%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG263^3 : 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 : n026.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 07:45:15 AM UTC 2026
% Result : Theorem 6.86s 1.31s
% Output : Refutation 6.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 16
% Syntax : Number of formulae : 150 ( 36 unt; 0 typ; 10 def)
% Number of atoms : 1581 ( 204 equ; 0 cnn)
% Maximal formula atoms : 6 ( 10 avg)
% Number of connectives : 1946 ( 71 ~; 142 |; 0 &; 776 @)
% ( 12 <=>; 829 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 510 ( 506 usr; 198 con; 0-4 aty)
% ( 116 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 200 ( 6 sgn 46 !; 0 ?; 200 :)
% 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,
vIFF: $o > $o > $o ).
thf(func_def_125,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_127,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_131,type,
vIMP: $o > $o > $o ).
thf(func_def_132,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_133,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_134,type,
vNOT: $o > $o ).
thf(func_def_135,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_138,type,
vAND: $o > $o > $o ).
thf(func_def_139,type,
sK0: subst ).
thf(func_def_140,type,
sK1: term ).
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: ( subst > term > subst > $o ) > term > term ).
thf(func_def_144,type,
sK5: ( subst > term > subst > $o ) > term > term ).
thf(func_def_145,type,
sK6: ( subst > term > subst > $o ) > term > term ).
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 ) > term ).
thf(func_def_149,type,
sK10: ( subst > term > term ) > subst ).
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: subst ).
thf(func_def_156,type,
sK17: ( subst > term > subst > $o ) > subst ).
thf(func_def_157,type,
sK18: ( subst > term > subst > $o ) > term ).
thf(func_def_158,type,
sK19: ( subst > term > subst > $o ) > subst ).
thf(func_def_159,type,
sK20: ( subst > term > subst > $o ) > subst ).
thf(func_def_160,type,
sK21: ( subst > term > subst > $o ) > subst ).
thf(func_def_161,type,
sK22: ( subst > term > subst > $o ) > term ).
thf(func_def_162,type,
sK23: ( subst > term > subst > $o ) > term ).
thf(func_def_163,type,
sK24: ( subst > term > subst > $o ) > subst ).
thf(func_def_164,type,
sK25: ( subst > term > subst > $o ) > subst ).
thf(func_def_165,type,
sK26: ( subst > term > subst > $o ) > subst ).
thf(func_def_166,type,
sK27: ( subst > term > subst > $o ) > term ).
thf(func_def_167,type,
sK28: ( subst > term > subst > $o ) > term ).
thf(func_def_168,type,
sK29: ( subst > term > subst > $o ) > subst ).
thf(func_def_169,type,
sK30: ( subst > term > subst > $o ) > subst ).
thf(func_def_170,type,
sK31: subst > term > subst > $o ).
thf(func_def_171,type,
sK32: term ).
thf(func_def_172,type,
sK33: subst > ( term > $o ) > term ).
thf(func_def_173,type,
sK34: subst ).
thf(func_def_174,type,
sK35: term > $o ).
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: subst ).
thf(func_def_179,type,
sK40: term ).
thf(func_def_180,type,
sK41: term ).
thf(func_def_181,type,
sK42: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_182,type,
sK43: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_183,type,
sK44: term > ( term > $o ) > term ).
thf(func_def_184,type,
sK45: term > ( term > $o ) > term ).
thf(func_def_185,type,
sK46: subst > term > subst > $o ).
thf(func_def_186,type,
sK47: term > $o ).
thf(func_def_187,type,
sK48: ( subst > term > term ) > term ).
thf(func_def_188,type,
sK49: ( subst > term > term ) > term ).
thf(func_def_189,type,
sK50: ( subst > term > term ) > subst ).
thf(func_def_190,type,
sK51: ( subst > term > term ) > subst ).
thf(func_def_191,type,
sK52: ( subst > term > term ) > subst ).
thf(func_def_192,type,
sK53: term ).
thf(func_def_193,type,
sK54: subst ).
thf(func_def_194,type,
sK55: term ).
thf(func_def_195,type,
sK56: term ).
thf(func_def_196,type,
sK57: term ).
thf(func_def_197,type,
sK58: term ).
thf(func_def_198,type,
sK59: term ).
thf(func_def_199,type,
sK60: term ).
thf(func_def_200,type,
sK61: subst ).
thf(func_def_201,type,
sK62: term ).
thf(func_def_202,type,
sK63: term ).
thf(func_def_203,type,
sK64: subst ).
thf(func_def_204,type,
sK65: term ).
thf(func_def_205,type,
sK66: term ).
thf(func_def_206,type,
sK67: term ).
thf(func_def_207,type,
sK68: term ).
thf(func_def_208,type,
sK69: term ).
thf(func_def_209,type,
sK70: term ).
thf(func_def_210,type,
sK71: ( subst > term > term ) > subst ).
thf(func_def_211,type,
sK72: ( subst > term > term ) > term ).
thf(func_def_212,type,
sK73: ( subst > term > term ) > subst ).
thf(func_def_213,type,
sK74: ( subst > term > term ) > subst ).
thf(func_def_214,type,
sK75: ( subst > term > term ) > term ).
thf(func_def_215,type,
sK76: ( subst > term > term ) > subst ).
thf(func_def_216,type,
sK77: subst > term > term ).
thf(func_def_217,type,
sK78: subst > term > term ).
thf(func_def_218,type,
sK79: subst ).
thf(func_def_219,type,
sK80: term ).
thf(func_def_220,type,
sK81: term ).
thf(func_def_221,type,
sK82: term ).
thf(func_def_222,type,
sK83: term ).
thf(func_def_223,type,
sK84: term ).
thf(func_def_224,type,
sK85: term ).
thf(func_def_225,type,
sK86: ( subst > term > subst > $o ) > term ).
thf(func_def_226,type,
sK87: ( subst > term > subst > $o ) > subst ).
thf(func_def_227,type,
sK88: ( subst > term > subst > $o ) > term ).
thf(func_def_228,type,
sK89: ( subst > term > subst > $o ) > term ).
thf(func_def_229,type,
sK90: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_230,type,
sK91: ( subst > term > subst > $o ) > subst ).
thf(func_def_231,type,
sK92: ( subst > term > subst > $o ) > term ).
thf(func_def_232,type,
sK93: ( subst > term > subst > $o ) > subst ).
thf(func_def_233,type,
sK94: ( subst > term > subst > $o ) > subst ).
thf(func_def_234,type,
sK95: ( subst > term > subst > $o ) > term ).
thf(func_def_235,type,
sK96: ( subst > term > subst > $o ) > subst ).
thf(func_def_236,type,
sK97: ( subst > term > subst > $o ) > subst ).
thf(func_def_237,type,
sK98: ( subst > term > subst > $o ) > term ).
thf(func_def_238,type,
sK99: ( subst > term > subst > $o ) > subst ).
thf(func_def_239,type,
sK100: ( subst > term > subst > $o ) > subst ).
thf(func_def_240,type,
sK101: ( subst > term > subst > $o ) > term ).
thf(func_def_241,type,
sK102: ( subst > term > subst > $o ) > subst ).
thf(func_def_242,type,
sK103: ( subst > term > subst > $o ) > subst ).
thf(func_def_243,type,
sK104: ( subst > term > subst > $o ) > subst ).
thf(func_def_244,type,
sK105: ( subst > term > subst > $o ) > term ).
thf(func_def_245,type,
sK106: ( subst > term > subst > $o ) > subst ).
thf(func_def_246,type,
sK107: ( subst > term > subst > $o ) > subst ).
thf(func_def_247,type,
sK108: ( subst > term > subst > $o ) > subst ).
thf(func_def_248,type,
sK109: ( subst > term > subst > $o ) > subst ).
thf(func_def_249,type,
sK110: ( subst > term > subst > $o ) > subst ).
thf(func_def_250,type,
sK111: ( subst > term > subst > $o ) > subst ).
thf(func_def_251,type,
sK112: ( subst > term > subst > $o ) > subst ).
thf(func_def_252,type,
sK113: ( subst > term > subst > $o ) > subst ).
thf(func_def_253,type,
sK114: ( subst > term > subst > $o ) > subst ).
thf(func_def_254,type,
sK115: ( subst > term > subst > $o ) > term ).
thf(func_def_255,type,
sK116: ( subst > term > subst > $o ) > subst ).
thf(func_def_256,type,
sK117: ( subst > term > subst > $o ) > subst ).
thf(func_def_257,type,
sK118: ( subst > term > subst > $o ) > subst ).
thf(func_def_258,type,
sK119: ( subst > term > subst > $o ) > subst ).
thf(func_def_259,type,
sK120: ( subst > term > subst > $o ) > subst ).
thf(func_def_260,type,
sK121: ( subst > term > subst > $o ) > subst ).
thf(func_def_261,type,
sK122: ( subst > term > subst > $o ) > subst ).
thf(func_def_262,type,
sK123: ( subst > term > subst > $o ) > subst ).
thf(func_def_263,type,
sK124: ( subst > term > subst > $o ) > subst ).
thf(func_def_264,type,
sK125: ( subst > term > subst > $o ) > term ).
thf(func_def_265,type,
sK126: ( subst > term > subst > $o ) > subst ).
thf(func_def_266,type,
sK127: ( subst > term > subst > $o ) > subst ).
thf(func_def_267,type,
sK128: ( subst > term > subst > $o ) > term ).
thf(func_def_268,type,
sK129: ( subst > term > subst > $o ) > subst ).
thf(func_def_269,type,
sK130: ( subst > term > subst > $o ) > subst ).
thf(func_def_270,type,
sK131: ( subst > term > subst > $o ) > subst ).
thf(func_def_271,type,
sK132: ( subst > term > subst > $o ) > subst ).
thf(func_def_272,type,
sK133: ( subst > term > subst > $o ) > subst ).
thf(func_def_273,type,
sK134: ( subst > term > subst > $o ) > subst ).
thf(func_def_274,type,
sK135: ( subst > term > subst > $o ) > term ).
thf(func_def_275,type,
sK136: ( subst > term > subst > $o ) > subst ).
thf(func_def_276,type,
sK137: ( subst > term > subst > $o ) > subst ).
thf(func_def_277,type,
sK138: ( subst > term > subst > $o ) > subst ).
thf(func_def_278,type,
sK139: ( subst > term > subst > $o ) > subst ).
thf(func_def_279,type,
sK140: ( subst > term > subst > $o ) > subst ).
thf(func_def_280,type,
sK141: ( subst > term > subst > $o ) > subst ).
thf(func_def_281,type,
sK142: ( subst > term > subst > $o ) > subst ).
thf(func_def_282,type,
sK143: ( subst > term > subst > $o ) > term ).
thf(func_def_283,type,
sK144: ( subst > term > subst > $o ) > subst ).
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: ( subst > term > subst > $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 ) > subst ).
thf(func_def_290,type,
sK151: ( subst > term > subst > $o ) > subst ).
thf(func_def_291,type,
sK152: ( subst > term > subst > $o ) > subst ).
thf(func_def_292,type,
sK153: ( subst > term > subst > $o ) > subst ).
thf(func_def_293,type,
sK154: subst > term > subst > $o ).
thf(func_def_294,type,
sK155: ( subst > term > term ) > term ).
thf(func_def_295,type,
sK156: ( subst > term > term ) > term ).
thf(func_def_296,type,
sK157: ( subst > term > term ) > subst ).
thf(func_def_297,type,
sK158: ( subst > term > term ) > subst ).
thf(func_def_298,type,
sK159: ( subst > term > term ) > subst ).
thf(func_def_299,type,
sK160: term ).
thf(func_def_300,type,
sK161: ( subst > term > subst > $o ) > subst ).
thf(func_def_301,type,
sK162: ( subst > term > subst > $o ) > term ).
thf(func_def_302,type,
sK163: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_303,type,
sK164: ( subst > term > subst > $o ) > term ).
thf(func_def_304,type,
sK165: ( subst > term > subst > $o ) > subst ).
thf(func_def_305,type,
sK166: ( subst > term > subst > $o ) > subst ).
thf(func_def_306,type,
sK167: ( subst > term > subst > $o ) > subst ).
thf(func_def_307,type,
sK168: ( subst > term > subst > $o ) > term ).
thf(func_def_308,type,
sK169: ( subst > term > subst > $o ) > subst ).
thf(func_def_309,type,
sK170: ( subst > term > subst > $o ) > subst ).
thf(func_def_310,type,
sK171: ( subst > term > subst > $o ) > subst ).
thf(func_def_311,type,
sK172: ( subst > term > subst > $o ) > term ).
thf(func_def_312,type,
sK173: ( subst > term > subst > $o ) > subst ).
thf(func_def_313,type,
sK174: ( subst > term > subst > $o ) > subst ).
thf(func_def_314,type,
sK175: ( subst > term > subst > $o ) > subst ).
thf(func_def_315,type,
sK176: subst > term > subst > $o ).
thf(func_def_316,type,
sK177: term > $o ).
thf(func_def_317,type,
sK178: term ).
thf(func_def_318,type,
sK179: term ).
thf(func_def_319,type,
sK180: ( term > $o ) > term ).
thf(func_def_320,type,
sK181: ( term > $o ) > term ).
thf(func_def_321,type,
sK182: ( term > $o ) > term ).
thf(func_def_322,type,
sK183: ( term > $o ) > subst > term ).
thf(func_def_323,type,
sK184: ( term > $o ) > term ).
thf(func_def_324,type,
sK185: ( term > $o ) > subst > term ).
thf(func_def_325,type,
sK186: ( term > $o ) > subst > term ).
thf(func_def_326,type,
sK187: ( term > $o ) > subst > term ).
thf(func_def_327,type,
sK188: term > $o ).
thf(func_def_328,type,
sK189: term > term ).
thf(func_def_329,type,
sK190: subst ).
thf(func_def_330,type,
sK191: term ).
thf(func_def_331,type,
sK192: ( term > $o ) > term ).
thf(func_def_332,type,
sK193: ( term > $o ) > term ).
thf(func_def_333,type,
sK194: ( term > $o ) > term ).
thf(func_def_334,type,
sK195: ( term > $o ) > term ).
thf(func_def_335,type,
sK196: ( term > $o ) > term ).
thf(func_def_336,type,
sK197: ( term > $o ) > term ).
thf(func_def_337,type,
sK198: term > $o ).
thf(func_def_338,type,
sK199: term > term ).
thf(func_def_339,type,
sK200: term ).
thf(func_def_340,type,
sK201: ( subst > term > subst > $o ) > subst ).
thf(func_def_341,type,
sK202: ( subst > term > subst > $o ) > term ).
thf(func_def_342,type,
sK203: ( subst > term > subst > $o ) > term ).
thf(func_def_343,type,
sK204: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_344,type,
sK205: ( subst > term > subst > $o ) > term ).
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 ) > term ).
thf(func_def_350,type,
sK211: ( subst > term > subst > $o ) > subst ).
thf(func_def_351,type,
sK212: ( subst > term > subst > $o ) > subst ).
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 ) > term ).
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 ) > term ).
thf(func_def_359,type,
sK220: subst > term > subst > $o ).
thf(func_def_360,type,
sK221: term > $o ).
thf(func_def_361,type,
sK222: term ).
thf(func_def_362,type,
sK223: term ).
thf(func_def_363,type,
sK224: ( subst > term > term ) > subst ).
thf(func_def_364,type,
sK225: ( subst > term > term ) > term ).
thf(func_def_365,type,
sK226: ( subst > term > term ) > subst ).
thf(func_def_366,type,
sK227: subst > term > term ).
thf(func_def_367,type,
sK228: term ).
thf(func_def_368,type,
sK229: subst ).
thf(func_def_369,type,
sK230: subst ).
thf(func_def_370,type,
sK231: ( subst > term > subst > $o ) > subst ).
thf(func_def_371,type,
sK232: ( subst > term > subst > $o ) > term ).
thf(func_def_372,type,
sK233: ( subst > term > subst > $o ) > term ).
thf(func_def_373,type,
sK234: ( subst > term > subst > $o ) > subst ).
thf(func_def_374,type,
sK235: ( subst > term > subst > $o ) > term ).
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 ) > term ).
thf(func_def_380,type,
sK241: ( subst > term > subst > $o ) > subst ).
thf(func_def_381,type,
sK242: ( subst > term > subst > $o ) > term ).
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 ) > term ).
thf(func_def_386,type,
sK247: subst > term > subst > $o ).
thf(func_def_387,type,
sK248: term ).
thf(func_def_388,type,
sK249: term ).
thf(func_def_389,type,
sK250: term ).
thf(func_def_390,type,
sK251: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_391,type,
sK252: subst > term > subst > $o ).
thf(func_def_392,type,
sK253: ( term > $o ) > term ).
thf(func_def_393,type,
sK254: term ).
thf(func_def_394,type,
sK255: term ).
thf(func_def_395,type,
sK256: ( subst > term > subst > $o ) > subst ).
thf(func_def_396,type,
sK257: ( subst > term > subst > $o ) > subst ).
thf(func_def_397,type,
sK258: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_398,type,
sK259: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_399,type,
sK260: ( subst > term > subst > $o ) > subst ).
thf(func_def_400,type,
sK261: term > ( term > $o ) > term ).
thf(func_def_401,type,
sK262: ( subst > term > subst > $o ) > subst ).
thf(func_def_402,type,
sK263: ( subst > term > subst > $o ) > subst ).
thf(func_def_403,type,
sK264: ( subst > term > subst > $o ) > subst ).
thf(func_def_404,type,
sK265: ( subst > term > subst > $o ) > term ).
thf(func_def_405,type,
sK266: ( subst > term > subst > $o ) > term ).
thf(func_def_406,type,
sK267: ( subst > term > subst > $o ) > term ).
thf(func_def_407,type,
sK268: ( subst > term > subst > $o ) > term ).
thf(func_def_408,type,
sK269: ( subst > term > subst > $o ) > subst ).
thf(func_def_409,type,
sK270: ( subst > term > subst > $o ) > subst ).
thf(func_def_410,type,
sK271: ( subst > term > subst > $o ) > term ).
thf(func_def_411,type,
sK272: ( subst > term > subst > $o ) > term ).
thf(func_def_412,type,
sK273: ( subst > term > subst > $o ) > subst ).
thf(func_def_413,type,
sK274: ( subst > term > subst > $o ) > term ).
thf(func_def_414,type,
sK275: ( subst > term > subst > $o ) > term ).
thf(func_def_415,type,
sK276: ( subst > term > subst > $o ) > subst ).
thf(func_def_416,type,
sK277: ( subst > term > subst > $o ) > subst ).
thf(func_def_417,type,
sK278: ( subst > term > subst > $o ) > term ).
thf(func_def_418,type,
sK279: ( subst > term > subst > $o ) > term ).
thf(func_def_419,type,
sK280: ( subst > term > subst > $o ) > subst ).
thf(func_def_420,type,
sK281: ( subst > term > subst > $o ) > term ).
thf(func_def_421,type,
sK282: ( subst > term > subst > $o ) > term ).
thf(func_def_422,type,
sK283: term > $o ).
thf(func_def_423,type,
sK284: subst > term > subst > $o ).
thf(func_def_424,type,
sK285: ( subst > term > term ) > subst ).
thf(func_def_425,type,
sK286: ( subst > term > term ) > term ).
thf(func_def_426,type,
sK287: ( subst > term > term ) > term ).
thf(func_def_427,type,
sK288: ( subst > term > term ) > subst ).
thf(func_def_428,type,
sK289: ( subst > term > term ) > term ).
thf(func_def_429,type,
sK290: ( subst > term > term ) > subst ).
thf(func_def_430,type,
sK291: term ).
thf(func_def_431,type,
sK292: term ).
thf(func_def_432,type,
sK293: term ).
thf(func_def_433,type,
sK294: term ).
thf(func_def_434,type,
sK295: ( term > $o ) > term ).
thf(func_def_435,type,
sK296: term > $o ).
thf(func_def_436,type,
sK297: term ).
thf(func_def_437,type,
sK298: subst ).
thf(func_def_438,type,
sK299: subst ).
thf(func_def_439,type,
sK300: ( subst > term > subst > $o ) > subst ).
thf(func_def_440,type,
sK301: ( subst > term > subst > $o ) > subst ).
thf(func_def_441,type,
sK302: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_442,type,
sK303: ( subst > term > subst > $o ) > subst ).
thf(func_def_443,type,
sK304: ( subst > term > subst > $o ) > subst ).
thf(func_def_444,type,
sK305: ( subst > term > subst > $o ) > term > term ).
thf(func_def_445,type,
sK306: ( subst > term > subst > $o ) > term ).
thf(func_def_446,type,
sK307: ( subst > term > subst > $o ) > subst ).
thf(func_def_447,type,
sK308: ( subst > term > subst > $o ) > term ).
thf(func_def_448,type,
sK309: ( subst > term > subst > $o ) > subst ).
thf(func_def_449,type,
sK310: ( subst > term > subst > $o ) > subst ).
thf(func_def_450,type,
sK311: ( subst > term > subst > $o ) > term ).
thf(func_def_451,type,
sK312: ( subst > term > subst > $o ) > subst ).
thf(func_def_452,type,
sK313: ( subst > term > subst > $o ) > term > term ).
thf(func_def_453,type,
sK314: ( subst > term > subst > $o ) > term ).
thf(func_def_454,type,
sK315: ( subst > term > subst > $o ) > subst ).
thf(func_def_455,type,
sK316: ( subst > term > subst > $o ) > subst ).
thf(func_def_456,type,
sK317: ( subst > term > subst > $o ) > term ).
thf(func_def_457,type,
sK318: ( subst > term > subst > $o ) > subst ).
thf(func_def_458,type,
sK319: ( subst > term > subst > $o ) > term ).
thf(func_def_459,type,
sK320: ( subst > term > subst > $o ) > term ).
thf(func_def_460,type,
sK321: ( subst > term > subst > $o ) > subst ).
thf(func_def_461,type,
sK322: ( subst > term > subst > $o ) > subst ).
thf(func_def_462,type,
sK323: ( subst > term > subst > $o ) > term > term ).
thf(func_def_463,type,
sK324: ( subst > term > subst > $o ) > term ).
thf(func_def_464,type,
sK325: ( subst > term > subst > $o ) > subst ).
thf(func_def_465,type,
sK326: ( subst > term > subst > $o ) > term ).
thf(func_def_466,type,
sK327: ( subst > term > subst > $o ) > subst ).
thf(func_def_467,type,
sK328: ( subst > term > subst > $o ) > subst ).
thf(func_def_468,type,
sK329: ( subst > term > subst > $o ) > term ).
thf(func_def_469,type,
sK330: ( subst > term > subst > $o ) > subst ).
thf(func_def_470,type,
sK331: ( subst > term > subst > $o ) > term ).
thf(func_def_471,type,
sK332: subst > term > subst > $o ).
thf(func_def_472,type,
sK333: ( subst > term > term ) > term ).
thf(func_def_473,type,
sK334: ( subst > term > term ) > term ).
thf(func_def_474,type,
sK335: ( subst > term > term ) > subst ).
thf(func_def_475,type,
sK336: ( subst > term > term ) > subst ).
thf(func_def_476,type,
sK337: ( subst > term > term ) > subst ).
thf(func_def_477,type,
sK338: ( subst > term > term ) > subst ).
thf(func_def_478,type,
sK339: term ).
thf(func_def_479,type,
sK340: term ).
thf(func_def_480,type,
sK341: term ).
thf(func_def_481,type,
sK342: term ).
thf(func_def_482,type,
sK343: term ).
thf(func_def_483,type,
sK344: ( subst > term > term ) > subst ).
thf(func_def_484,type,
sK345: ( subst > term > term ) > term ).
thf(func_def_485,type,
sK346: ( subst > term > term ) > subst ).
thf(func_def_486,type,
sK347: subst > term > term ).
thf(func_def_487,type,
sK348: term ).
thf(func_def_488,type,
sK349: term ).
thf(func_def_489,type,
sK350: ( term > $o ) > term ).
thf(func_def_490,type,
sK351: ( term > $o ) > term ).
thf(func_def_491,type,
sK352: ( term > $o ) > term ).
thf(func_def_492,type,
sK353: ( term > $o ) > term ).
thf(func_def_493,type,
sK354: term > $o ).
thf(func_def_494,type,
sK355: term ).
thf(func_def_495,type,
sK356: subst ).
thf(func_def_496,type,
sK357: subst ).
thf(func_def_497,type,
sK358: subst ).
thf(f3,axiom,
! [X0: term] :
( ( ( sub @ X0 @ id )
= X0 )
= axvarid ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarid) ).
thf(f57,axiom,
( hoasvar
= ( ^ [X0: subst,X1: term,X2: subst] : ( var @ ( sub @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasvar) ).
thf(f76,axiom,
( ( ^ [X0: subst > term > subst > $o,X1: term > $o] :
! [X2: term] :
( ( X0 @ id @ X2 @ id )
<=> ( X1 @ X2 ) ) )
= hoasinduction_p_and_p_prime ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasinduction_p_and_p_prime) ).
thf(f79,axiom,
! [X1: term > $o,X0: subst > term > subst > $o] :
( ( ! [X5: subst,X3: term,X2: subst,X4: subst] :
( ( X0 @ X2 @ X3 @ ( comp @ X5 @ X4 ) )
=> ( X0 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 ) )
=> ( ! [X5: subst,X2: subst,X4: subst,X3: term] :
( ( X0 @ ( comp @ X2 @ X5 ) @ ( sub @ X3 @ X5 ) @ X4 )
=> ( X0 @ X2 @ X3 @ ( comp @ X5 @ X4 ) ) )
=> ( ! [X3: term] :
( ( hoasvar @ id @ X3 @ id )
=> ( X0 @ id @ X3 @ id ) )
=> ( ( hoasinduction_p_and_p_prime @ X0 @ X1 )
=> ! [X3: term] :
( ( var @ X3 )
=> ( X1 @ X3 ) ) ) ) ) )
= hoasinduction_lem1v2 ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem1v2) ).
thf(f80,axiom,
( axapp
=> ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= hoasinduction_lem1v2_gthm ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem1v2_gthm) ).
thf(f114,conjecture,
hoasinduction_lem1v2_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ hoasinduction_lem1v2_gthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f150,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f216,plain,
( axapp
=> ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= hoasinduction_lem1v2_gthm ) ),
inference(rectify,[],[f80]) ).
thf(f217,plain,
( hoasinduction_lem1v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f216]) ).
thf(f227,plain,
~ hoasinduction_lem1v2_gthm,
inference(rectify,[],[f115]) ).
thf(f228,plain,
hoasinduction_lem1v2_gthm != $true,
inference(fool_elimination,[],[f227]) ).
thf(f248,plain,
( ( ^ [X0: subst > term > subst > $o,X1: term > $o] :
! [X2: term] :
( ( X0 @ id @ X2 @ id )
<=> ( X1 @ X2 ) ) )
= hoasinduction_p_and_p_prime ),
inference(rectify,[],[f76]) ).
thf(f249,plain,
( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f248]) ).
thf(f307,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f314,plain,
! [X0: term > $o,X1: subst > term > subst > $o] :
( ( ! [X2: subst,X3: term,X4: subst,X5: subst] :
( ( X1 @ X4 @ X3 @ ( comp @ X2 @ X5 ) )
=> ( X1 @ ( comp @ X4 @ X2 ) @ ( sub @ X3 @ X2 ) @ X5 ) )
=> ( ! [X6: subst,X7: subst,X8: subst,X9: term] :
( ( X1 @ ( comp @ X7 @ X6 ) @ ( sub @ X9 @ X6 ) @ X8 )
=> ( X1 @ X7 @ X9 @ ( comp @ X6 @ X8 ) ) )
=> ( ! [X10: term] :
( ( hoasvar @ id @ X10 @ id )
=> ( X1 @ id @ X10 @ id ) )
=> ( ( hoasinduction_p_and_p_prime @ X1 @ X0 )
=> ! [X11: term] :
( ( var @ X11 )
=> ( X0 @ X11 ) ) ) ) ) )
= hoasinduction_lem1v2 ),
inference(rectify,[],[f79]) ).
thf(f315,plain,
( hoasinduction_lem1v2
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y5 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y0 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y2 @ Y5 ) @ Y3 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y5 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( hoasvar @ id @ Y2 @ id )
=> ( Y0 @ id @ Y2 @ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f314]) ).
thf(f319,plain,
hoasinduction_lem1v2_gthm != $true,
inference(flattening,[],[f228]) ).
thf(f321,plain,
hoasinduction_lem1v2_gthm != $true,
inference(cnf_transformation,[],[f319]) ).
thf(f328,plain,
( hoasinduction_lem1v2_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f217]) ).
thf(f330,plain,
( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ id @ Y2 @ id )
= ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f249]) ).
thf(f333,plain,
( hoasinduction_lem1v2
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y5 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y0 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y2 @ Y5 ) @ Y3 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y5 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( hoasvar @ id @ Y2 @ id )
=> ( Y0 @ id @ Y2 @ id ) ) )
=> ( ( hoasinduction_p_and_p_prime @ Y0 @ Y1 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f315]) ).
thf(f349,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f307]) ).
thf(f355,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f150]) ).
thf(f374,plain,
( hoasinduction_lem1v2
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y5 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y0 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y2 @ Y5 ) @ Y3 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y5 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: term,Y5: subst] : ( var @ ( sub @ Y4 @ Y5 ) )
@ id
@ Y2
@ id )
=> ( Y0 @ id @ Y2 @ id ) ) )
=> ( ( ^ [Y2: subst > term > subst > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ id @ Y4 @ id )
= ( Y3 @ Y4 ) ) )
@ Y0
@ Y1 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f333,f355,f330]) ).
thf(f1267,plain,
( ( hoasinduction_lem1v2 = $true )
| ( $false
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y5 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y0 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y2 @ Y5 ) @ Y3 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y5 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: term,Y5: subst] : ( var @ ( sub @ Y4 @ Y5 ) )
@ id
@ Y2
@ id )
=> ( Y0 @ id @ Y2 @ id ) ) )
=> ( ( ^ [Y2: subst > term > subst > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ id @ Y4 @ id )
= ( Y3 @ Y4 ) ) )
@ Y0
@ Y1 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f374]) ).
thf(f1339,plain,
( ( hoasinduction_lem1v2 = $true )
| ( ( ^ [Y0: subst > term > subst > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y0 @ Y3 @ Y4 @ ( comp @ Y5 @ Y2 ) )
=> ( Y0 @ ( comp @ Y3 @ Y5 ) @ ( sub @ Y4 @ Y5 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( !! @ subst
@ ^ [Y5: subst] :
( ( Y0 @ ( comp @ Y4 @ Y5 ) @ ( sub @ Y2 @ Y5 ) @ Y3 )
=> ( Y0 @ Y4 @ Y2 @ ( comp @ Y5 @ Y3 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: term,Y5: subst] : ( var @ ( sub @ Y4 @ Y5 ) )
@ id
@ Y2
@ id )
=> ( Y0 @ id @ Y2 @ id ) ) )
=> ( ( ^ [Y2: subst > term > subst > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ id @ Y4 @ id )
= ( Y3 @ Y4 ) ) )
@ Y0
@ Y1 )
=> ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ) ) ) )
@ sK176 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1267]) ).
thf(f1340,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sK176 @ Y2 @ Y3 @ ( comp @ Y4 @ Y1 ) )
=> ( sK176 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sK176 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y2 )
=> ( sK176 @ Y3 @ Y1 @ ( comp @ Y4 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( sK176 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK176 @ id @ Y1 @ id )
= ( Y0 @ Y1 ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1v2 = $true ) ),
inference(beta-eta_normalization,[],[f1339]) ).
thf(f1341,plain,
( ( hoasinduction_lem1v2 = $true )
| ( ( ^ [Y0: term > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sK176 @ Y2 @ Y3 @ ( comp @ Y4 @ Y1 ) )
=> ( sK176 @ ( comp @ Y2 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ subst
@ ^ [Y4: subst] :
( ( sK176 @ ( comp @ Y3 @ Y4 ) @ ( sub @ Y1 @ Y4 ) @ Y2 )
=> ( sK176 @ Y3 @ Y1 @ ( comp @ Y4 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ ( sub @ Y1 @ id ) )
=> ( sK176 @ id @ Y1 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( sK176 @ id @ Y1 @ id )
= ( Y0 @ Y1 ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) ) ) ) ) )
@ sK177 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1340]) ).
thf(f1342,plain,
( ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK176 @ Y1 @ Y2 @ ( comp @ Y3 @ Y0 ) )
=> ( sK176 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y0 ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK176 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y0 @ Y3 ) @ Y1 )
=> ( sK176 @ Y2 @ Y0 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK176 @ id @ Y0 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK176 @ id @ Y0 @ id )
= ( sK177 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK177 @ Y0 ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1v2 = $true ) ),
inference(beta-eta_normalization,[],[f1341]) ).
thf(f1343,plain,
( ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK176 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y0 @ Y3 ) @ Y1 )
=> ( sK176 @ Y2 @ Y0 @ ( comp @ Y3 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK176 @ id @ Y0 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK176 @ id @ Y0 @ id )
= ( sK177 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK177 @ Y0 ) ) ) ) ) ) )
| ( hoasinduction_lem1v2 = $true ) ),
inference(imp_proxy_clausification,[],[f1342]) ).
thf(f1354,plain,
( ( hoasinduction_lem1v2 = $true )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK176 @ id @ Y0 @ id ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( sK176 @ id @ Y0 @ id )
= ( sK177 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK177 @ Y0 ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1343]) ).
thf(f1365,plain,
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( sK176 @ id @ Y0 @ id )
= ( sK177 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK177 @ Y0 ) ) ) )
= $false )
| ( hoasinduction_lem1v2 = $true ) ),
inference(imp_proxy_clausification,[],[f1354]) ).
thf(f1366,plain,
( ( hoasinduction_lem1v2 = $true )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK176 @ id @ Y0 @ id ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1354]) ).
thf(f1367,plain,
! [X1: term] :
( ( hoasinduction_lem1v2 = $true )
| ( $true
= ( ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK176 @ id @ Y0 @ id ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1366]) ).
thf(f1368,plain,
! [X1: term] :
( ( $true
= ( ( var @ ( sub @ X1 @ id ) )
=> ( sK176 @ id @ X1 @ id ) ) )
| ( hoasinduction_lem1v2 = $true ) ),
inference(beta-eta_normalization,[],[f1367]) ).
thf(f1369,plain,
! [X1: term] :
( ( ( var @ ( sub @ X1 @ id ) )
= $false )
| ( hoasinduction_lem1v2 = $true )
| ( $true
= ( sK176 @ id @ X1 @ id ) ) ),
inference(imp_proxy_clausification,[],[f1368]) ).
thf(f1370,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK177 @ Y0 ) ) )
= $false )
| ( hoasinduction_lem1v2 = $true ) ),
inference(imp_proxy_clausification,[],[f1365]) ).
thf(f1371,plain,
( ( hoasinduction_lem1v2 = $true )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sK176 @ id @ Y0 @ id )
= ( sK177 @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1365]) ).
thf(f1372,plain,
! [X1: term] :
( ( hoasinduction_lem1v2 = $true )
| ( ( ^ [Y0: term] :
( ( sK176 @ id @ Y0 @ id )
= ( sK177 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1371]) ).
thf(f1373,plain,
! [X1: term] :
( ( $true
= ( ( sK176 @ id @ X1 @ id )
= ( sK177 @ X1 ) ) )
| ( hoasinduction_lem1v2 = $true ) ),
inference(beta-eta_normalization,[],[f1372]) ).
thf(f1374,plain,
! [X1: term] :
( ( hoasinduction_lem1v2 = $true )
| ( ( sK177 @ X1 )
= ( sK176 @ id @ X1 @ id ) ) ),
inference(iff_proxy_clausification,[],[f1373]) ).
thf(f1375,plain,
! [X1: term] :
( ( hoasinduction_lem1v2 = $true )
| ( $true
= ( sK177 @ X1 ) )
| ( ( sK176 @ id @ X1 @ id )
= $false ) ),
inference(iff_proxy_clausification,[],[f1374]) ).
thf(f1377,plain,
( ( hoasinduction_lem1v2 = $true )
| ( ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK177 @ Y0 ) )
@ sK178 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1370]) ).
thf(f1378,plain,
( ( hoasinduction_lem1v2 = $true )
| ( $false
= ( ( var @ sK178 )
=> ( sK177 @ sK178 ) ) ) ),
inference(beta-eta_normalization,[],[f1377]) ).
thf(f1379,plain,
( ( hoasinduction_lem1v2 = $true )
| ( ( sK177 @ sK178 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1378]) ).
thf(f1380,plain,
( ( $true
= ( var @ sK178 ) )
| ( hoasinduction_lem1v2 = $true ) ),
inference(imp_proxy_clausification,[],[f1378]) ).
thf(f1381,plain,
( ( ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(iff_proxy_clausification,[],[f328]) ).
thf(f1417,plain,
( ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1381]) ).
thf(f1419,plain,
( ( $false
= ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1417]) ).
thf(f1421,plain,
( ( ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1419]) ).
thf(f1422,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( axvarid = $true ) ),
inference(imp_proxy_clausification,[],[f1419]) ).
thf(f1423,plain,
( ( ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1421]) ).
thf(f1425,plain,
( ( $false
= ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1423]) ).
thf(f1427,plain,
( ( ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1425]) ).
thf(f1429,plain,
( ( ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1427]) ).
thf(f1431,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1429]) ).
thf(f1433,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1431]) ).
thf(f1435,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1433]) ).
thf(f1437,plain,
( ( ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1435]) ).
thf(f1439,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1437]) ).
thf(f1441,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( $false
= ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1439]) ).
thf(f1443,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1441]) ).
thf(f1445,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1443]) ).
thf(f1447,plain,
( ( ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1445]) ).
thf(f1449,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( $false
= ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1447]) ).
thf(f1451,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( $false
= ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1449]) ).
thf(f1453,plain,
( ( ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1451]) ).
thf(f1455,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1453]) ).
thf(f1457,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( $false
= ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1455]) ).
thf(f1459,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1457]) ).
thf(f1461,plain,
( ( ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1459]) ).
thf(f1463,plain,
( ( $false
= ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) ) ) )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1461]) ).
thf(f1465,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1463]) ).
thf(f1467,plain,
( ( $false
= ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) ) ) )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1465]) ).
thf(f1469,plain,
( ( ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1467]) ).
thf(f1471,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1469]) ).
thf(f1473,plain,
( ( ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ) )
= $false )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1471]) ).
thf(f1475,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1473]) ).
thf(f1477,plain,
( ( ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) )
= $false )
| ( hoasinduction_lem1v2_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1475]) ).
thf(f1479,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( $false
= ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1v2 ) ) ) ),
inference(imp_proxy_clausification,[],[f1477]) ).
thf(f1481,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( ( hoasapnotvar
=> hoasinduction_lem1v2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1479]) ).
thf(f1483,plain,
( ( hoasinduction_lem1v2_gthm = $true )
| ( hoasinduction_lem1v2 = $false ) ),
inference(imp_proxy_clausification,[],[f1481]) ).
thf(f1486,plain,
( ( axvarid = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ) ),
inference(iff_proxy_clausification,[],[f349]) ).
thf(f1487,plain,
! [X1: term] :
( ( axvarid = $false )
| ( $true
= ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1486]) ).
thf(f1488,plain,
! [X1: term] :
( ( $true
= ( ( sub @ X1 @ id )
= X1 ) )
| ( axvarid = $false ) ),
inference(beta-eta_normalization,[],[f1487]) ).
thf(f1489,plain,
! [X1: term] :
( ( axvarid = $false )
| ( ( sub @ X1 @ id )
= X1 ) ),
inference(equality_proxy_clausification,[],[f1488]) ).
thf(f3433,definition,
( spl359_201
<=> ( hoasinduction_lem1v2 = $false ) ),
introduced(definition,[new_symbols(definition,[spl359_201])],[avatar_definition]) ).
thf(f3435,plain,
( ( hoasinduction_lem1v2 = $false )
| ~ spl359_201 ),
inference(avatar_component_clause,[],[f3433]) ).
thf(f3504,definition,
( spl359_219
<=> ( hoasinduction_lem1v2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl359_219])],[avatar_definition]) ).
thf(f3506,plain,
( ( hoasinduction_lem1v2 = $true )
| ~ spl359_219 ),
inference(avatar_component_clause,[],[f3504]) ).
thf(f3513,definition,
( spl359_221
<=> ! [X1: term] :
( ( ( var @ ( sub @ X1 @ id ) )
= $false )
| ( $true
= ( sK176 @ id @ X1 @ id ) ) ) ),
introduced(definition,[new_symbols(definition,[spl359_221])],[avatar_definition]) ).
thf(f3514,plain,
( ! [X1: term] :
( ( ( var @ ( sub @ X1 @ id ) )
= $false )
| ( $true
= ( sK176 @ id @ X1 @ id ) ) )
| ~ spl359_221 ),
inference(avatar_component_clause,[],[f3513]) ).
thf(f3515,plain,
( spl359_221
| spl359_219 ),
inference(avatar_split_clause,[],[f1369,f3504,f3513]) ).
thf(f3521,definition,
( spl359_223
<=> ! [X1: term] :
( ( $true
= ( sK177 @ X1 ) )
| ( ( sK176 @ id @ X1 @ id )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl359_223])],[avatar_definition]) ).
thf(f3522,plain,
( ! [X1: term] :
( ( ( sK176 @ id @ X1 @ id )
= $false )
| ( $true
= ( sK177 @ X1 ) ) )
| ~ spl359_223 ),
inference(avatar_component_clause,[],[f3521]) ).
thf(f3523,plain,
( spl359_219
| spl359_223 ),
inference(avatar_split_clause,[],[f1375,f3521,f3504]) ).
thf(f3525,definition,
( spl359_224
<=> ( $true
= ( var @ sK178 ) ) ),
introduced(definition,[new_symbols(definition,[spl359_224])],[avatar_definition]) ).
thf(f3527,plain,
( ( $true
= ( var @ sK178 ) )
| ~ spl359_224 ),
inference(avatar_component_clause,[],[f3525]) ).
thf(f3528,plain,
( spl359_224
| spl359_219 ),
inference(avatar_split_clause,[],[f1380,f3504,f3525]) ).
thf(f3530,definition,
( spl359_225
<=> ( ( sK177 @ sK178 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl359_225])],[avatar_definition]) ).
thf(f3532,plain,
( ( ( sK177 @ sK178 )
= $false )
| ~ spl359_225 ),
inference(avatar_component_clause,[],[f3530]) ).
thf(f3533,plain,
( spl359_225
| spl359_219 ),
inference(avatar_split_clause,[],[f1379,f3504,f3530]) ).
thf(f3547,definition,
( spl359_229
<=> ( axvarid = $false ) ),
introduced(definition,[new_symbols(definition,[spl359_229])],[avatar_definition]) ).
thf(f3549,plain,
( ( axvarid = $false )
| ~ spl359_229 ),
inference(avatar_component_clause,[],[f3547]) ).
thf(f3616,definition,
( spl359_246
<=> ( hoasinduction_lem1v2_gthm = $true ) ),
introduced(definition,[new_symbols(definition,[spl359_246])],[avatar_definition]) ).
thf(f3622,definition,
( spl359_247
<=> ( axvarid = $true ) ),
introduced(definition,[new_symbols(definition,[spl359_247])],[avatar_definition]) ).
thf(f3624,plain,
( ( axvarid = $true )
| ~ spl359_247 ),
inference(avatar_component_clause,[],[f3622]) ).
thf(f3625,plain,
( spl359_246
| spl359_247 ),
inference(avatar_split_clause,[],[f1422,f3622,f3616]) ).
thf(f3729,plain,
( spl359_201
| spl359_246 ),
inference(avatar_split_clause,[],[f1483,f3616,f3433]) ).
thf(f3731,definition,
( spl359_266
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl359_266])],[avatar_definition]) ).
thf(f3732,plain,
( ! [X1: term] :
( ( sub @ X1 @ id )
= X1 )
| ~ spl359_266 ),
inference(avatar_component_clause,[],[f3731]) ).
thf(f3733,plain,
( spl359_266
| spl359_229 ),
inference(avatar_split_clause,[],[f1489,f3547,f3731]) ).
thf(f4705,plain,
~ spl359_246,
inference(avatar_split_clause,[],[f321,f3616]) ).
thf(f4714,plain,
( ( $true = $false )
| ~ spl359_229
| ~ spl359_247 ),
inference(forward_demodulation,[],[f3624,f3549]) ).
thf(f4715,plain,
( $false
| ~ spl359_229
| ~ spl359_247 ),
inference(trivial_inequality_removal,[],[f4714]) ).
thf(f4716,plain,
( ~ spl359_229
| ~ spl359_247 ),
inference(avatar_contradiction_clause,[],[f4715]) ).
thf(f4809,plain,
( ( $true = $false )
| ~ spl359_201
| ~ spl359_219 ),
inference(superposition,[],[f3506,f3435]) ).
thf(f4812,plain,
( $false
| ~ spl359_201
| ~ spl359_219 ),
inference(trivial_inequality_removal,[],[f4809]) ).
thf(f4813,plain,
( ~ spl359_201
| ~ spl359_219 ),
inference(avatar_contradiction_clause,[],[f4812]) ).
thf(f4815,plain,
( ! [X1: term] :
( ( $true
= ( sK176 @ id @ X1 @ id ) )
| ( ( var @ X1 )
= $false ) )
| ~ spl359_221
| ~ spl359_266 ),
inference(forward_demodulation,[],[f3514,f3732]) ).
thf(f5957,plain,
( ! [X0: term] :
( ( ( var @ X0 )
= $false )
| ( $true
= ( sK177 @ X0 ) )
| ( $true = $false ) )
| ~ spl359_221
| ~ spl359_223
| ~ spl359_266 ),
inference(superposition,[],[f3522,f4815]) ).
thf(f5967,plain,
( ! [X0: term] :
( ( $true
= ( sK177 @ X0 ) )
| ( ( var @ X0 )
= $false ) )
| ~ spl359_221
| ~ spl359_223
| ~ spl359_266 ),
inference(trivial_inequality_removal,[],[f5957]) ).
thf(f6022,plain,
( ( $true = $false )
| ( $false
= ( var @ sK178 ) )
| ~ spl359_221
| ~ spl359_223
| ~ spl359_225
| ~ spl359_266 ),
inference(superposition,[],[f3532,f5967]) ).
thf(f6023,plain,
( ( $false
= ( var @ sK178 ) )
| ~ spl359_221
| ~ spl359_223
| ~ spl359_225
| ~ spl359_266 ),
inference(trivial_inequality_removal,[],[f6022]) ).
thf(f6030,plain,
( ( $true = $false )
| ~ spl359_221
| ~ spl359_223
| ~ spl359_224
| ~ spl359_225
| ~ spl359_266 ),
inference(superposition,[],[f3527,f6023]) ).
thf(f6034,plain,
( $false
| ~ spl359_221
| ~ spl359_223
| ~ spl359_224
| ~ spl359_225
| ~ spl359_266 ),
inference(trivial_inequality_removal,[],[f6030]) ).
thf(f6035,plain,
( ~ spl359_221
| ~ spl359_223
| ~ spl359_224
| ~ spl359_225
| ~ spl359_266 ),
inference(avatar_contradiction_clause,[],[f6034]) ).
cnf(s181,plain,
( spl359_219
| spl359_221 ),
inference(sat_conversion,[],[f3515]) ).
cnf(s183,plain,
( spl359_219
| spl359_223 ),
inference(sat_conversion,[],[f3523]) ).
cnf(s184,plain,
( spl359_219
| spl359_224 ),
inference(sat_conversion,[],[f3528]) ).
cnf(s185,plain,
( spl359_219
| spl359_225 ),
inference(sat_conversion,[],[f3533]) ).
cnf(s189,plain,
( spl359_246
| spl359_247 ),
inference(sat_conversion,[],[f3625]) ).
cnf(s221,plain,
( spl359_201
| spl359_246 ),
inference(sat_conversion,[],[f3729]) ).
cnf(s222,plain,
( spl359_229
| spl359_266 ),
inference(sat_conversion,[],[f3733]) ).
cnf(s449,plain,
~ spl359_246,
inference(sat_conversion,[],[f4705]) ).
cnf(s452,plain,
( ~ spl359_229
| ~ spl359_247 ),
inference(sat_conversion,[],[f4716]) ).
cnf(s468,plain,
( ~ spl359_201
| ~ spl359_219 ),
inference(sat_conversion,[],[f4813]) ).
cnf(s527,plain,
( ~ spl359_221
| ~ spl359_223
| ~ spl359_224
| ~ spl359_225
| ~ spl359_266 ),
inference(sat_conversion,[],[f6035]) ).
cnf(s528,plain,
spl359_201,
inference(rat,[],[s221,s449]) ).
cnf(s529,plain,
~ spl359_219,
inference(rat,[],[s468,s528]) ).
cnf(s646,plain,
spl359_247,
inference(rat,[],[s189,s449]) ).
cnf(s647,plain,
~ spl359_229,
inference(rat,[],[s452,s646]) ).
cnf(s648,plain,
spl359_266,
inference(rat,[],[s222,s647]) ).
cnf(s655,plain,
spl359_225,
inference(rat,[],[s185,s529]) ).
cnf(s656,plain,
spl359_224,
inference(rat,[],[s184,s529]) ).
cnf(s657,plain,
spl359_223,
inference(rat,[],[s183,s529]) ).
cnf(s658,plain,
~ spl359_221,
inference(rat,[],[s527,s648,s655,s656,s657]) ).
cnf(s660,plain,
$false,
inference(rat,[],[s181,s658,s529]) ).
thf(f6036,plain,
$false,
inference(avatar_sat_refutation,[],[s660]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG263^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n026.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 17:37:32 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.21/0.26 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
% 0.74/0.41 % (924080)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.74/0.41 % (924098)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2598479888:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.74/0.41 % (924098)Instruction limit reached!
% 0.74/0.41 % (924098)------------------------------
% 0.74/0.41 % (924098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.41 % (924098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.41 % (924098)CaDiCaL version: 2.1.3
% 0.74/0.41 % (924098)Termination reason: Instruction limit
% 0.74/0.41 % (924098)Termination phase: shuffling
% 0.74/0.41 % (924098)Time elapsed: 0.002 s
% 0.74/0.41 % (924098)Peak memory usage: 10 MB
% 0.74/0.41 % (924098)Instructions burned: 7 (million)
% 0.74/0.41 % (924096)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3393604918:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.74/0.41 % (924097)lrs+10_16_si=on:nwc=1.5:random_seed=1093435491:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.74/0.41 % (924099)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=4214185619: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)
% 0.74/0.41 % (924100)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2076566489:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.74/0.41 % (924101)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3187889508:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.74/0.41 % (924102)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.74/0.41 % (924102)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
% 0.74/0.41 % (924102)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=2042948828:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.74/0.41 % (924097)Instruction limit reached!
% 0.74/0.41 % (924097)------------------------------
% 0.74/0.41 % (924097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.41 % (924097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.41 % (924097)CaDiCaL version: 2.1.3
% 0.74/0.41 % (924097)Termination reason: Instruction limit
% 0.74/0.41 % (924097)Termination phase: shuffling
% 0.74/0.41 % (924097)Time elapsed: 0.008 s
% 0.74/0.41 % (924097)Peak memory usage: 10 MB
% 0.74/0.41 % (924097)Instructions burned: 18 (million)
% 0.74/0.41 % (924109)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3219918077:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.41 % (924109)Instruction limit reached!
% 0.74/0.41 % (924109)------------------------------
% 0.74/0.41 % (924109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.41 % (924109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.41 % (924109)CaDiCaL version: 2.1.3
% 0.74/0.41 % (924109)Termination reason: Instruction limit
% 0.74/0.41 % (924109)Termination phase: shuffling
% 0.74/0.41 % (924109)Time elapsed: 0.001 s
% 0.74/0.41 % (924109)Peak memory usage: 10 MB
% 0.74/0.41 % (924109)Instructions burned: 3 (million)
% 0.74/0.41 % (924100)Instruction limit reached!
% 0.74/0.41 % (924100)------------------------------
% 0.74/0.41 % (924100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.41 % (924100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.41 % (924100)CaDiCaL version: 2.1.3
% 0.74/0.41 % (924100)Termination reason: Instruction limit
% 0.74/0.41 % (924100)Termination phase: Naming
% 0.74/0.41 % (924100)Time elapsed: 0.012 s
% 0.74/0.41 % (924100)Peak memory usage: 11 MB
% 0.74/0.41 % (924100)Instructions burned: 25 (million)
% 0.74/0.41 % (924123)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.41 % (924123)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3279146093:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.74/0.43 % (924123)Instruction limit reached!
% 0.74/0.43 % (924123)------------------------------
% 0.74/0.43 % (924123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.43 % (924123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.43 % (924123)CaDiCaL version: 2.1.3
% 0.74/0.43 % (924123)Termination reason: Instruction limit
% 0.74/0.43 % (924123)Termination phase: shuffling
% 0.74/0.43 % (924123)Time elapsed: 0.002 s
% 0.74/0.43 % (924123)Peak memory usage: 10 MB
% 0.74/0.43 % (924123)Instructions burned: 8 (million)
% 0.74/0.43 % (924127)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
% 0.74/0.43 % (924127)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.43 % (924127)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1205652583:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.74/0.43 % (924101)Instruction limit reached!
% 0.74/0.43 % (924101)------------------------------
% 0.74/0.43 % (924101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.43 % (924101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.43 % (924101)CaDiCaL version: 2.1.3
% 0.74/0.43 % (924101)Termination reason: Instruction limit
% 0.74/0.43 % (924101)Termination phase: Property scanning
% 0.74/0.43 % (924101)Time elapsed: 0.035 s
% 0.74/0.43 % (924101)Peak memory usage: 12 MB
% 0.74/0.43 % (924101)Instructions burned: 77 (million)
% 0.74/0.43 % (924122)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2108791338:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.74/0.43 % (924096)Instruction limit reached!
% 0.74/0.43 % (924096)------------------------------
% 0.74/0.43 % (924096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.43 % (924096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.43 % (924096)CaDiCaL version: 2.1.3
% 0.74/0.43 % (924096)Termination reason: Instruction limit
% 0.74/0.43 % (924096)Termination phase: Function definition elimination
% 0.74/0.43 % (924096)Time elapsed: 0.040 s
% 0.74/0.43 % (924096)Peak memory usage: 12 MB
% 0.74/0.43 % (924096)Instructions burned: 89 (million)
% 0.74/0.43 % (924127)Instruction limit reached!
% 0.74/0.43 % (924127)------------------------------
% 0.74/0.43 % (924127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.43 % (924127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.43 % (924127)CaDiCaL version: 2.1.3
% 0.74/0.43 % (924127)Termination reason: Instruction limit
% 0.74/0.43 % (924127)Termination phase: Property scanning
% 0.74/0.43 % (924127)Time elapsed: 0.007 s
% 0.74/0.43 % (924127)Peak memory usage: 10 MB
% 0.74/0.43 % (924127)Instructions burned: 33 (million)
% 0.74/0.43 % (924122)Instruction limit reached!
% 0.74/0.43 % (924122)------------------------------
% 0.74/0.43 % (924122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.43 % (924122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.43 % (924122)CaDiCaL version: 2.1.3
% 0.74/0.43 % (924122)Termination reason: Instruction limit
% 0.74/0.43 % (924122)Termination phase: shuffling
% 0.74/0.43 % (924122)Time elapsed: 0.005 s
% 0.74/0.43 % (924122)Peak memory usage: 10 MB
% 0.74/0.43 % (924122)Instructions burned: 6 (million)
% 0.74/0.43 % (924132)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.74/0.43 % (924124)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=466220433:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.74/0.43 % (924132)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=3232305910:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.43 % (924132)Instruction limit reached!
% 0.74/0.43 % (924132)------------------------------
% 0.74/0.43 % (924132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.46 % (924132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.46 % (924132)CaDiCaL version: 2.1.3
% 0.74/0.46 % (924132)Termination reason: Instruction limit
% 0.74/0.46 % (924132)Termination phase: shuffling
% 0.74/0.46 % (924132)Time elapsed: 0.001 s
% 0.74/0.46 % (924132)Peak memory usage: 10 MB
% 0.74/0.46 % (924132)Instructions burned: 3 (million)
% 0.74/0.46 % (924129)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=853977037:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.74/0.46 % (924137)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2505914067:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.74/0.46 % (924131)lrs+10_1_si=on:cs=on:random_seed=2628810723:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.74/0.46 % (924124)Instruction limit reached!
% 0.74/0.46 % (924124)------------------------------
% 0.74/0.46 % (924124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.46 % (924124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.46 % (924124)CaDiCaL version: 2.1.3
% 0.74/0.46 % (924124)Termination reason: Instruction limit
% 0.74/0.46 % (924124)Termination phase: shuffling
% 0.74/0.46 % (924124)Time elapsed: 0.016 s
% 0.74/0.46 % (924124)Peak memory usage: 10 MB
% 0.74/0.46 % (924124)Instructions burned: 12 (million)
% 0.74/0.46 % (924133)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1999023089:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.74/0.46 % (924131)Instruction limit reached!
% 0.74/0.46 % (924131)------------------------------
% 0.74/0.46 % (924131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.46 % (924131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.46 % (924131)CaDiCaL version: 2.1.3
% 0.74/0.46 % (924131)Termination reason: Instruction limit
% 0.74/0.46 % (924131)Termination phase: shuffling
% 0.74/0.46 % (924131)Time elapsed: 0.004 s
% 0.74/0.46 % (924131)Peak memory usage: 10 MB
% 0.74/0.46 % (924131)Instructions burned: 9 (million)
% 0.74/0.46 % (924102)Instruction limit reached!
% 0.74/0.46 % (924102)------------------------------
% 0.74/0.46 % (924102)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.46 % (924102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.46 % (924102)CaDiCaL version: 2.1.3
% 0.74/0.46 % (924102)Termination reason: Instruction limit
% 0.74/0.46 % (924102)Termination phase: Saturation
% 0.74/0.46 % (924102)Time elapsed: 0.069 s
% 0.74/0.46 % (924102)Peak memory usage: 14 MB
% 0.74/0.46 % (924102)Instructions burned: 159 (million)
% 0.74/0.46 % (924137)Refutation not found, incomplete strategy
% 0.74/0.46 % (924137)------------------------------
% 0.74/0.46 % (924137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.46 % (924137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.46 % (924137)CaDiCaL version: 2.1.3
% 0.74/0.46 % (924137)Termination reason: Refutation not found, incomplete strategy
% 0.74/0.46 % (924137)Time elapsed: 0.012 s
% 0.74/0.46 % (924137)Peak memory usage: 12 MB
% 0.74/0.46 % (924137)Instructions burned: 52 (million)
% 0.74/0.46 % (924137)------------------------------
% 0.74/0.46 % (924137)------------------------------
% 0.74/0.46 % (924133)Instruction limit reached!
% 0.74/0.46 % (924133)------------------------------
% 0.74/0.46 % (924133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.46 % (924133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.46 % (924133)CaDiCaL version: 2.1.3
% 0.74/0.46 % (924133)Termination reason: Instruction limit
% 0.74/0.46 % (924133)Termination phase: Property scanning
% 0.74/0.46 % (924133)Time elapsed: 0.019 s
% 0.74/0.46 % (924133)Peak memory usage: 12 MB
% 0.74/0.46 % (924133)Instructions burned: 41 (million)
% 0.74/0.46 % (924157)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1351628945:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.74/0.46 % (924151)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1970524621:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.74/0.51 % (924150)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2575001509:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.74/0.51 % (924129)Instruction limit reached!
% 0.74/0.51 % (924129)------------------------------
% 0.74/0.51 % (924129)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.51 % (924129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.51 % (924129)CaDiCaL version: 2.1.3
% 0.74/0.51 % (924129)Termination reason: Instruction limit
% 0.74/0.51 % (924129)Termination phase: Saturation
% 0.74/0.51 % (924129)Time elapsed: 0.038 s
% 0.74/0.51 % (924129)Peak memory usage: 11 MB
% 0.74/0.51 % (924129)Instructions burned: 86 (million)
% 0.74/0.51 % (924157)Instruction limit reached!
% 0.74/0.51 % (924157)------------------------------
% 0.74/0.51 % (924157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.51 % (924157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.51 % (924157)CaDiCaL version: 2.1.3
% 0.74/0.51 % (924157)Termination reason: Instruction limit
% 0.74/0.51 % (924157)Termination phase: shuffling
% 0.74/0.51 % (924157)Time elapsed: 0.004 s
% 0.74/0.51 % (924157)Peak memory usage: 10 MB
% 0.74/0.51 % (924157)Instructions burned: 17 (million)
% 0.74/0.51 % (924151)Instruction limit reached!
% 0.74/0.51 % (924151)------------------------------
% 0.74/0.51 % (924151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.51 % (924151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.51 % (924151)CaDiCaL version: 2.1.3
% 0.74/0.51 % (924151)Termination reason: Instruction limit
% 0.74/0.51 % (924151)Termination phase: shuffling
% 0.74/0.51 % (924151)Time elapsed: 0.007 s
% 0.74/0.51 % (924151)Peak memory usage: 10 MB
% 0.74/0.51 % (924151)Instructions burned: 15 (million)
% 0.74/0.51 % (924155)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3546191484:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.74/0.51 % (924166)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3414993052:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.74/0.51 % (924150)Instruction limit reached!
% 0.74/0.51 % (924150)------------------------------
% 0.74/0.51 % (924150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.51 % (924150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.51 % (924150)CaDiCaL version: 2.1.3
% 0.74/0.51 % (924150)Termination reason: Instruction limit
% 0.74/0.51 % (924150)Termination phase: Preprocessing 1
% 0.74/0.51 % (924150)Time elapsed: 0.012 s
% 0.74/0.51 % (924150)Peak memory usage: 10 MB
% 0.74/0.51 % (924150)Instructions burned: 26 (million)
% 0.74/0.51 % (924160)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2845314647: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)
% 0.74/0.51 % (924160)Instruction limit reached!
% 0.74/0.51 % (924160)------------------------------
% 0.74/0.51 % (924160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.51 % (924160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.51 % (924160)CaDiCaL version: 2.1.3
% 0.74/0.51 % (924160)Termination reason: Instruction limit
% 0.74/0.51 % (924160)Termination phase: shuffling
% 0.74/0.51 % (924160)Time elapsed: 0.002 s
% 0.74/0.51 % (924160)Peak memory usage: 10 MB
% 0.74/0.51 % (924160)Instructions burned: 4 (million)
% 0.74/0.51 % (924166)Instruction limit reached!
% 0.74/0.51 % (924166)------------------------------
% 0.74/0.51 % (924166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.51 % (924166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.51 % (924166)CaDiCaL version: 2.1.3
% 0.74/0.51 % (924166)Termination reason: Instruction limit
% 0.74/0.51 % (924166)Termination phase: Property scanning
% 0.74/0.51 % (924166)Time elapsed: 0.006 s
% 0.74/0.51 % (924166)Peak memory usage: 10 MB
% 0.74/0.51 % (924166)Instructions burned: 28 (million)
% 0.74/0.51 % (924165)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2464201375:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.74/0.51 % (924167)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1929014747:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.70/0.57 % (924171)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
% 1.70/0.57 % (924171)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.70/0.57 % (924173)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=3479556706:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.70/0.57 % (924172)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.70/0.57 % (924171)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=1114172528:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.70/0.57 % (924165)Instruction limit reached!
% 1.70/0.57 % (924165)------------------------------
% 1.70/0.57 % (924165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.57 % (924165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.57 % (924165)CaDiCaL version: 2.1.3
% 1.70/0.57 % (924165)Termination reason: Instruction limit
% 1.70/0.57 % (924165)Termination phase: Property scanning
% 1.70/0.57 % (924165)Time elapsed: 0.011 s
% 1.70/0.57 % (924165)Peak memory usage: 10 MB
% 1.70/0.57 % (924165)Instructions burned: 27 (million)
% 1.70/0.57 % (924172)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=4119461886:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.70/0.57 % (924173)Instruction limit reached!
% 1.70/0.57 % (924173)------------------------------
% 1.70/0.57 % (924173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.57 % (924173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.57 % (924173)CaDiCaL version: 2.1.3
% 1.70/0.57 % (924173)Termination reason: Instruction limit
% 1.70/0.57 % (924173)Termination phase: Property scanning
% 1.70/0.57 % (924173)Time elapsed: 0.007 s
% 1.70/0.57 % (924173)Peak memory usage: 10 MB
% 1.70/0.57 % (924173)Instructions burned: 33 (million)
% 1.70/0.57 % (924171)Instruction limit reached!
% 1.70/0.57 % (924171)------------------------------
% 1.70/0.57 % (924171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.57 % (924171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.57 % (924171)CaDiCaL version: 2.1.3
% 1.70/0.57 % (924171)Termination reason: Instruction limit
% 1.70/0.57 % (924171)Termination phase: shuffling
% 1.70/0.57 % (924171)Time elapsed: 0.006 s
% 1.70/0.57 % (924171)Peak memory usage: 10 MB
% 1.70/0.57 % (924171)Instructions burned: 14 (million)
% 1.70/0.57 % (924172)Instruction limit reached!
% 1.70/0.57 % (924172)------------------------------
% 1.70/0.57 % (924172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.57 % (924172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.57 % (924172)CaDiCaL version: 2.1.3
% 1.70/0.57 % (924172)Termination reason: Instruction limit
% 1.70/0.57 % (924172)Termination phase: shuffling
% 1.70/0.57 % (924172)Time elapsed: 0.004 s
% 1.70/0.57 % (924172)Peak memory usage: 10 MB
% 1.70/0.57 % (924172)Instructions burned: 9 (million)
% 1.70/0.57 % (924184)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=802160945:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.70/0.57 % (924167)Instruction limit reached!
% 1.70/0.57 % (924167)------------------------------
% 1.70/0.57 % (924167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.57 % (924167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.57 % (924167)CaDiCaL version: 2.1.3
% 1.70/0.57 % (924167)Termination reason: Instruction limit
% 1.70/0.57 % (924167)Termination phase: Property scanning
% 1.70/0.57 % (924167)Time elapsed: 0.029 s
% 1.70/0.57 % (924167)Peak memory usage: 12 MB
% 1.70/0.57 % (924167)Instructions burned: 62 (million)
% 1.70/0.57 % (924182)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=192778251:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 2.44/0.69 % (924184)Instruction limit reached!
% 2.44/0.69 % (924184)------------------------------
% 2.44/0.69 % (924184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.69 % (924184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.69 % (924184)CaDiCaL version: 2.1.3
% 2.44/0.69 % (924184)Termination reason: Instruction limit
% 2.44/0.69 % (924184)Termination phase: Property scanning
% 2.44/0.69 % (924184)Time elapsed: 0.006 s
% 2.44/0.69 % (924184)Peak memory usage: 10 MB
% 2.44/0.69 % (924184)Instructions burned: 26 (million)
% 2.44/0.69 % (924185)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1598818089:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.44/0.69 % (924186)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=4250341956:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.44/0.69 % (924182)Instruction limit reached!
% 2.44/0.69 % (924182)------------------------------
% 2.44/0.69 % (924182)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.69 % (924182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.69 % (924182)CaDiCaL version: 2.1.3
% 2.44/0.69 % (924182)Termination reason: Instruction limit
% 2.44/0.69 % (924182)Termination phase: shuffling
% 2.44/0.69 % (924182)Time elapsed: 0.004 s
% 2.44/0.69 % (924182)Peak memory usage: 10 MB
% 2.44/0.69 % (924182)Instructions burned: 9 (million)
% 2.44/0.69 % (924194)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2234347789:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 2.44/0.69 % (924185)Instruction limit reached!
% 2.44/0.69 % (924185)------------------------------
% 2.44/0.69 % (924185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.69 % (924185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.69 % (924185)CaDiCaL version: 2.1.3
% 2.44/0.69 % (924185)Termination reason: Instruction limit
% 2.44/0.69 % (924185)Termination phase: Property scanning
% 2.44/0.69 % (924185)Time elapsed: 0.010 s
% 2.44/0.69 % (924185)Peak memory usage: 10 MB
% 2.44/0.69 % (924185)Instructions burned: 22 (million)
% 2.44/0.69 % (924192)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=720375368:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.44/0.69 % (924197)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=10391854:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 2.44/0.69 % (924201)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.44/0.69 % (924194)Refutation not found, incomplete strategy
% 2.44/0.69 % (924194)------------------------------
% 2.44/0.69 % (924194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.69 % (924194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.69 % (924194)CaDiCaL version: 2.1.3
% 2.44/0.69 % (924194)Termination reason: Refutation not found, incomplete strategy
% 2.44/0.69 % (924194)Time elapsed: 0.017 s
% 2.44/0.69 % (924194)Peak memory usage: 13 MB
% 2.44/0.69 % (924194)Instructions burned: 67 (million)
% 2.44/0.69 % (924194)------------------------------
% 2.44/0.69 % (924194)------------------------------
% 2.44/0.69 % (924201)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=970932161:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 2.44/0.69 % (924201)Instruction limit reached!
% 2.44/0.69 % (924201)------------------------------
% 2.44/0.69 % (924201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.44/0.69 % (924201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.44/0.69 % (924201)CaDiCaL version: 2.1.3
% 2.44/0.69 % (924201)Termination reason: Instruction limit
% 2.44/0.69 % (924201)Termination phase: shuffling
% 2.44/0.69 % (924201)Time elapsed: 0.005 s
% 2.44/0.69 % (924201)Peak memory usage: 10 MB
% 2.44/0.69 % (924201)Instructions burned: 9 (million)
% 2.44/0.69 % (924208)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1470448362:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.44/0.69 % (924197)Instruction limit reached!
% 2.44/0.69 % (924197)------------------------------
% 3.17/0.82 % (924197)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.17/0.82 % (924197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/0.82 % (924197)CaDiCaL version: 2.1.3
% 3.17/0.82 % (924197)Termination reason: Instruction limit
% 3.17/0.82 % (924197)Termination phase: Property scanning
% 3.17/0.82 % (924197)Time elapsed: 0.021 s
% 3.17/0.82 % (924197)Peak memory usage: 10 MB
% 3.17/0.82 % (924197)Instructions burned: 43 (million)
% 3.17/0.82 % (924208)Refutation not found, incomplete strategy
% 3.17/0.82 % (924208)------------------------------
% 3.17/0.82 % (924208)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.17/0.82 % (924208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/0.82 % (924208)CaDiCaL version: 2.1.3
% 3.17/0.82 % (924208)Termination reason: Refutation not found, incomplete strategy
% 3.17/0.82 % (924208)Time elapsed: 0.013 s
% 3.17/0.82 % (924208)Peak memory usage: 13 MB
% 3.17/0.82 % (924208)Instructions burned: 54 (million)
% 3.17/0.82 % (924208)------------------------------
% 3.17/0.82 % (924208)------------------------------
% 3.17/0.82 % (924212)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=4217277924: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)
% 3.17/0.82 % (924217)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 3.17/0.82 % (924217)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2500946634:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 3.17/0.82 % (924217)Instruction limit reached!
% 3.17/0.82 % (924217)------------------------------
% 3.17/0.82 % (924217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.17/0.82 % (924217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/0.82 % (924217)CaDiCaL version: 2.1.3
% 3.17/0.82 % (924217)Termination reason: Instruction limit
% 3.17/0.82 % (924217)Termination phase: shuffling
% 3.17/0.82 % (924217)Time elapsed: 0.003 s
% 3.17/0.82 % (924217)Peak memory usage: 10 MB
% 3.17/0.82 % (924217)Instructions burned: 6 (million)
% 3.17/0.82 % (924192)Instruction limit reached!
% 3.17/0.82 % (924192)------------------------------
% 3.17/0.82 % (924192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.17/0.82 % (924192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/0.82 % (924192)CaDiCaL version: 2.1.3
% 3.17/0.82 % (924192)Termination reason: Instruction limit
% 3.17/0.82 % (924192)Termination phase: Saturation
% 3.17/0.82 % (924192)Time elapsed: 0.060 s
% 3.17/0.82 % (924192)Peak memory usage: 13 MB
% 3.17/0.82 % (924192)Instructions burned: 145 (million)
% 3.17/0.82 % (924221)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=691092125:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 3.17/0.82 % (924225)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1888601108:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 3.17/0.82 % (924227)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=945368523:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 3.17/0.82 % (924221)Instruction limit reached!
% 3.17/0.82 % (924221)------------------------------
% 3.17/0.82 % (924221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.17/0.82 % (924221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/0.82 % (924221)CaDiCaL version: 2.1.3
% 3.17/0.82 % (924221)Termination reason: Instruction limit
% 3.17/0.82 % (924221)Termination phase: Property scanning
% 3.17/0.82 % (924221)Time elapsed: 0.014 s
% 3.17/0.82 % (924221)Peak memory usage: 10 MB
% 3.17/0.82 % (924221)Instructions burned: 32 (million)
% 3.17/0.82 % (924225)Instruction limit reached!
% 3.17/0.82 % (924225)------------------------------
% 3.17/0.82 % (924225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.17/0.82 % (924225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.17/0.82 % (924225)CaDiCaL version: 2.1.3
% 4.03/0.92 % (924225)Termination reason: Instruction limit
% 4.03/0.92 % (924225)Termination phase: shuffling
% 4.03/0.92 % (924225)Time elapsed: 0.012 s
% 4.03/0.92 % (924225)Peak memory usage: 10 MB
% 4.03/0.92 % (924225)Instructions burned: 20 (million)
% 4.03/0.92 % (924155)Instruction limit reached!
% 4.03/0.92 % (924155)------------------------------
% 4.03/0.92 % (924155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.03/0.92 % (924155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/0.92 % (924155)CaDiCaL version: 2.1.3
% 4.03/0.92 % (924155)Termination reason: Instruction limit
% 4.03/0.92 % (924155)Termination phase: Saturation
% 4.03/0.92 % (924155)Time elapsed: 0.168 s
% 4.03/0.92 % (924155)Peak memory usage: 16 MB
% 4.03/0.92 % (924155)Instructions burned: 327 (million)
% 4.03/0.92 % (924245)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=3071130017: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)
% 4.03/0.92 % (924246)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=2669441866: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)
% 4.03/0.92 % (924212)Instruction limit reached!
% 4.03/0.92 % (924212)------------------------------
% 4.03/0.92 % (924212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.03/0.92 % (924212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/0.92 % (924212)CaDiCaL version: 2.1.3
% 4.03/0.92 % (924212)Termination reason: Instruction limit
% 4.03/0.92 % (924212)Termination phase: Saturation
% 4.03/0.92 % (924212)Time elapsed: 0.094 s
% 4.03/0.92 % (924212)Peak memory usage: 14 MB
% 4.03/0.92 % (924212)Instructions burned: 169 (million)
% 4.03/0.92 % (924248)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=233186456:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 4.03/0.92 % (924257)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=3526926589: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)
% 4.03/0.92 % (924246)Instruction limit reached!
% 4.03/0.92 % (924246)------------------------------
% 4.03/0.92 % (924246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.03/0.92 % (924246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/0.92 % (924246)CaDiCaL version: 2.1.3
% 4.03/0.92 % (924246)Termination reason: Instruction limit
% 4.03/0.92 % (924246)Termination phase: Preprocessing 3
% 4.03/0.92 % (924246)Time elapsed: 0.039 s
% 4.03/0.92 % (924246)Peak memory usage: 12 MB
% 4.03/0.92 % (924246)Instructions burned: 45 (million)
% 4.03/0.92 % (924257)Instruction limit reached!
% 4.03/0.92 % (924257)------------------------------
% 4.03/0.92 % (924257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.03/0.92 % (924257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/0.92 % (924257)CaDiCaL version: 2.1.3
% 4.03/0.92 % (924257)Termination reason: Instruction limit
% 4.03/0.92 % (924257)Termination phase: Property scanning
% 4.03/0.92 % (924257)Time elapsed: 0.018 s
% 4.03/0.92 % (924257)Peak memory usage: 10 MB
% 4.03/0.92 % (924257)Instructions burned: 21 (million)
% 4.03/0.92 % (924261)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 4.03/0.92 % (924261)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=617504176:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 4.03/0.92 % (924099)Instruction limit reached!
% 4.03/0.92 % (924099)------------------------------
% 4.03/0.92 % (924099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.03/0.92 % (924099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/0.92 % (924099)CaDiCaL version: 2.1.3
% 4.03/0.92 % (924099)Termination reason: Instruction limit
% 4.03/0.92 % (924099)Termination phase: Saturation
% 4.03/0.92 % (924099)Time elapsed: 0.365 s
% 4.03/0.92 % (924099)Peak memory usage: 18 MB
% 4.03/0.92 % (924099)Instructions burned: 634 (million)
% 4.03/0.92 % (924264)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3137895814:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 5.30/1.08 % (924264)Instruction limit reached!
% 5.30/1.08 % (924264)------------------------------
% 5.30/1.08 % (924264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.30/1.08 % (924264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.30/1.08 % (924264)CaDiCaL version: 2.1.3
% 5.30/1.08 % (924264)Termination reason: Instruction limit
% 5.30/1.08 % (924264)Termination phase: shuffling
% 5.30/1.08 % (924264)Time elapsed: 0.012 s
% 5.30/1.08 % (924264)Peak memory usage: 10 MB
% 5.30/1.08 % (924264)Instructions burned: 15 (million)
% 5.30/1.08 % (924268)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=1735254170:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 5.30/1.08 % (924248)Refutation not found, incomplete strategy
% 5.30/1.08 % (924248)------------------------------
% 5.30/1.08 % (924248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.30/1.08 % (924248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.30/1.08 % (924248)CaDiCaL version: 2.1.3
% 5.30/1.08 % (924248)Termination reason: Refutation not found, incomplete strategy
% 5.30/1.08 % (924248)Time elapsed: 0.117 s
% 5.30/1.08 % (924248)Peak memory usage: 15 MB
% 5.30/1.08 % (924248)Instructions burned: 151 (million)
% 5.30/1.08 % (924248)------------------------------
% 5.30/1.08 % (924248)------------------------------
% 5.30/1.08 % (924272)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=1744825380:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 5.30/1.08 % (924268)Instruction limit reached!
% 5.30/1.08 % (924268)------------------------------
% 5.30/1.08 % (924268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.30/1.08 % (924268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.30/1.08 % (924268)CaDiCaL version: 2.1.3
% 5.30/1.08 % (924268)Termination reason: Instruction limit
% 5.30/1.08 % (924268)Termination phase: Property scanning
% 5.30/1.08 % (924268)Time elapsed: 0.051 s
% 5.30/1.08 % (924268)Peak memory usage: 11 MB
% 5.30/1.08 % (924268)Instructions burned: 67 (million)
% 5.30/1.08 % (924280)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2398206430:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 5.30/1.08 % (924272)Instruction limit reached!
% 5.30/1.08 % (924272)------------------------------
% 5.30/1.08 % (924272)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.30/1.08 % (924272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.30/1.08 % (924272)CaDiCaL version: 2.1.3
% 5.30/1.08 % (924272)Termination reason: Instruction limit
% 5.30/1.08 % (924272)Termination phase: Property scanning
% 5.30/1.08 % (924272)Time elapsed: 0.042 s
% 5.30/1.08 % (924272)Peak memory usage: 11 MB
% 5.30/1.08 % (924272)Instructions burned: 52 (million)
% 5.30/1.08 % (924280)Instruction limit reached!
% 5.30/1.08 % (924280)------------------------------
% 5.30/1.08 % (924280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.30/1.08 % (924280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.30/1.08 % (924280)CaDiCaL version: 2.1.3
% 5.30/1.08 % (924280)Termination reason: Instruction limit
% 5.30/1.08 % (924280)Termination phase: Property scanning
% 5.30/1.08 % (924280)Time elapsed: 0.027 s
% 5.30/1.08 % (924280)Peak memory usage: 10 MB
% 5.30/1.08 % (924280)Instructions burned: 32 (million)
% 5.30/1.08 % (924281)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=4038534572:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 5.30/1.08 % (924227)Instruction limit reached!
% 5.30/1.08 % (924227)------------------------------
% 5.30/1.08 % (924227)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.30/1.08 % (924227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.30/1.08 % (924227)CaDiCaL version: 2.1.3
% 5.30/1.08 % (924227)Termination reason: Instruction limit
% 5.30/1.08 % (924227)Termination phase: Saturation
% 5.30/1.08 % (924227)Time elapsed: 0.249 s
% 5.30/1.08 % (924227)Peak memory usage: 14 MB
% 5.30/1.08 % (924227)Instructions burned: 317 (million)
% 5.30/1.08 % (924283)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=278151807:cond=on:i=34:hud=10:nm=10:rtra=on_2994 on theBenchmark for (2994ds/34Mi)
% 6.86/1.31 % (924284)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=1628954314:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2994 on theBenchmark for (2994ds/67Mi)
% 6.86/1.31 % (924288)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 6.86/1.31 % (924261)Instruction limit reached!
% 6.86/1.31 % (924261)------------------------------
% 6.86/1.31 % (924261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.86/1.31 % (924261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.31 % (924261)CaDiCaL version: 2.1.3
% 6.86/1.31 % (924261)Termination reason: Instruction limit
% 6.86/1.31 % (924261)Termination phase: Saturation
% 6.86/1.31 % (924261)Time elapsed: 0.163 s
% 6.86/1.31 % (924261)Peak memory usage: 14 MB
% 6.86/1.31 % (924261)Instructions burned: 200 (million)
% 6.86/1.31 % (924288)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=2323383589:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2994 on theBenchmark for (2994ds/180Mi)
% 6.86/1.31 % (924283)Instruction limit reached!
% 6.86/1.31 % (924283)------------------------------
% 6.86/1.31 % (924283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.86/1.31 % (924283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.31 % (924283)CaDiCaL version: 2.1.3
% 6.86/1.31 % (924283)Termination reason: Instruction limit
% 6.86/1.31 % (924283)Termination phase: Property scanning
% 6.86/1.31 % (924283)Time elapsed: 0.028 s
% 6.86/1.31 % (924283)Peak memory usage: 10 MB
% 6.86/1.31 % (924283)Instructions burned: 34 (million)
% 6.86/1.31 % (924294)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=3332925152:st=2:i=246:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/246Mi)
% 6.86/1.31 % (924295)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=2514363380:cond=on:i=96:bd=all:rtra=on_2994 on theBenchmark for (2994ds/96Mi)
% 6.86/1.31 % (924245)Instruction limit reached!
% 6.86/1.31 % (924245)------------------------------
% 6.86/1.31 % (924245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.86/1.31 % (924245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.31 % (924245)CaDiCaL version: 2.1.3
% 6.86/1.31 % (924245)Termination reason: Instruction limit
% 6.86/1.31 % (924245)Termination phase: Saturation
% 6.86/1.31 % (924245)Time elapsed: 0.296 s
% 6.86/1.31 % (924245)Peak memory usage: 21 MB
% 6.86/1.31 % (924245)Instructions burned: 854 (million)
% 6.86/1.31 % (924284)Instruction limit reached!
% 6.86/1.31 % (924284)------------------------------
% 6.86/1.31 % (924284)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.86/1.31 % (924284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.31 % (924284)CaDiCaL version: 2.1.3
% 6.86/1.31 % (924284)Termination reason: Instruction limit
% 6.86/1.31 % (924284)Termination phase: Property scanning
% 6.86/1.31 % (924284)Time elapsed: 0.053 s
% 6.86/1.31 % (924284)Peak memory usage: 11 MB
% 6.86/1.31 % (924284)Instructions burned: 67 (million)
% 6.86/1.31 % (924299)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=3471875242:i=427:sd=1:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/427Mi)
% 6.86/1.31 % (924281)Instruction limit reached!
% 6.86/1.31 % (924281)------------------------------
% 6.86/1.31 % (924281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.86/1.31 % (924281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.31 % (924281)CaDiCaL version: 2.1.3
% 6.86/1.31 % (924281)Termination reason: Instruction limit
% 6.86/1.31 % (924281)Termination phase: Saturation
% 6.86/1.31 % (924281)Time elapsed: 0.109 s
% 6.86/1.31 % (924281)Peak memory usage: 13 MB
% 6.86/1.31 % (924281)Instructions burned: 137 (million)
% 6.86/1.31 % (924301)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=495019151:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/874Mi)
% 6.86/1.31 % (924299)Refutation not found, incomplete strategy
% 6.86/1.31 % (924299)------------------------------
% 6.86/1.31 % (924299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.86/1.31 % (924299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.31 % (924299)CaDiCaL version: 2.1.3
% 6.86/1.31 % (924299)Termination reason: Refutation not found, incomplete strategy
% 6.86/1.31 % (924299)Time elapsed: 0.020 s
% 6.86/1.31 % (924299)Peak memory usage: 12 MB
% 6.86/1.31 % (924299)Instructions burned: 47 (million)
% 6.86/1.31 % (924299)------------------------------
% 6.86/1.31 % (924299)------------------------------
% 6.86/1.31 % (924306)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=714836728:st=1.5:i=130:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/130Mi)
% 6.86/1.31 % (924304)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=1518557758:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/515Mi)
% 6.86/1.31 % (924295)Instruction limit reached!
% 6.86/1.31 % (924295)------------------------------
% 6.86/1.31 % (924295)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.86/1.31 % (924295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.31 % (924295)CaDiCaL version: 2.1.3
% 6.86/1.31 % (924295)Termination reason: Instruction limit
% 6.86/1.31 % (924295)Termination phase: Saturation
% 6.86/1.31 % (924295)Time elapsed: 0.076 s
% 6.86/1.31 % (924295)Peak memory usage: 12 MB
% 6.86/1.31 % (924295)Instructions burned: 96 (million)
% 6.86/1.31 % (924310)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=7693109:i=44:ep=R:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/44Mi)
% 6.86/1.31 % (924310)Instruction limit reached!
% 6.86/1.31 % (924310)------------------------------
% 6.86/1.31 % (924310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.86/1.31 % (924310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.31 % (924310)CaDiCaL version: 2.1.3
% 6.86/1.31 % (924310)Termination reason: Instruction limit
% 6.86/1.31 % (924310)Termination phase: Property scanning
% 6.86/1.31 % (924310)Time elapsed: 0.018 s
% 6.86/1.31 % (924310)Peak memory usage: 11 MB
% 6.86/1.31 % (924310)Instructions burned: 44 (million)
% 6.86/1.31 % (924288)Instruction limit reached!
% 6.86/1.31 % (924288)------------------------------
% 6.86/1.31 % (924288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.86/1.31 % (924288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.31 % (924288)CaDiCaL version: 2.1.3
% 6.86/1.31 % (924288)Termination reason: Instruction limit
% 6.86/1.31 % (924288)Termination phase: Saturation
% 6.86/1.31 % (924288)Time elapsed: 0.151 s
% 6.86/1.31 % (924288)Peak memory usage: 14 MB
% 6.86/1.31 % (924288)Instructions burned: 183 (million)
% 6.86/1.31 % (924306)Instruction limit reached!
% 6.86/1.31 % (924306)------------------------------
% 6.86/1.31 % (924306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.86/1.31 % (924306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.31 % (924306)CaDiCaL version: 2.1.3
% 6.86/1.31 % (924306)Termination reason: Instruction limit
% 6.86/1.31 % (924306)Termination phase: Saturation
% 6.86/1.31 % (924306)Time elapsed: 0.068 s
% 6.86/1.31 % (924306)Peak memory usage: 13 MB
% 6.86/1.31 % (924306)Instructions burned: 131 (million)
% 6.86/1.31 % (924312)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=2816396708:s2a=on:i=571:nm=16:rtra=on_2992 on theBenchmark for (2992ds/571Mi)
% 6.86/1.31 % (924313)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=2657146888:i=450:rtra=on:ixr=off:ntd=on_2992 on theBenchmark for (2992ds/450Mi)
% 6.86/1.31 % (924314)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=2972863148:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2992 on theBenchmark for (2992ds/95Mi)
% 6.86/1.31 % (924314)Instruction limit reached!
% 6.86/1.31 % (924314)------------------------------
% 6.86/1.31 % (924314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.86/1.31 % (924314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.31 % (924314)CaDiCaL version: 2.1.3
% 6.86/1.31 % (924314)Termination reason: Instruction limit
% 6.86/1.31 % (924314)Termination phase: Saturation
% 6.86/1.31 % (924314)Time elapsed: 0.039 s
% 6.86/1.31 % (924314)Peak memory usage: 12 MB
% 6.86/1.31 % (924314)Instructions burned: 96 (million)
% 6.86/1.31 % (924294)Instruction limit reached!
% 6.86/1.31 % (924294)------------------------------
% 6.86/1.31 % (924294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.86/1.31 % (924294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.31 % (924294)CaDiCaL version: 2.1.3
% 6.86/1.31 % (924294)Termination reason: Instruction limit
% 6.86/1.31 % (924294)Termination phase: Saturation
% 6.86/1.31 % (924294)Time elapsed: 0.205 s
% 6.86/1.31 % (924294)Peak memory usage: 15 MB
% 6.86/1.31 % (924294)Instructions burned: 247 (million)
% 6.86/1.31 % (924319)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=2804311300:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2991 on theBenchmark for (2991ds/65Mi)
% 6.86/1.31 % (924320)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=2437179739: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_2991 on theBenchmark for (2991ds/105Mi)
% 6.86/1.31 % (924319)Instruction limit reached!
% 6.86/1.31 % (924319)------------------------------
% 6.86/1.31 % (924319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.86/1.31 % (924319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.31 % (924319)CaDiCaL version: 2.1.3
% 6.86/1.31 % (924319)Termination reason: Instruction limit
% 6.86/1.31 % (924319)Termination phase: Function definition elimination
% 6.86/1.31 % (924319)Time elapsed: 0.029 s
% 6.86/1.31 % (924319)Peak memory usage: 11 MB
% 6.86/1.31 % (924319)Instructions burned: 67 (million)
% 6.86/1.31 % (924320)Instruction limit reached!
% 6.86/1.31 % (924320)------------------------------
% 6.86/1.31 % (924320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.86/1.31 % (924320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.31 % (924320)CaDiCaL version: 2.1.3
% 6.86/1.31 % (924320)Termination reason: Instruction limit
% 6.86/1.31 % (924320)Termination phase: Saturation
% 6.86/1.31 % (924320)Time elapsed: 0.049 s
% 6.86/1.31 % (924320)Peak memory usage: 12 MB
% 6.86/1.31 % (924320)Instructions burned: 107 (million)
% 6.86/1.31 % (924324)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=1851782492:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2991 on theBenchmark for (2991ds/5755Mi)
% 6.86/1.31 % (924327)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=3472221276:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2991 on theBenchmark for (2991ds/375Mi)
% 6.86/1.31 % (924301) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-924080-924301"...
% 6.86/1.31 % (924301)...printing done.
% 6.86/1.31 % (924301)Refutation found. Thanks to Tanya!
% 6.86/1.31 % SZS status Theorem for theBenchmark
% 6.86/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 6.86/1.32 % (924301)------------------------------
% 6.86/1.32 % (924301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.86/1.32 % (924301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.86/1.32 % (924301)CaDiCaL version: 2.1.3
% 6.86/1.32 % (924301)Termination reason: Refutation
% 6.86/1.32 % (924301)Time elapsed: 0.389 s
% 6.86/1.32 % (924301)Peak memory usage: 17 MB
% 6.86/1.32 % (924301)Instructions burned: 464 (million)
% 6.86/1.32 % (924080)Success in time 1.04 s
% 6.86/1.32 % Vampire exiting
%------------------------------------------------------------------------------