%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG256^2 : 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 : n017.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 07:45:13 AM UTC 2026
% Result : Theorem 2.15s 0.69s
% Output : Refutation 2.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 127 ( 37 unt; 0 typ; 11 def)
% Number of atoms : 533 ( 189 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 682 ( 73 ~; 102 |; 0 &; 403 @)
% ( 11 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 342 ( 338 usr; 183 con; 0-4 aty)
% ( 55 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 164 ( 9 sgn 64 !; 0 ?; 164 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_6,type,
subst: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
one: term ).
thf(func_def_1,type,
ap: term > term > term ).
thf(func_def_2,type,
lam: term > term ).
thf(func_def_3,type,
sub: term > subst > term ).
thf(func_def_4,type,
id: subst ).
thf(func_def_5,type,
sh: subst ).
thf(func_def_6,type,
push: term > subst > subst ).
thf(func_def_7,type,
comp: subst > subst > subst ).
thf(func_def_8,type,
var: term > $o ).
thf(func_def_9,type,
pushprop_lem1v2: $o ).
thf(func_def_10,type,
pushprop_lem1_gthm: $o ).
thf(func_def_11,type,
axmap: $o ).
thf(func_def_12,type,
pushprop_lem0_gthm: $o ).
thf(func_def_13,type,
shinj: $o ).
thf(func_def_14,type,
hoasinduction_lem1v2: $o ).
thf(func_def_15,type,
hoasinduction_lem1v2_gthm: $o ).
thf(func_def_16,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_17,type,
induction2lem: $o ).
thf(func_def_18,type,
hoasinduction_lem3v2_f: $o ).
thf(func_def_19,type,
axvarshift: $o ).
thf(func_def_20,type,
hoasapinj2: $o ).
thf(func_def_21,type,
hoasapnotvar_gthm: $o ).
thf(func_def_22,type,
hoasapinj1: $o ).
thf(func_def_23,type,
ulamvar1: $o ).
thf(func_def_24,type,
induction2lem_lthm: $o ).
thf(func_def_25,type,
hoasinduction_lem3v2_gthm: $o ).
thf(func_def_26,type,
apnotvar: $o ).
thf(func_def_27,type,
pushprop_lthm_orig: $o ).
thf(func_def_28,type,
hoasinduction_lem3v2_f_lthm: $o ).
thf(func_def_29,type,
hoasinduction_lthm: $o ).
thf(func_def_30,type,
hoasinduction_no_psi_cond_lthm: $o ).
thf(func_def_31,type,
hoaslaminj: $o ).
thf(func_def_32,type,
hoasinduction_lem3aaa: $o ).
thf(func_def_33,type,
induction2lem_gthm: $o ).
thf(func_def_34,type,
hoasinduction_lem3aa_lthm: $o ).
thf(func_def_35,type,
hoasinduction_lem3: $o ).
thf(func_def_36,type,
hoasinduction_lem2: $o ).
thf(func_def_37,type,
termmset_lthm: $o ).
thf(func_def_38,type,
hoasinduction_lem1: $o ).
thf(func_def_39,type,
hoaslamnotap_lthm: $o ).
thf(func_def_40,type,
pushprop_lem1v2_lthm: $o ).
thf(func_def_41,type,
hoasapnotvar: $o ).
thf(func_def_42,type,
hoasinduction_lem0: $o ).
thf(func_def_43,type,
hoasinduction: $o ).
thf(func_def_44,type,
hoasinduction_gthm: $o ).
thf(func_def_45,type,
axapp: $o ).
thf(func_def_46,type,
hoaslamnotvar_lthm: $o ).
thf(func_def_47,type,
pushprop_lem3v2_lthm: $o ).
thf(func_def_48,type,
hoasinduction_lem3b_lthm: $o ).
thf(func_def_49,type,
ulamvarind: $o ).
thf(func_def_50,type,
induction: $o ).
thf(func_def_51,type,
hoasinduction_lem3a_lthm: $o ).
thf(func_def_52,type,
termmset_gthm: $o ).
thf(func_def_53,type,
hoasinduction_lem3aa: $o ).
thf(func_def_54,type,
pushprop_lem1v2_gthm: $o ).
thf(func_def_55,type,
hoaslamnotap_gthm: $o ).
thf(func_def_56,type,
hoaslamnotvar_gthm: $o ).
thf(func_def_57,type,
hoasinduction_lem3b_gthm: $o ).
thf(func_def_58,type,
pushprop_lem2v2: $o ).
thf(func_def_59,type,
hoasinduction_lem3a_gthm: $o ).
thf(func_def_60,type,
axclos: $o ).
thf(func_def_61,type,
axassoc: $o ).
thf(func_def_62,type,
hoasinduction_lem2v2: $o ).
thf(func_def_63,type,
pushprop_lthm: $o ).
thf(func_def_64,type,
apinj2: $o ).
thf(func_def_65,type,
apinj1: $o ).
thf(func_def_66,type,
hoasapinj2_lthm: $o ).
thf(func_def_67,type,
hoasinduction_lem3v2a: $o ).
thf(func_def_68,type,
hoasapinj1_lthm: $o ).
thf(func_def_69,type,
hoaslaminj_lthm: $o ).
thf(func_def_70,type,
axvarcons: $o ).
thf(func_def_71,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_72,type,
axscons: $o ).
thf(func_def_73,type,
hoasinduction_lem2v2_gthm: $o ).
thf(func_def_74,type,
axidr: $o ).
thf(func_def_75,type,
pushprop_lem1: $o ).
thf(func_def_76,type,
laminj: $o ).
thf(func_def_77,type,
hoasinduction_lem3_lthm: $o ).
thf(func_def_78,type,
pushprop_lem0: $o ).
thf(func_def_79,type,
pushprop_gthm: $o ).
thf(func_def_80,type,
axabs: $o ).
thf(func_def_81,type,
hoasinduction_lem3v2a_lthm: $o ).
thf(func_def_82,type,
hoasinduction_lem2_lthm: $o ).
thf(func_def_83,type,
hoasapinj2_gthm: $o ).
thf(func_def_84,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_85,type,
hoasinduction_lem1_lthm: $o ).
thf(func_def_86,type,
lamnotap: $o ).
thf(func_def_87,type,
hoasapinj1_gthm: $o ).
thf(func_def_88,type,
hoaslamnotvar: $o ).
thf(func_def_89,type,
axidl: $o ).
thf(func_def_90,type,
hoaslaminj_gthm: $o ).
thf(func_def_91,type,
induction2_lthm: $o ).
thf(func_def_92,type,
hoasinduction_lem0_lthm: $o ).
thf(func_def_93,type,
substmonoid_lthm: $o ).
thf(func_def_94,type,
pushprop: $o ).
thf(func_def_95,type,
hoasinduction_lem3_gthm: $o ).
thf(func_def_96,type,
hoasinduction_lem2_gthm: $o ).
thf(func_def_97,type,
hoasinduction_lem3b: $o ).
thf(func_def_98,type,
substmonoid: $o ).
thf(func_def_99,type,
lamnotvar: $o ).
thf(func_def_100,type,
hoasinduction_lem3a: $o ).
thf(func_def_101,type,
hoasinduction_lem1_gthm: $o ).
thf(func_def_102,type,
hoasinduction_no_psi_cond: $o ).
thf(func_def_103,type,
induction2_gthm: $o ).
thf(func_def_104,type,
pushprop_lem2v2_lthm: $o ).
thf(func_def_105,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_106,type,
hoaslamnotap: $o ).
thf(func_def_107,type,
substmonoid_gthm: $o ).
thf(func_def_108,type,
ulamvarsh: $o ).
thf(func_def_109,type,
induction2: $o ).
thf(func_def_110,type,
pushprop_lem3v2: $o ).
thf(func_def_111,type,
pushprop_lem2v2_gthm: $o ).
thf(func_def_112,type,
pushprop_lem1_lthm: $o ).
thf(func_def_113,type,
hoasinduction_lem3v2: $o ).
thf(func_def_114,type,
axshiftcons: $o ).
thf(func_def_115,type,
termmset: $o ).
thf(func_def_116,type,
pushprop_lem0_lthm: $o ).
thf(func_def_117,type,
hoasapnotvar_lthm: $o ).
thf(func_def_118,type,
hoasinduction_lem3v2_lthm: $o ).
thf(func_def_119,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_120,type,
axvarid: $o ).
thf(func_def_121,type,
hoasinduction_lthm_3: $o ).
thf(func_def_123,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_124,type,
vIMP: $o > $o > $o ).
thf(func_def_125,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_127,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_128,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_129,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_131,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_133,type,
vNOT: $o > $o ).
thf(func_def_134,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_135,type,
vAND: $o > $o > $o ).
thf(func_def_136,type,
vIFF: $o > $o > $o ).
thf(func_def_139,type,
sK0: term ).
thf(func_def_140,type,
sK1: term ).
thf(func_def_141,type,
sK2: term ).
thf(func_def_142,type,
sK3: term ).
thf(func_def_143,type,
sK4: term ).
thf(func_def_144,type,
sK5: subst ).
thf(func_def_145,type,
sK6: ( subst > term > term ) > term ).
thf(func_def_146,type,
sK7: ( subst > term > term ) > subst ).
thf(func_def_147,type,
sK8: ( subst > term > term ) > subst ).
thf(func_def_148,type,
sK9: ( subst > term > term ) > subst ).
thf(func_def_149,type,
sK10: ( subst > term > term ) > subst ).
thf(func_def_150,type,
sK11: ( subst > term > term ) > term ).
thf(func_def_151,type,
sK12: subst > term > term ).
thf(func_def_152,type,
sK13: subst > term > 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: term ).
thf(func_def_157,type,
sK18: term ).
thf(func_def_158,type,
sK19: subst ).
thf(func_def_159,type,
sK20: subst ).
thf(func_def_160,type,
sK21: subst > ( term > $o ) > term ).
thf(func_def_161,type,
sK22: subst ).
thf(func_def_162,type,
sK23: term > $o ).
thf(func_def_163,type,
sK24: term ).
thf(func_def_164,type,
sK25: term ).
thf(func_def_165,type,
sK26: ( subst > term > subst > $o ) > subst ).
thf(func_def_166,type,
sK27: ( subst > term > subst > $o ) > subst ).
thf(func_def_167,type,
sK28: ( subst > term > subst > $o ) > term ).
thf(func_def_168,type,
sK29: ( subst > term > subst > $o ) > term ).
thf(func_def_169,type,
sK30: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_170,type,
sK31: ( subst > term > subst > $o ) > term ).
thf(func_def_171,type,
sK32: ( subst > term > subst > $o ) > subst ).
thf(func_def_172,type,
sK33: ( subst > term > subst > $o ) > subst ).
thf(func_def_173,type,
sK34: ( subst > term > subst > $o ) > subst ).
thf(func_def_174,type,
sK35: ( subst > term > subst > $o ) > term ).
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 ) > term ).
thf(func_def_180,type,
sK41: ( subst > term > subst > $o ) > term ).
thf(func_def_181,type,
sK42: ( subst > term > subst > $o ) > subst ).
thf(func_def_182,type,
sK43: ( subst > term > subst > $o ) > subst ).
thf(func_def_183,type,
sK44: ( subst > term > subst > $o ) > subst ).
thf(func_def_184,type,
sK45: ( subst > term > subst > $o ) > term ).
thf(func_def_185,type,
sK46: ( subst > term > subst > $o ) > subst ).
thf(func_def_186,type,
sK47: ( subst > term > subst > $o ) > subst ).
thf(func_def_187,type,
sK48: ( subst > term > subst > $o ) > term ).
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 ) > term ).
thf(func_def_192,type,
sK53: ( subst > term > subst > $o ) > subst ).
thf(func_def_193,type,
sK54: ( subst > term > subst > $o ) > subst ).
thf(func_def_194,type,
sK55: ( subst > term > subst > $o ) > subst ).
thf(func_def_195,type,
sK56: ( subst > term > subst > $o ) > term ).
thf(func_def_196,type,
sK57: ( subst > term > subst > $o ) > subst ).
thf(func_def_197,type,
sK58: ( subst > term > subst > $o ) > term ).
thf(func_def_198,type,
sK59: ( subst > term > subst > $o ) > term ).
thf(func_def_199,type,
sK60: ( subst > term > subst > $o ) > term ).
thf(func_def_200,type,
sK61: ( subst > term > subst > $o ) > subst ).
thf(func_def_201,type,
sK62: ( subst > term > subst > $o ) > subst ).
thf(func_def_202,type,
sK63: ( subst > term > subst > $o ) > term ).
thf(func_def_203,type,
sK64: ( subst > term > subst > $o ) > subst ).
thf(func_def_204,type,
sK65: ( subst > term > subst > $o ) > term ).
thf(func_def_205,type,
sK66: ( subst > term > subst > $o ) > subst ).
thf(func_def_206,type,
sK67: ( subst > term > subst > $o ) > term ).
thf(func_def_207,type,
sK68: ( subst > term > subst > $o ) > subst ).
thf(func_def_208,type,
sK69: ( subst > term > subst > $o ) > subst ).
thf(func_def_209,type,
sK70: ( subst > term > subst > $o ) > term ).
thf(func_def_210,type,
sK71: ( subst > term > subst > $o ) > term ).
thf(func_def_211,type,
sK72: ( subst > term > subst > $o ) > subst ).
thf(func_def_212,type,
sK73: ( subst > term > subst > $o ) > term ).
thf(func_def_213,type,
sK74: ( subst > term > subst > $o ) > term ).
thf(func_def_214,type,
sK75: ( subst > term > subst > $o ) > subst ).
thf(func_def_215,type,
sK76: ( subst > term > subst > $o ) > subst ).
thf(func_def_216,type,
sK77: ( subst > term > subst > $o ) > subst ).
thf(func_def_217,type,
sK78: ( subst > term > subst > $o ) > term ).
thf(func_def_218,type,
sK79: ( subst > term > subst > $o ) > subst ).
thf(func_def_219,type,
sK80: ( subst > term > subst > $o ) > term ).
thf(func_def_220,type,
sK81: ( subst > term > subst > $o ) > subst ).
thf(func_def_221,type,
sK82: ( subst > term > subst > $o ) > subst ).
thf(func_def_222,type,
sK83: ( subst > term > subst > $o ) > term ).
thf(func_def_223,type,
sK84: ( subst > term > subst > $o ) > subst ).
thf(func_def_224,type,
sK85: ( subst > term > subst > $o ) > term ).
thf(func_def_225,type,
sK86: ( subst > term > subst > $o ) > term ).
thf(func_def_226,type,
sK87: ( subst > term > subst > $o ) > subst ).
thf(func_def_227,type,
sK88: ( subst > term > subst > $o ) > term ).
thf(func_def_228,type,
sK89: ( subst > term > subst > $o ) > subst ).
thf(func_def_229,type,
sK90: ( subst > term > subst > $o ) > subst ).
thf(func_def_230,type,
sK91: ( subst > term > subst > $o ) > term ).
thf(func_def_231,type,
sK92: ( subst > term > subst > $o ) > subst ).
thf(func_def_232,type,
sK93: ( subst > term > subst > $o ) > subst ).
thf(func_def_233,type,
sK94: ( subst > term > subst > $o ) > subst ).
thf(func_def_234,type,
sK95: ( subst > term > subst > $o ) > term ).
thf(func_def_235,type,
sK96: subst > term > subst > $o ).
thf(func_def_236,type,
sK97: ( subst > term > term ) > subst ).
thf(func_def_237,type,
sK98: ( subst > term > term ) > term ).
thf(func_def_238,type,
sK99: ( subst > term > term ) > term ).
thf(func_def_239,type,
sK100: ( subst > term > term ) > subst ).
thf(func_def_240,type,
sK101: ( subst > term > term ) > subst ).
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: term ).
thf(func_def_246,type,
sK107: ( subst > term > subst > $o ) > subst ).
thf(func_def_247,type,
sK108: ( subst > term > subst > $o ) > term ).
thf(func_def_248,type,
sK109: ( subst > term > subst > $o ) > term ).
thf(func_def_249,type,
sK110: ( subst > term > subst > $o ) > subst ).
thf(func_def_250,type,
sK111: ( subst > term > subst > $o ) > term ).
thf(func_def_251,type,
sK112: ( subst > term > subst > $o ) > subst ).
thf(func_def_252,type,
sK113: ( subst > term > subst > $o ) > subst ).
thf(func_def_253,type,
sK114: ( subst > term > subst > $o ) > subst ).
thf(func_def_254,type,
sK115: ( subst > term > subst > $o ) > subst ).
thf(func_def_255,type,
sK116: ( subst > term > subst > $o ) > term ).
thf(func_def_256,type,
sK117: ( subst > term > subst > $o ) > subst ).
thf(func_def_257,type,
sK118: ( subst > term > subst > $o ) > term ).
thf(func_def_258,type,
sK119: ( subst > term > subst > $o ) > subst ).
thf(func_def_259,type,
sK120: ( subst > term > subst > $o ) > subst ).
thf(func_def_260,type,
sK121: ( subst > term > subst > $o ) > term ).
thf(func_def_261,type,
sK122: subst > term > subst > $o ).
thf(func_def_262,type,
sK123: term ).
thf(func_def_263,type,
sK124: term ).
thf(func_def_264,type,
sK125: subst ).
thf(func_def_265,type,
sK126: term ).
thf(func_def_266,type,
sK127: term ).
thf(func_def_267,type,
sK128: term ).
thf(func_def_268,type,
sK129: term ).
thf(func_def_269,type,
sK130: term ).
thf(func_def_270,type,
sK131: term ).
thf(func_def_271,type,
sK132: term ).
thf(func_def_272,type,
sK133: subst ).
thf(func_def_273,type,
sK134: term ).
thf(func_def_274,type,
sK135: term ).
thf(func_def_275,type,
sK136: subst ).
thf(func_def_276,type,
sK137: subst ).
thf(func_def_277,type,
sK138: subst ).
thf(func_def_278,type,
sK139: term ).
thf(func_def_279,type,
sK140: term ).
thf(func_def_280,type,
sK141: term ).
thf(func_def_281,type,
sK142: subst ).
thf(func_def_282,type,
sK143: subst ).
thf(func_def_283,type,
sK144: term ).
thf(func_def_284,type,
sK145: subst ).
thf(func_def_285,type,
sK146: ( term > $o ) > term ).
thf(func_def_286,type,
sK147: ( term > $o ) > term ).
thf(func_def_287,type,
sK148: ( term > $o ) > term ).
thf(func_def_288,type,
sK149: ( term > $o ) > term ).
thf(func_def_289,type,
sK150: ( term > $o ) > term ).
thf(func_def_290,type,
sK151: ( term > $o ) > term ).
thf(func_def_291,type,
sK152: ( term > $o ) > term ).
thf(func_def_292,type,
sK153: term > $o ).
thf(func_def_293,type,
sK154: term > term ).
thf(func_def_294,type,
sK155: term ).
thf(func_def_295,type,
sK156: ( subst > term > term ) > term ).
thf(func_def_296,type,
sK157: ( subst > term > term ) > subst ).
thf(func_def_297,type,
sK158: ( subst > term > term ) > subst ).
thf(func_def_298,type,
sK159: subst > term > term ).
thf(func_def_299,type,
sK160: term ).
thf(func_def_300,type,
sK161: term ).
thf(func_def_301,type,
sK162: ( term > $o ) > term ).
thf(func_def_302,type,
sK163: ( term > $o ) > term ).
thf(func_def_303,type,
sK164: ( term > $o ) > term ).
thf(func_def_304,type,
sK165: subst > ( term > $o ) > term ).
thf(func_def_305,type,
sK166: subst > ( term > $o ) > term ).
thf(func_def_306,type,
sK167: subst > ( term > $o ) > term ).
thf(func_def_307,type,
sK168: ( term > $o ) > term ).
thf(func_def_308,type,
sK169: subst > ( term > $o ) > term ).
thf(func_def_309,type,
sK170: subst > ( term > $o ) > term ).
thf(func_def_310,type,
sK171: term > $o ).
thf(func_def_311,type,
sK172: term > term ).
thf(func_def_312,type,
sK173: term ).
thf(func_def_313,type,
sK174: subst ).
thf(func_def_314,type,
sK175: ( term > $o ) > term ).
thf(func_def_315,type,
sK176: ( term > $o ) > term ).
thf(func_def_316,type,
sK177: ( term > $o ) > term ).
thf(func_def_317,type,
sK178: ( term > $o ) > term ).
thf(func_def_318,type,
sK179: ( term > $o ) > term ).
thf(func_def_319,type,
sK180: term > $o ).
thf(func_def_320,type,
sK181: term ).
thf(func_def_321,type,
sK182: term ).
thf(func_def_322,type,
sK183: term ).
thf(func_def_323,type,
sK184: term ).
thf(func_def_324,type,
sK185: term ).
thf(func_def_325,type,
sK186: term ).
thf(func_def_326,type,
sK187: term ).
thf(func_def_327,type,
sK188: term ).
thf(func_def_328,type,
sK189: term ).
thf(f3,axiom,
! [X0: term] :
( ( ( sub @ X0 @ id )
= X0 )
= axvarid ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axvarid) ).
thf(f16,axiom,
( apinj1
= ( ! [X3: term,X0: term,X1: term,X2: term] :
( ( ( ap @ X0 @ X2 )
= ( ap @ X1 @ X3 ) )
=> ( X0 = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',apinj1) ).
thf(f55,axiom,
( hoasap
= ( ^ [X0: subst,X1: term,X2: subst,X3: term] : ( ap @ ( sub @ X1 @ X2 ) @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasap) ).
thf(f58,axiom,
! [X0: term,X3: term,X1: term,X2: term] :
( ( ( ( hoasap @ id @ X0 @ id @ X2 )
= ( hoasap @ id @ X1 @ id @ X3 ) )
=> ( X0 = X1 ) )
= hoasapinj1 ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasapinj1) ).
thf(f60,axiom,
( axvarid
=> ( ( apinj1
=> hoasapinj1 )
= hoasapinj1_lthm ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasapinj1_lthm) ).
thf(f114,conjecture,
hoasapinj1_lthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ hoasapinj1_lthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f148,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( hoasap @ id @ X2 @ id @ X1 )
= ( hoasap @ id @ X0 @ id @ X3 ) )
=> ( X0 = X2 ) )
= hoasapinj1 ),
inference(rectify,[],[f58]) ).
thf(f149,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y1 @ id @ Y2 )
= ( hoasap @ id @ Y3 @ id @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f148]) ).
thf(f166,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f189,plain,
( apinj1
= ( ! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ap @ X1 @ X3 )
= ( ap @ X2 @ X0 ) )
=> ( X1 = X2 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f190,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y0 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f189]) ).
thf(f193,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f238,plain,
( axvarid
=> ( ( apinj1
=> hoasapinj1 )
= hoasapinj1_lthm ) ),
inference(rectify,[],[f60]) ).
thf(f239,plain,
( hoasapinj1_lthm
= ( axvarid
=> ( apinj1
=> hoasapinj1 ) ) ),
inference(fool_elimination,[],[f238]) ).
thf(f255,plain,
~ hoasapinj1_lthm,
inference(rectify,[],[f115]) ).
thf(f256,plain,
hoasapinj1_lthm != $true,
inference(fool_elimination,[],[f255]) ).
thf(f321,plain,
hoasapinj1_lthm != $true,
inference(flattening,[],[f256]) ).
thf(f331,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y1 @ id @ Y2 )
= ( hoasap @ id @ Y3 @ id @ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f149]) ).
thf(f335,plain,
( hoasapinj1_lthm
= ( axvarid
=> ( apinj1
=> hoasapinj1 ) ) ),
inference(cnf_transformation,[],[f239]) ).
thf(f342,plain,
( axvarid
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) ) ),
inference(cnf_transformation,[],[f166]) ).
thf(f345,plain,
hoasapinj1_lthm != $true,
inference(cnf_transformation,[],[f321]) ).
thf(f347,plain,
( apinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y0 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f190]) ).
thf(f349,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(cnf_transformation,[],[f193]) ).
thf(f356,plain,
( hoasapinj1
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f331,f349,f349]) ).
thf(f359,plain,
( ( hoasapinj1 = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f356]) ).
thf(f372,plain,
( ( hoasapinj1 = $true )
| ( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y0 ) )
=> ( Y3 = Y1 ) ) ) ) )
@ sK0 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f359]) ).
thf(f373,plain,
( ( hoasapinj1 = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y1 )
= ( ap @ ( sub @ Y2 @ id ) @ sK0 ) )
=> ( Y2 = Y0 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f372]) ).
thf(f374,plain,
( ( hoasapinj1 = $true )
| ( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ Y1 )
= ( ap @ ( sub @ Y2 @ id ) @ sK0 ) )
=> ( Y2 = Y0 ) ) ) )
@ sK1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f373]) ).
thf(f375,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( ap @ ( sub @ sK1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ sK0 ) )
=> ( Y1 = sK1 ) ) ) )
= $false )
| ( hoasapinj1 = $true ) ),
inference(beta-eta_normalization,[],[f374]) ).
thf(f376,plain,
( ( hoasapinj1 = $true )
| ( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( ap @ ( sub @ sK1 @ id ) @ Y0 )
= ( ap @ ( sub @ Y1 @ id ) @ sK0 ) )
=> ( Y1 = sK1 ) ) )
@ sK2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f375]) ).
thf(f377,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( ( ap @ ( sub @ sK1 @ id ) @ sK2 )
= ( ap @ ( sub @ Y0 @ id ) @ sK0 ) )
=> ( Y0 = sK1 ) ) )
= $false )
| ( hoasapinj1 = $true ) ),
inference(beta-eta_normalization,[],[f376]) ).
thf(f378,plain,
( ( ( ^ [Y0: term] :
( ( ( ap @ ( sub @ sK1 @ id ) @ sK2 )
= ( ap @ ( sub @ Y0 @ id ) @ sK0 ) )
=> ( Y0 = sK1 ) )
@ sK3 )
= $false )
| ( hoasapinj1 = $true ) ),
inference(sigma_proxy_clausification,[],[f377]) ).
thf(f379,plain,
( ( ( ( ( ap @ ( sub @ sK1 @ id ) @ sK2 )
= ( ap @ ( sub @ sK3 @ id ) @ sK0 ) )
=> ( sK3 = sK1 ) )
= $false )
| ( hoasapinj1 = $true ) ),
inference(beta-eta_normalization,[],[f378]) ).
thf(f380,plain,
( ( hoasapinj1 = $true )
| ( ( sK3 = sK1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f379]) ).
thf(f381,plain,
( ( ( ( ap @ ( sub @ sK1 @ id ) @ sK2 )
= ( ap @ ( sub @ sK3 @ id ) @ sK0 ) )
= $true )
| ( hoasapinj1 = $true ) ),
inference(imp_proxy_clausification,[],[f379]) ).
thf(f382,plain,
( ( ( ap @ ( sub @ sK3 @ id ) @ sK0 )
= ( ap @ ( sub @ sK1 @ id ) @ sK2 ) )
| ( hoasapinj1 = $true ) ),
inference(equality_proxy_clausification,[],[f381]) ).
thf(f383,plain,
( ( sK1 != sK3 )
| ( hoasapinj1 = $true ) ),
inference(equality_proxy_clausification,[],[f380]) ).
thf(f1026,plain,
( ( ( axvarid
=> ( apinj1
=> hoasapinj1 ) )
= $false )
| ( hoasapinj1_lthm = $true ) ),
inference(iff_proxy_clausification,[],[f335]) ).
thf(f1030,plain,
( ( ( apinj1
=> hoasapinj1 )
= $false )
| ( hoasapinj1_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f1026]) ).
thf(f1031,plain,
( ( hoasapinj1_lthm = $true )
| ( axvarid = $true ) ),
inference(imp_proxy_clausification,[],[f1026]) ).
thf(f1032,plain,
( ( hoasapinj1_lthm = $true )
| ( hoasapinj1 = $false ) ),
inference(imp_proxy_clausification,[],[f1030]) ).
thf(f1033,plain,
( ( hoasapinj1_lthm = $true )
| ( apinj1 = $true ) ),
inference(imp_proxy_clausification,[],[f1030]) ).
thf(f1035,plain,
( ( apinj1 = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y0 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f347]) ).
thf(f1036,plain,
! [X1: term] :
( ( $true
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y0 )
= ( ap @ Y1 @ Y3 ) )
=> ( Y2 = Y1 ) ) ) ) )
@ X1 ) )
| ( apinj1 = $false ) ),
inference(pi_proxy_clausification,[],[f1035]) ).
thf(f1037,plain,
! [X1: term] :
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ( ap @ Y1 @ X1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y1 = Y0 ) ) ) ) ) )
| ( apinj1 = $false ) ),
inference(beta-eta_normalization,[],[f1036]) ).
thf(f1038,plain,
! [X2: term,X1: term] :
( ( apinj1 = $false )
| ( $true
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ( ap @ Y1 @ X1 )
= ( ap @ Y0 @ Y2 ) )
=> ( Y1 = Y0 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1037]) ).
thf(f1039,plain,
! [X2: term,X1: term] :
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( ap @ Y0 @ X1 )
= ( ap @ X2 @ Y1 ) )
=> ( Y0 = X2 ) ) ) ) )
| ( apinj1 = $false ) ),
inference(beta-eta_normalization,[],[f1038]) ).
thf(f1040,plain,
! [X2: term,X3: term,X1: term] :
( ( apinj1 = $false )
| ( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( ap @ Y0 @ X1 )
= ( ap @ X2 @ Y1 ) )
=> ( Y0 = X2 ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1039]) ).
thf(f1041,plain,
! [X2: term,X3: term,X1: term] :
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( ( ap @ X3 @ X1 )
= ( ap @ X2 @ Y0 ) )
=> ( X3 = X2 ) ) ) )
| ( apinj1 = $false ) ),
inference(beta-eta_normalization,[],[f1040]) ).
thf(f1042,plain,
! [X2: term,X3: term,X1: term,X4: term] :
( ( ( ^ [Y0: term] :
( ( ( ap @ X3 @ X1 )
= ( ap @ X2 @ Y0 ) )
=> ( X3 = X2 ) )
@ X4 )
= $true )
| ( apinj1 = $false ) ),
inference(pi_proxy_clausification,[],[f1041]) ).
thf(f1043,plain,
! [X2: term,X3: term,X1: term,X4: term] :
( ( ( ( ( ap @ X3 @ X1 )
= ( ap @ X2 @ X4 ) )
=> ( X3 = X2 ) )
= $true )
| ( apinj1 = $false ) ),
inference(beta-eta_normalization,[],[f1042]) ).
thf(f1044,plain,
! [X2: term,X3: term,X1: term,X4: term] :
( ( ( ( ap @ X3 @ X1 )
= ( ap @ X2 @ X4 ) )
= $false )
| ( apinj1 = $false )
| ( $true
= ( X3 = X2 ) ) ),
inference(imp_proxy_clausification,[],[f1043]) ).
thf(f1045,plain,
! [X2: term,X3: term,X1: term,X4: term] :
( ( ( ap @ X3 @ X1 )
!= ( ap @ X2 @ X4 ) )
| ( apinj1 = $false )
| ( $true
= ( X3 = X2 ) ) ),
inference(equality_proxy_clausification,[],[f1044]) ).
thf(f1046,plain,
! [X2: term,X3: term,X1: term,X4: term] :
( ( X2 = X3 )
| ( ( ap @ X3 @ X1 )
!= ( ap @ X2 @ X4 ) )
| ( apinj1 = $false ) ),
inference(equality_proxy_clausification,[],[f1045]) ).
thf(f1092,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 ) )
= $true )
| ( axvarid = $false ) ),
inference(iff_proxy_clausification,[],[f342]) ).
thf(f1093,plain,
! [X1: term] :
( ( axvarid = $false )
| ( $true
= ( ^ [Y0: term] :
( ( sub @ Y0 @ id )
= Y0 )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1092]) ).
thf(f1094,plain,
! [X1: term] :
( ( axvarid = $false )
| ( ( ( sub @ X1 @ id )
= X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f1093]) ).
thf(f1095,plain,
! [X1: term] :
( ( ( sub @ X1 @ id )
= X1 )
| ( axvarid = $false ) ),
inference(equality_proxy_clausification,[],[f1094]) ).
thf(f1439,definition,
( spl190_1
<=> ( hoasapinj1 = $false ) ),
introduced(definition,[new_symbols(definition,[spl190_1])],[avatar_definition]) ).
thf(f1441,plain,
( ( hoasapinj1 = $false )
| ~ spl190_1 ),
inference(avatar_component_clause,[],[f1439]) ).
thf(f1447,definition,
( spl190_3
<=> ( ( ap @ ( sub @ sK3 @ id ) @ sK0 )
= ( ap @ ( sub @ sK1 @ id ) @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl190_3])],[avatar_definition]) ).
thf(f1449,plain,
( ( ( ap @ ( sub @ sK3 @ id ) @ sK0 )
= ( ap @ ( sub @ sK1 @ id ) @ sK2 ) )
| ~ spl190_3 ),
inference(avatar_component_clause,[],[f1447]) ).
thf(f1451,definition,
( spl190_4
<=> ( hoasapinj1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl190_4])],[avatar_definition]) ).
thf(f1453,plain,
( ( hoasapinj1 = $true )
| ~ spl190_4 ),
inference(avatar_component_clause,[],[f1451]) ).
thf(f1454,plain,
( spl190_3
| spl190_4 ),
inference(avatar_split_clause,[],[f382,f1451,f1447]) ).
thf(f1456,definition,
( spl190_5
<=> ( sK1 = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl190_5])],[avatar_definition]) ).
thf(f1458,plain,
( ( sK1 != sK3 )
| spl190_5 ),
inference(avatar_component_clause,[],[f1456]) ).
thf(f1459,plain,
( ~ spl190_5
| spl190_4 ),
inference(avatar_split_clause,[],[f383,f1451,f1456]) ).
thf(f2077,definition,
( spl190_155
<=> ( apinj1 = $false ) ),
introduced(definition,[new_symbols(definition,[spl190_155])],[avatar_definition]) ).
thf(f2079,plain,
( ( apinj1 = $false )
| ~ spl190_155 ),
inference(avatar_component_clause,[],[f2077]) ).
thf(f2085,definition,
( spl190_157
<=> ( axvarid = $false ) ),
introduced(definition,[new_symbols(definition,[spl190_157])],[avatar_definition]) ).
thf(f2087,plain,
( ( axvarid = $false )
| ~ spl190_157 ),
inference(avatar_component_clause,[],[f2085]) ).
thf(f2090,definition,
( spl190_158
<=> ( hoasapinj1_lthm = $true ) ),
introduced(definition,[new_symbols(definition,[spl190_158])],[avatar_definition]) ).
thf(f2094,definition,
( spl190_159
<=> ( axvarid = $true ) ),
introduced(definition,[new_symbols(definition,[spl190_159])],[avatar_definition]) ).
thf(f2096,plain,
( ( axvarid = $true )
| ~ spl190_159 ),
inference(avatar_component_clause,[],[f2094]) ).
thf(f2097,plain,
( spl190_158
| spl190_159 ),
inference(avatar_split_clause,[],[f1031,f2094,f2090]) ).
thf(f2099,definition,
( spl190_160
<=> ( apinj1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl190_160])],[avatar_definition]) ).
thf(f2101,plain,
( ( apinj1 = $true )
| ~ spl190_160 ),
inference(avatar_component_clause,[],[f2099]) ).
thf(f2102,plain,
( spl190_158
| spl190_160 ),
inference(avatar_split_clause,[],[f1033,f2099,f2090]) ).
thf(f2103,plain,
( spl190_158
| spl190_1 ),
inference(avatar_split_clause,[],[f1032,f1439,f2090]) ).
thf(f2105,definition,
( spl190_161
<=> ! [X4: term,X3: term,X2: term,X1: term] :
( ( X2 = X3 )
| ( ( ap @ X3 @ X1 )
!= ( ap @ X2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl190_161])],[avatar_definition]) ).
thf(f2106,plain,
( ! [X2: term,X3: term,X1: term,X4: term] :
( ( ( ap @ X3 @ X1 )
!= ( ap @ X2 @ X4 ) )
| ( X2 = X3 ) )
| ~ spl190_161 ),
inference(avatar_component_clause,[],[f2105]) ).
thf(f2107,plain,
( spl190_155
| spl190_161 ),
inference(avatar_split_clause,[],[f1046,f2105,f2077]) ).
thf(f2153,definition,
( spl190_172
<=> ! [X1: term] :
( ( sub @ X1 @ id )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl190_172])],[avatar_definition]) ).
thf(f2154,plain,
( ! [X1: term] :
( ( sub @ X1 @ id )
= X1 )
| ~ spl190_172 ),
inference(avatar_component_clause,[],[f2153]) ).
thf(f2155,plain,
( spl190_172
| spl190_157 ),
inference(avatar_split_clause,[],[f1095,f2085,f2153]) ).
thf(f2504,plain,
~ spl190_158,
inference(avatar_split_clause,[],[f345,f2090]) ).
thf(f2505,plain,
( ( $true = $false )
| ~ spl190_157
| ~ spl190_159 ),
inference(forward_demodulation,[],[f2096,f2087]) ).
thf(f2506,plain,
( $false
| ~ spl190_157
| ~ spl190_159 ),
inference(trivial_inequality_removal,[],[f2505]) ).
thf(f2507,plain,
( ~ spl190_157
| ~ spl190_159 ),
inference(avatar_contradiction_clause,[],[f2506]) ).
thf(f2509,plain,
( ( $true = $false )
| ~ spl190_155
| ~ spl190_160 ),
inference(forward_demodulation,[],[f2101,f2079]) ).
thf(f2510,plain,
( $false
| ~ spl190_155
| ~ spl190_160 ),
inference(trivial_inequality_removal,[],[f2509]) ).
thf(f2511,plain,
( ~ spl190_155
| ~ spl190_160 ),
inference(avatar_contradiction_clause,[],[f2510]) ).
thf(f2562,plain,
( ( $true = $false )
| ~ spl190_1
| ~ spl190_4 ),
inference(forward_demodulation,[],[f1453,f1441]) ).
thf(f2563,plain,
( $false
| ~ spl190_1
| ~ spl190_4 ),
inference(trivial_inequality_removal,[],[f2562]) ).
thf(f2564,plain,
( ~ spl190_1
| ~ spl190_4 ),
inference(avatar_contradiction_clause,[],[f2563]) ).
thf(f2701,plain,
( ( ( ap @ ( sub @ sK3 @ id ) @ sK0 )
= ( ap @ sK1 @ sK2 ) )
| ~ spl190_3
| ~ spl190_172 ),
inference(forward_demodulation,[],[f1449,f2154]) ).
thf(f2702,plain,
( ( ( ap @ sK3 @ sK0 )
= ( ap @ sK1 @ sK2 ) )
| ~ spl190_3
| ~ spl190_172 ),
inference(forward_demodulation,[],[f2701,f2154]) ).
thf(f2710,plain,
( ! [X0: term,X1: term] :
( ( ( ap @ X0 @ X1 )
!= ( ap @ sK1 @ sK2 ) )
| ( sK3 = X0 ) )
| ~ spl190_3
| ~ spl190_161
| ~ spl190_172 ),
inference(superposition,[],[f2106,f2702]) ).
thf(f2720,plain,
( ( sK1 = sK3 )
| ~ spl190_3
| ~ spl190_161
| ~ spl190_172 ),
inference(equality_resolution,[],[f2710]) ).
thf(f2721,plain,
( $false
| ~ spl190_3
| spl190_5
| ~ spl190_161
| ~ spl190_172 ),
inference(forward_subsumption_resolution,[],[f2720,f1458]) ).
thf(f2722,plain,
( ~ spl190_3
| spl190_5
| ~ spl190_161
| ~ spl190_172 ),
inference(avatar_contradiction_clause,[],[f2721]) ).
cnf(s2,plain,
( spl190_3
| spl190_4 ),
inference(sat_conversion,[],[f1454]) ).
cnf(s3,plain,
( spl190_4
| ~ spl190_5 ),
inference(sat_conversion,[],[f1459]) ).
cnf(s131,plain,
( spl190_158
| spl190_159 ),
inference(sat_conversion,[],[f2097]) ).
cnf(s132,plain,
( spl190_158
| spl190_160 ),
inference(sat_conversion,[],[f2102]) ).
cnf(s133,plain,
( spl190_1
| spl190_158 ),
inference(sat_conversion,[],[f2103]) ).
cnf(s134,plain,
( spl190_155
| spl190_161 ),
inference(sat_conversion,[],[f2107]) ).
cnf(s141,plain,
( spl190_157
| spl190_172 ),
inference(sat_conversion,[],[f2155]) ).
cnf(s208,plain,
~ spl190_158,
inference(sat_conversion,[],[f2504]) ).
cnf(s209,plain,
( ~ spl190_157
| ~ spl190_159 ),
inference(sat_conversion,[],[f2507]) ).
cnf(s210,plain,
( ~ spl190_155
| ~ spl190_160 ),
inference(sat_conversion,[],[f2511]) ).
cnf(s214,plain,
( ~ spl190_1
| ~ spl190_4 ),
inference(sat_conversion,[],[f2564]) ).
cnf(s234,plain,
( ~ spl190_3
| spl190_5
| ~ spl190_161
| ~ spl190_172 ),
inference(sat_conversion,[],[f2722]) ).
cnf(s236,plain,
spl190_1,
inference(rat,[],[s133,s208]) ).
cnf(s237,plain,
~ spl190_4,
inference(rat,[],[s214,s236]) ).
cnf(s238,plain,
spl190_160,
inference(rat,[],[s132,s208]) ).
cnf(s239,plain,
~ spl190_155,
inference(rat,[],[s210,s238]) ).
cnf(s240,plain,
spl190_161,
inference(rat,[],[s134,s239]) ).
cnf(s241,plain,
spl190_159,
inference(rat,[],[s131,s208]) ).
cnf(s242,plain,
~ spl190_157,
inference(rat,[],[s209,s241]) ).
cnf(s243,plain,
spl190_172,
inference(rat,[],[s141,s242]) ).
cnf(s245,plain,
~ spl190_5,
inference(rat,[],[s3,s237]) ).
cnf(s246,plain,
~ spl190_3,
inference(rat,[],[s234,s243,s240,s245]) ).
cnf(s247,plain,
$false,
inference(rat,[],[s2,s237,s246]) ).
thf(f2723,plain,
$false,
inference(avatar_sat_refutation,[],[s247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG256^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n017.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 17:28:22 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 Running higher-order theorem proving
% 0.26/0.34 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
% 0.95/0.54 % (642456)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.95/0.54 % (642464)lrs+10_16_si=on:nwc=1.5:random_seed=2554302574:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.95/0.54 % (642463)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4133776139:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.95/0.54 % (642464)Instruction limit reached!
% 0.95/0.54 % (642464)------------------------------
% 0.95/0.54 % (642464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.54 % (642469)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.95/0.54 % (642464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.54 % (642469)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
% 0.95/0.54 % (642464)CaDiCaL version: 2.1.3
% 0.95/0.54 % (642464)Termination reason: Instruction limit
% 0.95/0.54 % (642464)Termination phase: shuffling
% 0.95/0.54 % (642464)Time elapsed: 0.008 s
% 0.95/0.54 % (642464)Peak memory usage: 10 MB
% 0.95/0.54 % (642464)Instructions burned: 19 (million)
% 0.95/0.54 % (642465)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1965492331:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.95/0.54 % (642466)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=2957536065: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)
% 0.95/0.54 % (642468)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2537704442:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.95/0.54 % (642467)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4144790944:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.95/0.54 % (642469)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=2384638124:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.95/0.54 % (642465)Instruction limit reached!
% 0.95/0.54 % (642465)------------------------------
% 0.95/0.54 % (642465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.54 % (642465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.54 % (642465)CaDiCaL version: 2.1.3
% 0.95/0.54 % (642465)Termination reason: Instruction limit
% 0.95/0.54 % (642465)Termination phase: shuffling
% 0.95/0.54 % (642465)Time elapsed: 0.003 s
% 0.95/0.54 % (642465)Peak memory usage: 10 MB
% 0.95/0.54 % (642465)Instructions burned: 3 (million)
% 0.95/0.54 % (642472)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1907761760:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.95/0.54 % (642472)Instruction limit reached!
% 0.95/0.54 % (642472)------------------------------
% 0.95/0.54 % (642472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.54 % (642472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.54 % (642472)CaDiCaL version: 2.1.3
% 0.95/0.54 % (642472)Termination reason: Instruction limit
% 0.95/0.54 % (642472)Termination phase: shuffling
% 0.95/0.54 % (642472)Time elapsed: 0.002 s
% 0.95/0.54 % (642472)Peak memory usage: 10 MB
% 0.95/0.54 % (642472)Instructions burned: 3 (million)
% 0.95/0.54 % (642467)Instruction limit reached!
% 0.95/0.54 % (642467)------------------------------
% 0.95/0.54 % (642467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.95/0.54 % (642467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.95/0.54 % (642467)CaDiCaL version: 2.1.3
% 0.95/0.54 % (642467)Termination reason: Instruction limit
% 0.95/0.54 % (642467)Termination phase: Preprocessing 2
% 0.95/0.54 % (642467)Time elapsed: 0.020 s
% 0.95/0.54 % (642467)Peak memory usage: 11 MB
% 0.95/0.54 % (642467)Instructions burned: 24 (million)
% 0.95/0.54 % (642478)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2571489299:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.95/0.54 % (642478)Instruction limit reached!
% 1.70/0.59 % (642478)------------------------------
% 1.70/0.59 % (642478)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.59 % (642478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.59 % (642478)CaDiCaL version: 2.1.3
% 1.70/0.59 % (642478)Termination reason: Instruction limit
% 1.70/0.59 % (642478)Termination phase: shuffling
% 1.70/0.59 % (642478)Time elapsed: 0.005 s
% 1.70/0.59 % (642478)Peak memory usage: 10 MB
% 1.70/0.59 % (642478)Instructions burned: 6 (million)
% 1.70/0.59 % (642481)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=908360819:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.70/0.59 % (642480)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.70/0.59 % (642481)Instruction limit reached!
% 1.70/0.59 % (642481)------------------------------
% 1.70/0.59 % (642481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.59 % (642481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.59 % (642481)CaDiCaL version: 2.1.3
% 1.70/0.59 % (642481)Termination reason: Instruction limit
% 1.70/0.59 % (642481)Termination phase: shuffling
% 1.70/0.59 % (642481)Time elapsed: 0.006 s
% 1.70/0.59 % (642481)Peak memory usage: 10 MB
% 1.70/0.59 % (642481)Instructions burned: 13 (million)
% 1.70/0.59 % (642480)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3946751486:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.70/0.59 % (642480)Instruction limit reached!
% 1.70/0.59 % (642480)------------------------------
% 1.70/0.59 % (642480)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.59 % (642480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.59 % (642480)CaDiCaL version: 2.1.3
% 1.70/0.59 % (642480)Termination reason: Instruction limit
% 1.70/0.59 % (642480)Termination phase: shuffling
% 1.70/0.59 % (642480)Time elapsed: 0.007 s
% 1.70/0.59 % (642480)Peak memory usage: 9 MB
% 1.70/0.59 % (642480)Instructions burned: 7 (million)
% 1.70/0.59 % (642463)Instruction limit reached!
% 1.70/0.59 % (642463)------------------------------
% 1.70/0.59 % (642463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.59 % (642463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.59 % (642463)CaDiCaL version: 2.1.3
% 1.70/0.59 % (642463)Termination reason: Instruction limit
% 1.70/0.59 % (642463)Termination phase: Function definition elimination
% 1.70/0.59 % (642463)Time elapsed: 0.069 s
% 1.70/0.59 % (642463)Peak memory usage: 12 MB
% 1.70/0.59 % (642463)Instructions burned: 87 (million)
% 1.70/0.59 % (642468)Instruction limit reached!
% 1.70/0.59 % (642468)------------------------------
% 1.70/0.59 % (642468)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.59 % (642468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.59 % (642468)CaDiCaL version: 2.1.3
% 1.70/0.59 % (642468)Termination reason: Instruction limit
% 1.70/0.59 % (642468)Termination phase: Property scanning
% 1.70/0.59 % (642468)Time elapsed: 0.063 s
% 1.70/0.59 % (642468)Peak memory usage: 12 MB
% 1.70/0.59 % (642468)Instructions burned: 75 (million)
% 1.70/0.59 % (642485)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=3573213138:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 1.70/0.59 % (642483)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.70/0.59 % (642483)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.70/0.59 % (642483)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2365482523:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.70/0.59 % (642488)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.70/0.59 % (642487)lrs+10_1_si=on:cs=on:random_seed=1114350568:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.70/0.63 % (642488)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=913967226:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.70/0.63 % (642488)Instruction limit reached!
% 1.70/0.63 % (642488)------------------------------
% 1.70/0.63 % (642488)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.63 % (642488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.63 % (642488)CaDiCaL version: 2.1.3
% 1.70/0.63 % (642488)Termination reason: Instruction limit
% 1.70/0.63 % (642488)Termination phase: shuffling
% 1.70/0.63 % (642488)Time elapsed: 0.003 s
% 1.70/0.63 % (642488)Peak memory usage: 10 MB
% 1.70/0.63 % (642488)Instructions burned: 3 (million)
% 1.70/0.63 % (642483)Instruction limit reached!
% 1.70/0.63 % (642483)------------------------------
% 1.70/0.63 % (642483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.63 % (642483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.63 % (642483)CaDiCaL version: 2.1.3
% 1.70/0.63 % (642483)Termination reason: Instruction limit
% 1.70/0.63 % (642483)Termination phase: Property scanning
% 1.70/0.63 % (642483)Time elapsed: 0.023 s
% 1.70/0.63 % (642489)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2196234821:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.70/0.63 % (642483)Peak memory usage: 10 MB
% 1.70/0.63 % (642483)Instructions burned: 29 (million)
% 1.70/0.63 % (642487)Instruction limit reached!
% 1.70/0.63 % (642487)------------------------------
% 1.70/0.63 % (642487)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.63 % (642487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.63 % (642487)CaDiCaL version: 2.1.3
% 1.70/0.63 % (642487)Termination reason: Instruction limit
% 1.70/0.63 % (642487)Termination phase: shuffling
% 1.70/0.63 % (642487)Time elapsed: 0.008 s
% 1.70/0.63 % (642487)Peak memory usage: 10 MB
% 1.70/0.63 % (642487)Instructions burned: 9 (million)
% 1.70/0.63 % (642485)Instruction limit reached!
% 1.70/0.63 % (642485)------------------------------
% 1.70/0.63 % (642485)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.63 % (642485)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.63 % (642485)CaDiCaL version: 2.1.3
% 1.70/0.63 % (642485)Termination reason: Instruction limit
% 1.70/0.63 % (642485)Termination phase: Saturation
% 1.70/0.63 % (642485)Time elapsed: 0.036 s
% 1.70/0.63 % (642485)Peak memory usage: 12 MB
% 1.70/0.63 % (642485)Instructions burned: 86 (million)
% 1.70/0.63 % (642494)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2874890355:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.70/0.63 % (642489)Refutation not found, incomplete strategy
% 1.70/0.63 % (642489)------------------------------
% 1.70/0.63 % (642489)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.63 % (642489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.63 % (642489)CaDiCaL version: 2.1.3
% 1.70/0.63 % (642489)Termination reason: Refutation not found, incomplete strategy
% 1.70/0.63 % (642489)Time elapsed: 0.022 s
% 1.70/0.63 % (642489)Peak memory usage: 12 MB
% 1.70/0.63 % (642489)Instructions burned: 25 (million)
% 1.70/0.63 % (642489)------------------------------
% 1.70/0.63 % (642489)------------------------------
% 1.70/0.63 % (642498)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=121961790:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.70/0.63 % (642469)Instruction limit reached!
% 1.70/0.63 % (642469)------------------------------
% 1.70/0.63 % (642469)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.70/0.63 % (642469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.70/0.63 % (642469)CaDiCaL version: 2.1.3
% 1.70/0.63 % (642469)Termination reason: Instruction limit
% 1.70/0.63 % (642469)Termination phase: Saturation
% 1.70/0.63 % (642469)Time elapsed: 0.126 s
% 1.70/0.63 % (642469)Peak memory usage: 13 MB
% 1.70/0.63 % (642469)Instructions burned: 157 (million)
% 1.70/0.63 % (642496)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=539423538:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.70/0.63 % (642497)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3028798783:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.15/0.69 % (642494)Refutation not found, incomplete strategy
% 2.15/0.69 % (642494)------------------------------
% 2.15/0.69 % (642494)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.69 % (642494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (642494)CaDiCaL version: 2.1.3
% 2.15/0.69 % (642494)Termination reason: Refutation not found, incomplete strategy
% 2.15/0.69 % (642494)Time elapsed: 0.021 s
% 2.15/0.69 % (642494)Peak memory usage: 12 MB
% 2.15/0.69 % (642494)Instructions burned: 49 (million)
% 2.15/0.69 % (642494)------------------------------
% 2.15/0.69 % (642494)------------------------------
% 2.15/0.69 % (642497)Instruction limit reached!
% 2.15/0.69 % (642497)------------------------------
% 2.15/0.69 % (642497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.69 % (642497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (642497)CaDiCaL version: 2.1.3
% 2.15/0.69 % (642497)Termination reason: Instruction limit
% 2.15/0.69 % (642497)Termination phase: shuffling
% 2.15/0.69 % (642497)Time elapsed: 0.015 s
% 2.15/0.69 % (642497)Peak memory usage: 10 MB
% 2.15/0.69 % (642497)Instructions burned: 18 (million)
% 2.15/0.69 % (642496)Instruction limit reached!
% 2.15/0.69 % (642496)------------------------------
% 2.15/0.69 % (642496)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.69 % (642496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (642496)CaDiCaL version: 2.1.3
% 2.15/0.69 % (642496)Termination reason: Instruction limit
% 2.15/0.69 % (642496)Termination phase: Preprocessing 1
% 2.15/0.69 % (642496)Time elapsed: 0.021 s
% 2.15/0.69 % (642496)Peak memory usage: 10 MB
% 2.15/0.69 % (642496)Instructions burned: 25 (million)
% 2.15/0.69 % (642500)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1805195119:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.15/0.69 % (642505)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2151029748:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 2.15/0.69 % (642502)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2440126602: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)
% 2.15/0.69 % (642502)Instruction limit reached!
% 2.15/0.69 % (642502)------------------------------
% 2.15/0.69 % (642502)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.69 % (642502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (642502)CaDiCaL version: 2.1.3
% 2.15/0.69 % (642502)Termination reason: Instruction limit
% 2.15/0.69 % (642502)Termination phase: shuffling
% 2.15/0.69 % (642502)Time elapsed: 0.003 s
% 2.15/0.69 % (642502)Peak memory usage: 10 MB
% 2.15/0.69 % (642502)Instructions burned: 2 (million)
% 2.15/0.69 % (642500)Instruction limit reached!
% 2.15/0.69 % (642500)------------------------------
% 2.15/0.69 % (642500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.69 % (642500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (642500)CaDiCaL version: 2.1.3
% 2.15/0.69 % (642500)Termination reason: Instruction limit
% 2.15/0.69 % (642500)Termination phase: shuffling
% 2.15/0.69 % (642500)Time elapsed: 0.012 s
% 2.15/0.69 % (642500)Peak memory usage: 10 MB
% 2.15/0.69 % (642500)Instructions burned: 15 (million)
% 2.15/0.69 % (642505)Instruction limit reached!
% 2.15/0.69 % (642505)------------------------------
% 2.15/0.69 % (642505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.69 % (642505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (642505)CaDiCaL version: 2.1.3
% 2.15/0.69 % (642505)Termination reason: Instruction limit
% 2.15/0.69 % (642505)Termination phase: Property scanning
% 2.15/0.69 % (642505)Time elapsed: 0.012 s
% 2.15/0.69 % (642505)Peak memory usage: 10 MB
% 2.15/0.69 % (642505)Instructions burned: 28 (million)
% 2.15/0.69 % (642506)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1455998219:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.15/0.69 % (642512)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.15/0.69 % (642512)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=3565594978:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.15/0.69 % (642507)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2122714016:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 2.15/0.69 % (642512)Instruction limit reached!
% 2.15/0.69 % (642512)------------------------------
% 2.15/0.69 % (642512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.69 % (642512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (642512)CaDiCaL version: 2.1.3
% 2.15/0.69 % (642512)Termination reason: Instruction limit
% 2.15/0.69 % (642512)Termination phase: shuffling
% 2.15/0.69 % (642512)Time elapsed: 0.004 s
% 2.15/0.69 % (642512)Peak memory usage: 9 MB
% 2.15/0.69 % (642512)Instructions burned: 9 (million)
% 2.15/0.69 % (642511)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
% 2.15/0.69 % (642511)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.15/0.69 % (642511)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=3166930256:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.15/0.69 % (642506)Instruction limit reached!
% 2.15/0.69 % (642506)------------------------------
% 2.15/0.69 % (642506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.69 % (642506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (642506)CaDiCaL version: 2.1.3
% 2.15/0.69 % (642506)Termination reason: Instruction limit
% 2.15/0.69 % (642506)Termination phase: Property scanning
% 2.15/0.69 % (642506)Time elapsed: 0.020 s
% 2.15/0.69 % (642506)Peak memory usage: 10 MB
% 2.15/0.69 % (642506)Instructions burned: 23 (million)
% 2.15/0.69 % (642513)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=2362480310:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.15/0.69 % (642517)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2020104255:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.15/0.69 % (642511)Instruction limit reached!
% 2.15/0.69 % (642511)------------------------------
% 2.15/0.69 % (642511)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.69 % (642511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (642511)CaDiCaL version: 2.1.3
% 2.15/0.69 % (642511)Termination reason: Instruction limit
% 2.15/0.69 % (642511)Termination phase: shuffling
% 2.15/0.69 % (642511)Time elapsed: 0.012 s
% 2.15/0.69 % (642511)Peak memory usage: 10 MB
% 2.15/0.69 % (642511)Instructions burned: 14 (million)
% 2.15/0.69 % (642517)Instruction limit reached!
% 2.15/0.69 % (642517)------------------------------
% 2.15/0.69 % (642517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.69 % (642517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (642517)CaDiCaL version: 2.1.3
% 2.15/0.69 % (642517)Termination reason: Instruction limit
% 2.15/0.69 % (642517)Termination phase: shuffling
% 2.15/0.69 % (642517)Time elapsed: 0.004 s
% 2.15/0.69 % (642517)Peak memory usage: 10 MB
% 2.15/0.69 % (642517)Instructions burned: 9 (million)
% 2.15/0.69 % (642519)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2909710062:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.15/0.69 % (642513)Instruction limit reached!
% 2.15/0.69 % (642513)------------------------------
% 2.15/0.69 % (642513)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.69 % (642513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (642513)CaDiCaL version: 2.1.3
% 2.15/0.69 % (642513)Termination reason: Instruction limit
% 2.15/0.69 % (642513)Termination phase: Property scanning
% 2.15/0.69 % (642513)Time elapsed: 0.024 s
% 2.15/0.69 % (642513)Peak memory usage: 10 MB
% 2.15/0.69 % (642513)Instructions burned: 31 (million)
% 2.15/0.69 % (642519)Instruction limit reached!
% 2.15/0.69 % (642519)------------------------------
% 2.15/0.69 % (642519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.69 % (642519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (642519)CaDiCaL version: 2.1.3
% 2.15/0.69 % (642519)Termination reason: Instruction limit
% 2.15/0.69 % (642519)Termination phase: Property scanning
% 2.15/0.69 % (642519)Time elapsed: 0.013 s
% 2.15/0.69 % (642519)Peak memory usage: 10 MB
% 2.15/0.69 % (642519)Instructions burned: 24 (million)
% 2.15/0.69 % (642507)Instruction limit reached!
% 2.15/0.69 % (642507)------------------------------
% 2.15/0.69 % (642507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.69 % (642507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (642507)CaDiCaL version: 2.1.3
% 2.15/0.69 % (642507)Termination reason: Instruction limit
% 2.15/0.69 % (642507)Termination phase: Property scanning
% 2.15/0.69 % (642507)Time elapsed: 0.052 s
% 2.15/0.69 % (642507)Peak memory usage: 12 MB
% 2.15/0.69 % (642507)Instructions burned: 60 (million)
% 2.15/0.69 % (642522)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2791439230:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 2.15/0.69 % (642525)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1242035377:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.15/0.69 % (642523)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=1369241479:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.15/0.69 % (642522)Instruction limit reached!
% 2.15/0.69 % (642522)------------------------------
% 2.15/0.69 % (642522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.69 % (642522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (642522)CaDiCaL version: 2.1.3
% 2.15/0.69 % (642522)Termination reason: Instruction limit
% 2.15/0.69 % (642522)Termination phase: shuffling
% 2.15/0.69 % (642522)Time elapsed: 0.017 s
% 2.15/0.69 % (642522)Peak memory usage: 10 MB
% 2.15/0.69 % (642522)Instructions burned: 20 (million)
% 2.15/0.69 % (642498) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-642456-642498"...
% 2.15/0.69 % (642526)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1707179665:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.15/0.69 % (642527)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4241516041:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.15/0.69 % (642498)...printing done.
% 2.15/0.69 % (642498)Refutation found. Thanks to Tanya!
% 2.15/0.69 % SZS status Theorem for theBenchmark
% 2.15/0.69 % SZS output start Proof for theBenchmark
% See solution above
% 2.15/0.69 % (642498)------------------------------
% 2.15/0.69 % (642498)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.15/0.69 % (642498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.15/0.69 % (642498)CaDiCaL version: 2.1.3
% 2.15/0.69 % (642498)Termination reason: Refutation
% 2.15/0.69 % (642498)Time elapsed: 0.147 s
% 2.15/0.69 % (642498)Peak memory usage: 15 MB
% 2.15/0.69 % (642498)Instructions burned: 184 (million)
% 2.15/0.69 % (642456)Success in time 0.331 s
% 2.15/0.69 % Vampire exiting
%------------------------------------------------------------------------------