%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG261^1 : 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 : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:45:15 AM UTC 2026
% Result : Theorem 0.57s 0.44s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 17
% Syntax : Number of formulae : 141 ( 39 unt; 0 typ; 10 def)
% Number of atoms : 1262 ( 159 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 1143 ( 77 ~; 103 |; 0 &; 239 @)
% ( 10 <=>; 693 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 449 ( 445 usr; 195 con; 0-4 aty)
% ( 21 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 94 ( 12 sgn 26 !; 0 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_6,type,
subst: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
one: term ).
thf(func_def_1,type,
ap: term > term > term ).
thf(func_def_2,type,
lam: term > term ).
thf(func_def_3,type,
sub: term > subst > term ).
thf(func_def_4,type,
id: subst ).
thf(func_def_5,type,
sh: subst ).
thf(func_def_6,type,
push: term > subst > subst ).
thf(func_def_7,type,
comp: subst > subst > subst ).
thf(func_def_8,type,
var: term > $o ).
thf(func_def_9,type,
pushprop_lem1v2: $o ).
thf(func_def_10,type,
pushprop_lem1_gthm: $o ).
thf(func_def_11,type,
axmap: $o ).
thf(func_def_12,type,
pushprop_lem0_gthm: $o ).
thf(func_def_13,type,
shinj: $o ).
thf(func_def_14,type,
hoasinduction_lem1v2: $o ).
thf(func_def_15,type,
hoasinduction_lem1v2_gthm: $o ).
thf(func_def_16,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_17,type,
induction2lem: $o ).
thf(func_def_18,type,
hoasinduction_lem3v2_f: $o ).
thf(func_def_19,type,
axvarshift: $o ).
thf(func_def_20,type,
hoasapinj2: $o ).
thf(func_def_21,type,
hoasapnotvar_gthm: $o ).
thf(func_def_22,type,
hoasapinj1: $o ).
thf(func_def_23,type,
ulamvar1: $o ).
thf(func_def_24,type,
induction2lem_lthm: $o ).
thf(func_def_25,type,
hoasinduction_lem3v2_gthm: $o ).
thf(func_def_26,type,
apnotvar: $o ).
thf(func_def_27,type,
pushprop_lthm_orig: $o ).
thf(func_def_28,type,
hoasinduction_lem3v2_f_lthm: $o ).
thf(func_def_29,type,
hoasinduction_lthm: $o ).
thf(func_def_30,type,
hoasinduction_no_psi_cond_lthm: $o ).
thf(func_def_31,type,
hoaslaminj: $o ).
thf(func_def_32,type,
hoasinduction_lem3aaa: $o ).
thf(func_def_33,type,
induction2lem_gthm: $o ).
thf(func_def_34,type,
hoasinduction_lem3aa_lthm: $o ).
thf(func_def_35,type,
hoasinduction_lem3: $o ).
thf(func_def_36,type,
hoasinduction_lem2: $o ).
thf(func_def_37,type,
termmset_lthm: $o ).
thf(func_def_38,type,
hoasinduction_lem1: $o ).
thf(func_def_39,type,
hoaslamnotap_lthm: $o ).
thf(func_def_40,type,
pushprop_lem1v2_lthm: $o ).
thf(func_def_41,type,
hoasapnotvar: $o ).
thf(func_def_42,type,
hoasinduction_lem0: $o ).
thf(func_def_43,type,
hoasinduction: $o ).
thf(func_def_44,type,
hoasinduction_gthm: $o ).
thf(func_def_45,type,
axapp: $o ).
thf(func_def_46,type,
hoaslamnotvar_lthm: $o ).
thf(func_def_47,type,
pushprop_lem3v2_lthm: $o ).
thf(func_def_48,type,
hoasinduction_lem3b_lthm: $o ).
thf(func_def_49,type,
ulamvarind: $o ).
thf(func_def_50,type,
induction: $o ).
thf(func_def_51,type,
hoasinduction_lem3a_lthm: $o ).
thf(func_def_52,type,
termmset_gthm: $o ).
thf(func_def_53,type,
hoasinduction_lem3aa: $o ).
thf(func_def_54,type,
pushprop_lem1v2_gthm: $o ).
thf(func_def_55,type,
hoaslamnotap_gthm: $o ).
thf(func_def_56,type,
hoaslamnotvar_gthm: $o ).
thf(func_def_57,type,
hoasinduction_lem3b_gthm: $o ).
thf(func_def_58,type,
pushprop_lem2v2: $o ).
thf(func_def_59,type,
hoasinduction_lem3a_gthm: $o ).
thf(func_def_60,type,
axclos: $o ).
thf(func_def_61,type,
axassoc: $o ).
thf(func_def_62,type,
hoasinduction_lem2v2: $o ).
thf(func_def_63,type,
pushprop_lthm: $o ).
thf(func_def_64,type,
apinj2: $o ).
thf(func_def_65,type,
apinj1: $o ).
thf(func_def_66,type,
hoasapinj2_lthm: $o ).
thf(func_def_67,type,
hoasinduction_lem3v2a: $o ).
thf(func_def_68,type,
hoasapinj1_lthm: $o ).
thf(func_def_69,type,
hoaslaminj_lthm: $o ).
thf(func_def_70,type,
axvarcons: $o ).
thf(func_def_71,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_72,type,
axscons: $o ).
thf(func_def_73,type,
hoasinduction_lem2v2_gthm: $o ).
thf(func_def_74,type,
axidr: $o ).
thf(func_def_75,type,
pushprop_lem1: $o ).
thf(func_def_76,type,
laminj: $o ).
thf(func_def_77,type,
hoasinduction_lem3_lthm: $o ).
thf(func_def_78,type,
pushprop_lem0: $o ).
thf(func_def_79,type,
pushprop_gthm: $o ).
thf(func_def_80,type,
axabs: $o ).
thf(func_def_81,type,
hoasinduction_lem3v2a_lthm: $o ).
thf(func_def_82,type,
hoasinduction_lem2_lthm: $o ).
thf(func_def_83,type,
hoasapinj2_gthm: $o ).
thf(func_def_84,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_85,type,
hoasinduction_lem1_lthm: $o ).
thf(func_def_86,type,
lamnotap: $o ).
thf(func_def_87,type,
hoasapinj1_gthm: $o ).
thf(func_def_88,type,
hoaslamnotvar: $o ).
thf(func_def_89,type,
axidl: $o ).
thf(func_def_90,type,
hoaslaminj_gthm: $o ).
thf(func_def_91,type,
induction2_lthm: $o ).
thf(func_def_92,type,
hoasinduction_lem0_lthm: $o ).
thf(func_def_93,type,
substmonoid_lthm: $o ).
thf(func_def_94,type,
pushprop: $o ).
thf(func_def_95,type,
hoasinduction_lem3_gthm: $o ).
thf(func_def_96,type,
hoasinduction_lem2_gthm: $o ).
thf(func_def_97,type,
hoasinduction_lem3b: $o ).
thf(func_def_98,type,
substmonoid: $o ).
thf(func_def_99,type,
lamnotvar: $o ).
thf(func_def_100,type,
hoasinduction_lem3a: $o ).
thf(func_def_101,type,
hoasinduction_lem1_gthm: $o ).
thf(func_def_102,type,
hoasinduction_no_psi_cond: $o ).
thf(func_def_103,type,
induction2_gthm: $o ).
thf(func_def_104,type,
pushprop_lem2v2_lthm: $o ).
thf(func_def_105,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_106,type,
hoaslamnotap: $o ).
thf(func_def_107,type,
substmonoid_gthm: $o ).
thf(func_def_108,type,
ulamvarsh: $o ).
thf(func_def_109,type,
induction2: $o ).
thf(func_def_110,type,
pushprop_lem3v2: $o ).
thf(func_def_111,type,
pushprop_lem2v2_gthm: $o ).
thf(func_def_112,type,
pushprop_lem1_lthm: $o ).
thf(func_def_113,type,
hoasinduction_lem3v2: $o ).
thf(func_def_114,type,
axshiftcons: $o ).
thf(func_def_115,type,
termmset: $o ).
thf(func_def_116,type,
pushprop_lem0_lthm: $o ).
thf(func_def_117,type,
hoasapnotvar_lthm: $o ).
thf(func_def_118,type,
hoasinduction_lem3v2_lthm: $o ).
thf(func_def_119,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_120,type,
axvarid: $o ).
thf(func_def_121,type,
hoasinduction_lthm_3: $o ).
thf(func_def_123,type,
vIMP: $o > $o > $o ).
thf(func_def_124,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_125,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_127,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_130,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_131,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
vNOT: $o > $o ).
thf(func_def_133,type,
vIFF: $o > $o > $o ).
thf(func_def_134,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_135,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_136,type,
vAND: $o > $o > $o ).
thf(func_def_139,type,
sK0: term ).
thf(func_def_140,type,
sK1: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_141,type,
sK2: ( subst > term > subst > $o ) > term > term ).
thf(func_def_142,type,
sK3: ( subst > term > subst > $o ) > term > term ).
thf(func_def_143,type,
sK4: ( subst > term > subst > $o ) > term > term ).
thf(func_def_144,type,
sK5: subst > term > subst > $o ).
thf(func_def_145,type,
sK6: ( subst > term > term ) > subst ).
thf(func_def_146,type,
sK7: ( subst > term > term ) > term ).
thf(func_def_147,type,
sK8: ( subst > term > term ) > term ).
thf(func_def_148,type,
sK9: ( subst > term > term ) > subst ).
thf(func_def_149,type,
sK10: ( subst > term > term ) > term ).
thf(func_def_150,type,
sK11: ( subst > term > term ) > subst ).
thf(func_def_151,type,
sK12: term ).
thf(func_def_152,type,
sK13: term ).
thf(func_def_153,type,
sK14: subst ).
thf(func_def_154,type,
sK15: ( term > $o ) > term ).
thf(func_def_155,type,
sK16: ( term > $o ) > term ).
thf(func_def_156,type,
sK17: ( term > $o ) > term ).
thf(func_def_157,type,
sK18: ( term > $o ) > term ).
thf(func_def_158,type,
sK19: ( term > $o ) > term ).
thf(func_def_159,type,
sK20: term > $o ).
thf(func_def_160,type,
sK21: term > term ).
thf(func_def_161,type,
sK22: term ).
thf(func_def_162,type,
sK23: ( subst > term > subst > $o ) > term ).
thf(func_def_163,type,
sK24: ( subst > term > subst > $o ) > subst ).
thf(func_def_164,type,
sK25: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_165,type,
sK26: ( subst > term > subst > $o ) > subst ).
thf(func_def_166,type,
sK27: ( subst > term > subst > $o ) > term > term ).
thf(func_def_167,type,
sK28: ( subst > term > subst > $o ) > subst ).
thf(func_def_168,type,
sK29: ( subst > term > subst > $o ) > subst ).
thf(func_def_169,type,
sK30: ( subst > term > subst > $o ) > subst ).
thf(func_def_170,type,
sK31: ( subst > term > subst > $o ) > subst ).
thf(func_def_171,type,
sK32: ( subst > term > subst > $o ) > term ).
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 ) > term ).
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 > term ).
thf(func_def_178,type,
sK39: ( subst > term > subst > $o ) > subst ).
thf(func_def_179,type,
sK40: ( subst > term > subst > $o ) > subst ).
thf(func_def_180,type,
sK41: ( subst > term > subst > $o ) > term ).
thf(func_def_181,type,
sK42: ( subst > term > subst > $o ) > subst ).
thf(func_def_182,type,
sK43: ( subst > term > subst > $o ) > subst ).
thf(func_def_183,type,
sK44: ( subst > term > subst > $o ) > subst ).
thf(func_def_184,type,
sK45: ( subst > term > subst > $o ) > term ).
thf(func_def_185,type,
sK46: ( subst > term > subst > $o ) > term > term ).
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 ) > subst ).
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 ) > term ).
thf(func_def_193,type,
sK54: ( subst > term > subst > $o ) > subst ).
thf(func_def_194,type,
sK55: subst > term > subst > $o ).
thf(func_def_195,type,
sK56: ( subst > term > term ) > subst ).
thf(func_def_196,type,
sK57: ( subst > term > term ) > term ).
thf(func_def_197,type,
sK58: ( subst > term > term ) > subst ).
thf(func_def_198,type,
sK59: ( subst > term > term ) > term ).
thf(func_def_199,type,
sK60: ( subst > term > term ) > subst ).
thf(func_def_200,type,
sK61: ( subst > term > term ) > term ).
thf(func_def_201,type,
sK62: term ).
thf(func_def_202,type,
sK63: term ).
thf(func_def_203,type,
sK64: term ).
thf(func_def_204,type,
sK65: ( subst > term > term ) > subst ).
thf(func_def_205,type,
sK66: ( subst > term > term ) > subst ).
thf(func_def_206,type,
sK67: ( subst > term > term ) > term ).
thf(func_def_207,type,
sK68: subst > term > term ).
thf(func_def_208,type,
sK69: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_209,type,
sK70: term > ( term > $o ) > term ).
thf(func_def_210,type,
sK71: subst > term > subst > $o ).
thf(func_def_211,type,
sK72: term > $o ).
thf(func_def_212,type,
sK73: ( subst > term > term ) > subst ).
thf(func_def_213,type,
sK74: ( subst > term > term ) > term ).
thf(func_def_214,type,
sK75: ( subst > term > term ) > subst ).
thf(func_def_215,type,
sK76: ( subst > term > term ) > term ).
thf(func_def_216,type,
sK77: ( subst > term > term ) > term ).
thf(func_def_217,type,
sK78: term ).
thf(func_def_218,type,
sK79: ( subst > term > term ) > subst ).
thf(func_def_219,type,
sK80: ( subst > term > term ) > term ).
thf(func_def_220,type,
sK81: ( subst > term > term ) > subst ).
thf(func_def_221,type,
sK82: ( subst > term > term ) > term ).
thf(func_def_222,type,
sK83: ( subst > term > term ) > subst ).
thf(func_def_223,type,
sK84: ( subst > term > term ) > subst ).
thf(func_def_224,type,
sK85: subst > term > term ).
thf(func_def_225,type,
sK86: subst > term > term ).
thf(func_def_226,type,
sK87: term ).
thf(func_def_227,type,
sK88: subst ).
thf(func_def_228,type,
sK89: term ).
thf(func_def_229,type,
sK90: term ).
thf(func_def_230,type,
sK91: term ).
thf(func_def_231,type,
sK92: term ).
thf(func_def_232,type,
sK93: term ).
thf(func_def_233,type,
sK94: term ).
thf(func_def_234,type,
sK95: subst ).
thf(func_def_235,type,
sK96: subst ).
thf(func_def_236,type,
sK97: subst ).
thf(func_def_237,type,
sK98: term ).
thf(func_def_238,type,
sK99: term ).
thf(func_def_239,type,
sK100: term ).
thf(func_def_240,type,
sK101: term ).
thf(func_def_241,type,
sK102: subst ).
thf(func_def_242,type,
sK103: term ).
thf(func_def_243,type,
sK104: term ).
thf(func_def_244,type,
sK105: subst ).
thf(func_def_245,type,
sK106: term ).
thf(func_def_246,type,
sK107: ( subst > term > subst > $o ) > subst ).
thf(func_def_247,type,
sK108: ( subst > term > subst > $o ) > term ).
thf(func_def_248,type,
sK109: ( subst > term > subst > $o ) > term ).
thf(func_def_249,type,
sK110: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_250,type,
sK111: ( subst > term > subst > $o ) > term ).
thf(func_def_251,type,
sK112: ( subst > term > subst > $o ) > subst ).
thf(func_def_252,type,
sK113: ( subst > term > subst > $o ) > term ).
thf(func_def_253,type,
sK114: ( subst > term > subst > $o ) > term ).
thf(func_def_254,type,
sK115: ( subst > term > subst > $o ) > subst ).
thf(func_def_255,type,
sK116: ( subst > term > subst > $o ) > subst ).
thf(func_def_256,type,
sK117: ( subst > term > subst > $o ) > subst ).
thf(func_def_257,type,
sK118: ( subst > term > subst > $o ) > subst ).
thf(func_def_258,type,
sK119: ( subst > term > subst > $o ) > subst ).
thf(func_def_259,type,
sK120: ( subst > term > subst > $o ) > subst ).
thf(func_def_260,type,
sK121: ( subst > term > subst > $o ) > subst ).
thf(func_def_261,type,
sK122: ( subst > term > subst > $o ) > subst ).
thf(func_def_262,type,
sK123: ( subst > term > subst > $o ) > subst ).
thf(func_def_263,type,
sK124: ( subst > term > subst > $o ) > term ).
thf(func_def_264,type,
sK125: ( subst > term > subst > $o ) > term ).
thf(func_def_265,type,
sK126: ( subst > term > subst > $o ) > subst ).
thf(func_def_266,type,
sK127: ( subst > term > subst > $o ) > subst ).
thf(func_def_267,type,
sK128: ( subst > term > subst > $o ) > subst ).
thf(func_def_268,type,
sK129: ( subst > term > subst > $o ) > subst ).
thf(func_def_269,type,
sK130: ( subst > term > subst > $o ) > subst ).
thf(func_def_270,type,
sK131: ( subst > term > subst > $o ) > subst ).
thf(func_def_271,type,
sK132: ( subst > term > subst > $o ) > subst ).
thf(func_def_272,type,
sK133: ( subst > term > subst > $o ) > subst ).
thf(func_def_273,type,
sK134: ( subst > term > subst > $o ) > subst ).
thf(func_def_274,type,
sK135: ( subst > term > subst > $o ) > subst ).
thf(func_def_275,type,
sK136: ( subst > term > subst > $o ) > term ).
thf(func_def_276,type,
sK137: ( subst > term > subst > $o ) > term ).
thf(func_def_277,type,
sK138: ( subst > term > subst > $o ) > subst ).
thf(func_def_278,type,
sK139: ( subst > term > subst > $o ) > subst ).
thf(func_def_279,type,
sK140: ( subst > term > subst > $o ) > subst ).
thf(func_def_280,type,
sK141: ( subst > term > subst > $o ) > subst ).
thf(func_def_281,type,
sK142: ( subst > term > subst > $o ) > subst ).
thf(func_def_282,type,
sK143: ( subst > term > subst > $o ) > subst ).
thf(func_def_283,type,
sK144: ( subst > term > subst > $o ) > subst ).
thf(func_def_284,type,
sK145: ( subst > term > subst > $o ) > subst ).
thf(func_def_285,type,
sK146: ( subst > term > subst > $o ) > subst ).
thf(func_def_286,type,
sK147: ( subst > term > subst > $o ) > subst ).
thf(func_def_287,type,
sK148: ( subst > term > subst > $o ) > subst ).
thf(func_def_288,type,
sK149: ( subst > term > subst > $o ) > term ).
thf(func_def_289,type,
sK150: ( subst > term > subst > $o ) > term ).
thf(func_def_290,type,
sK151: ( subst > term > subst > $o ) > subst ).
thf(func_def_291,type,
sK152: ( subst > term > subst > $o ) > subst ).
thf(func_def_292,type,
sK153: ( subst > term > subst > $o ) > subst ).
thf(func_def_293,type,
sK154: ( subst > term > subst > $o ) > subst ).
thf(func_def_294,type,
sK155: ( subst > term > subst > $o ) > subst ).
thf(func_def_295,type,
sK156: ( subst > term > subst > $o ) > subst ).
thf(func_def_296,type,
sK157: ( subst > term > subst > $o ) > subst ).
thf(func_def_297,type,
sK158: ( subst > term > subst > $o ) > subst ).
thf(func_def_298,type,
sK159: ( subst > term > subst > $o ) > term ).
thf(func_def_299,type,
sK160: ( subst > term > subst > $o ) > term ).
thf(func_def_300,type,
sK161: ( subst > term > subst > $o ) > subst ).
thf(func_def_301,type,
sK162: ( 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 ) > subst ).
thf(func_def_304,type,
sK165: ( subst > term > subst > $o ) > subst ).
thf(func_def_305,type,
sK166: ( subst > term > subst > $o ) > subst ).
thf(func_def_306,type,
sK167: ( subst > term > subst > $o ) > subst ).
thf(func_def_307,type,
sK168: ( subst > term > subst > $o ) > subst ).
thf(func_def_308,type,
sK169: ( subst > term > subst > $o ) > subst ).
thf(func_def_309,type,
sK170: ( subst > term > subst > $o ) > subst ).
thf(func_def_310,type,
sK171: ( subst > term > subst > $o ) > subst ).
thf(func_def_311,type,
sK172: ( subst > term > subst > $o ) > subst ).
thf(func_def_312,type,
sK173: ( subst > term > subst > $o ) > subst ).
thf(func_def_313,type,
sK174: ( subst > term > subst > $o ) > subst ).
thf(func_def_314,type,
sK175: ( subst > term > subst > $o ) > subst ).
thf(func_def_315,type,
sK176: ( subst > term > subst > $o ) > subst ).
thf(func_def_316,type,
sK177: ( subst > term > subst > $o ) > subst ).
thf(func_def_317,type,
sK178: subst > term > subst > $o ).
thf(func_def_318,type,
sK179: ( subst > term > term ) > 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 ) > subst ).
thf(func_def_323,type,
sK184: ( subst > term > term ) > subst ).
thf(func_def_324,type,
sK185: term ).
thf(func_def_325,type,
sK186: term ).
thf(func_def_326,type,
sK187: term ).
thf(func_def_327,type,
sK188: term ).
thf(func_def_328,type,
sK189: term ).
thf(func_def_329,type,
sK190: ( subst > term > subst > $o ) > subst ).
thf(func_def_330,type,
sK191: ( subst > term > subst > $o ) > term ).
thf(func_def_331,type,
sK192: ( subst > term > subst > $o ) > term ).
thf(func_def_332,type,
sK193: ( subst > term > subst > $o ) > term ).
thf(func_def_333,type,
sK194: ( subst > term > subst > $o ) > term ).
thf(func_def_334,type,
sK195: ( subst > term > subst > $o ) > subst ).
thf(func_def_335,type,
sK196: ( subst > term > subst > $o ) > subst ).
thf(func_def_336,type,
sK197: ( subst > term > subst > $o ) > subst ).
thf(func_def_337,type,
sK198: ( subst > term > subst > $o ) > subst ).
thf(func_def_338,type,
sK199: ( subst > term > subst > $o ) > subst ).
thf(func_def_339,type,
sK200: ( subst > term > subst > $o ) > subst ).
thf(func_def_340,type,
sK201: ( subst > term > subst > $o ) > subst ).
thf(func_def_341,type,
sK202: ( subst > term > subst > $o ) > subst ).
thf(func_def_342,type,
sK203: ( subst > term > subst > $o ) > subst ).
thf(func_def_343,type,
sK204: subst > term > subst > $o ).
thf(func_def_344,type,
sK205: term ).
thf(func_def_345,type,
sK206: term ).
thf(func_def_346,type,
sK207: term ).
thf(func_def_347,type,
sK208: subst ).
thf(func_def_348,type,
sK209: subst ).
thf(func_def_349,type,
sK210: term ).
thf(func_def_350,type,
sK211: term ).
thf(func_def_351,type,
sK212: term ).
thf(func_def_352,type,
sK213: subst ).
thf(func_def_353,type,
sK214: subst ).
thf(func_def_354,type,
sK215: term ).
thf(func_def_355,type,
sK216: subst ).
thf(func_def_356,type,
sK217: subst ).
thf(func_def_357,type,
sK218: ( term > $o ) > term ).
thf(func_def_358,type,
sK219: ( term > $o ) > term ).
thf(func_def_359,type,
sK220: ( term > $o ) > term ).
thf(func_def_360,type,
sK221: subst > ( term > $o ) > term ).
thf(func_def_361,type,
sK222: subst > ( term > $o ) > term ).
thf(func_def_362,type,
sK223: subst > ( term > $o ) > term ).
thf(func_def_363,type,
sK224: subst > ( term > $o ) > term ).
thf(func_def_364,type,
sK225: term > $o ).
thf(func_def_365,type,
sK226: term > term ).
thf(func_def_366,type,
sK227: term ).
thf(func_def_367,type,
sK228: subst ).
thf(func_def_368,type,
sK229: ( subst > term > term ) > subst ).
thf(func_def_369,type,
sK230: ( subst > term > term ) > term ).
thf(func_def_370,type,
sK231: ( subst > term > term ) > subst ).
thf(func_def_371,type,
sK232: subst > term > term ).
thf(func_def_372,type,
sK233: term ).
thf(func_def_373,type,
sK234: term ).
thf(func_def_374,type,
sK235: ( term > $o ) > term ).
thf(func_def_375,type,
sK236: ( term > $o ) > term ).
thf(func_def_376,type,
sK237: ( term > $o ) > term ).
thf(func_def_377,type,
sK238: ( term > $o ) > term ).
thf(func_def_378,type,
sK239: ( term > $o ) > term ).
thf(func_def_379,type,
sK240: ( term > $o ) > term ).
thf(func_def_380,type,
sK241: ( term > $o ) > term ).
thf(func_def_381,type,
sK242: term > $o ).
thf(func_def_382,type,
sK243: term ).
thf(func_def_383,type,
sK244: ( subst > term > subst > $o ) > term ).
thf(func_def_384,type,
sK245: ( subst > term > subst > $o ) > subst ).
thf(func_def_385,type,
sK246: ( subst > term > subst > $o ) > term ).
thf(func_def_386,type,
sK247: ( subst > term > subst > $o ) > subst ).
thf(func_def_387,type,
sK248: ( subst > term > subst > $o ) > term ).
thf(func_def_388,type,
sK249: ( subst > term > subst > $o ) > subst ).
thf(func_def_389,type,
sK250: ( subst > term > subst > $o ) > subst ).
thf(func_def_390,type,
sK251: ( subst > term > subst > $o ) > subst ).
thf(func_def_391,type,
sK252: ( subst > term > subst > $o ) > subst ).
thf(func_def_392,type,
sK253: ( subst > term > subst > $o ) > term ).
thf(func_def_393,type,
sK254: ( subst > term > subst > $o ) > subst ).
thf(func_def_394,type,
sK255: ( subst > term > subst > $o ) > subst ).
thf(func_def_395,type,
sK256: ( subst > term > subst > $o ) > subst ).
thf(func_def_396,type,
sK257: ( subst > term > subst > $o ) > subst ).
thf(func_def_397,type,
sK258: subst > term > subst > $o ).
thf(func_def_398,type,
sK259: term > $o ).
thf(func_def_399,type,
sK260: term ).
thf(func_def_400,type,
sK261: subst > ( term > $o ) > term ).
thf(func_def_401,type,
sK262: subst ).
thf(func_def_402,type,
sK263: term > $o ).
thf(func_def_403,type,
sK264: term ).
thf(func_def_404,type,
sK265: term ).
thf(func_def_405,type,
sK266: ( subst > term > subst > $o ) > term ).
thf(func_def_406,type,
sK267: ( subst > term > subst > $o ) > subst ).
thf(func_def_407,type,
sK268: ( subst > term > subst > $o ) > term ).
thf(func_def_408,type,
sK269: ( subst > term > subst > $o ) > subst ).
thf(func_def_409,type,
sK270: ( subst > term > subst > $o ) > term ).
thf(func_def_410,type,
sK271: ( subst > term > subst > $o ) > subst ).
thf(func_def_411,type,
sK272: ( subst > term > subst > $o ) > subst ).
thf(func_def_412,type,
sK273: ( subst > term > subst > $o ) > subst ).
thf(func_def_413,type,
sK274: ( subst > term > subst > $o ) > subst ).
thf(func_def_414,type,
sK275: ( subst > term > subst > $o ) > term ).
thf(func_def_415,type,
sK276: ( subst > term > subst > $o ) > subst ).
thf(func_def_416,type,
sK277: ( subst > term > subst > $o ) > subst ).
thf(func_def_417,type,
sK278: ( subst > term > subst > $o ) > subst ).
thf(func_def_418,type,
sK279: ( subst > term > subst > $o ) > subst ).
thf(func_def_419,type,
sK280: subst > term > subst > $o ).
thf(func_def_420,type,
sK281: term ).
thf(func_def_421,type,
sK282: ( term > $o ) > term ).
thf(func_def_422,type,
sK283: term > $o ).
thf(func_def_423,type,
sK284: term ).
thf(func_def_424,type,
sK285: term ).
thf(func_def_425,type,
sK286: subst ).
thf(func_def_426,type,
sK287: subst ).
thf(func_def_427,type,
sK288: term ).
thf(func_def_428,type,
sK289: term ).
thf(func_def_429,type,
sK290: term ).
thf(func_def_430,type,
sK291: term ).
thf(func_def_431,type,
sK292: term ).
thf(func_def_432,type,
sK293: term ).
thf(func_def_433,type,
sK294: term ).
thf(func_def_434,type,
sK295: term ).
thf(func_def_435,type,
sK296: term ).
thf(func_def_436,type,
sK297: term ).
thf(f3,axiom,
( axvarid
= ( ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axvarid) ).
thf(f21,axiom,
( apnotvar
= ( ! [X1: term,X0: term] :
~ ( var @ ( ap @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',apnotvar) ).
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(f57,axiom,
( hoasvar
= ( ^ [X0: subst,X1: term,X2: subst] : ( var @ ( sub @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasvar) ).
thf(f73,axiom,
( hoasapnotvar
= ( ! [X0: term,X1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ X0 @ id @ X1 ) @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasapnotvar) ).
thf(f74,axiom,
( axapp
=> ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= hoasapnotvar_gthm ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasapnotvar_gthm) ).
thf(f114,conjecture,
hoasapnotvar_gthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ hoasapnotvar_gthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f151,plain,
( axapp
=> ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= hoasapnotvar_gthm ) ),
inference(rectify,[],[f74]) ).
thf(f152,plain,
( hoasapnotvar_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f151]) ).
thf(f206,plain,
( hoasapnotvar
= ( ! [X0: term,X1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ X0 @ id @ X1 ) @ id ) ) ),
inference(rectify,[],[f73]) ).
thf(f207,plain,
( hoasapnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ Y1 @ id @ Y0 ) @ id ) ) ) ),
inference(fool_elimination,[],[f206]) ).
thf(f219,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f232,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f255,plain,
( apnotvar
= ( ! [X0: term,X1: term] :
~ ( var @ ( ap @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f256,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f255]) ).
thf(f265,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f312,plain,
~ hoasapnotvar_gthm,
inference(rectify,[],[f115]) ).
thf(f313,plain,
hoasapnotvar_gthm != $true,
inference(fool_elimination,[],[f312]) ).
thf(f322,plain,
hoasapnotvar_gthm != $true,
inference(flattening,[],[f313]) ).
thf(f327,plain,
( hoasapnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( hoasvar @ id @ ( hoasap @ id @ Y1 @ id @ Y0 ) @ id ) ) ) ),
inference(cnf_transformation,[],[f207]) ).
thf(f336,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f232]) ).
thf(f337,plain,
( hoasapnotvar_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f152]) ).
thf(f341,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(cnf_transformation,[],[f265]) ).
thf(f346,plain,
( apnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f256]) ).
thf(f355,plain,
hoasapnotvar_gthm != $true,
inference(cnf_transformation,[],[f322]) ).
thf(f362,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f219]) ).
thf(f370,plain,
( hoasapnotvar
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ ( ^ [Y2: subst,Y3: term,Y4: subst,Y5: term] : ( ap @ ( sub @ Y3 @ Y4 ) @ Y5 )
@ id
@ Y1
@ id
@ Y0 )
@ id ) ) ) ),
inference(definition_unfolding,[],[f327,f336,f341]) ).
thf(f939,plain,
( ( hoasapnotvar = $true )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ ( ^ [Y2: subst,Y3: term,Y4: subst,Y5: term] : ( ap @ ( sub @ Y3 @ Y4 ) @ Y5 )
@ id
@ Y1
@ id
@ Y0 )
@ id ) ) ) ) ),
inference(iff_proxy_clausification,[],[f370]) ).
thf(f946,plain,
( ( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ ( ^ [Y2: subst,Y3: term,Y4: subst,Y5: term] : ( ap @ ( sub @ Y3 @ Y4 ) @ Y5 )
@ id
@ Y1
@ id
@ Y0 )
@ id ) )
@ sK98 )
= $false )
| ( hoasapnotvar = $true ) ),
inference(sigma_proxy_clausification,[],[f939]) ).
thf(f947,plain,
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ sK98 ) @ id ) ) ) )
| ( hoasapnotvar = $true ) ),
inference(beta-eta_normalization,[],[f946]) ).
thf(f948,plain,
( ( $false
= ( ^ [Y0: term] :
~ ( var @ ( sub @ ( ap @ ( sub @ Y0 @ id ) @ sK98 ) @ id ) )
@ sK99 ) )
| ( hoasapnotvar = $true ) ),
inference(sigma_proxy_clausification,[],[f947]) ).
thf(f949,plain,
( ( hoasapnotvar = $true )
| ( ( ~ ( var @ ( sub @ ( ap @ ( sub @ sK99 @ id ) @ sK98 ) @ id ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f948]) ).
thf(f950,plain,
( ( ( var @ ( sub @ ( ap @ ( sub @ sK99 @ id ) @ sK98 ) @ id ) )
= $true )
| ( hoasapnotvar = $true ) ),
inference(not_proxy_clausification,[],[f949]) ).
thf(f988,plain,
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) )
| ( axvarid = $false ) ),
inference(iff_proxy_clausification,[],[f362]) ).
thf(f989,plain,
! [X1: term] :
( ( axvarid = $false )
| ( $true
= ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f988]) ).
thf(f990,plain,
! [X1: term] :
( ( ( ( sub @ X1 @ id )
= X1 )
= $true )
| ( axvarid = $false ) ),
inference(beta-eta_normalization,[],[f989]) ).
thf(f991,plain,
! [X1: term] :
( ( axvarid = $false )
| ( ( sub @ X1 @ id )
= X1 ) ),
inference(equality_proxy_clausification,[],[f990]) ).
thf(f1374,plain,
( ( hoasapnotvar_gthm = $true )
| ( $false
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f337]) ).
thf(f1409,plain,
( ( hoasapnotvar_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
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1374]) ).
thf(f1411,plain,
( ( hoasapnotvar_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
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1409]) ).
thf(f1413,plain,
( ( $false
= ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1411]) ).
thf(f1414,plain,
( ( axvarid = $true )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1411]) ).
thf(f1415,plain,
( ( hoasapnotvar_gthm = $true )
| ( $false
= ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1413]) ).
thf(f1417,plain,
( ( $false
= ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1415]) ).
thf(f1419,plain,
( ( $false
= ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1417]) ).
thf(f1421,plain,
( ( hoasapnotvar_gthm = $true )
| ( $false
= ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1419]) ).
thf(f1423,plain,
( ( $false
= ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1421]) ).
thf(f1425,plain,
( ( $false
= ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1423]) ).
thf(f1427,plain,
( ( $false
= ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1425]) ).
thf(f1429,plain,
( ( hoasapnotvar_gthm = $true )
| ( $false
= ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1427]) ).
thf(f1431,plain,
( ( hoasapnotvar_gthm = $true )
| ( $false
= ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1429]) ).
thf(f1433,plain,
( ( hoasapnotvar_gthm = $true )
| ( $false
= ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1431]) ).
thf(f1435,plain,
( ( $false
= ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1433]) ).
thf(f1437,plain,
( ( $false
= ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1435]) ).
thf(f1439,plain,
( ( hoasapnotvar_gthm = $true )
| ( $false
= ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1437]) ).
thf(f1441,plain,
( ( ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1439]) ).
thf(f1443,plain,
( ( hoasapnotvar_gthm = $true )
| ( $false
= ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1441]) ).
thf(f1445,plain,
( ( $false
= ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1443]) ).
thf(f1447,plain,
( ( hoasapnotvar_gthm = $true )
| ( $false
= ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1445]) ).
thf(f1449,plain,
( ( $false
= ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1447]) ).
thf(f1450,plain,
( ( apnotvar = $true )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1447]) ).
thf(f1451,plain,
( ( hoasapnotvar_gthm = $true )
| ( $false
= ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1449]) ).
thf(f1453,plain,
( ( hoasapnotvar_gthm = $true )
| ( ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1451]) ).
thf(f1455,plain,
( ( $false
= ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ) ) )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1453]) ).
thf(f1457,plain,
( ( ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) )
= $false )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1455]) ).
thf(f1459,plain,
( ( $false
= ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1457]) ).
thf(f1461,plain,
( ( hoasapnotvar_gthm = $true )
| ( $false
= ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1459]) ).
thf(f1463,plain,
( ( hoasapnotvar_gthm = $true )
| ( ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1461]) ).
thf(f1465,plain,
( ( hoasapnotvar_gthm = $true )
| ( $false
= ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1463]) ).
thf(f1467,plain,
( ( $false
= ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) ) )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1465]) ).
thf(f1469,plain,
( ( $false
= ( hoaslamnotap
=> ( hoaslamnotvar
=> hoasapnotvar ) ) )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1467]) ).
thf(f1471,plain,
( ( $false
= ( hoaslamnotvar
=> hoasapnotvar ) )
| ( hoasapnotvar_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1469]) ).
thf(f1473,plain,
( ( hoasapnotvar_gthm = $true )
| ( hoasapnotvar = $false ) ),
inference(imp_proxy_clausification,[],[f1471]) ).
thf(f2090,plain,
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) ) ) )
| ( apnotvar = $false ) ),
inference(iff_proxy_clausification,[],[f346]) ).
thf(f2091,plain,
! [X1: term] :
( ( $true
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
~ ( var @ ( ap @ Y0 @ Y1 ) ) )
@ X1 ) )
| ( apnotvar = $false ) ),
inference(pi_proxy_clausification,[],[f2090]) ).
thf(f2092,plain,
! [X1: term] :
( ( ( !! @ term
@ ^ [Y0: term] :
~ ( var @ ( ap @ X1 @ Y0 ) ) )
= $true )
| ( apnotvar = $false ) ),
inference(beta-eta_normalization,[],[f2091]) ).
thf(f2093,plain,
! [X2: term,X1: term] :
( ( $true
= ( ^ [Y0: term] :
~ ( var @ ( ap @ X1 @ Y0 ) )
@ X2 ) )
| ( apnotvar = $false ) ),
inference(pi_proxy_clausification,[],[f2092]) ).
thf(f2094,plain,
! [X2: term,X1: term] :
( ( ( ~ ( var @ ( ap @ X1 @ X2 ) ) )
= $true )
| ( apnotvar = $false ) ),
inference(beta-eta_normalization,[],[f2093]) ).
thf(f2095,plain,
! [X2: term,X1: term] :
( ( $false
= ( var @ ( ap @ X1 @ X2 ) ) )
| ( apnotvar = $false ) ),
inference(not_proxy_clausification,[],[f2094]) ).
thf(f2609,definition,
( spl298_117
<=> ( hoasapnotvar = $false ) ),
introduced(definition,[new_symbols(definition,[spl298_117])],[avatar_definition]) ).
thf(f2611,plain,
( ( hoasapnotvar = $false )
| ~ spl298_117 ),
inference(avatar_component_clause,[],[f2609]) ).
thf(f2617,definition,
( spl298_119
<=> ( ( var @ ( sub @ ( ap @ ( sub @ sK99 @ id ) @ sK98 ) @ id ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl298_119])],[avatar_definition]) ).
thf(f2619,plain,
( ( ( var @ ( sub @ ( ap @ ( sub @ sK99 @ id ) @ sK98 ) @ id ) )
= $true )
| ~ spl298_119 ),
inference(avatar_component_clause,[],[f2617]) ).
thf(f2621,definition,
( spl298_120
<=> ( hoasapnotvar = $true ) ),
introduced(definition,[new_symbols(definition,[spl298_120])],[avatar_definition]) ).
thf(f2623,plain,
( ( hoasapnotvar = $true )
| ~ spl298_120 ),
inference(avatar_component_clause,[],[f2621]) ).
thf(f2624,plain,
( spl298_119
| spl298_120 ),
inference(avatar_split_clause,[],[f950,f2621,f2617]) ).
thf(f2677,definition,
( spl298_133
<=> ( axvarid = $false ) ),
introduced(definition,[new_symbols(definition,[spl298_133])],[avatar_definition]) ).
thf(f2679,plain,
( ( axvarid = $false )
| ~ spl298_133 ),
inference(avatar_component_clause,[],[f2677]) ).
thf(f2681,definition,
( spl298_134
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl298_134])],[avatar_definition]) ).
thf(f2682,plain,
( ! [X1: term] :
( ( sub @ X1 @ id )
= X1 )
| ~ spl298_134 ),
inference(avatar_component_clause,[],[f2681]) ).
thf(f2683,plain,
( spl298_133
| spl298_134 ),
inference(avatar_split_clause,[],[f991,f2681,f2677]) ).
thf(f2689,definition,
( spl298_136
<=> ( axvarid = $true ) ),
introduced(definition,[new_symbols(definition,[spl298_136])],[avatar_definition]) ).
thf(f2691,plain,
( ( axvarid = $true )
| ~ spl298_136 ),
inference(avatar_component_clause,[],[f2689]) ).
thf(f3113,definition,
( spl298_241
<=> ( apnotvar = $false ) ),
introduced(definition,[new_symbols(definition,[spl298_241])],[avatar_definition]) ).
thf(f3115,plain,
( ( apnotvar = $false )
| ~ spl298_241 ),
inference(avatar_component_clause,[],[f3113]) ).
thf(f3122,definition,
( spl298_243
<=> ( hoasapnotvar_gthm = $true ) ),
introduced(definition,[new_symbols(definition,[spl298_243])],[avatar_definition]) ).
thf(f3127,plain,
( spl298_243
| spl298_136 ),
inference(avatar_split_clause,[],[f1414,f2689,f3122]) ).
thf(f3190,definition,
( spl298_255
<=> ( apnotvar = $true ) ),
introduced(definition,[new_symbols(definition,[spl298_255])],[avatar_definition]) ).
thf(f3192,plain,
( ( apnotvar = $true )
| ~ spl298_255 ),
inference(avatar_component_clause,[],[f3190]) ).
thf(f3193,plain,
( spl298_243
| spl298_255 ),
inference(avatar_split_clause,[],[f1450,f3190,f3122]) ).
thf(f3234,plain,
( spl298_117
| spl298_243 ),
inference(avatar_split_clause,[],[f1473,f3122,f2609]) ).
thf(f3510,plain,
~ spl298_243,
inference(avatar_split_clause,[],[f355,f3122]) ).
thf(f3747,definition,
( spl298_383
<=> ! [X2: term,X1: term] :
( $false
= ( var @ ( ap @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl298_383])],[avatar_definition]) ).
thf(f3748,plain,
( ! [X2: term,X1: term] :
( $false
= ( var @ ( ap @ X1 @ X2 ) ) )
| ~ spl298_383 ),
inference(avatar_component_clause,[],[f3747]) ).
thf(f3749,plain,
( spl298_383
| spl298_241 ),
inference(avatar_split_clause,[],[f2095,f3113,f3747]) ).
thf(f3813,plain,
( ( $true = $false )
| ~ spl298_241
| ~ spl298_255 ),
inference(forward_demodulation,[],[f3192,f3115]) ).
thf(f3814,plain,
( $false
| ~ spl298_241
| ~ spl298_255 ),
inference(trivial_inequality_removal,[],[f3813]) ).
thf(f3815,plain,
( ~ spl298_241
| ~ spl298_255 ),
inference(avatar_contradiction_clause,[],[f3814]) ).
thf(f3907,plain,
( ( $true = $false )
| ~ spl298_133
| ~ spl298_136 ),
inference(forward_demodulation,[],[f2691,f2679]) ).
thf(f3908,plain,
( $false
| ~ spl298_133
| ~ spl298_136 ),
inference(trivial_inequality_removal,[],[f3907]) ).
thf(f3909,plain,
( ~ spl298_133
| ~ spl298_136 ),
inference(avatar_contradiction_clause,[],[f3908]) ).
thf(f3968,plain,
( ( $true
= ( var @ ( ap @ ( sub @ sK99 @ id ) @ sK98 ) ) )
| ~ spl298_119
| ~ spl298_134 ),
inference(forward_demodulation,[],[f2619,f2682]) ).
thf(f3969,plain,
( ( $true = $false )
| ~ spl298_119
| ~ spl298_134
| ~ spl298_383 ),
inference(forward_demodulation,[],[f3968,f3748]) ).
thf(f3970,plain,
( $false
| ~ spl298_119
| ~ spl298_134
| ~ spl298_383 ),
inference(trivial_inequality_removal,[],[f3969]) ).
thf(f3971,plain,
( ~ spl298_119
| ~ spl298_134
| ~ spl298_383 ),
inference(avatar_contradiction_clause,[],[f3970]) ).
thf(f3972,plain,
( ( $true = $false )
| ~ spl298_117
| ~ spl298_120 ),
inference(forward_demodulation,[],[f2623,f2611]) ).
thf(f3973,plain,
( $false
| ~ spl298_117
| ~ spl298_120 ),
inference(trivial_inequality_removal,[],[f3972]) ).
thf(f3974,plain,
( ~ spl298_117
| ~ spl298_120 ),
inference(avatar_contradiction_clause,[],[f3973]) ).
cnf(s94,plain,
( spl298_119
| spl298_120 ),
inference(sat_conversion,[],[f2624]) ).
cnf(s101,plain,
( spl298_133
| spl298_134 ),
inference(sat_conversion,[],[f2683]) ).
cnf(s188,plain,
( spl298_136
| spl298_243 ),
inference(sat_conversion,[],[f3127]) ).
cnf(s206,plain,
( spl298_243
| spl298_255 ),
inference(sat_conversion,[],[f3193]) ).
cnf(s219,plain,
( spl298_117
| spl298_243 ),
inference(sat_conversion,[],[f3234]) ).
cnf(s284,plain,
~ spl298_243,
inference(sat_conversion,[],[f3510]) ).
cnf(s336,plain,
( spl298_241
| spl298_383 ),
inference(sat_conversion,[],[f3749]) ).
cnf(s352,plain,
( ~ spl298_241
| ~ spl298_255 ),
inference(sat_conversion,[],[f3815]) ).
cnf(s363,plain,
( ~ spl298_133
| ~ spl298_136 ),
inference(sat_conversion,[],[f3909]) ).
cnf(s371,plain,
( ~ spl298_119
| ~ spl298_134
| ~ spl298_383 ),
inference(sat_conversion,[],[f3971]) ).
cnf(s372,plain,
( ~ spl298_117
| ~ spl298_120 ),
inference(sat_conversion,[],[f3974]) ).
cnf(s374,plain,
spl298_117,
inference(rat,[],[s219,s284]) ).
cnf(s375,plain,
~ spl298_120,
inference(rat,[],[s372,s374]) ).
cnf(s423,plain,
spl298_255,
inference(rat,[],[s206,s284]) ).
cnf(s424,plain,
~ spl298_241,
inference(rat,[],[s352,s423]) ).
cnf(s425,plain,
spl298_383,
inference(rat,[],[s336,s424]) ).
cnf(s473,plain,
spl298_136,
inference(rat,[],[s188,s284]) ).
cnf(s474,plain,
~ spl298_133,
inference(rat,[],[s363,s473]) ).
cnf(s479,plain,
spl298_134,
inference(rat,[],[s101,s474]) ).
cnf(s480,plain,
~ spl298_119,
inference(rat,[],[s371,s425,s479]) ).
cnf(s483,plain,
$false,
inference(rat,[],[s94,s375,s480]) ).
thf(f3977,plain,
$false,
inference(avatar_sat_refutation,[],[s483]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG261^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n006.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 17:33:40 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.26 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
% 0.57/0.39 % (1062241)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.57/0.39 % (1062246)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3764562272:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.57/0.39 % (1062252)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.57/0.39 % (1062252)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
% 0.57/0.39 % (1062247)lrs+10_16_si=on:nwc=1.5:random_seed=1954549794:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.57/0.39 % (1062248)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3128917229:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.57/0.39 % (1062249)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=2363985106: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)
% 0.57/0.39 % (1062250)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3586242270:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.57/0.39 % (1062251)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=987480661:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.57/0.39 % (1062252)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=2588740432:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.57/0.39 % (1062248)Instruction limit reached!
% 0.57/0.39 % (1062248)------------------------------
% 0.57/0.39 % (1062248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.39 % (1062248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.39 % (1062248)CaDiCaL version: 2.1.3
% 0.57/0.39 % (1062248)Termination reason: Instruction limit
% 0.57/0.39 % (1062248)Termination phase: shuffling
% 0.57/0.39 % (1062248)Time elapsed: 0.002 s
% 0.57/0.39 % (1062248)Peak memory usage: 10 MB
% 0.57/0.39 % (1062248)Instructions burned: 3 (million)
% 0.57/0.39 % (1062247)Instruction limit reached!
% 0.57/0.39 % (1062247)------------------------------
% 0.57/0.39 % (1062247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.39 % (1062247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.39 % (1062247)CaDiCaL version: 2.1.3
% 0.57/0.39 % (1062247)Termination reason: Instruction limit
% 0.57/0.39 % (1062247)Termination phase: shuffling
% 0.57/0.39 % (1062247)Time elapsed: 0.008 s
% 0.57/0.39 % (1062247)Peak memory usage: 10 MB
% 0.57/0.39 % (1062247)Instructions burned: 18 (million)
% 0.57/0.39 % (1062250)Instruction limit reached!
% 0.57/0.39 % (1062250)------------------------------
% 0.57/0.39 % (1062250)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.39 % (1062250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.39 % (1062250)CaDiCaL version: 2.1.3
% 0.57/0.39 % (1062250)Termination reason: Instruction limit
% 0.57/0.39 % (1062250)Termination phase: Naming
% 0.57/0.39 % (1062250)Time elapsed: 0.012 s
% 0.57/0.39 % (1062250)Peak memory usage: 11 MB
% 0.57/0.39 % (1062250)Instructions burned: 25 (million)
% 0.57/0.39 % (1062246)Instruction limit reached!
% 0.57/0.39 % (1062246)------------------------------
% 0.57/0.39 % (1062246)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.39 % (1062246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.39 % (1062246)CaDiCaL version: 2.1.3
% 0.57/0.39 % (1062246)Termination reason: Instruction limit
% 0.57/0.39 % (1062246)Termination phase: Function definition elimination
% 0.57/0.39 % (1062246)Time elapsed: 0.021 s
% 0.57/0.39 % (1062246)Peak memory usage: 12 MB
% 0.57/0.39 % (1062246)Instructions burned: 88 (million)
% 0.57/0.39 % (1062260)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=888289274:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.57/0.39 % (1062263)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=406174340:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.57/0.42 % (1062260)Instruction limit reached!
% 0.57/0.42 % (1062260)------------------------------
% 0.57/0.42 % (1062260)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.42 % (1062260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.42 % (1062260)CaDiCaL version: 2.1.3
% 0.57/0.42 % (1062260)Termination reason: Instruction limit
% 0.57/0.42 % (1062260)Termination phase: shuffling
% 0.57/0.42 % (1062260)Time elapsed: 0.003 s
% 0.57/0.42 % (1062260)Peak memory usage: 10 MB
% 0.57/0.42 % (1062260)Instructions burned: 5 (million)
% 0.57/0.42 % (1062263)Instruction limit reached!
% 0.57/0.42 % (1062263)------------------------------
% 0.57/0.42 % (1062263)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.42 % (1062263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.42 % (1062263)CaDiCaL version: 2.1.3
% 0.57/0.42 % (1062263)Termination reason: Instruction limit
% 0.57/0.42 % (1062263)Termination phase: shuffling
% 0.57/0.42 % (1062263)Time elapsed: 0.003 s
% 0.57/0.42 % (1062263)Peak memory usage: 10 MB
% 0.57/0.42 % (1062263)Instructions burned: 13 (million)
% 0.57/0.42 % (1062262)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.57/0.42 % (1062261)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2111174286:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.57/0.42 % (1062262)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2855186027:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.57/0.42 % (1062261)Instruction limit reached!
% 0.57/0.42 % (1062261)------------------------------
% 0.57/0.42 % (1062261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.42 % (1062261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.42 % (1062261)CaDiCaL version: 2.1.3
% 0.57/0.42 % (1062261)Termination reason: Instruction limit
% 0.57/0.42 % (1062261)Termination phase: shuffling
% 0.57/0.42 % (1062261)Time elapsed: 0.005 s
% 0.57/0.42 % (1062261)Peak memory usage: 10 MB
% 0.57/0.42 % (1062261)Instructions burned: 11 (million)
% 0.57/0.42 % (1062251)Instruction limit reached!
% 0.57/0.42 % (1062251)------------------------------
% 0.57/0.42 % (1062251)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.42 % (1062251)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.42 % (1062251)CaDiCaL version: 2.1.3
% 0.57/0.42 % (1062251)Termination reason: Instruction limit
% 0.57/0.42 % (1062251)Termination phase: Property scanning
% 0.57/0.42 % (1062251)Time elapsed: 0.035 s
% 0.57/0.42 % (1062251)Peak memory usage: 12 MB
% 0.57/0.42 % (1062251)Instructions burned: 77 (million)
% 0.57/0.42 % (1062262)Instruction limit reached!
% 0.57/0.42 % (1062262)------------------------------
% 0.57/0.42 % (1062262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.42 % (1062262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.42 % (1062262)CaDiCaL version: 2.1.3
% 0.57/0.42 % (1062262)Termination reason: Instruction limit
% 0.57/0.42 % (1062262)Termination phase: shuffling
% 0.57/0.42 % (1062262)Time elapsed: 0.003 s
% 0.57/0.42 % (1062262)Peak memory usage: 10 MB
% 0.57/0.42 % (1062262)Instructions burned: 7 (million)
% 0.57/0.42 % (1062268)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=1399475787:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.57/0.42 % (1062266)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
% 0.57/0.42 % (1062266)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.57/0.42 % (1062266)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1381561971:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.57/0.42 % (1062271)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.57/0.44 % (1062270)lrs+10_1_si=on:cs=on:random_seed=1354660144:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.57/0.44 % (1062271)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=601031778:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.57/0.44 % (1062272)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3516442570:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.57/0.44 % (1062266)Instruction limit reached!
% 0.57/0.44 % (1062266)------------------------------
% 0.57/0.44 % (1062266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (1062266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (1062266)CaDiCaL version: 2.1.3
% 0.57/0.44 % (1062266)Termination reason: Instruction limit
% 0.57/0.44 % (1062266)Termination phase: Property scanning
% 0.57/0.44 % (1062266)Time elapsed: 0.012 s
% 0.57/0.44 % (1062266)Peak memory usage: 10 MB
% 0.57/0.44 % (1062266)Instructions burned: 28 (million)
% 0.57/0.44 % (1062271)Instruction limit reached!
% 0.57/0.44 % (1062271)------------------------------
% 0.57/0.44 % (1062271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (1062271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (1062271)CaDiCaL version: 2.1.3
% 0.57/0.44 % (1062271)Termination reason: Instruction limit
% 0.57/0.44 % (1062271)Termination phase: shuffling
% 0.57/0.44 % (1062271)Time elapsed: 0.002 s
% 0.57/0.44 % (1062271)Peak memory usage: 10 MB
% 0.57/0.44 % (1062271)Instructions burned: 4 (million)
% 0.57/0.44 % (1062270)Instruction limit reached!
% 0.57/0.44 % (1062270)------------------------------
% 0.57/0.44 % (1062270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (1062270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (1062270)CaDiCaL version: 2.1.3
% 0.57/0.44 % (1062270)Termination reason: Instruction limit
% 0.57/0.44 % (1062270)Termination phase: shuffling
% 0.57/0.44 % (1062270)Time elapsed: 0.004 s
% 0.57/0.44 % (1062270)Peak memory usage: 10 MB
% 0.57/0.44 % (1062270)Instructions burned: 9 (million)
% 0.57/0.44 % (1062268)Instruction limit reached!
% 0.57/0.44 % (1062268)------------------------------
% 0.57/0.44 % (1062268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (1062268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (1062268)CaDiCaL version: 2.1.3
% 0.57/0.44 % (1062268)Termination reason: Instruction limit
% 0.57/0.44 % (1062268)Termination phase: Saturation
% 0.57/0.44 % (1062268)Time elapsed: 0.018 s
% 0.57/0.44 % (1062268)Peak memory usage: 11 MB
% 0.57/0.44 % (1062268)Instructions burned: 86 (million)
% 0.57/0.44 % (1062281)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1309533359:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.57/0.44 % (1062252)Instruction limit reached!
% 0.57/0.44 % (1062252)------------------------------
% 0.57/0.44 % (1062252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (1062252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (1062252)CaDiCaL version: 2.1.3
% 0.57/0.44 % (1062252)Termination reason: Instruction limit
% 0.57/0.44 % (1062252)Termination phase: Saturation
% 0.57/0.44 % (1062252)Time elapsed: 0.069 s
% 0.57/0.44 % (1062252)Peak memory usage: 13 MB
% 0.57/0.44 % (1062252)Instructions burned: 159 (million)
% 0.57/0.44 % (1062272)Refutation not found, incomplete strategy
% 0.57/0.44 % (1062272)------------------------------
% 0.57/0.44 % (1062272)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (1062272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (1062272)CaDiCaL version: 2.1.3
% 0.57/0.44 % (1062272)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.44 % (1062272)Time elapsed: 0.016 s
% 0.57/0.44 % (1062272)Peak memory usage: 13 MB
% 0.57/0.44 % (1062272)Instructions burned: 32 (million)
% 0.57/0.44 % (1062272)------------------------------
% 0.57/0.44 % (1062272)------------------------------
% 0.57/0.44 % (1062280)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1067598119:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.57/0.44 % (1062278)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=653023305:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.57/0.44 % (1062279)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2419476671:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.57/0.44 % (1062280)Instruction limit reached!
% 0.57/0.44 % (1062280)------------------------------
% 0.57/0.44 % (1062280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (1062280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (1062280)CaDiCaL version: 2.1.3
% 0.57/0.44 % (1062280)Termination reason: Instruction limit
% 0.57/0.44 % (1062280)Termination phase: shuffling
% 0.57/0.44 % (1062280)Time elapsed: 0.006 s
% 0.57/0.44 % (1062280)Peak memory usage: 10 MB
% 0.57/0.44 % (1062280)Instructions burned: 15 (million)
% 0.57/0.44 % (1062279)Instruction limit reached!
% 0.57/0.44 % (1062279)------------------------------
% 0.57/0.44 % (1062279)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (1062279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (1062279)CaDiCaL version: 2.1.3
% 0.57/0.44 % (1062279)Termination reason: Instruction limit
% 0.57/0.44 % (1062279)Termination phase: Preprocessing 1
% 0.57/0.44 % (1062279)Time elapsed: 0.012 s
% 0.57/0.44 % (1062279)Peak memory usage: 10 MB
% 0.57/0.44 % (1062279)Instructions burned: 25 (million)
% 0.57/0.44 % (1062283)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1870635034:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.57/0.44 % (1062284)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1655193232:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.57/0.44 % (1062284)Instruction limit reached!
% 0.57/0.44 % (1062284)------------------------------
% 0.57/0.44 % (1062284)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (1062284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (1062284)CaDiCaL version: 2.1.3
% 0.57/0.44 % (1062284)Termination reason: Instruction limit
% 0.57/0.44 % (1062284)Termination phase: shuffling
% 0.57/0.44 % (1062284)Time elapsed: 0.002 s
% 0.57/0.44 % (1062284)Peak memory usage: 10 MB
% 0.57/0.44 % (1062284)Instructions burned: 4 (million)
% 0.57/0.44 % (1062283)Instruction limit reached!
% 0.57/0.44 % (1062283)------------------------------
% 0.57/0.44 % (1062283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (1062283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (1062283)CaDiCaL version: 2.1.3
% 0.57/0.44 % (1062283)Termination reason: Instruction limit
% 0.57/0.44 % (1062283)Termination phase: shuffling
% 0.57/0.44 % (1062283)Time elapsed: 0.007 s
% 0.57/0.44 % (1062283)Peak memory usage: 10 MB
% 0.57/0.44 % (1062283)Instructions burned: 16 (million)
% 0.57/0.44 % (1062278)Refutation not found, incomplete strategy
% 0.57/0.44 % (1062278)------------------------------
% 0.57/0.44 % (1062278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (1062278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (1062278)CaDiCaL version: 2.1.3
% 0.57/0.44 % (1062278)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.44 % (1062278)Time elapsed: 0.023 s
% 0.57/0.44 % (1062278)Peak memory usage: 12 MB
% 0.57/0.44 % (1062278)Instructions burned: 52 (million)
% 0.57/0.44 % (1062278)------------------------------
% 0.57/0.44 % (1062278)------------------------------
% 0.57/0.44 % (1062288)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2839310191:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.57/0.44 % (1062289)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=4286072763:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.57/0.44 % (1062293)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
% 0.57/0.44 % (1062293)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.57/0.44 % (1062292)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3407427145:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.57/0.44 % (1062288)Instruction limit reached!
% 0.57/0.44 % (1062288)------------------------------
% 0.57/0.44 % (1062288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (1062288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (1062288)CaDiCaL version: 2.1.3
% 0.57/0.44 % (1062288)Termination reason: Instruction limit
% 0.57/0.44 % (1062288)Termination phase: Property scanning
% 0.57/0.44 % (1062288)Time elapsed: 0.012 s
% 0.57/0.44 % (1062288)Peak memory usage: 10 MB
% 0.57/0.44 % (1062288)Instructions burned: 27 (million)
% 0.57/0.44 % (1062294)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.57/0.44 % (1062293)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=2301889397:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.57/0.44 % (1062281) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1062241-1062281"...
% 0.57/0.44 % (1062289)Instruction limit reached!
% 0.57/0.44 % (1062289)------------------------------
% 0.57/0.44 % (1062289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (1062289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (1062289)CaDiCaL version: 2.1.3
% 0.57/0.44 % (1062289)Termination reason: Instruction limit
% 0.57/0.44 % (1062289)Termination phase: Property scanning
% 0.57/0.44 % (1062289)Time elapsed: 0.011 s
% 0.57/0.44 % (1062289)Peak memory usage: 10 MB
% 0.57/0.44 % (1062289)Instructions burned: 24 (million)
% 0.57/0.44 % (1062294)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=2684834227:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.57/0.44 % (1062281)...printing done.
% 0.57/0.44 % (1062281)Refutation found. Thanks to Tanya!
% 0.57/0.44 % SZS status Theorem for theBenchmark
% 0.57/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.57/0.44 % (1062281)------------------------------
% 0.57/0.44 % (1062281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.44 % (1062281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.44 % (1062281)CaDiCaL version: 2.1.3
% 0.57/0.44 % (1062281)Termination reason: Refutation
% 0.57/0.44 % (1062281)Time elapsed: 0.051 s
% 0.57/0.44 % (1062281)Peak memory usage: 16 MB
% 0.57/0.44 % (1062281)Instructions burned: 211 (million)
% 0.57/0.44 % (1062241)Success in time 0.171 s
% 0.57/0.44 % Vampire exiting
%------------------------------------------------------------------------------