o ).
thf(func_def_19,type,
axvarshift: $o ).
thf(func_def_20,type,
hoasapinj2: $o ).
thf(func_def_21,type,
hoasapnotvar_gthm: $o ).
thf(func_def_22,type,
hoasapinj1: $o ).
thf(func_def_23,type,
ulamvar1: $o ).
thf(func_def_24,type,
induction2lem_lthm: $o ).
thf(func_def_25,type,
hoasinduction_lem3v2_gthm: $o ).
thf(func_def_26,type,
apnotvar: $o ).
thf(func_def_27,type,
pushprop_lthm_orig: $o ).
thf(func_def_28,type,
hoasinduction_lem3v2_f_lthm: $o ).
thf(func_def_29,type,
hoasinduction_lthm: $o ).
thf(func_def_30,type,
hoasinduction_no_psi_cond_lthm: $o ).
thf(func_def_31,type,
hoaslaminj: $o ).
thf(func_def_32,type,
hoasinduction_lem3aaa: $o ).
thf(func_def_33,type,
induction2lem_gthm: $o ).
thf(func_def_34,type,
hoasinduction_lem3aa_lthm: $o ).
thf(func_def_35,type,
hoasinduction_lem3: $o ).
thf(func_def_36,type,
hoasinduction_lem2: $o ).
thf(func_def_37,type,
termmset_lthm: $o ).
thf(func_def_38,type,
hoasinduction_lem1: $o ).
thf(func_def_39,type,
hoaslamnotap_lthm: $o ).
thf(func_def_40,type,
pushprop_lem1v2_lthm: $o ).
thf(func_def_41,type,
hoasapnotvar: $o ).
thf(func_def_42,type,
hoasinduction_lem0: $o ).
thf(func_def_43,type,
hoasinduction: $o ).
thf(func_def_44,type,
hoasinduction_gthm: $o ).
thf(func_def_45,type,
axapp: $o ).
thf(func_def_46,type,
hoaslamnotvar_lthm: $o ).
thf(func_def_47,type,
pushprop_lem3v2_lthm: $o ).
thf(func_def_48,type,
hoasinduction_lem3b_lthm: $o ).
thf(func_def_49,type,
ulamvarind: $o ).
thf(func_def_50,type,
induction: $o ).
thf(func_def_51,type,
hoasinduction_lem3a_lthm: $o ).
thf(func_def_52,type,
termmset_gthm: $o ).
thf(func_def_53,type,
hoasinduction_lem3aa: $o ).
thf(func_def_54,type,
pushprop_lem1v2_gthm: $o ).
thf(func_def_55,type,
hoaslamnotap_gthm: $o ).
thf(func_def_56,type,
hoaslamnotvar_gthm: $o ).
thf(func_def_57,type,
hoasinduction_lem3b_gthm: $o ).
thf(func_def_58,type,
pushprop_lem2v2: $o ).
thf(func_def_59,type,
hoasinduction_lem3a_gthm: $o ).
thf(func_def_60,type,
axclos: $o ).
thf(func_def_61,type,
axassoc: $o ).
thf(func_def_62,type,
hoasinduction_lem2v2: $o ).
thf(func_def_63,type,
pushprop_lthm: $o ).
thf(func_def_64,type,
apinj2: $o ).
thf(func_def_65,type,
apinj1: $o ).
thf(func_def_66,type,
hoasapinj2_lthm: $o ).
thf(func_def_67,type,
hoasinduction_lem3v2a: $o ).
thf(func_def_68,type,
hoasapinj1_lthm: $o ).
thf(func_def_69,type,
hoaslaminj_lthm: $o ).
thf(func_def_70,type,
axvarcons: $o ).
thf(func_def_71,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_72,type,
axscons: $o ).
thf(func_def_73,type,
hoasinduction_lem2v2_gthm: $o ).
thf(func_def_74,type,
axidr: $o ).
thf(func_def_75,type,
pushprop_lem1: $o ).
thf(func_def_76,type,
laminj: $o ).
thf(func_def_77,type,
hoasinduction_lem3_lthm: $o ).
thf(func_def_78,type,
pushprop_lem0: $o ).
thf(func_def_79,type,
pushprop_gthm: $o ).
thf(func_def_80,type,
axabs: $o ).
thf(func_def_81,type,
hoasinduction_lem3v2a_lthm: $o ).
thf(func_def_82,type,
hoasinduction_lem2_lthm: $o ).
thf(func_def_83,type,
hoasapinj2_gthm: $o ).
thf(func_def_84,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_85,type,
hoasinduction_lem1_lthm: $o ).
thf(func_def_86,type,
lamnotap: $o ).
thf(func_def_87,type,
hoasapinj1_gthm: $o ).
thf(func_def_88,type,
hoaslamnotvar: $o ).
thf(func_def_89,type,
axidl: $o ).
thf(func_def_90,type,
hoaslaminj_gthm: $o ).
thf(func_def_91,type,
induction2_lthm: $o ).
thf(func_def_92,type,
hoasinduction_lem0_lthm: $o ).
thf(func_def_93,type,
substmonoid_lthm: $o ).
thf(func_def_94,type,
pushprop: $o ).
thf(func_def_95,type,
hoasinduction_lem3_gthm: $o ).
thf(func_def_96,type,
hoasinduction_lem2_gthm: $o ).
thf(func_def_97,type,
hoasinduction_lem3b: $o ).
thf(func_def_98,type,
substmonoid: $o ).
thf(func_def_99,type,
lamnotvar: $o ).
thf(func_def_100,type,
hoasinduction_lem3a: $o ).
thf(func_def_101,type,
hoasinduction_lem1_gthm: $o ).
thf(func_def_102,type,
hoasinduction_no_psi_cond: $o ).
thf(func_def_103,type,
induction2_gthm: $o ).
thf(func_def_104,type,
pushprop_lem2v2_lthm: $o ).
thf(func_def_105,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_106,type,
hoaslamnotap: $o ).
thf(func_def_107,type,
substmonoid_gthm: $o ).
thf(func_def_108,type,
ulamvarsh: $o ).
thf(func_def_109,type,
induction2: $o ).
thf(func_def_110,type,
pushprop_lem3v2: $o ).
thf(func_def_111,type,
pushprop_lem2v2_gthm: $o ).
thf(func_def_112,type,
pushprop_lem1_lthm: $o ).
thf(func_def_113,type,
hoasinduction_lem3v2: $o ).
thf(func_def_114,type,
axshiftcons: $o ).
thf(func_def_115,type,
termmset: $o ).
thf(func_def_116,type,
pushprop_lem0_lthm: $o ).
thf(func_def_117,type,
hoasapnotvar_lthm: $o ).
thf(func_def_118,type,
hoasinduction_lem3v2_lthm: $o ).
thf(func_def_119,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_120,type,
axvarid: $o ).
thf(func_def_121,type,
hoasinduction_lthm_3: $o ).
thf(func_def_123,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_124,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_125,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_127,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_130,type,
vIMP: $o > $o > $o ).
thf(func_def_131,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_132,type,
vIFF: $o > $o > $o ).
thf(func_def_133,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_134,type,
vAND: $o > $o > $o ).
thf(func_def_135,type,
vNOT: $o > $o ).
thf(func_def_136,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_139,type,
sK0: term ).
thf(func_def_140,type,
sK1: subst ).
thf(func_def_141,type,
sK2: subst ).
thf(func_def_142,type,
sK3: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_143,type,
sK4: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_144,type,
sK5: term > ( term > $o ) > term ).
thf(func_def_145,type,
sK6: term > $o ).
thf(func_def_146,type,
sK7: subst > term > subst > $o ).
thf(func_def_147,type,
sK8: ( subst > term > term ) > term ).
thf(func_def_148,type,
sK9: ( subst > term > term ) > subst ).
thf(func_def_149,type,
sK10: ( subst > term > term ) > term ).
thf(func_def_150,type,
sK11: ( subst > term > term ) > subst ).
thf(func_def_151,type,
sK12: ( subst > term > term ) > subst ).
thf(func_def_152,type,
sK13: term ).
thf(func_def_153,type,
sK14: term ).
thf(func_def_154,type,
sK15: term ).
thf(func_def_155,type,
sK16: ( term > $o ) > term ).
thf(func_def_156,type,
sK17: ( term > $o ) > term ).
thf(func_def_157,type,
sK18: ( term > $o ) > term ).
thf(func_def_158,type,
sK19: ( term > $o ) > term ).
thf(func_def_159,type,
sK20: ( term > $o ) > term ).
thf(func_def_160,type,
sK21: ( term > $o ) > term ).
thf(func_def_161,type,
sK22: term > $o ).
thf(func_def_162,type,
sK23: term > term ).
thf(func_def_163,type,
sK24: term ).
thf(func_def_164,type,
sK25: term > subst > term > term ).
thf(func_def_165,type,
sK26: term ).
thf(func_def_166,type,
sK27: ( subst > term > term ) > term ).
thf(func_def_167,type,
sK28: ( subst > term > term ) > subst ).
thf(func_def_168,type,
sK29: term ).
thf(func_def_169,type,
sK30: term ).
thf(func_def_170,type,
sK31: term ).
thf(func_def_171,type,
sK32: term ).
thf(func_def_172,type,
sK33: subst ).
thf(func_def_173,type,
sK34: subst ).
thf(func_def_174,type,
sK35: term ).
thf(func_def_175,type,
sK36: term ).
thf(func_def_176,type,
sK37: term ).
thf(func_def_177,type,
sK38: term ).
thf(func_def_178,type,
sK39: term ).
thf(func_def_179,type,
sK40: term ).
thf(func_def_180,type,
sK41: term ).
thf(func_def_181,type,
sK42: term ).
thf(func_def_182,type,
sK43: term ).
thf(func_def_183,type,
sK44: term ).
thf(func_def_184,type,
sK45: term ).
thf(func_def_185,type,
sK46: term ).
thf(func_def_186,type,
sK47: subst ).
thf(func_def_187,type,
sK48: subst > term > ( term > $o ) > term > $o ).
thf(func_def_188,type,
sK49: term ).
thf(func_def_189,type,
sK50: term > $o ).
thf(func_def_190,type,
sK51: subst ).
thf(func_def_191,type,
sK52: term > subst > term > term ).
thf(func_def_192,type,
sK53: term ).
thf(func_def_193,type,
sK54: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_194,type,
sK55: subst > term > subst > $o ).
thf(func_def_195,type,
sK56: ( term > $o ) > term ).
thf(func_def_196,type,
sK57: ( subst > term > subst > $o ) > term ).
thf(func_def_197,type,
sK58: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_198,type,
sK59: ( subst > term > subst > $o ) > subst ).
thf(func_def_199,type,
sK60: ( subst > term > subst > $o ) > subst ).
thf(func_def_200,type,
sK61: ( subst > term > subst > $o ) > subst ).
thf(func_def_201,type,
sK62: ( subst > term > subst > $o ) > term > term ).
thf(func_def_202,type,
sK63: ( subst > term > subst > $o ) > subst ).
thf(func_def_203,type,
sK64: ( subst > term > subst > $o ) > subst ).
thf(func_def_204,type,
sK65: ( subst > term > subst > $o ) > term ).
thf(func_def_205,type,
sK66: ( subst > term > subst > $o ) > subst ).
thf(func_def_206,type,
sK67: ( subst > term > subst > $o ) > subst ).
thf(func_def_207,type,
sK68: ( subst > term > subst > $o ) > term ).
thf(func_def_208,type,
sK69: ( subst > term > subst > $o ) > subst ).
thf(func_def_209,type,
sK70: ( subst > term > subst > $o ) > term > term ).
thf(func_def_210,type,
sK71: ( subst > term > subst > $o ) > subst ).
thf(func_def_211,type,
sK72: ( subst > term > subst > $o ) > subst ).
thf(func_def_212,type,
sK73: ( subst > term > subst > $o ) > term ).
thf(func_def_213,type,
sK74: ( subst > term > subst > $o ) > subst ).
thf(func_def_214,type,
sK75: ( subst > term > subst > $o ) > term ).
thf(func_def_215,type,
sK76: ( subst > term > subst > $o ) > subst ).
thf(func_def_216,type,
sK77: ( subst > term > subst > $o ) > term > term ).
thf(func_def_217,type,
sK78: ( subst > term > subst > $o ) > subst ).
thf(func_def_218,type,
sK79: ( subst > term > subst > $o ) > subst ).
thf(func_def_219,type,
sK80: ( subst > term > subst > $o ) > term ).
thf(func_def_220,type,
sK81: ( subst > term > subst > $o ) > subst ).
thf(func_def_221,type,
sK82: ( subst > term > subst > $o ) > subst ).
thf(func_def_222,type,
sK83: ( subst > term > subst > $o ) > subst ).
thf(func_def_223,type,
sK84: ( subst > term > subst > $o ) > subst ).
thf(func_def_224,type,
sK85: ( subst > term > subst > $o ) > term ).
thf(func_def_225,type,
sK86: subst > term > subst > $o ).
thf(func_def_226,type,
sK87: ( subst > term > term ) > subst ).
thf(func_def_227,type,
sK88: ( subst > term > term ) > term ).
thf(func_def_228,type,
sK89: ( subst > term > term ) > subst ).
thf(func_def_229,type,
sK90: ( subst > term > term ) > term ).
thf(func_def_230,type,
sK91: ( subst > term > term ) > term ).
thf(func_def_231,type,
sK92: term ).
thf(func_def_232,type,
sK93: ( subst > term > term ) > term ).
thf(func_def_233,type,
sK94: ( subst > term > term ) > subst ).
thf(func_def_234,type,
sK95: ( subst > term > term ) > subst ).
thf(func_def_235,type,
sK96: ( subst > term > term ) > subst ).
thf(func_def_236,type,
sK97: ( subst > term > term ) > subst ).
thf(func_def_237,type,
sK98: ( subst > term > term ) > term ).
thf(func_def_238,type,
sK99: subst > term > term ).
thf(func_def_239,type,
sK100: subst > term > term ).
thf(func_def_240,type,
sK101: subst ).
thf(func_def_241,type,
sK102: term ).
thf(func_def_242,type,
sK103: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_243,type,
sK104: ( subst > term > subst > $o ) > term > term ).
thf(func_def_244,type,
sK105: ( subst > term > subst > $o ) > term > term ).
thf(func_def_245,type,
sK106: subst > term > subst > $o ).
thf(func_def_246,type,
sK107: ( subst > term > term ) > term ).
thf(func_def_247,type,
sK108: ( subst > term > term ) > term ).
thf(func_def_248,type,
sK109: ( subst > term > term ) > subst ).
thf(func_def_249,type,
sK110: ( subst > term > term ) > subst ).
thf(func_def_250,type,
sK111: ( subst > term > term ) > subst ).
thf(func_def_251,type,
sK112: term ).
thf(func_def_252,type,
sK113: ( term > $o ) > term ).
thf(func_def_253,type,
sK114: ( term > $o ) > term ).
thf(func_def_254,type,
sK115: ( term > $o ) > term ).
thf(func_def_255,type,
sK116: ( term > $o ) > term ).
thf(func_def_256,type,
sK117: ( term > $o ) > term ).
thf(func_def_257,type,
sK118: ( term > $o ) > term ).
thf(func_def_258,type,
sK119: ( term > $o ) > term ).
thf(func_def_259,type,
sK120: term > $o ).
thf(func_def_260,type,
sK121: term ).
thf(func_def_261,type,
sK122: ( term > $o ) > term ).
thf(func_def_262,type,
sK123: ( term > $o ) > term ).
thf(func_def_263,type,
sK124: ( term > $o ) > term ).
thf(func_def_264,type,
sK125: subst > ( term > $o ) > term ).
thf(func_def_265,type,
sK126: subst > ( term > $o ) > term ).
thf(func_def_266,type,
sK127: ( term > $o ) > term ).
thf(func_def_267,type,
sK128: subst > ( term > $o ) > term ).
thf(func_def_268,type,
sK129: subst > ( term > $o ) > term ).
thf(func_def_269,type,
sK130: subst > ( term > $o ) > term ).
thf(func_def_270,type,
sK131: term > $o ).
thf(func_def_271,type,
sK132: term > term ).
thf(func_def_272,type,
sK133: term ).
thf(func_def_273,type,
sK134: subst ).
thf(func_def_274,type,
sK135: term ).
thf(func_def_275,type,
sK136: term ).
thf(func_def_276,type,
sK137: subst ).
thf(func_def_277,type,
sK138: subst ).
thf(func_def_278,type,
sK139: subst ).
thf(func_def_279,type,
sK140: term ).
thf(func_def_280,type,
sK141: ( subst > term > subst > $o ) > term ).
thf(func_def_281,type,
sK142: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_282,type,
sK143: ( subst > term > subst > $o ) > subst ).
thf(func_def_283,type,
sK144: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_284,type,
sK145: ( subst > term > subst > $o ) > subst ).
thf(func_def_285,type,
sK146: ( subst > term > subst > $o ) > subst ).
thf(func_def_286,type,
sK147: term > ( term > $o ) > term ).
thf(func_def_287,type,
sK148: ( subst > term > subst > $o ) > subst ).
thf(func_def_288,type,
sK149: ( subst > term > subst > $o ) > subst ).
thf(func_def_289,type,
sK150: ( subst > term > subst > $o ) > term ).
thf(func_def_290,type,
sK151: ( subst > term > subst > $o ) > subst ).
thf(func_def_291,type,
sK152: ( subst > term > subst > $o ) > term ).
thf(func_def_292,type,
sK153: ( subst > term > subst > $o ) > subst ).
thf(func_def_293,type,
sK154: term > ( term > $o ) > term ).
thf(func_def_294,type,
sK155: ( subst > term > subst > $o ) > subst ).
thf(func_def_295,type,
sK156: ( subst > term > subst > $o ) > subst ).
thf(func_def_296,type,
sK157: ( subst > term > subst > $o ) > term ).
thf(func_def_297,type,
sK158: ( subst > term > subst > $o ) > subst ).
thf(func_def_298,type,
sK159: ( subst > term > subst > $o ) > subst ).
thf(func_def_299,type,
sK160: ( subst > term > subst > $o ) > term ).
thf(func_def_300,type,
sK161: ( subst > term > subst > $o ) > subst ).
thf(func_def_301,type,
sK162: term > ( term > $o ) > term ).
thf(func_def_302,type,
sK163: ( subst > term > subst > $o ) > subst ).
thf(func_def_303,type,
sK164: ( subst > term > subst > $o ) > subst ).
thf(func_def_304,type,
sK165: ( subst > term > subst > $o ) > subst ).
thf(func_def_305,type,
sK166: ( subst > term > subst > $o ) > term ).
thf(func_def_306,type,
sK167: ( subst > term > subst > $o ) > subst ).
thf(func_def_307,type,
sK168: ( subst > term > subst > $o ) > subst ).
thf(func_def_308,type,
sK169: ( subst > term > subst > $o ) > subst ).
thf(func_def_309,type,
sK170: ( subst > term > subst > $o ) > term ).
thf(func_def_310,type,
sK171: term > $o ).
thf(func_def_311,type,
sK172: subst > term > subst > $o ).
thf(func_def_312,type,
sK173: ( subst > term > term ) > term ).
thf(func_def_313,type,
sK174: ( subst > term > term ) > subst ).
thf(func_def_314,type,
sK175: ( subst > term > term ) > subst ).
thf(func_def_315,type,
sK176: ( subst > term > term ) > term ).
thf(func_def_316,type,
sK177: ( subst > term > term ) > subst ).
thf(func_def_317,type,
sK178: ( subst > term > term ) > term ).
thf(func_def_318,type,
sK179: term ).
thf(func_def_319,type,
sK180: subst ).
thf(func_def_320,type,
sK181: subst ).
thf(func_def_321,type,
sK182: subst ).
thf(func_def_322,type,
sK183: ( subst > term > subst > $o ) > subst ).
thf(func_def_323,type,
sK184: ( subst > term > subst > $o ) > subst ).
thf(func_def_324,type,
sK185: ( subst > term > subst > $o ) > term ).
thf(func_def_325,type,
sK186: ( subst > term > subst > $o ) > term ).
thf(func_def_326,type,
sK187: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_327,type,
sK188: ( subst > term > subst > $o ) > term ).
thf(func_def_328,type,
sK189: ( subst > term > subst > $o ) > term ).
thf(func_def_329,type,
sK190: ( subst > term > subst > $o ) > term ).
thf(func_def_330,type,
sK191: ( subst > term > subst > $o ) > subst ).
thf(func_def_331,type,
sK192: ( subst > term > subst > $o ) > subst ).
thf(func_def_332,type,
sK193: ( subst > term > subst > $o ) > subst ).
thf(func_def_333,type,
sK194: ( subst > term > subst > $o ) > subst ).
thf(func_def_334,type,
sK195: ( subst > term > subst > $o ) > subst ).
thf(func_def_335,type,
sK196: ( subst > term > subst > $o ) > subst ).
thf(func_def_336,type,
sK197: ( subst > term > subst > $o ) > subst ).
thf(func_def_337,type,
sK198: ( subst > term > subst > $o ) > subst ).
thf(func_def_338,type,
sK199: ( subst > term > subst > $o ) > subst ).
thf(func_def_339,type,
sK200: ( subst > term > subst > $o ) > subst ).
thf(func_def_340,type,
sK201: ( subst > term > subst > $o ) > subst ).
thf(func_def_341,type,
sK202: ( subst > term > subst > $o ) > subst ).
thf(func_def_342,type,
sK203: ( subst > term > subst > $o ) > subst ).
thf(func_def_343,type,
sK204: ( subst > term > subst > $o ) > subst ).
thf(func_def_344,type,
sK205: ( subst > term > subst > $o ) > subst ).
thf(func_def_345,type,
sK206: ( subst > term > subst > $o ) > subst ).
thf(func_def_346,type,
sK207: ( subst > term > subst > $o ) > subst ).
thf(func_def_347,type,
sK208: ( subst > term > subst > $o ) > subst ).
thf(func_def_348,type,
sK209: ( subst > term > subst > $o ) > subst ).
thf(func_def_349,type,
sK210: ( subst > term > subst > $o ) > subst ).
thf(func_def_350,type,
sK211: ( subst > term > subst > $o ) > term ).
thf(func_def_351,type,
sK212: ( subst > term > subst > $o ) > term ).
thf(func_def_352,type,
sK213: ( subst > term > subst > $o ) > subst ).
thf(func_def_353,type,
sK214: ( subst > term > subst > $o ) > subst ).
thf(func_def_354,type,
sK215: ( subst > term > subst > $o ) > subst ).
thf(func_def_355,type,
sK216: ( subst > term > subst > $o ) > subst ).
thf(func_def_356,type,
sK217: ( subst > term > subst > $o ) > subst ).
thf(func_def_357,type,
sK218: ( subst > term > subst > $o ) > subst ).
thf(func_def_358,type,
sK219: ( subst > term > subst > $o ) > subst ).
thf(func_def_359,type,
sK220: ( subst > term > subst > $o ) > subst ).
thf(func_def_360,type,
sK221: ( subst > term > subst > $o ) > subst ).
thf(func_def_361,type,
sK222: ( subst > term > subst > $o ) > subst ).
thf(func_def_362,type,
sK223: ( subst > term > subst > $o ) > subst ).
thf(func_def_363,type,
sK224: ( subst > term > subst > $o ) > subst ).
thf(func_def_364,type,
sK225: ( subst > term > subst > $o ) > subst ).
thf(func_def_365,type,
sK226: ( subst > term > subst > $o ) > subst ).
thf(func_def_366,type,
sK227: ( subst > term > subst > $o ) > subst ).
thf(func_def_367,type,
sK228: ( subst > term > subst > $o ) > subst ).
thf(func_def_368,type,
sK229: ( subst > term > subst > $o ) > subst ).
thf(func_def_369,type,
sK230: ( subst > term > subst > $o ) > subst ).
thf(func_def_370,type,
sK231: ( subst > term > subst > $o ) > subst ).
thf(func_def_371,type,
sK232: ( subst > term > subst > $o ) > subst ).
thf(func_def_372,type,
sK233: ( subst > term > subst > $o ) > subst ).
thf(func_def_373,type,
sK234: ( subst > term > subst > $o ) > subst ).
thf(func_def_374,type,
sK235: ( subst > term > subst > $o ) > subst ).
thf(func_def_375,type,
sK236: ( subst > term > subst > $o ) > subst ).
thf(func_def_376,type,
sK237: ( subst > term > subst > $o ) > subst ).
thf(func_def_377,type,
sK238: ( subst > term > subst > $o ) > subst ).
thf(func_def_378,type,
sK239: ( subst > term > subst > $o ) > subst ).
thf(func_def_379,type,
sK240: ( subst > term > subst > $o ) > subst ).
thf(func_def_380,type,
sK241: ( subst > term > subst > $o ) > subst ).
thf(func_def_381,type,
sK242: ( subst > term > subst > $o ) > subst ).
thf(func_def_382,type,
sK243: ( subst > term > subst > $o ) > subst ).
thf(func_def_383,type,
sK244: ( subst > term > subst > $o ) > subst ).
thf(func_def_384,type,
sK245: ( subst > term > subst > $o ) > subst ).
thf(func_def_385,type,
sK246: ( subst > term > subst > $o ) > subst ).
thf(func_def_386,type,
sK247: ( subst > term > subst > $o ) > subst ).
thf(func_def_387,type,
sK248: ( subst > term > subst > $o ) > subst ).
thf(func_def_388,type,
sK249: ( subst > term > subst > $o ) > subst ).
thf(func_def_389,type,
sK250: subst > term > subst > $o ).
thf(func_def_390,type,
sK251: ( subst > term > term ) > subst ).
thf(func_def_391,type,
sK252: ( subst > term > term ) > term ).
thf(func_def_392,type,
sK253: ( subst > term > term ) > term ).
thf(func_def_393,type,
sK254: ( subst > term > term ) > subst ).
thf(func_def_394,type,
sK255: ( subst > term > term ) > subst ).
thf(func_def_395,type,
sK256: term ).
thf(func_def_396,type,
sK257: subst > ( term > $o ) > term ).
thf(func_def_397,type,
sK258: term > $o ).
thf(func_def_398,type,
sK259: term ).
thf(func_def_399,type,
sK260: subst ).
thf(func_def_400,type,
sK261: term ).
thf(func_def_401,type,
sK262: ( term > $o ) > term ).
thf(func_def_402,type,
sK263: term > $o ).
thf(func_def_403,type,
sK264: term ).
thf(func_def_404,type,
sK265: term ).
thf(func_def_405,type,
sK266: term ).
thf(func_def_406,type,
sK267: term ).
thf(func_def_407,type,
sK268: term ).
thf(func_def_408,type,
sK269: term ).
thf(func_def_409,type,
sK270: term ).
thf(func_def_410,type,
sK271: term ).
thf(func_def_411,type,
sK272: term ).
thf(func_def_412,type,
sK273: subst ).
thf(func_def_413,type,
sK274: ( subst > term > term ) > subst ).
thf(func_def_414,type,
sK275: ( subst > term > term ) > subst ).
thf(func_def_415,type,
sK276: ( subst > term > term ) > term ).
thf(func_def_416,type,
sK277: subst > term > term ).
thf(func_def_417,type,
sK278: ( subst > term > term ) > subst ).
thf(func_def_418,type,
sK279: ( subst > term > term ) > term ).
thf(func_def_419,type,
sK280: ( subst > term > term ) > subst ).
thf(func_def_420,type,
sK281: subst > term > term ).
thf(func_def_421,type,
sK282: term ).
thf(func_def_422,type,
sK283: term ).
thf(func_def_423,type,
sK284: term ).
thf(func_def_424,type,
sK285: subst ).
thf(func_def_425,type,
sK286: ( subst > term > subst > $o ) > term ).
thf(func_def_426,type,
sK287: ( subst > term > subst > $o ) > subst ).
thf(func_def_427,type,
sK288: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_428,type,
sK289: ( subst > term > subst > $o ) > term ).
thf(func_def_429,type,
sK290: ( subst > term > subst > $o ) > subst ).
thf(func_def_430,type,
sK291: ( subst > term > subst > $o ) > term ).
thf(func_def_431,type,
sK292: ( subst > term > subst > $o ) > subst ).
thf(func_def_432,type,
sK293: ( subst > term > subst > $o ) > subst ).
thf(func_def_433,type,
sK294: ( subst > term > subst > $o ) > subst ).
thf(func_def_434,type,
sK295: ( subst > term > subst > $o ) > subst ).
thf(func_def_435,type,
sK296: ( subst > term > subst > $o ) > term ).
thf(func_def_436,type,
sK297: ( subst > term > subst > $o ) > subst ).
thf(func_def_437,type,
sK298: ( subst > term > subst > $o ) > subst ).
thf(func_def_438,type,
sK299: ( subst > term > subst > $o ) > subst ).
thf(func_def_439,type,
sK300: ( subst > term > subst > $o ) > subst ).
thf(func_def_440,type,
sK301: term > $o ).
thf(func_def_441,type,
sK302: subst > term > subst > $o ).
thf(func_def_442,type,
sK303: term ).
thf(f3,axiom,
( axvarid
= ( ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarid) ).
thf(f5,axiom,
( axclos
= ( ! [X0: term,X2: subst,X1: subst] :
( ( sub @ ( sub @ X0 @ X1 ) @ X2 )
= ( sub @ X0 @ ( comp @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axclos) ).
thf(f9,axiom,
( axmap
= ( ! [X0: term,X2: subst,X1: subst] :
( ( comp @ ( push @ X0 @ X1 ) @ X2 )
= ( push @ ( sub @ X0 @ X2 ) @ ( comp @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axmap) ).
thf(f11,axiom,
( axvarshift
= ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarshift) ).
thf(f56,axiom,
( ( ^ [X0: subst,X1: subst > term > term] : ( lam @ ( X1 @ sh @ one ) ) )
= hoaslam ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoaslam) ).
thf(f76,axiom,
( ( ^ [X0: subst > term > subst > $o,X1: term > $o] :
! [X2: term] :
( ( X1 @ X2 )
<=> ( X0 @ id @ X2 @ id ) ) )
= hoasinduction_p_and_p_prime ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasinduction_p_and_p_prime) ).
thf(f83,axiom,
( hoasinduction_lem3v2_f
= ( ! [X0: term] :
? [X1: subst > term > term] :
! [X3: subst,X2: term] :
( ( X1 @ X3 @ X2 )
= ( sub @ X0 @ ( push @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3v2_f) ).
thf(f84,axiom,
hoasinduction_lem3v2_f_lthm = hoasinduction_lem3v2_f,
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3v2_f_lthm) ).
thf(f88,axiom,
( hoasinduction_lem3v2a
= ( ! [X0: subst > term > subst > $o,X1: term > $o] :
( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X4: term] :
( ( X0 @ id @ X4 @ id )
=> ( X0 @ id @ ( X2 @ id @ X4 ) @ id ) )
=> ( X0 @ id
@ ( hoaslam @ id
@ ^ [X3: subst,X4: term] : ( X2 @ X3 @ X4 ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ X0 @ X1 )
=> ! [X4: term] :
( ! [X6: term] :
( ( X1 @ X6 )
=> ( X1 @ ( sub @ X4 @ ( push @ X6 @ id ) ) ) )
=> ( X1 @ ( lam @ X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3v2a) ).
thf(f89,axiom,
( hoasinduction_lem3v2_f
=> ( ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2a ) ) ) )
= hoasinduction_lem3v2a_lthm ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3v2a_lthm) ).
thf(f114,conjecture,
hoasinduction_lem3v2a_lthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ hoasinduction_lem3v2a_lthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f120,plain,
( hoasinduction_lem3v2a
= ( ! [X0: subst > term > subst > $o,X1: term > $o] :
( ! [X2: subst > term > term] :
( ! [X3: subst,X4: term,X5: subst] :
( ( sub @ ( X2 @ X3 @ X4 ) @ X5 )
= ( X2 @ ( comp @ X3 @ X5 ) @ ( sub @ X4 @ X5 ) ) )
=> ( ! [X6: term] :
( ( X0 @ id @ X6 @ id )
=> ( X0 @ id @ ( X2 @ id @ X6 ) @ id ) )
=> ( X0 @ id
@ ( hoaslam @ id
@ ^ [X7: subst,X8: term] : ( X2 @ X7 @ X8 ) )
@ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ X0 @ X1 )
=> ! [X9: term] :
( ! [X10: term] :
( ( X1 @ X10 )
=> ( X1 @ ( sub @ X9 @ ( push @ X10 @ id ) ) ) )
=> ( X1 @ ( lam @ X9 ) ) ) ) ) ) ),
inference(rectify,[],[f88]) ).
thf(f121,plain,
( hoasinduction_lem3v2a
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( sub @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ ( comp @ Y5 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( Y1 @ id @ ( Y2 @ id @ Y3 ) @ id ) ) )
=> ( Y1 @ id
@ ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y2 @ Y3 @ Y4 ) )
@ id ) ) ) )
=> ( ( hoasinduction_p_and_p_prime @ Y1 @ Y0 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( Y0 @ ( sub @ Y2 @ ( push @ Y3 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y2 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f120]) ).
thf(f137,plain,
( axmap
= ( ! [X0: term,X1: subst,X2: subst] :
( ( comp @ ( push @ X0 @ X2 ) @ X1 )
= ( push @ ( sub @ X0 @ X1 ) @ ( comp @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f138,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f137]) ).
thf(f145,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f159,plain,
( axclos
= ( ! [X0: term,X1: subst,X2: subst] :
( ( sub @ X0 @ ( comp @ X2 @ X1 ) )
= ( sub @ ( sub @ X0 @ X2 ) @ X1 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f160,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) )
= ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f159]) ).
thf(f183,plain,
~ hoasinduction_lem3v2a_lthm,
inference(rectify,[],[f115]) ).
thf(f184,plain,
hoasinduction_lem3v2a_lthm != $true,
inference(fool_elimination,[],[f183]) ).
thf(f229,plain,
( ( ^ [X0: subst > term > subst > $o,X1: term > $o] :
! [X2: term] :
( ( X1 @ X2 )
<=> ( X0 @ id @ X2 @ id ) ) )
= hoasinduction_p_and_p_prime ),
inference(rectify,[],[f76]) ).
thf(f230,plain,
( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) ),
inference(fool_elimination,[],[f229]) ).
thf(f231,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f236,plain,
( hoasinduction_lem3v2_f
= ( ! [X0: term] :
? [X1: subst > term > term] :
! [X2: subst,X3: term] :
( ( X1 @ X2 @ X3 )
= ( sub @ X0 @ ( push @ X3 @ X2 ) ) ) ) ),
inference(rectify,[],[f83]) ).
thf(f237,plain,
( hoasinduction_lem3v2_f
= ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( sub @ Y0 @ ( push @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f236]) ).
thf(f240,plain,
( hoasinduction_lem3v2_f
=> ( ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2a ) ) ) )
= hoasinduction_lem3v2a_lthm ) ),
inference(rectify,[],[f89]) ).
thf(f241,plain,
( hoasinduction_lem3v2a_lthm
= ( hoasinduction_lem3v2_f
=> ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2a ) ) ) ) ) ),
inference(fool_elimination,[],[f240]) ).
thf(f275,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f323,plain,
hoasinduction_lem3v2a_lthm != $true,
inference(flattening,[],[f184]) ).
thf(f334,plain,
hoasinduction_lem3v2a_lthm != $true,
inference(cnf_transformation,[],[f323]) ).
thf(f335,plain,
( hoasinduction_lem3v2a
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( sub @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ ( comp @ Y5 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( Y1 @ id @ ( Y2 @ id @ Y3 ) @ id ) ) )
=> ( Y1 @ id
@ ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y2 @ Y3 @ Y4 ) )
@ id ) ) ) )
=> ( ( hoasinduction_p_and_p_prime @ Y1 @ Y0 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( Y0 @ ( sub @ Y2 @ ( push @ Y3 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y2 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f121]) ).
thf(f339,plain,
( hoasinduction_lem3v2a_lthm
= ( hoasinduction_lem3v2_f
=> ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2a ) ) ) ) ) ),
inference(cnf_transformation,[],[f241]) ).
thf(f340,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(cnf_transformation,[],[f145]) ).
thf(f349,plain,
( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) ),
inference(cnf_transformation,[],[f230]) ).
thf(f352,plain,
hoasinduction_lem3v2_f = hoasinduction_lem3v2_f_lthm,
inference(cnf_transformation,[],[f84]) ).
thf(f353,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f231]) ).
thf(f355,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) )
= ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f160]) ).
thf(f361,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(cnf_transformation,[],[f275]) ).
thf(f363,plain,
( hoasinduction_lem3v2_f
= ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( sub @ Y0 @ ( push @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f237]) ).
thf(f365,plain,
( axmap
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f373,plain,
( hoasinduction_lem3v2a
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( sub @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ ( comp @ Y5 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( Y1 @ id @ ( Y2 @ id @ Y3 ) @ id ) ) )
=> ( Y1 @ id
@ ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y2 @ Y3 @ Y4 ) )
@ id ) ) ) )
=> ( ( ^ [Y2: subst > term > subst > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ id @ Y4 @ id ) ) )
@ Y1
@ Y0 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( Y0 @ ( sub @ Y2 @ ( push @ Y3 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y2 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f335,f361,f349]) ).
thf(f376,plain,
( hoasinduction_lem3v2a_lthm
= ( hoasinduction_lem3v2_f_lthm
=> ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2a ) ) ) ) ) ),
inference(definition_unfolding,[],[f339,f352]) ).
thf(f380,plain,
( hoasinduction_lem3v2_f_lthm
= ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( sub @ Y0 @ ( push @ Y2 @ Y3 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f363,f352]) ).
thf(f402,plain,
( ( hoasinduction_lem3v2a = $true )
| ( $false
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( sub @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ ( comp @ Y5 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( Y1 @ id @ ( Y2 @ id @ Y3 ) @ id ) ) )
=> ( Y1 @ id
@ ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y2 @ Y3 @ Y4 ) )
@ id ) ) ) )
=> ( ( ^ [Y2: subst > term > subst > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ id @ Y4 @ id ) ) )
@ Y1
@ Y0 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( Y0 @ ( sub @ Y2 @ ( push @ Y3 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f373]) ).
thf(f460,plain,
( ( hoasinduction_lem3v2a = $true )
| ( $false
= ( ^ [Y0: term > $o] :
( !! @ ( subst > term > subst > $o )
@ ^ [Y1: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y2: subst > term > term] :
( ( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( sub @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ ( comp @ Y5 @ Y3 ) @ ( sub @ Y4 @ Y3 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ id @ Y3 @ id )
=> ( Y1 @ id @ ( Y2 @ id @ Y3 ) @ id ) ) )
=> ( Y1 @ id
@ ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y2 @ Y3 @ Y4 ) )
@ id ) ) ) )
=> ( ( ^ [Y2: subst > term > subst > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ id @ Y4 @ id ) ) )
@ Y1
@ Y0 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ Y3 )
=> ( Y0 @ ( sub @ Y2 @ ( push @ Y3 @ id ) ) ) ) )
=> ( Y0 @ ( lam @ Y2 ) ) ) ) ) ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f402]) ).
thf(f461,plain,
( ( $false
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK6 @ Y1 )
= ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( sK6 @ Y2 )
=> ( sK6 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( sK6 @ ( lam @ Y1 ) ) ) ) ) ) ) )
| ( hoasinduction_lem3v2a = $true ) ),
inference(beta-eta_normalization,[],[f460]) ).
thf(f462,plain,
( ( $false
= ( ^ [Y0: subst > term > subst > $o] :
( ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sub @ ( Y1 @ Y4 @ Y3 ) @ Y2 )
= ( Y1 @ ( comp @ Y4 @ Y2 ) @ ( sub @ Y3 @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
=> ( Y0 @ id @ ( Y1 @ id @ Y2 ) @ id ) ) )
=> ( Y0 @ id @ ( lam @ ( Y1 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK6 @ Y1 )
= ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( !! @ term
@ ^ [Y2: term] :
( ( sK6 @ Y2 )
=> ( sK6 @ ( sub @ Y1 @ ( push @ Y2 @ id ) ) ) ) )
=> ( sK6 @ ( lam @ Y1 ) ) ) ) ) )
@ sK7 ) )
| ( hoasinduction_lem3v2a = $true ) ),
inference(sigma_proxy_clausification,[],[f461]) ).
thf(f463,plain,
( ( hoasinduction_lem3v2a = $true )
| ( $false
= ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK7 @ id @ Y1 @ id )
=> ( sK7 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK7 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK6 @ Y0 )
= ( sK7 @ id @ Y0 @ id ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK6 @ Y1 )
=> ( sK6 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( sK6 @ ( lam @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f462]) ).
thf(f464,plain,
( ( hoasinduction_lem3v2a = $true )
| ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK6 @ Y0 )
= ( sK7 @ id @ Y0 @ id ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK6 @ Y1 )
=> ( sK6 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( sK6 @ ( lam @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f463]) ).
thf(f465,plain,
( ( hoasinduction_lem3v2a = $true )
| ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK7 @ id @ Y1 @ id )
=> ( sK7 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK7 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f463]) ).
thf(f466,plain,
! [X1: subst > term > term] :
( ( hoasinduction_lem3v2a = $true )
| ( ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK7 @ id @ Y1 @ id )
=> ( sK7 @ id @ ( Y0 @ id @ Y1 ) @ id ) ) )
=> ( sK7 @ id @ ( lam @ ( Y0 @ sh @ one ) ) @ id ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f465]) ).
thf(f467,plain,
! [X1: subst > term > term] :
( ( $true
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( X1 @ Y2 @ Y1 ) @ Y0 )
= ( X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK7 @ id @ Y0 @ id )
=> ( sK7 @ id @ ( X1 @ id @ Y0 ) @ id ) ) )
=> ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) ) ) )
| ( hoasinduction_lem3v2a = $true ) ),
inference(beta-eta_normalization,[],[f466]) ).
thf(f468,plain,
! [X1: subst > term > term] :
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sK7 @ id @ Y0 @ id )
=> ( sK7 @ id @ ( X1 @ id @ Y0 ) @ id ) ) )
=> ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id ) )
= $true )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( X1 @ Y2 @ Y1 ) @ Y0 )
= ( X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) ) )
| ( hoasinduction_lem3v2a = $true ) ),
inference(imp_proxy_clausification,[],[f467]) ).
thf(f469,plain,
! [X1: subst > term > term] :
( ( hoasinduction_lem3v2a = $true )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( sK7 @ id @ Y0 @ id )
=> ( sK7 @ id @ ( X1 @ id @ Y0 ) @ id ) ) ) )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( X1 @ Y2 @ Y1 ) @ Y0 )
= ( X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f468]) ).
thf(f470,plain,
! [X1: subst > term > term] :
( ( hoasinduction_lem3v2a = $true )
| ( $false
= ( ^ [Y0: term] :
( ( sK7 @ id @ Y0 @ id )
=> ( sK7 @ id @ ( X1 @ id @ Y0 ) @ id ) )
@ ( sK8 @ X1 ) ) )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( X1 @ Y2 @ Y1 ) @ Y0 )
= ( X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) ) )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true ) ),
inference(sigma_proxy_clausification,[],[f469]) ).
thf(f471,plain,
! [X1: subst > term > term] :
( ( $false
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( X1 @ Y2 @ Y1 ) @ Y0 )
= ( X1 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) )
@ ( sK9 @ X1 ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( $false
= ( ^ [Y0: term] :
( ( sK7 @ id @ Y0 @ id )
=> ( sK7 @ id @ ( X1 @ id @ Y0 ) @ id ) )
@ ( sK8 @ X1 ) ) )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true ) ),
inference(sigma_proxy_clausification,[],[f470]) ).
thf(f472,plain,
! [X1: subst > term > term] :
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( X1 @ Y1 @ Y0 ) @ ( sK9 @ X1 ) )
= ( X1 @ ( comp @ Y1 @ ( sK9 @ X1 ) ) @ ( sub @ Y0 @ ( sK9 @ X1 ) ) ) ) ) ) )
| ( $false
= ( ( sK7 @ id @ ( sK8 @ X1 ) @ id )
=> ( sK7 @ id @ ( X1 @ id @ ( sK8 @ X1 ) ) @ id ) ) )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true )
| ( hoasinduction_lem3v2a = $true ) ),
inference(beta-eta_normalization,[],[f471]) ).
thf(f473,plain,
! [X1: subst > term > term] :
( ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true )
| ( $false
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( X1 @ Y1 @ Y0 ) @ ( sK9 @ X1 ) )
= ( X1 @ ( comp @ Y1 @ ( sK9 @ X1 ) ) @ ( sub @ Y0 @ ( sK9 @ X1 ) ) ) ) )
@ ( sK10 @ X1 ) ) )
| ( $false
= ( ( sK7 @ id @ ( sK8 @ X1 ) @ id )
=> ( sK7 @ id @ ( X1 @ id @ ( sK8 @ X1 ) ) @ id ) ) )
| ( hoasinduction_lem3v2a = $true ) ),
inference(sigma_proxy_clausification,[],[f472]) ).
thf(f474,plain,
! [X1: subst > term > term] :
( ( $false
= ( sK7 @ id @ ( X1 @ id @ ( sK8 @ X1 ) ) @ id ) )
| ( hoasinduction_lem3v2a = $true )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true )
| ( $false
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( X1 @ Y1 @ Y0 ) @ ( sK9 @ X1 ) )
= ( X1 @ ( comp @ Y1 @ ( sK9 @ X1 ) ) @ ( sub @ Y0 @ ( sK9 @ X1 ) ) ) ) )
@ ( sK10 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f473]) ).
thf(f475,plain,
! [X1: subst > term > term] :
( ( ( sK7 @ id @ ( sK8 @ X1 ) @ id )
= $true )
| ( hoasinduction_lem3v2a = $true )
| ( $false
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( X1 @ Y1 @ Y0 ) @ ( sK9 @ X1 ) )
= ( X1 @ ( comp @ Y1 @ ( sK9 @ X1 ) ) @ ( sub @ Y0 @ ( sK9 @ X1 ) ) ) ) )
@ ( sK10 @ X1 ) ) )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true ) ),
inference(imp_proxy_clausification,[],[f473]) ).
thf(f476,plain,
! [X1: subst > term > term] :
( ( ( sK7 @ id @ ( sK8 @ X1 ) @ id )
= $true )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ ( X1 @ Y0 @ ( sK10 @ X1 ) ) @ ( sK9 @ X1 ) )
= ( X1 @ ( comp @ Y0 @ ( sK9 @ X1 ) ) @ ( sub @ ( sK10 @ X1 ) @ ( sK9 @ X1 ) ) ) ) ) )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true )
| ( hoasinduction_lem3v2a = $true ) ),
inference(beta-eta_normalization,[],[f475]) ).
thf(f477,plain,
! [X1: subst > term > term] :
( ( ( sK7 @ id @ ( sK8 @ X1 ) @ id )
= $true )
| ( $false
= ( ^ [Y0: subst] :
( ( sub @ ( X1 @ Y0 @ ( sK10 @ X1 ) ) @ ( sK9 @ X1 ) )
= ( X1 @ ( comp @ Y0 @ ( sK9 @ X1 ) ) @ ( sub @ ( sK10 @ X1 ) @ ( sK9 @ X1 ) ) ) )
@ ( sK11 @ X1 ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true ) ),
inference(sigma_proxy_clausification,[],[f476]) ).
thf(f478,plain,
! [X1: subst > term > term] :
( ( ( sK7 @ id @ ( sK8 @ X1 ) @ id )
= $true )
| ( hoasinduction_lem3v2a = $true )
| ( $false
= ( ( sub @ ( X1 @ ( sK11 @ X1 ) @ ( sK10 @ X1 ) ) @ ( sK9 @ X1 ) )
= ( X1 @ ( comp @ ( sK11 @ X1 ) @ ( sK9 @ X1 ) ) @ ( sub @ ( sK10 @ X1 ) @ ( sK9 @ X1 ) ) ) ) )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true ) ),
inference(beta-eta_normalization,[],[f477]) ).
thf(f479,plain,
! [X1: subst > term > term] :
( ( ( sK7 @ id @ ( sK8 @ X1 ) @ id )
= $true )
| ( ( sub @ ( X1 @ ( sK11 @ X1 ) @ ( sK10 @ X1 ) ) @ ( sK9 @ X1 ) )
!= ( X1 @ ( comp @ ( sK11 @ X1 ) @ ( sK9 @ X1 ) ) @ ( sub @ ( sK10 @ X1 ) @ ( sK9 @ X1 ) ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true ) ),
inference(equality_proxy_clausification,[],[f478]) ).
thf(f480,plain,
! [X1: subst > term > term] :
( ( $false
= ( sK7 @ id @ ( X1 @ id @ ( sK8 @ X1 ) ) @ id ) )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true )
| ( hoasinduction_lem3v2a = $true )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ ( X1 @ Y0 @ ( sK10 @ X1 ) ) @ ( sK9 @ X1 ) )
= ( X1 @ ( comp @ Y0 @ ( sK9 @ X1 ) ) @ ( sub @ ( sK10 @ X1 ) @ ( sK9 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f474]) ).
thf(f481,plain,
! [X1: subst > term > term] :
( ( $false
= ( sK7 @ id @ ( X1 @ id @ ( sK8 @ X1 ) ) @ id ) )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true )
| ( hoasinduction_lem3v2a = $true )
| ( $false
= ( ^ [Y0: subst] :
( ( sub @ ( X1 @ Y0 @ ( sK10 @ X1 ) ) @ ( sK9 @ X1 ) )
= ( X1 @ ( comp @ Y0 @ ( sK9 @ X1 ) ) @ ( sub @ ( sK10 @ X1 ) @ ( sK9 @ X1 ) ) ) )
@ ( sK12 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f480]) ).
thf(f482,plain,
! [X1: subst > term > term] :
( ( $false
= ( sK7 @ id @ ( X1 @ id @ ( sK8 @ X1 ) ) @ id ) )
| ( hoasinduction_lem3v2a = $true )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true )
| ( $false
= ( ( sub @ ( X1 @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) ) @ ( sK9 @ X1 ) )
= ( X1 @ ( comp @ ( sK12 @ X1 ) @ ( sK9 @ X1 ) ) @ ( sub @ ( sK10 @ X1 ) @ ( sK9 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f481]) ).
thf(f483,plain,
! [X1: subst > term > term] :
( ( ( X1 @ ( comp @ ( sK12 @ X1 ) @ ( sK9 @ X1 ) ) @ ( sub @ ( sK10 @ X1 ) @ ( sK9 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) ) @ ( sK9 @ X1 ) ) )
| ( hoasinduction_lem3v2a = $true )
| ( $false
= ( sK7 @ id @ ( X1 @ id @ ( sK8 @ X1 ) ) @ id ) )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true ) ),
inference(equality_proxy_clausification,[],[f482]) ).
thf(f484,plain,
( ( hoasinduction_lem3v2a = $true )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK6 @ Y1 )
=> ( sK6 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( sK6 @ ( lam @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f464]) ).
thf(f485,plain,
( ( hoasinduction_lem3v2a = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK6 @ Y0 )
= ( sK7 @ id @ Y0 @ id ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f464]) ).
thf(f486,plain,
! [X1: term] :
( ( ( ^ [Y0: term] :
( ( sK6 @ Y0 )
= ( sK7 @ id @ Y0 @ id ) )
@ X1 )
= $true )
| ( hoasinduction_lem3v2a = $true ) ),
inference(pi_proxy_clausification,[],[f485]) ).
thf(f487,plain,
! [X1: term] :
( ( hoasinduction_lem3v2a = $true )
| ( $true
= ( ( sK6 @ X1 )
= ( sK7 @ id @ X1 @ id ) ) ) ),
inference(beta-eta_normalization,[],[f486]) ).
thf(f488,plain,
! [X1: term] :
( ( ( sK7 @ id @ X1 @ id )
= ( sK6 @ X1 ) )
| ( hoasinduction_lem3v2a = $true ) ),
inference(iff_proxy_clausification,[],[f487]) ).
thf(f489,plain,
! [X1: term] :
( ( ( sK7 @ id @ X1 @ id )
= $true )
| ( $false
= ( sK6 @ X1 ) )
| ( hoasinduction_lem3v2a = $true ) ),
inference(iff_proxy_clausification,[],[f488]) ).
thf(f490,plain,
! [X1: term] :
( ( $true
= ( sK6 @ X1 ) )
| ( hoasinduction_lem3v2a = $true )
| ( $false
= ( sK7 @ id @ X1 @ id ) ) ),
inference(iff_proxy_clausification,[],[f488]) ).
thf(f491,plain,
( ( $false
= ( ^ [Y0: term] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK6 @ Y1 )
=> ( sK6 @ ( sub @ Y0 @ ( push @ Y1 @ id ) ) ) ) )
=> ( sK6 @ ( lam @ Y0 ) ) )
@ sK13 ) )
| ( hoasinduction_lem3v2a = $true ) ),
inference(sigma_proxy_clausification,[],[f484]) ).
thf(f492,plain,
( ( hoasinduction_lem3v2a = $true )
| ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK6 @ Y0 )
=> ( sK6 @ ( sub @ sK13 @ ( push @ Y0 @ id ) ) ) ) )
=> ( sK6 @ ( lam @ sK13 ) ) ) ) ),
inference(beta-eta_normalization,[],[f491]) ).
thf(f493,plain,
( ( hoasinduction_lem3v2a = $true )
| ( $false
= ( sK6 @ ( lam @ sK13 ) ) ) ),
inference(imp_proxy_clausification,[],[f492]) ).
thf(f494,plain,
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sK6 @ Y0 )
=> ( sK6 @ ( sub @ sK13 @ ( push @ Y0 @ id ) ) ) ) ) )
| ( hoasinduction_lem3v2a = $true ) ),
inference(imp_proxy_clausification,[],[f492]) ).
thf(f495,plain,
! [X1: term] :
( ( hoasinduction_lem3v2a = $true )
| ( $true
= ( ^ [Y0: term] :
( ( sK6 @ Y0 )
=> ( sK6 @ ( sub @ sK13 @ ( push @ Y0 @ id ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f494]) ).
thf(f496,plain,
! [X1: term] :
( ( hoasinduction_lem3v2a = $true )
| ( $true
= ( ( sK6 @ X1 )
=> ( sK6 @ ( sub @ sK13 @ ( push @ X1 @ id ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f495]) ).
thf(f497,plain,
! [X1: term] :
( ( $false
= ( sK6 @ X1 ) )
| ( hoasinduction_lem3v2a = $true )
| ( $true
= ( sK6 @ ( sub @ sK13 @ ( push @ X1 @ id ) ) ) ) ),
inference(imp_proxy_clausification,[],[f496]) ).
thf(f589,plain,
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( sub @ Y0 @ ( push @ Y2 @ Y3 ) ) ) ) ) ) ) )
| ( hoasinduction_lem3v2_f_lthm = $false ) ),
inference(iff_proxy_clausification,[],[f380]) ).
thf(f590,plain,
! [X1: term] :
( ( hoasinduction_lem3v2_f_lthm = $false )
| ( $true
= ( ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y1 @ Y3 @ Y2 )
= ( sub @ Y0 @ ( push @ Y2 @ Y3 ) ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f589]) ).
thf(f591,plain,
! [X1: term] :
( ( hoasinduction_lem3v2_f_lthm = $false )
| ( ( ?? @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( Y0 @ Y2 @ Y1 )
= ( sub @ X1 @ ( push @ Y1 @ Y2 ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f590]) ).
thf(f592,plain,
! [X1: term] :
( ( hoasinduction_lem3v2_f_lthm = $false )
| ( ( ^ [Y0: subst > term > term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( Y0 @ Y2 @ Y1 )
= ( sub @ X1 @ ( push @ Y1 @ Y2 ) ) ) ) )
@ ( sK25 @ X1 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f591]) ).
thf(f593,plain,
! [X1: term] :
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK25 @ X1 @ Y1 @ Y0 )
= ( sub @ X1 @ ( push @ Y0 @ Y1 ) ) ) ) ) )
| ( hoasinduction_lem3v2_f_lthm = $false ) ),
inference(beta-eta_normalization,[],[f592]) ).
thf(f594,plain,
! [X2: term,X1: term] :
( ( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK25 @ X1 @ Y1 @ Y0 )
= ( sub @ X1 @ ( push @ Y0 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( hoasinduction_lem3v2_f_lthm = $false ) ),
inference(pi_proxy_clausification,[],[f593]) ).
thf(f595,plain,
! [X2: term,X1: term] :
( ( hoasinduction_lem3v2_f_lthm = $false )
| ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( ( sK25 @ X1 @ Y0 @ X2 )
= ( sub @ X1 @ ( push @ X2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f594]) ).
thf(f596,plain,
! [X2: term,X3: subst,X1: term] :
( ( $true
= ( ^ [Y0: subst] :
( ( sK25 @ X1 @ Y0 @ X2 )
= ( sub @ X1 @ ( push @ X2 @ Y0 ) ) )
@ X3 ) )
| ( hoasinduction_lem3v2_f_lthm = $false ) ),
inference(pi_proxy_clausification,[],[f595]) ).
thf(f597,plain,
! [X2: term,X3: subst,X1: term] :
( ( ( ( sK25 @ X1 @ X3 @ X2 )
= ( sub @ X1 @ ( push @ X2 @ X3 ) ) )
= $true )
| ( hoasinduction_lem3v2_f_lthm = $false ) ),
inference(beta-eta_normalization,[],[f596]) ).
thf(f598,plain,
! [X2: term,X3: subst,X1: term] :
( ( ( sK25 @ X1 @ X3 @ X2 )
= ( sub @ X1 @ ( push @ X2 @ X3 ) ) )
| ( hoasinduction_lem3v2_f_lthm = $false ) ),
inference(equality_proxy_clausification,[],[f597]) ).
thf(f609,plain,
( ( $true
= ( id
= ( push @ one @ sh ) ) )
| ( axvarshift = $false ) ),
inference(iff_proxy_clausification,[],[f340]) ).
thf(f610,plain,
( ( axvarshift = $false )
| ( id
= ( push @ one @ sh ) ) ),
inference(equality_proxy_clausification,[],[f609]) ).
thf(f612,plain,
( ( hoasinduction_lem3v2a_lthm = $true )
| ( $false
= ( hoasinduction_lem3v2_f_lthm
=> ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2a ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f376]) ).
thf(f619,plain,
( ( $false
= ( axvarid
=> ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2a ) ) ) ) )
| ( hoasinduction_lem3v2a_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f612]) ).
thf(f620,plain,
( ( hoasinduction_lem3v2_f_lthm = $true )
| ( hoasinduction_lem3v2a_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f612]) ).
thf(f621,plain,
( ( $false
= ( axvarshift
=> ( axclos
=> ( axmap
=> hoasinduction_lem3v2a ) ) ) )
| ( hoasinduction_lem3v2a_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f619]) ).
thf(f622,plain,
( ( axvarid = $true )
| ( hoasinduction_lem3v2a_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f619]) ).
thf(f623,plain,
( ( hoasinduction_lem3v2a_lthm = $true )
| ( $false
= ( axclos
=> ( axmap
=> hoasinduction_lem3v2a ) ) ) ),
inference(imp_proxy_clausification,[],[f621]) ).
thf(f624,plain,
( ( axvarshift = $true )
| ( hoasinduction_lem3v2a_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f621]) ).
thf(f625,plain,
( ( hoasinduction_lem3v2a_lthm = $true )
| ( $false
= ( axmap
=> hoasinduction_lem3v2a ) ) ),
inference(imp_proxy_clausification,[],[f623]) ).
thf(f626,plain,
( ( hoasinduction_lem3v2a_lthm = $true )
| ( axclos = $true ) ),
inference(imp_proxy_clausification,[],[f623]) ).
thf(f627,plain,
( ( hoasinduction_lem3v2a_lthm = $true )
| ( hoasinduction_lem3v2a = $false ) ),
inference(imp_proxy_clausification,[],[f625]) ).
thf(f628,plain,
( ( axmap = $true )
| ( hoasinduction_lem3v2a_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f625]) ).
thf(f657,plain,
( ( axclos = $false )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) )
= ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f355]) ).
thf(f658,plain,
! [X1: subst] :
( ( $true
= ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ Y2 @ ( comp @ Y0 @ Y1 ) )
= ( sub @ ( sub @ Y2 @ Y0 ) @ Y1 ) ) ) )
@ X1 ) )
| ( axclos = $false ) ),
inference(pi_proxy_clausification,[],[f657]) ).
thf(f659,plain,
! [X1: subst] :
( ( axclos = $false )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ Y1 @ ( comp @ X1 @ Y0 ) )
= ( sub @ ( sub @ Y1 @ X1 ) @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f658]) ).
thf(f660,plain,
! [X2: subst,X1: subst] :
( ( $true
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ Y1 @ ( comp @ X1 @ Y0 ) )
= ( sub @ ( sub @ Y1 @ X1 ) @ Y0 ) ) )
@ X2 ) )
| ( axclos = $false ) ),
inference(pi_proxy_clausification,[],[f659]) ).
thf(f661,plain,
! [X2: subst,X1: subst] :
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ ( comp @ X1 @ X2 ) )
= ( sub @ ( sub @ Y0 @ X1 ) @ X2 ) ) ) )
| ( axclos = $false ) ),
inference(beta-eta_normalization,[],[f660]) ).
thf(f662,plain,
! [X2: subst,X3: term,X1: subst] :
( ( ( ^ [Y0: term] :
( ( sub @ Y0 @ ( comp @ X1 @ X2 ) )
= ( sub @ ( sub @ Y0 @ X1 ) @ X2 ) )
@ X3 )
= $true )
| ( axclos = $false ) ),
inference(pi_proxy_clausification,[],[f661]) ).
thf(f663,plain,
! [X2: subst,X3: term,X1: subst] :
( ( $true
= ( ( sub @ X3 @ ( comp @ X1 @ X2 ) )
= ( sub @ ( sub @ X3 @ X1 ) @ X2 ) ) )
| ( axclos = $false ) ),
inference(beta-eta_normalization,[],[f662]) ).
thf(f664,plain,
! [X2: subst,X3: term,X1: subst] :
( ( ( sub @ ( sub @ X3 @ X1 ) @ X2 )
= ( sub @ X3 @ ( comp @ X1 @ X2 ) ) )
| ( axclos = $false ) ),
inference(equality_proxy_clausification,[],[f663]) ).
thf(f1234,plain,
( ( axvarid = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ) ),
inference(iff_proxy_clausification,[],[f353]) ).
thf(f1235,plain,
! [X1: term] :
( ( axvarid = $false )
| ( ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1234]) ).
thf(f1236,plain,
! [X1: term] :
( ( $true
= ( ( sub @ X1 @ id )
= X1 ) )
| ( axvarid = $false ) ),
inference(beta-eta_normalization,[],[f1235]) ).
thf(f1237,plain,
! [X1: term] :
( ( axvarid = $false )
| ( ( sub @ X1 @ id )
= X1 ) ),
inference(equality_proxy_clausification,[],[f1236]) ).
thf(f1254,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ( axmap = $false ) ),
inference(iff_proxy_clausification,[],[f365]) ).
thf(f1255,plain,
! [X1: subst] :
( ( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( comp @ ( push @ Y2 @ Y0 ) @ Y1 )
= ( push @ ( sub @ Y2 @ Y1 ) @ ( comp @ Y0 @ Y1 ) ) ) ) )
@ X1 )
= $true )
| ( axmap = $false ) ),
inference(pi_proxy_clausification,[],[f1254]) ).
thf(f1256,plain,
! [X1: subst] :
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ ( push @ Y1 @ X1 ) @ Y0 )
= ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ X1 @ Y0 ) ) ) ) )
= $true )
| ( axmap = $false ) ),
inference(beta-eta_normalization,[],[f1255]) ).
thf(f1257,plain,
! [X2: subst,X1: subst] :
( ( axmap = $false )
| ( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ ( push @ Y1 @ X1 ) @ Y0 )
= ( push @ ( sub @ Y1 @ Y0 ) @ ( comp @ X1 @ Y0 ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1256]) ).
thf(f1258,plain,
! [X2: subst,X1: subst] :
( ( ( !! @ term
@ ^ [Y0: term] :
( ( comp @ ( push @ Y0 @ X1 ) @ X2 )
= ( push @ ( sub @ Y0 @ X2 ) @ ( comp @ X1 @ X2 ) ) ) )
= $true )
| ( axmap = $false ) ),
inference(beta-eta_normalization,[],[f1257]) ).
thf(f1259,plain,
! [X2: subst,X3: term,X1: subst] :
( ( axmap = $false )
| ( $true
= ( ^ [Y0: term] :
( ( comp @ ( push @ Y0 @ X1 ) @ X2 )
= ( push @ ( sub @ Y0 @ X2 ) @ ( comp @ X1 @ X2 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1258]) ).
thf(f1260,plain,
! [X2: subst,X3: term,X1: subst] :
( ( ( ( comp @ ( push @ X3 @ X1 ) @ X2 )
= ( push @ ( sub @ X3 @ X2 ) @ ( comp @ X1 @ X2 ) ) )
= $true )
| ( axmap = $false ) ),
inference(beta-eta_normalization,[],[f1259]) ).
thf(f1261,plain,
! [X2: subst,X3: term,X1: subst] :
( ( ( push @ ( sub @ X3 @ X2 ) @ ( comp @ X1 @ X2 ) )
= ( comp @ ( push @ X3 @ X1 ) @ X2 ) )
| ( axmap = $false ) ),
inference(equality_proxy_clausification,[],[f1260]) ).
thf(f2224,definition,
( spl304_9
<=> ( hoasinduction_lem3v2a = $false ) ),
introduced(definition,[new_symbols(definition,[spl304_9])],[avatar_definition]) ).
thf(f2226,plain,
( ( hoasinduction_lem3v2a = $false )
| ~ spl304_9 ),
inference(avatar_component_clause,[],[f2224]) ).
thf(f2276,definition,
( spl304_22
<=> ! [X1: subst > term > term] :
( ( ( sK7 @ id @ ( sK8 @ X1 ) @ id )
= $true )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true )
| ( ( sub @ ( X1 @ ( sK11 @ X1 ) @ ( sK10 @ X1 ) ) @ ( sK9 @ X1 ) )
!= ( X1 @ ( comp @ ( sK11 @ X1 ) @ ( sK9 @ X1 ) ) @ ( sub @ ( sK10 @ X1 ) @ ( sK9 @ X1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl304_22])],[avatar_definition]) ).
thf(f2277,plain,
( ! [X1: subst > term > term] :
( ( ( sub @ ( X1 @ ( sK11 @ X1 ) @ ( sK10 @ X1 ) ) @ ( sK9 @ X1 ) )
!= ( X1 @ ( comp @ ( sK11 @ X1 ) @ ( sK9 @ X1 ) ) @ ( sub @ ( sK10 @ X1 ) @ ( sK9 @ X1 ) ) ) )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true )
| ( ( sK7 @ id @ ( sK8 @ X1 ) @ id )
= $true ) )
| ~ spl304_22 ),
inference(avatar_component_clause,[],[f2276]) ).
thf(f2279,definition,
( spl304_23
<=> ( hoasinduction_lem3v2a = $true ) ),
introduced(definition,[new_symbols(definition,[spl304_23])],[avatar_definition]) ).
thf(f2281,plain,
( ( hoasinduction_lem3v2a = $true )
| ~ spl304_23 ),
inference(avatar_component_clause,[],[f2279]) ).
thf(f2282,plain,
( spl304_22
| spl304_23 ),
inference(avatar_split_clause,[],[f479,f2279,f2276]) ).
thf(f2284,definition,
( spl304_24
<=> ! [X1: subst > term > term] :
( ( ( X1 @ ( comp @ ( sK12 @ X1 ) @ ( sK9 @ X1 ) ) @ ( sub @ ( sK10 @ X1 ) @ ( sK9 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) ) @ ( sK9 @ X1 ) ) )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true )
| ( $false
= ( sK7 @ id @ ( X1 @ id @ ( sK8 @ X1 ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(definition,[spl304_24])],[avatar_definition]) ).
thf(f2285,plain,
( ! [X1: subst > term > term] :
( ( ( X1 @ ( comp @ ( sK12 @ X1 ) @ ( sK9 @ X1 ) ) @ ( sub @ ( sK10 @ X1 ) @ ( sK9 @ X1 ) ) )
!= ( sub @ ( X1 @ ( sK12 @ X1 ) @ ( sK10 @ X1 ) ) @ ( sK9 @ X1 ) ) )
| ( $false
= ( sK7 @ id @ ( X1 @ id @ ( sK8 @ X1 ) ) @ id ) )
| ( ( sK7 @ id @ ( lam @ ( X1 @ sh @ one ) ) @ id )
= $true ) )
| ~ spl304_24 ),
inference(avatar_component_clause,[],[f2284]) ).
thf(f2286,plain,
( spl304_23
| spl304_24 ),
inference(avatar_split_clause,[],[f483,f2284,f2279]) ).
thf(f2288,definition,
( spl304_25
<=> ! [X1: term] :
( ( $true
= ( sK6 @ X1 ) )
| ( $false
= ( sK7 @ id @ X1 @ id ) ) ) ),
introduced(definition,[new_symbols(definition,[spl304_25])],[avatar_definition]) ).
thf(f2289,plain,
( ! [X1: term] :
( ( $false
= ( sK7 @ id @ X1 @ id ) )
| ( $true
= ( sK6 @ X1 ) ) )
| ~ spl304_25 ),
inference(avatar_component_clause,[],[f2288]) ).
thf(f2290,plain,
( spl304_23
| spl304_25 ),
inference(avatar_split_clause,[],[f490,f2288,f2279]) ).
thf(f2292,definition,
( spl304_26
<=> ! [X1: term] :
( ( ( sK7 @ id @ X1 @ id )
= $true )
| ( $false
= ( sK6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl304_26])],[avatar_definition]) ).
thf(f2293,plain,
( ! [X1: term] :
( ( ( sK7 @ id @ X1 @ id )
= $true )
| ( $false
= ( sK6 @ X1 ) ) )
| ~ spl304_26 ),
inference(avatar_component_clause,[],[f2292]) ).
thf(f2294,plain,
( spl304_23
| spl304_26 ),
inference(avatar_split_clause,[],[f489,f2292,f2279]) ).
thf(f2296,definition,
( spl304_27
<=> ! [X1: term] :
( ( $false
= ( sK6 @ X1 ) )
| ( $true
= ( sK6 @ ( sub @ sK13 @ ( push @ X1 @ id ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl304_27])],[avatar_definition]) ).
thf(f2297,plain,
( ! [X1: term] :
( ( $true
= ( sK6 @ ( sub @ sK13 @ ( push @ X1 @ id ) ) ) )
| ( $false
= ( sK6 @ X1 ) ) )
| ~ spl304_27 ),
inference(avatar_component_clause,[],[f2296]) ).
thf(f2298,plain,
( spl304_23
| spl304_27 ),
inference(avatar_split_clause,[],[f497,f2296,f2279]) ).
thf(f2300,definition,
( spl304_28
<=> ( $false
= ( sK6 @ ( lam @ sK13 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl304_28])],[avatar_definition]) ).
thf(f2302,plain,
( ( $false
= ( sK6 @ ( lam @ sK13 ) ) )
| ~ spl304_28 ),
inference(avatar_component_clause,[],[f2300]) ).
thf(f2303,plain,
( spl304_28
| spl304_23 ),
inference(avatar_split_clause,[],[f493,f2279,f2300]) ).
thf(f2404,definition,
( spl304_53
<=> ! [X2: term,X1: term,X3: subst] :
( ( sK25 @ X1 @ X3 @ X2 )
= ( sub @ X1 @ ( push @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl304_53])],[avatar_definition]) ).
thf(f2405,plain,
( ! [X2: term,X3: subst,X1: term] :
( ( sK25 @ X1 @ X3 @ X2 )
= ( sub @ X1 @ ( push @ X2 @ X3 ) ) )
| ~ spl304_53 ),
inference(avatar_component_clause,[],[f2404]) ).
thf(f2407,definition,
( spl304_54
<=> ( hoasinduction_lem3v2_f_lthm = $false ) ),
introduced(definition,[new_symbols(definition,[spl304_54])],[avatar_definition]) ).
thf(f2409,plain,
( ( hoasinduction_lem3v2_f_lthm = $false )
| ~ spl304_54 ),
inference(avatar_component_clause,[],[f2407]) ).
thf(f2410,plain,
( spl304_53
| spl304_54 ),
inference(avatar_split_clause,[],[f598,f2407,f2404]) ).
thf(f2412,definition,
( spl304_55
<=> ( hoasinduction_lem3v2_f_lthm = $true ) ),
introduced(definition,[new_symbols(definition,[spl304_55])],[avatar_definition]) ).
thf(f2414,plain,
( ( hoasinduction_lem3v2_f_lthm = $true )
| ~ spl304_55 ),
inference(avatar_component_clause,[],[f2412]) ).
thf(f2420,definition,
( spl304_57
<=> ( id
= ( push @ one @ sh ) ) ),
introduced(definition,[new_symbols(definition,[spl304_57])],[avatar_definition]) ).
thf(f2422,plain,
( ( id
= ( push @ one @ sh ) )
| ~ spl304_57 ),
inference(avatar_component_clause,[],[f2420]) ).
thf(f2424,definition,
( spl304_58
<=> ( axvarshift = $false ) ),
introduced(definition,[new_symbols(definition,[spl304_58])],[avatar_definition]) ).
thf(f2426,plain,
( ( axvarshift = $false )
| ~ spl304_58 ),
inference(avatar_component_clause,[],[f2424]) ).
thf(f2427,plain,
( spl304_57
| spl304_58 ),
inference(avatar_split_clause,[],[f610,f2424,f2420]) ).
thf(f2429,definition,
( spl304_59
<=> ( axvarshift = $true ) ),
introduced(definition,[new_symbols(definition,[spl304_59])],[avatar_definition]) ).
thf(f2431,plain,
( ( axvarshift = $true )
| ~ spl304_59 ),
inference(avatar_component_clause,[],[f2429]) ).
thf(f2434,definition,
( spl304_60
<=> ( axmap = $false ) ),
introduced(definition,[new_symbols(definition,[spl304_60])],[avatar_definition]) ).
thf(f2436,plain,
( ( axmap = $false )
| ~ spl304_60 ),
inference(avatar_component_clause,[],[f2434]) ).
thf(f2438,definition,
( spl304_61
<=> ( axvarid = $false ) ),
introduced(definition,[new_symbols(definition,[spl304_61])],[avatar_definition]) ).
thf(f2440,plain,
( ( axvarid = $false )
| ~ spl304_61 ),
inference(avatar_component_clause,[],[f2438]) ).
thf(f2446,definition,
( spl304_63
<=> ( axclos = $false ) ),
introduced(definition,[new_symbols(definition,[spl304_63])],[avatar_definition]) ).
thf(f2448,plain,
( ( axclos = $false )
| ~ spl304_63 ),
inference(avatar_component_clause,[],[f2446]) ).
thf(f2451,definition,
( spl304_64
<=> ( hoasinduction_lem3v2a_lthm = $true ) ),
introduced(definition,[new_symbols(definition,[spl304_64])],[avatar_definition]) ).
thf(f2454,plain,
( spl304_64
| spl304_55 ),
inference(avatar_split_clause,[],[f620,f2412,f2451]) ).
thf(f2456,definition,
( spl304_65
<=> ( axvarid = $true ) ),
introduced(definition,[new_symbols(definition,[spl304_65])],[avatar_definition]) ).
thf(f2458,plain,
( ( axvarid = $true )
| ~ spl304_65 ),
inference(avatar_component_clause,[],[f2456]) ).
thf(f2459,plain,
( spl304_64
| spl304_65 ),
inference(avatar_split_clause,[],[f622,f2456,f2451]) ).
thf(f2460,plain,
( spl304_64
| spl304_59 ),
inference(avatar_split_clause,[],[f624,f2429,f2451]) ).
thf(f2462,definition,
( spl304_66
<=> ( axclos = $true ) ),
introduced(definition,[new_symbols(definition,[spl304_66])],[avatar_definition]) ).
thf(f2464,plain,
( ( axclos = $true )
| ~ spl304_66 ),
inference(avatar_component_clause,[],[f2462]) ).
thf(f2465,plain,
( spl304_66
| spl304_64 ),
inference(avatar_split_clause,[],[f626,f2451,f2462]) ).
thf(f2467,definition,
( spl304_67
<=> ( axmap = $true ) ),
introduced(definition,[new_symbols(definition,[spl304_67])],[avatar_definition]) ).
thf(f2469,plain,
( ( axmap = $true )
| ~ spl304_67 ),
inference(avatar_component_clause,[],[f2467]) ).
thf(f2470,plain,
( spl304_67
| spl304_64 ),
inference(avatar_split_clause,[],[f628,f2451,f2467]) ).
thf(f2471,plain,
( spl304_9
| spl304_64 ),
inference(avatar_split_clause,[],[f627,f2451,f2224]) ).
thf(f2512,definition,
( spl304_77
<=> ! [X2: subst,X1: subst,X3: term] :
( ( sub @ ( sub @ X3 @ X1 ) @ X2 )
= ( sub @ X3 @ ( comp @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl304_77])],[avatar_definition]) ).
thf(f2513,plain,
( ! [X2: subst,X3: term,X1: subst] :
( ( sub @ ( sub @ X3 @ X1 ) @ X2 )
= ( sub @ X3 @ ( comp @ X1 @ X2 ) ) )
| ~ spl304_77 ),
inference(avatar_component_clause,[],[f2512]) ).
thf(f2514,plain,
( spl304_63
| spl304_77 ),
inference(avatar_split_clause,[],[f664,f2512,f2446]) ).
thf(f3053,definition,
( spl304_208
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl304_208])],[avatar_definition]) ).
thf(f3054,plain,
( ! [X1: term] :
( ( sub @ X1 @ id )
= X1 )
| ~ spl304_208 ),
inference(avatar_component_clause,[],[f3053]) ).
thf(f3055,plain,
( spl304_61
| spl304_208 ),
inference(avatar_split_clause,[],[f1237,f3053,f2438]) ).
thf(f3079,definition,
( spl304_214
<=> ! [X2: subst,X1: subst,X3: term] :
( ( push @ ( sub @ X3 @ X2 ) @ ( comp @ X1 @ X2 ) )
= ( comp @ ( push @ X3 @ X1 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl304_214])],[avatar_definition]) ).
thf(f3080,plain,
( ! [X2: subst,X3: term,X1: subst] :
( ( push @ ( sub @ X3 @ X2 ) @ ( comp @ X1 @ X2 ) )
= ( comp @ ( push @ X3 @ X1 ) @ X2 ) )
| ~ spl304_214 ),
inference(avatar_component_clause,[],[f3079]) ).
thf(f3081,plain,
( spl304_60
| spl304_214 ),
inference(avatar_split_clause,[],[f1261,f3079,f2434]) ).
thf(f3958,plain,
~ spl304_64,
inference(avatar_split_clause,[],[f334,f2451]) ).
thf(f3959,plain,
( ( $false = $true )
| ~ spl304_61
| ~ spl304_65 ),
inference(forward_demodulation,[],[f2458,f2440]) ).
thf(f3960,plain,
( $false
| ~ spl304_61
| ~ spl304_65 ),
inference(trivial_inequality_removal,[],[f3959]) ).
thf(f3961,plain,
( ~ spl304_61
| ~ spl304_65 ),
inference(avatar_contradiction_clause,[],[f3960]) ).
thf(f3975,plain,
( ( $false = $true )
| ~ spl304_9
| ~ spl304_23 ),
inference(superposition,[],[f2226,f2281]) ).
thf(f3979,plain,
( $false
| ~ spl304_9
| ~ spl304_23 ),
inference(trivial_inequality_removal,[],[f3975]) ).
thf(f3980,plain,
( ~ spl304_9
| ~ spl304_23 ),
inference(avatar_contradiction_clause,[],[f3979]) ).
thf(f3981,plain,
( ! [X1: term] :
( ( $true
= ( sK6 @ ( sK25 @ sK13 @ id @ X1 ) ) )
| ( $false
= ( sK6 @ X1 ) ) )
| ~ spl304_27
| ~ spl304_53 ),
inference(forward_demodulation,[],[f2297,f2405]) ).
thf(f3985,plain,
( ( $false = $true )
| ~ spl304_63
| ~ spl304_66 ),
inference(forward_demodulation,[],[f2464,f2448]) ).
thf(f3986,plain,
( $false
| ~ spl304_63
| ~ spl304_66 ),
inference(trivial_inequality_removal,[],[f3985]) ).
thf(f3987,plain,
( ~ spl304_63
| ~ spl304_66 ),
inference(avatar_contradiction_clause,[],[f3986]) ).
thf(f3990,plain,
( ! [X2: term,X3: subst,X0: term,X1: subst] :
( ( sub @ X0 @ ( comp @ ( push @ X2 @ X1 ) @ X3 ) )
= ( sub @ ( sK25 @ X0 @ X1 @ X2 ) @ X3 ) )
| ~ spl304_53
| ~ spl304_77 ),
inference(superposition,[],[f2513,f2405]) ).
thf(f4001,plain,
( ( $false = $true )
| ~ spl304_60
| ~ spl304_67 ),
inference(forward_demodulation,[],[f2469,f2436]) ).
thf(f4002,plain,
( $false
| ~ spl304_60
| ~ spl304_67 ),
inference(trivial_inequality_removal,[],[f4001]) ).
thf(f4003,plain,
( ~ spl304_60
| ~ spl304_67 ),
inference(avatar_contradiction_clause,[],[f4002]) ).
thf(f4008,plain,
( ! [X2: subst,X3: term,X0: term,X1: subst] :
( ( sK25 @ X3 @ ( comp @ X1 @ X2 ) @ ( sub @ X0 @ X2 ) )
= ( sub @ X3 @ ( comp @ ( push @ X0 @ X1 ) @ X2 ) ) )
| ~ spl304_53
| ~ spl304_214 ),
inference(superposition,[],[f2405,f3080]) ).
thf(f4017,plain,
( ( $false = $true )
| ~ spl304_58
| ~ spl304_59 ),
inference(forward_demodulation,[],[f2431,f2426]) ).
thf(f4018,plain,
( $false
| ~ spl304_58
| ~ spl304_59 ),
inference(trivial_inequality_removal,[],[f4017]) ).
thf(f4019,plain,
( ~ spl304_58
| ~ spl304_59 ),
inference(avatar_contradiction_clause,[],[f4018]) ).
thf(f4021,plain,
( ( $false = $true )
| ~ spl304_54
| ~ spl304_55 ),
inference(superposition,[],[f2414,f2409]) ).
thf(f4024,plain,
( $false
| ~ spl304_54
| ~ spl304_55 ),
inference(trivial_inequality_removal,[],[f4021]) ).
thf(f4025,plain,
( ~ spl304_54
| ~ spl304_55 ),
inference(avatar_contradiction_clause,[],[f4024]) ).
thf(f4100,plain,
( ! [X2: subst,X3: term,X0: term,X1: subst] :
( ( sK25 @ X3 @ ( comp @ X1 @ X2 ) @ ( sub @ X0 @ X2 ) )
= ( sub @ ( sK25 @ X3 @ X1 @ X0 ) @ X2 ) )
| ~ spl304_53
| ~ spl304_77
| ~ spl304_214 ),
inference(forward_demodulation,[],[f4008,f3990]) ).
thf(f4168,plain,
( ! [X0: term] :
( ( $true
= ( sK7 @ id @ ( sK8 @ ( sK25 @ X0 ) ) @ id ) )
| ( ( sub @ ( sK25 @ X0 @ ( sK11 @ ( sK25 @ X0 ) ) @ ( sK10 @ ( sK25 @ X0 ) ) ) @ ( sK9 @ ( sK25 @ X0 ) ) )
!= ( sub @ ( sK25 @ X0 @ ( sK11 @ ( sK25 @ X0 ) ) @ ( sK10 @ ( sK25 @ X0 ) ) ) @ ( sK9 @ ( sK25 @ X0 ) ) ) )
| ( ( sK7 @ id @ ( lam @ ( sK25 @ X0 @ sh @ one ) ) @ id )
= $true ) )
| ~ spl304_22
| ~ spl304_53
| ~ spl304_77
| ~ spl304_214 ),
inference(superposition,[],[f2277,f4100]) ).
thf(f4171,plain,
( ! [X0: term] :
( ( ( sK7 @ id @ ( lam @ ( sK25 @ X0 @ sh @ one ) ) @ id )
= $true )
| ( $true
= ( sK7 @ id @ ( sK8 @ ( sK25 @ X0 ) ) @ id ) ) )
| ~ spl304_22
| ~ spl304_53
| ~ spl304_77
| ~ spl304_214 ),
inference(trivial_inequality_removal,[],[f4168]) ).
thf(f4185,plain,
( ! [X0: term] :
( ( ( sub @ ( sK25 @ X0 @ ( sK12 @ ( sK25 @ X0 ) ) @ ( sK10 @ ( sK25 @ X0 ) ) ) @ ( sK9 @ ( sK25 @ X0 ) ) )
!= ( sub @ ( sK25 @ X0 @ ( sK12 @ ( sK25 @ X0 ) ) @ ( sK10 @ ( sK25 @ X0 ) ) ) @ ( sK9 @ ( sK25 @ X0 ) ) ) )
| ( ( sK7 @ id @ ( lam @ ( sK25 @ X0 @ sh @ one ) ) @ id )
= $true )
| ( $false
= ( sK7 @ id @ ( sK25 @ X0 @ id @ ( sK8 @ ( sK25 @ X0 ) ) ) @ id ) ) )
| ~ spl304_24
| ~ spl304_53
| ~ spl304_77
| ~ spl304_214 ),
inference(superposition,[],[f2285,f4100]) ).
thf(f4188,plain,
( ! [X0: term] :
( ( $false
= ( sK7 @ id @ ( sK25 @ X0 @ id @ ( sK8 @ ( sK25 @ X0 ) ) ) @ id ) )
| ( ( sK7 @ id @ ( lam @ ( sK25 @ X0 @ sh @ one ) ) @ id )
= $true ) )
| ~ spl304_24
| ~ spl304_53
| ~ spl304_77
| ~ spl304_214 ),
inference(trivial_inequality_removal,[],[f4185]) ).
thf(f4429,plain,
( ! [X0: term] :
( ( $false = $true )
| ( ( sK6 @ ( lam @ ( sK25 @ X0 @ sh @ one ) ) )
= $true )
| ( $true
= ( sK7 @ id @ ( sK8 @ ( sK25 @ X0 ) ) @ id ) ) )
| ~ spl304_22
| ~ spl304_25
| ~ spl304_53
| ~ spl304_77
| ~ spl304_214 ),
inference(superposition,[],[f2289,f4171]) ).
thf(f4430,plain,
( ! [X0: term] :
( ( ( sK6 @ ( lam @ ( sK25 @ X0 @ sh @ one ) ) )
= $true )
| ( $true
= ( sK7 @ id @ ( sK8 @ ( sK25 @ X0 ) ) @ id ) ) )
| ~ spl304_22
| ~ spl304_25
| ~ spl304_53
| ~ spl304_77
| ~ spl304_214 ),
inference(trivial_inequality_removal,[],[f4429]) ).
thf(f4929,plain,
( ! [X0: term] :
( ( $false = $true )
| ( ( sK7 @ id @ ( lam @ ( sK25 @ X0 @ sh @ one ) ) @ id )
= $true )
| ( $false
= ( sK6 @ ( sK25 @ X0 @ id @ ( sK8 @ ( sK25 @ X0 ) ) ) ) ) )
| ~ spl304_24
| ~ spl304_26
| ~ spl304_53
| ~ spl304_77
| ~ spl304_214 ),
inference(superposition,[],[f2293,f4188]) ).
thf(f4930,plain,
( ! [X0: term] :
( ( $false
= ( sK6 @ ( sK25 @ X0 @ id @ ( sK8 @ ( sK25 @ X0 ) ) ) ) )
| ( ( sK7 @ id @ ( lam @ ( sK25 @ X0 @ sh @ one ) ) @ id )
= $true ) )
| ~ spl304_24
| ~ spl304_26
| ~ spl304_53
| ~ spl304_77
| ~ spl304_214 ),
inference(trivial_inequality_removal,[],[f4929]) ).
thf(f5159,plain,
( ! [X0: term] :
( ( sub @ X0 @ id )
= ( sK25 @ X0 @ sh @ one ) )
| ~ spl304_53
| ~ spl304_57 ),
inference(superposition,[],[f2405,f2422]) ).
thf(f5174,plain,
( ! [X0: term] :
( ( sK25 @ X0 @ sh @ one )
= X0 )
| ~ spl304_53
| ~ spl304_57
| ~ spl304_208 ),
inference(forward_demodulation,[],[f5159,f3054]) ).
thf(f6265,plain,
( ! [X0: term] :
( ( $true
= ( sK7 @ id @ ( sK8 @ ( sK25 @ X0 ) ) @ id ) )
| ( ( sK6 @ ( lam @ X0 ) )
= $true ) )
| ~ spl304_22
| ~ spl304_25
| ~ spl304_53
| ~ spl304_57
| ~ spl304_77
| ~ spl304_208
| ~ spl304_214 ),
inference(forward_demodulation,[],[f4430,f5174]) ).
thf(f6267,plain,
( ! [X0: term] :
( ( ( sK6 @ ( lam @ X0 ) )
= $true )
| ( $true
= ( sK6 @ ( sK8 @ ( sK25 @ X0 ) ) ) )
| ( $false = $true ) )
| ~ spl304_22
| ~ spl304_25
| ~ spl304_53
| ~ spl304_57
| ~ spl304_77
| ~ spl304_208
| ~ spl304_214 ),
inference(superposition,[],[f2289,f6265]) ).
thf(f6268,plain,
( ! [X0: term] :
( ( $true
= ( sK6 @ ( sK8 @ ( sK25 @ X0 ) ) ) )
| ( ( sK6 @ ( lam @ X0 ) )
= $true ) )
| ~ spl304_22
| ~ spl304_25
| ~ spl304_53
| ~ spl304_57
| ~ spl304_77
| ~ spl304_208
| ~ spl304_214 ),
inference(trivial_inequality_removal,[],[f6267]) ).
thf(f6502,plain,
( ! [X0: term] :
( ( $false
= ( sK6 @ ( sK25 @ X0 @ id @ ( sK8 @ ( sK25 @ X0 ) ) ) ) )
| ( $true
= ( sK7 @ id @ ( lam @ X0 ) @ id ) ) )
| ~ spl304_24
| ~ spl304_26
| ~ spl304_53
| ~ spl304_57
| ~ spl304_77
| ~ spl304_208
| ~ spl304_214 ),
inference(forward_demodulation,[],[f4930,f5174]) ).
thf(f6514,plain,
( ( $false
= ( sK6 @ ( sK8 @ ( sK25 @ sK13 ) ) ) )
| ( $true
= ( sK7 @ id @ ( lam @ sK13 ) @ id ) )
| ( $false = $true )
| ~ spl304_24
| ~ spl304_26
| ~ spl304_27
| ~ spl304_53
| ~ spl304_57
| ~ spl304_77
| ~ spl304_208
| ~ spl304_214 ),
inference(superposition,[],[f6502,f3981]) ).
thf(f6518,plain,
( ( $false
= ( sK6 @ ( sK8 @ ( sK25 @ sK13 ) ) ) )
| ( $true
= ( sK7 @ id @ ( lam @ sK13 ) @ id ) )
| ~ spl304_24
| ~ spl304_26
| ~ spl304_27
| ~ spl304_53
| ~ spl304_57
| ~ spl304_77
| ~ spl304_208
| ~ spl304_214 ),
inference(trivial_inequality_removal,[],[f6514]) ).
thf(f6521,definition,
( spl304_445
<=> ( $false
= ( sK6 @ ( sK8 @ ( sK25 @ sK13 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl304_445])],[avatar_definition]) ).
thf(f6523,plain,
( ( $false
= ( sK6 @ ( sK8 @ ( sK25 @ sK13 ) ) ) )
| ~ spl304_445 ),
inference(avatar_component_clause,[],[f6521]) ).
thf(f6525,definition,
( spl304_446
<=> ( $true
= ( sK7 @ id @ ( lam @ sK13 ) @ id ) ) ),
introduced(definition,[new_symbols(definition,[spl304_446])],[avatar_definition]) ).
thf(f6527,plain,
( ( $true
= ( sK7 @ id @ ( lam @ sK13 ) @ id ) )
| ~ spl304_446 ),
inference(avatar_component_clause,[],[f6525]) ).
thf(f6529,plain,
( spl304_445
| spl304_446
| ~ spl304_24
| ~ spl304_26
| ~ spl304_27
| ~ spl304_53
| ~ spl304_57
| ~ spl304_77
| ~ spl304_208
| ~ spl304_214 ),
inference(avatar_split_clause,[],[f6518,f3079,f3053,f2512,f2420,f2404,f2296,f2292,f2284,f6525,f6521]) ).
thf(f6530,plain,
( ( $false = $true )
| ( ( sK6 @ ( lam @ sK13 ) )
= $true )
| ~ spl304_22
| ~ spl304_25
| ~ spl304_53
| ~ spl304_57
| ~ spl304_77
| ~ spl304_208
| ~ spl304_214
| ~ spl304_445 ),
inference(superposition,[],[f6523,f6268]) ).
thf(f6535,plain,
( ( ( sK6 @ ( lam @ sK13 ) )
= $true )
| ~ spl304_22
| ~ spl304_25
| ~ spl304_53
| ~ spl304_57
| ~ spl304_77
| ~ spl304_208
| ~ spl304_214
| ~ spl304_445 ),
inference(trivial_inequality_removal,[],[f6530]) ).
thf(f6539,plain,
( ( $false = $true )
| ~ spl304_22
| ~ spl304_25
| ~ spl304_28
| ~ spl304_53
| ~ spl304_57
| ~ spl304_77
| ~ spl304_208
| ~ spl304_214
| ~ spl304_445 ),
inference(forward_demodulation,[],[f6535,f2302]) ).
thf(f6540,plain,
( $false
| ~ spl304_22
| ~ spl304_25
| ~ spl304_28
| ~ spl304_53
| ~ spl304_57
| ~ spl304_77
| ~ spl304_208
| ~ spl304_214
| ~ spl304_445 ),
inference(trivial_inequality_removal,[],[f6539]) ).
thf(f6541,plain,
( ~ spl304_22
| ~ spl304_25
| ~ spl304_28
| ~ spl304_53
| ~ spl304_57
| ~ spl304_77
| ~ spl304_208
| ~ spl304_214
| ~ spl304_445 ),
inference(avatar_contradiction_clause,[],[f6540]) ).
thf(f6576,plain,
( ( ( sK6 @ ( lam @ sK13 ) )
= $true )
| ( $false = $true )
| ~ spl304_25
| ~ spl304_446 ),
inference(superposition,[],[f2289,f6527]) ).
thf(f6579,plain,
( ( ( sK6 @ ( lam @ sK13 ) )
= $true )
| ~ spl304_25
| ~ spl304_446 ),
inference(trivial_inequality_removal,[],[f6576]) ).
thf(f6585,plain,
( ( $false = $true )
| ~ spl304_25
| ~ spl304_28
| ~ spl304_446 ),
inference(forward_demodulation,[],[f6579,f2302]) ).
thf(f6586,plain,
( $false
| ~ spl304_25
| ~ spl304_28
| ~ spl304_446 ),
inference(trivial_inequality_removal,[],[f6585]) ).
thf(f6587,plain,
( ~ spl304_25
| ~ spl304_28
| ~ spl304_446 ),
inference(avatar_contradiction_clause,[],[f6586]) ).
cnf(s17,plain,
( spl304_22
| spl304_23 ),
inference(sat_conversion,[],[f2282]) ).
cnf(s18,plain,
( spl304_23
| spl304_24 ),
inference(sat_conversion,[],[f2286]) ).
cnf(s19,plain,
( spl304_23
| spl304_25 ),
inference(sat_conversion,[],[f2290]) ).
cnf(s20,plain,
( spl304_23
| spl304_26 ),
inference(sat_conversion,[],[f2294]) ).
cnf(s21,plain,
( spl304_23
| spl304_27 ),
inference(sat_conversion,[],[f2298]) ).
cnf(s22,plain,
( spl304_23
| spl304_28 ),
inference(sat_conversion,[],[f2303]) ).
cnf(s43,plain,
( spl304_53
| spl304_54 ),
inference(sat_conversion,[],[f2410]) ).
cnf(s45,plain,
( spl304_57
| spl304_58 ),
inference(sat_conversion,[],[f2427]) ).
cnf(s48,plain,
( spl304_55
| spl304_64 ),
inference(sat_conversion,[],[f2454]) ).
cnf(s49,plain,
( spl304_64
| spl304_65 ),
inference(sat_conversion,[],[f2459]) ).
cnf(s50,plain,
( spl304_59
| spl304_64 ),
inference(sat_conversion,[],[f2460]) ).
cnf(s51,plain,
( spl304_64
| spl304_66 ),
inference(sat_conversion,[],[f2465]) ).
cnf(s52,plain,
( spl304_64
| spl304_67 ),
inference(sat_conversion,[],[f2470]) ).
cnf(s53,plain,
( spl304_9
| spl304_64 ),
inference(sat_conversion,[],[f2471]) ).
cnf(s59,plain,
( spl304_63
| spl304_77 ),
inference(sat_conversion,[],[f2514]) ).
cnf(s162,plain,
( spl304_61
| spl304_208 ),
inference(sat_conversion,[],[f3055]) ).
cnf(s166,plain,
( spl304_60
| spl304_214 ),
inference(sat_conversion,[],[f3081]) ).
cnf(s357,plain,
~ spl304_64,
inference(sat_conversion,[],[f3958]) ).
cnf(s358,plain,
( ~ spl304_61
| ~ spl304_65 ),
inference(sat_conversion,[],[f3961]) ).
cnf(s364,plain,
( ~ spl304_9
| ~ spl304_23 ),
inference(sat_conversion,[],[f3980]) ).
cnf(s366,plain,
( ~ spl304_63
| ~ spl304_66 ),
inference(sat_conversion,[],[f3987]) ).
cnf(s368,plain,
( ~ spl304_60
| ~ spl304_67 ),
inference(sat_conversion,[],[f4003]) ).
cnf(s370,plain,
( ~ spl304_58
| ~ spl304_59 ),
inference(sat_conversion,[],[f4019]) ).
cnf(s372,plain,
( ~ spl304_54
| ~ spl304_55 ),
inference(sat_conversion,[],[f4025]) ).
cnf(s410,plain,
( ~ spl304_24
| ~ spl304_26
| ~ spl304_27
| ~ spl304_53
| ~ spl304_57
| ~ spl304_77
| ~ spl304_208
| ~ spl304_214
| spl304_445
| spl304_446 ),
inference(sat_conversion,[],[f6529]) ).
cnf(s412,plain,
( ~ spl304_22
| ~ spl304_25
| ~ spl304_28
| ~ spl304_53
| ~ spl304_57
| ~ spl304_77
| ~ spl304_208
| ~ spl304_214
| ~ spl304_445 ),
inference(sat_conversion,[],[f6541]) ).
cnf(s414,plain,
( ~ spl304_25
| ~ spl304_28
| ~ spl304_446 ),
inference(sat_conversion,[],[f6587]) ).
cnf(s415,plain,
spl304_9,
inference(rat,[],[s53,s357]) ).
cnf(s416,plain,
~ spl304_23,
inference(rat,[],[s364,s415]) ).
cnf(s417,plain,
spl304_67,
inference(rat,[],[s52,s357]) ).
cnf(s418,plain,
~ spl304_60,
inference(rat,[],[s368,s417]) ).
cnf(s419,plain,
spl304_214,
inference(rat,[],[s166,s418]) ).
cnf(s421,plain,
spl304_66,
inference(rat,[],[s51,s357]) ).
cnf(s422,plain,
~ spl304_63,
inference(rat,[],[s366,s421]) ).
cnf(s423,plain,
spl304_77,
inference(rat,[],[s59,s422]) ).
cnf(s425,plain,
spl304_59,
inference(rat,[],[s50,s357]) ).
cnf(s426,plain,
~ spl304_58,
inference(rat,[],[s370,s425]) ).
cnf(s427,plain,
spl304_65,
inference(rat,[],[s49,s357]) ).
cnf(s428,plain,
~ spl304_61,
inference(rat,[],[s358,s427]) ).
cnf(s429,plain,
spl304_208,
inference(rat,[],[s162,s428]) ).
cnf(s431,plain,
spl304_55,
inference(rat,[],[s48,s357]) ).
cnf(s432,plain,
~ spl304_54,
inference(rat,[],[s372,s431]) ).
cnf(s434,plain,
spl304_57,
inference(rat,[],[s45,s426]) ).
cnf(s435,plain,
spl304_53,
inference(rat,[],[s43,s432]) ).
cnf(s438,plain,
spl304_28,
inference(rat,[],[s22,s416]) ).
cnf(s439,plain,
spl304_27,
inference(rat,[],[s21,s416]) ).
cnf(s440,plain,
spl304_26,
inference(rat,[],[s20,s416]) ).
cnf(s441,plain,
spl304_25,
inference(rat,[],[s19,s416]) ).
cnf(s442,plain,
~ spl304_446,
inference(rat,[],[s414,s438,s441]) ).
cnf(s443,plain,
spl304_24,
inference(rat,[],[s18,s416]) ).
cnf(s444,plain,
spl304_445,
inference(rat,[],[s410,s442,s440,s419,s429,s423,s434,s435,s439,s443]) ).
cnf(s445,plain,
~ spl304_22,
inference(rat,[],[s412,s441,s419,s429,s423,s434,s435,s438,s444]) ).
cnf(s446,plain,
$false,
inference(rat,[],[s17,s416,s445]) ).
thf(f6588,plain,
$false,
inference(avatar_sat_refutation,[],[s446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG268^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 % Computer : n015.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 17:38:34 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.20/0.29 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.47/0.41 % (3860706)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.47/0.41 % (3860713)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=478284927:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.47/0.41 % (3860713)Instruction limit reached!
% 0.47/0.41 % (3860713)------------------------------
% 0.47/0.41 % (3860713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.41 % (3860713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.41 % (3860713)CaDiCaL version: 2.1.3
% 0.47/0.41 % (3860713)Termination reason: Instruction limit
% 0.47/0.41 % (3860713)Termination phase: shuffling
% 0.47/0.41 % (3860713)Time elapsed: 0.002 s
% 0.47/0.41 % (3860713)Peak memory usage: 10 MB
% 0.47/0.41 % (3860713)Instructions burned: 8 (million)
% 0.47/0.41 % (3860717)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.47/0.41 % (3860717)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.47/0.41 % (3860711)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3427080807:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.47/0.41 % (3860716)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2814043465:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.47/0.41 % (3860715)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4136780097:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.47/0.41 % (3860714)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=4052554505:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.47/0.41 % (3860712)lrs+10_16_si=on:nwc=1.5:random_seed=1508336556:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.47/0.41 % (3860717)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2659847924:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.47/0.41 % (3860719)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=494814440:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.47/0.41 % (3860719)Instruction limit reached!
% 0.47/0.41 % (3860719)------------------------------
% 0.47/0.41 % (3860719)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.41 % (3860719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.41 % (3860719)CaDiCaL version: 2.1.3
% 0.47/0.41 % (3860719)Termination reason: Instruction limit
% 0.47/0.41 % (3860719)Termination phase: shuffling
% 0.47/0.41 % (3860719)Time elapsed: 0.001 s
% 0.47/0.41 % (3860719)Peak memory usage: 10 MB
% 0.47/0.41 % (3860719)Instructions burned: 6 (million)
% 0.47/0.41 % (3860712)Instruction limit reached!
% 0.47/0.41 % (3860712)------------------------------
% 0.47/0.41 % (3860712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.41 % (3860712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.41 % (3860712)CaDiCaL version: 2.1.3
% 0.47/0.41 % (3860712)Termination reason: Instruction limit
% 0.47/0.41 % (3860712)Termination phase: shuffling
% 0.47/0.41 % (3860712)Time elapsed: 0.009 s
% 0.47/0.41 % (3860712)Peak memory usage: 10 MB
% 0.47/0.41 % (3860712)Instructions burned: 18 (million)
% 0.47/0.41 % (3860715)Instruction limit reached!
% 0.47/0.41 % (3860715)------------------------------
% 0.47/0.41 % (3860715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.41 % (3860715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.41 % (3860715)CaDiCaL version: 2.1.3
% 0.47/0.41 % (3860715)Termination reason: Instruction limit
% 0.47/0.41 % (3860715)Termination phase: Naming
% 0.47/0.41 % (3860715)Time elapsed: 0.012 s
% 0.47/0.41 % (3860715)Peak memory usage: 11 MB
% 0.47/0.41 % (3860715)Instructions burned: 25 (million)
% 0.47/0.41 % (3860727)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=851336992:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.47/0.44 % (3860727)Instruction limit reached!
% 0.47/0.44 % (3860727)------------------------------
% 0.47/0.44 % (3860727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.44 % (3860727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.44 % (3860727)CaDiCaL version: 2.1.3
% 0.47/0.44 % (3860727)Termination reason: Instruction limit
% 0.47/0.44 % (3860727)Termination phase: shuffling
% 0.47/0.44 % (3860727)Time elapsed: 0.003 s
% 0.47/0.44 % (3860727)Peak memory usage: 10 MB
% 0.47/0.44 % (3860727)Instructions burned: 11 (million)
% 0.47/0.44 % (3860728)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.47/0.44 % (3860731)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.47/0.44 % (3860731)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.47/0.44 % (3860728)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4241977754:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.47/0.44 % (3860731)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2047828814:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.47/0.44 % (3860729)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2316952391:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.47/0.44 % (3860728)Instruction limit reached!
% 0.47/0.44 % (3860728)------------------------------
% 0.47/0.44 % (3860728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.44 % (3860728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.44 % (3860728)CaDiCaL version: 2.1.3
% 0.47/0.44 % (3860728)Termination reason: Instruction limit
% 0.47/0.44 % (3860728)Termination phase: shuffling
% 0.47/0.44 % (3860728)Time elapsed: 0.004 s
% 0.47/0.44 % (3860728)Peak memory usage: 10 MB
% 0.47/0.44 % (3860728)Instructions burned: 9 (million)
% 0.47/0.44 % (3860716)Instruction limit reached!
% 0.47/0.44 % (3860716)------------------------------
% 0.47/0.44 % (3860716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.44 % (3860716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.44 % (3860716)CaDiCaL version: 2.1.3
% 0.47/0.44 % (3860716)Termination reason: Instruction limit
% 0.47/0.44 % (3860716)Termination phase: Property scanning
% 0.47/0.44 % (3860716)Time elapsed: 0.035 s
% 0.47/0.44 % (3860716)Peak memory usage: 12 MB
% 0.47/0.44 % (3860716)Instructions burned: 76 (million)
% 0.47/0.44 % (3860729)Instruction limit reached!
% 0.47/0.44 % (3860729)------------------------------
% 0.47/0.44 % (3860729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.44 % (3860729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.44 % (3860729)CaDiCaL version: 2.1.3
% 0.47/0.44 % (3860729)Termination reason: Instruction limit
% 0.47/0.44 % (3860729)Termination phase: shuffling
% 0.47/0.44 % (3860729)Time elapsed: 0.006 s
% 0.47/0.44 % (3860729)Peak memory usage: 10 MB
% 0.47/0.44 % (3860729)Instructions burned: 12 (million)
% 0.47/0.44 % (3860731)Instruction limit reached!
% 0.47/0.44 % (3860731)------------------------------
% 0.47/0.44 % (3860731)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.44 % (3860731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.44 % (3860731)CaDiCaL version: 2.1.3
% 0.47/0.44 % (3860731)Termination reason: Instruction limit
% 0.47/0.44 % (3860731)Termination phase: Property scanning
% 0.47/0.44 % (3860731)Time elapsed: 0.006 s
% 0.47/0.44 % (3860731)Peak memory usage: 10 MB
% 0.47/0.44 % (3860731)Instructions burned: 28 (million)
% 0.47/0.44 % (3860711)Instruction limit reached!
% 0.47/0.44 % (3860711)------------------------------
% 0.47/0.44 % (3860711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.44 % (3860711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.44 % (3860711)CaDiCaL version: 2.1.3
% 0.47/0.44 % (3860711)Termination reason: Instruction limit
% 1.19/0.48 % (3860711)Termination phase: Function definition elimination
% 1.19/0.48 % (3860711)Time elapsed: 0.039 s
% 1.19/0.48 % (3860711)Peak memory usage: 12 MB
% 1.19/0.48 % (3860711)Instructions burned: 87 (million)
% 1.19/0.48 % (3860738)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=380652504:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.19/0.48 % (3860737)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.19/0.48 % (3860735)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1343895292:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.19/0.48 % (3860736)lrs+10_1_si=on:cs=on:random_seed=3098871562:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.19/0.48 % (3860737)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=665612811:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.19/0.48 % (3860739)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3756335135:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 1.19/0.48 % (3860736)Instruction limit reached!
% 1.19/0.48 % (3860736)------------------------------
% 1.19/0.48 % (3860736)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (3860736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (3860736)CaDiCaL version: 2.1.3
% 1.19/0.48 % (3860736)Termination reason: Instruction limit
% 1.19/0.48 % (3860736)Termination phase: shuffling
% 1.19/0.48 % (3860736)Time elapsed: 0.004 s
% 1.19/0.48 % (3860736)Peak memory usage: 10 MB
% 1.19/0.48 % (3860736)Instructions burned: 9 (million)
% 1.19/0.48 % (3860737)Instruction limit reached!
% 1.19/0.48 % (3860737)------------------------------
% 1.19/0.48 % (3860737)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (3860737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (3860737)CaDiCaL version: 2.1.3
% 1.19/0.48 % (3860737)Termination reason: Instruction limit
% 1.19/0.48 % (3860737)Termination phase: shuffling
% 1.19/0.48 % (3860737)Time elapsed: 0.002 s
% 1.19/0.48 % (3860737)Peak memory usage: 10 MB
% 1.19/0.48 % (3860737)Instructions burned: 4 (million)
% 1.19/0.48 % (3860738)Instruction limit reached!
% 1.19/0.48 % (3860738)------------------------------
% 1.19/0.48 % (3860738)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (3860738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (3860738)CaDiCaL version: 2.1.3
% 1.19/0.48 % (3860738)Termination reason: Instruction limit
% 1.19/0.48 % (3860738)Termination phase: Saturation
% 1.19/0.48 % (3860738)Time elapsed: 0.010 s
% 1.19/0.48 % (3860738)Peak memory usage: 13 MB
% 1.19/0.48 % (3860738)Instructions burned: 40 (million)
% 1.19/0.48 % (3860717)Instruction limit reached!
% 1.19/0.48 % (3860717)------------------------------
% 1.19/0.48 % (3860717)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (3860717)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.48 % (3860717)CaDiCaL version: 2.1.3
% 1.19/0.48 % (3860717)Termination reason: Instruction limit
% 1.19/0.48 % (3860717)Termination phase: Saturation
% 1.19/0.48 % (3860717)Time elapsed: 0.067 s
% 1.19/0.48 % (3860717)Peak memory usage: 13 MB
% 1.19/0.48 % (3860717)Instructions burned: 158 (million)
% 1.19/0.48 % (3860747)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2942929975:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 1.19/0.48 % (3860745)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3773842139:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 1.19/0.48 % (3860746)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3036097315:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 1.19/0.48 % (3860739)Refutation not found, incomplete strategy
% 1.19/0.48 % (3860739)------------------------------
% 1.19/0.48 % (3860739)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.48 % (3860739)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.51 % (3860739)CaDiCaL version: 2.1.3
% 1.19/0.51 % (3860739)Termination reason: Refutation not found, incomplete strategy
% 1.19/0.51 % (3860739)Time elapsed: 0.022 s
% 1.19/0.51 % (3860739)Peak memory usage: 12 MB
% 1.19/0.51 % (3860739)Instructions burned: 50 (million)
% 1.19/0.51 % (3860739)------------------------------
% 1.19/0.51 % (3860739)------------------------------
% 1.19/0.51 % (3860746)Instruction limit reached!
% 1.19/0.51 % (3860746)------------------------------
% 1.19/0.51 % (3860746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.51 % (3860746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.51 % (3860746)CaDiCaL version: 2.1.3
% 1.19/0.51 % (3860746)Termination reason: Instruction limit
% 1.19/0.51 % (3860746)Termination phase: shuffling
% 1.19/0.51 % (3860746)Time elapsed: 0.007 s
% 1.19/0.51 % (3860746)Peak memory usage: 10 MB
% 1.19/0.51 % (3860746)Instructions burned: 16 (million)
% 1.19/0.51 % (3860748)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=263365295:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.19/0.51 % (3860735)Instruction limit reached!
% 1.19/0.51 % (3860735)------------------------------
% 1.19/0.51 % (3860735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.51 % (3860735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.51 % (3860735)CaDiCaL version: 2.1.3
% 1.19/0.51 % (3860735)Termination reason: Instruction limit
% 1.19/0.51 % (3860735)Termination phase: Saturation
% 1.19/0.51 % (3860735)Time elapsed: 0.036 s
% 1.19/0.51 % (3860735)Peak memory usage: 12 MB
% 1.19/0.51 % (3860735)Instructions burned: 87 (million)
% 1.19/0.51 % (3860745)Instruction limit reached!
% 1.19/0.51 % (3860745)------------------------------
% 1.19/0.51 % (3860745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.51 % (3860745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.51 % (3860745)CaDiCaL version: 2.1.3
% 1.19/0.51 % (3860745)Termination reason: Instruction limit
% 1.19/0.51 % (3860745)Termination phase: Preprocessing 1
% 1.19/0.51 % (3860745)Time elapsed: 0.012 s
% 1.19/0.51 % (3860745)Peak memory usage: 10 MB
% 1.19/0.51 % (3860745)Instructions burned: 26 (million)
% 1.19/0.51 % (3860748)Instruction limit reached!
% 1.19/0.51 % (3860748)------------------------------
% 1.19/0.51 % (3860748)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.51 % (3860748)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.51 % (3860748)CaDiCaL version: 2.1.3
% 1.19/0.51 % (3860748)Termination reason: Instruction limit
% 1.19/0.51 % (3860748)Termination phase: shuffling
% 1.19/0.51 % (3860748)Time elapsed: 0.006 s
% 1.19/0.51 % (3860748)Peak memory usage: 10 MB
% 1.19/0.51 % (3860748)Instructions burned: 14 (million)
% 1.19/0.51 % (3860752)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3891805450:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.19/0.51 % (3860752)Instruction limit reached!
% 1.19/0.51 % (3860752)------------------------------
% 1.19/0.51 % (3860752)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.51 % (3860752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.51 % (3860752)CaDiCaL version: 2.1.3
% 1.19/0.51 % (3860752)Termination reason: Instruction limit
% 1.19/0.51 % (3860752)Termination phase: shuffling
% 1.19/0.51 % (3860752)Time elapsed: 0.003 s
% 1.19/0.51 % (3860752)Peak memory usage: 10 MB
% 1.19/0.51 % (3860752)Instructions burned: 5 (million)
% 1.19/0.51 % (3860753)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1219532964:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.19/0.51 % (3860755)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=532151764:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.19/0.51 % (3860757)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.19/0.51 % (3860757)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.19/0.51 % (3860756)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3040536026:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.90/0.57 % (3860757)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=2832451550:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.90/0.57 % (3860753)Instruction limit reached!
% 1.90/0.57 % (3860753)------------------------------
% 1.90/0.57 % (3860753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.90/0.57 % (3860753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.90/0.57 % (3860753)CaDiCaL version: 2.1.3
% 1.90/0.57 % (3860753)Termination reason: Instruction limit
% 1.90/0.57 % (3860753)Termination phase: Property scanning
% 1.90/0.57 % (3860753)Time elapsed: 0.011 s
% 1.90/0.57 % (3860753)Peak memory usage: 10 MB
% 1.90/0.57 % (3860753)Instructions burned: 26 (million)
% 1.90/0.57 % (3860755)Instruction limit reached!
% 1.90/0.57 % (3860755)------------------------------
% 1.90/0.57 % (3860755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.90/0.57 % (3860755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.90/0.57 % (3860755)CaDiCaL version: 2.1.3
% 1.90/0.57 % (3860755)Termination reason: Instruction limit
% 1.90/0.57 % (3860755)Termination phase: Property scanning
% 1.90/0.57 % (3860755)Time elapsed: 0.011 s
% 1.90/0.57 % (3860755)Peak memory usage: 10 MB
% 1.90/0.57 % (3860755)Instructions burned: 25 (million)
% 1.90/0.57 % (3860757)Instruction limit reached!
% 1.90/0.57 % (3860757)------------------------------
% 1.90/0.57 % (3860757)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.90/0.57 % (3860757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.90/0.57 % (3860757)CaDiCaL version: 2.1.3
% 1.90/0.57 % (3860757)Termination reason: Instruction limit
% 1.90/0.57 % (3860757)Termination phase: shuffling
% 1.90/0.57 % (3860757)Time elapsed: 0.006 s
% 1.90/0.57 % (3860757)Peak memory usage: 10 MB
% 1.90/0.57 % (3860757)Instructions burned: 14 (million)
% 1.90/0.57 % (3860760)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.90/0.57 % (3860760)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=3650967530:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.90/0.57 % (3860760)Instruction limit reached!
% 1.90/0.57 % (3860760)------------------------------
% 1.90/0.57 % (3860760)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.90/0.57 % (3860760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.90/0.57 % (3860760)CaDiCaL version: 2.1.3
% 1.90/0.57 % (3860760)Termination reason: Instruction limit
% 1.90/0.57 % (3860760)Termination phase: shuffling
% 1.90/0.57 % (3860760)Time elapsed: 0.004 s
% 1.90/0.57 % (3860760)Peak memory usage: 10 MB
% 1.90/0.57 % (3860760)Instructions burned: 8 (million)
% 1.90/0.57 % (3860764)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=1658256892:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.90/0.57 % (3860765)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=820729849:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.90/0.57 % (3860756)Instruction limit reached!
% 1.90/0.57 % (3860756)------------------------------
% 1.90/0.57 % (3860756)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.90/0.57 % (3860756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.90/0.57 % (3860756)CaDiCaL version: 2.1.3
% 1.90/0.57 % (3860756)Termination reason: Instruction limit
% 1.90/0.57 % (3860756)Termination phase: Property scanning
% 1.90/0.57 % (3860756)Time elapsed: 0.029 s
% 1.90/0.57 % (3860756)Peak memory usage: 12 MB
% 1.90/0.57 % (3860756)Instructions burned: 62 (million)
% 1.90/0.57 % (3860765)Instruction limit reached!
% 1.90/0.57 % (3860765)------------------------------
% 1.90/0.57 % (3860765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.90/0.57 % (3860765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.90/0.57 % (3860765)CaDiCaL version: 2.1.3
% 1.90/0.57 % (3860765)Termination reason: Instruction limit
% 2.21/0.66 % (3860765)Termination phase: shuffling
% 2.21/0.66 % (3860765)Time elapsed: 0.004 s
% 2.21/0.66 % (3860765)Peak memory usage: 10 MB
% 2.21/0.66 % (3860765)Instructions burned: 9 (million)
% 2.21/0.66 % (3860766)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2372946007:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.21/0.66 % (3860768)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3851299048:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.21/0.66 % (3860747)Instruction limit reached!
% 2.21/0.66 % (3860747)------------------------------
% 2.21/0.66 % (3860747)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.21/0.66 % (3860747)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/0.66 % (3860747)CaDiCaL version: 2.1.3
% 2.21/0.66 % (3860747)Termination reason: Instruction limit
% 2.21/0.66 % (3860747)Termination phase: Saturation
% 2.21/0.66 % (3860747)Time elapsed: 0.079 s
% 2.21/0.66 % (3860747)Peak memory usage: 15 MB
% 2.21/0.66 % (3860747)Instructions burned: 331 (million)
% 2.21/0.66 % (3860764)Instruction limit reached!
% 2.21/0.66 % (3860764)------------------------------
% 2.21/0.66 % (3860764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.21/0.66 % (3860764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/0.66 % (3860764)CaDiCaL version: 2.1.3
% 2.21/0.66 % (3860764)Termination reason: Instruction limit
% 2.21/0.66 % (3860764)Termination phase: Property scanning
% 2.21/0.66 % (3860764)Time elapsed: 0.014 s
% 2.21/0.66 % (3860764)Peak memory usage: 10 MB
% 2.21/0.66 % (3860764)Instructions burned: 33 (million)
% 2.21/0.66 % (3860766)Instruction limit reached!
% 2.21/0.66 % (3860766)------------------------------
% 2.21/0.66 % (3860766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.21/0.66 % (3860766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/0.66 % (3860766)CaDiCaL version: 2.1.3
% 2.21/0.66 % (3860766)Termination reason: Instruction limit
% 2.21/0.66 % (3860766)Termination phase: Property scanning
% 2.21/0.66 % (3860766)Time elapsed: 0.011 s
% 2.21/0.66 % (3860766)Peak memory usage: 10 MB
% 2.21/0.66 % (3860766)Instructions burned: 24 (million)
% 2.21/0.66 % (3860768)Instruction limit reached!
% 2.21/0.66 % (3860768)------------------------------
% 2.21/0.66 % (3860768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.21/0.66 % (3860768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/0.66 % (3860768)CaDiCaL version: 2.1.3
% 2.21/0.66 % (3860768)Termination reason: Instruction limit
% 2.21/0.66 % (3860768)Termination phase: Property scanning
% 2.21/0.66 % (3860768)Time elapsed: 0.010 s
% 2.21/0.66 % (3860768)Peak memory usage: 10 MB
% 2.21/0.66 % (3860768)Instructions burned: 21 (million)
% 2.21/0.66 % (3860771)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=294200487:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.21/0.66 % (3860775)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=295027237:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 2.21/0.66 % (3860773)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=80474645:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.21/0.66 % (3860777)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.21/0.66 % (3860776)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1333877652:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 2.21/0.66 % (3860777)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4999326:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 2.21/0.66 % (3860777)Instruction limit reached!
% 2.21/0.66 % (3860777)------------------------------
% 2.21/0.66 % (3860777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.21/0.66 % (3860777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.21/0.66 % (3860777)CaDiCaL version: 2.1.3
% 2.21/0.66 % (3860777)Termination reason: Instruction limit
% 2.21/0.66 % (3860777)Termination phase: shuffling
% 2.21/0.66 % (3860777)Time elapsed: 0.004 s
% 2.21/0.66 % (3860777)Peak memory usage: 10 MB
% 2.21/0.66 % (3860777)Instructions burned: 9 (million)
% 2.46/0.72 % (3860778)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1572894713:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/181Mi)
% 2.46/0.72 % (3860776)Instruction limit reached!
% 2.46/0.72 % (3860776)------------------------------
% 2.46/0.72 % (3860776)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.72 % (3860776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.72 % (3860776)CaDiCaL version: 2.1.3
% 2.46/0.72 % (3860776)Termination reason: Instruction limit
% 2.46/0.72 % (3860776)Termination phase: Property scanning
% 2.46/0.72 % (3860776)Time elapsed: 0.018 s
% 2.46/0.72 % (3860776)Peak memory usage: 10 MB
% 2.46/0.72 % (3860776)Instructions burned: 44 (million)
% 2.46/0.72 % (3860785)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3534397984:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.46/0.72 % (3860786)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.46/0.72 % (3860786)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3093120104:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.46/0.72 % (3860775)Instruction limit reached!
% 2.46/0.72 % (3860775)------------------------------
% 2.46/0.72 % (3860775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.72 % (3860775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.72 % (3860775)CaDiCaL version: 2.1.3
% 2.46/0.72 % (3860775)Termination reason: Instruction limit
% 2.46/0.72 % (3860775)Termination phase: Saturation
% 2.46/0.72 % (3860775)Time elapsed: 0.046 s
% 2.46/0.72 % (3860775)Peak memory usage: 13 MB
% 2.46/0.72 % (3860775)Instructions burned: 197 (million)
% 2.46/0.72 % (3860786)Instruction limit reached!
% 2.46/0.72 % (3860786)------------------------------
% 2.46/0.72 % (3860786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.72 % (3860786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.72 % (3860786)CaDiCaL version: 2.1.3
% 2.46/0.72 % (3860786)Termination reason: Instruction limit
% 2.46/0.72 % (3860786)Termination phase: shuffling
% 2.46/0.72 % (3860786)Time elapsed: 0.003 s
% 2.46/0.72 % (3860786)Peak memory usage: 10 MB
% 2.46/0.72 % (3860786)Instructions burned: 7 (million)
% 2.46/0.72 % (3860789)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3570698202:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.46/0.72 % (3860773)Instruction limit reached!
% 2.46/0.72 % (3860773)------------------------------
% 2.46/0.72 % (3860773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.72 % (3860773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.72 % (3860773)CaDiCaL version: 2.1.3
% 2.46/0.72 % (3860773)Termination reason: Instruction limit
% 2.46/0.72 % (3860773)Termination phase: Saturation
% 2.46/0.72 % (3860773)Time elapsed: 0.060 s
% 2.46/0.72 % (3860773)Peak memory usage: 13 MB
% 2.46/0.72 % (3860773)Instructions burned: 143 (million)
% 2.46/0.72 % (3860789)Instruction limit reached!
% 2.46/0.72 % (3860789)------------------------------
% 2.46/0.72 % (3860789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.72 % (3860789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.72 % (3860789)CaDiCaL version: 2.1.3
% 2.46/0.72 % (3860789)Termination reason: Instruction limit
% 2.46/0.72 % (3860789)Termination phase: Property scanning
% 2.46/0.72 % (3860789)Time elapsed: 0.005 s
% 2.46/0.72 % (3860789)Peak memory usage: 10 MB
% 2.46/0.72 % (3860789)Instructions burned: 23 (million)
% 2.46/0.72 % (3860790)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=2048056615:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.46/0.72 % (3860793)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3696605387:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 3.35/0.80 % (3860790)Instruction limit reached!
% 3.35/0.80 % (3860790)------------------------------
% 3.35/0.80 % (3860790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.80 % (3860790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.80 % (3860790)CaDiCaL version: 2.1.3
% 3.35/0.80 % (3860790)Termination reason: Instruction limit
% 3.35/0.80 % (3860790)Termination phase: shuffling
% 3.35/0.80 % (3860790)Time elapsed: 0.009 s
% 3.35/0.80 % (3860790)Peak memory usage: 10 MB
% 3.35/0.80 % (3860790)Instructions burned: 20 (million)
% 3.35/0.80 % (3860792)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=4212966062:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 3.35/0.80 % (3860796)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=3020750761:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 3.35/0.80 % (3860778)Instruction limit reached!
% 3.35/0.80 % (3860778)------------------------------
% 3.35/0.80 % (3860778)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.80 % (3860778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.80 % (3860778)CaDiCaL version: 2.1.3
% 3.35/0.80 % (3860778)Termination reason: Instruction limit
% 3.35/0.80 % (3860778)Termination phase: Saturation
% 3.35/0.80 % (3860778)Time elapsed: 0.081 s
% 3.35/0.80 % (3860778)Peak memory usage: 15 MB
% 3.35/0.80 % (3860778)Instructions burned: 181 (million)
% 3.35/0.80 % (3860785)Instruction limit reached!
% 3.35/0.80 % (3860785)------------------------------
% 3.35/0.80 % (3860785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.80 % (3860785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.80 % (3860785)CaDiCaL version: 2.1.3
% 3.35/0.80 % (3860785)Termination reason: Instruction limit
% 3.35/0.80 % (3860785)Termination phase: Saturation
% 3.35/0.80 % (3860785)Time elapsed: 0.078 s
% 3.35/0.80 % (3860785)Peak memory usage: 13 MB
% 3.35/0.80 % (3860785)Instructions burned: 169 (million)
% 3.35/0.80 % (3860796)Instruction limit reached!
% 3.35/0.80 % (3860796)------------------------------
% 3.35/0.80 % (3860796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.80 % (3860796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.80 % (3860796)CaDiCaL version: 2.1.3
% 3.35/0.80 % (3860796)Termination reason: Instruction limit
% 3.35/0.80 % (3860796)Termination phase: Preprocessing 3
% 3.35/0.80 % (3860796)Time elapsed: 0.021 s
% 3.35/0.80 % (3860796)Peak memory usage: 11 MB
% 3.35/0.80 % (3860796)Instructions burned: 45 (million)
% 3.35/0.80 % (3860799)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=3222662994:i=480:rtra=on_2997 on theBenchmark for (2997ds/480Mi)
% 3.35/0.80 % (3860800)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=2225017390:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 3.35/0.80 % (3860802)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 3.35/0.80 % (3860802)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=854130174:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 3.35/0.80 % (3860800)Instruction limit reached!
% 3.35/0.80 % (3860800)------------------------------
% 3.35/0.80 % (3860800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.80 % (3860800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.80 % (3860800)CaDiCaL version: 2.1.3
% 3.35/0.80 % (3860800)Termination reason: Instruction limit
% 3.35/0.80 % (3860800)Termination phase: Property scanning
% 3.35/0.80 % (3860800)Time elapsed: 0.009 s
% 3.35/0.80 % (3860800)Peak memory usage: 10 MB
% 3.35/0.80 % (3860800)Instructions burned: 21 (million)
% 3.35/0.80 % (3860805)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=4270641363:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 3.35/0.80 % (3860714)Instruction limit reached!
% 3.35/0.80 % (3860714)------------------------------
% 3.35/0.80 % (3860714)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.88 % (3860714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.88 % (3860714)CaDiCaL version: 2.1.3
% 3.35/0.88 % (3860714)Termination reason: Instruction limit
% 3.35/0.88 % (3860714)Termination phase: Saturation
% 3.35/0.88 % (3860714)Time elapsed: 0.323 s
% 3.35/0.88 % (3860714)Peak memory usage: 18 MB
% 3.35/0.88 % (3860714)Instructions burned: 635 (million)
% 3.35/0.88 % (3860805)Instruction limit reached!
% 3.35/0.88 % (3860805)------------------------------
% 3.35/0.88 % (3860805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.88 % (3860805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.88 % (3860805)CaDiCaL version: 2.1.3
% 3.35/0.88 % (3860805)Termination reason: Instruction limit
% 3.35/0.88 % (3860805)Termination phase: shuffling
% 3.35/0.88 % (3860805)Time elapsed: 0.007 s
% 3.35/0.88 % (3860805)Peak memory usage: 10 MB
% 3.35/0.88 % (3860805)Instructions burned: 15 (million)
% 3.35/0.88 % (3860807)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=1048506144:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 3.35/0.88 % (3860808)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=597976358:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 3.35/0.88 % (3860799)Refutation not found, incomplete strategy
% 3.35/0.88 % (3860799)------------------------------
% 3.35/0.88 % (3860799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.88 % (3860799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.88 % (3860799)CaDiCaL version: 2.1.3
% 3.35/0.88 % (3860799)Termination reason: Refutation not found, incomplete strategy
% 3.35/0.88 % (3860799)Time elapsed: 0.072 s
% 3.35/0.88 % (3860799)Peak memory usage: 15 MB
% 3.35/0.88 % (3860799)Instructions burned: 150 (million)
% 3.35/0.88 % (3860799)------------------------------
% 3.35/0.88 % (3860799)------------------------------
% 3.35/0.88 % (3860808)Instruction limit reached!
% 3.35/0.88 % (3860808)------------------------------
% 3.35/0.88 % (3860808)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.88 % (3860808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.88 % (3860808)CaDiCaL version: 2.1.3
% 3.35/0.88 % (3860808)Termination reason: Instruction limit
% 3.35/0.88 % (3860808)Termination phase: Property scanning
% 3.35/0.88 % (3860808)Time elapsed: 0.022 s
% 3.35/0.88 % (3860808)Peak memory usage: 10 MB
% 3.35/0.88 % (3860808)Instructions burned: 53 (million)
% 3.35/0.88 % (3860811)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3532789656:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/31Mi)
% 3.35/0.88 % (3860807)Instruction limit reached!
% 3.35/0.88 % (3860807)------------------------------
% 3.35/0.88 % (3860807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.88 % (3860807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.88 % (3860807)CaDiCaL version: 2.1.3
% 3.35/0.88 % (3860807)Termination reason: Instruction limit
% 3.35/0.88 % (3860807)Termination phase: Property scanning
% 3.35/0.88 % (3860807)Time elapsed: 0.028 s
% 3.35/0.88 % (3860807)Peak memory usage: 11 MB
% 3.35/0.88 % (3860807)Instructions burned: 68 (million)
% 3.35/0.88 % (3860802)Instruction limit reached!
% 3.35/0.88 % (3860802)------------------------------
% 3.35/0.88 % (3860802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.88 % (3860802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.88 % (3860802)CaDiCaL version: 2.1.3
% 3.35/0.88 % (3860802)Termination reason: Instruction limit
% 3.35/0.88 % (3860802)Termination phase: Saturation
% 3.35/0.88 % (3860802)Time elapsed: 0.085 s
% 3.35/0.88 % (3860802)Peak memory usage: 14 MB
% 3.35/0.88 % (3860802)Instructions burned: 200 (million)
% 3.35/0.88 % (3860811)Instruction limit reached!
% 3.35/0.88 % (3860811)------------------------------
% 3.35/0.88 % (3860811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.35/0.88 % (3860811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/0.88 % (3860811)CaDiCaL version: 2.1.3
% 3.35/0.88 % (3860811)Termination reason: Instruction limit
% 3.35/0.88 % (3860811)Termination phase: Property scanning
% 3.35/0.88 % (3860811)Time elapsed: 0.014 s
% 3.92/0.99 % (3860811)Peak memory usage: 10 MB
% 3.92/0.99 % (3860811)Instructions burned: 33 (million)
% 3.92/0.99 % (3860812)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=1175282232:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 3.92/0.99 % (3860792)Instruction limit reached!
% 3.92/0.99 % (3860792)------------------------------
% 3.92/0.99 % (3860792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.92/0.99 % (3860792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/0.99 % (3860792)CaDiCaL version: 2.1.3
% 3.92/0.99 % (3860792)Termination reason: Instruction limit
% 3.92/0.99 % (3860792)Termination phase: Saturation
% 3.92/0.99 % (3860792)Time elapsed: 0.146 s
% 3.92/0.99 % (3860792)Peak memory usage: 15 MB
% 3.92/0.99 % (3860792)Instructions burned: 317 (million)
% 3.92/0.99 % (3860814)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=210981525:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 3.92/0.99 % (3860816)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 3.92/0.99 % (3860815)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=366821082:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 3.92/0.99 % (3860816)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=3554208975:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 3.92/0.99 % (3860814)Instruction limit reached!
% 3.92/0.99 % (3860814)------------------------------
% 3.92/0.99 % (3860814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.92/0.99 % (3860814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/0.99 % (3860814)CaDiCaL version: 2.1.3
% 3.92/0.99 % (3860814)Termination reason: Instruction limit
% 3.92/0.99 % (3860814)Termination phase: Property scanning
% 3.92/0.99 % (3860814)Time elapsed: 0.015 s
% 3.92/0.99 % (3860814)Peak memory usage: 10 MB
% 3.92/0.99 % (3860814)Instructions burned: 35 (million)
% 3.92/0.99 % (3860818)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=1358378887:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 3.92/0.99 % (3860822)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=1928970738:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 3.92/0.99 % (3860815)Instruction limit reached!
% 3.92/0.99 % (3860815)------------------------------
% 3.92/0.99 % (3860815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.92/0.99 % (3860815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/0.99 % (3860815)CaDiCaL version: 2.1.3
% 3.92/0.99 % (3860815)Termination reason: Instruction limit
% 3.92/0.99 % (3860815)Termination phase: Property scanning
% 3.92/0.99 % (3860815)Time elapsed: 0.028 s
% 3.92/0.99 % (3860815)Peak memory usage: 11 MB
% 3.92/0.99 % (3860815)Instructions burned: 68 (million)
% 3.92/0.99 % (3860812)Instruction limit reached!
% 3.92/0.99 % (3860812)------------------------------
% 3.92/0.99 % (3860812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.92/0.99 % (3860812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/0.99 % (3860812)CaDiCaL version: 2.1.3
% 3.92/0.99 % (3860812)Termination reason: Instruction limit
% 3.92/0.99 % (3860812)Termination phase: Saturation
% 3.92/0.99 % (3860812)Time elapsed: 0.059 s
% 3.92/0.99 % (3860812)Peak memory usage: 13 MB
% 3.92/0.99 % (3860812)Instructions burned: 138 (million)
% 3.92/0.99 % (3860825)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=4266965863:i=427:sd=1:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/427Mi)
% 3.92/0.99 % (3860793)Instruction limit reached!
% 3.92/0.99 % (3860793)------------------------------
% 3.92/0.99 % (3860793)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.92/0.99 % (3860793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.92/0.99 % (3860793)CaDiCaL version: 2.1.3
% 3.92/0.99 % (3860793)Termination reason: Instruction limit
% 3.92/0.99 % (3860793)Termination phase: Saturation
% 3.92/0.99 % (3860793)Time elapsed: 0.222 s
% 3.92/0.99 % (3860793)Peak memory usage: 20 MB
% 3.92/0.99 % (3860793)Instructions burned: 854 (million)
% 3.92/0.99 % (3860826)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1054712973:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/874Mi)
% 5.22/1.10 % (3860822)Instruction limit reached!
% 5.22/1.10 % (3860822)------------------------------
% 5.22/1.10 % (3860822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.10 % (3860822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.10 % (3860822)CaDiCaL version: 2.1.3
% 5.22/1.10 % (3860822)Termination reason: Instruction limit
% 5.22/1.10 % (3860822)Termination phase: Saturation
% 5.22/1.10 % (3860822)Time elapsed: 0.040 s
% 5.22/1.10 % (3860822)Peak memory usage: 12 MB
% 5.22/1.10 % (3860822)Instructions burned: 98 (million)
% 5.22/1.10 % (3860828)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=3231785500:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/515Mi)
% 5.22/1.10 % (3860825)Refutation not found, incomplete strategy
% 5.22/1.10 % (3860825)------------------------------
% 5.22/1.10 % (3860825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.10 % (3860825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.10 % (3860825)CaDiCaL version: 2.1.3
% 5.22/1.10 % (3860825)Termination reason: Refutation not found, incomplete strategy
% 5.22/1.10 % (3860825)Time elapsed: 0.021 s
% 5.22/1.10 % (3860825)Peak memory usage: 13 MB
% 5.22/1.10 % (3860825)Instructions burned: 47 (million)
% 5.22/1.10 % (3860825)------------------------------
% 5.22/1.10 % (3860825)------------------------------
% 5.22/1.10 % (3860830)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=192794848:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 5.22/1.10 % (3860816)Instruction limit reached!
% 5.22/1.10 % (3860816)------------------------------
% 5.22/1.10 % (3860816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.10 % (3860816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.10 % (3860816)CaDiCaL version: 2.1.3
% 5.22/1.10 % (3860816)Termination reason: Instruction limit
% 5.22/1.10 % (3860816)Termination phase: Saturation
% 5.22/1.10 % (3860816)Time elapsed: 0.082 s
% 5.22/1.10 % (3860816)Peak memory usage: 13 MB
% 5.22/1.10 % (3860816)Instructions burned: 182 (million)
% 5.22/1.10 % (3860832)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3257846099:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 5.22/1.10 % (3860834)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=881273519:s2a=on:i=571:nm=16:rtra=on_2994 on theBenchmark for (2994ds/571Mi)
% 5.22/1.10 % (3860832)Instruction limit reached!
% 5.22/1.10 % (3860832)------------------------------
% 5.22/1.10 % (3860832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.10 % (3860832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.10 % (3860832)CaDiCaL version: 2.1.3
% 5.22/1.10 % (3860832)Termination reason: Instruction limit
% 5.22/1.10 % (3860832)Termination phase: Property scanning
% 5.22/1.10 % (3860832)Time elapsed: 0.018 s
% 5.22/1.10 % (3860832)Peak memory usage: 10 MB
% 5.22/1.10 % (3860832)Instructions burned: 44 (million)
% 5.22/1.10 % (3860818)Instruction limit reached!
% 5.22/1.10 % (3860818)------------------------------
% 5.22/1.10 % (3860818)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.10 % (3860818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.10 % (3860818)CaDiCaL version: 2.1.3
% 5.22/1.10 % (3860818)Termination reason: Instruction limit
% 5.22/1.10 % (3860818)Termination phase: Saturation
% 5.22/1.10 % (3860818)Time elapsed: 0.120 s
% 5.22/1.10 % (3860818)Peak memory usage: 15 MB
% 5.22/1.10 % (3860818)Instructions burned: 246 (million)
% 5.22/1.10 % (3860837)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=8021565:i=450:rtra=on:ixr=off:ntd=on_2994 on theBenchmark for (2994ds/450Mi)
% 5.22/1.10 % (3860830)Instruction limit reached!
% 5.22/1.10 % (3860830)------------------------------
% 5.22/1.10 % (3860830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.10 % (3860830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.10 % (3860830)CaDiCaL version: 2.1.3
% 5.22/1.10 % (3860830)Termination reason: Instruction limit
% 5.22/1.10 % (3860830)Termination phase: Saturation
% 5.22/1.10 % (3860830)Time elapsed: 0.061 s
% 5.22/1.11 % (3860830)Peak memory usage: 13 MB
% 5.22/1.11 % (3860830)Instructions burned: 130 (million)
% 5.22/1.11 % (3860838)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=2947954459:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/95Mi)
% 5.22/1.11 % (3860841)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=4192574978:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2994 on theBenchmark for (2994ds/65Mi)
% 5.22/1.11 % (3860838)Instruction limit reached!
% 5.22/1.11 % (3860838)------------------------------
% 5.22/1.11 % (3860838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.11 % (3860838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.11 % (3860838)CaDiCaL version: 2.1.3
% 5.22/1.11 % (3860838)Termination reason: Instruction limit
% 5.22/1.11 % (3860838)Termination phase: Saturation
% 5.22/1.11 % (3860838)Time elapsed: 0.040 s
% 5.22/1.11 % (3860838)Peak memory usage: 12 MB
% 5.22/1.11 % (3860838)Instructions burned: 97 (million)
% 5.22/1.11 % (3860841)Instruction limit reached!
% 5.22/1.11 % (3860841)------------------------------
% 5.22/1.11 % (3860841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.11 % (3860841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.11 % (3860841)CaDiCaL version: 2.1.3
% 5.22/1.11 % (3860841)Termination reason: Instruction limit
% 5.22/1.11 % (3860841)Termination phase: Clausification
% 5.22/1.11 % (3860841)Time elapsed: 0.027 s
% 5.22/1.11 % (3860841)Peak memory usage: 11 MB
% 5.22/1.11 % (3860841)Instructions burned: 66 (million)
% 5.22/1.11 % (3860828)Instruction limit reached!
% 5.22/1.11 % (3860828)------------------------------
% 5.22/1.11 % (3860828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.11 % (3860828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.11 % (3860828)CaDiCaL version: 2.1.3
% 5.22/1.11 % (3860828)Termination reason: Instruction limit
% 5.22/1.11 % (3860828)Termination phase: Saturation
% 5.22/1.11 % (3860828)Time elapsed: 0.128 s
% 5.22/1.11 % (3860828)Peak memory usage: 17 MB
% 5.22/1.11 % (3860828)Instructions burned: 516 (million)
% 5.22/1.11 % (3860834)Refutation not found, incomplete strategy
% 5.22/1.11 % (3860834)------------------------------
% 5.22/1.11 % (3860834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.11 % (3860834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.11 % (3860834)CaDiCaL version: 2.1.3
% 5.22/1.11 % (3860834)Termination reason: Refutation not found, incomplete strategy
% 5.22/1.11 % (3860834)Time elapsed: 0.095 s
% 5.22/1.11 % (3860834)Peak memory usage: 15 MB
% 5.22/1.11 % (3860834)Instructions burned: 192 (million)
% 5.22/1.11 % (3860834)------------------------------
% 5.22/1.11 % (3860834)------------------------------
% 5.22/1.11 % (3860845)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=740751313:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/375Mi)
% 5.22/1.11 % (3860843)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=3762484462:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2993 on theBenchmark for (2993ds/105Mi)
% 5.22/1.11 % (3860844)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=3684837303:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2993 on theBenchmark for (2993ds/5755Mi)
% 5.22/1.11 % (3860846)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2808055538:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2993 on theBenchmark for (2993ds/495Mi)
% 5.22/1.11 % (3860843)Instruction limit reached!
% 5.22/1.11 % (3860843)------------------------------
% 5.22/1.11 % (3860843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.11 % (3860843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.11 % (3860843)CaDiCaL version: 2.1.3
% 5.22/1.11 % (3860843)Termination reason: Instruction limit
% 5.22/1.11 % (3860843)Termination phase: Saturation
% 5.22/1.11 % (3860843)Time elapsed: 0.044 s
% 5.22/1.11 % (3860843)Peak memory usage: 12 MB
% 5.22/1.11 % (3860843)Instructions burned: 107 (million)
% 5.22/1.11 % (3860851)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=713284434:cond=on:i=34:hud=10:nm=10:rtra=on_2993 on theBenchmark for (2993ds/34Mi)
% 5.22/1.11 % (3860851)Instruction limit reached!
% 5.22/1.11 % (3860851)------------------------------
% 5.22/1.11 % (3860851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.11 % (3860851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.11 % (3860851)CaDiCaL version: 2.1.3
% 5.22/1.11 % (3860851)Termination reason: Instruction limit
% 5.22/1.11 % (3860851)Termination phase: Property scanning
% 5.22/1.11 % (3860851)Time elapsed: 0.015 s
% 5.22/1.11 % (3860851)Peak memory usage: 10 MB
% 5.22/1.11 % (3860851)Instructions burned: 34 (million)
% 5.22/1.11 % (3860853)ott+1002_4_tgt=ground:si=on:tsa=off:nwc=1:random_seed=3081450314:s2a=on:i=91:piset=or:hud=5:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/91Mi)
% 5.22/1.11 % (3860845)Instruction limit reached!
% 5.22/1.11 % (3860845)------------------------------
% 5.22/1.11 % (3860845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.11 % (3860845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.11 % (3860845)CaDiCaL version: 2.1.3
% 5.22/1.11 % (3860845)Termination reason: Instruction limit
% 5.22/1.11 % (3860845)Termination phase: Saturation
% 5.22/1.11 % (3860845)Time elapsed: 0.105 s
% 5.22/1.11 % (3860845)Peak memory usage: 14 MB
% 5.22/1.11 % (3860845)Instructions burned: 375 (million)
% 5.22/1.11 % (3860855)dis+2_1_sil=128000:tgt=ground:e2e=on:si=on:sos=on:urr=on:uwa=off:nwc=2:random_seed=3188038172:i=66:sd=50:kws=inv_arity:bd=preordered:nm=64:rtra=on:ss=axioms:c=on:ntd=on_2992 on theBenchmark for (2992ds/66Mi)
% 5.22/1.11 % (3860837)Instruction limit reached!
% 5.22/1.11 % (3860837)------------------------------
% 5.22/1.11 % (3860837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.11 % (3860837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.11 % (3860837)CaDiCaL version: 2.1.3
% 5.22/1.11 % (3860837)Termination reason: Instruction limit
% 5.22/1.11 % (3860837)Termination phase: Saturation
% 5.22/1.11 % (3860837)Time elapsed: 0.208 s
% 5.22/1.11 % (3860837)Peak memory usage: 18 MB
% 5.22/1.11 % (3860837)Instructions burned: 450 (million)
% 5.22/1.11 % (3860853)Instruction limit reached!
% 5.22/1.11 % (3860853)------------------------------
% 5.22/1.11 % (3860853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.11 % (3860853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.11 % (3860853)CaDiCaL version: 2.1.3
% 5.22/1.11 % (3860853)Termination reason: Instruction limit
% 5.22/1.11 % (3860853)Termination phase: Property scanning
% 5.22/1.11 % (3860853)Time elapsed: 0.038 s
% 5.22/1.11 % (3860853)Peak memory usage: 12 MB
% 5.22/1.11 % (3860853)Instructions burned: 92 (million)
% 5.22/1.11 % (3860855)Instruction limit reached!
% 5.22/1.11 % (3860855)------------------------------
% 5.22/1.11 % (3860855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.11 % (3860855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.11 % (3860855)CaDiCaL version: 2.1.3
% 5.22/1.11 % (3860855)Termination reason: Instruction limit
% 5.22/1.11 % (3860855)Termination phase: Saturation
% 5.22/1.11 % (3860855)Time elapsed: 0.019 s
% 5.22/1.11 % (3860855)Peak memory usage: 13 MB
% 5.22/1.11 % (3860855)Instructions burned: 67 (million)
% 5.22/1.11 % (3860858)lrs+21_16_anc=none:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:sas=cadical:si=on:plsqr=32,1:uwa=interpreted_only:foolp=on:nwc=3:random_seed=3213826849:i=338:bd=all:ins=4:rtra=on_2992 on theBenchmark for (2992ds/338Mi)
% 5.22/1.11 % (3860857)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1269723916:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2992 on theBenchmark for (2992ds/22Mi)
% 5.22/1.11 % (3860771)Instruction limit reached!
% 5.22/1.11 % (3860771)------------------------------
% 5.22/1.11 % (3860771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.11 % (3860771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.11 % (3860771)CaDiCaL version: 2.1.3
% 5.22/1.11 % (3860771)Termination reason: Instruction limit
% 5.22/1.11 % (3860771)Termination phase: Saturation
% 5.22/1.11 % (3860771)Time elapsed: 0.602 s
% 5.22/1.11 % (3860771)Peak memory usage: 21 MB
% 5.22/1.11 % (3860771)Instructions burned: 1240 (million)
% 5.22/1.11 % (3860859)lrs+10_1_sil=128000:si=on:urr=on:random_seed=185594651:i=28:sd=1:rtra=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/28Mi)
% 5.22/1.11 % (3860826) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3860706-3860826"...
% 5.22/1.11 % (3860857)Instruction limit reached!
% 5.22/1.11 % (3860857)------------------------------
% 5.22/1.11 % (3860857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.11 % (3860857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.11 % (3860857)CaDiCaL version: 2.1.3
% 5.22/1.11 % (3860857)Termination reason: Instruction limit
% 5.22/1.11 % (3860857)Termination phase: Property scanning
% 5.22/1.11 % (3860857)Time elapsed: 0.010 s
% 5.22/1.11 % (3860857)Peak memory usage: 10 MB
% 5.22/1.11 % (3860857)Instructions burned: 22 (million)
% 5.22/1.11 % (3860826)...printing done.
% 5.22/1.11 % (3860859)Instruction limit reached!
% 5.22/1.11 % (3860859)------------------------------
% 5.22/1.11 % (3860859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.11 % (3860859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.11 % (3860859)CaDiCaL version: 2.1.3
% 5.22/1.11 % (3860859)Termination reason: Instruction limit
% 5.22/1.11 % (3860859)Termination phase: Property scanning
% 5.22/1.11 % (3860859)Time elapsed: 0.013 s
% 5.22/1.11 % (3860859)Peak memory usage: 10 MB
% 5.22/1.11 % (3860859)Instructions burned: 30 (million)
% 5.22/1.11 % (3860826)Refutation found. Thanks to Tanya!
% 5.22/1.11 % SZS status Theorem for theBenchmark
% 5.22/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 5.22/1.12 % (3860826)------------------------------
% 5.22/1.12 % (3860826)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.12 % (3860826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.12 % (3860826)CaDiCaL version: 2.1.3
% 5.22/1.12 % (3860826)Termination reason: Refutation
% 5.22/1.12 % (3860826)Time elapsed: 0.308 s
% 5.22/1.12 % (3860826)Peak memory usage: 18 MB
% 5.22/1.12 % (3860826)Instructions burned: 668 (million)
% 5.22/1.12 % (3860706)Success in time 0.82 s
% 5.22/1.12 % Vampire exiting
%------------------------------------------------------------------------------