%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG257^2 : 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 : n005.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 1.42s 0.49s
% Output : Refutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 99 ( 31 unt; 0 typ; 8 def)
% Number of atoms : 427 ( 159 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 588 ( 52 ~; 74 |; 0 &; 370 @)
% ( 8 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 339 ( 335 usr; 180 con; 0-4 aty)
% ( 52 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 154 ( 9 sgn 58 !; 0 ?; 154 :)
% 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,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_127,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_130,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_131,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_132,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_133,type,
vNOT: $o > $o ).
thf(func_def_134,type,
vAND: $o > $o > $o ).
thf(func_def_137,type,
vIFF: $o > $o > $o ).
thf(func_def_138,type,
sK0: term ).
thf(func_def_139,type,
sK1: term ).
thf(func_def_140,type,
sK2: term ).
thf(func_def_141,type,
sK3: term ).
thf(func_def_142,type,
sK4: ( subst > term > subst > $o ) > subst ).
thf(func_def_143,type,
sK5: ( subst > term > subst > $o ) > term ).
thf(func_def_144,type,
sK6: ( subst > term > subst > $o ) > subst ).
thf(func_def_145,type,
sK7: ( subst > term > subst > $o ) > subst ).
thf(func_def_146,type,
sK8: ( subst > term > subst > $o ) > term ).
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 ) > term ).
thf(func_def_150,type,
sK12: ( subst > term > subst > $o ) > subst ).
thf(func_def_151,type,
sK13: ( subst > term > subst > $o ) > term ).
thf(func_def_152,type,
sK14: ( subst > term > subst > $o ) > term ).
thf(func_def_153,type,
sK15: ( subst > term > subst > $o ) > subst ).
thf(func_def_154,type,
sK16: ( subst > term > subst > $o ) > term ).
thf(func_def_155,type,
sK17: ( subst > term > subst > $o ) > subst ).
thf(func_def_156,type,
sK18: ( subst > term > subst > $o ) > term ).
thf(func_def_157,type,
sK19: subst > term > subst > $o ).
thf(func_def_158,type,
sK20: term ).
thf(func_def_159,type,
sK21: term ).
thf(func_def_160,type,
sK22: subst ).
thf(func_def_161,type,
sK23: ( term > $o ) > term ).
thf(func_def_162,type,
sK24: ( term > $o ) > term ).
thf(func_def_163,type,
sK25: ( term > $o ) > term ).
thf(func_def_164,type,
sK26: ( term > $o ) > term ).
thf(func_def_165,type,
sK27: ( term > $o ) > term ).
thf(func_def_166,type,
sK28: ( term > $o ) > term ).
thf(func_def_167,type,
sK29: term > $o ).
thf(func_def_168,type,
sK30: term ).
thf(func_def_169,type,
sK31: subst ).
thf(func_def_170,type,
sK32: term ).
thf(func_def_171,type,
sK33: subst ).
thf(func_def_172,type,
sK34: term ).
thf(func_def_173,type,
sK35: term ).
thf(func_def_174,type,
sK36: term ).
thf(func_def_175,type,
sK37: term ).
thf(func_def_176,type,
sK38: term ).
thf(func_def_177,type,
sK39: term ).
thf(func_def_178,type,
sK40: term ).
thf(func_def_179,type,
sK41: term ).
thf(func_def_180,type,
sK42: term ).
thf(func_def_181,type,
sK43: term ).
thf(func_def_182,type,
sK44: term ).
thf(func_def_183,type,
sK45: subst ).
thf(func_def_184,type,
sK46: term ).
thf(func_def_185,type,
sK47: subst ).
thf(func_def_186,type,
sK48: ( subst > term > subst > $o ) > term ).
thf(func_def_187,type,
sK49: ( subst > term > subst > $o ) > subst ).
thf(func_def_188,type,
sK50: ( subst > term > subst > $o ) > term ).
thf(func_def_189,type,
sK51: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_190,type,
sK52: ( subst > term > subst > $o ) > term ).
thf(func_def_191,type,
sK53: ( subst > term > subst > $o ) > term ).
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 ) > term ).
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 ) > term ).
thf(func_def_201,type,
sK63: ( subst > term > subst > $o ) > subst ).
thf(func_def_202,type,
sK64: ( subst > term > subst > $o ) > term ).
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 ) > term ).
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 ) > term ).
thf(func_def_211,type,
sK73: ( subst > term > subst > $o ) > subst ).
thf(func_def_212,type,
sK74: ( subst > term > subst > $o ) > term ).
thf(func_def_213,type,
sK75: ( subst > term > subst > $o ) > subst ).
thf(func_def_214,type,
sK76: ( subst > term > subst > $o ) > subst ).
thf(func_def_215,type,
sK77: ( subst > term > subst > $o ) > subst ).
thf(func_def_216,type,
sK78: ( subst > term > subst > $o ) > subst ).
thf(func_def_217,type,
sK79: ( subst > term > subst > $o ) > subst ).
thf(func_def_218,type,
sK80: ( subst > term > subst > $o ) > subst ).
thf(func_def_219,type,
sK81: ( subst > term > subst > $o ) > term ).
thf(func_def_220,type,
sK82: ( subst > term > subst > $o ) > subst ).
thf(func_def_221,type,
sK83: ( subst > term > subst > $o ) > term ).
thf(func_def_222,type,
sK84: ( subst > term > subst > $o ) > subst ).
thf(func_def_223,type,
sK85: ( subst > term > subst > $o ) > term ).
thf(func_def_224,type,
sK86: ( subst > term > subst > $o ) > subst ).
thf(func_def_225,type,
sK87: ( subst > term > subst > $o ) > subst ).
thf(func_def_226,type,
sK88: ( subst > term > subst > $o ) > term ).
thf(func_def_227,type,
sK89: ( subst > term > subst > $o ) > subst ).
thf(func_def_228,type,
sK90: ( subst > term > subst > $o ) > subst ).
thf(func_def_229,type,
sK91: ( subst > term > subst > $o ) > term ).
thf(func_def_230,type,
sK92: ( subst > term > subst > $o ) > subst ).
thf(func_def_231,type,
sK93: ( subst > term > subst > $o ) > subst ).
thf(func_def_232,type,
sK94: ( subst > term > subst > $o ) > subst ).
thf(func_def_233,type,
sK95: ( subst > term > subst > $o ) > term ).
thf(func_def_234,type,
sK96: ( subst > term > subst > $o ) > subst ).
thf(func_def_235,type,
sK97: ( subst > term > subst > $o ) > subst ).
thf(func_def_236,type,
sK98: ( subst > term > subst > $o ) > subst ).
thf(func_def_237,type,
sK99: ( subst > term > subst > $o ) > term ).
thf(func_def_238,type,
sK100: ( subst > term > subst > $o ) > subst ).
thf(func_def_239,type,
sK101: ( subst > term > subst > $o ) > subst ).
thf(func_def_240,type,
sK102: ( subst > term > subst > $o ) > subst ).
thf(func_def_241,type,
sK103: ( subst > term > subst > $o ) > term ).
thf(func_def_242,type,
sK104: ( subst > term > subst > $o ) > subst ).
thf(func_def_243,type,
sK105: ( subst > term > subst > $o ) > subst ).
thf(func_def_244,type,
sK106: ( subst > term > subst > $o ) > term ).
thf(func_def_245,type,
sK107: ( subst > term > subst > $o ) > term ).
thf(func_def_246,type,
sK108: ( subst > term > subst > $o ) > subst ).
thf(func_def_247,type,
sK109: ( subst > term > subst > $o ) > subst ).
thf(func_def_248,type,
sK110: ( subst > term > subst > $o ) > subst ).
thf(func_def_249,type,
sK111: ( subst > term > subst > $o ) > term ).
thf(func_def_250,type,
sK112: ( subst > term > subst > $o ) > subst ).
thf(func_def_251,type,
sK113: ( subst > term > subst > $o ) > subst ).
thf(func_def_252,type,
sK114: ( subst > term > subst > $o ) > subst ).
thf(func_def_253,type,
sK115: ( subst > term > subst > $o ) > term ).
thf(func_def_254,type,
sK116: ( subst > term > subst > $o ) > subst ).
thf(func_def_255,type,
sK117: ( subst > term > subst > $o ) > term ).
thf(func_def_256,type,
sK118: ( subst > term > subst > $o ) > subst ).
thf(func_def_257,type,
sK119: subst > term > subst > $o ).
thf(func_def_258,type,
sK120: ( subst > term > term ) > subst ).
thf(func_def_259,type,
sK121: ( subst > term > term ) > term ).
thf(func_def_260,type,
sK122: ( subst > term > term ) > term ).
thf(func_def_261,type,
sK123: ( subst > term > term ) > subst ).
thf(func_def_262,type,
sK124: ( subst > term > term ) > term ).
thf(func_def_263,type,
sK125: ( subst > term > term ) > subst ).
thf(func_def_264,type,
sK126: term ).
thf(func_def_265,type,
sK127: term ).
thf(func_def_266,type,
sK128: term ).
thf(func_def_267,type,
sK129: term ).
thf(func_def_268,type,
sK130: subst ).
thf(func_def_269,type,
sK131: term ).
thf(func_def_270,type,
sK132: subst ).
thf(func_def_271,type,
sK133: subst ).
thf(func_def_272,type,
sK134: subst ).
thf(func_def_273,type,
sK135: term ).
thf(func_def_274,type,
sK136: subst ).
thf(func_def_275,type,
sK137: ( term > $o ) > term ).
thf(func_def_276,type,
sK138: ( term > $o ) > term ).
thf(func_def_277,type,
sK139: ( term > $o ) > term ).
thf(func_def_278,type,
sK140: ( term > $o ) > subst > term ).
thf(func_def_279,type,
sK141: ( term > $o ) > subst > term ).
thf(func_def_280,type,
sK142: ( term > $o ) > term ).
thf(func_def_281,type,
sK143: subst > ( term > $o ) > term ).
thf(func_def_282,type,
sK144: subst > ( term > $o ) > term ).
thf(func_def_283,type,
sK145: term > $o ).
thf(func_def_284,type,
sK146: term > term ).
thf(func_def_285,type,
sK147: term ).
thf(func_def_286,type,
sK148: subst ).
thf(func_def_287,type,
sK149: term ).
thf(func_def_288,type,
sK150: term ).
thf(func_def_289,type,
sK151: term ).
thf(func_def_290,type,
sK152: ( term > $o ) > term ).
thf(func_def_291,type,
sK153: ( term > $o ) > term ).
thf(func_def_292,type,
sK154: ( term > $o ) > term ).
thf(func_def_293,type,
sK155: ( term > $o ) > term ).
thf(func_def_294,type,
sK156: ( term > $o ) > term ).
thf(func_def_295,type,
sK157: ( term > $o ) > term ).
thf(func_def_296,type,
sK158: term > $o ).
thf(func_def_297,type,
sK159: term > term ).
thf(func_def_298,type,
sK160: term ).
thf(func_def_299,type,
sK161: term ).
thf(func_def_300,type,
sK162: term ).
thf(func_def_301,type,
sK163: ( term > $o ) > subst > term ).
thf(func_def_302,type,
sK164: term ).
thf(func_def_303,type,
sK165: subst ).
thf(func_def_304,type,
sK166: term > $o ).
thf(func_def_305,type,
sK167: term ).
thf(func_def_306,type,
sK168: term ).
thf(func_def_307,type,
sK169: term ).
thf(func_def_308,type,
sK170: term ).
thf(func_def_309,type,
sK171: term ).
thf(func_def_310,type,
sK172: subst ).
thf(func_def_311,type,
sK173: term ).
thf(func_def_312,type,
sK174: term ).
thf(func_def_313,type,
sK175: ( subst > term > term ) > term ).
thf(func_def_314,type,
sK176: ( subst > term > term ) > subst ).
thf(func_def_315,type,
sK177: ( subst > term > term ) > subst ).
thf(func_def_316,type,
sK178: subst > term > term ).
thf(func_def_317,type,
sK179: term ).
thf(func_def_318,type,
sK180: term ).
thf(func_def_319,type,
sK181: ( subst > term > term ) > subst ).
thf(func_def_320,type,
sK182: ( subst > term > term ) > subst ).
thf(func_def_321,type,
sK183: ( subst > term > term ) > subst ).
thf(func_def_322,type,
sK184: ( subst > term > term ) > term ).
thf(func_def_323,type,
sK185: ( subst > term > term ) > term ).
thf(func_def_324,type,
sK186: ( subst > term > term ) > subst ).
thf(func_def_325,type,
sK187: subst > term > term ).
thf(func_def_326,type,
sK188: subst > term > term ).
thf(func_def_327,type,
sK189: subst ).
thf(func_def_328,type,
sK190: term ).
thf(f17,axiom,
! [X3: term,X1: term,X0: term,X2: term] :
( ( ( ( ap @ X0 @ X2 )
= ( ap @ X1 @ X3 ) )
=> ( X2 = X3 ) )
= apinj2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',apinj2) ).
thf(f55,axiom,
( ( ^ [X0: subst,X1: term,X2: subst,X3: term] : ( ap @ ( sub @ X1 @ X2 ) @ X3 ) )
= hoasap ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasap) ).
thf(f61,axiom,
! [X0: term,X2: term,X1: term,X3: term] :
( ( ( ( hoasap @ id @ X0 @ id @ X2 )
= ( hoasap @ id @ X1 @ id @ X3 ) )
=> ( X2 = X3 ) )
= hoasapinj2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasapinj2) ).
thf(f63,axiom,
( ( hoasapinj2_lthm = apinj2 )
=> hoasapinj2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',hoasapinj2_lthm) ).
thf(f114,conjecture,
hoasapinj2_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ hoasapinj2_lthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f123,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( ap @ X1 @ X0 )
= ( ap @ X2 @ X3 ) )
=> ( X0 = X3 ) )
= apinj2 ),
inference(rectify,[],[f17]) ).
thf(f124,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f123]) ).
thf(f131,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f172,plain,
( ( hoasapinj2_lthm = apinj2 )
=> hoasapinj2 ),
inference(rectify,[],[f63]) ).
thf(f173,plain,
( hoasapinj2_lthm
= ( apinj2
=> hoasapinj2 ) ),
inference(fool_elimination,[],[f172]) ).
thf(f184,plain,
~ hoasapinj2_lthm,
inference(rectify,[],[f115]) ).
thf(f185,plain,
hoasapinj2_lthm != $true,
inference(fool_elimination,[],[f184]) ).
thf(f319,plain,
! [X0: term,X1: term,X2: term,X3: term] :
( ( ( ( hoasap @ id @ X0 @ id @ X1 )
= ( hoasap @ id @ X2 @ id @ X3 ) )
=> ( X1 = X3 ) )
= hoasapinj2 ),
inference(rectify,[],[f61]) ).
thf(f320,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y3 @ id @ Y2 )
= ( hoasap @ id @ Y1 @ id @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f319]) ).
thf(f323,plain,
hoasapinj2_lthm != $true,
inference(flattening,[],[f185]) ).
thf(f328,plain,
( hoasapinj2_lthm
= ( apinj2
=> hoasapinj2 ) ),
inference(cnf_transformation,[],[f173]) ).
thf(f333,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(cnf_transformation,[],[f131]) ).
thf(f336,plain,
hoasapinj2_lthm != $true,
inference(cnf_transformation,[],[f323]) ).
thf(f350,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( hoasap @ id @ Y3 @ id @ Y2 )
= ( hoasap @ id @ Y1 @ id @ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f320]) ).
thf(f352,plain,
( apinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f124]) ).
thf(f360,plain,
( hoasapinj2
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f350,f333,f333]) ).
thf(f571,plain,
( ( hoasapinj2_lthm = $true )
| ( ( apinj2
=> hoasapinj2 )
= $false ) ),
inference(iff_proxy_clausification,[],[f328]) ).
thf(f574,plain,
( ( hoasapinj2 = $false )
| ( hoasapinj2_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f571]) ).
thf(f575,plain,
( ( apinj2 = $true )
| ( hoasapinj2_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f571]) ).
thf(f621,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) ) )
= $false )
| ( hoasapinj2 = $true ) ),
inference(iff_proxy_clausification,[],[f360]) ).
thf(f634,plain,
( ( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y3
@ id
@ Y2 )
= ( ^ [Y4: subst,Y5: term,Y6: subst,Y7: term] : ( ap @ ( sub @ Y5 @ Y6 ) @ Y7 )
@ id
@ Y1
@ id
@ Y0 ) )
=> ( Y2 = Y0 ) ) ) ) )
@ sK41 )
= $false )
| ( hoasapinj2 = $true ) ),
inference(sigma_proxy_clausification,[],[f621]) ).
thf(f635,plain,
( ( hoasapinj2 = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
= ( ap @ ( sub @ Y0 @ id ) @ sK41 ) )
=> ( Y1 = sK41 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f634]) ).
thf(f636,plain,
( ( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ( ap @ ( sub @ Y2 @ id ) @ Y1 )
= ( ap @ ( sub @ Y0 @ id ) @ sK41 ) )
=> ( Y1 = sK41 ) ) ) )
@ sK42 )
= $false )
| ( hoasapinj2 = $true ) ),
inference(sigma_proxy_clausification,[],[f635]) ).
thf(f637,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ sK42 @ id ) @ sK41 ) )
=> ( Y0 = sK41 ) ) ) )
= $false )
| ( hoasapinj2 = $true ) ),
inference(beta-eta_normalization,[],[f636]) ).
thf(f638,plain,
( ( hoasapinj2 = $true )
| ( ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( ap @ ( sub @ Y1 @ id ) @ Y0 )
= ( ap @ ( sub @ sK42 @ id ) @ sK41 ) )
=> ( Y0 = sK41 ) ) )
@ sK43 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f637]) ).
thf(f639,plain,
( ( hoasapinj2 = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ sK43 )
= ( ap @ ( sub @ sK42 @ id ) @ sK41 ) )
=> ( sK43 = sK41 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f638]) ).
thf(f640,plain,
( ( hoasapinj2 = $true )
| ( ( ^ [Y0: term] :
( ( ( ap @ ( sub @ Y0 @ id ) @ sK43 )
= ( ap @ ( sub @ sK42 @ id ) @ sK41 ) )
=> ( sK43 = sK41 ) )
@ sK44 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f639]) ).
thf(f641,plain,
( ( hoasapinj2 = $true )
| ( ( ( ( ap @ ( sub @ sK44 @ id ) @ sK43 )
= ( ap @ ( sub @ sK42 @ id ) @ sK41 ) )
=> ( sK43 = sK41 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f640]) ).
thf(f642,plain,
( ( hoasapinj2 = $true )
| ( ( sK43 = sK41 )
= $false ) ),
inference(imp_proxy_clausification,[],[f641]) ).
thf(f643,plain,
( ( $true
= ( ( ap @ ( sub @ sK44 @ id ) @ sK43 )
= ( ap @ ( sub @ sK42 @ id ) @ sK41 ) ) )
| ( hoasapinj2 = $true ) ),
inference(imp_proxy_clausification,[],[f641]) ).
thf(f644,plain,
( ( ( ap @ ( sub @ sK42 @ id ) @ sK41 )
= ( ap @ ( sub @ sK44 @ id ) @ sK43 ) )
| ( hoasapinj2 = $true ) ),
inference(equality_proxy_clausification,[],[f643]) ).
thf(f645,plain,
( ( hoasapinj2 = $true )
| ( sK43 != sK41 ) ),
inference(equality_proxy_clausification,[],[f642]) ).
thf(f1303,plain,
( ( apinj2 = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y3 = Y0 ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f352]) ).
thf(f1304,plain,
! [X1: term] :
( ( apinj2 = $false )
| ( $true
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( !! @ term
@ ^ [Y3: term] :
( ( ( ap @ Y2 @ Y3 )
= ( ap @ Y1 @ Y0 ) )
=> ( Y3 = Y0 ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f1303]) ).
thf(f1305,plain,
! [X1: term] :
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y0 @ X1 ) )
=> ( Y2 = X1 ) ) ) ) )
= $true )
| ( apinj2 = $false ) ),
inference(beta-eta_normalization,[],[f1304]) ).
thf(f1306,plain,
! [X2: term,X1: term] :
( ( apinj2 = $false )
| ( $true
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ( ap @ Y1 @ Y2 )
= ( ap @ Y0 @ X1 ) )
=> ( Y2 = X1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f1305]) ).
thf(f1307,plain,
! [X2: term,X1: term] :
( ( apinj2 = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( ap @ Y0 @ Y1 )
= ( ap @ X2 @ X1 ) )
=> ( Y1 = X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1306]) ).
thf(f1308,plain,
! [X2: term,X3: term,X1: term] :
( ( $true
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( ( ap @ Y0 @ Y1 )
= ( ap @ X2 @ X1 ) )
=> ( Y1 = X1 ) ) )
@ X3 ) )
| ( apinj2 = $false ) ),
inference(pi_proxy_clausification,[],[f1307]) ).
thf(f1309,plain,
! [X2: term,X3: term,X1: term] :
( ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( ( ap @ X3 @ Y0 )
= ( ap @ X2 @ X1 ) )
=> ( Y0 = X1 ) ) ) )
| ( apinj2 = $false ) ),
inference(beta-eta_normalization,[],[f1308]) ).
thf(f1310,plain,
! [X2: term,X3: term,X1: term,X4: term] :
( ( $true
= ( ^ [Y0: term] :
( ( ( ap @ X3 @ Y0 )
= ( ap @ X2 @ X1 ) )
=> ( Y0 = X1 ) )
@ X4 ) )
| ( apinj2 = $false ) ),
inference(pi_proxy_clausification,[],[f1309]) ).
thf(f1311,plain,
! [X2: term,X3: term,X1: term,X4: term] :
( ( $true
= ( ( ( ap @ X3 @ X4 )
= ( ap @ X2 @ X1 ) )
=> ( X4 = X1 ) ) )
| ( apinj2 = $false ) ),
inference(beta-eta_normalization,[],[f1310]) ).
thf(f1312,plain,
! [X2: term,X3: term,X1: term,X4: term] :
( ( apinj2 = $false )
| ( ( ( ap @ X3 @ X4 )
= ( ap @ X2 @ X1 ) )
= $false )
| ( $true
= ( X4 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f1311]) ).
thf(f1313,plain,
! [X2: term,X3: term,X1: term,X4: term] :
( ( $true
= ( X4 = X1 ) )
| ( apinj2 = $false )
| ( ( ap @ X3 @ X4 )
!= ( ap @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f1312]) ).
thf(f1314,plain,
! [X2: term,X3: term,X1: term,X4: term] :
( ( X1 = X4 )
| ( apinj2 = $false )
| ( ( ap @ X3 @ X4 )
!= ( ap @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f1313]) ).
thf(f1656,definition,
( spl191_53
<=> ( hoasapinj2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl191_53])],[avatar_definition]) ).
thf(f1658,plain,
( ( hoasapinj2 = $true )
| ~ spl191_53 ),
inference(avatar_component_clause,[],[f1656]) ).
thf(f1660,definition,
( spl191_54
<=> ( apinj2 = $false ) ),
introduced(definition,[new_symbols(definition,[spl191_54])],[avatar_definition]) ).
thf(f1662,plain,
( ( apinj2 = $false )
| ~ spl191_54 ),
inference(avatar_component_clause,[],[f1660]) ).
thf(f1665,definition,
( spl191_55
<=> ( apinj2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl191_55])],[avatar_definition]) ).
thf(f1667,plain,
( ( apinj2 = $true )
| ~ spl191_55 ),
inference(avatar_component_clause,[],[f1665]) ).
thf(f1669,definition,
( spl191_56
<=> ( hoasapinj2_lthm = $true ) ),
introduced(definition,[new_symbols(definition,[spl191_56])],[avatar_definition]) ).
thf(f1672,plain,
( spl191_55
| spl191_56 ),
inference(avatar_split_clause,[],[f575,f1669,f1665]) ).
thf(f1674,definition,
( spl191_57
<=> ( hoasapinj2 = $false ) ),
introduced(definition,[new_symbols(definition,[spl191_57])],[avatar_definition]) ).
thf(f1676,plain,
( ( hoasapinj2 = $false )
| ~ spl191_57 ),
inference(avatar_component_clause,[],[f1674]) ).
thf(f1677,plain,
( spl191_56
| spl191_57 ),
inference(avatar_split_clause,[],[f574,f1674,f1669]) ).
thf(f1739,definition,
( spl191_72
<=> ( ( ap @ ( sub @ sK42 @ id ) @ sK41 )
= ( ap @ ( sub @ sK44 @ id ) @ sK43 ) ) ),
introduced(definition,[new_symbols(definition,[spl191_72])],[avatar_definition]) ).
thf(f1741,plain,
( ( ( ap @ ( sub @ sK42 @ id ) @ sK41 )
= ( ap @ ( sub @ sK44 @ id ) @ sK43 ) )
| ~ spl191_72 ),
inference(avatar_component_clause,[],[f1739]) ).
thf(f1742,plain,
( spl191_53
| spl191_72 ),
inference(avatar_split_clause,[],[f644,f1739,f1656]) ).
thf(f1744,definition,
( spl191_73
<=> ( sK43 = sK41 ) ),
introduced(definition,[new_symbols(definition,[spl191_73])],[avatar_definition]) ).
thf(f1746,plain,
( ( sK43 != sK41 )
| spl191_73 ),
inference(avatar_component_clause,[],[f1744]) ).
thf(f1747,plain,
( spl191_53
| ~ spl191_73 ),
inference(avatar_split_clause,[],[f645,f1744,f1656]) ).
thf(f2365,plain,
~ spl191_56,
inference(avatar_split_clause,[],[f336,f1669]) ).
thf(f2402,definition,
( spl191_233
<=> ! [X4: term,X1: term,X3: term,X2: term] :
( ( X1 = X4 )
| ( ( ap @ X3 @ X4 )
!= ( ap @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl191_233])],[avatar_definition]) ).
thf(f2403,plain,
( ! [X2: term,X3: term,X1: term,X4: term] :
( ( ( ap @ X3 @ X4 )
!= ( ap @ X2 @ X1 ) )
| ( X1 = X4 ) )
| ~ spl191_233 ),
inference(avatar_component_clause,[],[f2402]) ).
thf(f2404,plain,
( spl191_233
| spl191_54 ),
inference(avatar_split_clause,[],[f1314,f1660,f2402]) ).
thf(f2505,plain,
( ( $true = $false )
| ~ spl191_54
| ~ spl191_55 ),
inference(forward_demodulation,[],[f1667,f1662]) ).
thf(f2506,plain,
( $false
| ~ spl191_54
| ~ spl191_55 ),
inference(trivial_inequality_removal,[],[f2505]) ).
thf(f2507,plain,
( ~ spl191_54
| ~ spl191_55 ),
inference(avatar_contradiction_clause,[],[f2506]) ).
thf(f2510,plain,
( ( $true = $false )
| ~ spl191_53
| ~ spl191_57 ),
inference(superposition,[],[f1658,f1676]) ).
thf(f2513,plain,
( $false
| ~ spl191_53
| ~ spl191_57 ),
inference(trivial_inequality_removal,[],[f2510]) ).
thf(f2514,plain,
( ~ spl191_53
| ~ spl191_57 ),
inference(avatar_contradiction_clause,[],[f2513]) ).
thf(f2673,plain,
( ! [X0: term,X1: term] :
( ( ( ap @ X0 @ X1 )
!= ( ap @ ( sub @ sK42 @ id ) @ sK41 ) )
| ( sK43 = X1 ) )
| ~ spl191_72
| ~ spl191_233 ),
inference(superposition,[],[f2403,f1741]) ).
thf(f2749,plain,
( ( sK43 = sK41 )
| ~ spl191_72
| ~ spl191_233 ),
inference(equality_resolution,[],[f2673]) ).
thf(f2750,plain,
( $false
| ~ spl191_72
| spl191_73
| ~ spl191_233 ),
inference(forward_subsumption_resolution,[],[f2749,f1746]) ).
thf(f2751,plain,
( ~ spl191_72
| spl191_73
| ~ spl191_233 ),
inference(avatar_contradiction_clause,[],[f2750]) ).
cnf(s43,plain,
( spl191_55
| spl191_56 ),
inference(sat_conversion,[],[f1672]) ).
cnf(s44,plain,
( spl191_56
| spl191_57 ),
inference(sat_conversion,[],[f1677]) ).
cnf(s53,plain,
( spl191_53
| spl191_72 ),
inference(sat_conversion,[],[f1742]) ).
cnf(s54,plain,
( spl191_53
| ~ spl191_73 ),
inference(sat_conversion,[],[f1747]) ).
cnf(s185,plain,
~ spl191_56,
inference(sat_conversion,[],[f2365]) ).
cnf(s192,plain,
( spl191_54
| spl191_233 ),
inference(sat_conversion,[],[f2404]) ).
cnf(s208,plain,
( ~ spl191_54
| ~ spl191_55 ),
inference(sat_conversion,[],[f2507]) ).
cnf(s210,plain,
( ~ spl191_53
| ~ spl191_57 ),
inference(sat_conversion,[],[f2514]) ).
cnf(s231,plain,
( ~ spl191_72
| spl191_73
| ~ spl191_233 ),
inference(sat_conversion,[],[f2751]) ).
cnf(s232,plain,
spl191_57,
inference(rat,[],[s44,s185]) ).
cnf(s233,plain,
~ spl191_53,
inference(rat,[],[s210,s232]) ).
cnf(s234,plain,
~ spl191_73,
inference(rat,[],[s54,s233]) ).
cnf(s235,plain,
spl191_72,
inference(rat,[],[s53,s233]) ).
cnf(s236,plain,
~ spl191_233,
inference(rat,[],[s231,s234,s235]) ).
cnf(s237,plain,
spl191_54,
inference(rat,[],[s192,s236]) ).
cnf(s238,plain,
~ spl191_55,
inference(rat,[],[s208,s237]) ).
cnf(s241,plain,
$false,
inference(rat,[],[s43,s185,s238]) ).
thf(f2752,plain,
$false,
inference(avatar_sat_refutation,[],[s241]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG257^2 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n005.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:33:42 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.22/0.26 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
% 0.68/0.39 % (1972064)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.68/0.39 % (1972073)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3579853999:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.68/0.39 % (1972075)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.68/0.39 % (1972075)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
% 0.68/0.39 % (1972073)Instruction limit reached!
% 0.68/0.39 % (1972073)------------------------------
% 0.68/0.39 % (1972073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.39 % (1972073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.39 % (1972073)CaDiCaL version: 2.1.3
% 0.68/0.39 % (1972073)Termination reason: Instruction limit
% 0.68/0.39 % (1972073)Termination phase: Preprocessing 3
% 0.68/0.39 % (1972073)Time elapsed: 0.007 s
% 0.68/0.39 % (1972073)Peak memory usage: 11 MB
% 0.68/0.39 % (1972073)Instructions burned: 28 (million)
% 0.68/0.39 % (1972070)lrs+10_16_si=on:nwc=1.5:random_seed=1047548429:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.68/0.39 % (1972071)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2939044781:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.68/0.39 % (1972072)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=3533764770: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)
% 0.68/0.39 % (1972074)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1575022793:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.68/0.39 % (1972075)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=3424056535:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.68/0.39 % (1972071)Instruction limit reached!
% 0.68/0.39 % (1972071)------------------------------
% 0.68/0.39 % (1972071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.39 % (1972071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.39 % (1972071)CaDiCaL version: 2.1.3
% 0.68/0.39 % (1972071)Termination reason: Instruction limit
% 0.68/0.39 % (1972071)Termination phase: shuffling
% 0.68/0.39 % (1972071)Time elapsed: 0.002 s
% 0.68/0.39 % (1972071)Peak memory usage: 10 MB
% 0.68/0.39 % (1972071)Instructions burned: 3 (million)
% 0.68/0.39 % (1972069)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1665068395:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.68/0.39 % (1972070)Instruction limit reached!
% 0.68/0.39 % (1972070)------------------------------
% 0.68/0.39 % (1972070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.39 % (1972070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.39 % (1972070)CaDiCaL version: 2.1.3
% 0.68/0.39 % (1972070)Termination reason: Instruction limit
% 0.68/0.39 % (1972070)Termination phase: shuffling
% 0.68/0.39 % (1972070)Time elapsed: 0.008 s
% 0.68/0.39 % (1972070)Peak memory usage: 10 MB
% 0.68/0.39 % (1972070)Instructions burned: 18 (million)
% 0.68/0.39 % (1972080)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=68272938:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.39 % (1972080)Instruction limit reached!
% 0.68/0.39 % (1972080)------------------------------
% 0.68/0.39 % (1972080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.39 % (1972080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.39 % (1972080)CaDiCaL version: 2.1.3
% 0.68/0.39 % (1972080)Termination reason: Instruction limit
% 0.68/0.39 % (1972080)Termination phase: shuffling
% 0.68/0.39 % (1972080)Time elapsed: 0.001 s
% 0.68/0.39 % (1972080)Peak memory usage: 10 MB
% 0.68/0.39 % (1972080)Instructions burned: 7 (million)
% 0.68/0.39 % (1972083)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3893028865:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.68/0.42 % (1972087)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2144704035:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.68/0.42 % (1972085)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.42 % (1972083)Instruction limit reached!
% 0.68/0.42 % (1972083)------------------------------
% 0.68/0.42 % (1972083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.42 % (1972083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.42 % (1972083)CaDiCaL version: 2.1.3
% 0.68/0.42 % (1972083)Termination reason: Instruction limit
% 0.68/0.42 % (1972083)Termination phase: shuffling
% 0.68/0.42 % (1972083)Time elapsed: 0.003 s
% 0.68/0.42 % (1972083)Peak memory usage: 10 MB
% 0.68/0.42 % (1972083)Instructions burned: 6 (million)
% 0.68/0.42 % (1972087)Instruction limit reached!
% 0.68/0.42 % (1972087)------------------------------
% 0.68/0.42 % (1972087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.42 % (1972087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.42 % (1972087)CaDiCaL version: 2.1.3
% 0.68/0.42 % (1972087)Termination reason: Instruction limit
% 0.68/0.42 % (1972087)Termination phase: shuffling
% 0.68/0.42 % (1972087)Time elapsed: 0.003 s
% 0.68/0.42 % (1972087)Peak memory usage: 10 MB
% 0.68/0.42 % (1972087)Instructions burned: 13 (million)
% 0.68/0.42 % (1972085)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=4183775433:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.68/0.42 % (1972085)Instruction limit reached!
% 0.68/0.42 % (1972085)------------------------------
% 0.68/0.42 % (1972085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.42 % (1972085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.42 % (1972085)CaDiCaL version: 2.1.3
% 0.68/0.42 % (1972085)Termination reason: Instruction limit
% 0.68/0.42 % (1972085)Termination phase: shuffling
% 0.68/0.42 % (1972085)Time elapsed: 0.004 s
% 0.68/0.42 % (1972085)Peak memory usage: 10 MB
% 0.68/0.42 % (1972085)Instructions burned: 8 (million)
% 0.68/0.42 % (1972074)Instruction limit reached!
% 0.68/0.42 % (1972074)------------------------------
% 0.68/0.42 % (1972074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.42 % (1972074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.42 % (1972074)CaDiCaL version: 2.1.3
% 0.68/0.42 % (1972074)Termination reason: Instruction limit
% 0.68/0.42 % (1972074)Termination phase: Property scanning
% 0.68/0.42 % (1972074)Time elapsed: 0.035 s
% 0.68/0.42 % (1972074)Peak memory usage: 12 MB
% 0.68/0.42 % (1972074)Instructions burned: 77 (million)
% 0.68/0.42 % (1972091)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=655598645:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.68/0.42 % (1972090)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
% 0.68/0.42 % (1972090)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.42 % (1972090)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3022872501:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.68/0.42 % (1972094)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.68/0.42 % (1972093)lrs+10_1_si=on:cs=on:random_seed=22500182:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.68/0.42 % (1972094)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=3176090997:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.42 % (1972091)Instruction limit reached!
% 0.68/0.42 % (1972091)------------------------------
% 0.68/0.42 % (1972091)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.42 % (1972091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.45 % (1972091)CaDiCaL version: 2.1.3
% 0.68/0.45 % (1972091)Termination reason: Instruction limit
% 0.68/0.45 % (1972091)Termination phase: Saturation
% 0.68/0.45 % (1972091)Time elapsed: 0.019 s
% 0.68/0.45 % (1972091)Peak memory usage: 12 MB
% 0.68/0.45 % (1972091)Instructions burned: 89 (million)
% 0.68/0.45 % (1972094)Instruction limit reached!
% 0.68/0.45 % (1972094)------------------------------
% 0.68/0.45 % (1972094)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.45 % (1972094)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.45 % (1972094)CaDiCaL version: 2.1.3
% 0.68/0.45 % (1972094)Termination reason: Instruction limit
% 0.68/0.45 % (1972094)Termination phase: shuffling
% 0.68/0.45 % (1972094)Time elapsed: 0.002 s
% 0.68/0.45 % (1972094)Peak memory usage: 10 MB
% 0.68/0.45 % (1972094)Instructions burned: 3 (million)
% 0.68/0.45 % (1972090)Instruction limit reached!
% 0.68/0.45 % (1972090)------------------------------
% 0.68/0.45 % (1972090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.45 % (1972090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.45 % (1972090)CaDiCaL version: 2.1.3
% 0.68/0.45 % (1972090)Termination reason: Instruction limit
% 0.68/0.45 % (1972090)Termination phase: Property scanning
% 0.68/0.45 % (1972090)Time elapsed: 0.013 s
% 0.68/0.45 % (1972090)Peak memory usage: 9 MB
% 0.68/0.45 % (1972090)Instructions burned: 30 (million)
% 0.68/0.45 % (1972093)Instruction limit reached!
% 0.68/0.45 % (1972093)------------------------------
% 0.68/0.45 % (1972093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.45 % (1972093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.45 % (1972093)CaDiCaL version: 2.1.3
% 0.68/0.45 % (1972093)Termination reason: Instruction limit
% 0.68/0.45 % (1972093)Termination phase: shuffling
% 0.68/0.45 % (1972093)Time elapsed: 0.007 s
% 0.68/0.45 % (1972093)Peak memory usage: 10 MB
% 0.68/0.45 % (1972093)Instructions burned: 8 (million)
% 0.68/0.45 % (1972075)Instruction limit reached!
% 0.68/0.45 % (1972075)------------------------------
% 0.68/0.45 % (1972075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.45 % (1972075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.45 % (1972075)CaDiCaL version: 2.1.3
% 0.68/0.45 % (1972075)Termination reason: Instruction limit
% 0.68/0.45 % (1972075)Termination phase: Saturation
% 0.68/0.45 % (1972075)Time elapsed: 0.067 s
% 0.68/0.45 % (1972075)Peak memory usage: 14 MB
% 0.68/0.45 % (1972075)Instructions burned: 158 (million)
% 0.68/0.45 % (1972099)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1569360214:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.68/0.45 % (1972069)Instruction limit reached!
% 0.68/0.45 % (1972069)------------------------------
% 0.68/0.45 % (1972069)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.45 % (1972069)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.45 % (1972069)CaDiCaL version: 2.1.3
% 0.68/0.45 % (1972069)Termination reason: Instruction limit
% 0.68/0.45 % (1972069)Termination phase: Function definition elimination
% 0.68/0.45 % (1972069)Time elapsed: 0.065 s
% 0.68/0.45 % (1972069)Peak memory usage: 12 MB
% 0.68/0.45 % (1972069)Instructions burned: 89 (million)
% 0.68/0.45 % (1972099)Refutation not found, incomplete strategy
% 0.68/0.45 % (1972099)------------------------------
% 0.68/0.45 % (1972099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.45 % (1972099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.45 % (1972099)CaDiCaL version: 2.1.3
% 0.68/0.45 % (1972099)Termination reason: Refutation not found, incomplete strategy
% 0.68/0.45 % (1972099)Time elapsed: 0.006 s
% 0.68/0.45 % (1972099)Peak memory usage: 13 MB
% 0.68/0.45 % (1972099)Instructions burned: 24 (million)
% 0.68/0.45 % (1972100)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1437946273:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.68/0.45 % (1972099)------------------------------
% 0.68/0.45 % (1972099)------------------------------
% 0.68/0.45 % (1972101)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2609493673:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 1.42/0.49 % (1972102)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2031310534:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.42/0.49 % (1972103)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1018065846:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.42/0.49 % (1972102)Instruction limit reached!
% 1.42/0.49 % (1972102)------------------------------
% 1.42/0.49 % (1972102)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (1972102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (1972102)CaDiCaL version: 2.1.3
% 1.42/0.49 % (1972102)Termination reason: Instruction limit
% 1.42/0.49 % (1972102)Termination phase: shuffling
% 1.42/0.49 % (1972102)Time elapsed: 0.007 s
% 1.42/0.49 % (1972102)Peak memory usage: 10 MB
% 1.42/0.49 % (1972102)Instructions burned: 16 (million)
% 1.42/0.49 % (1972107)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3136174645: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)
% 1.42/0.49 % (1972105)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3266829667:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.42/0.49 % (1972107)Instruction limit reached!
% 1.42/0.49 % (1972107)------------------------------
% 1.42/0.49 % (1972107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (1972107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (1972107)CaDiCaL version: 2.1.3
% 1.42/0.49 % (1972107)Termination reason: Instruction limit
% 1.42/0.49 % (1972107)Termination phase: shuffling
% 1.42/0.49 % (1972107)Time elapsed: 0.001 s
% 1.42/0.49 % (1972107)Peak memory usage: 10 MB
% 1.42/0.49 % (1972107)Instructions burned: 6 (million)
% 1.42/0.49 % (1972101)Instruction limit reached!
% 1.42/0.49 % (1972101)------------------------------
% 1.42/0.49 % (1972101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (1972101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (1972101)CaDiCaL version: 2.1.3
% 1.42/0.49 % (1972101)Termination reason: Instruction limit
% 1.42/0.49 % (1972101)Termination phase: Naming
% 1.42/0.49 % (1972101)Time elapsed: 0.012 s
% 1.42/0.49 % (1972101)Peak memory usage: 11 MB
% 1.42/0.49 % (1972101)Instructions burned: 26 (million)
% 1.42/0.49 % (1972105)Instruction limit reached!
% 1.42/0.49 % (1972105)------------------------------
% 1.42/0.49 % (1972105)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (1972105)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (1972105)CaDiCaL version: 2.1.3
% 1.42/0.49 % (1972105)Termination reason: Instruction limit
% 1.42/0.49 % (1972105)Termination phase: shuffling
% 1.42/0.49 % (1972105)Time elapsed: 0.007 s
% 1.42/0.49 % (1972105)Peak memory usage: 10 MB
% 1.42/0.49 % (1972105)Instructions burned: 15 (million)
% 1.42/0.49 % (1972100)Refutation not found, incomplete strategy
% 1.42/0.49 % (1972100)------------------------------
% 1.42/0.49 % (1972100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (1972100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (1972100)CaDiCaL version: 2.1.3
% 1.42/0.49 % (1972100)Termination reason: Refutation not found, incomplete strategy
% 1.42/0.49 % (1972100)Time elapsed: 0.021 s
% 1.42/0.49 % (1972100)Peak memory usage: 13 MB
% 1.42/0.49 % (1972100)Instructions burned: 49 (million)
% 1.42/0.49 % (1972100)------------------------------
% 1.42/0.49 % (1972100)------------------------------
% 1.42/0.49 % (1972114)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=441944294:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.42/0.49 % (1972111)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=292843722:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.42/0.49 % (1972114)Instruction limit reached!
% 1.42/0.49 % (1972114)------------------------------
% 1.42/0.49 % (1972114)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (1972114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (1972114)CaDiCaL version: 2.1.3
% 1.42/0.49 % (1972114)Termination reason: Instruction limit
% 1.42/0.49 % (1972114)Termination phase: Property scanning
% 1.42/0.49 % (1972114)Time elapsed: 0.005 s
% 1.42/0.49 % (1972114)Peak memory usage: 10 MB
% 1.42/0.49 % (1972114)Instructions burned: 23 (million)
% 1.42/0.49 % (1972115)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=561056835:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.42/0.49 % (1972116)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
% 1.42/0.49 % (1972116)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.42/0.49 % (1972118)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.42/0.49 % (1972116)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=3146990617:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.42/0.49 % (1972120)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=1201195931:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.42/0.49 % (1972111)Instruction limit reached!
% 1.42/0.49 % (1972111)------------------------------
% 1.42/0.49 % (1972111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (1972111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (1972111)CaDiCaL version: 2.1.3
% 1.42/0.49 % (1972111)Termination reason: Instruction limit
% 1.42/0.49 % (1972111)Termination phase: Property scanning
% 1.42/0.49 % (1972111)Time elapsed: 0.011 s
% 1.42/0.49 % (1972111)Peak memory usage: 10 MB
% 1.42/0.49 % (1972111)Instructions burned: 26 (million)
% 1.42/0.49 % (1972118)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=1321880831:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.42/0.49 % (1972116)Instruction limit reached!
% 1.42/0.49 % (1972116)------------------------------
% 1.42/0.49 % (1972116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (1972116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (1972116)CaDiCaL version: 2.1.3
% 1.42/0.49 % (1972116)Termination reason: Instruction limit
% 1.42/0.49 % (1972116)Termination phase: shuffling
% 1.42/0.49 % (1972116)Time elapsed: 0.007 s
% 1.42/0.49 % (1972116)Peak memory usage: 10 MB
% 1.42/0.49 % (1972116)Instructions burned: 15 (million)
% 1.42/0.49 % (1972118)Instruction limit reached!
% 1.42/0.49 % (1972118)------------------------------
% 1.42/0.49 % (1972118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (1972118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (1972118)CaDiCaL version: 2.1.3
% 1.42/0.49 % (1972118)Termination reason: Instruction limit
% 1.42/0.49 % (1972118)Termination phase: shuffling
% 1.42/0.49 % (1972118)Time elapsed: 0.004 s
% 1.42/0.49 % (1972118)Peak memory usage: 10 MB
% 1.42/0.49 % (1972118)Instructions burned: 9 (million)
% 1.42/0.49 % (1972120)Instruction limit reached!
% 1.42/0.49 % (1972120)------------------------------
% 1.42/0.49 % (1972120)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (1972120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (1972120)CaDiCaL version: 2.1.3
% 1.42/0.49 % (1972120)Termination reason: Instruction limit
% 1.42/0.49 % (1972120)Termination phase: Property scanning
% 1.42/0.49 % (1972120)Time elapsed: 0.008 s
% 1.42/0.49 % (1972120)Peak memory usage: 10 MB
% 1.42/0.49 % (1972120)Instructions burned: 36 (million)
% 1.42/0.49 % (1972128)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2243961867:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.42/0.49 % (1972124)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2572120023:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.42/0.49 % (1972115)Instruction limit reached!
% 1.42/0.49 % (1972115)------------------------------
% 1.42/0.49 % (1972115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (1972115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (1972115)CaDiCaL version: 2.1.3
% 1.42/0.49 % (1972115)Termination reason: Instruction limit
% 1.42/0.49 % (1972115)Termination phase: Property scanning
% 1.42/0.49 % (1972115)Time elapsed: 0.028 s
% 1.42/0.49 % (1972115)Peak memory usage: 12 MB
% 1.42/0.49 % (1972115)Instructions burned: 61 (million)
% 1.42/0.49 % (1972126)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3232821062:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.42/0.49 % (1972127)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=732415732:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.42/0.49 % (1972124)Instruction limit reached!
% 1.42/0.49 % (1972124)------------------------------
% 1.42/0.49 % (1972124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (1972124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (1972124)CaDiCaL version: 2.1.3
% 1.42/0.49 % (1972124)Termination reason: Instruction limit
% 1.42/0.49 % (1972124)Termination phase: shuffling
% 1.42/0.49 % (1972124)Time elapsed: 0.007 s
% 1.42/0.49 % (1972124)Peak memory usage: 10 MB
% 1.42/0.49 % (1972124)Instructions burned: 9 (million)
% 1.42/0.49 % (1972127)Instruction limit reached!
% 1.42/0.49 % (1972127)------------------------------
% 1.42/0.49 % (1972127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (1972127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (1972127)CaDiCaL version: 2.1.3
% 1.42/0.49 % (1972127)Termination reason: Instruction limit
% 1.42/0.49 % (1972127)Termination phase: Property scanning
% 1.42/0.49 % (1972127)Time elapsed: 0.010 s
% 1.42/0.49 % (1972127)Peak memory usage: 10 MB
% 1.42/0.49 % (1972127)Instructions burned: 22 (million)
% 1.42/0.49 % (1972126)Instruction limit reached!
% 1.42/0.49 % (1972126)------------------------------
% 1.42/0.49 % (1972126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (1972126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (1972126)CaDiCaL version: 2.1.3
% 1.42/0.49 % (1972126)Termination reason: Instruction limit
% 1.42/0.49 % (1972126)Termination phase: Property scanning
% 1.42/0.49 % (1972126)Time elapsed: 0.011 s
% 1.42/0.49 % (1972126)Peak memory usage: 10 MB
% 1.42/0.49 % (1972126)Instructions burned: 26 (million)
% 1.42/0.49 % (1972131)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3551015381:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.42/0.49 % (1972103) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1972064-1972103"...
% 1.42/0.49 % (1972136)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.42/0.49 % (1972135)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2482673523:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 1.42/0.49 % (1972103)...printing done.
% 1.42/0.49 % (1972136)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1772238964:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 1.42/0.49 % (1972103)Refutation found. Thanks to Tanya!
% 1.42/0.49 % SZS status Theorem for theBenchmark
% 1.42/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 1.42/0.49 % (1972103)------------------------------
% 1.42/0.49 % (1972103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.42/0.49 % (1972103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.42/0.49 % (1972103)CaDiCaL version: 2.1.3
% 1.42/0.49 % (1972103)Termination reason: Refutation
% 1.42/0.49 % (1972103)Time elapsed: 0.084 s
% 1.42/0.49 % (1972103)Peak memory usage: 15 MB
% 1.42/0.49 % (1972103)Instructions burned: 183 (million)
% 1.42/0.49 % (1972064)Success in time 0.216 s
% 1.42/0.49 % Vampire exiting
%------------------------------------------------------------------------------