%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG267^1 : 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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:45:17 AM UTC 2026
% Result : Theorem 1.30s 0.52s
% Output : Refutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 16
% Syntax : Number of formulae : 137 ( 34 unt; 0 typ; 10 def)
% Number of atoms : 1384 ( 167 equ; 0 cnn)
% Maximal formula atoms : 4 ( 10 avg)
% Number of connectives : 1189 ( 71 ~; 108 |; 0 &; 141 @)
% ( 10 <=>; 846 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 460 ( 455 usr; 200 con; 0-4 aty)
% ( 7 !!; 6 ??; 0 @@+; 0 @@-)
% Number of variables : 33 ( 2 sgn 14 !; 1 ?; 33 :)
% 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,
vIMP: $o > $o > $o ).
thf(func_def_124,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_125,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_127,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_130,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_131,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
vNOT: $o > $o ).
thf(func_def_133,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_134,type,
vAND: $o > $o > $o ).
thf(func_def_135,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_138,type,
vIFF: $o > $o > $o ).
thf(func_def_139,type,
sK0: term ).
thf(func_def_140,type,
sK1: term ).
thf(func_def_141,type,
sK2: term ).
thf(func_def_142,type,
sK3: term ).
thf(func_def_143,type,
sK4: term ).
thf(func_def_144,type,
sK5: term ).
thf(func_def_145,type,
sK6: ( subst > term > subst > $o ) > subst ).
thf(func_def_146,type,
sK7: ( subst > term > subst > $o ) > term ).
thf(func_def_147,type,
sK8: ( subst > term > subst > $o ) > subst ).
thf(func_def_148,type,
sK9: ( subst > term > subst > $o ) > term ).
thf(func_def_149,type,
sK10: ( subst > term > subst > $o ) > term ).
thf(func_def_150,type,
sK11: ( subst > term > subst > $o ) > subst ).
thf(func_def_151,type,
sK12: ( subst > term > subst > $o ) > subst ).
thf(func_def_152,type,
sK13: ( subst > term > subst > $o ) > subst ).
thf(func_def_153,type,
sK14: ( subst > term > subst > $o ) > subst ).
thf(func_def_154,type,
sK15: ( subst > term > subst > $o ) > term ).
thf(func_def_155,type,
sK16: ( subst > term > subst > $o ) > term ).
thf(func_def_156,type,
sK17: ( subst > term > subst > $o ) > subst ).
thf(func_def_157,type,
sK18: ( subst > term > subst > $o ) > subst ).
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 ).
thf(func_def_161,type,
sK22: term ).
thf(func_def_162,type,
sK23: term ).
thf(func_def_163,type,
sK24: term ).
thf(func_def_164,type,
sK25: term ).
thf(func_def_165,type,
sK26: term ).
thf(func_def_166,type,
sK27: term > subst > term > term ).
thf(func_def_167,type,
sK28: term ).
thf(func_def_168,type,
sK29: subst ).
thf(func_def_169,type,
sK30: term ).
thf(func_def_170,type,
sK31: ( subst > term > term ) > subst ).
thf(func_def_171,type,
sK32: ( subst > term > term ) > term ).
thf(func_def_172,type,
sK33: ( subst > term > term ) > subst ).
thf(func_def_173,type,
sK34: subst > term > term ).
thf(func_def_174,type,
sK35: term ).
thf(func_def_175,type,
sK36: term ).
thf(func_def_176,type,
sK37: term ).
thf(func_def_177,type,
sK38: subst ).
thf(func_def_178,type,
sK39: subst ).
thf(func_def_179,type,
sK40: term > subst > ( term > $o ) > term > $o ).
thf(func_def_180,type,
sK41: subst ).
thf(func_def_181,type,
sK42: term > $o ).
thf(func_def_182,type,
sK43: term ).
thf(func_def_183,type,
sK44: subst ).
thf(func_def_184,type,
sK45: term ).
thf(func_def_185,type,
sK46: term ).
thf(func_def_186,type,
sK47: term ).
thf(func_def_187,type,
sK48: subst ).
thf(func_def_188,type,
sK49: ( term > $o ) > subst > term ).
thf(func_def_189,type,
sK50: term ).
thf(func_def_190,type,
sK51: subst ).
thf(func_def_191,type,
sK52: term > $o ).
thf(func_def_192,type,
sK53: term ).
thf(func_def_193,type,
sK54: term ).
thf(func_def_194,type,
sK55: term ).
thf(func_def_195,type,
sK56: subst ).
thf(func_def_196,type,
sK57: ( term > $o ) > term ).
thf(func_def_197,type,
sK58: term > $o ).
thf(func_def_198,type,
sK59: term ).
thf(func_def_199,type,
sK60: term ).
thf(func_def_200,type,
sK61: term ).
thf(func_def_201,type,
sK62: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_202,type,
sK63: ( subst > term > subst > $o ) > term > term ).
thf(func_def_203,type,
sK64: ( subst > term > subst > $o ) > term > term ).
thf(func_def_204,type,
sK65: ( subst > term > subst > $o ) > term > term ).
thf(func_def_205,type,
sK66: subst > term > subst > $o ).
thf(func_def_206,type,
sK67: ( subst > term > term ) > subst ).
thf(func_def_207,type,
sK68: ( subst > term > term ) > term ).
thf(func_def_208,type,
sK69: ( subst > term > term ) > subst ).
thf(func_def_209,type,
sK70: ( subst > term > term ) > 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: term ).
thf(func_def_213,type,
sK74: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_214,type,
sK75: subst > term > subst > $o ).
thf(func_def_215,type,
sK76: term > subst > term > term ).
thf(func_def_216,type,
sK77: term ).
thf(func_def_217,type,
sK78: ( subst > term > term ) > term ).
thf(func_def_218,type,
sK79: ( subst > term > term ) > subst ).
thf(func_def_219,type,
sK80: ( subst > term > subst > $o ) > subst ).
thf(func_def_220,type,
sK81: ( subst > term > subst > $o ) > term ).
thf(func_def_221,type,
sK82: ( subst > term > subst > $o ) > subst ).
thf(func_def_222,type,
sK83: ( subst > term > subst > $o ) > term ).
thf(func_def_223,type,
sK84: ( subst > term > subst > $o ) > term ).
thf(func_def_224,type,
sK85: ( subst > term > subst > $o ) > subst ).
thf(func_def_225,type,
sK86: ( subst > term > subst > $o ) > subst ).
thf(func_def_226,type,
sK87: ( subst > term > subst > $o ) > subst ).
thf(func_def_227,type,
sK88: ( subst > term > subst > $o ) > subst ).
thf(func_def_228,type,
sK89: ( subst > term > subst > $o ) > term ).
thf(func_def_229,type,
sK90: ( subst > term > subst > $o ) > subst ).
thf(func_def_230,type,
sK91: ( subst > term > subst > $o ) > subst ).
thf(func_def_231,type,
sK92: ( subst > term > subst > $o ) > subst ).
thf(func_def_232,type,
sK93: ( subst > term > subst > $o ) > subst ).
thf(func_def_233,type,
sK94: subst > term > subst > $o ).
thf(func_def_234,type,
sK95: term > $o ).
thf(func_def_235,type,
sK96: term ).
thf(func_def_236,type,
sK97: ( subst > term > subst > $o ) > term ).
thf(func_def_237,type,
sK98: ( subst > term > subst > $o ) > subst ).
thf(func_def_238,type,
sK99: ( subst > term > subst > $o ) > term ).
thf(func_def_239,type,
sK100: ( subst > term > subst > $o ) > subst ).
thf(func_def_240,type,
sK101: ( subst > term > subst > $o ) > subst ).
thf(func_def_241,type,
sK102: ( subst > term > subst > $o ) > term ).
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 ) > subst ).
thf(func_def_245,type,
sK106: ( subst > term > subst > $o ) > term ).
thf(func_def_246,type,
sK107: ( subst > term > subst > $o ) > term ).
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 ) > term ).
thf(func_def_250,type,
sK111: subst > term > subst > $o ).
thf(func_def_251,type,
sK112: term ).
thf(func_def_252,type,
sK113: term ).
thf(func_def_253,type,
sK114: term ).
thf(func_def_254,type,
sK115: term ).
thf(func_def_255,type,
sK116: subst ).
thf(func_def_256,type,
sK117: term ).
thf(func_def_257,type,
sK118: subst ).
thf(func_def_258,type,
sK119: subst ).
thf(func_def_259,type,
sK120: subst ).
thf(func_def_260,type,
sK121: ( subst > term > subst > $o ) > term ).
thf(func_def_261,type,
sK122: ( subst > term > subst > $o ) > term ).
thf(func_def_262,type,
sK123: ( subst > term > subst > $o ) > subst ).
thf(func_def_263,type,
sK124: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_264,type,
sK125: ( subst > term > subst > $o ) > subst ).
thf(func_def_265,type,
sK126: ( subst > term > subst > $o ) > subst ).
thf(func_def_266,type,
sK127: ( subst > term > subst > $o ) > term ).
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 ) > term ).
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 ) > subst ).
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 ) > term ).
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 ) > subst ).
thf(func_def_283,type,
sK144: ( subst > term > subst > $o ) > subst ).
thf(func_def_284,type,
sK145: ( subst > term > subst > $o ) > term ).
thf(func_def_285,type,
sK146: ( subst > term > subst > $o ) > term ).
thf(func_def_286,type,
sK147: ( subst > term > subst > $o ) > subst ).
thf(func_def_287,type,
sK148: ( subst > term > subst > $o ) > term ).
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 ) > subst ).
thf(func_def_294,type,
sK155: ( subst > term > subst > $o ) > subst ).
thf(func_def_295,type,
sK156: ( subst > term > subst > $o ) > term ).
thf(func_def_296,type,
sK157: ( subst > term > subst > $o ) > subst ).
thf(func_def_297,type,
sK158: ( subst > term > subst > $o ) > subst ).
thf(func_def_298,type,
sK159: ( subst > term > subst > $o ) > subst ).
thf(func_def_299,type,
sK160: ( subst > term > subst > $o ) > subst ).
thf(func_def_300,type,
sK161: ( subst > term > subst > $o ) > subst ).
thf(func_def_301,type,
sK162: ( subst > term > subst > $o ) > subst ).
thf(func_def_302,type,
sK163: ( subst > term > subst > $o ) > subst ).
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 ) > term ).
thf(func_def_307,type,
sK168: ( subst > term > subst > $o ) > subst ).
thf(func_def_308,type,
sK169: ( subst > term > subst > $o ) > subst ).
thf(func_def_309,type,
sK170: ( subst > term > subst > $o ) > term ).
thf(func_def_310,type,
sK171: ( subst > term > subst > $o ) > subst ).
thf(func_def_311,type,
sK172: ( subst > term > subst > $o ) > subst ).
thf(func_def_312,type,
sK173: ( subst > term > subst > $o ) > term ).
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 ) > term ).
thf(func_def_316,type,
sK177: ( subst > term > subst > $o ) > subst ).
thf(func_def_317,type,
sK178: ( subst > term > subst > $o ) > subst ).
thf(func_def_318,type,
sK179: ( subst > term > subst > $o ) > term ).
thf(func_def_319,type,
sK180: ( subst > term > subst > $o ) > subst ).
thf(func_def_320,type,
sK181: ( subst > term > subst > $o ) > subst ).
thf(func_def_321,type,
sK182: ( subst > term > subst > $o ) > term ).
thf(func_def_322,type,
sK183: ( subst > term > subst > $o ) > subst ).
thf(func_def_323,type,
sK184: ( subst > term > subst > $o ) > subst ).
thf(func_def_324,type,
sK185: ( subst > term > subst > $o ) > term ).
thf(func_def_325,type,
sK186: ( subst > term > subst > $o ) > subst ).
thf(func_def_326,type,
sK187: ( subst > term > subst > $o ) > subst ).
thf(func_def_327,type,
sK188: subst > term > subst > $o ).
thf(func_def_328,type,
sK189: ( subst > term > term ) > term ).
thf(func_def_329,type,
sK190: ( subst > term > term ) > term ).
thf(func_def_330,type,
sK191: ( subst > term > term ) > subst ).
thf(func_def_331,type,
sK192: ( subst > term > term ) > subst ).
thf(func_def_332,type,
sK193: ( subst > term > term ) > subst ).
thf(func_def_333,type,
sK194: 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 ) > term ).
thf(func_def_338,type,
sK199: ( term > $o ) > term ).
thf(func_def_339,type,
sK200: ( term > $o ) > term ).
thf(func_def_340,type,
sK201: ( term > $o ) > term ).
thf(func_def_341,type,
sK202: term > $o ).
thf(func_def_342,type,
sK203: term > term ).
thf(func_def_343,type,
sK204: term ).
thf(func_def_344,type,
sK205: ( term > $o ) > term ).
thf(func_def_345,type,
sK206: ( term > $o ) > term ).
thf(func_def_346,type,
sK207: ( term > $o ) > term ).
thf(func_def_347,type,
sK208: ( term > $o ) > term ).
thf(func_def_348,type,
sK209: ( term > $o ) > term ).
thf(func_def_349,type,
sK210: ( term > $o ) > term ).
thf(func_def_350,type,
sK211: ( term > $o ) > term ).
thf(func_def_351,type,
sK212: term > $o ).
thf(func_def_352,type,
sK213: term ).
thf(func_def_353,type,
sK214: term ).
thf(func_def_354,type,
sK215: term ).
thf(func_def_355,type,
sK216: term ).
thf(func_def_356,type,
sK217: term ).
thf(func_def_357,type,
sK218: term ).
thf(func_def_358,type,
sK219: ( term > $o ) > term ).
thf(func_def_359,type,
sK220: ( term > $o ) > term ).
thf(func_def_360,type,
sK221: ( term > $o ) > term ).
thf(func_def_361,type,
sK222: ( term > $o ) > subst > term ).
thf(func_def_362,type,
sK223: ( term > $o ) > subst > term ).
thf(func_def_363,type,
sK224: ( term > $o ) > term ).
thf(func_def_364,type,
sK225: ( term > $o ) > subst > term ).
thf(func_def_365,type,
sK226: ( term > $o ) > subst > term ).
thf(func_def_366,type,
sK227: ( term > $o ) > subst > term ).
thf(func_def_367,type,
sK228: term > $o ).
thf(func_def_368,type,
sK229: term > term ).
thf(func_def_369,type,
sK230: subst ).
thf(func_def_370,type,
sK231: term ).
thf(func_def_371,type,
sK232: ( subst > term > subst > $o ) > subst ).
thf(func_def_372,type,
sK233: ( subst > term > subst > $o ) > subst ).
thf(func_def_373,type,
sK234: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_374,type,
sK235: ( subst > term > subst > $o ) > term > term ).
thf(func_def_375,type,
sK236: ( subst > term > subst > $o ) > subst ).
thf(func_def_376,type,
sK237: ( subst > term > subst > $o ) > term ).
thf(func_def_377,type,
sK238: ( subst > term > subst > $o ) > subst ).
thf(func_def_378,type,
sK239: ( subst > term > subst > $o ) > term ).
thf(func_def_379,type,
sK240: ( subst > term > subst > $o ) > subst ).
thf(func_def_380,type,
sK241: ( subst > term > subst > $o ) > subst ).
thf(func_def_381,type,
sK242: ( subst > term > subst > $o ) > subst ).
thf(func_def_382,type,
sK243: ( subst > term > subst > $o ) > subst ).
thf(func_def_383,type,
sK244: ( subst > term > subst > $o ) > term ).
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 ) > subst ).
thf(func_def_387,type,
sK248: ( subst > term > subst > $o ) > subst ).
thf(func_def_388,type,
sK249: ( subst > term > subst > $o ) > term ).
thf(func_def_389,type,
sK250: ( subst > term > subst > $o ) > subst ).
thf(func_def_390,type,
sK251: ( subst > term > subst > $o ) > subst ).
thf(func_def_391,type,
sK252: ( subst > term > subst > $o ) > term ).
thf(func_def_392,type,
sK253: ( subst > term > subst > $o ) > term ).
thf(func_def_393,type,
sK254: ( subst > term > subst > $o ) > subst ).
thf(func_def_394,type,
sK255: ( subst > term > subst > $o ) > subst ).
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 ).
thf(func_def_398,type,
sK259: ( subst > term > subst > $o ) > subst ).
thf(func_def_399,type,
sK260: subst > term > subst > $o ).
thf(func_def_400,type,
sK261: ( subst > term > term ) > subst ).
thf(func_def_401,type,
sK262: ( subst > term > term ) > term ).
thf(func_def_402,type,
sK263: ( subst > term > term ) > term ).
thf(func_def_403,type,
sK264: ( subst > term > term ) > subst ).
thf(func_def_404,type,
sK265: ( subst > term > term ) > term ).
thf(func_def_405,type,
sK266: ( subst > term > term ) > subst ).
thf(func_def_406,type,
sK267: term ).
thf(func_def_407,type,
sK268: ( subst > term > term ) > term ).
thf(func_def_408,type,
sK269: ( subst > term > term ) > subst ).
thf(func_def_409,type,
sK270: ( subst > term > term ) > term ).
thf(func_def_410,type,
sK271: ( subst > term > term ) > subst ).
thf(func_def_411,type,
sK272: ( subst > term > term ) > subst ).
thf(func_def_412,type,
sK273: ( subst > term > term ) > subst ).
thf(func_def_413,type,
sK274: subst > term > term ).
thf(func_def_414,type,
sK275: subst > term > term ).
thf(func_def_415,type,
sK276: term ).
thf(func_def_416,type,
sK277: subst ).
thf(func_def_417,type,
sK278: subst ).
thf(func_def_418,type,
sK279: term ).
thf(func_def_419,type,
sK280: term ).
thf(func_def_420,type,
sK281: term ).
thf(func_def_421,type,
sK282: term ).
thf(func_def_422,type,
sK283: term ).
thf(func_def_423,type,
sK284: subst ).
thf(func_def_424,type,
sK285: subst ).
thf(func_def_425,type,
sK286: subst ).
thf(func_def_426,type,
sK287: 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: subst > term > 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 ).
thf(func_def_435,type,
sK296: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_436,type,
sK297: term > ( term > $o ) > term ).
thf(func_def_437,type,
sK298: term > ( term > $o ) > term ).
thf(func_def_438,type,
sK299: term > $o ).
thf(func_def_439,type,
sK300: subst > term > subst > $o ).
thf(func_def_440,type,
sK301: ( subst > term > term ) > subst ).
thf(func_def_441,type,
sK302: ( subst > term > term ) > term ).
thf(func_def_442,type,
sK303: ( subst > term > term ) > term ).
thf(func_def_443,type,
sK304: ( subst > term > term ) > subst ).
thf(func_def_444,type,
sK305: ( subst > term > term ) > term ).
thf(func_def_445,type,
sK306: ( subst > term > term ) > subst ).
thf(func_def_446,type,
sK307: term ).
thf(f3,axiom,
! [X0: term] :
( ( ( sub @ X0 @ id )
= X0 )
= axvarid ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarid) ).
thf(f11,axiom,
( axvarshift
= ( ( push @ one @ sh )
= id ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarshift) ).
thf(f105,axiom,
( hoasinduction_lem3b
= ( ! [X0: term] :
? [X1: subst > term > term] :
( ( sub @ X0 @ ( push @ one @ sh ) )
= ( X1 @ sh @ one ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3b) ).
thf(f106,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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= hoasinduction_lem3b_gthm ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3b_gthm) ).
thf(f107,axiom,
hoasinduction_lem3b_lthm = hoasinduction_lem3b,
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem3b_lthm) ).
thf(f114,conjecture,
hoasinduction_lem3b_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ hoasinduction_lem3b_gthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f133,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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= hoasinduction_lem3b_gthm ) ),
inference(rectify,[],[f106]) ).
thf(f134,plain,
( hoasinduction_lem3b_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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f133]) ).
thf(f184,plain,
~ hoasinduction_lem3b_gthm,
inference(rectify,[],[f115]) ).
thf(f185,plain,
hoasinduction_lem3b_gthm != $true,
inference(fool_elimination,[],[f184]) ).
thf(f232,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f243,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f285,plain,
( hoasinduction_lem3b
= ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( Y1 @ sh @ one )
= ( sub @ Y0 @ ( push @ one @ sh ) ) ) ) ) ),
inference(fool_elimination,[],[f105]) ).
thf(f320,plain,
hoasinduction_lem3b_gthm != $true,
inference(flattening,[],[f185]) ).
thf(f321,plain,
hoasinduction_lem3b_gthm != $true,
inference(cnf_transformation,[],[f320]) ).
thf(f323,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f243]) ).
thf(f336,plain,
( hoasinduction_lem3b
= ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( Y1 @ sh @ one )
= ( sub @ Y0 @ ( push @ one @ sh ) ) ) ) ) ),
inference(cnf_transformation,[],[f285]) ).
thf(f355,plain,
( axvarshift
= ( id
= ( push @ one @ sh ) ) ),
inference(cnf_transformation,[],[f232]) ).
thf(f365,plain,
( hoasinduction_lem3b_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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f134]) ).
thf(f366,plain,
hoasinduction_lem3b = hoasinduction_lem3b_lthm,
inference(cnf_transformation,[],[f107]) ).
thf(f376,plain,
( hoasinduction_lem3b_lthm
= ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( Y1 @ sh @ one )
= ( sub @ Y0 @ ( push @ one @ sh ) ) ) ) ) ),
inference(definition_unfolding,[],[f336,f366]) ).
thf(f385,plain,
( hoasinduction_lem3b_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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f365,f366]) ).
thf(f388,plain,
( ( axvarshift = $false )
| ( $true
= ( id
= ( push @ one @ sh ) ) ) ),
inference(iff_proxy_clausification,[],[f355]) ).
thf(f389,plain,
( ( axvarshift = $false )
| ( id
= ( push @ one @ sh ) ) ),
inference(equality_proxy_clausification,[],[f388]) ).
thf(f537,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( Y1 @ sh @ one )
= ( sub @ Y0 @ ( push @ one @ sh ) ) ) ) )
= $false )
| ( hoasinduction_lem3b_lthm = $true ) ),
inference(iff_proxy_clausification,[],[f376]) ).
thf(f544,plain,
( ( ( ^ [Y0: term] :
( ?? @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( Y1 @ sh @ one )
= ( sub @ Y0 @ ( push @ one @ sh ) ) ) )
@ sK28 )
= $false )
| ( hoasinduction_lem3b_lthm = $true ) ),
inference(sigma_proxy_clausification,[],[f537]) ).
thf(f545,plain,
( ( $false
= ( ?? @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( Y0 @ sh @ one )
= ( sub @ sK28 @ ( push @ one @ sh ) ) ) ) )
| ( hoasinduction_lem3b_lthm = $true ) ),
inference(beta-eta_normalization,[],[f544]) ).
thf(f546,plain,
! [X1: subst > term > term] :
( ( ( ^ [Y0: subst > term > term] :
( ( Y0 @ sh @ one )
= ( sub @ sK28 @ ( push @ one @ sh ) ) )
@ X1 )
= $false )
| ( hoasinduction_lem3b_lthm = $true ) ),
inference(pi_proxy_clausification,[],[f545]) ).
thf(f547,plain,
! [X1: subst > term > term] :
( ( hoasinduction_lem3b_lthm = $true )
| ( $false
= ( ( X1 @ sh @ one )
= ( sub @ sK28 @ ( push @ one @ sh ) ) ) ) ),
inference(beta-eta_normalization,[],[f546]) ).
thf(f548,plain,
! [X1: subst > term > term] :
( ( ( X1 @ sh @ one )
!= ( sub @ sK28 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm = $true ) ),
inference(equality_proxy_clausification,[],[f547]) ).
thf(f647,plain,
( ( axvarid = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ) ),
inference(iff_proxy_clausification,[],[f323]) ).
thf(f648,plain,
! [X1: term] :
( ( $true
= ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 ) )
| ( axvarid = $false ) ),
inference(pi_proxy_clausification,[],[f647]) ).
thf(f649,plain,
! [X1: term] :
( ( $true
= ( ( sub @ X1 @ id )
= X1 ) )
| ( axvarid = $false ) ),
inference(beta-eta_normalization,[],[f648]) ).
thf(f650,plain,
! [X1: term] :
( ( ( sub @ X1 @ id )
= X1 )
| ( axvarid = $false ) ),
inference(equality_proxy_clausification,[],[f649]) ).
thf(f1080,plain,
( ( $false
= ( 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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasinduction_lem3b_gthm = $true ) ),
inference(iff_proxy_clausification,[],[f385]) ).
thf(f1118,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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem3b_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1080]) ).
thf(f1120,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1118]) ).
thf(f1122,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( 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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1120]) ).
thf(f1123,plain,
( ( axvarid = $true )
| ( hoasinduction_lem3b_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1120]) ).
thf(f1124,plain,
( ( $false
= ( 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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasinduction_lem3b_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1122]) ).
thf(f1126,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1124]) ).
thf(f1128,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( 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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1126]) ).
thf(f1130,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( 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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1128]) ).
thf(f1132,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( 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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1130]) ).
thf(f1134,plain,
( ( hoasinduction_lem3b_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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1132]) ).
thf(f1136,plain,
( ( ( 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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem3b_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1134]) ).
thf(f1138,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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem3b_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1136]) ).
thf(f1139,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( axvarshift = $true ) ),
inference(imp_proxy_clausification,[],[f1136]) ).
thf(f1140,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1138]) ).
thf(f1142,plain,
( ( hoasinduction_lem3b_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_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1140]) ).
thf(f1144,plain,
( ( $false
= ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasinduction_lem3b_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1142]) ).
thf(f1146,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1144]) ).
thf(f1148,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1146]) ).
thf(f1150,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1148]) ).
thf(f1152,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1150]) ).
thf(f1154,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1152]) ).
thf(f1156,plain,
( ( $false
= ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasinduction_lem3b_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1154]) ).
thf(f1158,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1156]) ).
thf(f1160,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1158]) ).
thf(f1162,plain,
( ( $false
= ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasinduction_lem3b_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1160]) ).
thf(f1164,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1162]) ).
thf(f1166,plain,
( ( $false
= ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasinduction_lem3b_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1164]) ).
thf(f1168,plain,
( ( ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem3b_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1166]) ).
thf(f1170,plain,
( ( $false
= ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) )
| ( hoasinduction_lem3b_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1168]) ).
thf(f1172,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1170]) ).
thf(f1174,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1172]) ).
thf(f1176,plain,
( ( $false
= ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) )
| ( hoasinduction_lem3b_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1174]) ).
thf(f1178,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1176]) ).
thf(f1180,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( hoaslamnotvar
=> ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1178]) ).
thf(f1182,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( ( hoasapnotvar
=> ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1180]) ).
thf(f1184,plain,
( ( hoasinduction_lem3b_gthm = $true )
| ( $false
= ( hoasinduction_lem1
=> ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) ) ) ),
inference(imp_proxy_clausification,[],[f1182]) ).
thf(f1186,plain,
( ( $false
= ( hoasinduction_lem2
=> hoasinduction_lem3b_lthm ) )
| ( hoasinduction_lem3b_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1184]) ).
thf(f1188,plain,
( ( hoasinduction_lem3b_lthm = $false )
| ( hoasinduction_lem3b_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1186]) ).
thf(f2195,definition,
( spl308_1
<=> ( id
= ( push @ one @ sh ) ) ),
introduced(definition,[new_symbols(definition,[spl308_1])],[avatar_definition]) ).
thf(f2197,plain,
( ( id
= ( push @ one @ sh ) )
| ~ spl308_1 ),
inference(avatar_component_clause,[],[f2195]) ).
thf(f2199,definition,
( spl308_2
<=> ( axvarshift = $false ) ),
introduced(definition,[new_symbols(definition,[spl308_2])],[avatar_definition]) ).
thf(f2201,plain,
( ( axvarshift = $false )
| ~ spl308_2 ),
inference(avatar_component_clause,[],[f2199]) ).
thf(f2202,plain,
( spl308_1
| spl308_2 ),
inference(avatar_split_clause,[],[f389,f2199,f2195]) ).
thf(f2204,definition,
( spl308_3
<=> ( axvarshift = $true ) ),
introduced(definition,[new_symbols(definition,[spl308_3])],[avatar_definition]) ).
thf(f2206,plain,
( ( axvarshift = $true )
| ~ spl308_3 ),
inference(avatar_component_clause,[],[f2204]) ).
thf(f2340,definition,
( spl308_35
<=> ( hoasinduction_lem3b_lthm = $false ) ),
introduced(definition,[new_symbols(definition,[spl308_35])],[avatar_definition]) ).
thf(f2342,plain,
( ( hoasinduction_lem3b_lthm = $false )
| ~ spl308_35 ),
inference(avatar_component_clause,[],[f2340]) ).
thf(f2345,definition,
( spl308_36
<=> ( hoasinduction_lem3b_lthm = $true ) ),
introduced(definition,[new_symbols(definition,[spl308_36])],[avatar_definition]) ).
thf(f2347,plain,
( ( hoasinduction_lem3b_lthm = $true )
| ~ spl308_36 ),
inference(avatar_component_clause,[],[f2345]) ).
thf(f2349,definition,
( spl308_37
<=> ! [X1: subst > term > term] :
( ( X1 @ sh @ one )
!= ( sub @ sK28 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[new_symbols(definition,[spl308_37])],[avatar_definition]) ).
thf(f2350,plain,
( ! [X1: subst > term > term] :
( ( X1 @ sh @ one )
!= ( sub @ sK28 @ ( push @ one @ sh ) ) )
| ~ spl308_37 ),
inference(avatar_component_clause,[],[f2349]) ).
thf(f2351,plain,
( spl308_36
| spl308_37 ),
inference(avatar_split_clause,[],[f548,f2349,f2345]) ).
thf(f2458,definition,
( spl308_63
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl308_63])],[avatar_definition]) ).
thf(f2459,plain,
( ! [X1: term] :
( ( sub @ X1 @ id )
= X1 )
| ~ spl308_63 ),
inference(avatar_component_clause,[],[f2458]) ).
thf(f2461,definition,
( spl308_64
<=> ( axvarid = $false ) ),
introduced(definition,[new_symbols(definition,[spl308_64])],[avatar_definition]) ).
thf(f2463,plain,
( ( axvarid = $false )
| ~ spl308_64 ),
inference(avatar_component_clause,[],[f2461]) ).
thf(f2464,plain,
( spl308_63
| spl308_64 ),
inference(avatar_split_clause,[],[f650,f2461,f2458]) ).
thf(f2466,definition,
( spl308_65
<=> ( axvarid = $true ) ),
introduced(definition,[new_symbols(definition,[spl308_65])],[avatar_definition]) ).
thf(f2468,plain,
( ( axvarid = $true )
| ~ spl308_65 ),
inference(avatar_component_clause,[],[f2466]) ).
thf(f2969,definition,
( spl308_185
<=> ( hoasinduction_lem3b_gthm = $true ) ),
introduced(definition,[new_symbols(definition,[spl308_185])],[avatar_definition]) ).
thf(f2978,plain,
( spl308_185
| spl308_65 ),
inference(avatar_split_clause,[],[f1123,f2466,f2969]) ).
thf(f2990,plain,
( spl308_185
| spl308_3 ),
inference(avatar_split_clause,[],[f1139,f2204,f2969]) ).
thf(f3068,plain,
( spl308_35
| spl308_185 ),
inference(avatar_split_clause,[],[f1188,f2969,f2340]) ).
thf(f3903,plain,
~ spl308_185,
inference(avatar_split_clause,[],[f321,f2969]) ).
thf(f3904,plain,
( ( $true = $false )
| ~ spl308_35
| ~ spl308_36 ),
inference(forward_demodulation,[],[f2347,f2342]) ).
thf(f3905,plain,
( $false
| ~ spl308_35
| ~ spl308_36 ),
inference(trivial_inequality_removal,[],[f3904]) ).
thf(f3906,plain,
( ~ spl308_35
| ~ spl308_36 ),
inference(avatar_contradiction_clause,[],[f3905]) ).
thf(f3910,plain,
( ( $true = $false )
| ~ spl308_2
| ~ spl308_3 ),
inference(forward_demodulation,[],[f2206,f2201]) ).
thf(f3911,plain,
( $false
| ~ spl308_2
| ~ spl308_3 ),
inference(trivial_inequality_removal,[],[f3910]) ).
thf(f3912,plain,
( ~ spl308_2
| ~ spl308_3 ),
inference(avatar_contradiction_clause,[],[f3911]) ).
thf(f3944,plain,
( ! [X0: subst > term > term] :
( ( sub @ sK28 @ id )
!= ( X0 @ sh @ one ) )
| ~ spl308_1
| ~ spl308_37 ),
inference(superposition,[],[f2350,f2197]) ).
thf(f3949,plain,
( ( $true = $false )
| ~ spl308_64
| ~ spl308_65 ),
inference(superposition,[],[f2463,f2468]) ).
thf(f3953,plain,
( $false
| ~ spl308_64
| ~ spl308_65 ),
inference(trivial_inequality_removal,[],[f3949]) ).
thf(f3954,plain,
( ~ spl308_64
| ~ spl308_65 ),
inference(avatar_contradiction_clause,[],[f3953]) ).
thf(f4306,plain,
( ! [X0: subst > term > term] :
( sK28
!= ( X0 @ sh @ one ) )
| ~ spl308_1
| ~ spl308_37
| ~ spl308_63 ),
inference(forward_demodulation,[],[f3944,f2459]) ).
thf(f4329,plain,
( ( ( ^ [Y0: subst,Y1: term] : sK28
@ sh
@ one )
!= sK28 )
| ~ spl308_1
| ~ spl308_37
| ~ spl308_63 ),
inference(imitation,[],[f4306]) ).
thf(f4330,plain,
( ( sK28 != sK28 )
| ~ spl308_1
| ~ spl308_37
| ~ spl308_63 ),
inference(beta-eta_normalization,[],[f4329]) ).
thf(f4331,plain,
( $false
| ~ spl308_1
| ~ spl308_37
| ~ spl308_63 ),
inference(trivial_inequality_removal,[],[f4330]) ).
thf(f4332,plain,
( ~ spl308_1
| ~ spl308_37
| ~ spl308_63 ),
inference(avatar_contradiction_clause,[],[f4331]) ).
cnf(s1,plain,
( spl308_1
| spl308_2 ),
inference(sat_conversion,[],[f2202]) ).
cnf(s26,plain,
( spl308_36
| spl308_37 ),
inference(sat_conversion,[],[f2351]) ).
cnf(s40,plain,
( spl308_63
| spl308_64 ),
inference(sat_conversion,[],[f2464]) ).
cnf(s119,plain,
( spl308_65
| spl308_185 ),
inference(sat_conversion,[],[f2978]) ).
cnf(s127,plain,
( spl308_3
| spl308_185 ),
inference(sat_conversion,[],[f2990]) ).
cnf(s153,plain,
( spl308_35
| spl308_185 ),
inference(sat_conversion,[],[f3068]) ).
cnf(s351,plain,
~ spl308_185,
inference(sat_conversion,[],[f3903]) ).
cnf(s352,plain,
( ~ spl308_35
| ~ spl308_36 ),
inference(sat_conversion,[],[f3906]) ).
cnf(s353,plain,
( ~ spl308_2
| ~ spl308_3 ),
inference(sat_conversion,[],[f3912]) ).
cnf(s364,plain,
( ~ spl308_64
| ~ spl308_65 ),
inference(sat_conversion,[],[f3954]) ).
cnf(s409,plain,
( ~ spl308_1
| ~ spl308_37
| ~ spl308_63 ),
inference(sat_conversion,[],[f4332]) ).
cnf(s410,plain,
spl308_35,
inference(rat,[],[s153,s351]) ).
cnf(s411,plain,
~ spl308_36,
inference(rat,[],[s352,s410]) ).
cnf(s499,plain,
spl308_3,
inference(rat,[],[s127,s351]) ).
cnf(s500,plain,
~ spl308_2,
inference(rat,[],[s353,s499]) ).
cnf(s517,plain,
spl308_65,
inference(rat,[],[s119,s351]) ).
cnf(s518,plain,
~ spl308_64,
inference(rat,[],[s364,s517]) ).
cnf(s554,plain,
spl308_63,
inference(rat,[],[s40,s518]) ).
cnf(s564,plain,
spl308_37,
inference(rat,[],[s26,s411]) ).
cnf(s565,plain,
~ spl308_1,
inference(rat,[],[s409,s554,s564]) ).
cnf(s568,plain,
$false,
inference(rat,[],[s1,s500,s565]) ).
thf(f4333,plain,
$false,
inference(avatar_sat_refutation,[],[s568]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG267^1 : 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 : n002.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 17:37:38 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.26 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
% 0.70/0.39 % (1616171)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.70/0.39 % (1616191)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1283498903:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.70/0.39 % (1616192)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.70/0.39 % (1616192)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
% 0.70/0.39 % (1616188)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2031217975:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.70/0.39 % (1616186)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2079309508:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.70/0.39 % (1616187)lrs+10_16_si=on:nwc=1.5:random_seed=1642884825:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.70/0.39 % (1616190)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3712429344:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.70/0.39 % (1616189)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=3751271861: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)
% 0.70/0.39 % (1616192)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=4043712214:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.70/0.39 % (1616188)Instruction limit reached!
% 0.70/0.39 % (1616188)------------------------------
% 0.70/0.39 % (1616188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.39 % (1616188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.39 % (1616188)CaDiCaL version: 2.1.3
% 0.70/0.39 % (1616188)Termination reason: Instruction limit
% 0.70/0.39 % (1616188)Termination phase: shuffling
% 0.70/0.39 % (1616188)Time elapsed: 0.002 s
% 0.70/0.39 % (1616188)Peak memory usage: 10 MB
% 0.70/0.39 % (1616188)Instructions burned: 3 (million)
% 0.70/0.39 % (1616187)Instruction limit reached!
% 0.70/0.39 % (1616187)------------------------------
% 0.70/0.39 % (1616187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.39 % (1616187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.39 % (1616187)CaDiCaL version: 2.1.3
% 0.70/0.39 % (1616187)Termination reason: Instruction limit
% 0.70/0.39 % (1616187)Termination phase: shuffling
% 0.70/0.39 % (1616187)Time elapsed: 0.008 s
% 0.70/0.39 % (1616187)Peak memory usage: 10 MB
% 0.70/0.39 % (1616187)Instructions burned: 18 (million)
% 0.70/0.39 % (1616191)Instruction limit reached!
% 0.70/0.39 % (1616191)------------------------------
% 0.70/0.39 % (1616191)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.39 % (1616191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.39 % (1616191)CaDiCaL version: 2.1.3
% 0.70/0.39 % (1616191)Termination reason: Instruction limit
% 0.70/0.39 % (1616191)Termination phase: Property scanning
% 0.70/0.39 % (1616191)Time elapsed: 0.019 s
% 0.70/0.39 % (1616191)Peak memory usage: 12 MB
% 0.70/0.39 % (1616191)Instructions burned: 78 (million)
% 0.70/0.39 % (1616190)Instruction limit reached!
% 0.70/0.39 % (1616190)------------------------------
% 0.70/0.39 % (1616190)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.39 % (1616190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.39 % (1616190)CaDiCaL version: 2.1.3
% 0.70/0.39 % (1616190)Termination reason: Instruction limit
% 0.70/0.39 % (1616190)Termination phase: shuffling
% 0.70/0.39 % (1616190)Time elapsed: 0.011 s
% 0.70/0.39 % (1616190)Peak memory usage: 11 MB
% 0.70/0.39 % (1616190)Instructions burned: 24 (million)
% 0.70/0.39 % (1616215)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.70/0.39 % (1616210)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2243169123:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.70/0.42 % (1616215)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3022974677:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.70/0.42 % (1616210)Instruction limit reached!
% 0.70/0.42 % (1616210)------------------------------
% 0.70/0.42 % (1616210)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.42 % (1616210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.42 % (1616210)CaDiCaL version: 2.1.3
% 0.70/0.42 % (1616210)Termination reason: Instruction limit
% 0.70/0.42 % (1616210)Termination phase: shuffling
% 0.70/0.42 % (1616210)Time elapsed: 0.002 s
% 0.70/0.42 % (1616210)Peak memory usage: 10 MB
% 0.70/0.42 % (1616210)Instructions burned: 3 (million)
% 0.70/0.42 % (1616215)Instruction limit reached!
% 0.70/0.42 % (1616215)------------------------------
% 0.70/0.42 % (1616215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.42 % (1616215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.42 % (1616215)CaDiCaL version: 2.1.3
% 0.70/0.42 % (1616215)Termination reason: Instruction limit
% 0.70/0.42 % (1616215)Termination phase: shuffling
% 0.70/0.42 % (1616215)Time elapsed: 0.002 s
% 0.70/0.42 % (1616215)Peak memory usage: 10 MB
% 0.70/0.42 % (1616215)Instructions burned: 8 (million)
% 0.70/0.42 % (1616213)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3305001404:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.70/0.42 % (1616216)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2315784535:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.70/0.42 % (1616213)Instruction limit reached!
% 0.70/0.42 % (1616213)------------------------------
% 0.70/0.42 % (1616213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.42 % (1616213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.42 % (1616213)CaDiCaL version: 2.1.3
% 0.70/0.42 % (1616213)Termination reason: Instruction limit
% 0.70/0.42 % (1616213)Termination phase: shuffling
% 0.70/0.42 % (1616213)Time elapsed: 0.003 s
% 0.70/0.42 % (1616213)Peak memory usage: 10 MB
% 0.70/0.42 % (1616213)Instructions burned: 6 (million)
% 0.70/0.42 % (1616225)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=401382739:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.70/0.42 % (1616216)Instruction limit reached!
% 0.70/0.42 % (1616216)------------------------------
% 0.70/0.42 % (1616216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.42 % (1616216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.42 % (1616216)CaDiCaL version: 2.1.3
% 0.70/0.42 % (1616216)Termination reason: Instruction limit
% 0.70/0.42 % (1616216)Termination phase: shuffling
% 0.70/0.42 % (1616216)Time elapsed: 0.006 s
% 0.70/0.42 % (1616216)Peak memory usage: 10 MB
% 0.70/0.42 % (1616216)Instructions burned: 12 (million)
% 0.70/0.42 % (1616186)Instruction limit reached!
% 0.70/0.42 % (1616186)------------------------------
% 0.70/0.42 % (1616186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.42 % (1616186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.42 % (1616186)CaDiCaL version: 2.1.3
% 0.70/0.42 % (1616186)Termination reason: Instruction limit
% 0.70/0.42 % (1616186)Termination phase: Function definition elimination
% 0.70/0.42 % (1616186)Time elapsed: 0.039 s
% 0.70/0.42 % (1616186)Peak memory usage: 12 MB
% 0.70/0.42 % (1616186)Instructions burned: 88 (million)
% 0.70/0.42 % (1616223)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
% 0.70/0.42 % (1616223)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.70/0.42 % (1616223)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4099579757:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.70/0.42 % (1616233)lrs+10_1_si=on:cs=on:random_seed=1283790346:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.70/0.42 % (1616238)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.70/0.45 % (1616233)Instruction limit reached!
% 0.70/0.45 % (1616233)------------------------------
% 0.70/0.45 % (1616233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.45 % (1616233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.45 % (1616225)Instruction limit reached!
% 0.70/0.45 % (1616225)------------------------------
% 0.70/0.45 % (1616225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.45 % (1616225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.45 % (1616233)CaDiCaL version: 2.1.3
% 0.70/0.45 % (1616233)Termination reason: Instruction limit
% 0.70/0.45 % (1616233)Termination phase: shuffling
% 0.70/0.45 % (1616225)CaDiCaL version: 2.1.3
% 0.70/0.45 % (1616233)Time elapsed: 0.004 s
% 0.70/0.45 % (1616225)Termination reason: Instruction limit
% 0.70/0.45 % (1616225)Termination phase: Saturation
% 0.70/0.45 % (1616225)Time elapsed: 0.020 s
% 0.70/0.45 % (1616233)Peak memory usage: 10 MB
% 0.70/0.45 % (1616225)Peak memory usage: 12 MB
% 0.70/0.45 % (1616225)Instructions burned: 87 (million)
% 0.70/0.45 % (1616233)Instructions burned: 9 (million)
% 0.70/0.45 % (1616238)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=2021857126:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.70/0.45 % (1616223)Instruction limit reached!
% 0.70/0.45 % (1616223)------------------------------
% 0.70/0.45 % (1616223)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.45 % (1616223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.45 % (1616223)CaDiCaL version: 2.1.3
% 0.70/0.45 % (1616223)Termination reason: Instruction limit
% 0.70/0.45 % (1616223)Termination phase: Property scanning
% 0.70/0.45 % (1616223)Time elapsed: 0.014 s
% 0.70/0.45 % (1616223)Peak memory usage: 10 MB
% 0.70/0.45 % (1616223)Instructions burned: 29 (million)
% 0.70/0.45 % (1616240)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2198556155:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.70/0.45 % (1616238)Instruction limit reached!
% 0.70/0.45 % (1616238)------------------------------
% 0.70/0.45 % (1616238)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.45 % (1616238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.45 % (1616238)CaDiCaL version: 2.1.3
% 0.70/0.45 % (1616238)Termination reason: Instruction limit
% 0.70/0.45 % (1616238)Termination phase: shuffling
% 0.70/0.45 % (1616238)Time elapsed: 0.003 s
% 0.70/0.45 % (1616238)Peak memory usage: 10 MB
% 0.70/0.45 % (1616238)Instructions burned: 5 (million)
% 0.70/0.45 % (1616246)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2773558062:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.70/0.45 % (1616192)Instruction limit reached!
% 0.70/0.45 % (1616192)------------------------------
% 0.70/0.45 % (1616192)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.45 % (1616192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.45 % (1616192)CaDiCaL version: 2.1.3
% 0.70/0.45 % (1616192)Termination reason: Instruction limit
% 0.70/0.45 % (1616192)Termination phase: Saturation
% 0.70/0.45 % (1616192)Time elapsed: 0.067 s
% 0.70/0.45 % (1616192)Peak memory usage: 13 MB
% 0.70/0.45 % (1616192)Instructions burned: 159 (million)
% 0.70/0.45 % (1616247)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1677797269:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.70/0.45 % (1616240)Instruction limit reached!
% 0.70/0.45 % (1616240)------------------------------
% 0.70/0.45 % (1616240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.70/0.45 % (1616240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.70/0.45 % (1616240)CaDiCaL version: 2.1.3
% 0.70/0.45 % (1616240)Termination reason: Instruction limit
% 0.70/0.45 % (1616240)Termination phase: Function definition elimination
% 0.70/0.45 % (1616240)Time elapsed: 0.018 s
% 0.70/0.45 % (1616240)Peak memory usage: 12 MB
% 0.70/0.45 % (1616240)Instructions burned: 38 (million)
% 0.70/0.45 % (1616251)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1464721078:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.30/0.50 % (1616252)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=681545480:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.30/0.50 % (1616246)Refutation not found, incomplete strategy
% 1.30/0.50 % (1616246)------------------------------
% 1.30/0.50 % (1616246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.50 % (1616246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.50 % (1616246)CaDiCaL version: 2.1.3
% 1.30/0.50 % (1616246)Termination reason: Refutation not found, incomplete strategy
% 1.30/0.50 % (1616246)Time elapsed: 0.012 s
% 1.30/0.50 % (1616246)Peak memory usage: 12 MB
% 1.30/0.50 % (1616246)Instructions burned: 52 (million)
% 1.30/0.50 % (1616246)------------------------------
% 1.30/0.50 % (1616246)------------------------------
% 1.30/0.50 % (1616251)Instruction limit reached!
% 1.30/0.50 % (1616251)------------------------------
% 1.30/0.50 % (1616251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.50 % (1616251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.50 % (1616251)CaDiCaL version: 2.1.3
% 1.30/0.50 % (1616251)Termination reason: Instruction limit
% 1.30/0.50 % (1616251)Termination phase: shuffling
% 1.30/0.50 % (1616251)Time elapsed: 0.007 s
% 1.30/0.50 % (1616251)Peak memory usage: 10 MB
% 1.30/0.50 % (1616251)Instructions burned: 15 (million)
% 1.30/0.50 % (1616247)Instruction limit reached!
% 1.30/0.50 % (1616247)------------------------------
% 1.30/0.50 % (1616247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.50 % (1616247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.50 % (1616247)CaDiCaL version: 2.1.3
% 1.30/0.50 % (1616247)Termination reason: Instruction limit
% 1.30/0.50 % (1616247)Termination phase: Naming
% 1.30/0.50 % (1616247)Time elapsed: 0.012 s
% 1.30/0.50 % (1616247)Peak memory usage: 11 MB
% 1.30/0.50 % (1616247)Instructions burned: 26 (million)
% 1.30/0.50 % (1616258)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2942530961:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.30/0.50 % (1616258)Instruction limit reached!
% 1.30/0.50 % (1616258)------------------------------
% 1.30/0.50 % (1616258)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.50 % (1616258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.50 % (1616258)CaDiCaL version: 2.1.3
% 1.30/0.50 % (1616258)Termination reason: Instruction limit
% 1.30/0.50 % (1616258)Termination phase: shuffling
% 1.30/0.50 % (1616258)Time elapsed: 0.007 s
% 1.30/0.50 % (1616258)Peak memory usage: 10 MB
% 1.30/0.50 % (1616258)Instructions burned: 16 (million)
% 1.30/0.50 % (1616266)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3094624859:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.30/0.50 % (1616266)Instruction limit reached!
% 1.30/0.50 % (1616266)------------------------------
% 1.30/0.50 % (1616266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.50 % (1616266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.50 % (1616266)CaDiCaL version: 2.1.3
% 1.30/0.50 % (1616266)Termination reason: Instruction limit
% 1.30/0.50 % (1616266)Termination phase: shuffling
% 1.30/0.50 % (1616266)Time elapsed: 0.002 s
% 1.30/0.50 % (1616266)Peak memory usage: 10 MB
% 1.30/0.50 % (1616266)Instructions burned: 3 (million)
% 1.30/0.50 % (1616268)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2960127032:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.30/0.50 % (1616271)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1626646113:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.30/0.50 % (1616274)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1302767326:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.30/0.50 % (1616278)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
% 1.30/0.52 % (1616278)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.30/0.52 % (1616268)Instruction limit reached!
% 1.30/0.52 % (1616268)------------------------------
% 1.30/0.52 % (1616268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.52 % (1616268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.52 % (1616268)CaDiCaL version: 2.1.3
% 1.30/0.52 % (1616268)Termination reason: Instruction limit
% 1.30/0.52 % (1616268)Termination phase: Property scanning
% 1.30/0.52 % (1616268)Time elapsed: 0.011 s
% 1.30/0.52 % (1616268)Peak memory usage: 10 MB
% 1.30/0.52 % (1616268)Instructions burned: 27 (million)
% 1.30/0.52 % (1616283)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.30/0.52 % (1616278)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=3223034747:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.30/0.52 % (1616271)Instruction limit reached!
% 1.30/0.52 % (1616271)------------------------------
% 1.30/0.52 % (1616271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.52 % (1616271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.52 % (1616271)CaDiCaL version: 2.1.3
% 1.30/0.52 % (1616271)Termination reason: Instruction limit
% 1.30/0.52 % (1616271)Termination phase: Property scanning
% 1.30/0.52 % (1616271)Time elapsed: 0.010 s
% 1.30/0.52 % (1616271)Peak memory usage: 10 MB
% 1.30/0.52 % (1616271)Instructions burned: 23 (million)
% 1.30/0.52 % (1616283)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=3635530535:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.30/0.52 % (1616278)Instruction limit reached!
% 1.30/0.52 % (1616278)------------------------------
% 1.30/0.52 % (1616278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.52 % (1616278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.52 % (1616278)CaDiCaL version: 2.1.3
% 1.30/0.52 % (1616278)Termination reason: Instruction limit
% 1.30/0.52 % (1616278)Termination phase: shuffling
% 1.30/0.52 % (1616278)Time elapsed: 0.007 s
% 1.30/0.52 % (1616278)Peak memory usage: 10 MB
% 1.30/0.52 % (1616278)Instructions burned: 15 (million)
% 1.30/0.52 % (1616294)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=2832479233:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.30/0.52 % (1616283)Instruction limit reached!
% 1.30/0.52 % (1616283)------------------------------
% 1.30/0.52 % (1616283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.52 % (1616283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.52 % (1616283)CaDiCaL version: 2.1.3
% 1.30/0.52 % (1616283)Termination reason: Instruction limit
% 1.30/0.52 % (1616283)Termination phase: shuffling
% 1.30/0.52 % (1616283)Time elapsed: 0.004 s
% 1.30/0.52 % (1616283)Peak memory usage: 9 MB
% 1.30/0.52 % (1616283)Instructions burned: 8 (million)
% 1.30/0.52 % (1616294)Instruction limit reached!
% 1.30/0.52 % (1616294)------------------------------
% 1.30/0.52 % (1616294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.52 % (1616294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.52 % (1616294)CaDiCaL version: 2.1.3
% 1.30/0.52 % (1616294)Termination reason: Instruction limit
% 1.30/0.52 % (1616294)Termination phase: Property scanning
% 1.30/0.52 % (1616294)Time elapsed: 0.008 s
% 1.30/0.52 % (1616294)Peak memory usage: 10 MB
% 1.30/0.52 % (1616294)Instructions burned: 35 (million)
% 1.30/0.52 % (1616297)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2181130010:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.30/0.52 % (1616274)Instruction limit reached!
% 1.30/0.52 % (1616274)------------------------------
% 1.30/0.52 % (1616274)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.52 % (1616274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.52 % (1616274)CaDiCaL version: 2.1.3
% 1.30/0.52 % (1616274)Termination reason: Instruction limit
% 1.30/0.52 % (1616274)Termination phase: Property scanning
% 1.30/0.52 % (1616274)Time elapsed: 0.028 s
% 1.30/0.52 % (1616274)Peak memory usage: 12 MB
% 1.30/0.52 % (1616274)Instructions burned: 61 (million)
% 1.30/0.52 % (1616297)Instruction limit reached!
% 1.30/0.52 % (1616297)------------------------------
% 1.30/0.52 % (1616297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.52 % (1616297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.52 % (1616297)CaDiCaL version: 2.1.3
% 1.30/0.52 % (1616297)Termination reason: Instruction limit
% 1.30/0.52 % (1616297)Termination phase: shuffling
% 1.30/0.52 % (1616297)Time elapsed: 0.003 s
% 1.30/0.52 % (1616297)Peak memory usage: 10 MB
% 1.30/0.52 % (1616297)Instructions burned: 7 (million)
% 1.30/0.52 % (1616300)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3814119856:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.30/0.52 % (1616306)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2131873627:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.30/0.52 % (1616301)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3776589884:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.30/0.52 % (1616300)Instruction limit reached!
% 1.30/0.52 % (1616300)------------------------------
% 1.30/0.52 % (1616300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.52 % (1616300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.52 % (1616300)CaDiCaL version: 2.1.3
% 1.30/0.52 % (1616300)Termination reason: Instruction limit
% 1.30/0.52 % (1616300)Termination phase: Property scanning
% 1.30/0.52 % (1616300)Time elapsed: 0.011 s
% 1.30/0.52 % (1616300)Peak memory usage: 10 MB
% 1.30/0.52 % (1616300)Instructions burned: 25 (million)
% 1.30/0.52 % (1616311)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1450051603:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 1.30/0.52 % (1616301)Instruction limit reached!
% 1.30/0.52 % (1616301)------------------------------
% 1.30/0.52 % (1616301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.52 % (1616301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.52 % (1616301)CaDiCaL version: 2.1.3
% 1.30/0.52 % (1616301)Termination reason: Instruction limit
% 1.30/0.52 % (1616301)Termination phase: Property scanning
% 1.30/0.52 % (1616301)Time elapsed: 0.009 s
% 1.30/0.52 % (1616301)Peak memory usage: 10 MB
% 1.30/0.52 % (1616301)Instructions burned: 21 (million)
% 1.30/0.52 % (1616310)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2078908346:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.30/0.52 % (1616318)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=584046566:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 1.30/0.52 % (1616323)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.30/0.52 % (1616323)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=478959231:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.30/0.52 % (1616323)Instruction limit reached!
% 1.30/0.52 % (1616323)------------------------------
% 1.30/0.52 % (1616323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.52 % (1616323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.52 % (1616323)CaDiCaL version: 2.1.3
% 1.30/0.52 % (1616323)Termination reason: Instruction limit
% 1.30/0.52 % (1616323)Termination phase: shuffling
% 1.30/0.52 % (1616323)Time elapsed: 0.004 s
% 1.30/0.52 % (1616323)Peak memory usage: 10 MB
% 1.30/0.52 % (1616323)Instructions burned: 9 (million)
% 1.30/0.52 % (1616311)Refutation not found, incomplete strategy
% 1.30/0.52 % (1616311)------------------------------
% 1.30/0.52 % (1616311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.52 % (1616311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.52 % (1616311)CaDiCaL version: 2.1.3
% 1.30/0.52 % (1616311)Termination reason: Refutation not found, incomplete strategy
% 1.30/0.52 % (1616311)Time elapsed: 0.031 s
% 1.30/0.52 % (1616311)Peak memory usage: 13 MB
% 1.30/0.52 % (1616311)Instructions burned: 68 (million)
% 1.30/0.52 % (1616311)------------------------------
% 1.30/0.52 % (1616311)------------------------------
% 1.30/0.52 % (1616318)Instruction limit reached!
% 1.30/0.52 % (1616318)------------------------------
% 1.30/0.52 % (1616318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.52 % (1616318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.52 % (1616318)CaDiCaL version: 2.1.3
% 1.30/0.52 % (1616318)Termination reason: Instruction limit
% 1.30/0.52 % (1616318)Termination phase: Property scanning
% 1.30/0.52 % (1616318)Time elapsed: 0.018 s
% 1.30/0.52 % (1616318)Peak memory usage: 10 MB
% 1.30/0.52 % (1616318)Instructions burned: 43 (million)
% 1.30/0.52 % (1616252) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1616171-1616252"...
% 1.30/0.52 % (1616335)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=2468834813:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.30/0.52 % (1616340)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 1.30/0.52 % (1616252)...printing done.
% 1.30/0.52 % (1616252)Refutation found. Thanks to Tanya!
% 1.30/0.52 % SZS status Theorem for theBenchmark
% 1.30/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 1.30/0.53 % (1616252)------------------------------
% 1.30/0.53 % (1616252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.30/0.53 % (1616252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.30/0.53 % (1616252)CaDiCaL version: 2.1.3
% 1.30/0.53 % (1616252)Termination reason: Refutation
% 1.30/0.53 % (1616252)Time elapsed: 0.127 s
% 1.30/0.53 % (1616252)Peak memory usage: 16 MB
% 1.30/0.53 % (1616252)Instructions burned: 277 (million)
% 1.30/0.53 % (1616171)Success in time 0.252 s
% 1.30/0.53 % Vampire exiting
%------------------------------------------------------------------------------