%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG259^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 07:45:14 AM UTC 2026
% Result : Theorem 1.77s 0.63s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 89 ( 33 unt; 0 typ; 7 def)
% Number of atoms : 352 ( 115 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 595 ( 65 ~; 52 |; 0 &; 405 @)
% ( 7 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 410 ( 406 usr; 183 con; 0-4 aty)
% ( 53 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 151 ( 12 sgn 42 !; 0 ?; 151 :)
% 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,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_133,type,
vNOT: $o > $o ).
thf(func_def_134,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_135,type,
vAND: $o > $o > $o ).
thf(func_def_136,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_139,type,
sK0: ( subst > term > subst > $o ) > term ).
thf(func_def_140,type,
sK1: ( subst > term > subst > $o ) > subst ).
thf(func_def_141,type,
sK2: ( subst > term > subst > $o ) > term ).
thf(func_def_142,type,
sK3: ( subst > term > subst > $o ) > term ).
thf(func_def_143,type,
sK4: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_144,type,
sK5: ( subst > term > subst > $o ) > subst ).
thf(func_def_145,type,
sK6: ( subst > term > subst > $o ) > term ).
thf(func_def_146,type,
sK7: ( subst > term > subst > $o ) > subst ).
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 ) > subst ).
thf(func_def_150,type,
sK11: ( subst > term > subst > $o ) > subst ).
thf(func_def_151,type,
sK12: ( subst > term > subst > $o ) > term ).
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 ) > subst ).
thf(func_def_155,type,
sK16: ( subst > term > subst > $o ) > subst ).
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 ) > term ).
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 ) > subst ).
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 ) > subst ).
thf(func_def_167,type,
sK28: ( subst > term > subst > $o ) > subst ).
thf(func_def_168,type,
sK29: ( subst > term > subst > $o ) > term ).
thf(func_def_169,type,
sK30: ( subst > term > subst > $o ) > subst ).
thf(func_def_170,type,
sK31: ( subst > term > subst > $o ) > term ).
thf(func_def_171,type,
sK32: ( subst > term > subst > $o ) > subst ).
thf(func_def_172,type,
sK33: ( subst > term > subst > $o ) > subst ).
thf(func_def_173,type,
sK34: ( subst > term > subst > $o ) > subst ).
thf(func_def_174,type,
sK35: ( subst > term > subst > $o ) > subst ).
thf(func_def_175,type,
sK36: ( subst > term > subst > $o ) > subst ).
thf(func_def_176,type,
sK37: ( subst > term > subst > $o ) > subst ).
thf(func_def_177,type,
sK38: ( subst > term > subst > $o ) > term ).
thf(func_def_178,type,
sK39: ( subst > term > subst > $o ) > subst ).
thf(func_def_179,type,
sK40: ( subst > term > subst > $o ) > term ).
thf(func_def_180,type,
sK41: ( subst > term > subst > $o ) > subst ).
thf(func_def_181,type,
sK42: ( subst > term > subst > $o ) > subst ).
thf(func_def_182,type,
sK43: ( subst > term > subst > $o ) > term ).
thf(func_def_183,type,
sK44: ( subst > term > subst > $o ) > subst ).
thf(func_def_184,type,
sK45: ( subst > term > subst > $o ) > subst ).
thf(func_def_185,type,
sK46: ( subst > term > subst > $o ) > subst ).
thf(func_def_186,type,
sK47: ( subst > term > subst > $o ) > subst ).
thf(func_def_187,type,
sK48: ( subst > term > subst > $o ) > subst ).
thf(func_def_188,type,
sK49: ( subst > term > subst > $o ) > term ).
thf(func_def_189,type,
sK50: ( subst > term > subst > $o ) > term ).
thf(func_def_190,type,
sK51: ( subst > term > subst > $o ) > subst ).
thf(func_def_191,type,
sK52: ( subst > term > subst > $o ) > subst ).
thf(func_def_192,type,
sK53: ( subst > term > subst > $o ) > subst ).
thf(func_def_193,type,
sK54: ( subst > term > subst > $o ) > subst ).
thf(func_def_194,type,
sK55: ( subst > term > subst > $o ) > subst ).
thf(func_def_195,type,
sK56: ( subst > term > subst > $o ) > subst ).
thf(func_def_196,type,
sK57: ( subst > term > subst > $o ) > subst ).
thf(func_def_197,type,
sK58: ( subst > term > subst > $o ) > subst ).
thf(func_def_198,type,
sK59: ( subst > term > subst > $o ) > subst ).
thf(func_def_199,type,
sK60: ( subst > term > subst > $o ) > term ).
thf(func_def_200,type,
sK61: ( subst > term > subst > $o ) > subst ).
thf(func_def_201,type,
sK62: ( subst > term > subst > $o ) > subst ).
thf(func_def_202,type,
sK63: ( subst > term > subst > $o ) > term ).
thf(func_def_203,type,
sK64: ( subst > term > subst > $o ) > subst ).
thf(func_def_204,type,
sK65: ( subst > term > subst > $o ) > subst ).
thf(func_def_205,type,
sK66: ( subst > term > subst > $o ) > subst ).
thf(func_def_206,type,
sK67: ( subst > term > subst > $o ) > subst ).
thf(func_def_207,type,
sK68: ( subst > term > subst > $o ) > term ).
thf(func_def_208,type,
sK69: ( subst > term > subst > $o ) > subst ).
thf(func_def_209,type,
sK70: ( subst > term > subst > $o ) > subst ).
thf(func_def_210,type,
sK71: subst > term > subst > $o ).
thf(func_def_211,type,
sK72: ( subst > term > term ) > subst ).
thf(func_def_212,type,
sK73: ( subst > term > term ) > term ).
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 ) > term ).
thf(func_def_217,type,
sK78: term ).
thf(func_def_218,type,
sK79: subst ).
thf(func_def_219,type,
sK80: subst ).
thf(func_def_220,type,
sK81: subst ).
thf(func_def_221,type,
sK82: ( term > $o ) > term ).
thf(func_def_222,type,
sK83: ( term > $o ) > term ).
thf(func_def_223,type,
sK84: ( term > $o ) > term ).
thf(func_def_224,type,
sK85: ( term > $o ) > term ).
thf(func_def_225,type,
sK86: term > $o ).
thf(func_def_226,type,
sK87: term > term ).
thf(func_def_227,type,
sK88: term ).
thf(func_def_228,type,
sK89: subst > ( term > $o ) > term ).
thf(func_def_229,type,
sK90: term > $o ).
thf(func_def_230,type,
sK91: term ).
thf(func_def_231,type,
sK92: subst ).
thf(func_def_232,type,
sK93: term ).
thf(func_def_233,type,
sK94: ( subst > term > term ) > term ).
thf(func_def_234,type,
sK95: ( subst > term > term ) > subst ).
thf(func_def_235,type,
sK96: ( subst > term > term ) > subst ).
thf(func_def_236,type,
sK97: subst > term > term ).
thf(func_def_237,type,
sK98: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_238,type,
sK99: ( subst > term > subst > $o ) > term > term ).
thf(func_def_239,type,
sK100: ( subst > term > subst > $o ) > term > term ).
thf(func_def_240,type,
sK101: subst > term > subst > $o ).
thf(func_def_241,type,
sK102: ( subst > term > term ) > term ).
thf(func_def_242,type,
sK103: ( subst > term > term ) > term ).
thf(func_def_243,type,
sK104: ( subst > term > term ) > subst ).
thf(func_def_244,type,
sK105: ( subst > term > term ) > subst ).
thf(func_def_245,type,
sK106: ( subst > term > term ) > subst ).
thf(func_def_246,type,
sK107: ( subst > term > term ) > subst ).
thf(func_def_247,type,
sK108: term ).
thf(func_def_248,type,
sK109: term ).
thf(func_def_249,type,
sK110: term ).
thf(func_def_250,type,
sK111: term ).
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: subst ).
thf(func_def_255,type,
sK116: term ).
thf(func_def_256,type,
sK117: subst ).
thf(func_def_257,type,
sK118: term ).
thf(func_def_258,type,
sK119: term ).
thf(func_def_259,type,
sK120: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_260,type,
sK121: term > ( term > $o ) > term ).
thf(func_def_261,type,
sK122: term > ( term > $o ) > term ).
thf(func_def_262,type,
sK123: term > ( term > $o ) > term ).
thf(func_def_263,type,
sK124: term > $o ).
thf(func_def_264,type,
sK125: subst > term > subst > $o ).
thf(func_def_265,type,
sK126: ( subst > term > term ) > subst ).
thf(func_def_266,type,
sK127: ( subst > term > term ) > term ).
thf(func_def_267,type,
sK128: ( subst > term > term ) > term ).
thf(func_def_268,type,
sK129: ( subst > term > term ) > subst ).
thf(func_def_269,type,
sK130: ( subst > term > term ) > term ).
thf(func_def_270,type,
sK131: ( subst > term > term ) > subst ).
thf(func_def_271,type,
sK132: term ).
thf(func_def_272,type,
sK133: subst ).
thf(func_def_273,type,
sK134: term ).
thf(func_def_274,type,
sK135: term ).
thf(func_def_275,type,
sK136: term ).
thf(func_def_276,type,
sK137: term ).
thf(func_def_277,type,
sK138: term ).
thf(func_def_278,type,
sK139: term ).
thf(func_def_279,type,
sK140: term ).
thf(func_def_280,type,
sK141: term ).
thf(func_def_281,type,
sK142: ( subst > term > term ) > subst ).
thf(func_def_282,type,
sK143: ( subst > term > term ) > subst ).
thf(func_def_283,type,
sK144: ( subst > term > term ) > subst ).
thf(func_def_284,type,
sK145: ( subst > term > term ) > term ).
thf(func_def_285,type,
sK146: ( subst > term > term ) > subst ).
thf(func_def_286,type,
sK147: ( subst > term > term ) > term ).
thf(func_def_287,type,
sK148: subst > term > term ).
thf(func_def_288,type,
sK149: subst > term > term ).
thf(func_def_289,type,
sK150: subst ).
thf(func_def_290,type,
sK151: term ).
thf(func_def_291,type,
sK152: term ).
thf(func_def_292,type,
sK153: term ).
thf(func_def_293,type,
sK154: term ).
thf(func_def_294,type,
sK155: ( subst > term > subst > $o ) > term ).
thf(func_def_295,type,
sK156: ( subst > term > subst > $o ) > subst ).
thf(func_def_296,type,
sK157: ( subst > term > subst > $o ) > term ).
thf(func_def_297,type,
sK158: ( subst > term > subst > $o ) > subst ).
thf(func_def_298,type,
sK159: ( subst > term > subst > $o ) > term ).
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 ).
thf(func_def_311,type,
sK172: term ).
thf(func_def_312,type,
sK173: term ).
thf(func_def_313,type,
sK174: subst ).
thf(func_def_314,type,
sK175: term ).
thf(func_def_315,type,
sK176: subst ).
thf(func_def_316,type,
sK177: subst ).
thf(func_def_317,type,
sK178: term ).
thf(func_def_318,type,
sK179: term ).
thf(func_def_319,type,
sK180: ( subst > term > term ) > term ).
thf(func_def_320,type,
sK181: ( subst > term > term ) > subst ).
thf(func_def_321,type,
sK182: ( subst > term > term ) > subst ).
thf(func_def_322,type,
sK183: subst > term > term ).
thf(func_def_323,type,
sK184: term ).
thf(func_def_324,type,
sK185: term ).
thf(func_def_325,type,
sK186: term ).
thf(func_def_326,type,
sK187: subst ).
thf(func_def_327,type,
sK188: term ).
thf(func_def_328,type,
sK189: subst ).
thf(func_def_329,type,
sK190: subst ).
thf(func_def_330,type,
sK191: term ).
thf(func_def_331,type,
sK192: term ).
thf(func_def_332,type,
sK193: ( subst > term > subst > $o ) > subst ).
thf(func_def_333,type,
sK194: ( subst > term > subst > $o ) > subst ).
thf(func_def_334,type,
sK195: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_335,type,
sK196: ( subst > term > subst > $o ) > term ).
thf(func_def_336,type,
sK197: ( subst > term > subst > $o ) > subst ).
thf(func_def_337,type,
sK198: ( subst > term > subst > $o ) > term > term ).
thf(func_def_338,type,
sK199: ( subst > term > subst > $o ) > subst ).
thf(func_def_339,type,
sK200: ( subst > term > subst > $o ) > subst ).
thf(func_def_340,type,
sK201: ( subst > term > subst > $o ) > subst ).
thf(func_def_341,type,
sK202: ( subst > term > subst > $o ) > term ).
thf(func_def_342,type,
sK203: ( subst > term > subst > $o ) > subst ).
thf(func_def_343,type,
sK204: ( subst > term > subst > $o ) > term ).
thf(func_def_344,type,
sK205: ( subst > term > subst > $o ) > subst ).
thf(func_def_345,type,
sK206: ( subst > term > subst > $o ) > term > term ).
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 ) > term ).
thf(func_def_349,type,
sK210: ( subst > term > subst > $o ) > subst ).
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 ) > term ).
thf(func_def_353,type,
sK214: ( subst > term > subst > $o ) > subst ).
thf(func_def_354,type,
sK215: ( subst > term > subst > $o ) > term > 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 ) > term ).
thf(func_def_360,type,
sK221: ( subst > term > subst > $o ) > subst ).
thf(func_def_361,type,
sK222: subst > term > subst > $o ).
thf(func_def_362,type,
sK223: ( subst > term > term ) > term ).
thf(func_def_363,type,
sK224: ( subst > term > term ) > subst ).
thf(func_def_364,type,
sK225: ( subst > term > term ) > subst ).
thf(func_def_365,type,
sK226: ( subst > term > term ) > term ).
thf(func_def_366,type,
sK227: ( subst > term > term ) > term ).
thf(func_def_367,type,
sK228: term ).
thf(func_def_368,type,
sK229: ( term > $o ) > term ).
thf(func_def_369,type,
sK230: ( term > $o ) > term ).
thf(func_def_370,type,
sK231: ( term > $o ) > term ).
thf(func_def_371,type,
sK232: ( term > $o ) > subst > term ).
thf(func_def_372,type,
sK233: ( term > $o ) > term ).
thf(func_def_373,type,
sK234: ( term > $o ) > subst > term ).
thf(func_def_374,type,
sK235: ( term > $o ) > subst > term ).
thf(func_def_375,type,
sK236: ( term > $o ) > subst > term ).
thf(func_def_376,type,
sK237: term > $o ).
thf(func_def_377,type,
sK238: term > term ).
thf(func_def_378,type,
sK239: subst ).
thf(func_def_379,type,
sK240: term ).
thf(func_def_380,type,
sK241: term ).
thf(func_def_381,type,
sK242: term ).
thf(func_def_382,type,
sK243: term ).
thf(func_def_383,type,
sK244: term ).
thf(func_def_384,type,
sK245: term ).
thf(func_def_385,type,
sK246: 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 ) > term ).
thf(func_def_390,type,
sK251: ( subst > term > subst > $o ) > term ).
thf(func_def_391,type,
sK252: ( subst > term > subst > $o ) > subst ).
thf(func_def_392,type,
sK253: ( subst > term > subst > $o ) > subst ).
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: term ).
thf(f20,axiom,
( lamnotap
= ( ! [X2: term,X0: term,X1: term] :
( ( lam @ X0 )
!= ( ap @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',lamnotap) ).
thf(f55,axiom,
( hoasap
= ( ^ [X0: subst,X1: term,X2: subst,X3: term] : ( ap @ ( sub @ X1 @ X2 ) @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasap) ).
thf(f56,axiom,
( ( ^ [X0: subst,X1: subst > term > term] : ( lam @ ( X1 @ sh @ one ) ) )
= hoaslam ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslam) ).
thf(f67,axiom,
( hoaslamnotap
= ( ! [X0: subst > term > term] :
( ! [X3: subst,X1: subst,X2: term] :
( ( sub @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
=> ! [X2: term,X4: term] :
( ( hoasap @ id @ X2 @ id @ X4 )
!= ( hoaslam @ id
@ ^ [X1: subst,X5: term] : ( X0 @ X1 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslamnotap) ).
thf(f69,axiom,
( ( hoaslamnotap_lthm = lamnotap )
=> hoaslamnotap ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslamnotap_lthm) ).
thf(f114,conjecture,
hoaslamnotap_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ hoaslamnotap_lthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f190,plain,
( ( hoaslamnotap_lthm = lamnotap )
=> hoaslamnotap ),
inference(rectify,[],[f69]) ).
thf(f191,plain,
( hoaslamnotap_lthm
= ( lamnotap
=> hoaslamnotap ) ),
inference(fool_elimination,[],[f190]) ).
thf(f205,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f221,plain,
( lamnotap
= ( ! [X0: term,X1: term,X2: term] :
( ( lam @ X1 )
!= ( ap @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f222,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f221]) ).
thf(f246,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f253,plain,
~ hoaslamnotap_lthm,
inference(rectify,[],[f115]) ).
thf(f254,plain,
hoaslamnotap_lthm != $true,
inference(fool_elimination,[],[f253]) ).
thf(f313,plain,
( hoaslamnotap
= ( ! [X0: subst > term > term] :
( ! [X1: subst,X2: subst,X3: term] :
( ( sub @ ( X0 @ X2 @ X3 ) @ X1 )
= ( X0 @ ( comp @ X2 @ X1 ) @ ( sub @ X3 @ X1 ) ) )
=> ! [X4: term,X5: term] :
( ( hoasap @ id @ X4 @ id @ X5 )
!= ( hoaslam @ id
@ ^ [X6: subst,X7: term] : ( X0 @ X6 @ X7 ) ) ) ) ) ),
inference(rectify,[],[f67]) ).
thf(f314,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 )
= ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( hoasap @ id @ Y2 @ id @ Y1 )
!= ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f313]) ).
thf(f321,plain,
hoaslamnotap_lthm != $true,
inference(flattening,[],[f254]) ).
thf(f325,plain,
( hoaslamnotap_lthm
= ( lamnotap
=> hoaslamnotap ) ),
inference(cnf_transformation,[],[f191]) ).
thf(f327,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f222]) ).
thf(f335,plain,
hoaslamnotap_lthm != $true,
inference(cnf_transformation,[],[f321]) ).
thf(f340,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(cnf_transformation,[],[f205]) ).
thf(f349,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 )
= ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( hoasap @ id @ Y2 @ id @ Y1 )
!= ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f314]) ).
thf(f355,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(cnf_transformation,[],[f246]) ).
thf(f368,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 )
= ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ Y1 )
!= ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f349,f355,f340]) ).
thf(f1206,plain,
( ( lamnotap = $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f327]) ).
thf(f1207,plain,
! [X1: term] :
( ( lamnotap = $false )
| ( $true
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ Y2 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1206]) ).
thf(f1208,plain,
! [X1: term] :
( ( lamnotap = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( lam @ Y0 )
!= ( ap @ X1 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1207]) ).
thf(f1209,plain,
! [X2: term,X1: term] :
( ( lamnotap = $false )
| ( $true
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( lam @ Y0 )
!= ( ap @ X1 @ Y1 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1208]) ).
thf(f1210,plain,
! [X2: term,X1: term] :
( ( lamnotap = $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( lam @ X2 )
!= ( ap @ X1 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1209]) ).
thf(f1211,plain,
! [X2: term,X3: term,X1: term] :
( ( lamnotap = $false )
| ( ( ^ [Y0: term] :
( ( lam @ X2 )
!= ( ap @ X1 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1210]) ).
thf(f1212,plain,
! [X2: term,X3: term,X1: term] :
( ( lamnotap = $false )
| ( $true
= ( ( lam @ X2 )
!= ( ap @ X1 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f1211]) ).
thf(f1213,plain,
! [X2: term,X3: term,X1: term] :
( ( lamnotap = $false )
| ( $false
= ( ( lam @ X2 )
= ( ap @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f1212]) ).
thf(f1214,plain,
! [X2: term,X3: term,X1: term] :
( ( ( ap @ X1 @ X3 )
!= ( lam @ X2 ) )
| ( lamnotap = $false ) ),
inference(equality_proxy_clausification,[],[f1213]) ).
thf(f1362,plain,
( ( hoaslamnotap = $true )
| ( $false
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 )
= ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ Y1 )
!= ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f368]) ).
thf(f1378,plain,
( ( hoaslamnotap = $true )
| ( ( ^ [Y0: subst > term > term] :
( ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y2 @ Y1 ) @ Y3 )
= ( Y0 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y1 @ Y3 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ Y1 )
!= ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) )
@ sK183 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1362]) ).
thf(f1379,plain,
( ( hoaslamnotap = $true )
| ( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK183 @ Y1 @ Y0 ) @ Y2 )
= ( sK183 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y0 @ Y2 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
!= ( lam @ ( sK183 @ sh @ one ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f1378]) ).
thf(f1380,plain,
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
!= ( lam @ ( sK183 @ sh @ one ) ) ) ) ) )
| ( hoaslamnotap = $true ) ),
inference(imp_proxy_clausification,[],[f1379]) ).
thf(f1389,plain,
( ( hoaslamnotap = $true )
| ( $false
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
!= ( lam @ ( sK183 @ sh @ one ) ) ) )
@ sK184 ) ) ),
inference(sigma_proxy_clausification,[],[f1380]) ).
thf(f1390,plain,
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( ap @ ( sub @ Y0 @ id ) @ sK184 )
!= ( lam @ ( sK183 @ sh @ one ) ) ) ) )
| ( hoaslamnotap = $true ) ),
inference(beta-eta_normalization,[],[f1389]) ).
thf(f1391,plain,
( ( ( ^ [Y0: term] :
( ( ap @ ( sub @ Y0 @ id ) @ sK184 )
!= ( lam @ ( sK183 @ sh @ one ) ) )
@ sK185 )
= $false )
| ( hoaslamnotap = $true ) ),
inference(sigma_proxy_clausification,[],[f1390]) ).
thf(f1392,plain,
( ( hoaslamnotap = $true )
| ( $false
= ( ( ap @ ( sub @ sK185 @ id ) @ sK184 )
!= ( lam @ ( sK183 @ sh @ one ) ) ) ) ),
inference(beta-eta_normalization,[],[f1391]) ).
thf(f1393,plain,
( ( $true
= ( ( ap @ ( sub @ sK185 @ id ) @ sK184 )
= ( lam @ ( sK183 @ sh @ one ) ) ) )
| ( hoaslamnotap = $true ) ),
inference(not_proxy_clausification,[],[f1392]) ).
thf(f1394,plain,
( ( ( lam @ ( sK183 @ sh @ one ) )
= ( ap @ ( sub @ sK185 @ id ) @ sK184 ) )
| ( hoaslamnotap = $true ) ),
inference(equality_proxy_clausification,[],[f1393]) ).
thf(f1427,plain,
( ( $false
= ( lamnotap
=> hoaslamnotap ) )
| ( hoaslamnotap_lthm = $true ) ),
inference(iff_proxy_clausification,[],[f325]) ).
thf(f1430,plain,
( ( hoaslamnotap = $false )
| ( hoaslamnotap_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f1427]) ).
thf(f1431,plain,
( ( hoaslamnotap_lthm = $true )
| ( lamnotap = $true ) ),
inference(imp_proxy_clausification,[],[f1427]) ).
thf(f2567,definition,
( spl262_185
<=> ! [X2: term,X1: term,X3: term] :
( ( ap @ X1 @ X3 )
!= ( lam @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl262_185])],[avatar_definition]) ).
thf(f2568,plain,
( ! [X2: term,X3: term,X1: term] :
( ( ap @ X1 @ X3 )
!= ( lam @ X2 ) )
| ~ spl262_185 ),
inference(avatar_component_clause,[],[f2567]) ).
thf(f2570,definition,
( spl262_186
<=> ( lamnotap = $false ) ),
introduced(definition,[new_symbols(definition,[spl262_186])],[avatar_definition]) ).
thf(f2572,plain,
( ( lamnotap = $false )
| ~ spl262_186 ),
inference(avatar_component_clause,[],[f2570]) ).
thf(f2573,plain,
( spl262_185
| spl262_186 ),
inference(avatar_split_clause,[],[f1214,f2570,f2567]) ).
thf(f2579,definition,
( spl262_188
<=> ( lamnotap = $true ) ),
introduced(definition,[new_symbols(definition,[spl262_188])],[avatar_definition]) ).
thf(f2581,plain,
( ( lamnotap = $true )
| ~ spl262_188 ),
inference(avatar_component_clause,[],[f2579]) ).
thf(f2735,definition,
( spl262_225
<=> ( hoaslamnotap = $false ) ),
introduced(definition,[new_symbols(definition,[spl262_225])],[avatar_definition]) ).
thf(f2737,plain,
( ( hoaslamnotap = $false )
| ~ spl262_225 ),
inference(avatar_component_clause,[],[f2735]) ).
thf(f2746,definition,
( spl262_228
<=> ( hoaslamnotap = $true ) ),
introduced(definition,[new_symbols(definition,[spl262_228])],[avatar_definition]) ).
thf(f2748,plain,
( ( hoaslamnotap = $true )
| ~ spl262_228 ),
inference(avatar_component_clause,[],[f2746]) ).
thf(f2751,definition,
( spl262_229
<=> ( ( lam @ ( sK183 @ sh @ one ) )
= ( ap @ ( sub @ sK185 @ id ) @ sK184 ) ) ),
introduced(definition,[new_symbols(definition,[spl262_229])],[avatar_definition]) ).
thf(f2753,plain,
( ( ( lam @ ( sK183 @ sh @ one ) )
= ( ap @ ( sub @ sK185 @ id ) @ sK184 ) )
| ~ spl262_229 ),
inference(avatar_component_clause,[],[f2751]) ).
thf(f2754,plain,
( spl262_228
| spl262_229 ),
inference(avatar_split_clause,[],[f1394,f2751,f2746]) ).
thf(f2812,definition,
( spl262_243
<=> ( hoaslamnotap_lthm = $true ) ),
introduced(definition,[new_symbols(definition,[spl262_243])],[avatar_definition]) ).
thf(f2815,plain,
( spl262_188
| spl262_243 ),
inference(avatar_split_clause,[],[f1431,f2812,f2579]) ).
thf(f2816,plain,
( spl262_225
| spl262_243 ),
inference(avatar_split_clause,[],[f1430,f2812,f2735]) ).
thf(f3146,plain,
~ spl262_243,
inference(avatar_split_clause,[],[f335,f2812]) ).
thf(f3214,plain,
( ( $false = $true )
| ~ spl262_225
| ~ spl262_228 ),
inference(forward_demodulation,[],[f2748,f2737]) ).
thf(f3215,plain,
( $false
| ~ spl262_225
| ~ spl262_228 ),
inference(trivial_inequality_removal,[],[f3214]) ).
thf(f3216,plain,
( ~ spl262_225
| ~ spl262_228 ),
inference(avatar_contradiction_clause,[],[f3215]) ).
thf(f3217,plain,
( $false
| ~ spl262_185
| ~ spl262_229 ),
inference(forward_subsumption_resolution,[],[f2753,f2568]) ).
thf(f3218,plain,
( ~ spl262_185
| ~ spl262_229 ),
inference(avatar_contradiction_clause,[],[f3217]) ).
thf(f3222,plain,
( ( $false = $true )
| ~ spl262_186
| ~ spl262_188 ),
inference(superposition,[],[f2581,f2572]) ).
thf(f3226,plain,
( $false
| ~ spl262_186
| ~ spl262_188 ),
inference(trivial_inequality_removal,[],[f3222]) ).
thf(f3227,plain,
( ~ spl262_186
| ~ spl262_188 ),
inference(avatar_contradiction_clause,[],[f3226]) ).
cnf(s154,plain,
( spl262_185
| spl262_186 ),
inference(sat_conversion,[],[f2573]) ).
cnf(s184,plain,
( spl262_228
| spl262_229 ),
inference(sat_conversion,[],[f2754]) ).
cnf(s192,plain,
( spl262_188
| spl262_243 ),
inference(sat_conversion,[],[f2815]) ).
cnf(s193,plain,
( spl262_225
| spl262_243 ),
inference(sat_conversion,[],[f2816]) ).
cnf(s262,plain,
~ spl262_243,
inference(sat_conversion,[],[f3146]) ).
cnf(s269,plain,
( ~ spl262_225
| ~ spl262_228 ),
inference(sat_conversion,[],[f3216]) ).
cnf(s270,plain,
( ~ spl262_185
| ~ spl262_229 ),
inference(sat_conversion,[],[f3218]) ).
cnf(s272,plain,
( ~ spl262_186
| ~ spl262_188 ),
inference(sat_conversion,[],[f3227]) ).
cnf(s274,plain,
spl262_225,
inference(rat,[],[s193,s262]) ).
cnf(s275,plain,
~ spl262_228,
inference(rat,[],[s269,s274]) ).
cnf(s276,plain,
spl262_188,
inference(rat,[],[s192,s262]) ).
cnf(s277,plain,
~ spl262_186,
inference(rat,[],[s272,s276]) ).
cnf(s278,plain,
spl262_229,
inference(rat,[],[s184,s275]) ).
cnf(s279,plain,
~ spl262_185,
inference(rat,[],[s270,s278]) ).
cnf(s281,plain,
$false,
inference(rat,[],[s154,s277,s279]) ).
thf(f3228,plain,
$false,
inference(avatar_sat_refutation,[],[s281]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG259^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n004.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 17:34:42 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.22/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.49 % (1610630)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.47/0.49 % (1610637)lrs+10_16_si=on:nwc=1.5:random_seed=1159695551:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.47/0.49 % (1610637)Instruction limit reached!
% 0.47/0.49 % (1610637)------------------------------
% 0.47/0.49 % (1610637)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.49 % (1610637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.49 % (1610637)CaDiCaL version: 2.1.3
% 0.47/0.49 % (1610637)Termination reason: Instruction limit
% 0.47/0.49 % (1610637)Termination phase: shuffling
% 0.47/0.49 % (1610637)Time elapsed: 0.009 s
% 0.47/0.49 % (1610637)Peak memory usage: 10 MB
% 0.47/0.49 % (1610637)Instructions burned: 19 (million)
% 0.47/0.49 % (1610641)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2940274655:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.47/0.49 % (1610640)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=413438866:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.47/0.49 % (1610639)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=221265882:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.47/0.49 % (1610642)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.47/0.49 % (1610642)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.47/0.49 % (1610638)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=348451225:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.47/0.49 % (1610636)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1805419924:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.47/0.49 % (1610642)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=3304714462:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.47/0.49 % (1610638)Instruction limit reached!
% 0.47/0.49 % (1610638)------------------------------
% 0.47/0.49 % (1610638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.49 % (1610638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.49 % (1610638)CaDiCaL version: 2.1.3
% 0.47/0.49 % (1610638)Termination reason: Instruction limit
% 0.47/0.49 % (1610638)Termination phase: shuffling
% 0.47/0.49 % (1610638)Time elapsed: 0.007 s
% 0.47/0.49 % (1610638)Peak memory usage: 10 MB
% 0.47/0.49 % (1610638)Instructions burned: 5 (million)
% 0.47/0.49 % (1610644)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=784152285:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.47/0.49 % (1610644)Instruction limit reached!
% 0.47/0.49 % (1610644)------------------------------
% 0.47/0.49 % (1610644)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.49 % (1610644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.49 % (1610644)CaDiCaL version: 2.1.3
% 0.47/0.49 % (1610644)Termination reason: Instruction limit
% 0.47/0.49 % (1610644)Termination phase: shuffling
% 0.47/0.49 % (1610644)Time elapsed: 0.002 s
% 0.47/0.49 % (1610644)Peak memory usage: 10 MB
% 0.47/0.49 % (1610644)Instructions burned: 4 (million)
% 0.47/0.49 % (1610640)Instruction limit reached!
% 0.47/0.49 % (1610640)------------------------------
% 0.47/0.49 % (1610640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.47/0.49 % (1610640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.47/0.49 % (1610640)CaDiCaL version: 2.1.3
% 0.47/0.49 % (1610640)Termination reason: Instruction limit
% 0.47/0.49 % (1610640)Termination phase: Naming
% 0.47/0.49 % (1610640)Time elapsed: 0.021 s
% 0.47/0.49 % (1610640)Peak memory usage: 11 MB
% 0.47/0.49 % (1610640)Instructions burned: 24 (million)
% 0.47/0.49 % (1610651)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3575641957:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.19/0.53 % (1610651)Instruction limit reached!
% 1.19/0.53 % (1610651)------------------------------
% 1.19/0.53 % (1610651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1610651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1610651)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1610651)Termination reason: Instruction limit
% 1.19/0.53 % (1610651)Termination phase: shuffling
% 1.19/0.53 % (1610651)Time elapsed: 0.002 s
% 1.19/0.53 % (1610651)Peak memory usage: 10 MB
% 1.19/0.53 % (1610651)Instructions burned: 5 (million)
% 1.19/0.53 % (1610653)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.19/0.53 % (1610653)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1818252826:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.19/0.53 % (1610653)Instruction limit reached!
% 1.19/0.53 % (1610653)------------------------------
% 1.19/0.53 % (1610653)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1610653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1610653)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1610653)Termination reason: Instruction limit
% 1.19/0.53 % (1610653)Termination phase: shuffling
% 1.19/0.53 % (1610653)Time elapsed: 0.004 s
% 1.19/0.53 % (1610653)Peak memory usage: 10 MB
% 1.19/0.53 % (1610653)Instructions burned: 9 (million)
% 1.19/0.53 % (1610654)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1408829596:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.19/0.53 % (1610641)Instruction limit reached!
% 1.19/0.53 % (1610641)------------------------------
% 1.19/0.53 % (1610641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1610641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1610641)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1610641)Termination reason: Instruction limit
% 1.19/0.53 % (1610641)Termination phase: Property scanning
% 1.19/0.53 % (1610641)Time elapsed: 0.061 s
% 1.19/0.53 % (1610641)Peak memory usage: 12 MB
% 1.19/0.53 % (1610641)Instructions burned: 75 (million)
% 1.19/0.53 % (1610656)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
% 1.19/0.53 % (1610656)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.19/0.53 % (1610658)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=3738497304:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.19/0.53 % (1610654)Instruction limit reached!
% 1.19/0.53 % (1610654)------------------------------
% 1.19/0.53 % (1610654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1610654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1610654)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1610654)Termination reason: Instruction limit
% 1.19/0.53 % (1610654)Termination phase: shuffling
% 1.19/0.53 % (1610654)Time elapsed: 0.014 s
% 1.19/0.53 % (1610654)Peak memory usage: 10 MB
% 1.19/0.53 % (1610654)Instructions burned: 12 (million)
% 1.19/0.53 % (1610656)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1822653803:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2998 on theBenchmark for (2998ds/28Mi)
% 1.19/0.53 % (1610656)Instruction limit reached!
% 1.19/0.53 % (1610656)------------------------------
% 1.19/0.53 % (1610656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.53 % (1610656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.53 % (1610656)CaDiCaL version: 2.1.3
% 1.19/0.53 % (1610656)Termination reason: Instruction limit
% 1.19/0.53 % (1610656)Termination phase: Property scanning
% 1.19/0.53 % (1610656)Time elapsed: 0.013 s
% 1.19/0.53 % (1610656)Peak memory usage: 10 MB
% 1.19/0.53 % (1610656)Instructions burned: 30 (million)
% 1.19/0.53 % (1610661)lrs+10_1_si=on:cs=on:random_seed=605843862:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.19/0.53 % (1610661)Instruction limit reached!
% 1.19/0.57 % (1610661)------------------------------
% 1.19/0.57 % (1610661)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.57 % (1610661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.57 % (1610661)CaDiCaL version: 2.1.3
% 1.19/0.57 % (1610661)Termination reason: Instruction limit
% 1.19/0.57 % (1610661)Termination phase: shuffling
% 1.19/0.57 % (1610661)Time elapsed: 0.004 s
% 1.19/0.57 % (1610661)Peak memory usage: 10 MB
% 1.19/0.57 % (1610661)Instructions burned: 9 (million)
% 1.19/0.57 % (1610636)Instruction limit reached!
% 1.19/0.57 % (1610636)------------------------------
% 1.19/0.57 % (1610636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.57 % (1610636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.57 % (1610636)CaDiCaL version: 2.1.3
% 1.19/0.57 % (1610636)Termination reason: Instruction limit
% 1.19/0.57 % (1610636)Termination phase: Function definition elimination
% 1.19/0.57 % (1610636)Time elapsed: 0.082 s
% 1.19/0.57 % (1610636)Peak memory usage: 12 MB
% 1.19/0.57 % (1610636)Instructions burned: 89 (million)
% 1.19/0.57 % (1610662)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.19/0.57 % (1610662)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=1372969676:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.19/0.57 % (1610662)Instruction limit reached!
% 1.19/0.57 % (1610662)------------------------------
% 1.19/0.57 % (1610662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.57 % (1610662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.57 % (1610662)CaDiCaL version: 2.1.3
% 1.19/0.57 % (1610662)Termination reason: Instruction limit
% 1.19/0.57 % (1610662)Termination phase: shuffling
% 1.19/0.57 % (1610662)Time elapsed: 0.003 s
% 1.19/0.57 % (1610662)Peak memory usage: 10 MB
% 1.19/0.57 % (1610662)Instructions burned: 2 (million)
% 1.19/0.57 % (1610666)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3175675856:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.19/0.57 % (1610664)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=76836828:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.19/0.57 % (1610669)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=296824346:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.19/0.57 % (1610666)Refutation not found, incomplete strategy
% 1.19/0.57 % (1610666)------------------------------
% 1.19/0.57 % (1610666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.57 % (1610666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.57 % (1610666)CaDiCaL version: 2.1.3
% 1.19/0.57 % (1610666)Termination reason: Refutation not found, incomplete strategy
% 1.19/0.57 % (1610666)Time elapsed: 0.021 s
% 1.19/0.57 % (1610666)Peak memory usage: 12 MB
% 1.19/0.57 % (1610666)Instructions burned: 49 (million)
% 1.19/0.57 % (1610658)Instruction limit reached!
% 1.19/0.57 % (1610658)------------------------------
% 1.19/0.57 % (1610658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.57 % (1610658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.57 % (1610658)CaDiCaL version: 2.1.3
% 1.19/0.57 % (1610658)Termination reason: Instruction limit
% 1.19/0.57 % (1610658)Termination phase: Saturation
% 1.19/0.57 % (1610658)Time elapsed: 0.066 s
% 1.19/0.57 % (1610658)Peak memory usage: 11 MB
% 1.19/0.57 % (1610658)Instructions burned: 86 (million)
% 1.19/0.57 % (1610669)Instruction limit reached!
% 1.19/0.57 % (1610669)------------------------------
% 1.19/0.57 % (1610669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.19/0.57 % (1610669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.19/0.57 % (1610669)CaDiCaL version: 2.1.3
% 1.19/0.57 % (1610669)Termination reason: Instruction limit
% 1.19/0.57 % (1610669)Termination phase: shuffling
% 1.19/0.57 % (1610669)Time elapsed: 0.007 s
% 1.19/0.57 % (1610669)Peak memory usage: 10 MB
% 1.19/0.57 % (1610669)Instructions burned: 16 (million)
% 1.19/0.57 % (1610667)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3232618448:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.77/0.63 % (1610666)------------------------------
% 1.77/0.63 % (1610666)------------------------------
% 1.77/0.63 % (1610664)Refutation not found, incomplete strategy
% 1.77/0.63 % (1610664)------------------------------
% 1.77/0.63 % (1610664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.63 % (1610664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.63 % (1610664)CaDiCaL version: 2.1.3
% 1.77/0.63 % (1610664)Termination reason: Refutation not found, incomplete strategy
% 1.77/0.63 % (1610664)Time elapsed: 0.023 s
% 1.77/0.63 % (1610664)Peak memory usage: 12 MB
% 1.77/0.63 % (1610664)Instructions burned: 24 (million)
% 1.77/0.63 % (1610664)------------------------------
% 1.77/0.63 % (1610664)------------------------------
% 1.77/0.63 % (1610642)Instruction limit reached!
% 1.77/0.63 % (1610642)------------------------------
% 1.77/0.63 % (1610642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.63 % (1610642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.63 % (1610642)CaDiCaL version: 2.1.3
% 1.77/0.63 % (1610642)Termination reason: Instruction limit
% 1.77/0.63 % (1610642)Termination phase: Saturation
% 1.77/0.63 % (1610642)Time elapsed: 0.140 s
% 1.77/0.63 % (1610642)Peak memory usage: 13 MB
% 1.77/0.63 % (1610642)Instructions burned: 158 (million)
% 1.77/0.63 % (1610674)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=251807823:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/327Mi)
% 1.77/0.63 % (1610675)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2400117786:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/14Mi)
% 1.77/0.63 % (1610667)Instruction limit reached!
% 1.77/0.63 % (1610667)------------------------------
% 1.77/0.63 % (1610667)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.63 % (1610667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.63 % (1610667)CaDiCaL version: 2.1.3
% 1.77/0.63 % (1610667)Termination reason: Instruction limit
% 1.77/0.63 % (1610667)Termination phase: Preprocessing 1
% 1.77/0.63 % (1610667)Time elapsed: 0.022 s
% 1.77/0.63 % (1610667)Peak memory usage: 10 MB
% 1.77/0.63 % (1610667)Instructions burned: 25 (million)
% 1.77/0.63 % (1610677)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1595677210:i=26:ep=R:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/26Mi)
% 1.77/0.63 % (1610675)Instruction limit reached!
% 1.77/0.63 % (1610675)------------------------------
% 1.77/0.63 % (1610675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.63 % (1610675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.63 % (1610675)CaDiCaL version: 2.1.3
% 1.77/0.63 % (1610675)Termination reason: Instruction limit
% 1.77/0.63 % (1610675)Termination phase: shuffling
% 1.77/0.63 % (1610675)Time elapsed: 0.006 s
% 1.77/0.63 % (1610675)Peak memory usage: 10 MB
% 1.77/0.63 % (1610675)Instructions burned: 14 (million)
% 1.77/0.63 % (1610676)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3194833610:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2997 on theBenchmark for (2997ds/2Mi)
% 1.77/0.63 % (1610676)Instruction limit reached!
% 1.77/0.63 % (1610676)------------------------------
% 1.77/0.63 % (1610676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.63 % (1610676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.63 % (1610676)CaDiCaL version: 2.1.3
% 1.77/0.63 % (1610676)Termination reason: Instruction limit
% 1.77/0.63 % (1610676)Termination phase: shuffling
% 1.77/0.63 % (1610676)Time elapsed: 0.002 s
% 1.77/0.63 % (1610676)Peak memory usage: 10 MB
% 1.77/0.63 % (1610676)Instructions burned: 2 (million)
% 1.77/0.63 % (1610677)Instruction limit reached!
% 1.77/0.63 % (1610677)------------------------------
% 1.77/0.63 % (1610677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.63 % (1610677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.63 % (1610677)CaDiCaL version: 2.1.3
% 1.77/0.63 % (1610677)Termination reason: Instruction limit
% 1.77/0.63 % (1610677)Termination phase: Property scanning
% 1.77/0.63 % (1610677)Time elapsed: 0.014 s
% 1.77/0.63 % (1610677)Peak memory usage: 10 MB
% 1.77/0.63 % (1610677)Instructions burned: 27 (million)
% 1.77/0.63 % (1610681)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1701091754:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 1.77/0.63 % (1610683)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
% 1.77/0.63 % (1610683)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.77/0.63 % (1610680)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3264778239:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 1.77/0.63 % (1610683)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=2508718819:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 1.77/0.63 % (1610683)Instruction limit reached!
% 1.77/0.63 % (1610683)------------------------------
% 1.77/0.63 % (1610683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.63 % (1610683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.63 % (1610683)CaDiCaL version: 2.1.3
% 1.77/0.63 % (1610683)Termination reason: Instruction limit
% 1.77/0.63 % (1610683)Termination phase: shuffling
% 1.77/0.63 % (1610683)Time elapsed: 0.007 s
% 1.77/0.63 % (1610683)Peak memory usage: 10 MB
% 1.77/0.63 % (1610683)Instructions burned: 14 (million)
% 1.77/0.63 % (1610686)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=3046051649:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 1.77/0.63 % (1610680)Instruction limit reached!
% 1.77/0.63 % (1610680)------------------------------
% 1.77/0.63 % (1610680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.63 % (1610680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.63 % (1610680)CaDiCaL version: 2.1.3
% 1.77/0.63 % (1610681)Instruction limit reached!
% 1.77/0.63 % (1610681)------------------------------
% 1.77/0.63 % (1610681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.63 % (1610680)Termination reason: Instruction limit
% 1.77/0.63 % (1610680)Termination phase: Property scanning
% 1.77/0.63 % (1610680)Time elapsed: 0.022 s
% 1.77/0.63 % (1610680)Peak memory usage: 10 MB
% 1.77/0.63 % (1610680)Instructions burned: 23 (million)
% 1.77/0.63 % (1610681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.63 % (1610681)CaDiCaL version: 2.1.3
% 1.77/0.63 % (1610681)Termination reason: Instruction limit
% 1.77/0.63 % (1610681)Termination phase: Property scanning
% 1.77/0.63 % (1610681)Time elapsed: 0.028 s
% 1.77/0.63 % (1610681)Peak memory usage: 12 MB
% 1.77/0.63 % (1610681)Instructions burned: 60 (million)
% 1.77/0.63 % (1610685)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.77/0.63 % (1610690)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3449052199:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 1.77/0.63 % (1610685)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=3075482071:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 1.77/0.63 % (1610685)Instruction limit reached!
% 1.77/0.63 % (1610685)------------------------------
% 1.77/0.63 % (1610685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.63 % (1610685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.63 % (1610685)CaDiCaL version: 2.1.3
% 1.77/0.63 % (1610685)Termination reason: Instruction limit
% 1.77/0.63 % (1610685)Termination phase: shuffling
% 1.77/0.63 % (1610685)Time elapsed: 0.004 s
% 1.77/0.63 % (1610685)Peak memory usage: 10 MB
% 1.77/0.63 % (1610685)Instructions burned: 8 (million)
% 1.77/0.63 % (1610690)Instruction limit reached!
% 1.77/0.63 % (1610690)------------------------------
% 1.77/0.63 % (1610690)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.63 % (1610690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.63 % (1610690)CaDiCaL version: 2.1.3
% 1.77/0.63 % (1610690)Termination reason: Instruction limit
% 1.77/0.63 % (1610690)Termination phase: shuffling
% 1.77/0.63 % (1610690)Time elapsed: 0.007 s
% 1.77/0.63 % (1610690)Peak memory usage: 10 MB
% 1.77/0.63 % (1610690)Instructions burned: 7 (million)
% 1.77/0.63 % (1610686)Instruction limit reached!
% 1.77/0.63 % (1610686)------------------------------
% 1.77/0.63 % (1610686)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.63 % (1610686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.63 % (1610686)CaDiCaL version: 2.1.3
% 1.77/0.63 % (1610686)Termination reason: Instruction limit
% 1.77/0.63 % (1610686)Termination phase: Property scanning
% 1.77/0.63 % (1610686)Time elapsed: 0.026 s
% 1.77/0.63 % (1610686)Peak memory usage: 10 MB
% 1.77/0.63 % (1610686)Instructions burned: 32 (million)
% 1.77/0.63 % (1610693)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=862163459:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 1.77/0.63 % (1610693)Instruction limit reached!
% 1.77/0.63 % (1610693)------------------------------
% 1.77/0.63 % (1610693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.63 % (1610693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.63 % (1610693)CaDiCaL version: 2.1.3
% 1.77/0.63 % (1610693)Termination reason: Instruction limit
% 1.77/0.63 % (1610693)Termination phase: Property scanning
% 1.77/0.63 % (1610693)Time elapsed: 0.010 s
% 1.77/0.63 % (1610693)Peak memory usage: 10 MB
% 1.77/0.63 % (1610693)Instructions burned: 22 (million)
% 1.77/0.63 % (1610696)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1737725051:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 1.77/0.63 % (1610692)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3723945153:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 1.77/0.63 % (1610699)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1814318142:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.77/0.63 % (1610700)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2582035075:i=42:hud=10:rtra=on_2996 on theBenchmark for (2996ds/42Mi)
% 1.77/0.63 % (1610697)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1803850111:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.77/0.63 % (1610674) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1610630-1610674"...
% 1.77/0.63 % (1610692)Instruction limit reached!
% 1.77/0.63 % (1610692)------------------------------
% 1.77/0.63 % (1610692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.63 % (1610692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.63 % (1610692)CaDiCaL version: 2.1.3
% 1.77/0.63 % (1610692)Termination reason: Instruction limit
% 1.77/0.63 % (1610692)Termination phase: Property scanning
% 1.77/0.63 % (1610692)Time elapsed: 0.021 s
% 1.77/0.63 % (1610692)Peak memory usage: 10 MB
% 1.77/0.63 % (1610692)Instructions burned: 25 (million)
% 1.77/0.63 % (1610674)...printing done.
% 1.77/0.63 % (1610674)Refutation found. Thanks to Tanya!
% 1.77/0.63 % SZS status Theorem for theBenchmark
% 1.77/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 1.77/0.63 % (1610674)------------------------------
% 1.77/0.63 % (1610674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.63 % (1610674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.63 % (1610674)CaDiCaL version: 2.1.3
% 1.77/0.63 % (1610674)Termination reason: Refutation
% 1.77/0.63 % (1610674)Time elapsed: 0.119 s
% 1.77/0.63 % (1610674)Peak memory usage: 15 MB
% 1.77/0.63 % (1610674)Instructions burned: 183 (million)
% 1.77/0.63 % (1610630)Success in time 0.347 s
% 1.77/0.63 % Vampire exiting
%------------------------------------------------------------------------------