%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG250^3 : 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 : 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 07:45:11 AM UTC 2026
% Result : Theorem 2.03s 0.70s
% Output : Refutation 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 74 ( 25 unt; 0 typ; 5 def)
% Number of atoms : 439 ( 99 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 718 ( 38 ~; 68 |; 0 &; 471 @)
% ( 7 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 411 ( 407 usr; 177 con; 0-4 aty)
% ( 69 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 129 ( 0 sgn 25 !; 0 ?; 129 :)
% 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,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_131,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
vIFF: $o > $o > $o ).
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_138,type,
sK0: ( subst > term > subst > $o ) > term ).
thf(func_def_139,type,
sK1: ( subst > term > subst > $o ) > term ).
thf(func_def_140,type,
sK2: ( subst > term > subst > $o ) > term ).
thf(func_def_141,type,
sK3: ( subst > term > subst > $o ) > term ).
thf(func_def_142,type,
sK4: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_143,type,
sK5: ( subst > term > subst > $o ) > subst ).
thf(func_def_144,type,
sK6: ( subst > term > subst > $o ) > subst ).
thf(func_def_145,type,
sK7: ( subst > term > subst > $o ) > term ).
thf(func_def_146,type,
sK8: ( subst > term > subst > $o ) > subst ).
thf(func_def_147,type,
sK9: ( subst > term > subst > $o ) > subst ).
thf(func_def_148,type,
sK10: ( subst > term > subst > $o ) > subst ).
thf(func_def_149,type,
sK11: ( subst > term > subst > $o ) > subst ).
thf(func_def_150,type,
sK12: ( subst > term > subst > $o ) > subst ).
thf(func_def_151,type,
sK13: ( subst > term > subst > $o ) > subst ).
thf(func_def_152,type,
sK14: ( subst > term > subst > $o ) > subst ).
thf(func_def_153,type,
sK15: ( subst > term > subst > $o ) > subst ).
thf(func_def_154,type,
sK16: ( subst > term > subst > $o ) > subst ).
thf(func_def_155,type,
sK17: ( subst > term > subst > $o ) > subst ).
thf(func_def_156,type,
sK18: ( subst > term > subst > $o ) > subst ).
thf(func_def_157,type,
sK19: ( subst > term > subst > $o ) > term ).
thf(func_def_158,type,
sK20: ( subst > term > subst > $o ) > subst ).
thf(func_def_159,type,
sK21: ( subst > term > subst > $o ) > subst ).
thf(func_def_160,type,
sK22: ( subst > term > subst > $o ) > subst ).
thf(func_def_161,type,
sK23: ( subst > term > subst > $o ) > subst ).
thf(func_def_162,type,
sK24: ( subst > term > subst > $o ) > subst ).
thf(func_def_163,type,
sK25: ( subst > term > subst > $o ) > subst ).
thf(func_def_164,type,
sK26: ( subst > term > subst > $o ) > subst ).
thf(func_def_165,type,
sK27: ( subst > term > subst > $o ) > subst ).
thf(func_def_166,type,
sK28: ( subst > term > subst > $o ) > subst ).
thf(func_def_167,type,
sK29: ( subst > term > subst > $o ) > term ).
thf(func_def_168,type,
sK30: ( subst > term > subst > $o ) > subst ).
thf(func_def_169,type,
sK31: ( subst > term > subst > $o ) > subst ).
thf(func_def_170,type,
sK32: ( subst > term > subst > $o ) > subst ).
thf(func_def_171,type,
sK33: ( subst > term > subst > $o ) > subst ).
thf(func_def_172,type,
sK34: ( subst > term > subst > $o ) > subst ).
thf(func_def_173,type,
sK35: ( subst > term > subst > $o ) > subst ).
thf(func_def_174,type,
sK36: ( subst > term > subst > $o ) > subst ).
thf(func_def_175,type,
sK37: ( subst > term > subst > $o ) > subst ).
thf(func_def_176,type,
sK38: ( subst > term > subst > $o ) > subst ).
thf(func_def_177,type,
sK39: ( subst > term > subst > $o ) > subst ).
thf(func_def_178,type,
sK40: ( subst > term > subst > $o ) > subst ).
thf(func_def_179,type,
sK41: ( subst > term > subst > $o ) > subst ).
thf(func_def_180,type,
sK42: ( subst > term > subst > $o ) > subst ).
thf(func_def_181,type,
sK43: ( subst > term > subst > $o ) > subst ).
thf(func_def_182,type,
sK44: ( subst > term > subst > $o ) > subst ).
thf(func_def_183,type,
sK45: ( subst > term > subst > $o ) > subst ).
thf(func_def_184,type,
sK46: ( subst > term > subst > $o ) > subst ).
thf(func_def_185,type,
sK47: ( subst > term > subst > $o ) > subst ).
thf(func_def_186,type,
sK48: ( subst > term > subst > $o ) > subst ).
thf(func_def_187,type,
sK49: ( subst > term > subst > $o ) > subst ).
thf(func_def_188,type,
sK50: ( subst > term > subst > $o ) > subst ).
thf(func_def_189,type,
sK51: ( subst > term > subst > $o ) > subst ).
thf(func_def_190,type,
sK52: ( subst > term > subst > $o ) > subst ).
thf(func_def_191,type,
sK53: ( subst > term > subst > $o ) > subst ).
thf(func_def_192,type,
sK54: ( subst > term > subst > $o ) > subst ).
thf(func_def_193,type,
sK55: ( subst > term > subst > $o ) > subst ).
thf(func_def_194,type,
sK56: ( subst > term > subst > $o ) > subst ).
thf(func_def_195,type,
sK57: ( subst > term > subst > $o ) > subst ).
thf(func_def_196,type,
sK58: ( subst > term > subst > $o ) > subst ).
thf(func_def_197,type,
sK59: ( subst > term > subst > $o ) > subst ).
thf(func_def_198,type,
sK60: ( subst > term > subst > $o ) > subst ).
thf(func_def_199,type,
sK61: ( subst > term > subst > $o ) > subst ).
thf(func_def_200,type,
sK62: ( subst > term > subst > $o ) > subst ).
thf(func_def_201,type,
sK63: ( subst > term > subst > $o ) > subst ).
thf(func_def_202,type,
sK64: ( subst > term > subst > $o ) > subst ).
thf(func_def_203,type,
sK65: ( subst > term > subst > $o ) > subst ).
thf(func_def_204,type,
sK66: ( subst > term > subst > $o ) > subst ).
thf(func_def_205,type,
sK67: ( subst > term > subst > $o ) > subst ).
thf(func_def_206,type,
sK68: ( subst > term > subst > $o ) > subst ).
thf(func_def_207,type,
sK69: ( subst > term > subst > $o ) > subst ).
thf(func_def_208,type,
sK70: ( subst > term > subst > $o ) > subst ).
thf(func_def_209,type,
sK71: ( subst > term > subst > $o ) > subst ).
thf(func_def_210,type,
sK72: ( subst > term > subst > $o ) > subst ).
thf(func_def_211,type,
sK73: ( subst > term > subst > $o ) > subst ).
thf(func_def_212,type,
sK74: ( subst > term > subst > $o ) > subst ).
thf(func_def_213,type,
sK75: subst > term > subst > $o ).
thf(func_def_214,type,
sK76: ( subst > term > term ) > subst ).
thf(func_def_215,type,
sK77: ( subst > term > term ) > term ).
thf(func_def_216,type,
sK78: ( subst > term > term ) > term ).
thf(func_def_217,type,
sK79: ( subst > term > term ) > subst ).
thf(func_def_218,type,
sK80: ( subst > term > term ) > subst ).
thf(func_def_219,type,
sK81: term ).
thf(func_def_220,type,
sK82: ( term > $o ) > term ).
thf(func_def_221,type,
sK83: ( term > $o ) > term ).
thf(func_def_222,type,
sK84: ( term > $o ) > term ).
thf(func_def_223,type,
sK85: ( term > $o ) > subst > term ).
thf(func_def_224,type,
sK86: ( term > $o ) > subst > term ).
thf(func_def_225,type,
sK87: ( term > $o ) > subst > term ).
thf(func_def_226,type,
sK88: ( term > $o ) > subst > term ).
thf(func_def_227,type,
sK89: term > $o ).
thf(func_def_228,type,
sK90: term > term ).
thf(func_def_229,type,
sK91: subst ).
thf(func_def_230,type,
sK92: term ).
thf(func_def_231,type,
sK93: term ).
thf(func_def_232,type,
sK94: ( term > $o ) > term ).
thf(func_def_233,type,
sK95: term > $o ).
thf(func_def_234,type,
sK96: term ).
thf(func_def_235,type,
sK97: subst ).
thf(func_def_236,type,
sK98: ( subst > term > term ) > term ).
thf(func_def_237,type,
sK99: ( subst > term > term ) > subst ).
thf(func_def_238,type,
sK100: ( subst > term > term ) > subst ).
thf(func_def_239,type,
sK101: subst > term > term ).
thf(func_def_240,type,
sK102: term ).
thf(func_def_241,type,
sK103: term ).
thf(func_def_242,type,
sK104: term ).
thf(func_def_243,type,
sK105: term ).
thf(func_def_244,type,
sK106: term ).
thf(func_def_245,type,
sK107: term ).
thf(func_def_246,type,
sK108: term ).
thf(func_def_247,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_248,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_249,type,
sK109: subst > ( term > $o ) > term > term > $o ).
thf(func_def_250,type,
sK110: term > $o ).
thf(func_def_251,type,
sK111: term ).
thf(func_def_252,type,
sK112: subst ).
thf(func_def_253,type,
sK113: ( term > $o ) > term ).
thf(func_def_254,type,
sK114: subst > term > ( term > $o ) > ( term > $o ) > term ).
thf(func_def_255,type,
sK115: ( term > $o ) > term ).
thf(func_def_256,type,
sK116: term ).
thf(func_def_257,type,
sK117: term > $o ).
thf(func_def_258,type,
sK118: subst ).
thf(func_def_259,type,
sK119: term > $o ).
thf(func_def_260,type,
sK120: term ).
thf(func_def_261,type,
sK121: ( subst > term > subst > $o ) > subst ).
thf(func_def_262,type,
sK122: ( subst > term > subst > $o ) > term ).
thf(func_def_263,type,
sK123: ( subst > term > subst > $o ) > term ).
thf(func_def_264,type,
sK124: ( subst > term > subst > $o ) > term ).
thf(func_def_265,type,
sK125: ( subst > term > subst > $o ) > subst ).
thf(func_def_266,type,
sK126: ( subst > term > subst > $o ) > term ).
thf(func_def_267,type,
sK127: ( subst > term > subst > $o ) > subst ).
thf(func_def_268,type,
sK128: ( subst > term > subst > $o ) > subst ).
thf(func_def_269,type,
sK129: ( subst > term > subst > $o ) > subst ).
thf(func_def_270,type,
sK130: ( subst > term > subst > $o ) > subst ).
thf(func_def_271,type,
sK131: ( subst > term > subst > $o ) > subst ).
thf(func_def_272,type,
sK132: ( subst > term > subst > $o ) > subst ).
thf(func_def_273,type,
sK133: ( subst > term > subst > $o ) > subst ).
thf(func_def_274,type,
sK134: ( subst > term > subst > $o ) > subst ).
thf(func_def_275,type,
sK135: ( subst > term > subst > $o ) > subst ).
thf(func_def_276,type,
sK136: ( subst > term > subst > $o ) > subst ).
thf(func_def_277,type,
sK137: subst > term > subst > $o ).
thf(func_def_278,type,
sK138: term ).
thf(func_def_279,type,
sK139: term ).
thf(func_def_280,type,
sK140: term ).
thf(func_def_281,type,
sK141: subst ).
thf(func_def_282,type,
sK142: ( term > $o ) > term > ( term > $o ) > subst > term ).
thf(func_def_283,type,
sK143: ( term > $o ) > subst > term ).
thf(func_def_284,type,
sK144: term ).
thf(func_def_285,type,
sK145: subst ).
thf(func_def_286,type,
sK146: term > $o ).
thf(func_def_287,type,
sK147: term > $o ).
thf(func_def_288,type,
sK148: term ).
thf(func_def_289,type,
sK149: ( subst > term > term ) > subst ).
thf(func_def_290,type,
sK150: ( subst > term > term ) > subst ).
thf(func_def_291,type,
sK151: ( subst > term > term ) > subst ).
thf(func_def_292,type,
sK152: ( subst > term > term ) > term ).
thf(func_def_293,type,
sK153: ( subst > term > term ) > term ).
thf(func_def_294,type,
sK154: ( subst > term > term ) > subst ).
thf(func_def_295,type,
sK155: subst > term > term ).
thf(func_def_296,type,
sK156: subst > term > term ).
thf(func_def_297,type,
sK157: term ).
thf(func_def_298,type,
sK158: subst ).
thf(func_def_299,type,
sK159: ( subst > term > subst > $o ) > subst ).
thf(func_def_300,type,
sK160: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_301,type,
sK161: ( subst > term > subst > $o ) > subst ).
thf(func_def_302,type,
sK162: ( subst > term > subst > $o ) > term ).
thf(func_def_303,type,
sK163: ( subst > term > subst > $o ) > subst ).
thf(func_def_304,type,
sK164: ( subst > term > subst > $o ) > term > term ).
thf(func_def_305,type,
sK165: ( subst > term > subst > $o ) > subst ).
thf(func_def_306,type,
sK166: ( subst > term > subst > $o ) > term ).
thf(func_def_307,type,
sK167: ( subst > term > subst > $o ) > subst ).
thf(func_def_308,type,
sK168: ( subst > term > subst > $o ) > subst ).
thf(func_def_309,type,
sK169: ( subst > term > subst > $o ) > subst ).
thf(func_def_310,type,
sK170: ( subst > term > subst > $o ) > term ).
thf(func_def_311,type,
sK171: ( subst > term > subst > $o ) > subst ).
thf(func_def_312,type,
sK172: ( subst > term > subst > $o ) > subst ).
thf(func_def_313,type,
sK173: ( subst > term > subst > $o ) > subst ).
thf(func_def_314,type,
sK174: ( subst > term > subst > $o ) > term > term ).
thf(func_def_315,type,
sK175: ( subst > term > subst > $o ) > term ).
thf(func_def_316,type,
sK176: ( subst > term > subst > $o ) > subst ).
thf(func_def_317,type,
sK177: ( subst > term > subst > $o ) > subst ).
thf(func_def_318,type,
sK178: ( subst > term > subst > $o ) > subst ).
thf(func_def_319,type,
sK179: ( subst > term > subst > $o ) > term ).
thf(func_def_320,type,
sK180: ( subst > term > subst > $o ) > subst ).
thf(func_def_321,type,
sK181: ( subst > term > subst > $o ) > subst ).
thf(func_def_322,type,
sK182: ( subst > term > subst > $o ) > subst ).
thf(func_def_323,type,
sK183: ( subst > term > subst > $o ) > term ).
thf(func_def_324,type,
sK184: ( subst > term > subst > $o ) > subst ).
thf(func_def_325,type,
sK185: ( subst > term > subst > $o ) > subst ).
thf(func_def_326,type,
sK186: ( subst > term > subst > $o ) > subst ).
thf(func_def_327,type,
sK187: ( subst > term > subst > $o ) > subst ).
thf(func_def_328,type,
sK188: ( subst > term > subst > $o ) > subst ).
thf(func_def_329,type,
sK189: subst > term > subst > $o ).
thf(func_def_330,type,
sK190: ( subst > term > term ) > subst ).
thf(func_def_331,type,
sK191: ( subst > term > term ) > term ).
thf(func_def_332,type,
sK192: ( subst > term > term ) > subst ).
thf(func_def_333,type,
sK193: ( subst > term > term ) > term ).
thf(func_def_334,type,
sK194: ( subst > term > term ) > subst ).
thf(func_def_335,type,
sK195: ( subst > term > term ) > term ).
thf(func_def_336,type,
sK196: term ).
thf(func_def_337,type,
sK197: ( term > $o ) > subst > ( term > $o ) > term > term ).
thf(func_def_338,type,
sK198: subst ).
thf(func_def_339,type,
sK199: term ).
thf(func_def_340,type,
sK200: term > $o ).
thf(func_def_341,type,
sK201: term > $o ).
thf(func_def_342,type,
sK202: ( term > $o ) > term ).
thf(func_def_343,type,
sK203: ( term > $o ) > term ).
thf(func_def_344,type,
sK204: ( term > $o ) > term ).
thf(func_def_345,type,
sK205: ( term > $o ) > term ).
thf(func_def_346,type,
sK206: ( term > $o ) > term ).
thf(func_def_347,type,
sK207: ( term > $o ) > term ).
thf(func_def_348,type,
sK208: ( term > $o ) > term ).
thf(func_def_349,type,
sK209: term > $o ).
thf(func_def_350,type,
sK210: term > term ).
thf(func_def_351,type,
sK211: term ).
thf(func_def_352,type,
sK212: subst ).
thf(func_def_353,type,
sK213: term ).
thf(func_def_354,type,
sK214: ( subst > term > subst > $o ) > subst ).
thf(func_def_355,type,
sK215: ( subst > term > subst > $o ) > term ).
thf(func_def_356,type,
sK216: ( subst > term > subst > $o ) > term ).
thf(func_def_357,type,
sK217: ( subst > term > subst > $o ) > subst ).
thf(func_def_358,type,
sK218: ( subst > term > subst > $o ) > subst ).
thf(func_def_359,type,
sK219: ( subst > term > subst > $o ) > term ).
thf(func_def_360,type,
sK220: ( subst > term > subst > $o ) > subst ).
thf(func_def_361,type,
sK221: ( subst > term > subst > $o ) > subst ).
thf(func_def_362,type,
sK222: ( subst > term > subst > $o ) > subst ).
thf(func_def_363,type,
sK223: ( subst > term > subst > $o ) > subst ).
thf(func_def_364,type,
sK224: ( subst > term > subst > $o ) > subst ).
thf(func_def_365,type,
sK225: ( subst > term > subst > $o ) > subst ).
thf(func_def_366,type,
sK226: ( subst > term > subst > $o ) > term ).
thf(func_def_367,type,
sK227: ( subst > term > subst > $o ) > subst ).
thf(func_def_368,type,
sK228: ( subst > term > subst > $o ) > subst ).
thf(func_def_369,type,
sK229: subst > term > subst > $o ).
thf(func_def_370,type,
sK230: term ).
thf(func_def_371,type,
sK231: subst ).
thf(func_def_372,type,
sK232: term ).
thf(func_def_373,type,
sK233: subst ).
thf(func_def_374,type,
sK234: term ).
thf(func_def_375,type,
sK235: term ).
thf(func_def_376,type,
sK236: term ).
thf(func_def_377,type,
sK237: term ).
thf(func_def_378,type,
sK238: term ).
thf(func_def_379,type,
sK239: term ).
thf(func_def_380,type,
sK240: ( term > $o ) > term ).
thf(func_def_381,type,
sK241: ( term > $o ) > term ).
thf(func_def_382,type,
sK242: ( term > $o ) > term ).
thf(func_def_383,type,
sK243: ( term > $o ) > term ).
thf(func_def_384,type,
sK244: ( term > $o ) > term ).
thf(func_def_385,type,
sK245: ( term > $o ) > term ).
thf(func_def_386,type,
sK246: term > $o ).
thf(func_def_387,type,
sK247: term ).
thf(func_def_388,type,
sK248: subst ).
thf(func_def_389,type,
sK249: subst ).
thf(func_def_390,type,
sK250: term ).
thf(func_def_391,type,
sK251: subst ).
thf(func_def_392,type,
sK252: term ).
thf(func_def_393,type,
sK253: subst ).
thf(func_def_394,type,
sK254: subst > ( term > $o ) > term ).
thf(func_def_395,type,
sK255: term > $o ).
thf(func_def_396,type,
sK256: term ).
thf(func_def_397,type,
sK257: subst ).
thf(func_def_398,type,
sK258: term ).
thf(func_def_399,type,
sK259: subst ).
thf(func_def_400,type,
sK260: subst ).
thf(func_def_401,type,
sK261: subst ).
thf(func_def_402,type,
sK262: subst ).
thf(func_def_403,type,
sK263: term ).
thf(f24,axiom,
( pushprop_p_and_p_prime
= ( ^ [X0: term,X1: subst,X2: term > $o,X3: term > $o] :
! [X4: term] :
( ( X2 @ ( sub @ X4 @ ( push @ X0 @ X1 ) ) )
<=> ( X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',pushprop_p_and_p_prime) ).
thf(f37,axiom,
! [X1: term > $o,X3: subst,X0: term > $o,X2: term] :
( ( ( pushprop_p_and_p_prime @ X2 @ X3 @ X0 @ X1 )
=> ( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ X4 ) )
=> ! [X4: term] :
( ( var @ X4 )
=> ( X0 @ ( sub @ X4 @ ( push @ X2 @ X3 ) ) ) ) ) )
= pushprop_lem3v2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',pushprop_lem3v2) ).
thf(f38,axiom,
pushprop_lem3v2_lthm = pushprop_lem3v2,
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',pushprop_lem3v2_lthm) ).
thf(f114,conjecture,
pushprop_lem3v2_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ pushprop_lem3v2_lthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f164,plain,
( pushprop_p_and_p_prime
= ( ^ [X0: term,X1: subst,X2: term > $o,X3: term > $o] :
! [X4: term] :
( ( X2 @ ( sub @ X4 @ ( push @ X0 @ X1 ) ) )
<=> ( X3 @ X4 ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f165,plain,
( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) ),
inference(fool_elimination,[],[f164]) ).
thf(f187,plain,
~ pushprop_lem3v2_lthm,
inference(rectify,[],[f115]) ).
thf(f188,plain,
pushprop_lem3v2_lthm != $true,
inference(fool_elimination,[],[f187]) ).
thf(f219,plain,
! [X0: term > $o,X1: subst,X2: term > $o,X3: term] :
( ( ( pushprop_p_and_p_prime @ X3 @ X1 @ X2 @ X0 )
=> ( ! [X4: term] :
( ( var @ X4 )
=> ( X0 @ X4 ) )
=> ! [X5: term] :
( ( var @ X5 )
=> ( X2 @ ( sub @ X5 @ ( push @ X3 @ X1 ) ) ) ) ) )
= pushprop_lem3v2 ),
inference(rectify,[],[f37]) ).
thf(f220,plain,
( pushprop_lem3v2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ ( term > $o )
@ ^ [Y3: term > $o] :
( ( pushprop_p_and_p_prime @ Y0 @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y3 @ Y4 ) ) )
=> ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y1 @ ( sub @ Y4 @ ( push @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f219]) ).
thf(f319,plain,
pushprop_lem3v2_lthm != $true,
inference(flattening,[],[f188]) ).
thf(f328,plain,
( pushprop_lem3v2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ ( term > $o )
@ ^ [Y3: term > $o] :
( ( pushprop_p_and_p_prime @ Y0 @ Y2 @ Y1 @ Y3 )
=> ( ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y3 @ Y4 ) ) )
=> ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y1 @ ( sub @ Y4 @ ( push @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f220]) ).
thf(f335,plain,
( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) ),
inference(cnf_transformation,[],[f165]) ).
thf(f342,plain,
pushprop_lem3v2 = pushprop_lem3v2_lthm,
inference(cnf_transformation,[],[f38]) ).
thf(f345,plain,
pushprop_lem3v2_lthm != $true,
inference(cnf_transformation,[],[f319]) ).
thf(f359,plain,
( pushprop_lem3v2_lthm
= ( !! @ term
@ ^ [Y0: term] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ ( term > $o )
@ ^ [Y3: term > $o] :
( ( ^ [Y4: term,Y5: subst,Y6: term > $o,Y7: term > $o] :
( !! @ term
@ ^ [Y8: term] :
( ( Y6 @ ( sub @ Y8 @ ( push @ Y4 @ Y5 ) ) )
= ( Y7 @ Y8 ) ) )
@ Y0
@ Y2
@ Y1
@ Y3 )
=> ( ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y3 @ Y4 ) ) )
=> ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y1 @ ( sub @ Y4 @ ( push @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f328,f342,f335]) ).
thf(f944,plain,
( ( pushprop_lem3v2_lthm = $true )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ ( term > $o )
@ ^ [Y3: term > $o] :
( ( ^ [Y4: term,Y5: subst,Y6: term > $o,Y7: term > $o] :
( !! @ term
@ ^ [Y8: term] :
( ( Y6 @ ( sub @ Y8 @ ( push @ Y4 @ Y5 ) ) )
= ( Y7 @ Y8 ) ) )
@ Y0
@ Y2
@ Y1
@ Y3 )
=> ( ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y3 @ Y4 ) ) )
=> ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y1 @ ( sub @ Y4 @ ( push @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f359]) ).
thf(f970,plain,
( ( $false
= ( ^ [Y0: term] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ subst
@ ^ [Y2: subst] :
( !! @ ( term > $o )
@ ^ [Y3: term > $o] :
( ( ^ [Y4: term,Y5: subst,Y6: term > $o,Y7: term > $o] :
( !! @ term
@ ^ [Y8: term] :
( ( Y6 @ ( sub @ Y8 @ ( push @ Y4 @ Y5 ) ) )
= ( Y7 @ Y8 ) ) )
@ Y0
@ Y2
@ Y1
@ Y3 )
=> ( ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y3 @ Y4 ) ) )
=> ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y1 @ ( sub @ Y4 @ ( push @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) )
@ sK116 ) )
| ( pushprop_lem3v2_lthm = $true ) ),
inference(sigma_proxy_clausification,[],[f944]) ).
thf(f971,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( sub @ Y3 @ ( push @ sK116 @ Y1 ) ) )
= ( Y2 @ Y3 ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ sK116 @ Y1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( pushprop_lem3v2_lthm = $true ) ),
inference(beta-eta_normalization,[],[f970]) ).
thf(f972,plain,
( ( $false
= ( ^ [Y0: term > $o] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y0 @ ( sub @ Y3 @ ( push @ sK116 @ Y1 ) ) )
= ( Y2 @ Y3 ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ Y3 ) ) )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y0 @ ( sub @ Y3 @ ( push @ sK116 @ Y1 ) ) ) ) ) ) ) ) )
@ sK117 ) )
| ( pushprop_lem3v2_lthm = $true ) ),
inference(sigma_proxy_clausification,[],[f971]) ).
thf(f973,plain,
( ( pushprop_lem3v2_lthm = $true )
| ( $false
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ term
@ ^ [Y2: term] :
( ( sK117 @ ( sub @ Y2 @ ( push @ sK116 @ Y0 ) ) )
= ( Y1 @ Y2 ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( sK117 @ ( sub @ Y2 @ ( push @ sK116 @ Y0 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f972]) ).
thf(f974,plain,
( ( $false
= ( ^ [Y0: subst] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ term
@ ^ [Y2: term] :
( ( sK117 @ ( sub @ Y2 @ ( push @ sK116 @ Y0 ) ) )
= ( Y1 @ Y2 ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y1 @ Y2 ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( sK117 @ ( sub @ Y2 @ ( push @ sK116 @ Y0 ) ) ) ) ) ) ) )
@ sK118 ) )
| ( pushprop_lem3v2_lthm = $true ) ),
inference(sigma_proxy_clausification,[],[f973]) ).
thf(f975,plain,
( ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK117 @ ( sub @ Y1 @ ( push @ sK116 @ sK118 ) ) )
= ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK117 @ ( sub @ Y1 @ ( push @ sK116 @ sK118 ) ) ) ) ) ) ) )
= $false )
| ( pushprop_lem3v2_lthm = $true ) ),
inference(beta-eta_normalization,[],[f974]) ).
thf(f976,plain,
( ( ( ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK117 @ ( sub @ Y1 @ ( push @ sK116 @ sK118 ) ) )
= ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ Y1 ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK117 @ ( sub @ Y1 @ ( push @ sK116 @ sK118 ) ) ) ) ) ) )
@ sK119 )
= $false )
| ( pushprop_lem3v2_lthm = $true ) ),
inference(sigma_proxy_clausification,[],[f975]) ).
thf(f977,plain,
( ( pushprop_lem3v2_lthm = $true )
| ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK117 @ ( sub @ Y0 @ ( push @ sK116 @ sK118 ) ) )
= ( sK119 @ Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK119 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK117 @ ( sub @ Y0 @ ( push @ sK116 @ sK118 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f976]) ).
thf(f978,plain,
( ( pushprop_lem3v2_lthm = $true )
| ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK119 @ Y0 ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK117 @ ( sub @ Y0 @ ( push @ sK116 @ sK118 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f977]) ).
thf(f979,plain,
( ( pushprop_lem3v2_lthm = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK117 @ ( sub @ Y0 @ ( push @ sK116 @ sK118 ) ) )
= ( sK119 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f977]) ).
thf(f980,plain,
! [X1: term] :
( ( ( ^ [Y0: term] :
( ( sK117 @ ( sub @ Y0 @ ( push @ sK116 @ sK118 ) ) )
= ( sK119 @ Y0 ) )
@ X1 )
= $true )
| ( pushprop_lem3v2_lthm = $true ) ),
inference(pi_proxy_clausification,[],[f979]) ).
thf(f981,plain,
! [X1: term] :
( ( pushprop_lem3v2_lthm = $true )
| ( ( ( sK117 @ ( sub @ X1 @ ( push @ sK116 @ sK118 ) ) )
= ( sK119 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f980]) ).
thf(f982,plain,
! [X1: term] :
( ( ( sK119 @ X1 )
= ( sK117 @ ( sub @ X1 @ ( push @ sK116 @ sK118 ) ) ) )
| ( pushprop_lem3v2_lthm = $true ) ),
inference(iff_proxy_clausification,[],[f981]) ).
thf(f984,plain,
! [X1: term] :
( ( pushprop_lem3v2_lthm = $true )
| ( $false
= ( sK119 @ X1 ) )
| ( ( sK117 @ ( sub @ X1 @ ( push @ sK116 @ sK118 ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f982]) ).
thf(f985,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK117 @ ( sub @ Y0 @ ( push @ sK116 @ sK118 ) ) ) ) )
= $false )
| ( pushprop_lem3v2_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f978]) ).
thf(f986,plain,
( ( pushprop_lem3v2_lthm = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK119 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f978]) ).
thf(f987,plain,
! [X1: term] :
( ( ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK119 @ Y0 ) )
@ X1 )
= $true )
| ( pushprop_lem3v2_lthm = $true ) ),
inference(pi_proxy_clausification,[],[f986]) ).
thf(f988,plain,
! [X1: term] :
( ( pushprop_lem3v2_lthm = $true )
| ( ( ( var @ X1 )
=> ( sK119 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f987]) ).
thf(f989,plain,
! [X1: term] :
( ( pushprop_lem3v2_lthm = $true )
| ( ( sK119 @ X1 )
= $true )
| ( ( var @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f988]) ).
thf(f990,plain,
( ( pushprop_lem3v2_lthm = $true )
| ( ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK117 @ ( sub @ Y0 @ ( push @ sK116 @ sK118 ) ) ) )
@ sK120 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f985]) ).
thf(f991,plain,
( ( pushprop_lem3v2_lthm = $true )
| ( ( ( var @ sK120 )
=> ( sK117 @ ( sub @ sK120 @ ( push @ sK116 @ sK118 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f990]) ).
thf(f992,plain,
( ( ( sK117 @ ( sub @ sK120 @ ( push @ sK116 @ sK118 ) ) )
= $false )
| ( pushprop_lem3v2_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f991]) ).
thf(f993,plain,
( ( ( var @ sK120 )
= $true )
| ( pushprop_lem3v2_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f991]) ).
thf(f2380,definition,
( spl264_144
<=> ( pushprop_lem3v2_lthm = $true ) ),
introduced(definition,[new_symbols(definition,[spl264_144])],[avatar_definition]) ).
thf(f2384,definition,
( spl264_145
<=> ! [X1: term] :
( ( $false
= ( sK119 @ X1 ) )
| ( ( sK117 @ ( sub @ X1 @ ( push @ sK116 @ sK118 ) ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl264_145])],[avatar_definition]) ).
thf(f2385,plain,
( ! [X1: term] :
( ( ( sK117 @ ( sub @ X1 @ ( push @ sK116 @ sK118 ) ) )
= $true )
| ( $false
= ( sK119 @ X1 ) ) )
| ~ spl264_145 ),
inference(avatar_component_clause,[],[f2384]) ).
thf(f2386,plain,
( spl264_144
| spl264_145 ),
inference(avatar_split_clause,[],[f984,f2384,f2380]) ).
thf(f2392,definition,
( spl264_147
<=> ! [X1: term] :
( ( ( sK119 @ X1 )
= $true )
| ( ( var @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl264_147])],[avatar_definition]) ).
thf(f2393,plain,
( ! [X1: term] :
( ( ( sK119 @ X1 )
= $true )
| ( ( var @ X1 )
= $false ) )
| ~ spl264_147 ),
inference(avatar_component_clause,[],[f2392]) ).
thf(f2394,plain,
( spl264_144
| spl264_147 ),
inference(avatar_split_clause,[],[f989,f2392,f2380]) ).
thf(f2396,definition,
( spl264_148
<=> ( ( var @ sK120 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl264_148])],[avatar_definition]) ).
thf(f2398,plain,
( ( ( var @ sK120 )
= $true )
| ~ spl264_148 ),
inference(avatar_component_clause,[],[f2396]) ).
thf(f2399,plain,
( spl264_148
| spl264_144 ),
inference(avatar_split_clause,[],[f993,f2380,f2396]) ).
thf(f2401,definition,
( spl264_149
<=> ( ( sK117 @ ( sub @ sK120 @ ( push @ sK116 @ sK118 ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl264_149])],[avatar_definition]) ).
thf(f2403,plain,
( ( ( sK117 @ ( sub @ sK120 @ ( push @ sK116 @ sK118 ) ) )
= $false )
| ~ spl264_149 ),
inference(avatar_component_clause,[],[f2401]) ).
thf(f2404,plain,
( spl264_149
| spl264_144 ),
inference(avatar_split_clause,[],[f992,f2380,f2401]) ).
thf(f3169,plain,
~ spl264_144,
inference(avatar_split_clause,[],[f345,f2380]) ).
thf(f3219,plain,
( ( $false = $true )
| ( $false
= ( sK119 @ sK120 ) )
| ~ spl264_145
| ~ spl264_149 ),
inference(superposition,[],[f2385,f2403]) ).
thf(f3220,plain,
( ( $false
= ( sK119 @ sK120 ) )
| ~ spl264_145
| ~ spl264_149 ),
inference(trivial_inequality_removal,[],[f3219]) ).
thf(f3317,plain,
( ( ( var @ sK120 )
= $false )
| ( $false = $true )
| ~ spl264_145
| ~ spl264_147
| ~ spl264_149 ),
inference(superposition,[],[f2393,f3220]) ).
thf(f3318,plain,
( ( ( var @ sK120 )
= $false )
| ~ spl264_145
| ~ spl264_147
| ~ spl264_149 ),
inference(trivial_inequality_removal,[],[f3317]) ).
thf(f3325,plain,
( ( $false = $true )
| ~ spl264_145
| ~ spl264_147
| ~ spl264_148
| ~ spl264_149 ),
inference(superposition,[],[f3318,f2398]) ).
thf(f3329,plain,
( $false
| ~ spl264_145
| ~ spl264_147
| ~ spl264_148
| ~ spl264_149 ),
inference(trivial_inequality_removal,[],[f3325]) ).
thf(f3330,plain,
( ~ spl264_145
| ~ spl264_147
| ~ spl264_148
| ~ spl264_149 ),
inference(avatar_contradiction_clause,[],[f3329]) ).
cnf(s125,plain,
( spl264_144
| spl264_145 ),
inference(sat_conversion,[],[f2386]) ).
cnf(s127,plain,
( spl264_144
| spl264_147 ),
inference(sat_conversion,[],[f2394]) ).
cnf(s128,plain,
( spl264_144
| spl264_148 ),
inference(sat_conversion,[],[f2399]) ).
cnf(s129,plain,
( spl264_144
| spl264_149 ),
inference(sat_conversion,[],[f2404]) ).
cnf(s274,plain,
~ spl264_144,
inference(sat_conversion,[],[f3169]) ).
cnf(s292,plain,
( ~ spl264_145
| ~ spl264_147
| ~ spl264_148
| ~ spl264_149 ),
inference(sat_conversion,[],[f3330]) ).
cnf(s293,plain,
spl264_149,
inference(rat,[],[s129,s274]) ).
cnf(s294,plain,
spl264_148,
inference(rat,[],[s128,s274]) ).
cnf(s295,plain,
spl264_147,
inference(rat,[],[s127,s274]) ).
cnf(s296,plain,
~ spl264_145,
inference(rat,[],[s292,s293,s294,s295]) ).
cnf(s298,plain,
$false,
inference(rat,[],[s125,s296,s274]) ).
thf(f3331,plain,
$false,
inference(avatar_sat_refutation,[],[s298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG250^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 % Computer : n017.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Tue Sep 29 17:27:37 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.30 Running higher-order theorem proving
% 0.26/0.37 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
% 1.01/0.59 % (640805)Detected a higher-order problem, will run a greedy HOL sequence.
% 1.01/0.59 % (640811)lrs+10_16_si=on:nwc=1.5:random_seed=4050852425:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 1.01/0.59 % (640811)Instruction limit reached!
% 1.01/0.59 % (640811)------------------------------
% 1.01/0.59 % (640811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.59 % (640811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.59 % (640816)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 1.01/0.59 % (640811)CaDiCaL version: 2.1.3
% 1.01/0.59 % (640811)Termination reason: Instruction limit
% 1.01/0.59 % (640811)Termination phase: shuffling
% 1.01/0.59 % (640811)Time elapsed: 0.008 s
% 1.01/0.59 % (640811)Peak memory usage: 10 MB
% 1.01/0.59 % (640811)Instructions burned: 19 (million)
% 1.01/0.59 % (640816)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
% 1.01/0.59 % (640810)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4010964580:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 1.01/0.59 % (640812)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1152237996:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 1.01/0.59 % (640813)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=3415305105: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)
% 1.01/0.59 % (640816)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=3444632123:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 1.01/0.59 % (640814)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=999036191:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 1.01/0.59 % (640815)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4172928801:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 1.01/0.59 % (640812)Instruction limit reached!
% 1.01/0.59 % (640812)------------------------------
% 1.01/0.59 % (640812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.59 % (640812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.59 % (640812)CaDiCaL version: 2.1.3
% 1.01/0.59 % (640812)Termination reason: Instruction limit
% 1.01/0.59 % (640812)Termination phase: shuffling
% 1.01/0.59 % (640812)Time elapsed: 0.004 s
% 1.01/0.59 % (640812)Peak memory usage: 10 MB
% 1.01/0.59 % (640812)Instructions burned: 3 (million)
% 1.01/0.59 % (640818)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3178767100:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.01/0.59 % (640818)Instruction limit reached!
% 1.01/0.59 % (640818)------------------------------
% 1.01/0.59 % (640818)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.59 % (640818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.59 % (640818)CaDiCaL version: 2.1.3
% 1.01/0.59 % (640818)Termination reason: Instruction limit
% 1.01/0.59 % (640818)Termination phase: shuffling
% 1.01/0.59 % (640818)Time elapsed: 0.004 s
% 1.01/0.59 % (640818)Peak memory usage: 10 MB
% 1.01/0.59 % (640818)Instructions burned: 8 (million)
% 1.01/0.59 % (640814)Instruction limit reached!
% 1.01/0.59 % (640814)------------------------------
% 1.01/0.59 % (640814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.59 % (640814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.59 % (640814)CaDiCaL version: 2.1.3
% 1.01/0.59 % (640814)Termination reason: Instruction limit
% 1.01/0.59 % (640814)Termination phase: Naming
% 1.01/0.59 % (640814)Time elapsed: 0.022 s
% 1.01/0.59 % (640814)Peak memory usage: 11 MB
% 1.01/0.59 % (640814)Instructions burned: 25 (million)
% 1.01/0.59 % (640827)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.01/0.59 % (640827)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2475490609:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.77/0.65 % (640827)Instruction limit reached!
% 1.77/0.65 % (640827)------------------------------
% 1.77/0.65 % (640827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.65 % (640827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.65 % (640827)CaDiCaL version: 2.1.3
% 1.77/0.65 % (640827)Termination reason: Instruction limit
% 1.77/0.65 % (640827)Termination phase: shuffling
% 1.77/0.65 % (640827)Time elapsed: 0.003 s
% 1.77/0.65 % (640827)Peak memory usage: 10 MB
% 1.77/0.65 % (640827)Instructions burned: 8 (million)
% 1.77/0.65 % (640830)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
% 1.77/0.65 % (640830)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.77/0.65 % (640825)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1689387293:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.77/0.65 % (640828)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=251690547:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.77/0.65 % (640830)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=445761644:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.77/0.65 % (640825)Instruction limit reached!
% 1.77/0.65 % (640825)------------------------------
% 1.77/0.65 % (640825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.65 % (640825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.65 % (640825)CaDiCaL version: 2.1.3
% 1.77/0.65 % (640825)Termination reason: Instruction limit
% 1.77/0.65 % (640825)Termination phase: shuffling
% 1.77/0.65 % (640825)Time elapsed: 0.006 s
% 1.77/0.65 % (640825)Peak memory usage: 10 MB
% 1.77/0.65 % (640825)Instructions burned: 5 (million)
% 1.77/0.65 % (640815)Instruction limit reached!
% 1.77/0.65 % (640815)------------------------------
% 1.77/0.65 % (640815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.65 % (640815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.65 % (640815)CaDiCaL version: 2.1.3
% 1.77/0.65 % (640815)Termination reason: Instruction limit
% 1.77/0.65 % (640815)Termination phase: Property scanning
% 1.77/0.65 % (640815)Time elapsed: 0.062 s
% 1.77/0.65 % (640815)Peak memory usage: 12 MB
% 1.77/0.65 % (640815)Instructions burned: 75 (million)
% 1.77/0.65 % (640828)Instruction limit reached!
% 1.77/0.65 % (640828)------------------------------
% 1.77/0.65 % (640828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.65 % (640828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.65 % (640828)CaDiCaL version: 2.1.3
% 1.77/0.65 % (640828)Termination reason: Instruction limit
% 1.77/0.65 % (640828)Termination phase: shuffling
% 1.77/0.65 % (640828)Time elapsed: 0.011 s
% 1.77/0.65 % (640828)Peak memory usage: 10 MB
% 1.77/0.65 % (640828)Instructions burned: 12 (million)
% 1.77/0.65 % (640830)Instruction limit reached!
% 1.77/0.65 % (640830)------------------------------
% 1.77/0.65 % (640830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.65 % (640830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.65 % (640830)CaDiCaL version: 2.1.3
% 1.77/0.65 % (640830)Termination reason: Instruction limit
% 1.77/0.65 % (640830)Termination phase: Property scanning
% 1.77/0.65 % (640830)Time elapsed: 0.013 s
% 1.77/0.65 % (640830)Peak memory usage: 10 MB
% 1.77/0.65 % (640830)Instructions burned: 30 (million)
% 1.77/0.65 % (640810)Instruction limit reached!
% 1.77/0.65 % (640810)------------------------------
% 1.77/0.65 % (640810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.77/0.65 % (640810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.77/0.65 % (640810)CaDiCaL version: 2.1.3
% 1.77/0.65 % (640810)Termination reason: Instruction limit
% 1.77/0.65 % (640810)Termination phase: Function definition elimination
% 1.77/0.65 % (640810)Time elapsed: 0.073 s
% 1.77/0.65 % (640810)Peak memory usage: 12 MB
% 2.03/0.70 % (640810)Instructions burned: 87 (million)
% 2.03/0.70 % (640837)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=264368813:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 2.03/0.70 % (640836)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 2.03/0.70 % (640835)lrs+10_1_si=on:cs=on:random_seed=449798021:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 2.03/0.70 % (640834)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=4073099059:i=86:piset=equals:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/86Mi)
% 2.03/0.70 % (640836)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=3884702422:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 2.03/0.70 % (640836)Instruction limit reached!
% 2.03/0.70 % (640836)------------------------------
% 2.03/0.70 % (640836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.70 % (640836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.70 % (640836)CaDiCaL version: 2.1.3
% 2.03/0.70 % (640836)Termination reason: Instruction limit
% 2.03/0.70 % (640836)Termination phase: shuffling
% 2.03/0.70 % (640836)Time elapsed: 0.003 s
% 2.03/0.70 % (640836)Peak memory usage: 10 MB
% 2.03/0.70 % (640836)Instructions burned: 3 (million)
% 2.03/0.70 % (640835)Instruction limit reached!
% 2.03/0.70 % (640835)------------------------------
% 2.03/0.70 % (640835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.70 % (640835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.70 % (640835)CaDiCaL version: 2.1.3
% 2.03/0.70 % (640835)Termination reason: Instruction limit
% 2.03/0.70 % (640835)Termination phase: shuffling
% 2.03/0.70 % (640835)Time elapsed: 0.007 s
% 2.03/0.70 % (640835)Peak memory usage: 10 MB
% 2.03/0.70 % (640835)Instructions burned: 8 (million)
% 2.03/0.70 % (640837)Refutation not found, incomplete strategy
% 2.03/0.70 % (640837)------------------------------
% 2.03/0.70 % (640837)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.70 % (640837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.70 % (640837)CaDiCaL version: 2.1.3
% 2.03/0.70 % (640837)Termination reason: Refutation not found, incomplete strategy
% 2.03/0.70 % (640837)Time elapsed: 0.016 s
% 2.03/0.70 % (640837)Peak memory usage: 13 MB
% 2.03/0.70 % (640837)Instructions burned: 33 (million)
% 2.03/0.70 % (640837)------------------------------
% 2.03/0.70 % (640837)------------------------------
% 2.03/0.70 % (640838)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3171551775:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 2.03/0.70 % (640816)Instruction limit reached!
% 2.03/0.70 % (640816)------------------------------
% 2.03/0.70 % (640816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.70 % (640816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.70 % (640816)CaDiCaL version: 2.1.3
% 2.03/0.70 % (640816)Termination reason: Instruction limit
% 2.03/0.70 % (640816)Termination phase: Saturation
% 2.03/0.70 % (640816)Time elapsed: 0.128 s
% 2.03/0.70 % (640816)Peak memory usage: 13 MB
% 2.03/0.70 % (640816)Instructions burned: 158 (million)
% 2.03/0.70 % (640843)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1902798151:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 2.03/0.70 % (640844)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2956510999:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.03/0.70 % (640838)Refutation not found, incomplete strategy
% 2.03/0.70 % (640838)------------------------------
% 2.03/0.70 % (640838)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.70 % (640838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.70 % (640838)CaDiCaL version: 2.1.3
% 2.03/0.70 % (640838)Termination reason: Refutation not found, incomplete strategy
% 2.03/0.70 % (640838)Time elapsed: 0.040 s
% 2.03/0.70 % (640838)Peak memory usage: 12 MB
% 2.03/0.70 % (640838)Instructions burned: 49 (million)
% 2.03/0.70 % (640838)------------------------------
% 2.03/0.70 % (640838)------------------------------
% 2.03/0.70 % (640844)Instruction limit reached!
% 2.03/0.70 % (640844)------------------------------
% 2.03/0.70 % (640844)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.70 % (640844)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.70 % (640844)CaDiCaL version: 2.1.3
% 2.03/0.70 % (640844)Termination reason: Instruction limit
% 2.03/0.70 % (640844)Termination phase: shuffling
% 2.03/0.70 % (640844)Time elapsed: 0.012 s
% 2.03/0.70 % (640844)Peak memory usage: 10 MB
% 2.03/0.70 % (640844)Instructions burned: 14 (million)
% 2.03/0.70 % (640845)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1873978728:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 2.03/0.70 % (640843)Instruction limit reached!
% 2.03/0.70 % (640843)------------------------------
% 2.03/0.70 % (640843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.70 % (640843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.70 % (640843)CaDiCaL version: 2.1.3
% 2.03/0.70 % (640843)Termination reason: Instruction limit
% 2.03/0.70 % (640843)Termination phase: Preprocessing 1
% 2.03/0.70 % (640843)Time elapsed: 0.021 s
% 2.03/0.70 % (640843)Peak memory usage: 10 MB
% 2.03/0.70 % (640843)Instructions burned: 25 (million)
% 2.03/0.70 % (640847)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1985671582:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 2.03/0.70 % (640834)Instruction limit reached!
% 2.03/0.70 % (640834)------------------------------
% 2.03/0.70 % (640834)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.70 % (640834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.70 % (640834)CaDiCaL version: 2.1.3
% 2.03/0.70 % (640834)Termination reason: Instruction limit
% 2.03/0.70 % (640834)Termination phase: Property scanning
% 2.03/0.70 % (640834)Time elapsed: 0.072 s
% 2.03/0.70 % (640834)Peak memory usage: 11 MB
% 2.03/0.70 % (640834)Instructions burned: 86 (million)
% 2.03/0.70 % (640847)Instruction limit reached!
% 2.03/0.70 % (640847)------------------------------
% 2.03/0.70 % (640847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.70 % (640847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.70 % (640847)CaDiCaL version: 2.1.3
% 2.03/0.70 % (640847)Termination reason: Instruction limit
% 2.03/0.70 % (640847)Termination phase: shuffling
% 2.03/0.70 % (640847)Time elapsed: 0.014 s
% 2.03/0.70 % (640847)Peak memory usage: 10 MB
% 2.03/0.70 % (640847)Instructions burned: 17 (million)
% 2.03/0.70 % (640851)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=48486423:i=26:ep=R:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/26Mi)
% 2.03/0.70 % (640850)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2702981518:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2997 on theBenchmark for (2997ds/2Mi)
% 2.03/0.70 % (640850)Instruction limit reached!
% 2.03/0.70 % (640850)------------------------------
% 2.03/0.70 % (640850)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.70 % (640850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.70 % (640850)CaDiCaL version: 2.1.3
% 2.03/0.70 % (640850)Termination reason: Instruction limit
% 2.03/0.70 % (640850)Termination phase: shuffling
% 2.03/0.70 % (640850)Time elapsed: 0.003 s
% 2.03/0.70 % (640850)Peak memory usage: 10 MB
% 2.03/0.70 % (640850)Instructions burned: 3 (million)
% 2.03/0.70 % (640853)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=153577457:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 2.03/0.70 % (640855)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3232943526:cond=on:i=60:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/60Mi)
% 2.03/0.70 % (640851)Instruction limit reached!
% 2.03/0.70 % (640851)------------------------------
% 2.03/0.70 % (640851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.70 % (640851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.70 % (640851)CaDiCaL version: 2.1.3
% 2.03/0.70 % (640856)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
% 2.03/0.70 % (640856)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 2.03/0.70 % (640851)Termination reason: Instruction limit
% 2.03/0.70 % (640851)Termination phase: Property scanning
% 2.03/0.70 % (640851)Time elapsed: 0.022 s
% 2.03/0.70 % (640851)Peak memory usage: 10 MB
% 2.03/0.70 % (640851)Instructions burned: 26 (million)
% 2.03/0.70 % (640853)Instruction limit reached!
% 2.03/0.70 % (640853)------------------------------
% 2.03/0.70 % (640853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.70 % (640853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.70 % (640853)CaDiCaL version: 2.1.3
% 2.03/0.70 % (640853)Termination reason: Instruction limit
% 2.03/0.70 % (640853)Termination phase: Property scanning
% 2.03/0.70 % (640853)Time elapsed: 0.020 s
% 2.03/0.70 % (640853)Peak memory usage: 10 MB
% 2.03/0.70 % (640853)Instructions burned: 23 (million)
% 2.03/0.70 % (640856)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=1022598474:i=14:add=off:nm=40:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 2.03/0.70 % (640859)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 2.03/0.70 % (640859)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=1990413230:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 2.03/0.70 % (640856)Instruction limit reached!
% 2.03/0.70 % (640856)------------------------------
% 2.03/0.70 % (640856)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.70 % (640856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.70 % (640856)CaDiCaL version: 2.1.3
% 2.03/0.70 % (640856)Termination reason: Instruction limit
% 2.03/0.70 % (640856)Termination phase: shuffling
% 2.03/0.70 % (640856)Time elapsed: 0.013 s
% 2.03/0.70 % (640856)Peak memory usage: 10 MB
% 2.03/0.70 % (640856)Instructions burned: 15 (million)
% 2.03/0.70 % (640859)Instruction limit reached!
% 2.03/0.70 % (640859)------------------------------
% 2.03/0.70 % (640859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/0.70 % (640859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/0.70 % (640859)CaDiCaL version: 2.1.3
% 2.03/0.70 % (640859)Termination reason: Instruction limit
% 2.03/0.70 % (640859)Termination phase: shuffling
% 2.03/0.70 % (640859)Time elapsed: 0.007 s
% 2.03/0.70 % (640859)Peak memory usage: 10 MB
% 2.03/0.70 % (640859)Instructions burned: 8 (million)
% 2.03/0.70 % (640862)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=1890929885:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 2.03/0.70 % (640845) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-640805-640845"...
% 2.03/0.70 % (640864)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2601462774:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 2.03/0.70 % (640845)...printing done.
% 2.03/0.70 % (640845)Refutation found. Thanks to Tanya!
% 2.03/0.70 % SZS status Theorem for theBenchmark
% 2.03/0.70 % SZS output start Proof for theBenchmark
% See solution above
% 2.31/0.70 % (640845)------------------------------
% 2.31/0.70 % (640845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.31/0.70 % (640845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.31/0.70 % (640845)CaDiCaL version: 2.1.3
% 2.31/0.70 % (640845)Termination reason: Refutation
% 2.31/0.70 % (640845)Time elapsed: 0.092 s
% 2.31/0.70 % (640845)Peak memory usage: 15 MB
% 2.31/0.70 % (640845)Instructions burned: 180 (million)
% 2.31/0.70 % (640805)Success in time 0.316 s
% 2.31/0.70 % Vampire exiting
%------------------------------------------------------------------------------