%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG258^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:45:14 AM UTC 2026
% Result : Theorem 1.28s 0.46s
% Output : Refutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 23
% Syntax : Number of formulae : 188 ( 47 unt; 0 typ; 16 def)
% Number of atoms : 870 ( 295 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 1547 ( 118 ~; 176 |; 0 &;1057 @)
% ( 16 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 74 ( 74 >; 0 *; 0 +; 0 <<)
% Number of symbols : 404 ( 400 usr; 190 con; 0-4 aty)
% ( 122 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 313 ( 9 sgn 129 !; 0 ?; 313 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_6,type,
subst: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
one: term ).
thf(func_def_1,type,
ap: term > term > term ).
thf(func_def_2,type,
lam: term > term ).
thf(func_def_3,type,
sub: term > subst > term ).
thf(func_def_4,type,
id: subst ).
thf(func_def_5,type,
sh: subst ).
thf(func_def_6,type,
push: term > subst > subst ).
thf(func_def_7,type,
comp: subst > subst > subst ).
thf(func_def_8,type,
var: term > $o ).
thf(func_def_9,type,
pushprop_lem1v2: $o ).
thf(func_def_10,type,
pushprop_lem1_gthm: $o ).
thf(func_def_11,type,
axmap: $o ).
thf(func_def_12,type,
pushprop_lem0_gthm: $o ).
thf(func_def_13,type,
shinj: $o ).
thf(func_def_14,type,
hoasinduction_lem1v2: $o ).
thf(func_def_15,type,
hoasinduction_lem1v2_gthm: $o ).
thf(func_def_16,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_17,type,
induction2lem: $o ).
thf(func_def_18,type,
hoasinduction_lem3v2_f: $o ).
thf(func_def_19,type,
axvarshift: $o ).
thf(func_def_20,type,
hoasapinj2: $o ).
thf(func_def_21,type,
hoasapnotvar_gthm: $o ).
thf(func_def_22,type,
hoasapinj1: $o ).
thf(func_def_23,type,
ulamvar1: $o ).
thf(func_def_24,type,
induction2lem_lthm: $o ).
thf(func_def_25,type,
hoasinduction_lem3v2_gthm: $o ).
thf(func_def_26,type,
apnotvar: $o ).
thf(func_def_27,type,
pushprop_lthm_orig: $o ).
thf(func_def_28,type,
hoasinduction_lem3v2_f_lthm: $o ).
thf(func_def_29,type,
hoasinduction_lthm: $o ).
thf(func_def_30,type,
hoasinduction_no_psi_cond_lthm: $o ).
thf(func_def_31,type,
hoaslaminj: $o ).
thf(func_def_32,type,
hoasinduction_lem3aaa: $o ).
thf(func_def_33,type,
induction2lem_gthm: $o ).
thf(func_def_34,type,
hoasinduction_lem3aa_lthm: $o ).
thf(func_def_35,type,
hoasinduction_lem3: $o ).
thf(func_def_36,type,
hoasinduction_lem2: $o ).
thf(func_def_37,type,
termmset_lthm: $o ).
thf(func_def_38,type,
hoasinduction_lem1: $o ).
thf(func_def_39,type,
hoaslamnotap_lthm: $o ).
thf(func_def_40,type,
pushprop_lem1v2_lthm: $o ).
thf(func_def_41,type,
hoasapnotvar: $o ).
thf(func_def_42,type,
hoasinduction_lem0: $o ).
thf(func_def_43,type,
hoasinduction: $o ).
thf(func_def_44,type,
hoasinduction_gthm: $o ).
thf(func_def_45,type,
axapp: $o ).
thf(func_def_46,type,
hoaslamnotvar_lthm: $o ).
thf(func_def_47,type,
pushprop_lem3v2_lthm: $o ).
thf(func_def_48,type,
hoasinduction_lem3b_lthm: $o ).
thf(func_def_49,type,
ulamvarind: $o ).
thf(func_def_50,type,
induction: $o ).
thf(func_def_51,type,
hoasinduction_lem3a_lthm: $o ).
thf(func_def_52,type,
termmset_gthm: $o ).
thf(func_def_53,type,
hoasinduction_lem3aa: $o ).
thf(func_def_54,type,
pushprop_lem1v2_gthm: $o ).
thf(func_def_55,type,
hoaslamnotap_gthm: $o ).
thf(func_def_56,type,
hoaslamnotvar_gthm: $o ).
thf(func_def_57,type,
hoasinduction_lem3b_gthm: $o ).
thf(func_def_58,type,
pushprop_lem2v2: $o ).
thf(func_def_59,type,
hoasinduction_lem3a_gthm: $o ).
thf(func_def_60,type,
axclos: $o ).
thf(func_def_61,type,
axassoc: $o ).
thf(func_def_62,type,
hoasinduction_lem2v2: $o ).
thf(func_def_63,type,
pushprop_lthm: $o ).
thf(func_def_64,type,
apinj2: $o ).
thf(func_def_65,type,
apinj1: $o ).
thf(func_def_66,type,
hoasapinj2_lthm: $o ).
thf(func_def_67,type,
hoasinduction_lem3v2a: $o ).
thf(func_def_68,type,
hoasapinj1_lthm: $o ).
thf(func_def_69,type,
hoaslaminj_lthm: $o ).
thf(func_def_70,type,
axvarcons: $o ).
thf(func_def_71,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_72,type,
axscons: $o ).
thf(func_def_73,type,
hoasinduction_lem2v2_gthm: $o ).
thf(func_def_74,type,
axidr: $o ).
thf(func_def_75,type,
pushprop_lem1: $o ).
thf(func_def_76,type,
laminj: $o ).
thf(func_def_77,type,
hoasinduction_lem3_lthm: $o ).
thf(func_def_78,type,
pushprop_lem0: $o ).
thf(func_def_79,type,
pushprop_gthm: $o ).
thf(func_def_80,type,
axabs: $o ).
thf(func_def_81,type,
hoasinduction_lem3v2a_lthm: $o ).
thf(func_def_82,type,
hoasinduction_lem2_lthm: $o ).
thf(func_def_83,type,
hoasapinj2_gthm: $o ).
thf(func_def_84,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_85,type,
hoasinduction_lem1_lthm: $o ).
thf(func_def_86,type,
lamnotap: $o ).
thf(func_def_87,type,
hoasapinj1_gthm: $o ).
thf(func_def_88,type,
hoaslamnotvar: $o ).
thf(func_def_89,type,
axidl: $o ).
thf(func_def_90,type,
hoaslaminj_gthm: $o ).
thf(func_def_91,type,
induction2_lthm: $o ).
thf(func_def_92,type,
hoasinduction_lem0_lthm: $o ).
thf(func_def_93,type,
substmonoid_lthm: $o ).
thf(func_def_94,type,
pushprop: $o ).
thf(func_def_95,type,
hoasinduction_lem3_gthm: $o ).
thf(func_def_96,type,
hoasinduction_lem2_gthm: $o ).
thf(func_def_97,type,
hoasinduction_lem3b: $o ).
thf(func_def_98,type,
substmonoid: $o ).
thf(func_def_99,type,
lamnotvar: $o ).
thf(func_def_100,type,
hoasinduction_lem3a: $o ).
thf(func_def_101,type,
hoasinduction_lem1_gthm: $o ).
thf(func_def_102,type,
hoasinduction_no_psi_cond: $o ).
thf(func_def_103,type,
induction2_gthm: $o ).
thf(func_def_104,type,
pushprop_lem2v2_lthm: $o ).
thf(func_def_105,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_106,type,
hoaslamnotap: $o ).
thf(func_def_107,type,
substmonoid_gthm: $o ).
thf(func_def_108,type,
ulamvarsh: $o ).
thf(func_def_109,type,
induction2: $o ).
thf(func_def_110,type,
pushprop_lem3v2: $o ).
thf(func_def_111,type,
pushprop_lem2v2_gthm: $o ).
thf(func_def_112,type,
pushprop_lem1_lthm: $o ).
thf(func_def_113,type,
hoasinduction_lem3v2: $o ).
thf(func_def_114,type,
axshiftcons: $o ).
thf(func_def_115,type,
termmset: $o ).
thf(func_def_116,type,
pushprop_lem0_lthm: $o ).
thf(func_def_117,type,
hoasapnotvar_lthm: $o ).
thf(func_def_118,type,
hoasinduction_lem3v2_lthm: $o ).
thf(func_def_119,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_120,type,
axvarid: $o ).
thf(func_def_121,type,
hoasinduction_lthm_3: $o ).
thf(func_def_123,type,
vIMP: $o > $o > $o ).
thf(func_def_124,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_125,type,
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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_131,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_133,type,
vNOT: $o > $o ).
thf(func_def_136,type,
vAND: $o > $o > $o ).
thf(func_def_137,type,
vIFF: $o > $o > $o ).
thf(func_def_138,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_139,type,
sK0: ( term > $o ) > term ).
thf(func_def_140,type,
sK1: ( term > $o ) > 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 ).
thf(func_def_145,type,
sK6: term > term ).
thf(func_def_146,type,
sK7: term ).
thf(func_def_147,type,
sK8: term ).
thf(func_def_148,type,
sK9: term ).
thf(func_def_149,type,
sK10: term ).
thf(func_def_150,type,
sK11: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_151,type,
sK12: ( subst > term > subst > $o ) > term > term ).
thf(func_def_152,type,
sK13: ( subst > term > subst > $o ) > term > term ).
thf(func_def_153,type,
sK14: ( subst > term > subst > $o ) > term > term ).
thf(func_def_154,type,
sK15: subst > term > subst > $o ).
thf(func_def_155,type,
sK16: ( subst > term > term ) > term ).
thf(func_def_156,type,
sK17: ( subst > term > term ) > term ).
thf(func_def_157,type,
sK18: ( subst > term > term ) > subst ).
thf(func_def_158,type,
sK19: ( subst > term > term ) > subst ).
thf(func_def_159,type,
sK20: ( subst > term > term ) > subst ).
thf(func_def_160,type,
sK21: term ).
thf(func_def_161,type,
sK22: term ).
thf(func_def_162,type,
sK23: ( subst > term > term ) > subst ).
thf(func_def_163,type,
sK24: ( subst > term > term ) > subst ).
thf(func_def_164,type,
sK25: ( subst > term > term ) > term ).
thf(func_def_165,type,
sK26: subst > term > term ).
thf(func_def_166,type,
sK27: term ).
thf(func_def_167,type,
sK28: term ).
thf(func_def_168,type,
sK29: subst ).
thf(func_def_169,type,
sK30: subst ).
thf(func_def_170,type,
sK31: term ).
thf(func_def_171,type,
sK32: subst ).
thf(func_def_172,type,
sK33: term ).
thf(func_def_173,type,
sK34: term ).
thf(func_def_174,type,
sK35: term ).
thf(func_def_175,type,
sK36: term ).
thf(func_def_176,type,
sK37: ( subst > term > subst > $o ) > subst ).
thf(func_def_177,type,
sK38: ( subst > term > subst > $o ) > subst ).
thf(func_def_178,type,
sK39: ( subst > term > subst > $o ) > term ).
thf(func_def_179,type,
sK40: ( subst > term > subst > $o ) > term ).
thf(func_def_180,type,
sK41: ( subst > term > subst > $o ) > subst > term > 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: ( subst > term > subst > $o ) > subst ).
thf(func_def_185,type,
sK46: ( subst > term > subst > $o ) > subst ).
thf(func_def_186,type,
sK47: ( subst > term > subst > $o ) > term ).
thf(func_def_187,type,
sK48: ( subst > term > subst > $o ) > term ).
thf(func_def_188,type,
sK49: ( subst > term > subst > $o ) > term ).
thf(func_def_189,type,
sK50: ( subst > term > subst > $o ) > term ).
thf(func_def_190,type,
sK51: ( subst > term > subst > $o ) > term ).
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 ) > term ).
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 ) > subst ).
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 ) > term ).
thf(func_def_204,type,
sK65: ( subst > term > subst > $o ) > subst ).
thf(func_def_205,type,
sK66: ( subst > term > subst > $o ) > term ).
thf(func_def_206,type,
sK67: ( subst > term > subst > $o ) > subst ).
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 ) > subst ).
thf(func_def_213,type,
sK74: ( subst > term > subst > $o ) > term ).
thf(func_def_214,type,
sK75: ( subst > term > subst > $o ) > term ).
thf(func_def_215,type,
sK76: ( subst > term > subst > $o ) > subst ).
thf(func_def_216,type,
sK77: ( subst > term > subst > $o ) > term ).
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 ) > subst ).
thf(func_def_220,type,
sK81: ( subst > term > subst > $o ) > subst ).
thf(func_def_221,type,
sK82: ( subst > term > subst > $o ) > term ).
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 ) > term ).
thf(func_def_229,type,
sK90: ( subst > term > subst > $o ) > term ).
thf(func_def_230,type,
sK91: ( subst > term > subst > $o ) > subst ).
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 ) > term ).
thf(func_def_236,type,
sK97: ( subst > term > subst > $o ) > subst ).
thf(func_def_237,type,
sK98: ( subst > term > subst > $o ) > term ).
thf(func_def_238,type,
sK99: ( subst > term > subst > $o ) > term ).
thf(func_def_239,type,
sK100: ( subst > term > subst > $o ) > subst ).
thf(func_def_240,type,
sK101: ( subst > term > subst > $o ) > term ).
thf(func_def_241,type,
sK102: ( subst > term > subst > $o ) > term ).
thf(func_def_242,type,
sK103: ( subst > term > subst > $o ) > subst ).
thf(func_def_243,type,
sK104: ( subst > term > subst > $o ) > subst ).
thf(func_def_244,type,
sK105: ( subst > term > subst > $o ) > subst ).
thf(func_def_245,type,
sK106: ( subst > term > subst > $o ) > term ).
thf(func_def_246,type,
sK107: ( subst > term > subst > $o ) > term ).
thf(func_def_247,type,
sK108: ( subst > term > subst > $o ) > subst ).
thf(func_def_248,type,
sK109: ( subst > term > subst > $o ) > term ).
thf(func_def_249,type,
sK110: ( subst > term > subst > $o ) > term ).
thf(func_def_250,type,
sK111: ( subst > term > subst > $o ) > term ).
thf(func_def_251,type,
sK112: ( subst > term > subst > $o ) > term ).
thf(func_def_252,type,
sK113: subst > term > subst > $o ).
thf(func_def_253,type,
sK114: ( subst > term > term ) > subst ).
thf(func_def_254,type,
sK115: ( subst > term > term ) > term ).
thf(func_def_255,type,
sK116: ( subst > term > term ) > subst ).
thf(func_def_256,type,
sK117: ( subst > term > term ) > term ).
thf(func_def_257,type,
sK118: ( subst > term > term ) > subst ).
thf(func_def_258,type,
sK119: ( subst > term > term ) > term ).
thf(func_def_259,type,
sK120: term ).
thf(func_def_260,type,
sK121: subst ).
thf(func_def_261,type,
sK122: subst ).
thf(func_def_262,type,
sK123: subst ).
thf(func_def_263,type,
sK124: subst ).
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: subst ).
thf(func_def_271,type,
sK132: term ).
thf(func_def_272,type,
sK133: term ).
thf(func_def_273,type,
sK134: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_274,type,
sK135: term > ( term > $o ) > term ).
thf(func_def_275,type,
sK136: term > ( term > $o ) > term ).
thf(func_def_276,type,
sK137: subst > term > subst > $o ).
thf(func_def_277,type,
sK138: term > $o ).
thf(func_def_278,type,
sK139: ( subst > term > term ) > subst ).
thf(func_def_279,type,
sK140: ( subst > term > term ) > term ).
thf(func_def_280,type,
sK141: ( subst > term > term ) > subst ).
thf(func_def_281,type,
sK142: ( subst > term > term ) > term ).
thf(func_def_282,type,
sK143: ( subst > term > term ) > term ).
thf(func_def_283,type,
sK144: term ).
thf(func_def_284,type,
sK145: term ).
thf(func_def_285,type,
sK146: term ).
thf(func_def_286,type,
sK147: subst ).
thf(func_def_287,type,
sK148: term ).
thf(func_def_288,type,
sK149: term ).
thf(func_def_289,type,
sK150: term ).
thf(func_def_290,type,
sK151: term ).
thf(func_def_291,type,
sK152: ( subst > term > subst > $o ) > subst ).
thf(func_def_292,type,
sK153: ( subst > term > subst > $o ) > term ).
thf(func_def_293,type,
sK154: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_294,type,
sK155: ( subst > term > subst > $o ) > subst ).
thf(func_def_295,type,
sK156: ( subst > term > subst > $o ) > term > term ).
thf(func_def_296,type,
sK157: ( subst > term > subst > $o ) > term ).
thf(func_def_297,type,
sK158: ( subst > term > subst > $o ) > subst ).
thf(func_def_298,type,
sK159: ( subst > term > subst > $o ) > subst ).
thf(func_def_299,type,
sK160: ( subst > term > subst > $o ) > subst ).
thf(func_def_300,type,
sK161: ( subst > term > subst > $o ) > subst ).
thf(func_def_301,type,
sK162: ( subst > term > subst > $o ) > subst ).
thf(func_def_302,type,
sK163: ( subst > term > subst > $o ) > subst ).
thf(func_def_303,type,
sK164: ( subst > term > subst > $o ) > subst ).
thf(func_def_304,type,
sK165: ( subst > term > subst > $o ) > subst ).
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 ) > term > term ).
thf(func_def_308,type,
sK169: ( subst > term > subst > $o ) > subst ).
thf(func_def_309,type,
sK170: ( subst > term > subst > $o ) > subst ).
thf(func_def_310,type,
sK171: ( subst > term > subst > $o ) > subst ).
thf(func_def_311,type,
sK172: ( subst > term > subst > $o ) > subst ).
thf(func_def_312,type,
sK173: ( subst > term > subst > $o ) > subst ).
thf(func_def_313,type,
sK174: ( subst > term > subst > $o ) > subst ).
thf(func_def_314,type,
sK175: ( subst > term > subst > $o ) > subst ).
thf(func_def_315,type,
sK176: ( subst > term > subst > $o ) > subst ).
thf(func_def_316,type,
sK177: ( subst > term > subst > $o ) > term > term ).
thf(func_def_317,type,
sK178: ( subst > term > subst > $o ) > subst ).
thf(func_def_318,type,
sK179: ( subst > term > subst > $o ) > term ).
thf(func_def_319,type,
sK180: ( subst > term > subst > $o ) > subst ).
thf(func_def_320,type,
sK181: ( subst > term > subst > $o ) > subst ).
thf(func_def_321,type,
sK182: ( subst > term > subst > $o ) > subst ).
thf(func_def_322,type,
sK183: ( subst > term > subst > $o ) > subst ).
thf(func_def_323,type,
sK184: ( subst > term > subst > $o ) > subst ).
thf(func_def_324,type,
sK185: ( subst > term > subst > $o ) > subst ).
thf(func_def_325,type,
sK186: subst > term > subst > $o ).
thf(func_def_326,type,
sK187: ( subst > term > term ) > term ).
thf(func_def_327,type,
sK188: ( subst > term > term ) > term ).
thf(func_def_328,type,
sK189: ( subst > term > term ) > subst ).
thf(func_def_329,type,
sK190: ( subst > term > term ) > subst ).
thf(func_def_330,type,
sK191: ( subst > term > term ) > subst ).
thf(func_def_331,type,
sK192: ( subst > term > term ) > subst ).
thf(func_def_332,type,
sK193: term ).
thf(func_def_333,type,
sK194: term ).
thf(func_def_334,type,
sK195: term ).
thf(func_def_335,type,
sK196: term ).
thf(func_def_336,type,
sK197: term ).
thf(func_def_337,type,
sK198: term ).
thf(func_def_338,type,
sK199: subst ).
thf(func_def_339,type,
sK200: subst > ( term > $o ) > term ).
thf(func_def_340,type,
sK201: term > $o ).
thf(func_def_341,type,
sK202: term ).
thf(func_def_342,type,
sK203: subst ).
thf(func_def_343,type,
sK204: term ).
thf(func_def_344,type,
sK205: subst ).
thf(func_def_345,type,
sK206: term ).
thf(func_def_346,type,
sK207: subst ).
thf(func_def_347,type,
sK208: ( subst > term > term ) > subst ).
thf(func_def_348,type,
sK209: ( subst > term > term ) > term ).
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: ( term > $o ) > term ).
thf(func_def_354,type,
sK215: ( term > $o ) > term ).
thf(func_def_355,type,
sK216: ( term > $o ) > term ).
thf(func_def_356,type,
sK217: subst > ( term > $o ) > term ).
thf(func_def_357,type,
sK218: subst > ( term > $o ) > term ).
thf(func_def_358,type,
sK219: subst > ( term > $o ) > term ).
thf(func_def_359,type,
sK220: subst > ( term > $o ) > term ).
thf(func_def_360,type,
sK221: subst > ( term > $o ) > term ).
thf(func_def_361,type,
sK222: subst > ( term > $o ) > term ).
thf(func_def_362,type,
sK223: term > $o ).
thf(func_def_363,type,
sK224: term > term ).
thf(func_def_364,type,
sK225: term ).
thf(func_def_365,type,
sK226: subst ).
thf(func_def_366,type,
sK227: ( subst > term > term ) > subst ).
thf(func_def_367,type,
sK228: ( subst > term > term ) > term ).
thf(func_def_368,type,
sK229: ( subst > term > term ) > subst ).
thf(func_def_369,type,
sK230: ( subst > term > term ) > subst ).
thf(func_def_370,type,
sK231: ( subst > term > term ) > subst ).
thf(func_def_371,type,
sK232: ( subst > term > term ) > term ).
thf(func_def_372,type,
sK233: subst > term > term ).
thf(func_def_373,type,
sK234: subst > term > term ).
thf(func_def_374,type,
sK235: term ).
thf(func_def_375,type,
sK236: subst ).
thf(func_def_376,type,
sK237: term ).
thf(func_def_377,type,
sK238: ( term > $o ) > term ).
thf(func_def_378,type,
sK239: ( term > $o ) > term ).
thf(func_def_379,type,
sK240: ( term > $o ) > term ).
thf(func_def_380,type,
sK241: ( term > $o ) > term ).
thf(func_def_381,type,
sK242: term > $o ).
thf(func_def_382,type,
sK243: term ).
thf(func_def_383,type,
sK244: ( term > $o ) > term ).
thf(func_def_384,type,
sK245: term > $o ).
thf(func_def_385,type,
sK246: term ).
thf(f2,axiom,
( axvarcons
= ( ! [X1: subst,X0: term] :
( ( sub @ one @ ( push @ X0 @ X1 ) )
= X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axvarcons) ).
thf(f7,axiom,
( axshiftcons
= ( ! [X1: subst,X0: term] :
( ( comp @ sh @ ( push @ X0 @ X1 ) )
= X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axshiftcons) ).
thf(f18,axiom,
! [X1: term,X0: term] :
( ( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) )
= laminj ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',laminj) ).
thf(f56,axiom,
( hoaslam
= ( ^ [X0: subst,X1: subst > term > term] : ( lam @ ( X1 @ sh @ one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslam) ).
thf(f64,axiom,
( hoaslaminj
= ( ! [X0: subst > term > term] :
( ! [X3: subst,X2: term,X1: subst] :
( ( sub @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
=> ! [X4: subst > term > term] :
( ! [X2: term,X3: subst,X1: subst] :
( ( sub @ ( X4 @ X1 @ X2 ) @ X3 )
= ( X4 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
=> ( ( ( hoaslam @ id
@ ^ [X1: subst,X2: term] : ( X0 @ X1 @ X2 ) )
= ( hoaslam @ id
@ ^ [X1: subst,X2: term] : ( X4 @ X1 @ X2 ) ) )
=> ! [X1: subst,X2: term] :
( ( X0 @ X1 @ X2 )
= ( X4 @ X1 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslaminj) ).
thf(f66,axiom,
( axvarcons
=> ( ( axshiftcons
=> ( laminj
=> hoaslaminj ) )
= hoaslaminj_lthm ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoaslaminj_lthm) ).
thf(f114,conjecture,
hoaslaminj_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ hoaslaminj_lthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f131,plain,
( axshiftcons
= ( ! [X0: subst,X1: term] :
( ( comp @ sh @ ( push @ X1 @ X0 ) )
= X0 ) ) ),
inference(rectify,[],[f7]) ).
thf(f132,plain,
( axshiftcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[],[f131]) ).
thf(f152,plain,
! [X0: term,X1: term] :
( ( ( ( lam @ X0 )
= ( lam @ X1 ) )
=> ( X0 = X1 ) )
= laminj ),
inference(rectify,[],[f18]) ).
thf(f153,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[],[f152]) ).
thf(f185,plain,
~ hoaslaminj_lthm,
inference(rectify,[],[f115]) ).
thf(f186,plain,
hoaslaminj_lthm != $true,
inference(fool_elimination,[],[f185]) ).
thf(f253,plain,
( axvarcons
=> ( ( axshiftcons
=> ( laminj
=> hoaslaminj ) )
= hoaslaminj_lthm ) ),
inference(rectify,[],[f66]) ).
thf(f254,plain,
( hoaslaminj_lthm
= ( axvarcons
=> ( axshiftcons
=> ( laminj
=> hoaslaminj ) ) ) ),
inference(fool_elimination,[],[f253]) ).
thf(f265,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f295,plain,
( hoaslaminj
= ( ! [X0: subst > term > term] :
( ! [X1: subst,X2: term,X3: subst] :
( ( sub @ ( X0 @ X3 @ X2 ) @ X1 )
= ( X0 @ ( comp @ X3 @ X1 ) @ ( sub @ X2 @ X1 ) ) )
=> ! [X4: subst > term > term] :
( ! [X5: term,X6: subst,X7: subst] :
( ( X4 @ ( comp @ X7 @ X6 ) @ ( sub @ X5 @ X6 ) )
= ( sub @ ( X4 @ X7 @ X5 ) @ X6 ) )
=> ( ( ( hoaslam @ id
@ ^ [X8: subst,X9: term] : ( X0 @ X8 @ X9 ) )
= ( hoaslam @ id
@ ^ [X10: subst,X11: term] : ( X4 @ X10 @ X11 ) ) )
=> ! [X12: subst,X13: term] :
( ( X0 @ X12 @ X13 )
= ( X4 @ X12 @ X13 ) ) ) ) ) ) ),
inference(rectify,[],[f64]) ).
thf(f296,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f295]) ).
thf(f315,plain,
( axvarcons
= ( ! [X0: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X0 ) )
= X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f316,plain,
( axvarcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f315]) ).
thf(f321,plain,
hoaslaminj_lthm != $true,
inference(flattening,[],[f186]) ).
thf(f325,plain,
hoaslaminj_lthm != $true,
inference(cnf_transformation,[],[f321]) ).
thf(f329,plain,
( axshiftcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[],[f132]) ).
thf(f335,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( hoaslam @ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f296]) ).
thf(f341,plain,
( hoaslaminj_lthm
= ( axvarcons
=> ( axshiftcons
=> ( laminj
=> hoaslaminj ) ) ) ),
inference(cnf_transformation,[],[f254]) ).
thf(f345,plain,
( laminj
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f153]) ).
thf(f346,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(cnf_transformation,[],[f265]) ).
thf(f355,plain,
( axvarcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f316]) ).
thf(f361,plain,
( hoaslaminj
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f335,f346,f346]) ).
thf(f587,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) ) )
= $true )
| ( axvarcons = $false ) ),
inference(iff_proxy_clausification,[],[f355]) ).
thf(f588,plain,
! [X1: term] :
( ( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ one @ ( push @ Y0 @ Y1 ) )
= Y0 ) )
@ X1 )
= $true )
| ( axvarcons = $false ) ),
inference(pi_proxy_clausification,[],[f587]) ).
thf(f589,plain,
! [X1: term] :
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ one @ ( push @ X1 @ Y0 ) )
= X1 ) )
= $true )
| ( axvarcons = $false ) ),
inference(beta-eta_normalization,[],[f588]) ).
thf(f590,plain,
! [X2: subst,X1: term] :
( ( axvarcons = $false )
| ( $true
= ( ^ [Y0: subst] :
( ( sub @ one @ ( push @ X1 @ Y0 ) )
= X1 )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f589]) ).
thf(f591,plain,
! [X2: subst,X1: term] :
( ( axvarcons = $false )
| ( ( ( sub @ one @ ( push @ X1 @ X2 ) )
= X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f590]) ).
thf(f592,plain,
! [X2: subst,X1: term] :
( ( axvarcons = $false )
| ( ( sub @ one @ ( push @ X1 @ X2 ) )
= X1 ) ),
inference(equality_proxy_clausification,[],[f591]) ).
thf(f1051,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) ) )
= $true )
| ( laminj = $false ) ),
inference(iff_proxy_clausification,[],[f345]) ).
thf(f1052,plain,
! [X1: term] :
( ( $true
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( lam @ Y1 )
= ( lam @ Y0 ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) )
| ( laminj = $false ) ),
inference(pi_proxy_clausification,[],[f1051]) ).
thf(f1053,plain,
! [X1: term] :
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( ( lam @ Y0 )
= ( lam @ X1 ) )
=> ( Y0 = X1 ) ) ) )
| ( laminj = $false ) ),
inference(beta-eta_normalization,[],[f1052]) ).
thf(f1054,plain,
! [X2: term,X1: term] :
( ( laminj = $false )
| ( ( ^ [Y0: term] :
( ( ( lam @ Y0 )
= ( lam @ X1 ) )
=> ( Y0 = X1 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1053]) ).
thf(f1055,plain,
! [X2: term,X1: term] :
( ( ( ( ( lam @ X2 )
= ( lam @ X1 ) )
=> ( X2 = X1 ) )
= $true )
| ( laminj = $false ) ),
inference(beta-eta_normalization,[],[f1054]) ).
thf(f1056,plain,
! [X2: term,X1: term] :
( ( $false
= ( ( lam @ X2 )
= ( lam @ X1 ) ) )
| ( laminj = $false )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f1055]) ).
thf(f1057,plain,
! [X2: term,X1: term] :
( ( $true
= ( X2 = X1 ) )
| ( ( lam @ X1 )
!= ( lam @ X2 ) )
| ( laminj = $false ) ),
inference(equality_proxy_clausification,[],[f1056]) ).
thf(f1058,plain,
! [X2: term,X1: term] :
( ( X1 = X2 )
| ( laminj = $false )
| ( ( lam @ X1 )
!= ( lam @ X2 ) ) ),
inference(equality_proxy_clausification,[],[f1057]) ).
thf(f1390,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
= $true )
| ( axshiftcons = $false ) ),
inference(iff_proxy_clausification,[],[f329]) ).
thf(f1391,plain,
! [X1: term] :
( ( axshiftcons = $false )
| ( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1390]) ).
thf(f1392,plain,
! [X1: term] :
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ sh @ ( push @ X1 @ Y0 ) )
= Y0 ) )
= $true )
| ( axshiftcons = $false ) ),
inference(beta-eta_normalization,[],[f1391]) ).
thf(f1393,plain,
! [X2: subst,X1: term] :
( ( axshiftcons = $false )
| ( $true
= ( ^ [Y0: subst] :
( ( comp @ sh @ ( push @ X1 @ Y0 ) )
= Y0 )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1392]) ).
thf(f1394,plain,
! [X2: subst,X1: term] :
( ( $true
= ( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 ) )
| ( axshiftcons = $false ) ),
inference(beta-eta_normalization,[],[f1393]) ).
thf(f1395,plain,
! [X2: subst,X1: term] :
( ( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 )
| ( axshiftcons = $false ) ),
inference(equality_proxy_clausification,[],[f1394]) ).
thf(f1571,plain,
( ( hoaslaminj = $true )
| ( $false
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f361]) ).
thf(f1595,plain,
( ( $false
= ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y1 @ Y2 ) @ Y3 )
= ( Y0 @ ( comp @ Y1 @ Y3 ) @ ( sub @ Y2 @ Y3 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y1: subst > term > term] :
( ( !! @ subst
@ ^ [Y2: subst] :
( !! @ subst
@ ^ [Y3: subst] :
( !! @ term
@ ^ [Y4: term] :
( ( Y1 @ ( comp @ Y2 @ Y3 ) @ ( sub @ Y4 @ Y3 ) )
= ( sub @ ( Y1 @ Y2 @ Y4 ) @ Y3 ) ) ) ) )
=> ( ( ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y0 @ Y2 @ Y3 ) )
= ( ^ [Y2: subst,Y3: subst > term > term] : ( lam @ ( Y3 @ sh @ one ) )
@ id
@ ^ [Y2: subst,Y3: term] : ( Y1 @ Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( Y0 @ Y3 @ Y2 )
= ( Y1 @ Y3 @ Y2 ) ) ) ) ) ) ) )
@ sK233 ) )
| ( hoaslaminj = $true ) ),
inference(sigma_proxy_clausification,[],[f1571]) ).
thf(f1596,plain,
( ( hoaslaminj = $true )
| ( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK233 @ Y0 @ Y1 ) @ Y2 )
= ( sK233 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) )
=> ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( ( ( lam @ ( sK233 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK233 @ Y2 @ Y1 )
= ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1595]) ).
thf(f1597,plain,
( ( hoaslaminj = $true )
| ( ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( ( ( lam @ ( sK233 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK233 @ Y2 @ Y1 )
= ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f1596]) ).
thf(f1598,plain,
( ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK233 @ Y0 @ Y1 ) @ Y2 )
= ( sK233 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) ) ) )
| ( hoaslaminj = $true ) ),
inference(imp_proxy_clausification,[],[f1596]) ).
thf(f1599,plain,
! [X1: subst] :
( ( hoaslaminj = $true )
| ( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK233 @ Y0 @ Y1 ) @ Y2 )
= ( sK233 @ ( comp @ Y0 @ Y2 ) @ ( sub @ Y1 @ Y2 ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1598]) ).
thf(f1600,plain,
! [X1: subst] :
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sK233 @ X1 @ Y0 ) @ Y1 )
= ( sK233 @ ( comp @ X1 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( hoaslaminj = $true ) ),
inference(beta-eta_normalization,[],[f1599]) ).
thf(f1601,plain,
! [X2: term,X1: subst] :
( ( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sK233 @ X1 @ Y0 ) @ Y1 )
= ( sK233 @ ( comp @ X1 @ Y1 ) @ ( sub @ Y0 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( hoaslaminj = $true ) ),
inference(pi_proxy_clausification,[],[f1600]) ).
thf(f1602,plain,
! [X2: term,X1: subst] :
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ ( sK233 @ X1 @ X2 ) @ Y0 )
= ( sK233 @ ( comp @ X1 @ Y0 ) @ ( sub @ X2 @ Y0 ) ) ) )
= $true )
| ( hoaslaminj = $true ) ),
inference(beta-eta_normalization,[],[f1601]) ).
thf(f1603,plain,
! [X2: term,X3: subst,X1: subst] :
( ( hoaslaminj = $true )
| ( $true
= ( ^ [Y0: subst] :
( ( sub @ ( sK233 @ X1 @ X2 ) @ Y0 )
= ( sK233 @ ( comp @ X1 @ Y0 ) @ ( sub @ X2 @ Y0 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1602]) ).
thf(f1604,plain,
! [X2: term,X3: subst,X1: subst] :
( ( $true
= ( ( sub @ ( sK233 @ X1 @ X2 ) @ X3 )
= ( sK233 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) ) )
| ( hoaslaminj = $true ) ),
inference(beta-eta_normalization,[],[f1603]) ).
thf(f1605,plain,
! [X2: term,X3: subst,X1: subst] :
( ( ( sub @ ( sK233 @ X1 @ X2 ) @ X3 )
= ( sK233 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
| ( hoaslaminj = $true ) ),
inference(equality_proxy_clausification,[],[f1604]) ).
thf(f1606,plain,
( ( $false
= ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( comp @ Y1 @ Y2 ) @ ( sub @ Y3 @ Y2 ) )
= ( sub @ ( Y0 @ Y1 @ Y3 ) @ Y2 ) ) ) ) )
=> ( ( ( lam @ ( sK233 @ sh @ one ) )
= ( lam @ ( Y0 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sK233 @ Y2 @ Y1 )
= ( Y0 @ Y2 @ Y1 ) ) ) ) ) )
@ sK234 ) )
| ( hoaslaminj = $true ) ),
inference(sigma_proxy_clausification,[],[f1597]) ).
thf(f1607,plain,
( ( hoaslaminj = $true )
| ( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK234 @ ( comp @ Y0 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( sK234 @ Y0 @ Y2 ) @ Y1 ) ) ) ) )
=> ( ( ( lam @ ( sK233 @ sh @ one ) )
= ( lam @ ( sK234 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK233 @ Y1 @ Y0 )
= ( sK234 @ Y1 @ Y0 ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f1606]) ).
thf(f1608,plain,
( ( hoaslaminj = $true )
| ( $false
= ( ( ( lam @ ( sK233 @ sh @ one ) )
= ( lam @ ( sK234 @ sh @ one ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK233 @ Y1 @ Y0 )
= ( sK234 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1607]) ).
thf(f1609,plain,
( ( hoaslaminj = $true )
| ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK234 @ ( comp @ Y0 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( sK234 @ Y0 @ Y2 ) @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1607]) ).
thf(f1610,plain,
! [X1: subst] :
( ( hoaslaminj = $true )
| ( ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sK234 @ ( comp @ Y0 @ Y1 ) @ ( sub @ Y2 @ Y1 ) )
= ( sub @ ( sK234 @ Y0 @ Y2 ) @ Y1 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1609]) ).
thf(f1611,plain,
! [X1: subst] :
( ( hoaslaminj = $true )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK234 @ ( comp @ X1 @ Y0 ) @ ( sub @ Y1 @ Y0 ) )
= ( sub @ ( sK234 @ X1 @ Y1 ) @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1610]) ).
thf(f1612,plain,
! [X2: subst,X1: subst] :
( ( hoaslaminj = $true )
| ( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sK234 @ ( comp @ X1 @ Y0 ) @ ( sub @ Y1 @ Y0 ) )
= ( sub @ ( sK234 @ X1 @ Y1 ) @ Y0 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1611]) ).
thf(f1613,plain,
! [X2: subst,X1: subst] :
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sK234 @ ( comp @ X1 @ X2 ) @ ( sub @ Y0 @ X2 ) )
= ( sub @ ( sK234 @ X1 @ Y0 ) @ X2 ) ) ) )
| ( hoaslaminj = $true ) ),
inference(beta-eta_normalization,[],[f1612]) ).
thf(f1614,plain,
! [X2: subst,X3: term,X1: subst] :
( ( ( ^ [Y0: term] :
( ( sK234 @ ( comp @ X1 @ X2 ) @ ( sub @ Y0 @ X2 ) )
= ( sub @ ( sK234 @ X1 @ Y0 ) @ X2 ) )
@ X3 )
= $true )
| ( hoaslaminj = $true ) ),
inference(pi_proxy_clausification,[],[f1613]) ).
thf(f1615,plain,
! [X2: subst,X3: term,X1: subst] :
( ( ( ( sK234 @ ( comp @ X1 @ X2 ) @ ( sub @ X3 @ X2 ) )
= ( sub @ ( sK234 @ X1 @ X3 ) @ X2 ) )
= $true )
| ( hoaslaminj = $true ) ),
inference(beta-eta_normalization,[],[f1614]) ).
thf(f1616,plain,
! [X2: subst,X3: term,X1: subst] :
( ( hoaslaminj = $true )
| ( ( sub @ ( sK234 @ X1 @ X3 ) @ X2 )
= ( sK234 @ ( comp @ X1 @ X2 ) @ ( sub @ X3 @ X2 ) ) ) ),
inference(equality_proxy_clausification,[],[f1615]) ).
thf(f1617,plain,
( ( hoaslaminj = $true )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK233 @ Y1 @ Y0 )
= ( sK234 @ Y1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1608]) ).
thf(f1618,plain,
( ( $true
= ( ( lam @ ( sK233 @ sh @ one ) )
= ( lam @ ( sK234 @ sh @ one ) ) ) )
| ( hoaslaminj = $true ) ),
inference(imp_proxy_clausification,[],[f1608]) ).
thf(f1619,plain,
( ( ( lam @ ( sK233 @ sh @ one ) )
= ( lam @ ( sK234 @ sh @ one ) ) )
| ( hoaslaminj = $true ) ),
inference(equality_proxy_clausification,[],[f1618]) ).
thf(f1620,plain,
( ( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sK233 @ Y1 @ Y0 )
= ( sK234 @ Y1 @ Y0 ) ) )
@ sK235 )
= $false )
| ( hoaslaminj = $true ) ),
inference(sigma_proxy_clausification,[],[f1617]) ).
thf(f1621,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( ( sK233 @ Y0 @ sK235 )
= ( sK234 @ Y0 @ sK235 ) ) )
= $false )
| ( hoaslaminj = $true ) ),
inference(beta-eta_normalization,[],[f1620]) ).
thf(f1622,plain,
( ( hoaslaminj = $true )
| ( $false
= ( ^ [Y0: subst] :
( ( sK233 @ Y0 @ sK235 )
= ( sK234 @ Y0 @ sK235 ) )
@ sK236 ) ) ),
inference(sigma_proxy_clausification,[],[f1621]) ).
thf(f1623,plain,
( ( $false
= ( ( sK233 @ sK236 @ sK235 )
= ( sK234 @ sK236 @ sK235 ) ) )
| ( hoaslaminj = $true ) ),
inference(beta-eta_normalization,[],[f1622]) ).
thf(f1624,plain,
( ( ( sK233 @ sK236 @ sK235 )
!= ( sK234 @ sK236 @ sK235 ) )
| ( hoaslaminj = $true ) ),
inference(equality_proxy_clausification,[],[f1623]) ).
thf(f1633,plain,
( ( hoaslaminj_lthm = $true )
| ( $false
= ( axvarcons
=> ( axshiftcons
=> ( laminj
=> hoaslaminj ) ) ) ) ),
inference(iff_proxy_clausification,[],[f341]) ).
thf(f1638,plain,
( ( ( axshiftcons
=> ( laminj
=> hoaslaminj ) )
= $false )
| ( hoaslaminj_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f1633]) ).
thf(f1639,plain,
( ( axvarcons = $true )
| ( hoaslaminj_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f1633]) ).
thf(f1640,plain,
( ( hoaslaminj_lthm = $true )
| ( $false
= ( laminj
=> hoaslaminj ) ) ),
inference(imp_proxy_clausification,[],[f1638]) ).
thf(f1641,plain,
( ( hoaslaminj_lthm = $true )
| ( axshiftcons = $true ) ),
inference(imp_proxy_clausification,[],[f1638]) ).
thf(f1642,plain,
( ( hoaslaminj = $false )
| ( hoaslaminj_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f1640]) ).
thf(f1643,plain,
( ( hoaslaminj_lthm = $true )
| ( laminj = $true ) ),
inference(imp_proxy_clausification,[],[f1640]) ).
thf(f1968,definition,
( spl247_57
<=> ! [X2: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X2 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[spl247_57])],[avatar_definition]) ).
thf(f1969,plain,
( ! [X2: subst,X1: term] :
( ( sub @ one @ ( push @ X1 @ X2 ) )
= X1 )
| ~ spl247_57 ),
inference(avatar_component_clause,[],[f1968]) ).
thf(f1971,definition,
( spl247_58
<=> ( axvarcons = $false ) ),
introduced(definition,[new_symbols(definition,[spl247_58])],[avatar_definition]) ).
thf(f1973,plain,
( ( axvarcons = $false )
| ~ spl247_58 ),
inference(avatar_component_clause,[],[f1971]) ).
thf(f1974,plain,
( spl247_57
| spl247_58 ),
inference(avatar_split_clause,[],[f592,f1971,f1968]) ).
thf(f1980,definition,
( spl247_60
<=> ( axvarcons = $true ) ),
introduced(definition,[new_symbols(definition,[spl247_60])],[avatar_definition]) ).
thf(f1982,plain,
( ( axvarcons = $true )
| ~ spl247_60 ),
inference(avatar_component_clause,[],[f1980]) ).
thf(f2405,definition,
( spl247_164
<=> ( laminj = $false ) ),
introduced(definition,[new_symbols(definition,[spl247_164])],[avatar_definition]) ).
thf(f2407,plain,
( ( laminj = $false )
| ~ spl247_164 ),
inference(avatar_component_clause,[],[f2405]) ).
thf(f2409,definition,
( spl247_165
<=> ! [X2: term,X1: term] :
( ( X1 = X2 )
| ( ( lam @ X1 )
!= ( lam @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl247_165])],[avatar_definition]) ).
thf(f2410,plain,
( ! [X2: term,X1: term] :
( ( ( lam @ X1 )
!= ( lam @ X2 ) )
| ( X1 = X2 ) )
| ~ spl247_165 ),
inference(avatar_component_clause,[],[f2409]) ).
thf(f2411,plain,
( spl247_164
| spl247_165 ),
inference(avatar_split_clause,[],[f1058,f2409,f2405]) ).
thf(f2413,definition,
( spl247_166
<=> ( laminj = $true ) ),
introduced(definition,[new_symbols(definition,[spl247_166])],[avatar_definition]) ).
thf(f2415,plain,
( ( laminj = $true )
| ~ spl247_166 ),
inference(avatar_component_clause,[],[f2413]) ).
thf(f2693,definition,
( spl247_233
<=> ! [X2: subst,X1: term] :
( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 ) ),
introduced(definition,[new_symbols(definition,[spl247_233])],[avatar_definition]) ).
thf(f2694,plain,
( ! [X2: subst,X1: term] :
( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 )
| ~ spl247_233 ),
inference(avatar_component_clause,[],[f2693]) ).
thf(f2696,definition,
( spl247_234
<=> ( axshiftcons = $false ) ),
introduced(definition,[new_symbols(definition,[spl247_234])],[avatar_definition]) ).
thf(f2698,plain,
( ( axshiftcons = $false )
| ~ spl247_234 ),
inference(avatar_component_clause,[],[f2696]) ).
thf(f2699,plain,
( spl247_233
| spl247_234 ),
inference(avatar_split_clause,[],[f1395,f2696,f2693]) ).
thf(f2701,definition,
( spl247_235
<=> ( axshiftcons = $true ) ),
introduced(definition,[new_symbols(definition,[spl247_235])],[avatar_definition]) ).
thf(f2703,plain,
( ( axshiftcons = $true )
| ~ spl247_235 ),
inference(avatar_component_clause,[],[f2701]) ).
thf(f2895,definition,
( spl247_281
<=> ( hoaslaminj = $false ) ),
introduced(definition,[new_symbols(definition,[spl247_281])],[avatar_definition]) ).
thf(f2897,plain,
( ( hoaslaminj = $false )
| ~ spl247_281 ),
inference(avatar_component_clause,[],[f2895]) ).
thf(f2903,definition,
( spl247_283
<=> ( hoaslaminj = $true ) ),
introduced(definition,[new_symbols(definition,[spl247_283])],[avatar_definition]) ).
thf(f2905,plain,
( ( hoaslaminj = $true )
| ~ spl247_283 ),
inference(avatar_component_clause,[],[f2903]) ).
thf(f2907,definition,
( spl247_284
<=> ! [X2: term,X1: subst,X3: subst] :
( ( sub @ ( sK233 @ X1 @ X2 ) @ X3 )
= ( sK233 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl247_284])],[avatar_definition]) ).
thf(f2908,plain,
( ! [X2: term,X3: subst,X1: subst] :
( ( sub @ ( sK233 @ X1 @ X2 ) @ X3 )
= ( sK233 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
| ~ spl247_284 ),
inference(avatar_component_clause,[],[f2907]) ).
thf(f2909,plain,
( spl247_283
| spl247_284 ),
inference(avatar_split_clause,[],[f1605,f2907,f2903]) ).
thf(f2911,definition,
( spl247_285
<=> ! [X2: subst,X1: subst,X3: term] :
( ( sub @ ( sK234 @ X1 @ X3 ) @ X2 )
= ( sK234 @ ( comp @ X1 @ X2 ) @ ( sub @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl247_285])],[avatar_definition]) ).
thf(f2912,plain,
( ! [X2: subst,X3: term,X1: subst] :
( ( sub @ ( sK234 @ X1 @ X3 ) @ X2 )
= ( sK234 @ ( comp @ X1 @ X2 ) @ ( sub @ X3 @ X2 ) ) )
| ~ spl247_285 ),
inference(avatar_component_clause,[],[f2911]) ).
thf(f2913,plain,
( spl247_285
| spl247_283 ),
inference(avatar_split_clause,[],[f1616,f2903,f2911]) ).
thf(f2915,definition,
( spl247_286
<=> ( ( lam @ ( sK233 @ sh @ one ) )
= ( lam @ ( sK234 @ sh @ one ) ) ) ),
introduced(definition,[new_symbols(definition,[spl247_286])],[avatar_definition]) ).
thf(f2917,plain,
( ( ( lam @ ( sK233 @ sh @ one ) )
= ( lam @ ( sK234 @ sh @ one ) ) )
| ~ spl247_286 ),
inference(avatar_component_clause,[],[f2915]) ).
thf(f2918,plain,
( spl247_286
| spl247_283 ),
inference(avatar_split_clause,[],[f1619,f2903,f2915]) ).
thf(f2920,definition,
( spl247_287
<=> ( ( sK233 @ sK236 @ sK235 )
= ( sK234 @ sK236 @ sK235 ) ) ),
introduced(definition,[new_symbols(definition,[spl247_287])],[avatar_definition]) ).
thf(f2922,plain,
( ( ( sK233 @ sK236 @ sK235 )
!= ( sK234 @ sK236 @ sK235 ) )
| spl247_287 ),
inference(avatar_component_clause,[],[f2920]) ).
thf(f2923,plain,
( spl247_283
| ~ spl247_287 ),
inference(avatar_split_clause,[],[f1624,f2920,f2903]) ).
thf(f2947,definition,
( spl247_293
<=> ( hoaslaminj_lthm = $true ) ),
introduced(definition,[new_symbols(definition,[spl247_293])],[avatar_definition]) ).
thf(f2950,plain,
( spl247_293
| spl247_60 ),
inference(avatar_split_clause,[],[f1639,f1980,f2947]) ).
thf(f2951,plain,
( spl247_235
| spl247_293 ),
inference(avatar_split_clause,[],[f1641,f2947,f2701]) ).
thf(f2952,plain,
( spl247_166
| spl247_293 ),
inference(avatar_split_clause,[],[f1643,f2947,f2413]) ).
thf(f2953,plain,
( spl247_281
| spl247_293 ),
inference(avatar_split_clause,[],[f1642,f2947,f2895]) ).
thf(f3066,plain,
~ spl247_293,
inference(avatar_split_clause,[],[f325,f2947]) ).
thf(f3138,plain,
( ( $false = $true )
| ~ spl247_164
| ~ spl247_166 ),
inference(forward_demodulation,[],[f2415,f2407]) ).
thf(f3139,plain,
( $false
| ~ spl247_164
| ~ spl247_166 ),
inference(trivial_inequality_removal,[],[f3138]) ).
thf(f3140,plain,
( ~ spl247_164
| ~ spl247_166 ),
inference(avatar_contradiction_clause,[],[f3139]) ).
thf(f3167,plain,
( ( $false = $true )
| ~ spl247_281
| ~ spl247_283 ),
inference(forward_demodulation,[],[f2905,f2897]) ).
thf(f3168,plain,
( $false
| ~ spl247_281
| ~ spl247_283 ),
inference(trivial_inequality_removal,[],[f3167]) ).
thf(f3169,plain,
( ~ spl247_281
| ~ spl247_283 ),
inference(avatar_contradiction_clause,[],[f3168]) ).
thf(f3302,plain,
( ! [X2: subst,X0: term,X1: subst] :
( ( sK233 @ ( comp @ X1 @ ( push @ X0 @ X2 ) ) @ X0 )
= ( sub @ ( sK233 @ X1 @ one ) @ ( push @ X0 @ X2 ) ) )
| ~ spl247_57
| ~ spl247_284 ),
inference(superposition,[],[f2908,f1969]) ).
thf(f3527,plain,
( ! [X0: term] :
( ( ( lam @ X0 )
!= ( lam @ ( sK233 @ sh @ one ) ) )
| ( ( sK234 @ sh @ one )
= X0 ) )
| ~ spl247_165
| ~ spl247_286 ),
inference(superposition,[],[f2410,f2917]) ).
thf(f3531,plain,
( ! [X2: term,X0: subst,X1: term] :
( ( sK234 @ X0 @ ( sub @ X1 @ ( push @ X2 @ X0 ) ) )
= ( sub @ ( sK234 @ sh @ X1 ) @ ( push @ X2 @ X0 ) ) )
| ~ spl247_233
| ~ spl247_285 ),
inference(superposition,[],[f2912,f2694]) ).
thf(f3540,plain,
( ( ( sK234 @ sh @ one )
= ( sK233 @ sh @ one ) )
| ~ spl247_165
| ~ spl247_286 ),
inference(equality_resolution,[],[f3527]) ).
thf(f3542,plain,
( ! [X0: subst,X1: term] :
( ( sub @ ( sK233 @ sh @ one ) @ ( push @ X1 @ X0 ) )
= ( sK233 @ X0 @ X1 ) )
| ~ spl247_57
| ~ spl247_233
| ~ spl247_284 ),
inference(superposition,[],[f3302,f2694]) ).
thf(f3573,plain,
( ( $false = $true )
| ~ spl247_58
| ~ spl247_60 ),
inference(superposition,[],[f1973,f1982]) ).
thf(f3578,plain,
( $false
| ~ spl247_58
| ~ spl247_60 ),
inference(trivial_inequality_removal,[],[f3573]) ).
thf(f3579,plain,
( ~ spl247_58
| ~ spl247_60 ),
inference(avatar_contradiction_clause,[],[f3578]) ).
thf(f3881,plain,
( ! [X0: term,X1: subst] :
( ( sub @ ( sK234 @ sh @ one ) @ ( push @ X0 @ X1 ) )
= ( sK234 @ X1 @ X0 ) )
| ~ spl247_57
| ~ spl247_233
| ~ spl247_285 ),
inference(superposition,[],[f3531,f1969]) ).
thf(f3883,plain,
( ! [X0: term,X1: subst] :
( ( sub @ ( sK233 @ sh @ one ) @ ( push @ X0 @ X1 ) )
= ( sK234 @ X1 @ X0 ) )
| ~ spl247_57
| ~ spl247_165
| ~ spl247_233
| ~ spl247_285
| ~ spl247_286 ),
inference(forward_demodulation,[],[f3881,f3540]) ).
thf(f3884,plain,
( ! [X0: term,X1: subst] :
( ( sK233 @ X1 @ X0 )
= ( sK234 @ X1 @ X0 ) )
| ~ spl247_57
| ~ spl247_165
| ~ spl247_233
| ~ spl247_284
| ~ spl247_285
| ~ spl247_286 ),
inference(forward_demodulation,[],[f3883,f3542]) ).
thf(f3893,plain,
( ( ( sK233 @ sK236 @ sK235 )
!= ( sK233 @ sK236 @ sK235 ) )
| ~ spl247_57
| ~ spl247_165
| ~ spl247_233
| ~ spl247_284
| ~ spl247_285
| ~ spl247_286
| spl247_287 ),
inference(superposition,[],[f2922,f3884]) ).
thf(f3894,plain,
( $false
| ~ spl247_57
| ~ spl247_165
| ~ spl247_233
| ~ spl247_284
| ~ spl247_285
| ~ spl247_286
| spl247_287 ),
inference(trivial_inequality_removal,[],[f3893]) ).
thf(f3895,plain,
( ~ spl247_57
| ~ spl247_165
| ~ spl247_233
| ~ spl247_284
| ~ spl247_285
| ~ spl247_286
| spl247_287 ),
inference(avatar_contradiction_clause,[],[f3894]) ).
thf(f3912,plain,
( ( $false = $true )
| ~ spl247_234
| ~ spl247_235 ),
inference(superposition,[],[f2698,f2703]) ).
thf(f3918,plain,
( $false
| ~ spl247_234
| ~ spl247_235 ),
inference(trivial_inequality_removal,[],[f3912]) ).
thf(f3919,plain,
( ~ spl247_234
| ~ spl247_235 ),
inference(avatar_contradiction_clause,[],[f3918]) ).
cnf(s42,plain,
( spl247_57
| spl247_58 ),
inference(sat_conversion,[],[f1974]) ).
cnf(s135,plain,
( spl247_164
| spl247_165 ),
inference(sat_conversion,[],[f2411]) ).
cnf(s190,plain,
( spl247_233
| spl247_234 ),
inference(sat_conversion,[],[f2699]) ).
cnf(s225,plain,
( spl247_283
| spl247_284 ),
inference(sat_conversion,[],[f2909]) ).
cnf(s226,plain,
( spl247_283
| spl247_285 ),
inference(sat_conversion,[],[f2913]) ).
cnf(s227,plain,
( spl247_283
| spl247_286 ),
inference(sat_conversion,[],[f2918]) ).
cnf(s228,plain,
( spl247_283
| ~ spl247_287 ),
inference(sat_conversion,[],[f2923]) ).
cnf(s232,plain,
( spl247_60
| spl247_293 ),
inference(sat_conversion,[],[f2950]) ).
cnf(s233,plain,
( spl247_235
| spl247_293 ),
inference(sat_conversion,[],[f2951]) ).
cnf(s234,plain,
( spl247_166
| spl247_293 ),
inference(sat_conversion,[],[f2952]) ).
cnf(s235,plain,
( spl247_281
| spl247_293 ),
inference(sat_conversion,[],[f2953]) ).
cnf(s259,plain,
~ spl247_293,
inference(sat_conversion,[],[f3066]) ).
cnf(s267,plain,
( ~ spl247_164
| ~ spl247_166 ),
inference(sat_conversion,[],[f3140]) ).
cnf(s271,plain,
( ~ spl247_281
| ~ spl247_283 ),
inference(sat_conversion,[],[f3169]) ).
cnf(s304,plain,
( ~ spl247_58
| ~ spl247_60 ),
inference(sat_conversion,[],[f3579]) ).
cnf(s312,plain,
( ~ spl247_57
| ~ spl247_165
| ~ spl247_233
| ~ spl247_284
| ~ spl247_285
| ~ spl247_286
| spl247_287 ),
inference(sat_conversion,[],[f3895]) ).
cnf(s314,plain,
( ~ spl247_234
| ~ spl247_235 ),
inference(sat_conversion,[],[f3919]) ).
cnf(s316,plain,
spl247_281,
inference(rat,[],[s235,s259]) ).
cnf(s317,plain,
~ spl247_283,
inference(rat,[],[s271,s316]) ).
cnf(s318,plain,
spl247_166,
inference(rat,[],[s234,s259]) ).
cnf(s319,plain,
~ spl247_164,
inference(rat,[],[s267,s318]) ).
cnf(s320,plain,
spl247_235,
inference(rat,[],[s233,s259]) ).
cnf(s321,plain,
~ spl247_234,
inference(rat,[],[s314,s320]) ).
cnf(s322,plain,
spl247_60,
inference(rat,[],[s232,s259]) ).
cnf(s323,plain,
~ spl247_58,
inference(rat,[],[s304,s322]) ).
cnf(s324,plain,
~ spl247_287,
inference(rat,[],[s228,s317]) ).
cnf(s325,plain,
spl247_286,
inference(rat,[],[s227,s317]) ).
cnf(s326,plain,
spl247_285,
inference(rat,[],[s226,s317]) ).
cnf(s327,plain,
spl247_284,
inference(rat,[],[s225,s317]) ).
cnf(s328,plain,
spl247_233,
inference(rat,[],[s190,s321]) ).
cnf(s329,plain,
spl247_165,
inference(rat,[],[s135,s319]) ).
cnf(s330,plain,
~ spl247_57,
inference(rat,[],[s312,s324,s325,s326,s327,s328,s329]) ).
cnf(s331,plain,
$false,
inference(rat,[],[s42,s323,s330]) ).
thf(f3920,plain,
$false,
inference(avatar_sat_refutation,[],[s331]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG258^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:33:36 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.20/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.59/0.39 % (1061326)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.59/0.39 % (1061331)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1286567791:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.59/0.39 % (1061337)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.59/0.39 % (1061337)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
% 0.59/0.39 % (1061332)lrs+10_16_si=on:nwc=1.5:random_seed=283841533:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.59/0.39 % (1061333)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1617951421:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.59/0.39 % (1061334)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=153116960: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)
% 0.59/0.39 % (1061335)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1881619819:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.59/0.39 % (1061336)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2241287639:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.59/0.39 % (1061337)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=1682618181:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.59/0.39 % (1061333)Instruction limit reached!
% 0.59/0.39 % (1061333)------------------------------
% 0.59/0.39 % (1061333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.39 % (1061333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.39 % (1061333)CaDiCaL version: 2.1.3
% 0.59/0.39 % (1061333)Termination reason: Instruction limit
% 0.59/0.39 % (1061333)Termination phase: shuffling
% 0.59/0.39 % (1061333)Time elapsed: 0.002 s
% 0.59/0.39 % (1061333)Peak memory usage: 10 MB
% 0.59/0.39 % (1061333)Instructions burned: 3 (million)
% 0.59/0.39 % (1061332)Instruction limit reached!
% 0.59/0.39 % (1061332)------------------------------
% 0.59/0.39 % (1061332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.39 % (1061332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.39 % (1061332)CaDiCaL version: 2.1.3
% 0.59/0.39 % (1061332)Termination reason: Instruction limit
% 0.59/0.39 % (1061332)Termination phase: shuffling
% 0.59/0.39 % (1061332)Time elapsed: 0.008 s
% 0.59/0.39 % (1061332)Peak memory usage: 10 MB
% 0.59/0.39 % (1061332)Instructions burned: 18 (million)
% 0.59/0.39 % (1061335)Instruction limit reached!
% 0.59/0.39 % (1061335)------------------------------
% 0.59/0.39 % (1061335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.39 % (1061335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.39 % (1061335)CaDiCaL version: 2.1.3
% 0.59/0.39 % (1061335)Termination reason: Instruction limit
% 0.59/0.39 % (1061335)Termination phase: shuffling
% 0.59/0.39 % (1061335)Time elapsed: 0.011 s
% 0.59/0.39 % (1061335)Peak memory usage: 11 MB
% 0.59/0.39 % (1061335)Instructions burned: 24 (million)
% 0.59/0.39 % (1061331)Instruction limit reached!
% 0.59/0.39 % (1061331)------------------------------
% 0.59/0.39 % (1061331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.39 % (1061331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.39 % (1061331)CaDiCaL version: 2.1.3
% 0.59/0.39 % (1061331)Termination reason: Instruction limit
% 0.59/0.39 % (1061331)Termination phase: shuffling
% 0.59/0.39 % (1061331)Time elapsed: 0.022 s
% 0.59/0.39 % (1061331)Peak memory usage: 12 MB
% 0.59/0.39 % (1061331)Instructions burned: 91 (million)
% 0.59/0.39 % (1061345)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3792366524:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.59/0.39 % (1061348)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=515242893:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.59/0.42 % (1061345)Instruction limit reached!
% 0.59/0.42 % (1061345)------------------------------
% 0.59/0.42 % (1061345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.42 % (1061345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.42 % (1061345)CaDiCaL version: 2.1.3
% 0.59/0.42 % (1061345)Termination reason: Instruction limit
% 0.59/0.42 % (1061345)Termination phase: shuffling
% 0.59/0.42 % (1061345)Time elapsed: 0.002 s
% 0.59/0.42 % (1061345)Peak memory usage: 10 MB
% 0.59/0.42 % (1061345)Instructions burned: 2 (million)
% 0.59/0.42 % (1061346)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2389738105:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.59/0.42 % (1061347)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.59/0.42 % (1061348)Instruction limit reached!
% 0.59/0.42 % (1061348)------------------------------
% 0.59/0.42 % (1061348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.42 % (1061348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.42 % (1061348)CaDiCaL version: 2.1.3
% 0.59/0.42 % (1061348)Termination reason: Instruction limit
% 0.59/0.42 % (1061348)Termination phase: Property scanning
% 0.59/0.42 % (1061348)Time elapsed: 0.005 s
% 0.59/0.42 % (1061348)Peak memory usage: 10 MB
% 0.59/0.42 % (1061348)Instructions burned: 22 (million)
% 0.59/0.42 % (1061346)Instruction limit reached!
% 0.59/0.42 % (1061346)------------------------------
% 0.59/0.42 % (1061346)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.42 % (1061346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.42 % (1061346)CaDiCaL version: 2.1.3
% 0.59/0.42 % (1061346)Termination reason: Instruction limit
% 0.59/0.42 % (1061346)Termination phase: shuffling
% 0.59/0.42 % (1061346)Time elapsed: 0.003 s
% 0.59/0.42 % (1061346)Peak memory usage: 10 MB
% 0.59/0.42 % (1061346)Instructions burned: 7 (million)
% 0.59/0.42 % (1061347)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1620586386:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.59/0.42 % (1061336)Instruction limit reached!
% 0.59/0.42 % (1061336)------------------------------
% 0.59/0.42 % (1061336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.42 % (1061336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.42 % (1061336)CaDiCaL version: 2.1.3
% 0.59/0.42 % (1061336)Termination reason: Instruction limit
% 0.59/0.42 % (1061336)Termination phase: Property scanning
% 0.59/0.42 % (1061336)Time elapsed: 0.034 s
% 0.59/0.42 % (1061336)Peak memory usage: 12 MB
% 0.59/0.42 % (1061336)Instructions burned: 75 (million)
% 0.59/0.42 % (1061347)Instruction limit reached!
% 0.59/0.42 % (1061347)------------------------------
% 0.59/0.42 % (1061347)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.42 % (1061347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.42 % (1061347)CaDiCaL version: 2.1.3
% 0.59/0.42 % (1061347)Termination reason: Instruction limit
% 0.59/0.42 % (1061347)Termination phase: shuffling
% 0.59/0.42 % (1061347)Time elapsed: 0.007 s
% 0.59/0.42 % (1061347)Peak memory usage: 10 MB
% 0.59/0.42 % (1061347)Instructions burned: 15 (million)
% 0.59/0.42 % (1061353)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=1699801574:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.59/0.42 % (1061351)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
% 0.59/0.42 % (1061351)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.59/0.42 % (1061351)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=115148834:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.59/0.42 % (1061356)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.59/0.46 % (1061355)lrs+10_1_si=on:cs=on:random_seed=1941909467:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.59/0.46 % (1061356)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=1141557206:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.59/0.46 % (1061355)Instruction limit reached!
% 0.59/0.46 % (1061355)------------------------------
% 0.59/0.46 % (1061355)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (1061355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % (1061355)CaDiCaL version: 2.1.3
% 0.59/0.46 % (1061355)Termination reason: Instruction limit
% 0.59/0.46 % (1061355)Termination phase: shuffling
% 0.59/0.46 % (1061355)Time elapsed: 0.004 s
% 0.59/0.46 % (1061355)Peak memory usage: 10 MB
% 0.59/0.46 % (1061355)Instructions burned: 9 (million)
% 0.59/0.46 % (1061356)Instruction limit reached!
% 0.59/0.46 % (1061356)------------------------------
% 0.59/0.46 % (1061356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (1061356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % (1061356)CaDiCaL version: 2.1.3
% 0.59/0.46 % (1061356)Termination reason: Instruction limit
% 0.59/0.46 % (1061356)Termination phase: shuffling
% 0.59/0.46 % (1061356)Time elapsed: 0.002 s
% 0.59/0.46 % (1061356)Peak memory usage: 10 MB
% 0.59/0.46 % (1061356)Instructions burned: 4 (million)
% 0.59/0.46 % (1061351)Instruction limit reached!
% 0.59/0.46 % (1061351)------------------------------
% 0.59/0.46 % (1061351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (1061351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % (1061351)CaDiCaL version: 2.1.3
% 0.59/0.46 % (1061351)Termination reason: Instruction limit
% 0.59/0.46 % (1061351)Termination phase: Property scanning
% 0.59/0.46 % (1061351)Time elapsed: 0.013 s
% 0.59/0.46 % (1061351)Peak memory usage: 10 MB
% 0.59/0.46 % (1061351)Instructions burned: 29 (million)
% 0.59/0.46 % (1061357)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=786813421:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.59/0.46 % (1061353)Instruction limit reached!
% 0.59/0.46 % (1061353)------------------------------
% 0.59/0.46 % (1061353)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (1061353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % (1061353)CaDiCaL version: 2.1.3
% 0.59/0.46 % (1061353)Termination reason: Instruction limit
% 0.59/0.46 % (1061353)Termination phase: Saturation
% 0.59/0.46 % (1061353)Time elapsed: 0.019 s
% 0.59/0.46 % (1061353)Peak memory usage: 12 MB
% 0.59/0.46 % (1061353)Instructions burned: 88 (million)
% 0.59/0.46 % (1061337)Instruction limit reached!
% 0.59/0.46 % (1061337)------------------------------
% 0.59/0.46 % (1061337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (1061337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % (1061337)CaDiCaL version: 2.1.3
% 0.59/0.46 % (1061337)Termination reason: Instruction limit
% 0.59/0.46 % (1061337)Termination phase: Saturation
% 0.59/0.46 % (1061337)Time elapsed: 0.066 s
% 0.59/0.46 % (1061337)Peak memory usage: 13 MB
% 0.59/0.46 % (1061337)Instructions burned: 158 (million)
% 0.59/0.46 % (1061366)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3597268328:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.59/0.46 % (1061357)Refutation not found, incomplete strategy
% 0.59/0.46 % (1061357)------------------------------
% 0.59/0.46 % (1061357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.59/0.46 % (1061357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.59/0.46 % (1061357)CaDiCaL version: 2.1.3
% 0.59/0.46 % (1061357)Termination reason: Refutation not found, incomplete strategy
% 0.59/0.46 % (1061357)Time elapsed: 0.012 s
% 0.59/0.46 % (1061357)Peak memory usage: 13 MB
% 0.59/0.46 % (1061357)Instructions burned: 25 (million)
% 0.59/0.46 % (1061357)------------------------------
% 0.59/0.46 % (1061357)------------------------------
% 0.59/0.46 % (1061362)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1175572984:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.59/0.46 % (1061363)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3009791966:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.28/0.46 % (1061364)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=680521594:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.28/0.46 % (1061364)Instruction limit reached!
% 1.28/0.46 % (1061364)------------------------------
% 1.28/0.46 % (1061364)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.46 % (1061364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.46 % (1061364)CaDiCaL version: 2.1.3
% 1.28/0.46 % (1061364)Termination reason: Instruction limit
% 1.28/0.46 % (1061364)Termination phase: shuffling
% 1.28/0.46 % (1061364)Time elapsed: 0.007 s
% 1.28/0.46 % (1061364)Peak memory usage: 10 MB
% 1.28/0.46 % (1061364)Instructions burned: 16 (million)
% 1.28/0.46 % (1061367)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=191656114:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.28/0.46 % (1061363)Instruction limit reached!
% 1.28/0.46 % (1061363)------------------------------
% 1.28/0.46 % (1061363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.46 % (1061363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.46 % (1061363)CaDiCaL version: 2.1.3
% 1.28/0.46 % (1061363)Termination reason: Instruction limit
% 1.28/0.46 % (1061363)Termination phase: Naming
% 1.28/0.46 % (1061363)Time elapsed: 0.012 s
% 1.28/0.46 % (1061363)Peak memory usage: 11 MB
% 1.28/0.46 % (1061363)Instructions burned: 26 (million)
% 1.28/0.46 % (1061369)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1163405758: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)
% 1.28/0.46 % (1061367)Instruction limit reached!
% 1.28/0.46 % (1061367)------------------------------
% 1.28/0.46 % (1061367)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.46 % (1061367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.46 % (1061367)CaDiCaL version: 2.1.3
% 1.28/0.46 % (1061367)Termination reason: Instruction limit
% 1.28/0.46 % (1061367)Termination phase: shuffling
% 1.28/0.46 % (1061367)Time elapsed: 0.006 s
% 1.28/0.46 % (1061367)Peak memory usage: 10 MB
% 1.28/0.46 % (1061367)Instructions burned: 14 (million)
% 1.28/0.46 % (1061369)Instruction limit reached!
% 1.28/0.46 % (1061369)------------------------------
% 1.28/0.46 % (1061369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.46 % (1061369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.46 % (1061369)CaDiCaL version: 2.1.3
% 1.28/0.46 % (1061369)Termination reason: Instruction limit
% 1.28/0.46 % (1061369)Termination phase: shuffling
% 1.28/0.46 % (1061369)Time elapsed: 0.002 s
% 1.28/0.46 % (1061369)Peak memory usage: 10 MB
% 1.28/0.46 % (1061369)Instructions burned: 3 (million)
% 1.28/0.46 % (1061362)Refutation not found, incomplete strategy
% 1.28/0.46 % (1061362)------------------------------
% 1.28/0.46 % (1061362)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.46 % (1061362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.46 % (1061362)CaDiCaL version: 2.1.3
% 1.28/0.46 % (1061362)Termination reason: Refutation not found, incomplete strategy
% 1.28/0.46 % (1061362)Time elapsed: 0.021 s
% 1.28/0.46 % (1061362)Peak memory usage: 12 MB
% 1.28/0.46 % (1061362)Instructions burned: 49 (million)
% 1.28/0.46 % (1061362)------------------------------
% 1.28/0.46 % (1061362)------------------------------
% 1.28/0.46 % (1061373)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1183172437:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.28/0.46 % (1061375)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=641782038:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.28/0.46 % (1061378)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.28/0.46 % (1061378)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.28/0.46 % (1061377)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2421419528:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.28/0.46 % (1061378)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=1873474774:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.28/0.46 % (1061379)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.28/0.46 % (1061379)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=3894579349:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.28/0.46 % (1061373)Instruction limit reached!
% 1.28/0.46 % (1061373)------------------------------
% 1.28/0.46 % (1061373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.46 % (1061373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.46 % (1061373)CaDiCaL version: 2.1.3
% 1.28/0.46 % (1061373)Termination reason: Instruction limit
% 1.28/0.46 % (1061373)Termination phase: Property scanning
% 1.28/0.46 % (1061373)Time elapsed: 0.013 s
% 1.28/0.46 % (1061373)Peak memory usage: 10 MB
% 1.28/0.46 % (1061373)Instructions burned: 31 (million)
% 1.28/0.46 % (1061379)Instruction limit reached!
% 1.28/0.46 % (1061379)------------------------------
% 1.28/0.46 % (1061379)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.46 % (1061379)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.46 % (1061379)CaDiCaL version: 2.1.3
% 1.28/0.46 % (1061379)Termination reason: Instruction limit
% 1.28/0.46 % (1061379)Termination phase: shuffling
% 1.28/0.46 % (1061379)Time elapsed: 0.004 s
% 1.28/0.46 % (1061379)Peak memory usage: 10 MB
% 1.28/0.46 % (1061379)Instructions burned: 8 (million)
% 1.28/0.46 % (1061375)Instruction limit reached!
% 1.28/0.46 % (1061375)------------------------------
% 1.28/0.46 % (1061375)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.46 % (1061378)Instruction limit reached!
% 1.28/0.46 % (1061378)------------------------------
% 1.28/0.46 % (1061378)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.46 % (1061378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.46 % (1061375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.46 % (1061378)CaDiCaL version: 2.1.3
% 1.28/0.46 % (1061375)CaDiCaL version: 2.1.3
% 1.28/0.46 % (1061378)Termination reason: Instruction limit
% 1.28/0.46 % (1061378)Termination phase: shuffling
% 1.28/0.46 % (1061375)Termination reason: Instruction limit
% 1.28/0.46 % (1061375)Termination phase: Property scanning
% 1.28/0.46 % (1061378)Time elapsed: 0.008 s
% 1.28/0.46 % (1061375)Time elapsed: 0.013 s
% 1.28/0.46 % (1061378)Peak memory usage: 10 MB
% 1.28/0.46 % (1061375)Peak memory usage: 10 MB
% 1.28/0.46 % (1061378)Instructions burned: 15 (million)
% 1.28/0.46 % (1061375)Instructions burned: 32 (million)
% 1.28/0.46 % (1061385)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=835532:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.28/0.46 % (1061366) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1061326-1061366"...
% 1.28/0.46 % (1061377)Instruction limit reached!
% 1.28/0.46 % (1061377)------------------------------
% 1.28/0.46 % (1061377)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.46 % (1061377)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.46 % (1061377)CaDiCaL version: 2.1.3
% 1.28/0.46 % (1061377)Termination reason: Instruction limit
% 1.28/0.46 % (1061377)Termination phase: Property scanning
% 1.28/0.46 % (1061377)Time elapsed: 0.028 s
% 1.28/0.46 % (1061377)Peak memory usage: 12 MB
% 1.28/0.46 % (1061377)Instructions burned: 62 (million)
% 1.28/0.46 % (1061387)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=240962111:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.28/0.46 % (1061386)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3748519196:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.28/0.46 % (1061388)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2073541843:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.28/0.46 % (1061366)...printing done.
% 1.28/0.46 % (1061366)Refutation found. Thanks to Tanya!
% 1.28/0.46 % SZS status Theorem for theBenchmark
% 1.28/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 1.28/0.47 % (1061366)------------------------------
% 1.28/0.47 % (1061366)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.28/0.47 % (1061366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.28/0.47 % (1061366)CaDiCaL version: 2.1.3
% 1.28/0.47 % (1061366)Termination reason: Refutation
% 1.28/0.47 % (1061366)Time elapsed: 0.071 s
% 1.28/0.47 % (1061366)Peak memory usage: 16 MB
% 1.28/0.47 % (1061366)Instructions burned: 274 (million)
% 1.28/0.47 % (1061326)Success in time 0.191 s
% 1.28/0.47 % Vampire exiting
%------------------------------------------------------------------------------