%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG249^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 1.73s 0.61s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 19
% Syntax : Number of formulae : 152 ( 41 unt; 0 typ; 13 def)
% Number of atoms : 774 ( 192 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 1167 ( 94 ~; 147 |; 0 &; 724 @)
% ( 15 <=>; 95 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 425 ( 421 usr; 193 con; 0-4 aty)
% ( 92 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 203 ( 0 sgn 71 !; 0 ?; 203 :)
% 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,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_127,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_128,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_130,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_131,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_132,type,
vNOT: $o > $o ).
thf(func_def_133,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_134,type,
vAND: $o > $o > $o ).
thf(func_def_135,type,
vIFF: $o > $o > $o ).
thf(func_def_136,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_139,type,
sK0: subst ).
thf(func_def_140,type,
sK1: ( subst > term > term ) > term ).
thf(func_def_141,type,
sK2: ( subst > term > term ) > subst ).
thf(func_def_142,type,
sK3: ( subst > term > term ) > subst ).
thf(func_def_143,type,
sK4: subst > term > term ).
thf(func_def_144,type,
sK5: term ).
thf(func_def_145,type,
sK6: term ).
thf(func_def_146,type,
sK7: subst ).
thf(func_def_147,type,
sK8: term ).
thf(func_def_148,type,
sK9: subst ).
thf(func_def_149,type,
sK10: term ).
thf(func_def_150,type,
sK11: term > ( term > $o ) > subst > ( term > $o ) > term ).
thf(func_def_151,type,
sK12: ( term > $o ) > term ).
thf(func_def_152,type,
sK13: term > $o ).
thf(func_def_153,type,
sK14: term > $o ).
thf(func_def_154,type,
sK15: term ).
thf(func_def_155,type,
sK16: subst ).
thf(func_def_156,type,
sK17: term ).
thf(func_def_157,type,
sK18: term ).
thf(func_def_158,type,
sK19: term ).
thf(func_def_159,type,
sK20: term ).
thf(func_def_160,type,
sK21: term ).
thf(func_def_161,type,
sK22: term ).
thf(func_def_162,type,
sK23: ( term > $o ) > term ).
thf(func_def_163,type,
sK24: term > $o ).
thf(func_def_164,type,
sK25: term ).
thf(func_def_165,type,
sK26: subst ).
thf(func_def_166,type,
sK27: term ).
thf(func_def_167,type,
sK28: ( term > $o ) > term ).
thf(func_def_168,type,
sK29: ( term > $o ) > term ).
thf(func_def_169,type,
sK30: ( term > $o ) > term ).
thf(func_def_170,type,
sK31: ( term > $o ) > term ).
thf(func_def_171,type,
sK32: ( term > $o ) > term ).
thf(func_def_172,type,
sK33: ( term > $o ) > term ).
thf(func_def_173,type,
sK34: term > $o ).
thf(func_def_174,type,
sK35: term > term ).
thf(func_def_175,type,
sK36: term ).
thf(func_def_176,type,
sK37: subst ).
thf(func_def_177,type,
sK38: ( term > $o ) > term ).
thf(func_def_178,type,
sK39: ( term > $o ) > term ).
thf(func_def_179,type,
sK40: ( term > $o ) > term ).
thf(func_def_180,type,
sK41: ( term > $o ) > subst > term ).
thf(func_def_181,type,
sK42: ( term > $o ) > subst > term ).
thf(func_def_182,type,
sK43: ( term > $o ) > subst > term ).
thf(func_def_183,type,
sK44: ( term > $o ) > term ).
thf(func_def_184,type,
sK45: subst > ( term > $o ) > term ).
thf(func_def_185,type,
sK46: subst > ( term > $o ) > term ).
thf(func_def_186,type,
sK47: term > $o ).
thf(func_def_187,type,
sK48: term > term ).
thf(func_def_188,type,
sK49: term ).
thf(func_def_189,type,
sK50: subst ).
thf(func_def_190,type,
sK51: term ).
thf(func_def_191,type,
sK52: ( subst > term > subst > $o ) > subst ).
thf(func_def_192,type,
sK53: ( subst > term > subst > $o ) > subst ).
thf(func_def_193,type,
sK54: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_194,type,
sK55: ( subst > term > subst > $o ) > subst ).
thf(func_def_195,type,
sK56: ( subst > term > subst > $o ) > subst ).
thf(func_def_196,type,
sK57: ( subst > term > subst > $o ) > term > term ).
thf(func_def_197,type,
sK58: ( subst > term > subst > $o ) > term ).
thf(func_def_198,type,
sK59: ( subst > term > subst > $o ) > subst ).
thf(func_def_199,type,
sK60: ( subst > term > subst > $o ) > subst ).
thf(func_def_200,type,
sK61: ( subst > term > subst > $o ) > term ).
thf(func_def_201,type,
sK62: ( subst > term > subst > $o ) > subst ).
thf(func_def_202,type,
sK63: ( subst > term > subst > $o ) > subst ).
thf(func_def_203,type,
sK64: ( subst > term > subst > $o ) > term ).
thf(func_def_204,type,
sK65: ( subst > term > subst > $o ) > subst ).
thf(func_def_205,type,
sK66: ( subst > term > subst > $o ) > term > term ).
thf(func_def_206,type,
sK67: ( subst > term > subst > $o ) > subst ).
thf(func_def_207,type,
sK68: ( subst > term > subst > $o ) > term ).
thf(func_def_208,type,
sK69: ( subst > term > subst > $o ) > subst ).
thf(func_def_209,type,
sK70: ( subst > term > subst > $o ) > term ).
thf(func_def_210,type,
sK71: ( subst > term > subst > $o ) > subst ).
thf(func_def_211,type,
sK72: ( subst > term > subst > $o ) > subst ).
thf(func_def_212,type,
sK73: ( subst > term > subst > $o ) > term ).
thf(func_def_213,type,
sK74: ( subst > term > subst > $o ) > subst ).
thf(func_def_214,type,
sK75: ( subst > term > subst > $o ) > subst ).
thf(func_def_215,type,
sK76: ( subst > term > subst > $o ) > term > term ).
thf(func_def_216,type,
sK77: ( subst > term > subst > $o ) > term ).
thf(func_def_217,type,
sK78: ( subst > term > subst > $o ) > subst ).
thf(func_def_218,type,
sK79: ( subst > term > subst > $o ) > term ).
thf(func_def_219,type,
sK80: ( subst > term > subst > $o ) > subst ).
thf(func_def_220,type,
sK81: ( subst > term > subst > $o ) > subst ).
thf(func_def_221,type,
sK82: ( subst > term > subst > $o ) > term ).
thf(func_def_222,type,
sK83: ( subst > term > subst > $o ) > subst ).
thf(func_def_223,type,
sK84: subst > term > subst > $o ).
thf(func_def_224,type,
sK85: ( subst > term > term ) > subst ).
thf(func_def_225,type,
sK86: ( subst > term > term ) > term ).
thf(func_def_226,type,
sK87: ( subst > term > term ) > term ).
thf(func_def_227,type,
sK88: ( subst > term > term ) > subst ).
thf(func_def_228,type,
sK89: ( subst > term > term ) > term ).
thf(func_def_229,type,
sK90: ( subst > term > term ) > subst ).
thf(func_def_230,type,
sK91: term ).
thf(func_def_231,type,
sK92: subst > ( term > $o ) > term ).
thf(func_def_232,type,
sK93: subst ).
thf(func_def_233,type,
sK94: term > $o ).
thf(func_def_234,type,
sK95: term ).
thf(func_def_235,type,
sK96: term ).
thf(func_def_236,type,
sK97: ( term > $o ) > term > ( term > $o ) > subst > term ).
thf(func_def_237,type,
sK98: term ).
thf(func_def_238,type,
sK99: subst ).
thf(func_def_239,type,
sK100: term > $o ).
thf(func_def_240,type,
sK101: term > $o ).
thf(func_def_241,type,
sK102: term ).
thf(func_def_242,type,
sK103: subst ).
thf(func_def_243,type,
sK104: term ).
thf(func_def_244,type,
sK105: term ).
thf(func_def_245,type,
sK106: subst ).
thf(func_def_246,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_247,type,
sK107: ( term > $o ) > subst > term > term > $o ).
thf(func_def_248,type,
sK108: subst ).
thf(func_def_249,type,
sK109: term ).
thf(func_def_250,type,
sK110: term > $o ).
thf(func_def_251,type,
sK111: ( term > $o ) > term ).
thf(func_def_252,type,
sK112: ( subst > term > subst > $o ) > subst ).
thf(func_def_253,type,
sK113: ( subst > term > subst > $o ) > subst ).
thf(func_def_254,type,
sK114: ( subst > term > subst > $o ) > term ).
thf(func_def_255,type,
sK115: ( subst > term > subst > $o ) > term ).
thf(func_def_256,type,
sK116: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_257,type,
sK117: ( subst > term > subst > $o ) > term ).
thf(func_def_258,type,
sK118: ( subst > term > subst > $o ) > term ).
thf(func_def_259,type,
sK119: ( subst > term > subst > $o ) > subst ).
thf(func_def_260,type,
sK120: ( subst > term > subst > $o ) > subst ).
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 ) > subst ).
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 ) > subst ).
thf(func_def_267,type,
sK127: ( subst > term > subst > $o ) > term ).
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 ) > term ).
thf(func_def_273,type,
sK133: ( subst > term > subst > $o ) > term ).
thf(func_def_274,type,
sK134: ( subst > term > subst > $o ) > subst ).
thf(func_def_275,type,
sK135: ( subst > term > subst > $o ) > term ).
thf(func_def_276,type,
sK136: ( subst > term > subst > $o ) > subst ).
thf(func_def_277,type,
sK137: ( subst > term > subst > $o ) > subst ).
thf(func_def_278,type,
sK138: ( subst > term > subst > $o ) > subst ).
thf(func_def_279,type,
sK139: ( subst > term > subst > $o ) > subst ).
thf(func_def_280,type,
sK140: ( subst > term > subst > $o ) > term ).
thf(func_def_281,type,
sK141: ( subst > term > subst > $o ) > subst ).
thf(func_def_282,type,
sK142: ( subst > term > subst > $o ) > subst ).
thf(func_def_283,type,
sK143: ( subst > term > subst > $o ) > term ).
thf(func_def_284,type,
sK144: ( subst > term > subst > $o ) > term ).
thf(func_def_285,type,
sK145: ( subst > term > subst > $o ) > subst ).
thf(func_def_286,type,
sK146: ( subst > term > subst > $o ) > term ).
thf(func_def_287,type,
sK147: ( subst > term > subst > $o ) > subst ).
thf(func_def_288,type,
sK148: ( subst > term > subst > $o ) > subst ).
thf(func_def_289,type,
sK149: ( subst > term > subst > $o ) > subst ).
thf(func_def_290,type,
sK150: ( subst > term > subst > $o ) > term ).
thf(func_def_291,type,
sK151: ( subst > term > subst > $o ) > subst ).
thf(func_def_292,type,
sK152: ( subst > term > subst > $o ) > subst ).
thf(func_def_293,type,
sK153: ( subst > term > subst > $o ) > term ).
thf(func_def_294,type,
sK154: ( subst > term > subst > $o ) > subst ).
thf(func_def_295,type,
sK155: ( subst > term > subst > $o ) > term ).
thf(func_def_296,type,
sK156: ( subst > term > subst > $o ) > subst ).
thf(func_def_297,type,
sK157: ( subst > term > subst > $o ) > subst ).
thf(func_def_298,type,
sK158: ( subst > term > subst > $o ) > subst ).
thf(func_def_299,type,
sK159: ( subst > term > subst > $o ) > term ).
thf(func_def_300,type,
sK160: ( subst > term > subst > $o ) > term ).
thf(func_def_301,type,
sK161: ( subst > term > subst > $o ) > subst ).
thf(func_def_302,type,
sK162: ( subst > term > subst > $o ) > subst ).
thf(func_def_303,type,
sK163: ( subst > term > subst > $o ) > term ).
thf(func_def_304,type,
sK164: ( subst > term > subst > $o ) > subst ).
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 ) > term ).
thf(func_def_314,type,
sK174: ( subst > term > subst > $o ) > subst ).
thf(func_def_315,type,
sK175: subst > term > subst > $o ).
thf(func_def_316,type,
sK176: ( subst > term > term ) > subst ).
thf(func_def_317,type,
sK177: ( subst > term > term ) > term ).
thf(func_def_318,type,
sK178: ( subst > term > term ) > term ).
thf(func_def_319,type,
sK179: ( subst > term > term ) > subst ).
thf(func_def_320,type,
sK180: ( subst > term > term ) > subst ).
thf(func_def_321,type,
sK181: term ).
thf(func_def_322,type,
sK182: subst ).
thf(func_def_323,type,
sK183: subst ).
thf(func_def_324,type,
sK184: subst ).
thf(func_def_325,type,
sK185: ( subst > term > subst > $o ) > term ).
thf(func_def_326,type,
sK186: ( subst > term > subst > $o ) > subst ).
thf(func_def_327,type,
sK187: ( subst > term > subst > $o ) > term ).
thf(func_def_328,type,
sK188: ( subst > term > subst > $o ) > term ).
thf(func_def_329,type,
sK189: ( subst > term > subst > $o ) > subst ).
thf(func_def_330,type,
sK190: ( subst > term > subst > $o ) > term ).
thf(func_def_331,type,
sK191: ( subst > term > subst > $o ) > subst ).
thf(func_def_332,type,
sK192: ( subst > term > subst > $o ) > subst ).
thf(func_def_333,type,
sK193: ( subst > term > subst > $o ) > subst ).
thf(func_def_334,type,
sK194: ( subst > term > subst > $o ) > subst ).
thf(func_def_335,type,
sK195: ( subst > term > subst > $o ) > subst ).
thf(func_def_336,type,
sK196: ( subst > term > subst > $o ) > subst ).
thf(func_def_337,type,
sK197: ( subst > term > subst > $o ) > subst ).
thf(func_def_338,type,
sK198: ( subst > term > subst > $o ) > subst ).
thf(func_def_339,type,
sK199: subst > term > subst > $o ).
thf(func_def_340,type,
sK200: term ).
thf(func_def_341,type,
sK201: term ).
thf(func_def_342,type,
sK202: term ).
thf(func_def_343,type,
sK203: term ).
thf(func_def_344,type,
sK204: ( subst > term > subst > $o ) > term ).
thf(func_def_345,type,
sK205: ( subst > term > subst > $o ) > subst ).
thf(func_def_346,type,
sK206: ( subst > term > subst > $o ) > subst ).
thf(func_def_347,type,
sK207: ( subst > term > subst > $o ) > subst ).
thf(func_def_348,type,
sK208: ( subst > term > subst > $o ) > term ).
thf(func_def_349,type,
sK209: ( subst > term > subst > $o ) > subst ).
thf(func_def_350,type,
sK210: ( subst > term > subst > $o ) > subst ).
thf(func_def_351,type,
sK211: ( subst > term > subst > $o ) > term ).
thf(func_def_352,type,
sK212: ( subst > term > subst > $o ) > subst ).
thf(func_def_353,type,
sK213: ( subst > term > subst > $o ) > subst ).
thf(func_def_354,type,
sK214: ( subst > term > subst > $o ) > term ).
thf(func_def_355,type,
sK215: ( subst > term > subst > $o ) > subst ).
thf(func_def_356,type,
sK216: ( subst > term > subst > $o ) > subst ).
thf(func_def_357,type,
sK217: ( subst > term > subst > $o ) > subst ).
thf(func_def_358,type,
sK218: ( subst > term > subst > $o ) > term ).
thf(func_def_359,type,
sK219: subst > term > subst > $o ).
thf(func_def_360,type,
sK220: term ).
thf(func_def_361,type,
sK221: term ).
thf(func_def_362,type,
sK222: term ).
thf(func_def_363,type,
sK223: term ).
thf(func_def_364,type,
sK224: term ).
thf(func_def_365,type,
sK225: ( term > $o ) > term ).
thf(func_def_366,type,
sK226: ( term > $o ) > term ).
thf(func_def_367,type,
sK227: ( term > $o ) > term ).
thf(func_def_368,type,
sK228: ( term > $o ) > term ).
thf(func_def_369,type,
sK229: term > $o ).
thf(func_def_370,type,
sK230: term ).
thf(func_def_371,type,
sK231: ( term > $o ) > subst > ( term > $o ) > term > term ).
thf(func_def_372,type,
sK232: ( term > $o ) > subst > term ).
thf(func_def_373,type,
sK233: subst ).
thf(func_def_374,type,
sK234: term ).
thf(func_def_375,type,
sK235: term > $o ).
thf(func_def_376,type,
sK236: term > $o ).
thf(func_def_377,type,
sK237: term ).
thf(func_def_378,type,
sK238: ( subst > term > term ) > subst ).
thf(func_def_379,type,
sK239: ( subst > term > term ) > subst ).
thf(func_def_380,type,
sK240: ( subst > term > term ) > term ).
thf(func_def_381,type,
sK241: ( subst > term > term ) > subst ).
thf(func_def_382,type,
sK242: ( subst > term > term ) > term ).
thf(func_def_383,type,
sK243: ( subst > term > term ) > subst ).
thf(func_def_384,type,
sK244: subst > term > term ).
thf(func_def_385,type,
sK245: subst > term > term ).
thf(func_def_386,type,
sK246: subst ).
thf(func_def_387,type,
sK247: term ).
thf(func_def_388,type,
sK248: subst ).
thf(func_def_389,type,
sK249: term ).
thf(func_def_390,type,
sK250: subst ).
thf(func_def_391,type,
sK251: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_392,type,
sK252: ( subst > term > subst > $o ) > term > term ).
thf(func_def_393,type,
sK253: ( subst > term > subst > $o ) > term > term ).
thf(func_def_394,type,
sK254: ( subst > term > subst > $o ) > term > term ).
thf(func_def_395,type,
sK255: subst > term > subst > $o ).
thf(func_def_396,type,
sK256: ( subst > term > term ) > term ).
thf(func_def_397,type,
sK257: ( subst > term > term ) > term ).
thf(func_def_398,type,
sK258: ( subst > term > term ) > subst ).
thf(func_def_399,type,
sK259: ( subst > term > term ) > subst ).
thf(func_def_400,type,
sK260: ( subst > term > term ) > subst ).
thf(func_def_401,type,
sK261: ( subst > term > term ) > subst ).
thf(func_def_402,type,
sK262: term ).
thf(func_def_403,type,
sK263: term ).
thf(func_def_404,type,
sK264: subst ).
thf(func_def_405,type,
sK265: term ).
thf(func_def_406,type,
sK266: term ).
thf(func_def_407,type,
sK267: term ).
thf(func_def_408,type,
sK268: term ).
thf(func_def_409,type,
sK269: subst ).
thf(f5,axiom,
( axclos
= ( ! [X2: subst,X0: term,X1: subst] :
( ( sub @ ( sub @ X0 @ X1 ) @ X2 )
= ( sub @ X0 @ ( comp @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axclos) ).
thf(f7,axiom,
( axshiftcons
= ( ! [X1: subst,X0: term] :
( ( comp @ sh @ ( push @ X0 @ X1 ) )
= X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axshiftcons) ).
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/sandbox/benchmark/Axioms/ALG003^0.ax',pushprop_p_and_p_prime) ).
thf(f34,axiom,
! [X1: term > $o,X0: term > $o,X2: term,X3: subst] :
( ( ( pushprop_p_and_p_prime @ X2 @ X3 @ X0 @ X1 )
=> ( ! [X4: term] :
( ( var @ X4 )
=> ( X0 @ ( sub @ X4 @ X3 ) ) )
=> ! [X5: term] :
( ( var @ X5 )
=> ( ( X1 @ X5 )
=> ( X1 @ ( sub @ X5 @ sh ) ) ) ) ) )
= pushprop_lem2v2 ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',pushprop_lem2v2) ).
thf(f36,axiom,
( axclos
=> ( ( axshiftcons
=> pushprop_lem2v2 )
= pushprop_lem2v2_lthm ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',pushprop_lem2v2_lthm) ).
thf(f114,conjecture,
pushprop_lem2v2_lthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ pushprop_lem2v2_lthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f214,plain,
( axshiftcons
= ( ! [X0: subst,X1: term] :
( ( comp @ sh @ ( push @ X1 @ X0 ) )
= X0 ) ) ),
inference(rectify,[],[f7]) ).
thf(f215,plain,
( axshiftcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[],[f214]) ).
thf(f221,plain,
~ pushprop_lem2v2_lthm,
inference(rectify,[],[f115]) ).
thf(f222,plain,
pushprop_lem2v2_lthm != $true,
inference(fool_elimination,[],[f221]) ).
thf(f241,plain,
( axclos
= ( ! [X0: subst,X1: term,X2: subst] :
( ( sub @ ( sub @ X1 @ X2 ) @ X0 )
= ( sub @ X1 @ ( comp @ X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f242,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 )
= ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f241]) ).
thf(f292,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(f293,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,[],[f292]) ).
thf(f304,plain,
( axclos
=> ( ( axshiftcons
=> pushprop_lem2v2 )
= pushprop_lem2v2_lthm ) ),
inference(rectify,[],[f36]) ).
thf(f305,plain,
( pushprop_lem2v2_lthm
= ( axclos
=> ( axshiftcons
=> pushprop_lem2v2 ) ) ),
inference(fool_elimination,[],[f304]) ).
thf(f312,plain,
! [X0: term > $o,X1: term > $o,X2: term,X3: subst] :
( ( ( pushprop_p_and_p_prime @ X2 @ X3 @ X1 @ X0 )
=> ( ! [X4: term] :
( ( var @ X4 )
=> ( X1 @ ( sub @ X4 @ X3 ) ) )
=> ! [X5: term] :
( ( var @ X5 )
=> ( ( X0 @ X5 )
=> ( X0 @ ( sub @ X5 @ sh ) ) ) ) ) )
= pushprop_lem2v2 ),
inference(rectify,[],[f34]) ).
thf(f313,plain,
( pushprop_lem2v2
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( !! @ ( term > $o )
@ ^ [Y3: term > $o] :
( ( pushprop_p_and_p_prime @ Y1 @ Y0 @ Y2 @ Y3 )
=> ( ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y2 @ ( sub @ Y4 @ Y0 ) ) ) )
=> ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( ( Y3 @ Y4 )
=> ( Y3 @ ( sub @ Y4 @ sh ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f312]) ).
thf(f322,plain,
pushprop_lem2v2_lthm != $true,
inference(flattening,[],[f222]) ).
thf(f328,plain,
( axshiftcons
= ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[],[f215]) ).
thf(f335,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 )
= ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f242]) ).
thf(f340,plain,
( pushprop_lem2v2
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( !! @ ( term > $o )
@ ^ [Y3: term > $o] :
( ( pushprop_p_and_p_prime @ Y1 @ Y0 @ Y2 @ Y3 )
=> ( ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y2 @ ( sub @ Y4 @ Y0 ) ) ) )
=> ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( ( Y3 @ Y4 )
=> ( Y3 @ ( sub @ Y4 @ sh ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f313]) ).
thf(f346,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,[],[f293]) ).
thf(f350,plain,
( pushprop_lem2v2_lthm
= ( axclos
=> ( axshiftcons
=> pushprop_lem2v2 ) ) ),
inference(cnf_transformation,[],[f305]) ).
thf(f353,plain,
pushprop_lem2v2_lthm != $true,
inference(cnf_transformation,[],[f322]) ).
thf(f371,plain,
( pushprop_lem2v2
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( !! @ ( 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 ) ) )
@ Y1
@ Y0
@ Y2
@ Y3 )
=> ( ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y2 @ ( sub @ Y4 @ Y0 ) ) ) )
=> ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( ( Y3 @ Y4 )
=> ( Y3 @ ( sub @ Y4 @ sh ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f340,f346]) ).
thf(f1687,plain,
( ( pushprop_lem2v2_lthm = $true )
| ( $false
= ( axclos
=> ( axshiftcons
=> pushprop_lem2v2 ) ) ) ),
inference(iff_proxy_clausification,[],[f350]) ).
thf(f1691,plain,
( ( $false
= ( axshiftcons
=> pushprop_lem2v2 ) )
| ( pushprop_lem2v2_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f1687]) ).
thf(f1692,plain,
( ( axclos = $true )
| ( pushprop_lem2v2_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f1687]) ).
thf(f1693,plain,
( ( pushprop_lem2v2_lthm = $true )
| ( pushprop_lem2v2 = $false ) ),
inference(imp_proxy_clausification,[],[f1691]) ).
thf(f1694,plain,
( ( axshiftcons = $true )
| ( pushprop_lem2v2_lthm = $true ) ),
inference(imp_proxy_clausification,[],[f1691]) ).
thf(f1755,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( !! @ ( 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 ) ) )
@ Y1
@ Y0
@ Y2
@ Y3 )
=> ( ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y2 @ ( sub @ Y4 @ Y0 ) ) ) )
=> ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( ( Y3 @ Y4 )
=> ( Y3 @ ( sub @ Y4 @ sh ) ) ) ) ) ) ) ) ) ) )
= $false )
| ( pushprop_lem2v2 = $true ) ),
inference(iff_proxy_clausification,[],[f371]) ).
thf(f1782,plain,
( ( pushprop_lem2v2 = $true )
| ( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( !! @ ( 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 ) ) )
@ Y1
@ Y0
@ Y2
@ Y3 )
=> ( ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y2 @ ( sub @ Y4 @ Y0 ) ) ) )
=> ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( ( Y3 @ Y4 )
=> ( Y3 @ ( sub @ Y4 @ sh ) ) ) ) ) ) ) ) ) )
@ sK233 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1755]) ).
thf(f1783,plain,
( ( pushprop_lem2v2 = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ ( sub @ Y3 @ ( push @ Y0 @ sK233 ) ) )
= ( Y2 @ Y3 ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ sK233 ) ) ) )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( ( Y2 @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ sh ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f1782]) ).
thf(f1784,plain,
( ( pushprop_lem2v2 = $true )
| ( ( ^ [Y0: term] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ ( sub @ Y3 @ ( push @ Y0 @ sK233 ) ) )
= ( Y2 @ Y3 ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ sK233 ) ) ) )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( ( Y2 @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ sh ) ) ) ) ) ) ) ) )
@ sK234 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1783]) ).
thf(f1785,plain,
( ( pushprop_lem2v2 = $true )
| ( ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( sub @ Y2 @ ( push @ sK234 @ sK233 ) ) )
= ( Y1 @ Y2 ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y0 @ ( sub @ Y2 @ sK233 ) ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( ( Y1 @ Y2 )
=> ( Y1 @ ( sub @ Y2 @ sh ) ) ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f1784]) ).
thf(f1786,plain,
( ( ( ^ [Y0: term > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ ( sub @ Y2 @ ( push @ sK234 @ sK233 ) ) )
= ( Y1 @ Y2 ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y0 @ ( sub @ Y2 @ sK233 ) ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( ( Y1 @ Y2 )
=> ( Y1 @ ( sub @ Y2 @ sh ) ) ) ) ) ) ) )
@ sK235 )
= $false )
| ( pushprop_lem2v2 = $true ) ),
inference(sigma_proxy_clausification,[],[f1785]) ).
thf(f1787,plain,
( ( $false
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK235 @ ( sub @ Y1 @ ( push @ sK234 @ sK233 ) ) )
= ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK235 @ ( sub @ Y1 @ sK233 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) ) ) ) ) )
| ( pushprop_lem2v2 = $true ) ),
inference(beta-eta_normalization,[],[f1786]) ).
thf(f1788,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK235 @ ( sub @ Y1 @ ( push @ sK234 @ sK233 ) ) )
= ( Y0 @ Y1 ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( sK235 @ ( sub @ Y1 @ sK233 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( Y0 @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sh ) ) ) ) ) ) )
@ sK236 ) ) ),
inference(sigma_proxy_clausification,[],[f1787]) ).
thf(f1789,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK235 @ ( sub @ Y0 @ ( push @ sK234 @ sK233 ) ) )
= ( sK236 @ Y0 ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK235 @ ( sub @ Y0 @ sK233 ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( sK236 @ Y0 )
=> ( sK236 @ ( sub @ Y0 @ sh ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1788]) ).
thf(f1790,plain,
( ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK235 @ ( sub @ Y0 @ sK233 ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( sK236 @ Y0 )
=> ( sK236 @ ( sub @ Y0 @ sh ) ) ) ) ) ) )
| ( pushprop_lem2v2 = $true ) ),
inference(imp_proxy_clausification,[],[f1789]) ).
thf(f1791,plain,
( ( pushprop_lem2v2 = $true )
| ( ( !! @ term
@ ^ [Y0: term] :
( ( sK235 @ ( sub @ Y0 @ ( push @ sK234 @ sK233 ) ) )
= ( sK236 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1789]) ).
thf(f1792,plain,
! [X1: term] :
( ( $true
= ( ^ [Y0: term] :
( ( sK235 @ ( sub @ Y0 @ ( push @ sK234 @ sK233 ) ) )
= ( sK236 @ Y0 ) )
@ X1 ) )
| ( pushprop_lem2v2 = $true ) ),
inference(pi_proxy_clausification,[],[f1791]) ).
thf(f1793,plain,
! [X1: term] :
( ( pushprop_lem2v2 = $true )
| ( ( ( sK235 @ ( sub @ X1 @ ( push @ sK234 @ sK233 ) ) )
= ( sK236 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1792]) ).
thf(f1794,plain,
! [X1: term] :
( ( pushprop_lem2v2 = $true )
| ( ( sK236 @ X1 )
= ( sK235 @ ( sub @ X1 @ ( push @ sK234 @ sK233 ) ) ) ) ),
inference(iff_proxy_clausification,[],[f1793]) ).
thf(f1795,plain,
! [X1: term] :
( ( ( sK236 @ X1 )
= $true )
| ( pushprop_lem2v2 = $true )
| ( $false
= ( sK235 @ ( sub @ X1 @ ( push @ sK234 @ sK233 ) ) ) ) ),
inference(iff_proxy_clausification,[],[f1794]) ).
thf(f1797,plain,
( ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( sK236 @ Y0 )
=> ( sK236 @ ( sub @ Y0 @ sh ) ) ) ) ) )
| ( pushprop_lem2v2 = $true ) ),
inference(imp_proxy_clausification,[],[f1790]) ).
thf(f1798,plain,
( ( pushprop_lem2v2 = $true )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK235 @ ( sub @ Y0 @ sK233 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1790]) ).
thf(f1799,plain,
! [X1: term] :
( ( ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK235 @ ( sub @ Y0 @ sK233 ) ) )
@ X1 )
= $true )
| ( pushprop_lem2v2 = $true ) ),
inference(pi_proxy_clausification,[],[f1798]) ).
thf(f1800,plain,
! [X1: term] :
( ( pushprop_lem2v2 = $true )
| ( ( ( var @ X1 )
=> ( sK235 @ ( sub @ X1 @ sK233 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1799]) ).
thf(f1801,plain,
! [X1: term] :
( ( pushprop_lem2v2 = $true )
| ( ( var @ X1 )
= $false )
| ( ( sK235 @ ( sub @ X1 @ sK233 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f1800]) ).
thf(f1802,plain,
( ( pushprop_lem2v2 = $true )
| ( ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( sK236 @ Y0 )
=> ( sK236 @ ( sub @ Y0 @ sh ) ) ) )
@ sK237 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1797]) ).
thf(f1803,plain,
( ( pushprop_lem2v2 = $true )
| ( ( ( var @ sK237 )
=> ( ( sK236 @ sK237 )
=> ( sK236 @ ( sub @ sK237 @ sh ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f1802]) ).
thf(f1804,plain,
( ( $false
= ( ( sK236 @ sK237 )
=> ( sK236 @ ( sub @ sK237 @ sh ) ) ) )
| ( pushprop_lem2v2 = $true ) ),
inference(imp_proxy_clausification,[],[f1803]) ).
thf(f1805,plain,
( ( ( var @ sK237 )
= $true )
| ( pushprop_lem2v2 = $true ) ),
inference(imp_proxy_clausification,[],[f1803]) ).
thf(f1806,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( sK236 @ ( sub @ sK237 @ sh ) ) ) ),
inference(imp_proxy_clausification,[],[f1804]) ).
thf(f1863,plain,
( ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 )
= ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) ) ) ) ) )
= $true )
| ( axclos = $false ) ),
inference(iff_proxy_clausification,[],[f335]) ).
thf(f1864,plain,
! [X1: subst] :
( ( ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sub @ Y1 @ Y0 ) @ Y2 )
= ( sub @ Y1 @ ( comp @ Y0 @ Y2 ) ) ) ) )
@ X1 )
= $true )
| ( axclos = $false ) ),
inference(pi_proxy_clausification,[],[f1863]) ).
thf(f1865,plain,
! [X1: subst] :
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sub @ Y0 @ X1 ) @ Y1 )
= ( sub @ Y0 @ ( comp @ X1 @ Y1 ) ) ) ) )
= $true )
| ( axclos = $false ) ),
inference(beta-eta_normalization,[],[f1864]) ).
thf(f1866,plain,
! [X2: term,X1: subst] :
( ( $true
= ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( sub @ ( sub @ Y0 @ X1 ) @ Y1 )
= ( sub @ Y0 @ ( comp @ X1 @ Y1 ) ) ) )
@ X2 ) )
| ( axclos = $false ) ),
inference(pi_proxy_clausification,[],[f1865]) ).
thf(f1867,plain,
! [X2: term,X1: subst] :
( ( axclos = $false )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( ( sub @ ( sub @ X2 @ X1 ) @ Y0 )
= ( sub @ X2 @ ( comp @ X1 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1866]) ).
thf(f1868,plain,
! [X2: term,X3: subst,X1: subst] :
( ( ( ^ [Y0: subst] :
( ( sub @ ( sub @ X2 @ X1 ) @ Y0 )
= ( sub @ X2 @ ( comp @ X1 @ Y0 ) ) )
@ X3 )
= $true )
| ( axclos = $false ) ),
inference(pi_proxy_clausification,[],[f1867]) ).
thf(f1869,plain,
! [X2: term,X3: subst,X1: subst] :
( ( axclos = $false )
| ( $true
= ( ( sub @ ( sub @ X2 @ X1 ) @ X3 )
= ( sub @ X2 @ ( comp @ X1 @ X3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1868]) ).
thf(f1870,plain,
! [X2: term,X3: subst,X1: subst] :
( ( axclos = $false )
| ( ( sub @ X2 @ ( comp @ X1 @ X3 ) )
= ( sub @ ( sub @ X2 @ X1 ) @ X3 ) ) ),
inference(equality_proxy_clausification,[],[f1869]) ).
thf(f1948,plain,
( ( ( !! @ term
@ ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) ) )
= $true )
| ( axshiftcons = $false ) ),
inference(iff_proxy_clausification,[],[f328]) ).
thf(f1949,plain,
! [X1: term] :
( ( axshiftcons = $false )
| ( ( ^ [Y0: term] :
( !! @ subst
@ ^ [Y1: subst] :
( ( comp @ sh @ ( push @ Y0 @ Y1 ) )
= Y1 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1948]) ).
thf(f1950,plain,
! [X1: term] :
( ( axshiftcons = $false )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( ( comp @ sh @ ( push @ X1 @ Y0 ) )
= Y0 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1949]) ).
thf(f1951,plain,
! [X2: subst,X1: term] :
( ( axshiftcons = $false )
| ( ( ^ [Y0: subst] :
( ( comp @ sh @ ( push @ X1 @ Y0 ) )
= Y0 )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1950]) ).
thf(f1952,plain,
! [X2: subst,X1: term] :
( ( axshiftcons = $false )
| ( ( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 )
= $true ) ),
inference(beta-eta_normalization,[],[f1951]) ).
thf(f1953,plain,
! [X2: subst,X1: term] :
( ( axshiftcons = $false )
| ( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 ) ),
inference(equality_proxy_clausification,[],[f1952]) ).
thf(f2129,definition,
( spl270_34
<=> ( pushprop_lem2v2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl270_34])],[avatar_definition]) ).
thf(f2131,plain,
( ( pushprop_lem2v2 = $true )
| ~ spl270_34 ),
inference(avatar_component_clause,[],[f2129]) ).
thf(f2133,definition,
( spl270_35
<=> ( axshiftcons = $false ) ),
introduced(definition,[new_symbols(definition,[spl270_35])],[avatar_definition]) ).
thf(f2135,plain,
( ( axshiftcons = $false )
| ~ spl270_35 ),
inference(avatar_component_clause,[],[f2133]) ).
thf(f2141,definition,
( spl270_37
<=> ( axclos = $false ) ),
introduced(definition,[new_symbols(definition,[spl270_37])],[avatar_definition]) ).
thf(f2143,plain,
( ( axclos = $false )
| ~ spl270_37 ),
inference(avatar_component_clause,[],[f2141]) ).
thf(f2178,definition,
( spl270_45
<=> ( axclos = $true ) ),
introduced(definition,[new_symbols(definition,[spl270_45])],[avatar_definition]) ).
thf(f2180,plain,
( ( axclos = $true )
| ~ spl270_45 ),
inference(avatar_component_clause,[],[f2178]) ).
thf(f2184,definition,
( spl270_46
<=> ( axshiftcons = $true ) ),
introduced(definition,[new_symbols(definition,[spl270_46])],[avatar_definition]) ).
thf(f2186,plain,
( ( axshiftcons = $true )
| ~ spl270_46 ),
inference(avatar_component_clause,[],[f2184]) ).
thf(f2261,definition,
( spl270_61
<=> ( pushprop_lem2v2 = $false ) ),
introduced(definition,[new_symbols(definition,[spl270_61])],[avatar_definition]) ).
thf(f2263,plain,
( ( pushprop_lem2v2 = $false )
| ~ spl270_61 ),
inference(avatar_component_clause,[],[f2261]) ).
thf(f3329,definition,
( spl270_318
<=> ( pushprop_lem2v2_lthm = $true ) ),
introduced(definition,[new_symbols(definition,[spl270_318])],[avatar_definition]) ).
thf(f3332,plain,
( spl270_318
| spl270_45 ),
inference(avatar_split_clause,[],[f1692,f2178,f3329]) ).
thf(f3333,plain,
( spl270_46
| spl270_318 ),
inference(avatar_split_clause,[],[f1694,f3329,f2184]) ).
thf(f3334,plain,
( spl270_318
| spl270_61 ),
inference(avatar_split_clause,[],[f1693,f2261,f3329]) ).
thf(f3421,definition,
( spl270_340
<=> ! [X1: term] :
( ( ( sK236 @ X1 )
= $true )
| ( $false
= ( sK235 @ ( sub @ X1 @ ( push @ sK234 @ sK233 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl270_340])],[avatar_definition]) ).
thf(f3422,plain,
( ! [X1: term] :
( ( $false
= ( sK235 @ ( sub @ X1 @ ( push @ sK234 @ sK233 ) ) ) )
| ( ( sK236 @ X1 )
= $true ) )
| ~ spl270_340 ),
inference(avatar_component_clause,[],[f3421]) ).
thf(f3423,plain,
( spl270_340
| spl270_34 ),
inference(avatar_split_clause,[],[f1795,f2129,f3421]) ).
thf(f3425,definition,
( spl270_341
<=> ! [X1: term] :
( ( ( var @ X1 )
= $false )
| ( ( sK235 @ ( sub @ X1 @ sK233 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl270_341])],[avatar_definition]) ).
thf(f3426,plain,
( ! [X1: term] :
( ( ( sK235 @ ( sub @ X1 @ sK233 ) )
= $true )
| ( ( var @ X1 )
= $false ) )
| ~ spl270_341 ),
inference(avatar_component_clause,[],[f3425]) ).
thf(f3427,plain,
( spl270_34
| spl270_341 ),
inference(avatar_split_clause,[],[f1801,f3425,f2129]) ).
thf(f3429,definition,
( spl270_342
<=> ( ( var @ sK237 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl270_342])],[avatar_definition]) ).
thf(f3431,plain,
( ( ( var @ sK237 )
= $true )
| ~ spl270_342 ),
inference(avatar_component_clause,[],[f3429]) ).
thf(f3432,plain,
( spl270_34
| spl270_342 ),
inference(avatar_split_clause,[],[f1805,f3429,f2129]) ).
thf(f3439,definition,
( spl270_344
<=> ( $false
= ( sK236 @ ( sub @ sK237 @ sh ) ) ) ),
introduced(definition,[new_symbols(definition,[spl270_344])],[avatar_definition]) ).
thf(f3441,plain,
( ( $false
= ( sK236 @ ( sub @ sK237 @ sh ) ) )
| ~ spl270_344 ),
inference(avatar_component_clause,[],[f3439]) ).
thf(f3442,plain,
( spl270_344
| spl270_34 ),
inference(avatar_split_clause,[],[f1806,f2129,f3439]) ).
thf(f3474,definition,
( spl270_352
<=> ! [X2: term,X1: subst,X3: subst] :
( ( sub @ X2 @ ( comp @ X1 @ X3 ) )
= ( sub @ ( sub @ X2 @ X1 ) @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl270_352])],[avatar_definition]) ).
thf(f3475,plain,
( ! [X2: term,X3: subst,X1: subst] :
( ( sub @ X2 @ ( comp @ X1 @ X3 ) )
= ( sub @ ( sub @ X2 @ X1 ) @ X3 ) )
| ~ spl270_352 ),
inference(avatar_component_clause,[],[f3474]) ).
thf(f3476,plain,
( spl270_37
| spl270_352 ),
inference(avatar_split_clause,[],[f1870,f3474,f2141]) ).
thf(f3532,definition,
( spl270_366
<=> ! [X2: subst,X1: term] :
( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 ) ),
introduced(definition,[new_symbols(definition,[spl270_366])],[avatar_definition]) ).
thf(f3533,plain,
( ! [X2: subst,X1: term] :
( ( comp @ sh @ ( push @ X1 @ X2 ) )
= X2 )
| ~ spl270_366 ),
inference(avatar_component_clause,[],[f3532]) ).
thf(f3534,plain,
( spl270_35
| spl270_366 ),
inference(avatar_split_clause,[],[f1953,f3532,f2133]) ).
thf(f3563,plain,
~ spl270_318,
inference(avatar_split_clause,[],[f353,f3329]) ).
thf(f4073,plain,
( ( $false = $true )
| ~ spl270_37
| ~ spl270_45 ),
inference(forward_demodulation,[],[f2180,f2143]) ).
thf(f4074,plain,
( $false
| ~ spl270_37
| ~ spl270_45 ),
inference(trivial_inequality_removal,[],[f4073]) ).
thf(f4075,plain,
( ~ spl270_37
| ~ spl270_45 ),
inference(avatar_contradiction_clause,[],[f4074]) ).
thf(f4108,plain,
( ( $false = $true )
| ~ spl270_35
| ~ spl270_46 ),
inference(forward_demodulation,[],[f2186,f2135]) ).
thf(f4109,plain,
( $false
| ~ spl270_35
| ~ spl270_46 ),
inference(trivial_inequality_removal,[],[f4108]) ).
thf(f4110,plain,
( ~ spl270_35
| ~ spl270_46 ),
inference(avatar_contradiction_clause,[],[f4109]) ).
thf(f4292,plain,
( ( $false = $true )
| ~ spl270_34
| ~ spl270_61 ),
inference(superposition,[],[f2263,f2131]) ).
thf(f4298,plain,
( $false
| ~ spl270_34
| ~ spl270_61 ),
inference(trivial_inequality_removal,[],[f4292]) ).
thf(f4299,plain,
( ~ spl270_34
| ~ spl270_61 ),
inference(avatar_contradiction_clause,[],[f4298]) ).
thf(f4362,plain,
( ! [X0: term,X1: subst] :
( ( ( sK235 @ ( sub @ X0 @ ( comp @ X1 @ ( push @ sK234 @ sK233 ) ) ) )
= $false )
| ( ( sK236 @ ( sub @ X0 @ X1 ) )
= $true ) )
| ~ spl270_340
| ~ spl270_352 ),
inference(superposition,[],[f3422,f3475]) ).
thf(f4380,plain,
( ! [X0: term] :
( ( $true
= ( sK236 @ ( sub @ X0 @ sh ) ) )
| ( $false
= ( sK235 @ ( sub @ X0 @ sK233 ) ) ) )
| ~ spl270_340
| ~ spl270_352
| ~ spl270_366 ),
inference(superposition,[],[f4362,f3533]) ).
thf(f4397,plain,
( ( ( sK235 @ ( sub @ sK237 @ sK233 ) )
= $false )
| ( $false = $true )
| ~ spl270_340
| ~ spl270_344
| ~ spl270_352
| ~ spl270_366 ),
inference(superposition,[],[f4380,f3441]) ).
thf(f4401,plain,
( ( ( sK235 @ ( sub @ sK237 @ sK233 ) )
= $false )
| ~ spl270_340
| ~ spl270_344
| ~ spl270_352
| ~ spl270_366 ),
inference(trivial_inequality_removal,[],[f4397]) ).
thf(f4424,plain,
( ( ( var @ sK237 )
= $false )
| ( $false = $true )
| ~ spl270_340
| ~ spl270_341
| ~ spl270_344
| ~ spl270_352
| ~ spl270_366 ),
inference(superposition,[],[f4401,f3426]) ).
thf(f4427,plain,
( ( ( var @ sK237 )
= $false )
| ~ spl270_340
| ~ spl270_341
| ~ spl270_344
| ~ spl270_352
| ~ spl270_366 ),
inference(trivial_inequality_removal,[],[f4424]) ).
thf(f4444,plain,
( ( $false = $true )
| ~ spl270_340
| ~ spl270_341
| ~ spl270_342
| ~ spl270_344
| ~ spl270_352
| ~ spl270_366 ),
inference(superposition,[],[f4427,f3431]) ).
thf(f4449,plain,
( $false
| ~ spl270_340
| ~ spl270_341
| ~ spl270_342
| ~ spl270_344
| ~ spl270_352
| ~ spl270_366 ),
inference(trivial_inequality_removal,[],[f4444]) ).
thf(f4450,plain,
( ~ spl270_340
| ~ spl270_341
| ~ spl270_342
| ~ spl270_344
| ~ spl270_352
| ~ spl270_366 ),
inference(avatar_contradiction_clause,[],[f4449]) ).
cnf(s272,plain,
( spl270_45
| spl270_318 ),
inference(sat_conversion,[],[f3332]) ).
cnf(s273,plain,
( spl270_46
| spl270_318 ),
inference(sat_conversion,[],[f3333]) ).
cnf(s274,plain,
( spl270_61
| spl270_318 ),
inference(sat_conversion,[],[f3334]) ).
cnf(s296,plain,
( spl270_34
| spl270_340 ),
inference(sat_conversion,[],[f3423]) ).
cnf(s297,plain,
( spl270_34
| spl270_341 ),
inference(sat_conversion,[],[f3427]) ).
cnf(s298,plain,
( spl270_34
| spl270_342 ),
inference(sat_conversion,[],[f3432]) ).
cnf(s300,plain,
( spl270_34
| spl270_344 ),
inference(sat_conversion,[],[f3442]) ).
cnf(s306,plain,
( spl270_37
| spl270_352 ),
inference(sat_conversion,[],[f3476]) ).
cnf(s318,plain,
( spl270_35
| spl270_366 ),
inference(sat_conversion,[],[f3534]) ).
cnf(s325,plain,
~ spl270_318,
inference(sat_conversion,[],[f3563]) ).
cnf(s354,plain,
( ~ spl270_37
| ~ spl270_45 ),
inference(sat_conversion,[],[f4075]) ).
cnf(s357,plain,
( ~ spl270_35
| ~ spl270_46 ),
inference(sat_conversion,[],[f4110]) ).
cnf(s368,plain,
( ~ spl270_34
| ~ spl270_61 ),
inference(sat_conversion,[],[f4299]) ).
cnf(s379,plain,
( ~ spl270_340
| ~ spl270_341
| ~ spl270_342
| ~ spl270_344
| ~ spl270_352
| ~ spl270_366 ),
inference(sat_conversion,[],[f4450]) ).
cnf(s381,plain,
spl270_61,
inference(rat,[],[s274,s325]) ).
cnf(s382,plain,
~ spl270_34,
inference(rat,[],[s368,s381]) ).
cnf(s383,plain,
spl270_344,
inference(rat,[],[s300,s382]) ).
cnf(s385,plain,
spl270_342,
inference(rat,[],[s298,s382]) ).
cnf(s386,plain,
spl270_341,
inference(rat,[],[s297,s382]) ).
cnf(s387,plain,
spl270_340,
inference(rat,[],[s296,s382]) ).
cnf(s389,plain,
spl270_46,
inference(rat,[],[s273,s325]) ).
cnf(s390,plain,
~ spl270_35,
inference(rat,[],[s357,s389]) ).
cnf(s391,plain,
spl270_366,
inference(rat,[],[s318,s390]) ).
cnf(s392,plain,
~ spl270_352,
inference(rat,[],[s379,s387,s386,s383,s385,s391]) ).
cnf(s393,plain,
spl270_37,
inference(rat,[],[s306,s392]) ).
cnf(s394,plain,
~ spl270_45,
inference(rat,[],[s354,s393]) ).
cnf(s396,plain,
$false,
inference(rat,[],[s272,s325,s394]) ).
thf(f4452,plain,
$false,
inference(avatar_sat_refutation,[],[s396]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG249^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n014.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 17:32:00 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.22/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.52/0.45 % (2968400)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.52/0.45 % (2968409)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2545125292:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.52/0.45 % (2968406)lrs+10_16_si=on:nwc=1.5:random_seed=2647531701:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.52/0.45 % (2968405)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1605369664:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.52/0.45 % (2968407)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3931897658:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.52/0.45 % (2968408)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=1425056391: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)
% 0.52/0.45 % (2968407)Instruction limit reached!
% 0.52/0.45 % (2968407)------------------------------
% 0.52/0.45 % (2968407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.45 % (2968407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.45 % (2968407)CaDiCaL version: 2.1.3
% 0.52/0.45 % (2968407)Termination reason: Instruction limit
% 0.52/0.45 % (2968407)Termination phase: shuffling
% 0.52/0.45 % (2968407)Time elapsed: 0.006 s
% 0.52/0.45 % (2968407)Peak memory usage: 10 MB
% 0.52/0.45 % (2968407)Instructions burned: 5 (million)
% 0.52/0.45 % (2968406)Instruction limit reached!
% 0.52/0.45 % (2968406)------------------------------
% 0.52/0.45 % (2968406)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.45 % (2968406)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.45 % (2968406)CaDiCaL version: 2.1.3
% 0.52/0.45 % (2968406)Termination reason: Instruction limit
% 0.52/0.45 % (2968406)Termination phase: shuffling
% 0.52/0.45 % (2968406)Time elapsed: 0.008 s
% 0.52/0.45 % (2968406)Peak memory usage: 10 MB
% 0.52/0.45 % (2968406)Instructions burned: 18 (million)
% 0.52/0.45 % (2968409)Instruction limit reached!
% 0.52/0.45 % (2968409)------------------------------
% 0.52/0.45 % (2968409)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.45 % (2968409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.45 % (2968409)CaDiCaL version: 2.1.3
% 0.52/0.45 % (2968409)Termination reason: Instruction limit
% 0.52/0.45 % (2968409)Termination phase: Naming
% 0.52/0.45 % (2968409)Time elapsed: 0.011 s
% 0.52/0.45 % (2968409)Peak memory usage: 11 MB
% 0.52/0.45 % (2968409)Instructions burned: 24 (million)
% 0.52/0.45 % (2968411)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.52/0.45 % (2968411)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
% 0.52/0.45 % (2968411)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=3138813353:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.52/0.45 % (2968410)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1935017330:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.52/0.45 % (2968419)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.52/0.45 % (2968419)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2199246903:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.52/0.45 % (2968419)Instruction limit reached!
% 0.52/0.45 % (2968419)------------------------------
% 0.52/0.45 % (2968419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.45 % (2968419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.45 % (2968419)CaDiCaL version: 2.1.3
% 0.52/0.45 % (2968419)Termination reason: Instruction limit
% 0.52/0.45 % (2968419)Termination phase: shuffling
% 0.52/0.45 % (2968419)Time elapsed: 0.004 s
% 0.52/0.50 % (2968419)Peak memory usage: 10 MB
% 0.52/0.50 % (2968419)Instructions burned: 9 (million)
% 0.52/0.50 % (2968418)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1811660339:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.52/0.50 % (2968417)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2990198885:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.52/0.50 % (2968417)Instruction limit reached!
% 0.52/0.50 % (2968417)------------------------------
% 0.52/0.50 % (2968417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.50 % (2968417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.50 % (2968417)CaDiCaL version: 2.1.3
% 0.52/0.50 % (2968417)Termination reason: Instruction limit
% 0.52/0.50 % (2968417)Termination phase: shuffling
% 0.52/0.50 % (2968417)Time elapsed: 0.002 s
% 0.52/0.50 % (2968417)Peak memory usage: 10 MB
% 0.52/0.50 % (2968417)Instructions burned: 3 (million)
% 0.52/0.50 % (2968418)Instruction limit reached!
% 0.52/0.50 % (2968418)------------------------------
% 0.52/0.50 % (2968418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.50 % (2968418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.50 % (2968418)CaDiCaL version: 2.1.3
% 0.52/0.50 % (2968418)Termination reason: Instruction limit
% 0.52/0.50 % (2968418)Termination phase: shuffling
% 0.52/0.50 % (2968418)Time elapsed: 0.007 s
% 0.52/0.50 % (2968418)Peak memory usage: 10 MB
% 0.52/0.50 % (2968418)Instructions burned: 5 (million)
% 0.52/0.50 % (2968423)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=645259438:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.52/0.50 % (2968405)Instruction limit reached!
% 0.52/0.50 % (2968405)------------------------------
% 0.52/0.50 % (2968405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.50 % (2968405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.50 % (2968405)CaDiCaL version: 2.1.3
% 0.52/0.50 % (2968405)Termination reason: Instruction limit
% 0.52/0.50 % (2968405)Termination phase: Function definition elimination
% 0.52/0.50 % (2968405)Time elapsed: 0.057 s
% 0.52/0.50 % (2968405)Peak memory usage: 12 MB
% 0.52/0.50 % (2968405)Instructions burned: 89 (million)
% 0.52/0.50 % (2968423)Instruction limit reached!
% 0.52/0.50 % (2968423)------------------------------
% 0.52/0.50 % (2968423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.50 % (2968423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.50 % (2968423)CaDiCaL version: 2.1.3
% 0.52/0.50 % (2968423)Termination reason: Instruction limit
% 0.52/0.50 % (2968423)Termination phase: shuffling
% 0.52/0.50 % (2968423)Time elapsed: 0.006 s
% 0.52/0.50 % (2968423)Peak memory usage: 10 MB
% 0.52/0.50 % (2968423)Instructions burned: 14 (million)
% 0.52/0.50 % (2968410)Instruction limit reached!
% 0.52/0.50 % (2968410)------------------------------
% 0.52/0.50 % (2968410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.52/0.50 % (2968410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.52/0.50 % (2968410)CaDiCaL version: 2.1.3
% 0.52/0.50 % (2968410)Termination reason: Instruction limit
% 0.52/0.50 % (2968410)Termination phase: Property scanning
% 0.52/0.50 % (2968410)Time elapsed: 0.041 s
% 0.52/0.50 % (2968410)Peak memory usage: 12 MB
% 0.52/0.50 % (2968410)Instructions burned: 75 (million)
% 0.52/0.50 % (2968426)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
% 0.52/0.50 % (2968426)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.52/0.50 % (2968426)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1756426715:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.52/0.50 % (2968430)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.52/0.50 % (2968430)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=248378652:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.22/0.55 % (2968429)lrs+10_1_si=on:cs=on:random_seed=2627174266:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.22/0.55 % (2968430)Instruction limit reached!
% 1.22/0.55 % (2968430)------------------------------
% 1.22/0.55 % (2968430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.55 % (2968430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.55 % (2968430)CaDiCaL version: 2.1.3
% 1.22/0.55 % (2968430)Termination reason: Instruction limit
% 1.22/0.55 % (2968430)Termination phase: shuffling
% 1.22/0.55 % (2968430)Time elapsed: 0.003 s
% 1.22/0.55 % (2968430)Peak memory usage: 10 MB
% 1.22/0.55 % (2968430)Instructions burned: 7 (million)
% 1.22/0.55 % (2968429)Instruction limit reached!
% 1.22/0.55 % (2968429)------------------------------
% 1.22/0.55 % (2968429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.55 % (2968429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.55 % (2968429)CaDiCaL version: 2.1.3
% 1.22/0.55 % (2968429)Termination reason: Instruction limit
% 1.22/0.55 % (2968429)Termination phase: shuffling
% 1.22/0.55 % (2968429)Time elapsed: 0.004 s
% 1.22/0.55 % (2968429)Peak memory usage: 10 MB
% 1.22/0.55 % (2968429)Instructions burned: 9 (million)
% 1.22/0.55 % (2968426)Instruction limit reached!
% 1.22/0.55 % (2968426)------------------------------
% 1.22/0.55 % (2968426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.55 % (2968426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.55 % (2968426)CaDiCaL version: 2.1.3
% 1.22/0.55 % (2968426)Termination reason: Instruction limit
% 1.22/0.55 % (2968426)Termination phase: Property scanning
% 1.22/0.55 % (2968426)Time elapsed: 0.013 s
% 1.22/0.55 % (2968426)Peak memory usage: 10 MB
% 1.22/0.55 % (2968426)Instructions burned: 30 (million)
% 1.22/0.55 % (2968428)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=973407961:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.22/0.55 % (2968431)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2704701619:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 1.22/0.55 % (2968435)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1169189998:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 1.22/0.55 % (2968436)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3602677096:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 1.22/0.55 % (2968437)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4592395:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.22/0.55 % (2968411)Instruction limit reached!
% 1.22/0.55 % (2968411)------------------------------
% 1.22/0.55 % (2968411)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.55 % (2968411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.55 % (2968411)CaDiCaL version: 2.1.3
% 1.22/0.55 % (2968411)Termination reason: Instruction limit
% 1.22/0.55 % (2968411)Termination phase: Saturation
% 1.22/0.55 % (2968411)Time elapsed: 0.089 s
% 1.22/0.55 % (2968411)Peak memory usage: 13 MB
% 1.22/0.55 % (2968411)Instructions burned: 159 (million)
% 1.22/0.55 % (2968437)Instruction limit reached!
% 1.22/0.55 % (2968437)------------------------------
% 1.22/0.55 % (2968437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.55 % (2968437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.55 % (2968437)CaDiCaL version: 2.1.3
% 1.22/0.55 % (2968437)Termination reason: Instruction limit
% 1.22/0.55 % (2968437)Termination phase: shuffling
% 1.22/0.55 % (2968437)Time elapsed: 0.007 s
% 1.22/0.55 % (2968437)Peak memory usage: 10 MB
% 1.22/0.55 % (2968437)Instructions burned: 15 (million)
% 1.22/0.55 % (2968436)Instruction limit reached!
% 1.22/0.55 % (2968436)------------------------------
% 1.22/0.55 % (2968436)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.22/0.55 % (2968436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.22/0.55 % (2968436)CaDiCaL version: 2.1.3
% 1.22/0.55 % (2968436)Termination reason: Instruction limit
% 1.22/0.55 % (2968436)Termination phase: SInE selection
% 1.73/0.61 % (2968436)Time elapsed: 0.011 s
% 1.73/0.61 % (2968436)Peak memory usage: 10 MB
% 1.73/0.61 % (2968436)Instructions burned: 25 (million)
% 1.73/0.61 % (2968443)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3364394350:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.73/0.61 % (2968435)Refutation not found, incomplete strategy
% 1.73/0.61 % (2968435)------------------------------
% 1.73/0.61 % (2968435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.61 % (2968435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.61 % (2968435)CaDiCaL version: 2.1.3
% 1.73/0.61 % (2968435)Termination reason: Refutation not found, incomplete strategy
% 1.73/0.61 % (2968435)Time elapsed: 0.026 s
% 1.73/0.61 % (2968435)Peak memory usage: 12 MB
% 1.73/0.61 % (2968435)Instructions burned: 50 (million)
% 1.73/0.61 % (2968431)Instruction limit reached!
% 1.73/0.61 % (2968431)------------------------------
% 1.73/0.61 % (2968431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.61 % (2968431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.61 % (2968431)CaDiCaL version: 2.1.3
% 1.73/0.61 % (2968431)Termination reason: Instruction limit
% 1.73/0.61 % (2968431)Termination phase: Saturation
% 1.73/0.61 % (2968431)Time elapsed: 0.034 s
% 1.73/0.61 % (2968431)Peak memory usage: 13 MB
% 1.73/0.61 % (2968431)Instructions burned: 38 (million)
% 1.73/0.61 % (2968435)------------------------------
% 1.73/0.61 % (2968435)------------------------------
% 1.73/0.61 % (2968444)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=175349206:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.73/0.61 % (2968444)Instruction limit reached!
% 1.73/0.61 % (2968444)------------------------------
% 1.73/0.61 % (2968444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.61 % (2968444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.61 % (2968444)CaDiCaL version: 2.1.3
% 1.73/0.61 % (2968444)Termination reason: Instruction limit
% 1.73/0.61 % (2968444)Termination phase: shuffling
% 1.73/0.61 % (2968444)Time elapsed: 0.007 s
% 1.73/0.61 % (2968444)Peak memory usage: 10 MB
% 1.73/0.61 % (2968444)Instructions burned: 16 (million)
% 1.73/0.61 % (2968445)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2225168173: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)
% 1.73/0.61 % (2968445)Instruction limit reached!
% 1.73/0.61 % (2968445)------------------------------
% 1.73/0.61 % (2968445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.61 % (2968445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.61 % (2968445)CaDiCaL version: 2.1.3
% 1.73/0.61 % (2968445)Termination reason: Instruction limit
% 1.73/0.61 % (2968445)Termination phase: shuffling
% 1.73/0.61 % (2968445)Time elapsed: 0.001 s
% 1.73/0.61 % (2968445)Peak memory usage: 10 MB
% 1.73/0.61 % (2968445)Instructions burned: 2 (million)
% 1.73/0.61 % (2968447)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2547273038:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.73/0.61 % (2968428)Instruction limit reached!
% 1.73/0.61 % (2968428)------------------------------
% 1.73/0.61 % (2968428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.61 % (2968428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.61 % (2968428)CaDiCaL version: 2.1.3
% 1.73/0.61 % (2968428)Termination reason: Instruction limit
% 1.73/0.61 % (2968428)Termination phase: Saturation
% 1.73/0.61 % (2968428)Time elapsed: 0.071 s
% 1.73/0.61 % (2968428)Peak memory usage: 12 MB
% 1.73/0.61 % (2968428)Instructions burned: 87 (million)
% 1.73/0.61 % (2968448)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1255043433:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.73/0.61 % (2968447)Instruction limit reached!
% 1.73/0.61 % (2968447)------------------------------
% 1.73/0.61 % (2968447)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.61 % (2968447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.61 % (2968447)CaDiCaL version: 2.1.3
% 1.73/0.61 % (2968447)Termination reason: Instruction limit
% 1.73/0.61 % (2968447)Termination phase: Property scanning
% 1.73/0.61 % (2968447)Time elapsed: 0.012 s
% 1.73/0.61 % (2968447)Peak memory usage: 10 MB
% 1.73/0.61 % (2968447)Instructions burned: 29 (million)
% 1.73/0.61 % (2968450)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=193852354:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.73/0.61 % (2968452)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
% 1.73/0.61 % (2968452)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.73/0.61 % (2968452)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=3546871789:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.73/0.61 % (2968454)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.73/0.61 % (2968454)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=3385586746:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2997 on theBenchmark for (2997ds/8Mi)
% 1.73/0.61 % (2968448)Instruction limit reached!
% 1.73/0.61 % (2968448)------------------------------
% 1.73/0.61 % (2968448)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.61 % (2968448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.61 % (2968448)CaDiCaL version: 2.1.3
% 1.73/0.61 % (2968448)Termination reason: Instruction limit
% 1.73/0.61 % (2968448)Termination phase: Property scanning
% 1.73/0.61 % (2968448)Time elapsed: 0.020 s
% 1.73/0.61 % (2968448)Peak memory usage: 10 MB
% 1.73/0.61 % (2968448)Instructions burned: 23 (million)
% 1.73/0.61 % (2968454)Instruction limit reached!
% 1.73/0.61 % (2968454)------------------------------
% 1.73/0.61 % (2968454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.61 % (2968454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.61 % (2968454)CaDiCaL version: 2.1.3
% 1.73/0.61 % (2968454)Termination reason: Instruction limit
% 1.73/0.61 % (2968454)Termination phase: shuffling
% 1.73/0.61 % (2968454)Time elapsed: 0.004 s
% 1.73/0.61 % (2968454)Peak memory usage: 10 MB
% 1.73/0.61 % (2968454)Instructions burned: 9 (million)
% 1.73/0.61 % (2968452)Instruction limit reached!
% 1.73/0.61 % (2968452)------------------------------
% 1.73/0.61 % (2968452)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.61 % (2968452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.61 % (2968452)CaDiCaL version: 2.1.3
% 1.73/0.61 % (2968452)Termination reason: Instruction limit
% 1.73/0.61 % (2968452)Termination phase: shuffling
% 1.73/0.61 % (2968452)Time elapsed: 0.013 s
% 1.73/0.61 % (2968452)Peak memory usage: 10 MB
% 1.73/0.61 % (2968452)Instructions burned: 15 (million)
% 1.73/0.61 % (2968450)Instruction limit reached!
% 1.73/0.61 % (2968450)------------------------------
% 1.73/0.61 % (2968450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.61 % (2968450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.61 % (2968450)CaDiCaL version: 2.1.3
% 1.73/0.61 % (2968450)Termination reason: Instruction limit
% 1.73/0.61 % (2968450)Termination phase: Property scanning
% 1.73/0.61 % (2968450)Time elapsed: 0.028 s
% 1.73/0.61 % (2968450)Peak memory usage: 12 MB
% 1.73/0.61 % (2968450)Instructions burned: 62 (million)
% 1.73/0.61 % (2968461)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3257451495:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 1.73/0.61 % (2968457)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=914809165:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 1.73/0.61 % (2968462)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3058531328:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 1.73/0.61 % (2968460)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2359535904:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 1.73/0.61 % (2968460)Instruction limit reached!
% 1.73/0.61 % (2968460)------------------------------
% 1.73/0.61 % (2968460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.61 % (2968460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.61 % (2968460)CaDiCaL version: 2.1.3
% 1.73/0.61 % (2968460)Termination reason: Instruction limit
% 1.73/0.61 % (2968460)Termination phase: shuffling
% 1.73/0.61 % (2968460)Time elapsed: 0.003 s
% 1.73/0.61 % (2968460)Peak memory usage: 10 MB
% 1.73/0.61 % (2968460)Instructions burned: 7 (million)
% 1.73/0.61 % (2968461)Instruction limit reached!
% 1.73/0.61 % (2968461)------------------------------
% 1.73/0.61 % (2968461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.61 % (2968461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.61 % (2968461)CaDiCaL version: 2.1.3
% 1.73/0.61 % (2968461)Termination reason: Instruction limit
% 1.73/0.61 % (2968461)Termination phase: Property scanning
% 1.73/0.61 % (2968461)Time elapsed: 0.011 s
% 1.73/0.61 % (2968461)Peak memory usage: 10 MB
% 1.73/0.61 % (2968461)Instructions burned: 25 (million)
% 1.73/0.61 % (2968462)Instruction limit reached!
% 1.73/0.61 % (2968462)------------------------------
% 1.73/0.61 % (2968462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.61 % (2968462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.61 % (2968462)CaDiCaL version: 2.1.3
% 1.73/0.61 % (2968462)Termination reason: Instruction limit
% 1.73/0.61 % (2968462)Termination phase: Property scanning
% 1.73/0.61 % (2968462)Time elapsed: 0.009 s
% 1.73/0.61 % (2968462)Peak memory usage: 10 MB
% 1.73/0.61 % (2968462)Instructions burned: 21 (million)
% 1.73/0.61 % (2968463)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=4244776032:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 1.73/0.61 % (2968457)Instruction limit reached!
% 1.73/0.61 % (2968457)------------------------------
% 1.73/0.61 % (2968457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.61 % (2968457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.61 % (2968457)CaDiCaL version: 2.1.3
% 1.73/0.61 % (2968457)Termination reason: Instruction limit
% 1.73/0.61 % (2968457)Termination phase: Property scanning
% 1.73/0.61 % (2968457)Time elapsed: 0.024 s
% 1.73/0.61 % (2968457)Peak memory usage: 10 MB
% 1.73/0.61 % (2968457)Instructions burned: 33 (million)
% 1.73/0.61 % (2968469)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2590628501:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.73/0.61 % (2968468)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=859601253:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.73/0.61 % (2968470)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3945024626:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.73/0.61 % (2968443) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2968400-2968443"...
% 1.73/0.61 % (2968443)...printing done.
% 1.73/0.61 % (2968443)Refutation found. Thanks to Tanya!
% 1.73/0.61 % SZS status Theorem for theBenchmark
% 1.73/0.61 % SZS output start Proof for theBenchmark
% See solution above
% 1.73/0.62 % (2968443)------------------------------
% 1.73/0.62 % (2968443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.73/0.62 % (2968443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.73/0.62 % (2968443)CaDiCaL version: 2.1.3
% 1.73/0.62 % (2968443)Termination reason: Refutation
% 1.73/0.62 % (2968443)Time elapsed: 0.148 s
% 1.73/0.62 % (2968443)Peak memory usage: 16 MB
% 1.73/0.62 % (2968443)Instructions burned: 309 (million)
% 1.73/0.62 % (2968400)Success in time 0.328 s
% 1.73/0.62 % Vampire exiting
%------------------------------------------------------------------------------