%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG263^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 1.72s 0.61s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 14
% Syntax : Number of formulae : 131 ( 31 unt; 0 typ; 9 def)
% Number of atoms : 1392 ( 160 equ; 0 cnn)
% Maximal formula atoms : 5 ( 10 avg)
% Number of connectives : 1622 ( 58 ~; 113 |; 0 &; 564 @)
% ( 9 <=>; 801 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 451 ( 447 usr; 194 con; 0-4 aty)
% ( 77 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 133 ( 6 sgn 34 !; 0 ?; 133 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_125,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_126,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_127,type,
vIMP: $o > $o > $o ).
thf(func_def_128,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_131,type,
vIFF: $o > $o > $o ).
thf(func_def_132,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_133,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_134,type,
vNOT: $o > $o ).
thf(func_def_137,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_138,type,
vAND: $o > $o > $o ).
thf(func_def_139,type,
sK0: term ).
thf(func_def_140,type,
sK1: term ).
thf(func_def_141,type,
sK2: ( term > $o ) > term ).
thf(func_def_142,type,
sK3: ( term > $o ) > term ).
thf(func_def_143,type,
sK4: ( term > $o ) > term ).
thf(func_def_144,type,
sK5: ( term > $o ) > term ).
thf(func_def_145,type,
sK6: ( term > $o ) > term ).
thf(func_def_146,type,
sK7: ( term > $o ) > term ).
thf(func_def_147,type,
sK8: ( term > $o ) > term ).
thf(func_def_148,type,
sK9: term > $o ).
thf(func_def_149,type,
sK10: term > term ).
thf(func_def_150,type,
sK11: term ).
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 ).
thf(func_def_155,type,
sK16: term ).
thf(func_def_156,type,
sK17: subst ).
thf(func_def_157,type,
sK18: ( term > $o ) > subst > term ).
thf(func_def_158,type,
sK19: term > $o ).
thf(func_def_159,type,
sK20: subst ).
thf(func_def_160,type,
sK21: term ).
thf(func_def_161,type,
sK22: term ).
thf(func_def_162,type,
sK23: term ).
thf(func_def_163,type,
sK24: term ).
thf(func_def_164,type,
sK25: term ).
thf(func_def_165,type,
sK26: term ).
thf(func_def_166,type,
sK27: term ).
thf(func_def_167,type,
sK28: term ).
thf(func_def_168,type,
sK29: term ).
thf(func_def_169,type,
sK30: term ).
thf(func_def_170,type,
sK31: ( subst > term > subst > $o ) > subst ).
thf(func_def_171,type,
sK32: ( subst > term > subst > $o ) > subst ).
thf(func_def_172,type,
sK33: ( subst > term > subst > $o ) > term ).
thf(func_def_173,type,
sK34: ( subst > term > subst > $o ) > subst ).
thf(func_def_174,type,
sK35: ( subst > term > subst > $o ) > subst ).
thf(func_def_175,type,
sK36: ( subst > term > subst > $o ) > subst ).
thf(func_def_176,type,
sK37: ( subst > term > subst > $o ) > term ).
thf(func_def_177,type,
sK38: ( subst > term > subst > $o ) > term ).
thf(func_def_178,type,
sK39: ( subst > term > subst > $o ) > subst ).
thf(func_def_179,type,
sK40: ( subst > term > subst > $o ) > 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 ) > term ).
thf(func_def_184,type,
sK45: term > $o ).
thf(func_def_185,type,
sK46: subst > term > subst > $o ).
thf(func_def_186,type,
sK47: term ).
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 ) > subst ).
thf(func_def_195,type,
sK56: ( subst > term > subst > $o ) > term ).
thf(func_def_196,type,
sK57: ( subst > term > subst > $o ) > term ).
thf(func_def_197,type,
sK58: ( subst > term > subst > $o ) > subst ).
thf(func_def_198,type,
sK59: ( subst > term > subst > $o ) > term ).
thf(func_def_199,type,
sK60: ( subst > term > subst > $o ) > subst ).
thf(func_def_200,type,
sK61: subst > term > subst > $o ).
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: term ).
thf(func_def_205,type,
sK66: term ).
thf(func_def_206,type,
sK67: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_207,type,
sK68: term > ( term > $o ) > term ).
thf(func_def_208,type,
sK69: term > ( term > $o ) > 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 ) > term ).
thf(func_def_215,type,
sK76: ( subst > term > term ) > subst ).
thf(func_def_216,type,
sK77: ( subst > term > term ) > term ).
thf(func_def_217,type,
sK78: ( subst > term > term ) > subst ).
thf(func_def_218,type,
sK79: term ).
thf(func_def_219,type,
sK80: term ).
thf(func_def_220,type,
sK81: subst ).
thf(func_def_221,type,
sK82: term ).
thf(func_def_222,type,
sK83: term ).
thf(func_def_223,type,
sK84: subst ).
thf(func_def_224,type,
sK85: term ).
thf(func_def_225,type,
sK86: subst ).
thf(func_def_226,type,
sK87: subst ).
thf(func_def_227,type,
sK88: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_228,type,
sK89: ( subst > term > subst > $o ) > term > term ).
thf(func_def_229,type,
sK90: ( subst > term > subst > $o ) > term > term ).
thf(func_def_230,type,
sK91: ( subst > term > subst > $o ) > term > term ).
thf(func_def_231,type,
sK92: subst > term > subst > $o ).
thf(func_def_232,type,
sK93: ( subst > term > term ) > term ).
thf(func_def_233,type,
sK94: ( subst > term > term ) > term ).
thf(func_def_234,type,
sK95: ( subst > term > term ) > subst ).
thf(func_def_235,type,
sK96: ( subst > term > term ) > subst ).
thf(func_def_236,type,
sK97: ( subst > term > term ) > subst ).
thf(func_def_237,type,
sK98: ( subst > term > term ) > subst ).
thf(func_def_238,type,
sK99: term ).
thf(func_def_239,type,
sK100: subst ).
thf(func_def_240,type,
sK101: term ).
thf(func_def_241,type,
sK102: term ).
thf(func_def_242,type,
sK103: term ).
thf(func_def_243,type,
sK104: term ).
thf(func_def_244,type,
sK105: term ).
thf(func_def_245,type,
sK106: subst ).
thf(func_def_246,type,
sK107: subst ).
thf(func_def_247,type,
sK108: term ).
thf(func_def_248,type,
sK109: ( term > $o ) > term ).
thf(func_def_249,type,
sK110: ( term > $o ) > term ).
thf(func_def_250,type,
sK111: ( term > $o ) > term ).
thf(func_def_251,type,
sK112: ( term > $o ) > term ).
thf(func_def_252,type,
sK113: ( term > $o ) > term ).
thf(func_def_253,type,
sK114: term > $o ).
thf(func_def_254,type,
sK115: term ).
thf(func_def_255,type,
sK116: term ).
thf(func_def_256,type,
sK117: term ).
thf(func_def_257,type,
sK118: term ).
thf(func_def_258,type,
sK119: ( subst > term > subst > $o ) > term ).
thf(func_def_259,type,
sK120: ( subst > term > subst > $o ) > subst ).
thf(func_def_260,type,
sK121: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_261,type,
sK122: ( subst > term > subst > $o ) > term ).
thf(func_def_262,type,
sK123: ( subst > term > subst > $o ) > term > term ).
thf(func_def_263,type,
sK124: ( subst > term > subst > $o ) > subst ).
thf(func_def_264,type,
sK125: ( subst > term > subst > $o ) > subst ).
thf(func_def_265,type,
sK126: ( subst > term > subst > $o ) > subst ).
thf(func_def_266,type,
sK127: ( subst > term > subst > $o ) > 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 ) > subst ).
thf(func_def_276,type,
sK137: ( subst > term > subst > $o ) > subst ).
thf(func_def_277,type,
sK138: ( subst > term > subst > $o ) > subst ).
thf(func_def_278,type,
sK139: ( subst > term > subst > $o ) > subst ).
thf(func_def_279,type,
sK140: ( subst > term > subst > $o ) > subst ).
thf(func_def_280,type,
sK141: ( subst > term > subst > $o ) > subst ).
thf(func_def_281,type,
sK142: ( subst > term > subst > $o ) > subst ).
thf(func_def_282,type,
sK143: ( subst > term > subst > $o ) > 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 ).
thf(func_def_286,type,
sK147: ( subst > term > term ) > term ).
thf(func_def_287,type,
sK148: ( subst > term > term ) > term ).
thf(func_def_288,type,
sK149: ( subst > term > term ) > subst ).
thf(func_def_289,type,
sK150: ( subst > term > term ) > subst ).
thf(func_def_290,type,
sK151: ( subst > term > term ) > subst ).
thf(func_def_291,type,
sK152: ( subst > term > term ) > subst ).
thf(func_def_292,type,
sK153: term ).
thf(func_def_293,type,
sK154: ( subst > term > subst > $o ) > subst ).
thf(func_def_294,type,
sK155: ( subst > term > subst > $o ) > subst ).
thf(func_def_295,type,
sK156: ( subst > term > subst > $o ) > term ).
thf(func_def_296,type,
sK157: ( subst > term > subst > $o ) > subst ).
thf(func_def_297,type,
sK158: ( subst > term > subst > $o ) > term ).
thf(func_def_298,type,
sK159: ( subst > term > subst > $o ) > subst ).
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 ) > term ).
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 ) > term ).
thf(func_def_305,type,
sK166: ( subst > term > subst > $o ) > term ).
thf(func_def_306,type,
sK167: ( subst > term > subst > $o ) > subst ).
thf(func_def_307,type,
sK168: subst > term > subst > $o ).
thf(func_def_308,type,
sK169: term ).
thf(func_def_309,type,
sK170: term ).
thf(func_def_310,type,
sK171: subst ).
thf(func_def_311,type,
sK172: term ).
thf(func_def_312,type,
sK173: ( subst > term > term ) > term ).
thf(func_def_313,type,
sK174: ( subst > term > term ) > subst ).
thf(func_def_314,type,
sK175: ( subst > term > term ) > subst ).
thf(func_def_315,type,
sK176: ( subst > term > term ) > subst ).
thf(func_def_316,type,
sK177: ( subst > term > term ) > term ).
thf(func_def_317,type,
sK178: ( subst > term > term ) > subst ).
thf(func_def_318,type,
sK179: subst > term > term ).
thf(func_def_319,type,
sK180: subst > term > term ).
thf(func_def_320,type,
sK181: term ).
thf(func_def_321,type,
sK182: subst ).
thf(func_def_322,type,
sK183: term ).
thf(func_def_323,type,
sK184: term ).
thf(func_def_324,type,
sK185: subst ).
thf(func_def_325,type,
sK186: subst ).
thf(func_def_326,type,
sK187: subst ).
thf(func_def_327,type,
sK188: subst ).
thf(func_def_328,type,
sK189: term ).
thf(func_def_329,type,
sK190: term ).
thf(func_def_330,type,
sK191: term ).
thf(func_def_331,type,
sK192: ( term > $o ) > term ).
thf(func_def_332,type,
sK193: term > $o ).
thf(func_def_333,type,
sK194: term ).
thf(func_def_334,type,
sK195: ( term > $o ) > term ).
thf(func_def_335,type,
sK196: ( term > $o ) > term ).
thf(func_def_336,type,
sK197: ( term > $o ) > term ).
thf(func_def_337,type,
sK198: subst > ( term > $o ) > term ).
thf(func_def_338,type,
sK199: subst > ( term > $o ) > term ).
thf(func_def_339,type,
sK200: subst > ( term > $o ) > term ).
thf(func_def_340,type,
sK201: subst > ( term > $o ) > term ).
thf(func_def_341,type,
sK202: subst > ( term > $o ) > term ).
thf(func_def_342,type,
sK203: subst > ( term > $o ) > term ).
thf(func_def_343,type,
sK204: term > $o ).
thf(func_def_344,type,
sK205: term > term ).
thf(func_def_345,type,
sK206: term ).
thf(func_def_346,type,
sK207: subst ).
thf(func_def_347,type,
sK208: ( subst > term > term ) > term ).
thf(func_def_348,type,
sK209: ( subst > term > term ) > subst ).
thf(func_def_349,type,
sK210: ( subst > term > term ) > subst ).
thf(func_def_350,type,
sK211: subst > term > term ).
thf(func_def_351,type,
sK212: term ).
thf(func_def_352,type,
sK213: term ).
thf(func_def_353,type,
sK214: ( subst > term > term ) > term ).
thf(func_def_354,type,
sK215: ( subst > term > term ) > subst ).
thf(func_def_355,type,
sK216: ( subst > term > term ) > subst ).
thf(func_def_356,type,
sK217: subst > term > term ).
thf(func_def_357,type,
sK218: ( subst > term > subst > $o ) > subst ).
thf(func_def_358,type,
sK219: ( subst > term > subst > $o ) > subst ).
thf(func_def_359,type,
sK220: ( subst > term > subst > $o ) > term ).
thf(func_def_360,type,
sK221: ( subst > term > subst > $o ) > term ).
thf(func_def_361,type,
sK222: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_362,type,
sK223: ( subst > term > subst > $o ) > term ).
thf(func_def_363,type,
sK224: ( subst > term > subst > $o ) > term ).
thf(func_def_364,type,
sK225: ( subst > term > subst > $o ) > subst ).
thf(func_def_365,type,
sK226: ( subst > term > subst > $o ) > subst ).
thf(func_def_366,type,
sK227: ( subst > term > subst > $o ) > subst ).
thf(func_def_367,type,
sK228: ( subst > term > subst > $o ) > subst ).
thf(func_def_368,type,
sK229: ( subst > term > subst > $o ) > term ).
thf(func_def_369,type,
sK230: ( subst > term > subst > $o ) > subst ).
thf(func_def_370,type,
sK231: ( subst > term > subst > $o ) > subst ).
thf(func_def_371,type,
sK232: ( subst > term > subst > $o ) > subst ).
thf(func_def_372,type,
sK233: ( subst > term > subst > $o ) > term ).
thf(func_def_373,type,
sK234: ( subst > term > subst > $o ) > subst ).
thf(func_def_374,type,
sK235: ( subst > term > subst > $o ) > subst ).
thf(func_def_375,type,
sK236: ( subst > term > subst > $o ) > term ).
thf(func_def_376,type,
sK237: ( subst > term > subst > $o ) > subst ).
thf(func_def_377,type,
sK238: ( subst > term > subst > $o ) > term ).
thf(func_def_378,type,
sK239: ( subst > term > subst > $o ) > subst ).
thf(func_def_379,type,
sK240: ( subst > term > subst > $o ) > subst ).
thf(func_def_380,type,
sK241: ( subst > term > subst > $o ) > subst ).
thf(func_def_381,type,
sK242: ( subst > term > subst > $o ) > term ).
thf(func_def_382,type,
sK243: ( subst > term > subst > $o ) > subst ).
thf(func_def_383,type,
sK244: ( subst > term > subst > $o ) > subst ).
thf(func_def_384,type,
sK245: ( subst > term > subst > $o ) > subst ).
thf(func_def_385,type,
sK246: ( subst > term > subst > $o ) > term ).
thf(func_def_386,type,
sK247: ( subst > term > subst > $o ) > subst ).
thf(func_def_387,type,
sK248: ( subst > term > subst > $o ) > subst ).
thf(func_def_388,type,
sK249: ( subst > term > subst > $o ) > term ).
thf(func_def_389,type,
sK250: ( subst > term > subst > $o ) > term ).
thf(func_def_390,type,
sK251: ( subst > term > subst > $o ) > subst ).
thf(func_def_391,type,
sK252: ( subst > term > subst > $o ) > subst ).
thf(func_def_392,type,
sK253: ( subst > term > subst > $o ) > subst ).
thf(func_def_393,type,
sK254: ( subst > term > subst > $o ) > term ).
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 ) > term ).
thf(func_def_398,type,
sK259: ( subst > term > subst > $o ) > subst ).
thf(func_def_399,type,
sK260: ( subst > term > subst > $o ) > term ).
thf(func_def_400,type,
sK261: ( subst > term > subst > $o ) > subst ).
thf(func_def_401,type,
sK262: ( subst > term > subst > $o ) > subst ).
thf(func_def_402,type,
sK263: ( subst > term > subst > $o ) > subst ).
thf(func_def_403,type,
sK264: ( subst > term > subst > $o ) > subst ).
thf(func_def_404,type,
sK265: ( subst > term > subst > $o ) > term ).
thf(func_def_405,type,
sK266: ( subst > term > subst > $o ) > subst ).
thf(func_def_406,type,
sK267: ( subst > term > subst > $o ) > subst ).
thf(func_def_407,type,
sK268: ( subst > term > subst > $o ) > subst ).
thf(func_def_408,type,
sK269: ( subst > term > subst > $o ) > term ).
thf(func_def_409,type,
sK270: ( subst > term > subst > $o ) > subst ).
thf(func_def_410,type,
sK271: ( subst > term > subst > $o ) > subst ).
thf(func_def_411,type,
sK272: ( subst > term > subst > $o ) > term ).
thf(func_def_412,type,
sK273: ( subst > term > subst > $o ) > subst ).
thf(func_def_413,type,
sK274: ( subst > term > subst > $o ) > term ).
thf(func_def_414,type,
sK275: ( subst > term > subst > $o ) > subst ).
thf(func_def_415,type,
sK276: ( subst > term > subst > $o ) > subst ).
thf(func_def_416,type,
sK277: ( subst > term > subst > $o ) > subst ).
thf(func_def_417,type,
sK278: ( subst > term > subst > $o ) > term ).
thf(func_def_418,type,
sK279: ( subst > term > subst > $o ) > subst ).
thf(func_def_419,type,
sK280: ( subst > term > subst > $o ) > subst ).
thf(func_def_420,type,
sK281: ( subst > term > subst > $o ) > subst ).
thf(func_def_421,type,
sK282: ( subst > term > subst > $o ) > term ).
thf(func_def_422,type,
sK283: ( subst > term > subst > $o ) > subst ).
thf(func_def_423,type,
sK284: ( subst > term > subst > $o ) > term ).
thf(func_def_424,type,
sK285: ( subst > term > subst > $o ) > subst ).
thf(func_def_425,type,
sK286: ( subst > term > subst > $o ) > subst ).
thf(func_def_426,type,
sK287: ( subst > term > subst > $o ) > subst ).
thf(func_def_427,type,
sK288: ( subst > term > subst > $o ) > term ).
thf(func_def_428,type,
sK289: ( subst > term > subst > $o ) > subst ).
thf(func_def_429,type,
sK290: ( subst > term > subst > $o ) > subst ).
thf(func_def_430,type,
sK291: ( subst > term > subst > $o ) > term ).
thf(func_def_431,type,
sK292: ( subst > term > subst > $o ) > term ).
thf(func_def_432,type,
sK293: ( subst > term > subst > $o ) > subst ).
thf(func_def_433,type,
sK294: subst > term > subst > $o ).
thf(func_def_434,type,
sK295: ( subst > term > term ) > subst ).
thf(func_def_435,type,
sK296: ( subst > term > term ) > term ).
thf(func_def_436,type,
sK297: ( subst > term > term ) > subst ).
thf(func_def_437,type,
sK298: ( subst > term > term ) > term ).
thf(func_def_438,type,
sK299: ( subst > term > term ) > term ).
thf(func_def_439,type,
sK300: term ).
thf(f3,axiom,
( axvarid
= ( ! [X0: term] :
( ( sub @ X0 @ id )
= X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarid) ).
thf(f57,axiom,
( hoasvar
= ( ^ [X0: subst,X1: term,X2: subst] : ( var @ ( sub @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasvar) ).
thf(f90,axiom,
! [X0: subst > term > subst > $o] :
( ( ! [X4: subst,X2: term,X3: subst,X1: subst] :
( ( X0 @ X1 @ X2 @ ( comp @ X4 @ X3 ) )
=> ( X0 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 ) )
=> ( ! [X2: term,X4: subst,X3: subst,X1: subst] :
( ( X0 @ ( comp @ X1 @ X4 ) @ ( sub @ X2 @ X4 ) @ X3 )
=> ( X0 @ X1 @ X2 @ ( comp @ X4 @ X3 ) ) )
=> ( ! [X2: term] :
( ( hoasvar @ id @ X2 @ id )
=> ( X0 @ id @ X2 @ id ) )
=> ! [X2: term] :
( ( var @ X2 )
=> ( X0 @ id @ X2 @ id ) ) ) ) )
= hoasinduction_lem1 ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem1) ).
thf(f91,axiom,
( axapp
=> ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= hoasinduction_lem1_gthm ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasinduction_lem1_gthm) ).
thf(f114,conjecture,
hoasinduction_lem1_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ hoasinduction_lem1_gthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f116,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f167,plain,
~ hoasinduction_lem1_gthm,
inference(rectify,[],[f115]) ).
thf(f168,plain,
hoasinduction_lem1_gthm != $true,
inference(fool_elimination,[],[f167]) ).
thf(f229,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f280,plain,
( axapp
=> ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= hoasinduction_lem1_gthm ) ),
inference(rectify,[],[f91]) ).
thf(f281,plain,
( hoasinduction_lem1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f280]) ).
thf(f307,plain,
! [X0: subst > term > subst > $o] :
( ( ! [X1: subst,X2: term,X3: subst,X4: subst] :
( ( X0 @ X4 @ X2 @ ( comp @ X1 @ X3 ) )
=> ( X0 @ ( comp @ X4 @ X1 ) @ ( sub @ X2 @ X1 ) @ X3 ) )
=> ( ! [X5: term,X6: subst,X7: subst,X8: subst] :
( ( X0 @ ( comp @ X8 @ X6 ) @ ( sub @ X5 @ X6 ) @ X7 )
=> ( X0 @ X8 @ X5 @ ( comp @ X6 @ X7 ) ) )
=> ( ! [X9: term] :
( ( hoasvar @ id @ X9 @ id )
=> ( X0 @ id @ X9 @ id ) )
=> ! [X10: term] :
( ( var @ X10 )
=> ( X0 @ id @ X10 @ id ) ) ) ) )
= hoasinduction_lem1 ),
inference(rectify,[],[f90]) ).
thf(f308,plain,
( hoasinduction_lem1
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 )
=> ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ id @ Y1 @ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f307]) ).
thf(f319,plain,
hoasinduction_lem1_gthm != $true,
inference(flattening,[],[f168]) ).
thf(f321,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f116]) ).
thf(f340,plain,
( hoasinduction_lem1
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 )
=> ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( hoasvar @ id @ Y1 @ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f308]) ).
thf(f345,plain,
( hoasinduction_lem1_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f281]) ).
thf(f361,plain,
( hoasvar
= ( ^ [Y0: subst,Y1: term,Y2: subst] : ( var @ ( sub @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f229]) ).
thf(f362,plain,
hoasinduction_lem1_gthm != $true,
inference(cnf_transformation,[],[f319]) ).
thf(f370,plain,
( hoasinduction_lem1
= ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 )
=> ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ Y1
@ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f340,f361]) ).
thf(f667,plain,
( ( ( !! @ ( subst > term > subst > $o )
@ ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 )
=> ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ Y1
@ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1 = $true ) ),
inference(iff_proxy_clausification,[],[f370]) ).
thf(f710,plain,
( ( ( ^ [Y0: subst > term > subst > $o] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( !! @ subst
@ ^ [Y4: subst] :
( ( Y0 @ Y1 @ Y3 @ ( comp @ Y4 @ Y2 ) )
=> ( Y0 @ ( comp @ Y1 @ Y4 ) @ ( sub @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y4 @ Y3 ) @ Y2 )
=> ( Y0 @ Y1 @ Y4 @ ( comp @ Y3 @ Y2 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( ^ [Y2: subst,Y3: term,Y4: subst] : ( var @ ( sub @ Y3 @ Y4 ) )
@ id
@ Y1
@ id )
=> ( Y0 @ id @ Y1 @ id ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ id @ Y1 @ id ) ) ) ) ) )
@ sK61 )
= $false )
| ( hoasinduction_lem1 = $true ) ),
inference(sigma_proxy_clausification,[],[f667]) ).
thf(f711,plain,
( ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sK61 @ Y0 @ Y2 @ ( comp @ Y3 @ Y1 ) )
=> ( sK61 @ ( comp @ Y0 @ Y3 ) @ ( sub @ Y2 @ Y3 ) @ Y1 ) ) ) ) ) )
=> ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK61 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 )
=> ( sK61 @ Y0 @ Y3 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK61 @ id @ Y0 @ id ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK61 @ id @ Y0 @ id ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1 = $true ) ),
inference(beta-eta_normalization,[],[f710]) ).
thf(f712,plain,
( ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( sK61 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y3 @ Y2 ) @ Y1 )
=> ( sK61 @ Y0 @ Y3 @ ( comp @ Y2 @ Y1 ) ) ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK61 @ id @ Y0 @ id ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK61 @ id @ Y0 @ id ) ) ) ) )
= $false )
| ( hoasinduction_lem1 = $true ) ),
inference(imp_proxy_clausification,[],[f711]) ).
thf(f723,plain,
( ( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK61 @ id @ Y0 @ id ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK61 @ id @ Y0 @ id ) ) ) )
= $false )
| ( hoasinduction_lem1 = $true ) ),
inference(imp_proxy_clausification,[],[f712]) ).
thf(f734,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK61 @ id @ Y0 @ id ) ) )
= $false )
| ( hoasinduction_lem1 = $true ) ),
inference(imp_proxy_clausification,[],[f723]) ).
thf(f735,plain,
( ( hoasinduction_lem1 = $true )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK61 @ id @ Y0 @ id ) ) ) ) ),
inference(imp_proxy_clausification,[],[f723]) ).
thf(f736,plain,
! [X1: term] :
( ( hoasinduction_lem1 = $true )
| ( $true
= ( ^ [Y0: term] :
( ( var @ ( sub @ Y0 @ id ) )
=> ( sK61 @ id @ Y0 @ id ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f735]) ).
thf(f737,plain,
! [X1: term] :
( ( hoasinduction_lem1 = $true )
| ( $true
= ( ( var @ ( sub @ X1 @ id ) )
=> ( sK61 @ id @ X1 @ id ) ) ) ),
inference(beta-eta_normalization,[],[f736]) ).
thf(f738,plain,
! [X1: term] :
( ( hoasinduction_lem1 = $true )
| ( ( var @ ( sub @ X1 @ id ) )
= $false )
| ( $true
= ( sK61 @ id @ X1 @ id ) ) ),
inference(imp_proxy_clausification,[],[f737]) ).
thf(f739,plain,
( ( hoasinduction_lem1 = $true )
| ( ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK61 @ id @ Y0 @ id ) )
@ sK62 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f734]) ).
thf(f740,plain,
( ( ( ( var @ sK62 )
=> ( sK61 @ id @ sK62 @ id ) )
= $false )
| ( hoasinduction_lem1 = $true ) ),
inference(beta-eta_normalization,[],[f739]) ).
thf(f741,plain,
( ( ( sK61 @ id @ sK62 @ id )
= $false )
| ( hoasinduction_lem1 = $true ) ),
inference(imp_proxy_clausification,[],[f740]) ).
thf(f742,plain,
( ( $true
= ( var @ sK62 ) )
| ( hoasinduction_lem1 = $true ) ),
inference(imp_proxy_clausification,[],[f740]) ).
thf(f847,plain,
( ( axvarid = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ) ),
inference(iff_proxy_clausification,[],[f321]) ).
thf(f848,plain,
! [X1: term] :
( ( axvarid = $false )
| ( $true
= ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f847]) ).
thf(f849,plain,
! [X1: term] :
( ( $true
= ( ( sub @ X1 @ id )
= X1 ) )
| ( axvarid = $false ) ),
inference(beta-eta_normalization,[],[f848]) ).
thf(f850,plain,
! [X1: term] :
( ( axvarid = $false )
| ( ( sub @ X1 @ id )
= X1 ) ),
inference(equality_proxy_clausification,[],[f849]) ).
thf(f1023,plain,
( ( ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1_gthm = $true ) ),
inference(iff_proxy_clausification,[],[f345]) ).
thf(f1059,plain,
( ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1023]) ).
thf(f1061,plain,
( ( ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1059]) ).
thf(f1063,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1061]) ).
thf(f1064,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( axvarid = $true ) ),
inference(imp_proxy_clausification,[],[f1061]) ).
thf(f1065,plain,
( ( hoasinduction_lem1_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
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1063]) ).
thf(f1067,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
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1065]) ).
thf(f1069,plain,
( ( hoasinduction_lem1_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
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1067]) ).
thf(f1071,plain,
( ( ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1069]) ).
thf(f1073,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
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1071]) ).
thf(f1075,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1073]) ).
thf(f1077,plain,
( ( ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1075]) ).
thf(f1079,plain,
( ( ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1077]) ).
thf(f1081,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1079]) ).
thf(f1083,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1081]) ).
thf(f1085,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1083]) ).
thf(f1087,plain,
( ( ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1085]) ).
thf(f1089,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1087]) ).
thf(f1091,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1089]) ).
thf(f1093,plain,
( ( ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1091]) ).
thf(f1095,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1093]) ).
thf(f1097,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1095]) ).
thf(f1099,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1097]) ).
thf(f1101,plain,
( ( ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1099]) ).
thf(f1103,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1101]) ).
thf(f1105,plain,
( ( ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1103]) ).
thf(f1107,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1105]) ).
thf(f1109,plain,
( ( ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) ) )
= $false )
| ( hoasinduction_lem1_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1107]) ).
thf(f1111,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1109]) ).
thf(f1113,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1111]) ).
thf(f1115,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( ( hoasapinj2
=> ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1113]) ).
thf(f1117,plain,
( ( ( hoaslaminj
=> ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) )
= $false )
| ( hoasinduction_lem1_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1115]) ).
thf(f1119,plain,
( ( $false
= ( hoaslamnotap
=> ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) ) ) )
| ( hoasinduction_lem1_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1117]) ).
thf(f1121,plain,
( ( ( hoaslamnotvar
=> ( hoasapnotvar
=> hoasinduction_lem1 ) )
= $false )
| ( hoasinduction_lem1_gthm = $true ) ),
inference(imp_proxy_clausification,[],[f1119]) ).
thf(f1123,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( ( hoasapnotvar
=> hoasinduction_lem1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1121]) ).
thf(f1125,plain,
( ( hoasinduction_lem1_gthm = $true )
| ( hoasinduction_lem1 = $false ) ),
inference(imp_proxy_clausification,[],[f1123]) ).
thf(f2421,definition,
( spl301_70
<=> ( hoasinduction_lem1 = $false ) ),
introduced(definition,[new_symbols(definition,[spl301_70])],[avatar_definition]) ).
thf(f2423,plain,
( ( hoasinduction_lem1 = $false )
| ~ spl301_70 ),
inference(avatar_component_clause,[],[f2421]) ).
thf(f2460,definition,
( spl301_80
<=> ( hoasinduction_lem1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl301_80])],[avatar_definition]) ).
thf(f2462,plain,
( ( hoasinduction_lem1 = $true )
| ~ spl301_80 ),
inference(avatar_component_clause,[],[f2460]) ).
thf(f2469,definition,
( spl301_82
<=> ! [X1: term] :
( ( ( var @ ( sub @ X1 @ id ) )
= $false )
| ( $true
= ( sK61 @ id @ X1 @ id ) ) ) ),
introduced(definition,[new_symbols(definition,[spl301_82])],[avatar_definition]) ).
thf(f2470,plain,
( ! [X1: term] :
( ( $true
= ( sK61 @ id @ X1 @ id ) )
| ( ( var @ ( sub @ X1 @ id ) )
= $false ) )
| ~ spl301_82 ),
inference(avatar_component_clause,[],[f2469]) ).
thf(f2471,plain,
( spl301_82
| spl301_80 ),
inference(avatar_split_clause,[],[f738,f2460,f2469]) ).
thf(f2473,definition,
( spl301_83
<=> ( $true
= ( var @ sK62 ) ) ),
introduced(definition,[new_symbols(definition,[spl301_83])],[avatar_definition]) ).
thf(f2475,plain,
( ( $true
= ( var @ sK62 ) )
| ~ spl301_83 ),
inference(avatar_component_clause,[],[f2473]) ).
thf(f2476,plain,
( spl301_83
| spl301_80 ),
inference(avatar_split_clause,[],[f742,f2460,f2473]) ).
thf(f2478,definition,
( spl301_84
<=> ( ( sK61 @ id @ sK62 @ id )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl301_84])],[avatar_definition]) ).
thf(f2480,plain,
( ( ( sK61 @ id @ sK62 @ id )
= $false )
| ~ spl301_84 ),
inference(avatar_component_clause,[],[f2478]) ).
thf(f2481,plain,
( spl301_80
| spl301_84 ),
inference(avatar_split_clause,[],[f741,f2478,f2460]) ).
thf(f2559,definition,
( spl301_103
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl301_103])],[avatar_definition]) ).
thf(f2560,plain,
( ! [X1: term] :
( ( sub @ X1 @ id )
= X1 )
| ~ spl301_103 ),
inference(avatar_component_clause,[],[f2559]) ).
thf(f2562,definition,
( spl301_104
<=> ( axvarid = $false ) ),
introduced(definition,[new_symbols(definition,[spl301_104])],[avatar_definition]) ).
thf(f2564,plain,
( ( axvarid = $false )
| ~ spl301_104 ),
inference(avatar_component_clause,[],[f2562]) ).
thf(f2565,plain,
( spl301_103
| spl301_104 ),
inference(avatar_split_clause,[],[f850,f2562,f2559]) ).
thf(f2567,definition,
( spl301_105
<=> ( axvarid = $true ) ),
introduced(definition,[new_symbols(definition,[spl301_105])],[avatar_definition]) ).
thf(f2569,plain,
( ( axvarid = $true )
| ~ spl301_105 ),
inference(avatar_component_clause,[],[f2567]) ).
thf(f2841,definition,
( spl301_170
<=> ( hoasinduction_lem1_gthm = $true ) ),
introduced(definition,[new_symbols(definition,[spl301_170])],[avatar_definition]) ).
thf(f2846,plain,
( spl301_105
| spl301_170 ),
inference(avatar_split_clause,[],[f1064,f2841,f2567]) ).
thf(f2942,plain,
( spl301_170
| spl301_70 ),
inference(avatar_split_clause,[],[f1125,f2421,f2841]) ).
thf(f3772,plain,
~ spl301_170,
inference(avatar_split_clause,[],[f362,f2841]) ).
thf(f3931,plain,
( ( $true = $false )
| ~ spl301_104
| ~ spl301_105 ),
inference(superposition,[],[f2569,f2564]) ).
thf(f3935,plain,
( $false
| ~ spl301_104
| ~ spl301_105 ),
inference(trivial_inequality_removal,[],[f3931]) ).
thf(f3936,plain,
( ~ spl301_104
| ~ spl301_105 ),
inference(avatar_contradiction_clause,[],[f3935]) ).
thf(f4047,plain,
( ( $true = $false )
| ~ spl301_70
| ~ spl301_80 ),
inference(superposition,[],[f2462,f2423]) ).
thf(f4051,plain,
( $false
| ~ spl301_70
| ~ spl301_80 ),
inference(trivial_inequality_removal,[],[f4047]) ).
thf(f4052,plain,
( ~ spl301_70
| ~ spl301_80 ),
inference(avatar_contradiction_clause,[],[f4051]) ).
thf(f4054,plain,
( ! [X1: term] :
( ( $true
= ( sK61 @ id @ X1 @ id ) )
| ( ( var @ X1 )
= $false ) )
| ~ spl301_82
| ~ spl301_103 ),
inference(forward_demodulation,[],[f2470,f2560]) ).
thf(f4352,plain,
( ( ( var @ sK62 )
= $false )
| ( $true = $false )
| ~ spl301_82
| ~ spl301_84
| ~ spl301_103 ),
inference(superposition,[],[f4054,f2480]) ).
thf(f4354,plain,
( ( ( var @ sK62 )
= $false )
| ~ spl301_82
| ~ spl301_84
| ~ spl301_103 ),
inference(trivial_inequality_removal,[],[f4352]) ).
thf(f4369,plain,
( ( $true = $false )
| ~ spl301_82
| ~ spl301_83
| ~ spl301_84
| ~ spl301_103 ),
inference(superposition,[],[f4354,f2475]) ).
thf(f4375,plain,
( $false
| ~ spl301_82
| ~ spl301_83
| ~ spl301_84
| ~ spl301_103 ),
inference(trivial_inequality_removal,[],[f4369]) ).
thf(f4376,plain,
( ~ spl301_82
| ~ spl301_83
| ~ spl301_84
| ~ spl301_103 ),
inference(avatar_contradiction_clause,[],[f4375]) ).
cnf(s62,plain,
( spl301_80
| spl301_82 ),
inference(sat_conversion,[],[f2471]) ).
cnf(s63,plain,
( spl301_80
| spl301_83 ),
inference(sat_conversion,[],[f2476]) ).
cnf(s64,plain,
( spl301_80
| spl301_84 ),
inference(sat_conversion,[],[f2481]) ).
cnf(s79,plain,
( spl301_103
| spl301_104 ),
inference(sat_conversion,[],[f2565]) ).
cnf(s112,plain,
( spl301_105
| spl301_170 ),
inference(sat_conversion,[],[f2846]) ).
cnf(s144,plain,
( spl301_70
| spl301_170 ),
inference(sat_conversion,[],[f2942]) ).
cnf(s341,plain,
~ spl301_170,
inference(sat_conversion,[],[f3772]) ).
cnf(s370,plain,
( ~ spl301_104
| ~ spl301_105 ),
inference(sat_conversion,[],[f3936]) ).
cnf(s386,plain,
( ~ spl301_70
| ~ spl301_80 ),
inference(sat_conversion,[],[f4052]) ).
cnf(s407,plain,
( ~ spl301_82
| ~ spl301_83
| ~ spl301_84
| ~ spl301_103 ),
inference(sat_conversion,[],[f4376]) ).
cnf(s409,plain,
spl301_70,
inference(rat,[],[s144,s341]) ).
cnf(s410,plain,
~ spl301_80,
inference(rat,[],[s386,s409]) ).
cnf(s508,plain,
spl301_105,
inference(rat,[],[s112,s341]) ).
cnf(s509,plain,
~ spl301_104,
inference(rat,[],[s370,s508]) ).
cnf(s527,plain,
spl301_103,
inference(rat,[],[s79,s509]) ).
cnf(s529,plain,
spl301_84,
inference(rat,[],[s64,s410]) ).
cnf(s530,plain,
spl301_83,
inference(rat,[],[s63,s410]) ).
cnf(s531,plain,
~ spl301_82,
inference(rat,[],[s407,s527,s529,s530]) ).
cnf(s532,plain,
$false,
inference(rat,[],[s62,s531,s410]) ).
thf(f4377,plain,
$false,
inference(avatar_sat_refutation,[],[s532]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG263^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 % Computer : n003.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Tue Sep 29 17:36:34 UTC 2026
% 0.10/0.28 % CPUTime :
% 0.10/0.28 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.29/0.32 Running higher-order theorem proving
% 0.29/0.35 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.34/0.47 % (2816948)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.34/0.47 % (2816953)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=253356382:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.34/0.47 % (2816959)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.34/0.47 % (2816959)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
% 0.34/0.47 % (2816954)lrs+10_16_si=on:nwc=1.5:random_seed=48008804:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.34/0.47 % (2816957)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2686192071:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.34/0.47 % (2816956)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=1652249524: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)
% 0.34/0.47 % (2816958)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4282730214:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.34/0.47 % (2816959)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=4086077369:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.34/0.47 % (2816955)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4203609548:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.34/0.47 % (2816954)Instruction limit reached!
% 0.34/0.47 % (2816954)------------------------------
% 0.34/0.47 % (2816954)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.47 % (2816954)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.47 % (2816954)CaDiCaL version: 2.1.3
% 0.34/0.47 % (2816954)Termination reason: Instruction limit
% 0.34/0.47 % (2816954)Termination phase: shuffling
% 0.34/0.47 % (2816954)Time elapsed: 0.008 s
% 0.34/0.47 % (2816954)Peak memory usage: 10 MB
% 0.34/0.47 % (2816954)Instructions burned: 18 (million)
% 0.34/0.47 % (2816955)Instruction limit reached!
% 0.34/0.47 % (2816955)------------------------------
% 0.34/0.47 % (2816955)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.47 % (2816955)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.47 % (2816955)CaDiCaL version: 2.1.3
% 0.34/0.47 % (2816955)Termination reason: Instruction limit
% 0.34/0.47 % (2816955)Termination phase: shuffling
% 0.34/0.47 % (2816955)Time elapsed: 0.003 s
% 0.34/0.47 % (2816955)Peak memory usage: 10 MB
% 0.34/0.47 % (2816955)Instructions burned: 3 (million)
% 0.34/0.47 % (2816957)Instruction limit reached!
% 0.34/0.47 % (2816957)------------------------------
% 0.34/0.47 % (2816957)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.47 % (2816957)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.47 % (2816957)CaDiCaL version: 2.1.3
% 0.34/0.47 % (2816957)Termination reason: Instruction limit
% 0.34/0.47 % (2816957)Termination phase: Naming
% 0.34/0.47 % (2816957)Time elapsed: 0.012 s
% 0.34/0.47 % (2816957)Peak memory usage: 11 MB
% 0.34/0.47 % (2816957)Instructions burned: 25 (million)
% 0.34/0.47 % (2816953)Instruction limit reached!
% 0.34/0.47 % (2816953)------------------------------
% 0.34/0.47 % (2816953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.47 % (2816953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.47 % (2816953)CaDiCaL version: 2.1.3
% 0.34/0.47 % (2816953)Termination reason: Instruction limit
% 0.34/0.47 % (2816953)Termination phase: Function definition elimination
% 0.34/0.47 % (2816953)Time elapsed: 0.021 s
% 0.34/0.47 % (2816953)Peak memory usage: 12 MB
% 0.34/0.47 % (2816953)Instructions burned: 88 (million)
% 0.34/0.47 % (2816970)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=92126532:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.34/0.47 % (2816969)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.94/0.49 % (2816967)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2375684460:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.94/0.49 % (2816970)Instruction limit reached!
% 0.94/0.49 % (2816970)------------------------------
% 0.94/0.49 % (2816970)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.49 % (2816970)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.49 % (2816970)CaDiCaL version: 2.1.3
% 0.94/0.49 % (2816970)Termination reason: Instruction limit
% 0.94/0.49 % (2816970)Termination phase: shuffling
% 0.94/0.49 % (2816970)Time elapsed: 0.003 s
% 0.94/0.49 % (2816970)Peak memory usage: 10 MB
% 0.94/0.49 % (2816970)Instructions burned: 15 (million)
% 0.94/0.49 % (2816968)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2694473846:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.94/0.49 % (2816967)Instruction limit reached!
% 0.94/0.49 % (2816967)------------------------------
% 0.94/0.49 % (2816967)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.49 % (2816967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.49 % (2816967)CaDiCaL version: 2.1.3
% 0.94/0.49 % (2816967)Termination reason: Instruction limit
% 0.94/0.49 % (2816967)Termination phase: shuffling
% 0.94/0.49 % (2816967)Time elapsed: 0.001 s
% 0.94/0.49 % (2816967)Peak memory usage: 10 MB
% 0.94/0.49 % (2816967)Instructions burned: 2 (million)
% 0.94/0.49 % (2816969)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4182477798:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.94/0.49 % (2816968)Instruction limit reached!
% 0.94/0.49 % (2816968)------------------------------
% 0.94/0.49 % (2816968)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.49 % (2816968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.49 % (2816968)CaDiCaL version: 2.1.3
% 0.94/0.49 % (2816968)Termination reason: Instruction limit
% 0.94/0.49 % (2816968)Termination phase: shuffling
% 0.94/0.49 % (2816968)Time elapsed: 0.003 s
% 0.94/0.49 % (2816968)Peak memory usage: 10 MB
% 0.94/0.49 % (2816968)Instructions burned: 6 (million)
% 0.94/0.49 % (2816973)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
% 0.94/0.49 % (2816973)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.94/0.49 % (2816969)Instruction limit reached!
% 0.94/0.49 % (2816969)------------------------------
% 0.94/0.49 % (2816969)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.49 % (2816969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.49 % (2816969)CaDiCaL version: 2.1.3
% 0.94/0.49 % (2816969)Termination reason: Instruction limit
% 0.94/0.49 % (2816969)Termination phase: shuffling
% 0.94/0.49 % (2816969)Time elapsed: 0.005 s
% 0.94/0.49 % (2816969)Peak memory usage: 10 MB
% 0.94/0.49 % (2816969)Instructions burned: 12 (million)
% 0.94/0.49 % (2816958)Instruction limit reached!
% 0.94/0.49 % (2816958)------------------------------
% 0.94/0.49 % (2816958)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.49 % (2816958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.49 % (2816958)CaDiCaL version: 2.1.3
% 0.94/0.49 % (2816958)Termination reason: Instruction limit
% 0.94/0.49 % (2816958)Termination phase: Property scanning
% 0.94/0.49 % (2816958)Time elapsed: 0.037 s
% 0.94/0.49 % (2816958)Peak memory usage: 12 MB
% 0.94/0.49 % (2816958)Instructions burned: 83 (million)
% 0.94/0.49 % (2816973)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1854501631:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.94/0.49 % (2816973)Instruction limit reached!
% 0.94/0.49 % (2816973)------------------------------
% 0.94/0.49 % (2816973)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.49 % (2816973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.49 % (2816973)CaDiCaL version: 2.1.3
% 0.94/0.49 % (2816973)Termination reason: Instruction limit
% 0.94/0.53 % (2816973)Termination phase: Property scanning
% 0.94/0.53 % (2816973)Time elapsed: 0.007 s
% 0.94/0.53 % (2816973)Peak memory usage: 10 MB
% 0.94/0.53 % (2816973)Instructions burned: 32 (million)
% 0.94/0.53 % (2816975)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=3314954685:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.94/0.53 % (2816977)lrs+10_1_si=on:cs=on:random_seed=810031700:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.94/0.53 % (2816978)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.94/0.53 % (2816977)Instruction limit reached!
% 0.94/0.53 % (2816977)------------------------------
% 0.94/0.53 % (2816977)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.53 % (2816977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.53 % (2816977)CaDiCaL version: 2.1.3
% 0.94/0.53 % (2816977)Termination reason: Instruction limit
% 0.94/0.53 % (2816977)Termination phase: shuffling
% 0.94/0.53 % (2816977)Time elapsed: 0.004 s
% 0.94/0.53 % (2816977)Peak memory usage: 10 MB
% 0.94/0.53 % (2816977)Instructions burned: 9 (million)
% 0.94/0.53 % (2816978)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=1316313052:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.94/0.53 % (2816980)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3608966520:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.94/0.53 % (2816978)Instruction limit reached!
% 0.94/0.53 % (2816978)------------------------------
% 0.94/0.53 % (2816978)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.53 % (2816978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.53 % (2816978)CaDiCaL version: 2.1.3
% 0.94/0.53 % (2816978)Termination reason: Instruction limit
% 0.94/0.53 % (2816978)Termination phase: shuffling
% 0.94/0.53 % (2816978)Time elapsed: 0.003 s
% 0.94/0.53 % (2816978)Peak memory usage: 10 MB
% 0.94/0.53 % (2816978)Instructions burned: 7 (million)
% 0.94/0.53 % (2816982)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1800356211:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.94/0.53 % (2816959)Instruction limit reached!
% 0.94/0.53 % (2816959)------------------------------
% 0.94/0.53 % (2816959)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.53 % (2816959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.53 % (2816959)CaDiCaL version: 2.1.3
% 0.94/0.53 % (2816959)Termination reason: Instruction limit
% 0.94/0.53 % (2816959)Termination phase: Saturation
% 0.94/0.53 % (2816959)Time elapsed: 0.066 s
% 0.94/0.53 % (2816959)Peak memory usage: 13 MB
% 0.94/0.53 % (2816959)Instructions burned: 157 (million)
% 0.94/0.53 % (2816982)Refutation not found, incomplete strategy
% 0.94/0.53 % (2816982)------------------------------
% 0.94/0.53 % (2816982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.53 % (2816982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.53 % (2816982)CaDiCaL version: 2.1.3
% 0.94/0.53 % (2816982)Termination reason: Refutation not found, incomplete strategy
% 0.94/0.53 % (2816982)Time elapsed: 0.012 s
% 0.94/0.53 % (2816982)Peak memory usage: 12 MB
% 0.94/0.53 % (2816982)Instructions burned: 52 (million)
% 0.94/0.53 % (2816982)------------------------------
% 0.94/0.53 % (2816982)------------------------------
% 0.94/0.53 % (2816985)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2484669039:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.94/0.53 % (2816980)Refutation not found, incomplete strategy
% 0.94/0.53 % (2816980)------------------------------
% 0.94/0.53 % (2816980)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.53 % (2816980)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.53 % (2816980)CaDiCaL version: 2.1.3
% 0.94/0.53 % (2816980)Termination reason: Refutation not found, incomplete strategy
% 0.94/0.53 % (2816980)Time elapsed: 0.017 s
% 0.94/0.53 % (2816980)Peak memory usage: 13 MB
% 0.94/0.53 % (2816980)Instructions burned: 32 (million)
% 0.94/0.57 % (2816980)------------------------------
% 0.94/0.57 % (2816980)------------------------------
% 0.94/0.57 % (2816988)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3180281608:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.94/0.57 % (2816975)Instruction limit reached!
% 0.94/0.57 % (2816975)------------------------------
% 0.94/0.57 % (2816975)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.57 % (2816975)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.57 % (2816975)CaDiCaL version: 2.1.3
% 0.94/0.57 % (2816975)Termination reason: Instruction limit
% 0.94/0.57 % (2816975)Termination phase: Saturation
% 0.94/0.57 % (2816975)Time elapsed: 0.035 s
% 0.94/0.57 % (2816975)Peak memory usage: 12 MB
% 0.94/0.57 % (2816975)Instructions burned: 87 (million)
% 0.94/0.57 % (2816990)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1756608816:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.94/0.57 % (2816988)Instruction limit reached!
% 0.94/0.57 % (2816988)------------------------------
% 0.94/0.57 % (2816988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.57 % (2816988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.57 % (2816988)CaDiCaL version: 2.1.3
% 0.94/0.57 % (2816988)Termination reason: Instruction limit
% 0.94/0.57 % (2816988)Termination phase: shuffling
% 0.94/0.57 % (2816988)Time elapsed: 0.006 s
% 0.94/0.57 % (2816988)Peak memory usage: 10 MB
% 0.94/0.57 % (2816988)Instructions burned: 14 (million)
% 0.94/0.57 % (2816989)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2158425391:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.94/0.57 % (2816985)Instruction limit reached!
% 0.94/0.57 % (2816985)------------------------------
% 0.94/0.57 % (2816985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.57 % (2816985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.57 % (2816985)CaDiCaL version: 2.1.3
% 0.94/0.57 % (2816985)Termination reason: Instruction limit
% 0.94/0.57 % (2816985)Termination phase: Preprocessing 2
% 0.94/0.57 % (2816985)Time elapsed: 0.012 s
% 0.94/0.57 % (2816985)Peak memory usage: 10 MB
% 0.94/0.57 % (2816985)Instructions burned: 26 (million)
% 0.94/0.57 % (2816990)Instruction limit reached!
% 0.94/0.57 % (2816990)------------------------------
% 0.94/0.57 % (2816990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.57 % (2816990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.57 % (2816990)CaDiCaL version: 2.1.3
% 0.94/0.57 % (2816990)Termination reason: Instruction limit
% 0.94/0.57 % (2816990)Termination phase: shuffling
% 0.94/0.57 % (2816990)Time elapsed: 0.003 s
% 0.94/0.57 % (2816990)Peak memory usage: 10 MB
% 0.94/0.57 % (2816990)Instructions burned: 15 (million)
% 0.94/0.57 % (2816992)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=4253396413: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)
% 0.94/0.57 % (2816999)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
% 0.94/0.57 % (2816999)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.94/0.57 % (2816992)Instruction limit reached!
% 0.94/0.57 % (2816992)------------------------------
% 0.94/0.57 % (2816992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.57 % (2816992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.57 % (2816992)CaDiCaL version: 2.1.3
% 0.94/0.57 % (2816992)Termination reason: Instruction limit
% 0.94/0.57 % (2816992)Termination phase: shuffling
% 0.94/0.57 % (2816992)Time elapsed: 0.002 s
% 0.94/0.57 % (2816992)Peak memory usage: 10 MB
% 0.94/0.57 % (2816992)Instructions burned: 3 (million)
% 0.94/0.57 % (2816999)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=769890197:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.94/0.57 % (2816995)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2924157252:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.72/0.61 % (2816999)Instruction limit reached!
% 1.72/0.61 % (2816999)------------------------------
% 1.72/0.61 % (2816999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.61 % (2816999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.61 % (2816999)CaDiCaL version: 2.1.3
% 1.72/0.61 % (2816999)Termination reason: Instruction limit
% 1.72/0.61 % (2816999)Termination phase: shuffling
% 1.72/0.61 % (2816999)Time elapsed: 0.004 s
% 1.72/0.61 % (2816999)Peak memory usage: 10 MB
% 1.72/0.61 % (2816999)Instructions burned: 17 (million)
% 1.72/0.61 % (2816996)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2925463148:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.72/0.61 % (2816998)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2043208723:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.72/0.61 % (2817004)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.72/0.61 % (2816995)Instruction limit reached!
% 1.72/0.61 % (2816995)------------------------------
% 1.72/0.61 % (2816995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.61 % (2816995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.61 % (2816995)CaDiCaL version: 2.1.3
% 1.72/0.61 % (2816995)Termination reason: Instruction limit
% 1.72/0.61 % (2816995)Termination phase: Property scanning
% 1.72/0.61 % (2816995)Time elapsed: 0.011 s
% 1.72/0.61 % (2816995)Peak memory usage: 10 MB
% 1.72/0.61 % (2816995)Instructions burned: 26 (million)
% 1.72/0.61 % (2816996)Instruction limit reached!
% 1.72/0.61 % (2816996)------------------------------
% 1.72/0.61 % (2816996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.61 % (2816996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.61 % (2816996)CaDiCaL version: 2.1.3
% 1.72/0.61 % (2816996)Termination reason: Instruction limit
% 1.72/0.61 % (2816996)Termination phase: Property scanning
% 1.72/0.61 % (2816996)Time elapsed: 0.010 s
% 1.72/0.61 % (2816996)Peak memory usage: 10 MB
% 1.72/0.61 % (2816996)Instructions burned: 24 (million)
% 1.72/0.61 % (2817004)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=2740371092:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.72/0.61 % (2817004)Instruction limit reached!
% 1.72/0.61 % (2817004)------------------------------
% 1.72/0.61 % (2817004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.61 % (2817004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.61 % (2817004)CaDiCaL version: 2.1.3
% 1.72/0.61 % (2817004)Termination reason: Instruction limit
% 1.72/0.61 % (2817004)Termination phase: shuffling
% 1.72/0.61 % (2817004)Time elapsed: 0.004 s
% 1.72/0.61 % (2817004)Peak memory usage: 10 MB
% 1.72/0.61 % (2817004)Instructions burned: 9 (million)
% 1.72/0.61 % (2817007)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=628914146:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.72/0.61 % (2817015)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3554504816:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.72/0.61 % (2817016)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=1531582866:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.72/0.61 % (2816998)Instruction limit reached!
% 1.72/0.61 % (2816998)------------------------------
% 1.72/0.61 % (2816998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.61 % (2816998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.61 % (2816998)CaDiCaL version: 2.1.3
% 1.72/0.61 % (2816998)Termination reason: Instruction limit
% 1.72/0.61 % (2816998)Termination phase: Property scanning
% 1.72/0.61 % (2816998)Time elapsed: 0.027 s
% 1.72/0.61 % (2816998)Peak memory usage: 12 MB
% 1.72/0.61 % (2816998)Instructions burned: 60 (million)
% 1.72/0.61 % (2817007)Instruction limit reached!
% 1.72/0.61 % (2817007)------------------------------
% 1.72/0.61 % (2817007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.61 % (2817007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.61 % (2817007)CaDiCaL version: 2.1.3
% 1.72/0.61 % (2817007)Termination reason: Instruction limit
% 1.72/0.61 % (2817007)Termination phase: Property scanning
% 1.72/0.61 % (2817007)Time elapsed: 0.014 s
% 1.72/0.61 % (2817007)Peak memory usage: 10 MB
% 1.72/0.61 % (2817007)Instructions burned: 33 (million)
% 1.72/0.61 % (2817015)Instruction limit reached!
% 1.72/0.61 % (2817015)------------------------------
% 1.72/0.61 % (2817015)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.61 % (2817015)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.61 % (2817015)CaDiCaL version: 2.1.3
% 1.72/0.61 % (2817015)Termination reason: Instruction limit
% 1.72/0.61 % (2817015)Termination phase: shuffling
% 1.72/0.61 % (2817015)Time elapsed: 0.004 s
% 1.72/0.61 % (2817015)Peak memory usage: 10 MB
% 1.72/0.61 % (2817015)Instructions burned: 9 (million)
% 1.72/0.61 % (2817021)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2559528963:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.72/0.61 % (2817016)Instruction limit reached!
% 1.72/0.61 % (2817016)------------------------------
% 1.72/0.61 % (2817016)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.61 % (2817016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.61 % (2817016)CaDiCaL version: 2.1.3
% 1.72/0.61 % (2817016)Termination reason: Instruction limit
% 1.72/0.61 % (2817016)Termination phase: Property scanning
% 1.72/0.61 % (2817016)Time elapsed: 0.010 s
% 1.72/0.61 % (2817016)Peak memory usage: 10 MB
% 1.72/0.61 % (2817016)Instructions burned: 24 (million)
% 1.72/0.61 % (2817021)Instruction limit reached!
% 1.72/0.61 % (2817021)------------------------------
% 1.72/0.61 % (2817021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.61 % (2817021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.61 % (2817021)CaDiCaL version: 2.1.3
% 1.72/0.61 % (2817021)Termination reason: Instruction limit
% 1.72/0.61 % (2817021)Termination phase: Property scanning
% 1.72/0.61 % (2817021)Time elapsed: 0.009 s
% 1.72/0.61 % (2817021)Peak memory usage: 10 MB
% 1.72/0.61 % (2817021)Instructions burned: 21 (million)
% 1.72/0.61 % (2817031)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1904392585:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.72/0.61 % (2817032)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3008854411:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.72/0.61 % (2817034)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=911439945:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 1.72/0.61 % (2817038)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2025894373:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 1.72/0.61 % (2817042)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.72/0.61 % (2817042)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4027176715:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 1.72/0.61 % (2817042)Instruction limit reached!
% 1.72/0.61 % (2817042)------------------------------
% 1.72/0.61 % (2817042)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.61 % (2817042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.61 % (2817042)CaDiCaL version: 2.1.3
% 1.72/0.61 % (2817042)Termination reason: Instruction limit
% 1.72/0.61 % (2817042)Termination phase: shuffling
% 1.72/0.61 % (2817042)Time elapsed: 0.003 s
% 1.72/0.61 % (2817042)Peak memory usage: 10 MB
% 1.72/0.61 % (2817042)Instructions burned: 7 (million)
% 1.72/0.61 % (2817038)Instruction limit reached!
% 1.72/0.61 % (2817038)------------------------------
% 1.72/0.61 % (2817038)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.61 % (2817038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.61 % (2817038)CaDiCaL version: 2.1.3
% 1.72/0.61 % (2817038)Termination reason: Instruction limit
% 1.72/0.61 % (2817038)Termination phase: Property scanning
% 1.72/0.61 % (2817038)Time elapsed: 0.018 s
% 1.72/0.61 % (2817038)Peak memory usage: 10 MB
% 1.72/0.61 % (2817038)Instructions burned: 42 (million)
% 1.72/0.61 % (2817034)Refutation not found, incomplete strategy
% 1.72/0.61 % (2817034)------------------------------
% 1.72/0.61 % (2817034)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.61 % (2817034)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.61 % (2817034)CaDiCaL version: 2.1.3
% 1.72/0.61 % (2817034)Termination reason: Refutation not found, incomplete strategy
% 1.72/0.61 % (2817034)Time elapsed: 0.030 s
% 1.72/0.61 % (2817034)Peak memory usage: 13 MB
% 1.72/0.61 % (2817034)Instructions burned: 65 (million)
% 1.72/0.61 % (2817034)------------------------------
% 1.72/0.61 % (2817034)------------------------------
% 1.72/0.61 % (2817032)Instruction limit reached!
% 1.72/0.61 % (2817032)------------------------------
% 1.72/0.61 % (2817032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.61 % (2817032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.61 % (2817032)CaDiCaL version: 2.1.3
% 1.72/0.61 % (2817032)Termination reason: Instruction limit
% 1.72/0.61 % (2817032)Termination phase: Saturation
% 1.72/0.61 % (2817032)Time elapsed: 0.034 s
% 1.72/0.61 % (2817032)Peak memory usage: 13 MB
% 1.72/0.61 % (2817032)Instructions burned: 144 (million)
% 1.72/0.61 % (2817059)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1078629523:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.72/0.61 % (2817064)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=2146030429:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 1.72/0.61 % (2817067)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=211289123:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 1.72/0.61 % (2817066)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 1.72/0.61 % (2817067)Instruction limit reached!
% 1.72/0.61 % (2817067)------------------------------
% 1.72/0.61 % (2817067)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.61 % (2817067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.61 % (2817067)CaDiCaL version: 2.1.3
% 1.72/0.61 % (2817067)Termination reason: Instruction limit
% 1.72/0.61 % (2817067)Termination phase: Property scanning
% 1.72/0.61 % (2817067)Time elapsed: 0.005 s
% 1.72/0.61 % (2817067)Peak memory usage: 10 MB
% 1.72/0.61 % (2817067)Instructions burned: 22 (million)
% 1.72/0.61 % (2817066)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=2407642599:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 1.72/0.61 % (2816989) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2816948-2816989"...
% 1.72/0.61 % (2817066)Instruction limit reached!
% 1.72/0.61 % (2817066)------------------------------
% 1.72/0.61 % (2817066)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.61 % (2817066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.61 % (2817066)CaDiCaL version: 2.1.3
% 1.72/0.61 % (2817066)Termination reason: Instruction limit
% 1.72/0.61 % (2817066)Termination phase: shuffling
% 1.72/0.61 % (2817066)Time elapsed: 0.003 s
% 1.72/0.61 % (2817066)Peak memory usage: 10 MB
% 1.72/0.61 % (2817066)Instructions burned: 6 (million)
% 1.72/0.61 % (2817077)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3979915628:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 1.72/0.61 % (2816989)...printing done.
% 1.72/0.61 % (2816989)Refutation found. Thanks to Tanya!
% 1.72/0.61 % SZS status Theorem for theBenchmark
% 1.72/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 1.72/0.61 % (2816989)------------------------------
% 1.72/0.61 % (2816989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.72/0.61 % (2816989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.72/0.61 % (2816989)CaDiCaL version: 2.1.3
% 1.72/0.61 % (2816989)Termination reason: Refutation
% 1.72/0.61 % (2816989)Time elapsed: 0.128 s
% 1.72/0.61 % (2816989)Peak memory usage: 16 MB
% 1.72/0.61 % (2816989)Instructions burned: 283 (million)
% 1.72/0.61 % (2816948)Success in time 0.249 s
% 1.72/0.61 % Vampire exiting
%------------------------------------------------------------------------------