%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG260^1 : 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 : n012.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 0.41s 0.31s
% Output : Refutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 17
% Syntax : Number of formulae : 137 ( 39 unt; 0 typ; 10 def)
% Number of atoms : 1216 ( 159 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 1171 ( 74 ~; 99 |; 0 &; 296 @)
% ( 10 <=>; 664 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 448 ( 444 usr; 195 con; 0-4 aty)
% ( 28 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 96 ( 12 sgn 21 !; 0 ?; 96 :)
% 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,
vIMP: $o > $o > $o ).
thf(func_def_125,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_127,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_130,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_131,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
vNOT: $o > $o ).
thf(func_def_133,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_134,type,
vAND: $o > $o > $o ).
thf(func_def_135,type,
vIFF: $o > $o > $o ).
thf(func_def_138,type,
sK0: ( subst > term > term ) > term ).
thf(func_def_139,type,
sK1: ( subst > term > term ) > subst ).
thf(func_def_140,type,
sK2: ( subst > term > term ) > subst ).
thf(func_def_141,type,
sK3: subst > term > term ).
thf(func_def_142,type,
sK4: term ).
thf(func_def_143,type,
sK5: term ).
thf(func_def_144,type,
sK6: term ).
thf(func_def_145,type,
sK7: term ).
thf(func_def_146,type,
sK8: term ).
thf(func_def_147,type,
sK9: subst ).
thf(func_def_148,type,
sK10: subst ).
thf(func_def_149,type,
sK11: subst ).
thf(func_def_150,type,
sK12: ( term > $o ) > term ).
thf(func_def_151,type,
sK13: ( term > $o ) > term ).
thf(func_def_152,type,
sK14: ( term > $o ) > term ).
thf(func_def_153,type,
sK15: ( term > $o ) > term ).
thf(func_def_154,type,
sK16: ( term > $o ) > term ).
thf(func_def_155,type,
sK17: ( term > $o ) > term ).
thf(func_def_156,type,
sK18: term > $o ).
thf(func_def_157,type,
sK19: term > term ).
thf(func_def_158,type,
sK20: term ).
thf(func_def_159,type,
sK21: term ).
thf(func_def_160,type,
sK22: ( subst > term > subst > $o ) > subst ).
thf(func_def_161,type,
sK23: ( subst > term > subst > $o ) > term ).
thf(func_def_162,type,
sK24: ( subst > term > subst > $o ) > term ).
thf(func_def_163,type,
sK25: ( subst > term > subst > $o ) > term ).
thf(func_def_164,type,
sK26: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_165,type,
sK27: ( subst > term > subst > $o ) > term ).
thf(func_def_166,type,
sK28: ( subst > term > subst > $o ) > subst ).
thf(func_def_167,type,
sK29: ( subst > term > subst > $o ) > subst ).
thf(func_def_168,type,
sK30: ( subst > term > subst > $o ) > subst ).
thf(func_def_169,type,
sK31: ( subst > term > subst > $o ) > subst ).
thf(func_def_170,type,
sK32: ( subst > term > subst > $o ) > term ).
thf(func_def_171,type,
sK33: ( subst > term > subst > $o ) > subst ).
thf(func_def_172,type,
sK34: ( subst > term > subst > $o ) > subst ).
thf(func_def_173,type,
sK35: ( subst > term > subst > $o ) > subst ).
thf(func_def_174,type,
sK36: ( subst > term > subst > $o ) > term ).
thf(func_def_175,type,
sK37: ( subst > term > subst > $o ) > subst ).
thf(func_def_176,type,
sK38: ( subst > term > subst > $o ) > subst ).
thf(func_def_177,type,
sK39: ( subst > term > subst > $o ) > subst ).
thf(func_def_178,type,
sK40: ( subst > term > subst > $o ) > term ).
thf(func_def_179,type,
sK41: ( subst > term > subst > $o ) > subst ).
thf(func_def_180,type,
sK42: ( subst > term > subst > $o ) > subst ).
thf(func_def_181,type,
sK43: ( subst > term > subst > $o ) > subst ).
thf(func_def_182,type,
sK44: ( subst > term > subst > $o ) > term ).
thf(func_def_183,type,
sK45: ( subst > term > subst > $o ) > subst ).
thf(func_def_184,type,
sK46: ( subst > term > subst > $o ) > subst ).
thf(func_def_185,type,
sK47: ( subst > term > subst > $o ) > subst ).
thf(func_def_186,type,
sK48: ( subst > term > subst > $o ) > subst ).
thf(func_def_187,type,
sK49: ( subst > term > subst > $o ) > term ).
thf(func_def_188,type,
sK50: ( subst > term > subst > $o ) > subst ).
thf(func_def_189,type,
sK51: ( subst > term > subst > $o ) > term ).
thf(func_def_190,type,
sK52: ( subst > term > subst > $o ) > subst ).
thf(func_def_191,type,
sK53: ( subst > term > subst > $o ) > subst ).
thf(func_def_192,type,
sK54: ( subst > term > subst > $o ) > term ).
thf(func_def_193,type,
sK55: ( subst > term > subst > $o ) > subst ).
thf(func_def_194,type,
sK56: ( subst > term > subst > $o ) > subst ).
thf(func_def_195,type,
sK57: ( subst > term > subst > $o ) > subst ).
thf(func_def_196,type,
sK58: ( subst > term > subst > $o ) > subst ).
thf(func_def_197,type,
sK59: ( subst > term > subst > $o ) > term ).
thf(func_def_198,type,
sK60: ( subst > term > subst > $o ) > subst ).
thf(func_def_199,type,
sK61: ( subst > term > subst > $o ) > subst ).
thf(func_def_200,type,
sK62: ( subst > term > subst > $o ) > subst ).
thf(func_def_201,type,
sK63: ( subst > term > subst > $o ) > term ).
thf(func_def_202,type,
sK64: ( subst > term > subst > $o ) > subst ).
thf(func_def_203,type,
sK65: ( subst > term > subst > $o ) > subst ).
thf(func_def_204,type,
sK66: ( subst > term > subst > $o ) > subst ).
thf(func_def_205,type,
sK67: ( subst > term > subst > $o ) > subst ).
thf(func_def_206,type,
sK68: ( subst > term > subst > $o ) > term ).
thf(func_def_207,type,
sK69: ( subst > term > subst > $o ) > subst ).
thf(func_def_208,type,
sK70: ( subst > term > subst > $o ) > subst ).
thf(func_def_209,type,
sK71: ( subst > term > subst > $o ) > subst ).
thf(func_def_210,type,
sK72: ( subst > term > subst > $o ) > term ).
thf(func_def_211,type,
sK73: ( subst > term > subst > $o ) > subst ).
thf(func_def_212,type,
sK74: ( subst > term > subst > $o ) > term ).
thf(func_def_213,type,
sK75: ( subst > term > subst > $o ) > subst ).
thf(func_def_214,type,
sK76: ( subst > term > subst > $o ) > subst ).
thf(func_def_215,type,
sK77: ( subst > term > subst > $o ) > subst ).
thf(func_def_216,type,
sK78: ( subst > term > subst > $o ) > subst ).
thf(func_def_217,type,
sK79: ( subst > term > subst > $o ) > term ).
thf(func_def_218,type,
sK80: ( subst > term > subst > $o ) > subst ).
thf(func_def_219,type,
sK81: ( subst > term > subst > $o ) > subst ).
thf(func_def_220,type,
sK82: ( subst > term > subst > $o ) > term ).
thf(func_def_221,type,
sK83: ( subst > term > subst > $o ) > subst ).
thf(func_def_222,type,
sK84: ( subst > term > subst > $o ) > term ).
thf(func_def_223,type,
sK85: ( subst > term > subst > $o ) > subst ).
thf(func_def_224,type,
sK86: ( subst > term > subst > $o ) > subst ).
thf(func_def_225,type,
sK87: ( subst > term > subst > $o ) > subst ).
thf(func_def_226,type,
sK88: ( subst > term > subst > $o ) > term ).
thf(func_def_227,type,
sK89: ( subst > term > subst > $o ) > subst ).
thf(func_def_228,type,
sK90: ( subst > term > subst > $o ) > subst ).
thf(func_def_229,type,
sK91: ( subst > term > subst > $o ) > subst ).
thf(func_def_230,type,
sK92: ( subst > term > subst > $o ) > term ).
thf(func_def_231,type,
sK93: ( subst > term > subst > $o ) > term ).
thf(func_def_232,type,
sK94: ( subst > term > subst > $o ) > subst ).
thf(func_def_233,type,
sK95: subst > term > subst > $o ).
thf(func_def_234,type,
sK96: ( subst > term > term ) > term ).
thf(func_def_235,type,
sK97: ( subst > term > term ) > subst ).
thf(func_def_236,type,
sK98: ( subst > term > term ) > subst ).
thf(func_def_237,type,
sK99: ( subst > term > term ) > term ).
thf(func_def_238,type,
sK100: ( subst > term > term ) > subst ).
thf(func_def_239,type,
sK101: ( subst > term > term ) > term ).
thf(func_def_240,type,
sK102: term ).
thf(func_def_241,type,
sK103: ( subst > term > subst > $o ) > subst ).
thf(func_def_242,type,
sK104: ( subst > term > subst > $o ) > subst ).
thf(func_def_243,type,
sK105: ( subst > term > subst > $o ) > term ).
thf(func_def_244,type,
sK106: ( subst > term > subst > $o ) > subst ).
thf(func_def_245,type,
sK107: ( subst > term > subst > $o ) > term ).
thf(func_def_246,type,
sK108: ( subst > term > subst > $o ) > term ).
thf(func_def_247,type,
sK109: ( subst > term > subst > $o ) > subst ).
thf(func_def_248,type,
sK110: ( subst > term > subst > $o ) > subst ).
thf(func_def_249,type,
sK111: ( subst > term > subst > $o ) > subst ).
thf(func_def_250,type,
sK112: ( subst > term > subst > $o ) > term ).
thf(func_def_251,type,
sK113: ( subst > term > subst > $o ) > term ).
thf(func_def_252,type,
sK114: ( subst > term > subst > $o ) > subst ).
thf(func_def_253,type,
sK115: ( subst > term > subst > $o ) > subst ).
thf(func_def_254,type,
sK116: ( subst > term > subst > $o ) > subst ).
thf(func_def_255,type,
sK117: term > $o ).
thf(func_def_256,type,
sK118: subst > term > subst > $o ).
thf(func_def_257,type,
sK119: term ).
thf(func_def_258,type,
sK120: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_259,type,
sK121: term > ( term > $o ) > term ).
thf(func_def_260,type,
sK122: subst > term > subst > $o ).
thf(func_def_261,type,
sK123: term > $o ).
thf(func_def_262,type,
sK124: ( subst > term > term ) > subst ).
thf(func_def_263,type,
sK125: ( subst > term > term ) > term ).
thf(func_def_264,type,
sK126: ( subst > term > term ) > term ).
thf(func_def_265,type,
sK127: ( subst > term > term ) > subst ).
thf(func_def_266,type,
sK128: ( subst > term > term ) > subst ).
thf(func_def_267,type,
sK129: term ).
thf(func_def_268,type,
sK130: term ).
thf(func_def_269,type,
sK131: subst ).
thf(func_def_270,type,
sK132: term ).
thf(func_def_271,type,
sK133: ( subst > term > subst > $o ) > subst ).
thf(func_def_272,type,
sK134: ( subst > term > subst > $o ) > subst ).
thf(func_def_273,type,
sK135: ( subst > term > subst > $o ) > term ).
thf(func_def_274,type,
sK136: ( subst > term > subst > $o ) > subst ).
thf(func_def_275,type,
sK137: ( subst > term > subst > $o ) > term ).
thf(func_def_276,type,
sK138: ( subst > term > subst > $o ) > subst ).
thf(func_def_277,type,
sK139: ( subst > term > subst > $o ) > subst ).
thf(func_def_278,type,
sK140: ( subst > term > subst > $o ) > term ).
thf(func_def_279,type,
sK141: ( subst > term > subst > $o ) > subst ).
thf(func_def_280,type,
sK142: ( subst > term > subst > $o ) > term ).
thf(func_def_281,type,
sK143: ( subst > term > subst > $o ) > subst ).
thf(func_def_282,type,
sK144: ( subst > term > subst > $o ) > term ).
thf(func_def_283,type,
sK145: ( subst > term > subst > $o ) > term ).
thf(func_def_284,type,
sK146: ( subst > term > subst > $o ) > subst ).
thf(func_def_285,type,
sK147: subst > term > subst > $o ).
thf(func_def_286,type,
sK148: term ).
thf(func_def_287,type,
sK149: term ).
thf(func_def_288,type,
sK150: subst ).
thf(func_def_289,type,
sK151: term ).
thf(func_def_290,type,
sK152: ( subst > term > term ) > subst ).
thf(func_def_291,type,
sK153: ( subst > term > term ) > term ).
thf(func_def_292,type,
sK154: ( subst > term > term ) > subst ).
thf(func_def_293,type,
sK155: subst > term > term ).
thf(func_def_294,type,
sK156: term ).
thf(func_def_295,type,
sK157: term ).
thf(func_def_296,type,
sK158: term ).
thf(func_def_297,type,
sK159: term ).
thf(func_def_298,type,
sK160: ( subst > term > subst > $o ) > subst ).
thf(func_def_299,type,
sK161: ( subst > term > subst > $o ) > subst ).
thf(func_def_300,type,
sK162: ( subst > term > subst > $o ) > term ).
thf(func_def_301,type,
sK163: ( subst > term > subst > $o ) > term ).
thf(func_def_302,type,
sK164: ( subst > term > subst > $o ) > subst ).
thf(func_def_303,type,
sK165: ( subst > term > subst > $o ) > subst ).
thf(func_def_304,type,
sK166: ( subst > term > subst > $o ) > subst ).
thf(func_def_305,type,
sK167: ( subst > term > subst > $o ) > subst ).
thf(func_def_306,type,
sK168: ( subst > term > subst > $o ) > term ).
thf(func_def_307,type,
sK169: ( subst > term > subst > $o ) > subst ).
thf(func_def_308,type,
sK170: ( subst > term > subst > $o ) > subst ).
thf(func_def_309,type,
sK171: ( subst > term > subst > $o ) > subst ).
thf(func_def_310,type,
sK172: ( subst > term > subst > $o ) > subst ).
thf(func_def_311,type,
sK173: ( subst > term > subst > $o ) > term ).
thf(func_def_312,type,
sK174: subst > term > subst > $o ).
thf(func_def_313,type,
sK175: term ).
thf(func_def_314,type,
sK176: term ).
thf(func_def_315,type,
sK177: subst ).
thf(func_def_316,type,
sK178: subst ).
thf(func_def_317,type,
sK179: ( term > $o ) > term ).
thf(func_def_318,type,
sK180: term > $o ).
thf(func_def_319,type,
sK181: term ).
thf(func_def_320,type,
sK182: term ).
thf(func_def_321,type,
sK183: term ).
thf(func_def_322,type,
sK184: term ).
thf(func_def_323,type,
sK185: ( term > $o ) > subst > term ).
thf(func_def_324,type,
sK186: subst ).
thf(func_def_325,type,
sK187: term ).
thf(func_def_326,type,
sK188: term > $o ).
thf(func_def_327,type,
sK189: term ).
thf(func_def_328,type,
sK190: term ).
thf(func_def_329,type,
sK191: term ).
thf(func_def_330,type,
sK192: subst ).
thf(func_def_331,type,
sK193: subst ).
thf(func_def_332,type,
sK194: term ).
thf(func_def_333,type,
sK195: term ).
thf(func_def_334,type,
sK196: term ).
thf(func_def_335,type,
sK197: term ).
thf(func_def_336,type,
sK198: ( term > $o ) > term ).
thf(func_def_337,type,
sK199: ( term > $o ) > term ).
thf(func_def_338,type,
sK200: ( term > $o ) > term ).
thf(func_def_339,type,
sK201: ( term > $o ) > term ).
thf(func_def_340,type,
sK202: term > $o ).
thf(func_def_341,type,
sK203: term ).
thf(func_def_342,type,
sK204: term ).
thf(func_def_343,type,
sK205: term ).
thf(func_def_344,type,
sK206: term ).
thf(func_def_345,type,
sK207: term ).
thf(func_def_346,type,
sK208: term ).
thf(func_def_347,type,
sK209: term ).
thf(func_def_348,type,
sK210: term ).
thf(func_def_349,type,
sK211: term ).
thf(func_def_350,type,
sK212: term ).
thf(func_def_351,type,
sK213: term ).
thf(func_def_352,type,
sK214: term ).
thf(func_def_353,type,
sK215: term ).
thf(func_def_354,type,
sK216: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_355,type,
sK217: ( subst > term > subst > $o ) > term > term ).
thf(func_def_356,type,
sK218: ( subst > term > subst > $o ) > term > term ).
thf(func_def_357,type,
sK219: subst > term > subst > $o ).
thf(func_def_358,type,
sK220: ( subst > term > term ) > term ).
thf(func_def_359,type,
sK221: ( subst > term > term ) > subst ).
thf(func_def_360,type,
sK222: ( subst > term > term ) > subst ).
thf(func_def_361,type,
sK223: ( subst > term > term ) > term ).
thf(func_def_362,type,
sK224: ( subst > term > term ) > subst ).
thf(func_def_363,type,
sK225: ( subst > term > term ) > term ).
thf(func_def_364,type,
sK226: term ).
thf(func_def_365,type,
sK227: subst ).
thf(func_def_366,type,
sK228: term ).
thf(func_def_367,type,
sK229: subst ).
thf(func_def_368,type,
sK230: subst ).
thf(func_def_369,type,
sK231: term ).
thf(func_def_370,type,
sK232: subst ).
thf(func_def_371,type,
sK233: term ).
thf(func_def_372,type,
sK234: term ).
thf(func_def_373,type,
sK235: subst ).
thf(func_def_374,type,
sK236: ( subst > term > term ) > term ).
thf(func_def_375,type,
sK237: ( subst > term > term ) > subst ).
thf(func_def_376,type,
sK238: ( subst > term > term ) > subst ).
thf(func_def_377,type,
sK239: ( subst > term > term ) > term ).
thf(func_def_378,type,
sK240: ( subst > term > term ) > subst ).
thf(func_def_379,type,
sK241: ( subst > term > term ) > subst ).
thf(func_def_380,type,
sK242: subst > term > term ).
thf(func_def_381,type,
sK243: subst > term > term ).
thf(func_def_382,type,
sK244: subst ).
thf(func_def_383,type,
sK245: term ).
thf(func_def_384,type,
sK246: ( term > $o ) > term ).
thf(func_def_385,type,
sK247: ( term > $o ) > term ).
thf(func_def_386,type,
sK248: ( term > $o ) > term ).
thf(func_def_387,type,
sK249: ( term > $o ) > subst > term ).
thf(func_def_388,type,
sK250: ( term > $o ) > subst > term ).
thf(func_def_389,type,
sK251: ( term > $o ) > subst > term ).
thf(func_def_390,type,
sK252: ( term > $o ) > term ).
thf(func_def_391,type,
sK253: ( term > $o ) > subst > term ).
thf(func_def_392,type,
sK254: term > $o ).
thf(func_def_393,type,
sK255: term > term ).
thf(func_def_394,type,
sK256: subst ).
thf(func_def_395,type,
sK257: term ).
thf(func_def_396,type,
sK258: ( subst > term > subst > $o ) > subst ).
thf(func_def_397,type,
sK259: ( subst > term > subst > $o ) > subst ).
thf(func_def_398,type,
sK260: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_399,type,
sK261: ( subst > term > subst > $o ) > subst ).
thf(func_def_400,type,
sK262: ( subst > term > subst > $o ) > subst ).
thf(func_def_401,type,
sK263: ( subst > term > subst > $o ) > term > term ).
thf(func_def_402,type,
sK264: ( subst > term > subst > $o ) > term ).
thf(func_def_403,type,
sK265: ( subst > term > subst > $o ) > subst ).
thf(func_def_404,type,
sK266: ( subst > term > subst > $o ) > subst ).
thf(func_def_405,type,
sK267: ( subst > term > subst > $o ) > term ).
thf(func_def_406,type,
sK268: ( subst > term > subst > $o ) > subst ).
thf(func_def_407,type,
sK269: ( subst > term > subst > $o ) > term ).
thf(func_def_408,type,
sK270: ( subst > term > subst > $o ) > subst ).
thf(func_def_409,type,
sK271: ( subst > term > subst > $o ) > subst ).
thf(func_def_410,type,
sK272: ( subst > term > subst > $o ) > term > term ).
thf(func_def_411,type,
sK273: ( subst > term > subst > $o ) > subst ).
thf(func_def_412,type,
sK274: ( subst > term > subst > $o ) > term ).
thf(func_def_413,type,
sK275: ( subst > term > subst > $o ) > subst ).
thf(func_def_414,type,
sK276: ( subst > term > subst > $o ) > term ).
thf(func_def_415,type,
sK277: ( subst > term > subst > $o ) > subst ).
thf(func_def_416,type,
sK278: ( subst > term > subst > $o ) > subst ).
thf(func_def_417,type,
sK279: ( subst > term > subst > $o ) > term ).
thf(func_def_418,type,
sK280: ( subst > term > subst > $o ) > subst ).
thf(func_def_419,type,
sK281: ( subst > term > subst > $o ) > term > term ).
thf(func_def_420,type,
sK282: ( subst > term > subst > $o ) > subst ).
thf(func_def_421,type,
sK283: ( subst > term > subst > $o ) > subst ).
thf(func_def_422,type,
sK284: ( subst > term > subst > $o ) > subst ).
thf(func_def_423,type,
sK285: ( subst > term > subst > $o ) > term ).
thf(func_def_424,type,
sK286: ( subst > term > subst > $o ) > subst ).
thf(func_def_425,type,
sK287: ( subst > term > subst > $o ) > term ).
thf(func_def_426,type,
sK288: ( subst > term > subst > $o ) > term ).
thf(func_def_427,type,
sK289: ( subst > term > subst > $o ) > subst ).
thf(func_def_428,type,
sK290: subst > term > subst > $o ).
thf(func_def_429,type,
sK291: ( subst > term > term ) > term ).
thf(func_def_430,type,
sK292: ( subst > term > term ) > term ).
thf(func_def_431,type,
sK293: ( subst > term > term ) > subst ).
thf(func_def_432,type,
sK294: ( subst > term > term ) > subst ).
thf(func_def_433,type,
sK295: ( subst > term > term ) > subst ).
thf(func_def_434,type,
sK296: ( subst > term > term ) > subst ).
thf(func_def_435,type,
sK297: term ).
thf(f3,axiom,
( axvarid
= ( ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axvarid) ).
thf(f22,axiom,
( lamnotvar
= ( ! [X0: term] :
~ ( var @ ( lam @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',lamnotvar) ).
thf(f56,axiom,
( hoaslam
= ( ^ [X0: subst,X1: subst > term > term] : ( lam @ ( X1 @ sh @ one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslam) ).
thf(f57,axiom,
( ( ^ [X0: subst,X1: term,X2: subst] : ( var @ ( sub @ X1 @ X2 ) ) )
= hoasvar ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasvar) ).
thf(f70,axiom,
( hoaslamnotvar
= ( ! [X0: subst > term > term] :
( ! [X1: subst,X2: term,X3: subst] :
( ( sub @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [X1: subst,X2: term] : ( X0 @ X1 @ X2 ) )
@ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslamnotvar) ).
thf(f71,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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= hoaslamnotvar_gthm ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslamnotvar_gthm) ).
thf(f114,conjecture,
hoaslamnotvar_gthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ hoaslamnotvar_gthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f122,plain,
( hoaslamnotvar
= ( ! [X0: subst > term > term] :
( ! [X1: subst,X2: term,X3: subst] :
( ( sub @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [X4: subst,X5: term] : ( X0 @ X4 @ X5 ) )
@ id ) ) ) ),
inference(rectify,[],[f70]) ).
thf(f123,plain,
( hoaslamnotvar
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) ) ),
inference(fool_elimination,[],[f122]) ).
thf(f136,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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= hoaslamnotvar_gthm ) ),
inference(rectify,[],[f71]) ).
thf(f137,plain,
( hoaslamnotvar_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f136]) ).
thf(f213,plain,
~ hoaslamnotvar_gthm,
inference(rectify,[],[f115]) ).
thf(f214,plain,
hoaslamnotvar_gthm != $true,
inference(fool_elimination,[],[f213]) ).
thf(f222,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f251,plain,
( lamnotvar
= ( ! [X0: term] :
~ ( var @ ( lam @ X0 ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f252,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(fool_elimination,[],[f251]) ).
thf(f287,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f308,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f318,plain,
hoaslamnotvar_gthm != $true,
inference(flattening,[],[f214]) ).
thf(f323,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f222]) ).
thf(f327,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f308]) ).
thf(f338,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(cnf_transformation,[],[f287]) ).
thf(f339,plain,
hoaslamnotvar_gthm != $true,
inference(cnf_transformation,[],[f318]) ).
thf(f343,plain,
( hoaslamnotvar_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f137]) ).
thf(f345,plain,
( hoaslamnotvar
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ~ ( hoasvar @ id
@ ( hoaslam @ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) ) ),
inference(cnf_transformation,[],[f123]) ).
thf(f360,plain,
( lamnotvar
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f372,plain,
( hoaslamnotvar
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ~ ( ^ [Y1: subst,Y2: term,Y3: subst] : ( var @ ( sub @ Y2 @ Y3 ) )
@ id
@ ( ^ [Y1: subst,Y2: subst > term > term] : ( lam @ ( Y2 @ sh @ one ) )
@ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) ) ),
inference(definition_unfolding,[],[f345,f327,f338]) ).
thf(f516,plain,
( ( lamnotvar = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) ) ) ) ),
inference(iff_proxy_clausification,[],[f360]) ).
thf(f517,plain,
! [X1: term] :
( ( ( ^ [Y0: term] :
~ ( var @ ( lam @ Y0 ) )
@ X1 )
= $true )
| ( lamnotvar = $false ) ),
inference(pi_proxy_clausification,[],[f516]) ).
thf(f518,plain,
! [X1: term] :
( ( $true
= ( ~ ( var @ ( lam @ X1 ) ) ) )
| ( lamnotvar = $false ) ),
inference(beta-eta_normalization,[],[f517]) ).
thf(f519,plain,
! [X1: term] :
( ( ( var @ ( lam @ X1 ) )
= $false )
| ( lamnotvar = $false ) ),
inference(not_proxy_clausification,[],[f518]) ).
thf(f1171,plain,
( ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ~ ( ^ [Y1: subst,Y2: term,Y3: subst] : ( var @ ( sub @ Y2 @ Y3 ) )
@ id
@ ( ^ [Y1: subst,Y2: subst > term > term] : ( lam @ ( Y2 @ sh @ one ) )
@ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) ) )
= $false )
| ( hoaslamnotvar = $true ) ),
inference(iff_proxy_clausification,[],[f372]) ).
thf(f1184,plain,
( ( hoaslamnotvar = $true )
| ( ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ~ ( ^ [Y1: subst,Y2: term,Y3: subst] : ( var @ ( sub @ Y2 @ Y3 ) )
@ id
@ ( ^ [Y1: subst,Y2: subst > term > term] : ( lam @ ( Y2 @ sh @ one ) )
@ id
@ ^ [Y1: subst,Y2: term] : ( Y0 @ Y1 @ Y2 ) )
@ id ) )
@ sK155 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1171]) ).
thf(f1185,plain,
( ( hoaslamnotvar = $true )
| ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK155 @ Y2 @ Y1 ) @ Y0 )
= ( sK155 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) )
=> ~ ( var @ ( sub @ ( lam @ ( sK155 @ sh @ one ) ) @ id ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f1184]) ).
thf(f1186,plain,
( ( ( ~ ( var @ ( sub @ ( lam @ ( sK155 @ sh @ one ) ) @ id ) ) )
= $false )
| ( hoaslamnotvar = $true ) ),
inference(imp_proxy_clausification,[],[f1185]) ).
thf(f1195,plain,
( ( hoaslamnotvar = $true )
| ( ( var @ ( sub @ ( lam @ ( sK155 @ sh @ one ) ) @ id ) )
= $true ) ),
inference(not_proxy_clausification,[],[f1186]) ).
thf(f1314,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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(iff_proxy_clausification,[],[f343]) ).
thf(f1348,plain,
( ( hoaslamnotvar_gthm = $true )
| ( $false
= ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1314]) ).
thf(f1350,plain,
( ( hoaslamnotvar_gthm = $true )
| ( ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1348]) ).
thf(f1352,plain,
( ( ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1350]) ).
thf(f1353,plain,
( ( axvarid = $true )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1350]) ).
thf(f1354,plain,
( ( hoaslamnotvar_gthm = $true )
| ( ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1352]) ).
thf(f1356,plain,
( ( ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1354]) ).
thf(f1358,plain,
( ( hoaslamnotvar_gthm = $true )
| ( ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1356]) ).
thf(f1360,plain,
( ( hoaslamnotvar_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1358]) ).
thf(f1362,plain,
( ( ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1360]) ).
thf(f1364,plain,
( ( hoaslamnotvar_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1362]) ).
thf(f1366,plain,
( ( ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1364]) ).
thf(f1368,plain,
( ( ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1366]) ).
thf(f1370,plain,
( ( hoaslamnotvar_gthm = $true )
| ( ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1368]) ).
thf(f1372,plain,
( ( ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1370]) ).
thf(f1374,plain,
( ( ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1372]) ).
thf(f1376,plain,
( ( ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1374]) ).
thf(f1378,plain,
( ( ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1376]) ).
thf(f1380,plain,
( ( hoaslamnotvar_gthm = $true )
| ( ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1378]) ).
thf(f1382,plain,
( ( hoaslamnotvar_gthm = $true )
| ( ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1380]) ).
thf(f1384,plain,
( ( ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1382]) ).
thf(f1386,plain,
( ( ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1384]) ).
thf(f1388,plain,
( ( ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1386]) ).
thf(f1390,plain,
( ( ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1388]) ).
thf(f1391,plain,
( ( lamnotvar = $true )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1388]) ).
thf(f1392,plain,
( ( hoaslamnotvar_gthm = $true )
| ( ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1390]) ).
thf(f1394,plain,
( ( ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1392]) ).
thf(f1396,plain,
( ( hoaslamnotvar_gthm = $true )
| ( ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1394]) ).
thf(f1398,plain,
( ( ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1396]) ).
thf(f1400,plain,
( ( hoaslamnotvar_gthm = $true )
| ( ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1398]) ).
thf(f1402,plain,
( ( ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) ) )
= $false )
| ( hoaslamnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1400]) ).
thf(f1404,plain,
( ( hoaslamnotvar_gthm = $true )
| ( ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1402]) ).
thf(f1406,plain,
( ( hoaslamnotvar_gthm = $true )
| ( ( hoaslaminj
=> ( hoaslamnotap
=> hoaslamnotvar ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1404]) ).
thf(f1408,plain,
( ( hoaslamnotvar_gthm = $true )
| ( ( hoaslamnotap
=> hoaslamnotvar )
= $false ) ),
inference(imp_proxy_clausification,[],[f1406]) ).
thf(f1410,plain,
( ( hoaslamnotvar_gthm = $true )
| ( hoaslamnotvar = $false ) ),
inference(imp_proxy_clausification,[],[f1408]) ).
thf(f1501,plain,
( ( axvarid = $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f323]) ).
thf(f1502,plain,
! [X1: term] :
( ( ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 )
= $true )
| ( axvarid = $false ) ),
inference(pi_proxy_clausification,[],[f1501]) ).
thf(f1503,plain,
! [X1: term] :
( ( axvarid = $false )
| ( $true
= ( ( sub @ X1 @ id )
= X1 ) ) ),
inference(beta-eta_normalization,[],[f1502]) ).
thf(f1504,plain,
! [X1: term] :
( ( axvarid = $false )
| ( ( sub @ X1 @ id )
= X1 ) ),
inference(equality_proxy_clausification,[],[f1503]) ).
thf(f2249,definition,
( spl298_33
<=> ( lamnotvar = $false ) ),
introduced(definition,[new_symbols(definition,[spl298_33])],[avatar_definition]) ).
thf(f2251,plain,
( ( lamnotvar = $false )
| ~ spl298_33 ),
inference(avatar_component_clause,[],[f2249]) ).
thf(f2253,definition,
( spl298_34
<=> ! [X1: term] :
( ( var @ ( lam @ X1 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl298_34])],[avatar_definition]) ).
thf(f2254,plain,
( ! [X1: term] :
( ( var @ ( lam @ X1 ) )
= $false )
| ~ spl298_34 ),
inference(avatar_component_clause,[],[f2253]) ).
thf(f2255,plain,
( spl298_33
| spl298_34 ),
inference(avatar_split_clause,[],[f519,f2253,f2249]) ).
thf(f2257,definition,
( spl298_35
<=> ( lamnotvar = $true ) ),
introduced(definition,[new_symbols(definition,[spl298_35])],[avatar_definition]) ).
thf(f2259,plain,
( ( lamnotvar = $true )
| ~ spl298_35 ),
inference(avatar_component_clause,[],[f2257]) ).
thf(f2846,definition,
( spl298_179
<=> ( hoaslamnotvar = $false ) ),
introduced(definition,[new_symbols(definition,[spl298_179])],[avatar_definition]) ).
thf(f2848,plain,
( ( hoaslamnotvar = $false )
| ~ spl298_179 ),
inference(avatar_component_clause,[],[f2846]) ).
thf(f2854,definition,
( spl298_181
<=> ( hoaslamnotvar = $true ) ),
introduced(definition,[new_symbols(definition,[spl298_181])],[avatar_definition]) ).
thf(f2856,plain,
( ( hoaslamnotvar = $true )
| ~ spl298_181 ),
inference(avatar_component_clause,[],[f2854]) ).
thf(f2859,definition,
( spl298_182
<=> ( ( var @ ( sub @ ( lam @ ( sK155 @ sh @ one ) ) @ id ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl298_182])],[avatar_definition]) ).
thf(f2861,plain,
( ( ( var @ ( sub @ ( lam @ ( sK155 @ sh @ one ) ) @ id ) )
= $true )
| ~ spl298_182 ),
inference(avatar_component_clause,[],[f2859]) ).
thf(f2862,plain,
( spl298_182
| spl298_181 ),
inference(avatar_split_clause,[],[f1195,f2854,f2859]) ).
thf(f3041,definition,
( spl298_226
<=> ( axvarid = $false ) ),
introduced(definition,[new_symbols(definition,[spl298_226])],[avatar_definition]) ).
thf(f3043,plain,
( ( axvarid = $false )
| ~ spl298_226 ),
inference(avatar_component_clause,[],[f3041]) ).
thf(f3058,definition,
( spl298_230
<=> ( hoaslamnotvar_gthm = $true ) ),
introduced(definition,[new_symbols(definition,[spl298_230])],[avatar_definition]) ).
thf(f3068,definition,
( spl298_232
<=> ( axvarid = $true ) ),
introduced(definition,[new_symbols(definition,[spl298_232])],[avatar_definition]) ).
thf(f3070,plain,
( ( axvarid = $true )
| ~ spl298_232 ),
inference(avatar_component_clause,[],[f3068]) ).
thf(f3071,plain,
( spl298_230
| spl298_232 ),
inference(avatar_split_clause,[],[f1353,f3068,f3058]) ).
thf(f3142,plain,
( spl298_230
| spl298_35 ),
inference(avatar_split_clause,[],[f1391,f2257,f3058]) ).
thf(f3181,plain,
( spl298_179
| spl298_230 ),
inference(avatar_split_clause,[],[f1410,f3058,f2846]) ).
thf(f3269,definition,
( spl298_272
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl298_272])],[avatar_definition]) ).
thf(f3270,plain,
( ! [X1: term] :
( ( sub @ X1 @ id )
= X1 )
| ~ spl298_272 ),
inference(avatar_component_clause,[],[f3269]) ).
thf(f3271,plain,
( spl298_226
| spl298_272 ),
inference(avatar_split_clause,[],[f1504,f3269,f3041]) ).
thf(f3757,plain,
~ spl298_230,
inference(avatar_split_clause,[],[f339,f3058]) ).
thf(f3762,plain,
( ( $true = $false )
| ~ spl298_226
| ~ spl298_232 ),
inference(forward_demodulation,[],[f3070,f3043]) ).
thf(f3763,plain,
( $false
| ~ spl298_226
| ~ spl298_232 ),
inference(trivial_inequality_removal,[],[f3762]) ).
thf(f3764,plain,
( ~ spl298_226
| ~ spl298_232 ),
inference(avatar_contradiction_clause,[],[f3763]) ).
thf(f3873,plain,
( ( $true = $false )
| ~ spl298_33
| ~ spl298_35 ),
inference(forward_demodulation,[],[f2259,f2251]) ).
thf(f3874,plain,
( $false
| ~ spl298_33
| ~ spl298_35 ),
inference(trivial_inequality_removal,[],[f3873]) ).
thf(f3875,plain,
( ~ spl298_33
| ~ spl298_35 ),
inference(avatar_contradiction_clause,[],[f3874]) ).
thf(f3900,plain,
( ( $true = $false )
| ~ spl298_179
| ~ spl298_181 ),
inference(forward_demodulation,[],[f2856,f2848]) ).
thf(f3901,plain,
( $false
| ~ spl298_179
| ~ spl298_181 ),
inference(trivial_inequality_removal,[],[f3900]) ).
thf(f3902,plain,
( ~ spl298_179
| ~ spl298_181 ),
inference(avatar_contradiction_clause,[],[f3901]) ).
thf(f3904,plain,
( ( $true
= ( var @ ( lam @ ( sK155 @ sh @ one ) ) ) )
| ~ spl298_182
| ~ spl298_272 ),
inference(forward_demodulation,[],[f2861,f3270]) ).
thf(f3905,plain,
( ( $true = $false )
| ~ spl298_34
| ~ spl298_182
| ~ spl298_272 ),
inference(forward_demodulation,[],[f3904,f2254]) ).
thf(f3906,plain,
( $false
| ~ spl298_34
| ~ spl298_182
| ~ spl298_272 ),
inference(trivial_inequality_removal,[],[f3905]) ).
thf(f3907,plain,
( ~ spl298_34
| ~ spl298_182
| ~ spl298_272 ),
inference(avatar_contradiction_clause,[],[f3906]) ).
cnf(s25,plain,
( spl298_33
| spl298_34 ),
inference(sat_conversion,[],[f2255]) ).
cnf(s157,plain,
( spl298_181
| spl298_182 ),
inference(sat_conversion,[],[f2862]) ).
cnf(s179,plain,
( spl298_230
| spl298_232 ),
inference(sat_conversion,[],[f3071]) ).
cnf(s198,plain,
( spl298_35
| spl298_230 ),
inference(sat_conversion,[],[f3142]) ).
cnf(s209,plain,
( spl298_179
| spl298_230 ),
inference(sat_conversion,[],[f3181]) ).
cnf(s229,plain,
( spl298_226
| spl298_272 ),
inference(sat_conversion,[],[f3271]) ).
cnf(s339,plain,
~ spl298_230,
inference(sat_conversion,[],[f3757]) ).
cnf(s341,plain,
( ~ spl298_226
| ~ spl298_232 ),
inference(sat_conversion,[],[f3764]) ).
cnf(s361,plain,
( ~ spl298_33
| ~ spl298_35 ),
inference(sat_conversion,[],[f3875]) ).
cnf(s365,plain,
( ~ spl298_179
| ~ spl298_181 ),
inference(sat_conversion,[],[f3902]) ).
cnf(s366,plain,
( ~ spl298_34
| ~ spl298_182
| ~ spl298_272 ),
inference(sat_conversion,[],[f3907]) ).
cnf(s368,plain,
spl298_179,
inference(rat,[],[s209,s339]) ).
cnf(s369,plain,
~ spl298_181,
inference(rat,[],[s365,s368]) ).
cnf(s413,plain,
spl298_35,
inference(rat,[],[s198,s339]) ).
cnf(s414,plain,
~ spl298_33,
inference(rat,[],[s361,s413]) ).
cnf(s463,plain,
spl298_232,
inference(rat,[],[s179,s339]) ).
cnf(s464,plain,
~ spl298_226,
inference(rat,[],[s341,s463]) ).
cnf(s465,plain,
spl298_272,
inference(rat,[],[s229,s464]) ).
cnf(s472,plain,
spl298_182,
inference(rat,[],[s157,s369]) ).
cnf(s473,plain,
~ spl298_34,
inference(rat,[],[s366,s465,s472]) ).
cnf(s476,plain,
$false,
inference(rat,[],[s25,s473,s414]) ).
thf(f3908,plain,
$false,
inference(avatar_sat_refutation,[],[s476]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG260^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.12 % Computer : n012.cluster.edu
% 0.07/0.12 % Model : x86_64 x86_64
% 0.07/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.12 % Memory : 8046.5625MB
% 0.07/0.12 % OS : Linux 6.8.0-71-generic
% 0.07/0.12 % CPULimit : 300
% 0.07/0.12 % WCLimit : 300
% 0.07/0.12 % DateTime : Tue Sep 29 17:34:24 UTC 2026
% 0.07/0.12 % CPUTime :
% 0.07/0.12 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.14 Running higher-order theorem proving
% 0.07/0.16 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
% 0.41/0.25 % (430104)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.41/0.25 % (430110)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3542978182:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.41/0.25 % (430111)lrs+10_16_si=on:nwc=1.5:random_seed=3119577217:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.41/0.25 % (430114)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1852472934:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.41/0.25 % (430113)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=4202179452: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)
% 0.41/0.25 % (430112)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3245481883:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.41/0.25 % (430111)Instruction limit reached!
% 0.41/0.25 % (430111)------------------------------
% 0.41/0.25 % (430111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.25 % (430111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.25 % (430111)CaDiCaL version: 2.1.3
% 0.41/0.25 % (430111)Termination reason: Instruction limit
% 0.41/0.25 % (430111)Termination phase: Property scanning
% 0.41/0.25 % (430111)Time elapsed: 0.005 s
% 0.41/0.25 % (430111)Peak memory usage: 10 MB
% 0.41/0.25 % (430111)Instructions burned: 21 (million)
% 0.41/0.25 % (430112)Instruction limit reached!
% 0.41/0.25 % (430112)------------------------------
% 0.41/0.25 % (430112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.25 % (430112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.25 % (430112)CaDiCaL version: 2.1.3
% 0.41/0.25 % (430112)Termination reason: Instruction limit
% 0.41/0.25 % (430112)Termination phase: shuffling
% 0.41/0.25 % (430112)Time elapsed: 0.001 s
% 0.41/0.25 % (430112)Peak memory usage: 10 MB
% 0.41/0.25 % (430112)Instructions burned: 3 (million)
% 0.41/0.25 % (430116)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.41/0.25 % (430116)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
% 0.41/0.25 % (430114)Instruction limit reached!
% 0.41/0.25 % (430114)------------------------------
% 0.41/0.25 % (430114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.25 % (430114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.25 % (430114)CaDiCaL version: 2.1.3
% 0.41/0.25 % (430114)Termination reason: Instruction limit
% 0.41/0.25 % (430114)Termination phase: shuffling
% 0.41/0.25 % (430114)Time elapsed: 0.006 s
% 0.41/0.25 % (430114)Peak memory usage: 11 MB
% 0.41/0.25 % (430114)Instructions burned: 24 (million)
% 0.41/0.25 % (430115)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3335539706:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.41/0.25 % (430116)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=191561813:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.41/0.25 % (430124)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.41/0.25 % (430123)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1116535449:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.41/0.25 % (430122)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1014841664:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.41/0.25 % (430124)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4092115840:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.41/0.25 % (430122)Instruction limit reached!
% 0.41/0.25 % (430122)------------------------------
% 0.41/0.25 % (430122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.27 % (430122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.27 % (430122)CaDiCaL version: 2.1.3
% 0.41/0.27 % (430122)Termination reason: Instruction limit
% 0.41/0.27 % (430122)Termination phase: shuffling
% 0.41/0.27 % (430122)Time elapsed: 0.001 s
% 0.41/0.27 % (430122)Peak memory usage: 10 MB
% 0.41/0.27 % (430122)Instructions burned: 3 (million)
% 0.41/0.27 % (430123)Instruction limit reached!
% 0.41/0.27 % (430123)------------------------------
% 0.41/0.27 % (430123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.27 % (430123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.27 % (430123)CaDiCaL version: 2.1.3
% 0.41/0.27 % (430123)Termination reason: Instruction limit
% 0.41/0.27 % (430123)Termination phase: shuffling
% 0.41/0.27 % (430123)Time elapsed: 0.002 s
% 0.41/0.27 % (430123)Peak memory usage: 10 MB
% 0.41/0.27 % (430123)Instructions burned: 8 (million)
% 0.41/0.27 % (430124)Instruction limit reached!
% 0.41/0.27 % (430124)------------------------------
% 0.41/0.27 % (430124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.27 % (430124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.27 % (430124)CaDiCaL version: 2.1.3
% 0.41/0.27 % (430124)Termination reason: Instruction limit
% 0.41/0.27 % (430124)Termination phase: shuffling
% 0.41/0.27 % (430124)Time elapsed: 0.002 s
% 0.41/0.27 % (430124)Peak memory usage: 10 MB
% 0.41/0.27 % (430124)Instructions burned: 7 (million)
% 0.41/0.27 % (430110)Instruction limit reached!
% 0.41/0.27 % (430110)------------------------------
% 0.41/0.27 % (430110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.27 % (430110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.27 % (430110)CaDiCaL version: 2.1.3
% 0.41/0.27 % (430110)Termination reason: Instruction limit
% 0.41/0.27 % (430110)Termination phase: Function definition elimination
% 0.41/0.27 % (430110)Time elapsed: 0.022 s
% 0.41/0.27 % (430110)Peak memory usage: 12 MB
% 0.41/0.27 % (430110)Instructions burned: 90 (million)
% 0.41/0.27 % (430131)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
% 0.41/0.27 % (430131)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.41/0.27 % (430130)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=448329291:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.41/0.27 % (430131)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=278640701:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.41/0.27 % (430132)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=1769597121:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.41/0.27 % (430130)Instruction limit reached!
% 0.41/0.27 % (430130)------------------------------
% 0.41/0.27 % (430130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.27 % (430130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.27 % (430130)CaDiCaL version: 2.1.3
% 0.41/0.27 % (430130)Termination reason: Instruction limit
% 0.41/0.27 % (430130)Termination phase: shuffling
% 0.41/0.27 % (430130)Time elapsed: 0.003 s
% 0.41/0.27 % (430130)Peak memory usage: 10 MB
% 0.41/0.27 % (430130)Instructions burned: 14 (million)
% 0.41/0.27 % (430133)lrs+10_1_si=on:cs=on:random_seed=944802477:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.41/0.27 % (430131)Instruction limit reached!
% 0.41/0.27 % (430131)------------------------------
% 0.41/0.27 % (430131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.27 % (430131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.27 % (430131)CaDiCaL version: 2.1.3
% 0.41/0.27 % (430131)Termination reason: Instruction limit
% 0.41/0.27 % (430131)Termination phase: Property scanning
% 0.41/0.27 % (430131)Time elapsed: 0.006 s
% 0.41/0.27 % (430131)Peak memory usage: 10 MB
% 0.41/0.27 % (430131)Instructions burned: 29 (million)
% 0.41/0.27 % (430133)Instruction limit reached!
% 0.41/0.27 % (430133)------------------------------
% 0.41/0.27 % (430133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.29 % (430133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.29 % (430133)CaDiCaL version: 2.1.3
% 0.41/0.29 % (430133)Termination reason: Instruction limit
% 0.41/0.29 % (430133)Termination phase: shuffling
% 0.41/0.29 % (430133)Time elapsed: 0.003 s
% 0.41/0.29 % (430133)Peak memory usage: 10 MB
% 0.41/0.29 % (430133)Instructions burned: 14 (million)
% 0.41/0.29 % (430137)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.41/0.29 % (430115)Instruction limit reached!
% 0.41/0.29 % (430115)------------------------------
% 0.41/0.29 % (430115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.29 % (430115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.29 % (430115)CaDiCaL version: 2.1.3
% 0.41/0.29 % (430115)Termination reason: Instruction limit
% 0.41/0.29 % (430115)Termination phase: Property scanning
% 0.41/0.29 % (430115)Time elapsed: 0.033 s
% 0.41/0.29 % (430115)Peak memory usage: 12 MB
% 0.41/0.29 % (430115)Instructions burned: 76 (million)
% 0.41/0.29 % (430137)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=76979220:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.41/0.29 % (430137)Instruction limit reached!
% 0.41/0.29 % (430137)------------------------------
% 0.41/0.29 % (430137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.29 % (430137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.29 % (430137)CaDiCaL version: 2.1.3
% 0.41/0.29 % (430137)Termination reason: Instruction limit
% 0.41/0.29 % (430137)Termination phase: shuffling
% 0.41/0.29 % (430137)Time elapsed: 0.002 s
% 0.41/0.29 % (430137)Peak memory usage: 10 MB
% 0.41/0.29 % (430137)Instructions burned: 10 (million)
% 0.41/0.29 % (430140)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3435710325:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.41/0.29 % (430139)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1863821853:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.41/0.29 % (430132)Instruction limit reached!
% 0.41/0.29 % (430132)------------------------------
% 0.41/0.29 % (430132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.29 % (430132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.29 % (430132)CaDiCaL version: 2.1.3
% 0.41/0.29 % (430132)Termination reason: Instruction limit
% 0.41/0.29 % (430132)Termination phase: Property scanning
% 0.41/0.29 % (430132)Time elapsed: 0.019 s
% 0.41/0.29 % (430132)Peak memory usage: 11 MB
% 0.41/0.29 % (430132)Instructions burned: 86 (million)
% 0.41/0.29 % (430141)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2319819773:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.41/0.29 % (430143)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3689816745:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.41/0.29 % (430139)Refutation not found, incomplete strategy
% 0.41/0.29 % (430139)------------------------------
% 0.41/0.29 % (430139)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.29 % (430139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.29 % (430139)CaDiCaL version: 2.1.3
% 0.41/0.29 % (430139)Termination reason: Refutation not found, incomplete strategy
% 0.41/0.29 % (430139)Time elapsed: 0.008 s
% 0.41/0.29 % (430139)Peak memory usage: 13 MB
% 0.41/0.29 % (430139)Instructions burned: 32 (million)
% 0.41/0.29 % (430139)------------------------------
% 0.41/0.29 % (430139)------------------------------
% 0.41/0.29 % (430141)Instruction limit reached!
% 0.41/0.29 % (430141)------------------------------
% 0.41/0.29 % (430141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.29 % (430141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.29 % (430141)CaDiCaL version: 2.1.3
% 0.41/0.29 % (430141)Termination reason: Instruction limit
% 0.41/0.29 % (430141)Termination phase: Preprocessing 2
% 0.41/0.29 % (430141)Time elapsed: 0.006 s
% 0.41/0.29 % (430141)Peak memory usage: 11 MB
% 0.41/0.31 % (430141)Instructions burned: 26 (million)
% 0.41/0.31 % (430146)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3250731116:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.41/0.31 % (430140)Refutation not found, incomplete strategy
% 0.41/0.31 % (430140)------------------------------
% 0.41/0.31 % (430140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.31 % (430140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.31 % (430143)Instruction limit reached!
% 0.41/0.31 % (430143)------------------------------
% 0.41/0.31 % (430143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.31 % (430140)CaDiCaL version: 2.1.3
% 0.41/0.31 % (430140)Termination reason: Refutation not found, incomplete strategy
% 0.41/0.31 % (430140)Time elapsed: 0.013 s
% 0.41/0.31 % (430140)Peak memory usage: 13 MB
% 0.41/0.31 % (430140)Instructions burned: 52 (million)
% 0.41/0.31 % (430143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.31 % (430143)CaDiCaL version: 2.1.3
% 0.41/0.31 % (430143)Termination reason: Instruction limit
% 0.41/0.31 % (430143)Termination phase: shuffling
% 0.41/0.31 % (430143)Time elapsed: 0.004 s
% 0.41/0.31 % (430143)Peak memory usage: 10 MB
% 0.41/0.31 % (430143)Instructions burned: 18 (million)
% 0.41/0.31 % (430140)------------------------------
% 0.41/0.31 % (430140)------------------------------
% 0.41/0.31 % (430150)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1079396904:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.41/0.31 % (430149)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2003105693:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/14Mi)
% 0.41/0.31 % (430150)Instruction limit reached!
% 0.41/0.31 % (430150)------------------------------
% 0.41/0.31 % (430150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.31 % (430150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.31 % (430150)CaDiCaL version: 2.1.3
% 0.41/0.31 % (430150)Termination reason: Instruction limit
% 0.41/0.31 % (430150)Termination phase: shuffling
% 0.41/0.31 % (430150)Time elapsed: 0.001 s
% 0.41/0.31 % (430150)Peak memory usage: 10 MB
% 0.41/0.31 % (430150)Instructions burned: 6 (million)
% 0.41/0.31 % (430152)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3152022366:i=26:ep=R:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/26Mi)
% 0.41/0.31 % (430149)Instruction limit reached!
% 0.41/0.31 % (430149)------------------------------
% 0.41/0.31 % (430149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.31 % (430149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.31 % (430149)CaDiCaL version: 2.1.3
% 0.41/0.31 % (430149)Termination reason: Instruction limit
% 0.41/0.31 % (430149)Termination phase: shuffling
% 0.41/0.31 % (430149)Time elapsed: 0.003 s
% 0.41/0.31 % (430149)Peak memory usage: 10 MB
% 0.41/0.31 % (430149)Instructions burned: 14 (million)
% 0.41/0.31 % (430116)Instruction limit reached!
% 0.41/0.31 % (430116)------------------------------
% 0.41/0.31 % (430116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.31 % (430116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.31 % (430116)CaDiCaL version: 2.1.3
% 0.41/0.31 % (430116)Termination reason: Instruction limit
% 0.41/0.31 % (430116)Termination phase: Saturation
% 0.41/0.31 % (430116)Time elapsed: 0.065 s
% 0.41/0.31 % (430116)Peak memory usage: 13 MB
% 0.41/0.31 % (430116)Instructions burned: 158 (million)
% 0.41/0.31 % (430153)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=238835141:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/23Mi)
% 0.41/0.31 % (430152)Instruction limit reached!
% 0.41/0.31 % (430152)------------------------------
% 0.41/0.31 % (430152)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.31 % (430152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.31 % (430152)CaDiCaL version: 2.1.3
% 0.41/0.31 % (430152)Termination reason: Instruction limit
% 0.41/0.31 % (430152)Termination phase: Property scanning
% 0.41/0.31 % (430152)Time elapsed: 0.006 s
% 0.41/0.31 % (430152)Peak memory usage: 10 MB
% 0.41/0.31 % (430152)Instructions burned: 27 (million)
% 0.41/0.31 % (430158)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
% 0.41/0.31 % (430158)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.41/0.31 % (430157)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=1786231979:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.41/0.31 % (430153)Instruction limit reached!
% 0.41/0.31 % (430153)------------------------------
% 0.41/0.31 % (430153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.31 % (430153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.31 % (430153)CaDiCaL version: 2.1.3
% 0.41/0.31 % (430153)Termination reason: Instruction limit
% 0.41/0.31 % (430153)Termination phase: Property scanning
% 0.41/0.31 % (430153)Time elapsed: 0.006 s
% 0.41/0.31 % (430153)Peak memory usage: 10 MB
% 0.41/0.31 % (430153)Instructions burned: 25 (million)
% 0.41/0.31 % (430158)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=2406166545:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.41/0.31 % (430158)Instruction limit reached!
% 0.41/0.31 % (430158)------------------------------
% 0.41/0.31 % (430158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.31 % (430158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.31 % (430158)CaDiCaL version: 2.1.3
% 0.41/0.31 % (430158)Termination reason: Instruction limit
% 0.41/0.31 % (430158)Termination phase: shuffling
% 0.41/0.31 % (430158)Time elapsed: 0.004 s
% 0.41/0.31 % (430158)Peak memory usage: 10 MB
% 0.41/0.31 % (430158)Instructions burned: 17 (million)
% 0.41/0.31 % (430161)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=1847928344:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 0.41/0.31 % (430160)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.41/0.31 % (430163)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1206981126:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 0.41/0.31 % (430160)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=469314520:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.41/0.31 % (430163)Instruction limit reached!
% 0.41/0.31 % (430163)------------------------------
% 0.41/0.31 % (430163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.31 % (430163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.31 % (430163)CaDiCaL version: 2.1.3
% 0.41/0.31 % (430163)Termination reason: Instruction limit
% 0.41/0.31 % (430163)Termination phase: shuffling
% 0.41/0.31 % (430163)Time elapsed: 0.002 s
% 0.41/0.31 % (430163)Peak memory usage: 10 MB
% 0.41/0.31 % (430163)Instructions burned: 9 (million)
% 0.41/0.31 % (430161)Instruction limit reached!
% 0.41/0.31 % (430161)------------------------------
% 0.41/0.31 % (430161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.31 % (430161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.31 % (430161)CaDiCaL version: 2.1.3
% 0.41/0.31 % (430161)Termination reason: Instruction limit
% 0.41/0.31 % (430161)Termination phase: Property scanning
% 0.41/0.31 % (430161)Time elapsed: 0.007 s
% 0.41/0.31 % (430161)Peak memory usage: 10 MB
% 0.41/0.31 % (430161)Instructions burned: 34 (million)
% 0.41/0.31 % (430157)Instruction limit reached!
% 0.41/0.31 % (430157)------------------------------
% 0.41/0.31 % (430157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.31 % (430157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.31 % (430157)CaDiCaL version: 2.1.3
% 0.41/0.31 % (430157)Termination reason: Instruction limit
% 0.41/0.31 % (430157)Termination phase: Property scanning
% 0.41/0.31 % (430157)Time elapsed: 0.015 s
% 0.41/0.31 % (430157)Peak memory usage: 12 MB
% 0.41/0.31 % (430157)Instructions burned: 63 (million)
% 0.41/0.31 % (430160)Instruction limit reached!
% 0.41/0.31 % (430160)------------------------------
% 0.41/0.31 % (430160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.31 % (430160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.31 % (430160)CaDiCaL version: 2.1.3
% 0.41/0.31 % (430160)Termination reason: Instruction limit
% 0.41/0.31 % (430160)Termination phase: shuffling
% 0.41/0.31 % (430160)Time elapsed: 0.004 s
% 0.41/0.31 % (430160)Peak memory usage: 10 MB
% 0.41/0.31 % (430160)Instructions burned: 10 (million)
% 0.41/0.31 % (430166)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1631610406:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.41/0.31 % (430146) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-430104-430146"...
% 0.41/0.31 % (430169)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1876338164:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 0.41/0.31 % (430171)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2451606840:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 0.41/0.31 % (430166)Instruction limit reached!
% 0.41/0.31 % (430166)------------------------------
% 0.41/0.31 % (430166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.31 % (430166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.31 % (430166)CaDiCaL version: 2.1.3
% 0.41/0.31 % (430166)Termination reason: Instruction limit
% 0.41/0.31 % (430166)Termination phase: Property scanning
% 0.41/0.31 % (430166)Time elapsed: 0.007 s
% 0.41/0.31 % (430166)Peak memory usage: 10 MB
% 0.41/0.31 % (430166)Instructions burned: 26 (million)
% 0.41/0.31 % (430146)...printing done.
% 0.41/0.31 % (430146)Refutation found. Thanks to Tanya!
% 0.41/0.31 % SZS status Theorem for theBenchmark
% 0.41/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.41/0.31 % (430146)------------------------------
% 0.41/0.31 % (430146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.31 % (430146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.31 % (430146)CaDiCaL version: 2.1.3
% 0.41/0.31 % (430146)Termination reason: Refutation
% 0.41/0.31 % (430146)Time elapsed: 0.050 s
% 0.41/0.31 % (430146)Peak memory usage: 16 MB
% 0.41/0.31 % (430146)Instructions burned: 207 (million)
% 0.41/0.31 % (430104)Success in time 0.144 s
% 0.41/0.31 % Vampire exiting
%------------------------------------------------------------------------------