%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG249^3 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 07:45:24 AM UTC 2026
% Result : Theorem 33.35s 5.08s
% Output : Refutation 33.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 6
% Syntax : Number of formulae : 92 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 604 ( 183 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 970 ( 5 ~; 62 |; 0 &; 714 @)
% ( 2 <=>; 95 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 571 ( 567 usr; 215 con; 0-4 aty)
% ( 92 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 200 ( 132 ^; 68 !; 0 ?; 200 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_125,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_126,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_127,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_128,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_129,type,
vIMP: $o > $o > $o ).
thf(func_def_130,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_131,type,
vNOT: $o > $o ).
thf(func_def_132,type,
vIFF: $o > $o > $o ).
thf(func_def_133,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_134,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_135,type,
vAND: $o > $o > $o ).
thf(func_def_138,type,
sK0: ( subst > term > subst > $o ) > term ).
thf(func_def_139,type,
sK1: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_140,type,
sK2: ( subst > term > subst > $o ) > term ).
thf(func_def_141,type,
sK3: subst > term > subst > $o ).
thf(func_def_142,type,
sK4: ( subst > term > term ) > subst ).
thf(func_def_143,type,
sK5: ( subst > term > term ) > term ).
thf(func_def_144,type,
sK6: ( subst > term > term ) > term ).
thf(func_def_145,type,
sK7: ( subst > term > term ) > subst ).
thf(func_def_146,type,
sK8: ( subst > term > term ) > subst ).
thf(func_def_147,type,
sK9: term ).
thf(func_def_148,type,
sK10: ( subst > term > subst > $o ) > subst ).
thf(func_def_149,type,
sK11: ( subst > term > subst > $o ) > subst ).
thf(func_def_150,type,
sK12: ( subst > term > subst > $o ) > term ).
thf(func_def_151,type,
sK13: ( subst > term > subst > $o ) > term ).
thf(func_def_152,type,
sK14: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_153,type,
sK15: ( subst > term > subst > $o ) > subst ).
thf(func_def_154,type,
sK16: ( subst > term > subst > $o ) > subst ).
thf(func_def_155,type,
sK17: ( subst > term > subst > $o ) > term ).
thf(func_def_156,type,
sK18: ( subst > term > subst > $o ) > term ).
thf(func_def_157,type,
sK19: ( subst > term > subst > $o ) > term ).
thf(func_def_158,type,
sK20: ( subst > term > subst > $o ) > subst ).
thf(func_def_159,type,
sK21: ( subst > term > subst > $o ) > subst ).
thf(func_def_160,type,
sK22: ( subst > term > subst > $o ) > subst ).
thf(func_def_161,type,
sK23: ( subst > term > subst > $o ) > subst ).
thf(func_def_162,type,
sK24: ( subst > term > subst > $o ) > subst ).
thf(func_def_163,type,
sK25: ( subst > term > subst > $o ) > subst ).
thf(func_def_164,type,
sK26: ( subst > term > subst > $o ) > term ).
thf(func_def_165,type,
sK27: ( subst > term > subst > $o ) > term ).
thf(func_def_166,type,
sK28: ( subst > term > subst > $o ) > subst ).
thf(func_def_167,type,
sK29: ( subst > term > subst > $o ) > subst ).
thf(func_def_168,type,
sK30: ( subst > term > subst > $o ) > subst ).
thf(func_def_169,type,
sK31: ( subst > term > subst > $o ) > subst ).
thf(func_def_170,type,
sK32: ( subst > term > subst > $o ) > subst ).
thf(func_def_171,type,
sK33: ( subst > term > subst > $o ) > subst ).
thf(func_def_172,type,
sK34: ( subst > term > subst > $o ) > term ).
thf(func_def_173,type,
sK35: ( subst > term > subst > $o ) > term ).
thf(func_def_174,type,
sK36: ( subst > term > subst > $o ) > subst ).
thf(func_def_175,type,
sK37: ( subst > term > subst > $o ) > subst ).
thf(func_def_176,type,
sK38: ( subst > term > subst > $o ) > subst ).
thf(func_def_177,type,
sK39: ( subst > term > subst > $o ) > subst ).
thf(func_def_178,type,
sK40: ( subst > term > subst > $o ) > subst ).
thf(func_def_179,type,
sK41: ( subst > term > subst > $o ) > subst ).
thf(func_def_180,type,
sK42: ( subst > term > subst > $o ) > term ).
thf(func_def_181,type,
sK43: ( subst > term > subst > $o ) > term ).
thf(func_def_182,type,
sK44: ( subst > term > subst > $o ) > term ).
thf(func_def_183,type,
sK45: ( subst > term > subst > $o ) > subst ).
thf(func_def_184,type,
sK46: ( subst > term > subst > $o ) > subst ).
thf(func_def_185,type,
sK47: ( subst > term > subst > $o ) > subst ).
thf(func_def_186,type,
sK48: ( subst > term > subst > $o ) > subst ).
thf(func_def_187,type,
sK49: ( subst > term > subst > $o ) > subst ).
thf(func_def_188,type,
sK50: ( subst > term > subst > $o ) > subst ).
thf(func_def_189,type,
sK51: ( subst > term > subst > $o ) > term ).
thf(func_def_190,type,
sK52: ( subst > term > subst > $o ) > term ).
thf(func_def_191,type,
sK53: ( subst > term > subst > $o ) > subst ).
thf(func_def_192,type,
sK54: ( subst > term > subst > $o ) > subst ).
thf(func_def_193,type,
sK55: ( subst > term > subst > $o ) > subst ).
thf(func_def_194,type,
sK56: ( subst > term > subst > $o ) > subst ).
thf(func_def_195,type,
sK57: ( subst > term > subst > $o ) > subst ).
thf(func_def_196,type,
sK58: ( subst > term > subst > $o ) > subst ).
thf(func_def_197,type,
sK59: ( subst > term > subst > $o ) > term ).
thf(func_def_198,type,
sK60: ( subst > term > subst > $o ) > term ).
thf(func_def_199,type,
sK61: ( subst > term > subst > $o ) > subst ).
thf(func_def_200,type,
sK62: ( subst > term > subst > $o ) > subst ).
thf(func_def_201,type,
sK63: ( subst > term > subst > $o ) > subst ).
thf(func_def_202,type,
sK64: ( subst > term > subst > $o ) > subst ).
thf(func_def_203,type,
sK65: ( subst > term > subst > $o ) > subst ).
thf(func_def_204,type,
sK66: ( subst > term > subst > $o ) > subst ).
thf(func_def_205,type,
sK67: subst > term > subst > $o ).
thf(func_def_206,type,
sK68: ( subst > term > term ) > subst ).
thf(func_def_207,type,
sK69: ( subst > term > term ) > term ).
thf(func_def_208,type,
sK70: ( subst > term > term ) > term ).
thf(func_def_209,type,
sK71: ( subst > term > term ) > subst ).
thf(func_def_210,type,
sK72: ( subst > term > term ) > subst ).
thf(func_def_211,type,
sK73: term ).
thf(func_def_212,type,
sK74: term > subst > term > term ).
thf(func_def_213,type,
sK75: term ).
thf(func_def_214,type,
sK76: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_215,type,
sK77: ( subst > term > subst > $o ) > term > term ).
thf(func_def_216,type,
sK78: ( subst > term > subst > $o ) > term > term ).
thf(func_def_217,type,
sK79: ( subst > term > subst > $o ) > term > term ).
thf(func_def_218,type,
sK80: subst > term > subst > $o ).
thf(func_def_219,type,
sK81: ( subst > term > term ) > subst ).
thf(func_def_220,type,
sK82: ( subst > term > term ) > term ).
thf(func_def_221,type,
sK83: ( subst > term > term ) > term ).
thf(func_def_222,type,
sK84: ( subst > term > term ) > subst ).
thf(func_def_223,type,
sK85: ( subst > term > term ) > subst ).
thf(func_def_224,type,
sK86: term ).
thf(func_def_225,type,
sK87: ( subst > term > subst > $o ) > subst ).
thf(func_def_226,type,
sK88: ( subst > term > subst > $o ) > subst ).
thf(func_def_227,type,
sK89: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_228,type,
sK90: ( subst > term > subst > $o ) > subst ).
thf(func_def_229,type,
sK91: ( subst > term > subst > $o ) > subst ).
thf(func_def_230,type,
sK92: ( subst > term > subst > $o ) > term > term ).
thf(func_def_231,type,
sK93: ( subst > term > subst > $o ) > term ).
thf(func_def_232,type,
sK94: ( subst > term > subst > $o ) > term ).
thf(func_def_233,type,
sK95: ( subst > term > subst > $o ) > subst ).
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 > term ).
thf(func_def_238,type,
sK100: ( subst > term > subst > $o ) > term ).
thf(func_def_239,type,
sK101: ( subst > term > subst > $o ) > term ).
thf(func_def_240,type,
sK102: ( subst > term > subst > $o ) > subst ).
thf(func_def_241,type,
sK103: ( subst > term > subst > $o ) > subst ).
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 > term ).
thf(func_def_245,type,
sK107: ( subst > term > subst > $o ) > term ).
thf(func_def_246,type,
sK108: ( subst > term > subst > $o ) > term ).
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 ) > subst ).
thf(func_def_250,type,
sK112: ( subst > term > subst > $o ) > subst ).
thf(func_def_251,type,
sK113: subst > term > subst > $o ).
thf(func_def_252,type,
sK114: ( subst > term > term ) > subst ).
thf(func_def_253,type,
sK115: ( subst > term > term ) > term ).
thf(func_def_254,type,
sK116: ( subst > term > term ) > term ).
thf(func_def_255,type,
sK117: ( subst > term > term ) > subst ).
thf(func_def_256,type,
sK118: ( subst > term > term ) > subst ).
thf(func_def_257,type,
sK119: term ).
thf(func_def_258,type,
sK120: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_259,type,
sK121: ( subst > term > subst > $o ) > term ).
thf(func_def_260,type,
sK122: ( subst > term > subst > $o ) > term > term ).
thf(func_def_261,type,
sK123: ( subst > term > subst > $o ) > term > term ).
thf(func_def_262,type,
sK124: ( subst > term > subst > $o ) > term > term ).
thf(func_def_263,type,
sK125: subst > term > subst > $o ).
thf(func_def_264,type,
sK126: ( subst > term > term ) > term ).
thf(func_def_265,type,
sK127: ( subst > term > term ) > term > subst ).
thf(func_def_266,type,
sK128: ( subst > term > term ) > term > term ).
thf(func_def_267,type,
sK129: ( subst > term > term ) > term > subst ).
thf(func_def_268,type,
sK130: ( subst > term > term ) > term > term ).
thf(func_def_269,type,
sK131: ( subst > term > term ) > term > subst ).
thf(func_def_270,type,
sK132: term ).
thf(func_def_271,type,
sK133: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_272,type,
sK134: ( subst > term > subst > $o ) > term > term ).
thf(func_def_273,type,
sK135: ( subst > term > subst > $o ) > term > term ).
thf(func_def_274,type,
sK136: ( subst > term > subst > $o ) > term > term ).
thf(func_def_275,type,
sK137: subst > term > subst > $o ).
thf(func_def_276,type,
sK138: ( subst > term > term ) > subst ).
thf(func_def_277,type,
sK139: ( subst > term > term ) > term ).
thf(func_def_278,type,
sK140: ( subst > term > term ) > term ).
thf(func_def_279,type,
sK141: ( subst > term > term ) > subst ).
thf(func_def_280,type,
sK142: ( subst > term > term ) > subst ).
thf(func_def_281,type,
sK143: term ).
thf(func_def_282,type,
sK144: ( subst > term > subst > $o ) > subst ).
thf(func_def_283,type,
sK145: ( subst > term > subst > $o ) > subst ).
thf(func_def_284,type,
sK146: ( subst > term > subst > $o ) > term ).
thf(func_def_285,type,
sK147: ( subst > term > subst > $o ) > subst ).
thf(func_def_286,type,
sK148: ( subst > term > subst > $o ) > subst ).
thf(func_def_287,type,
sK149: ( subst > term > subst > $o ) > term ).
thf(func_def_288,type,
sK150: ( subst > term > subst > $o ) > term ).
thf(func_def_289,type,
sK151: ( subst > term > subst > $o ) > term ).
thf(func_def_290,type,
sK152: ( subst > term > subst > $o ) > subst ).
thf(func_def_291,type,
sK153: ( subst > term > subst > $o ) > subst ).
thf(func_def_292,type,
sK154: ( subst > term > subst > $o ) > subst ).
thf(func_def_293,type,
sK155: ( subst > term > subst > $o ) > subst ).
thf(func_def_294,type,
sK156: ( subst > term > subst > $o ) > subst ).
thf(func_def_295,type,
sK157: ( subst > term > subst > $o ) > subst ).
thf(func_def_296,type,
sK158: subst > term > subst > $o ).
thf(func_def_297,type,
sK159: term ).
thf(func_def_298,type,
sK160: term ).
thf(func_def_299,type,
sK161: ( subst > term > subst > $o ) > subst ).
thf(func_def_300,type,
sK162: ( subst > term > subst > $o ) > subst ).
thf(func_def_301,type,
sK163: ( subst > term > subst > $o ) > term ).
thf(func_def_302,type,
sK164: ( subst > term > subst > $o ) > subst ).
thf(func_def_303,type,
sK165: ( subst > term > subst > $o ) > subst ).
thf(func_def_304,type,
sK166: ( subst > term > subst > $o ) > term ).
thf(func_def_305,type,
sK167: ( subst > term > subst > $o ) > term ).
thf(func_def_306,type,
sK168: ( subst > term > subst > $o ) > subst ).
thf(func_def_307,type,
sK169: ( subst > term > subst > $o ) > subst ).
thf(func_def_308,type,
sK170: ( subst > term > subst > $o ) > term ).
thf(func_def_309,type,
sK171: ( subst > term > subst > $o ) > term ).
thf(func_def_310,type,
sK172: ( subst > term > subst > $o ) > subst ).
thf(func_def_311,type,
sK173: ( subst > term > subst > $o ) > subst ).
thf(func_def_312,type,
sK174: subst > term > subst > $o ).
thf(func_def_313,type,
sK175: term ).
thf(func_def_314,type,
sK176: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_315,type,
sK177: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_316,type,
sK178: term > ( term > $o ) > term ).
thf(func_def_317,type,
sK179: term > ( term > $o ) > term ).
thf(func_def_318,type,
sK180: term > ( term > $o ) > term ).
thf(func_def_319,type,
sK181: term > $o ).
thf(func_def_320,type,
sK182: subst > term > subst > $o ).
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 ) > subst ).
thf(func_def_326,type,
sK188: term ).
thf(func_def_327,type,
sK189: ( subst > term > subst > $o ) > subst ).
thf(func_def_328,type,
sK190: ( subst > term > subst > $o ) > subst ).
thf(func_def_329,type,
sK191: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_330,type,
sK192: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_331,type,
sK193: ( subst > term > subst > $o ) > subst ).
thf(func_def_332,type,
sK194: ( subst > term > subst > $o ) > subst ).
thf(func_def_333,type,
sK195: term > ( term > $o ) > term ).
thf(func_def_334,type,
sK196: ( subst > term > subst > $o ) > term ).
thf(func_def_335,type,
sK197: ( subst > term > subst > $o ) > term ).
thf(func_def_336,type,
sK198: ( subst > term > subst > $o ) > subst ).
thf(func_def_337,type,
sK199: ( subst > term > subst > $o ) > subst ).
thf(func_def_338,type,
sK200: ( subst > term > subst > $o ) > subst ).
thf(func_def_339,type,
sK201: ( subst > term > subst > $o ) > subst ).
thf(func_def_340,type,
sK202: term > ( term > $o ) > term ).
thf(func_def_341,type,
sK203: ( subst > term > subst > $o ) > term ).
thf(func_def_342,type,
sK204: ( subst > term > subst > $o ) > term ).
thf(func_def_343,type,
sK205: ( subst > term > subst > $o ) > subst ).
thf(func_def_344,type,
sK206: ( subst > term > subst > $o ) > subst ).
thf(func_def_345,type,
sK207: ( subst > term > subst > $o ) > subst ).
thf(func_def_346,type,
sK208: ( subst > term > subst > $o ) > subst ).
thf(func_def_347,type,
sK209: term > ( term > $o ) > term ).
thf(func_def_348,type,
sK210: ( subst > term > subst > $o ) > term ).
thf(func_def_349,type,
sK211: ( subst > term > subst > $o ) > term ).
thf(func_def_350,type,
sK212: ( subst > term > subst > $o ) > subst ).
thf(func_def_351,type,
sK213: ( subst > term > subst > $o ) > subst ).
thf(func_def_352,type,
sK214: ( subst > term > subst > $o ) > subst ).
thf(func_def_353,type,
sK215: ( subst > term > subst > $o ) > subst ).
thf(func_def_354,type,
sK216: term > $o ).
thf(func_def_355,type,
sK217: subst > term > subst > $o ).
thf(func_def_356,type,
sK218: ( subst > term > term ) > subst ).
thf(func_def_357,type,
sK219: ( subst > term > term ) > term ).
thf(func_def_358,type,
sK220: ( subst > term > term ) > term ).
thf(func_def_359,type,
sK221: ( subst > term > term ) > subst ).
thf(func_def_360,type,
sK222: ( subst > term > term ) > subst ).
thf(func_def_361,type,
sK223: term ).
thf(func_def_362,type,
sK224: term > subst > term > term ).
thf(func_def_363,type,
sK225: term ).
thf(func_def_364,type,
sK226: ( subst > term > term ) > subst ).
thf(func_def_365,type,
sK227: ( subst > term > term ) > term ).
thf(func_def_366,type,
sK228: ( subst > term > subst > $o ) > subst ).
thf(func_def_367,type,
sK229: ( subst > term > subst > $o ) > subst ).
thf(func_def_368,type,
sK230: ( subst > term > subst > $o ) > term ).
thf(func_def_369,type,
sK231: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_370,type,
sK232: ( subst > term > subst > $o ) > subst ).
thf(func_def_371,type,
sK233: ( subst > term > subst > $o ) > subst ).
thf(func_def_372,type,
sK234: ( subst > term > subst > $o ) > term ).
thf(func_def_373,type,
sK235: ( subst > term > subst > $o ) > term ).
thf(func_def_374,type,
sK236: ( subst > term > subst > $o ) > term ).
thf(func_def_375,type,
sK237: ( subst > term > subst > $o ) > subst ).
thf(func_def_376,type,
sK238: ( subst > term > subst > $o ) > subst ).
thf(func_def_377,type,
sK239: ( subst > term > subst > $o ) > subst ).
thf(func_def_378,type,
sK240: ( subst > term > subst > $o ) > subst ).
thf(func_def_379,type,
sK241: ( subst > term > subst > $o ) > subst ).
thf(func_def_380,type,
sK242: ( subst > term > subst > $o ) > subst ).
thf(func_def_381,type,
sK243: term > $o ).
thf(func_def_382,type,
sK244: subst > term > subst > $o ).
thf(func_def_383,type,
sK245: term ).
thf(func_def_384,type,
sK246: term ).
thf(func_def_385,type,
sK247: ( subst > term > subst > $o ) > subst ).
thf(func_def_386,type,
sK248: ( subst > term > subst > $o ) > subst ).
thf(func_def_387,type,
sK249: ( subst > term > subst > $o ) > term ).
thf(func_def_388,type,
sK250: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_389,type,
sK251: ( subst > term > subst > $o ) > subst ).
thf(func_def_390,type,
sK252: ( subst > term > subst > $o ) > subst ).
thf(func_def_391,type,
sK253: ( subst > term > subst > $o ) > term ).
thf(func_def_392,type,
sK254: ( subst > term > subst > $o ) > term ).
thf(func_def_393,type,
sK255: ( subst > term > subst > $o ) > subst ).
thf(func_def_394,type,
sK256: ( subst > term > subst > $o ) > subst ).
thf(func_def_395,type,
sK257: ( subst > term > subst > $o ) > term ).
thf(func_def_396,type,
sK258: ( subst > term > subst > $o ) > term ).
thf(func_def_397,type,
sK259: ( subst > term > subst > $o ) > subst ).
thf(func_def_398,type,
sK260: ( subst > term > subst > $o ) > subst ).
thf(func_def_399,type,
sK261: term > $o ).
thf(func_def_400,type,
sK262: subst > term > subst > $o ).
thf(func_def_401,type,
sK263: term ).
thf(func_def_402,type,
sK264: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_403,type,
sK265: subst > term > subst > $o ).
thf(func_def_404,type,
sK266: ( term > $o ) > term ).
thf(func_def_405,type,
sK267: term ).
thf(func_def_406,type,
sK268: term ).
thf(func_def_407,type,
sK269: ( subst > term > term ) > subst ).
thf(func_def_408,type,
sK270: ( subst > term > term ) > term ).
thf(func_def_409,type,
sK271: ( subst > term > term ) > subst ).
thf(func_def_410,type,
sK272: subst > term > term ).
thf(func_def_411,type,
sK273: ( subst > term > term ) > subst ).
thf(func_def_412,type,
sK274: ( subst > term > term ) > term ).
thf(func_def_413,type,
sK275: ( subst > term > term ) > subst ).
thf(func_def_414,type,
sK276: subst > term > term ).
thf(func_def_415,type,
sK277: term ).
thf(func_def_416,type,
sK278: term ).
thf(func_def_417,type,
sK279: ( subst > term > term ) > subst ).
thf(func_def_418,type,
sK280: ( subst > term > term ) > term ).
thf(func_def_419,type,
sK281: ( subst > term > term ) > subst ).
thf(func_def_420,type,
sK282: ( subst > term > term ) > subst ).
thf(func_def_421,type,
sK283: ( subst > term > term ) > term ).
thf(func_def_422,type,
sK284: ( subst > term > term ) > subst ).
thf(func_def_423,type,
sK285: subst > term > term ).
thf(func_def_424,type,
sK286: subst > term > term ).
thf(func_def_425,type,
sK287: term ).
thf(func_def_426,type,
sK288: subst ).
thf(func_def_427,type,
sK289: term ).
thf(func_def_428,type,
sK290: term ).
thf(func_def_429,type,
sK291: term ).
thf(func_def_430,type,
sK292: term ).
thf(func_def_431,type,
sK293: term ).
thf(func_def_432,type,
sK294: term ).
thf(func_def_433,type,
sK295: term ).
thf(func_def_434,type,
sK296: term ).
thf(func_def_435,type,
sK297: term ).
thf(func_def_436,type,
sK298: subst ).
thf(func_def_437,type,
sK299: subst ).
thf(func_def_438,type,
sK300: term ).
thf(func_def_439,type,
sK301: subst ).
thf(func_def_440,type,
sK302: subst ).
thf(func_def_441,type,
sK303: subst ).
thf(func_def_442,type,
sK304: subst ).
thf(func_def_443,type,
sK305: subst ).
thf(func_def_444,type,
sK306: ( term > $o ) > term ).
thf(func_def_445,type,
sK307: ( term > $o ) > term ).
thf(func_def_446,type,
sK308: ( term > $o ) > term ).
thf(func_def_447,type,
sK309: ( term > $o ) > term ).
thf(func_def_448,type,
sK310: ( term > $o ) > term ).
thf(func_def_449,type,
sK311: term > $o ).
thf(func_def_450,type,
sK312: term > term ).
thf(func_def_451,type,
sK313: term ).
thf(func_def_452,type,
sK314: ( term > $o ) > term ).
thf(func_def_453,type,
sK315: ( term > $o ) > term ).
thf(func_def_454,type,
sK316: ( term > $o ) > term ).
thf(func_def_455,type,
sK317: ( term > $o ) > subst > term ).
thf(func_def_456,type,
sK318: ( term > $o ) > subst > term ).
thf(func_def_457,type,
sK319: ( term > $o ) > subst > term ).
thf(func_def_458,type,
sK320: ( term > $o ) > subst > term ).
thf(func_def_459,type,
sK321: ( term > $o ) > subst > term ).
thf(func_def_460,type,
sK322: ( term > $o ) > subst > term ).
thf(func_def_461,type,
sK323: term > $o ).
thf(func_def_462,type,
sK324: term > term ).
thf(func_def_463,type,
sK325: subst ).
thf(func_def_464,type,
sK326: term ).
thf(func_def_465,type,
sK327: ( term > $o ) > subst > term ).
thf(func_def_466,type,
sK328: subst ).
thf(func_def_467,type,
sK329: term ).
thf(func_def_468,type,
sK330: term > $o ).
thf(func_def_469,type,
sK331: term ).
thf(func_def_470,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_471,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_472,type,
sK332: ( term > $o ) > subst > term > ( term > $o ) > term ).
thf(func_def_473,type,
sK333: ( term > $o ) > term ).
thf(func_def_474,type,
sK334: subst ).
thf(func_def_475,type,
sK335: term ).
thf(func_def_476,type,
sK336: term > $o ).
thf(func_def_477,type,
sK337: term > $o ).
thf(func_def_478,type,
sK338: term ).
thf(func_def_479,type,
sK339: ( term > $o ) > subst > term > ( term > $o ) > term ).
thf(func_def_480,type,
sK340: subst > ( term > $o ) > term ).
thf(func_def_481,type,
sK341: subst ).
thf(func_def_482,type,
sK342: term ).
thf(func_def_483,type,
sK343: term > $o ).
thf(func_def_484,type,
sK344: term > $o ).
thf(func_def_485,type,
sK345: term ).
thf(func_def_486,type,
sK346: ( term > $o ) > subst > term > ( term > $o ) > term ).
thf(func_def_487,type,
sK347: subst ).
thf(func_def_488,type,
sK348: term ).
thf(func_def_489,type,
sK349: term > $o ).
thf(func_def_490,type,
sK350: term > $o ).
thf(func_def_491,type,
sK351: term ).
thf(func_def_492,type,
sK352: subst ).
thf(func_def_493,type,
sK353: term ).
thf(func_def_494,type,
sK354: term > $o ).
thf(func_def_495,type,
sK355: term > $o ).
thf(func_def_496,type,
sK356: ( term > $o ) > subst > term > term > $o ).
thf(func_def_497,type,
sK357: subst ).
thf(func_def_498,type,
sK358: term ).
thf(func_def_499,type,
sK359: term > $o ).
thf(func_def_500,type,
sK360: ( term > $o ) > term ).
thf(func_def_501,type,
sK361: ( term > $o ) > term ).
thf(func_def_502,type,
sK362: ( term > $o ) > term ).
thf(func_def_503,type,
sK363: ( term > $o ) > term ).
thf(func_def_504,type,
sK364: ( term > $o ) > term ).
thf(func_def_505,type,
sK365: ( term > $o ) > term ).
thf(func_def_506,type,
sK366: term > $o ).
thf(func_def_507,type,
sK367: term ).
thf(func_def_508,type,
sK368: term ).
thf(func_def_509,type,
sK369: term ).
thf(func_def_510,type,
sK370: term ).
thf(func_def_511,type,
sK371: term ).
thf(func_def_512,type,
sK372: term ).
thf(func_def_513,type,
sK373: term ).
thf(func_def_514,type,
sK374: term ).
thf(func_def_515,type,
sK375: term ).
thf(func_def_516,type,
sK376: term ).
thf(func_def_517,type,
sK377: term ).
thf(func_def_518,type,
sK378: term ).
thf(func_def_519,type,
sK379: term ).
thf(func_def_520,type,
sK380: term ).
thf(func_def_521,type,
sK381: term ).
thf(func_def_522,type,
sK382: term ).
thf(func_def_523,type,
sK383: term ).
thf(func_def_524,type,
sK384: term ).
thf(func_def_525,type,
sK385: term ).
thf(func_def_526,type,
sK386: ( term > $o ) > term ).
thf(func_def_527,type,
sK387: term > $o ).
thf(func_def_528,type,
sK388: term ).
thf(func_def_529,type,
sK389: term ).
thf(func_def_530,type,
sK390: subst ).
thf(func_def_531,type,
sK391: subst ).
thf(func_def_532,type,
sK392: subst ).
thf(func_def_533,type,
sK393: subst ).
thf(func_def_534,type,
sK394: term ).
thf(func_def_535,type,
sK395: subst ).
thf(func_def_536,type,
sK396: subst ).
thf(func_def_537,type,
sK397: subst ).
thf(func_def_538,type,
sK398: subst ).
thf(func_def_539,type,
sK399: term ).
thf(func_def_540,type,
sK400: subst ).
thf(func_def_541,type,
sK401: subst ).
thf(func_def_542,type,
sK402: subst ).
thf(func_def_543,type,
sK403: term ).
thf(func_def_544,type,
sK404: subst ).
thf(func_def_545,type,
sK405: term ).
thf(func_def_546,type,
sK406: term ).
thf(func_def_547,type,
sK407: subst ).
thf(func_def_548,type,
sK408: term ).
thf(func_def_549,type,
sK409: subst ).
thf(func_def_550,type,
sK410: term ).
thf(func_def_551,type,
sK411: term ).
thf(func_def_553,type,
sK413: ( term > term > term ) > term ).
thf(func_def_554,type,
sK414: ( term > term > term ) > term ).
thf(func_def_555,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_556,type,
sK415: term > ( subst > term > subst > subst > term > subst > subst > term > subst > $o ) > subst ).
thf(func_def_557,type,
db8:
!>[X0: $tType] : X0 ).
thf(func_def_558,type,
sK416: term > ( subst > term > subst > subst > term > subst > subst > term > subst > $o ) > subst ).
thf(func_def_559,type,
sK417: ( subst > term > subst > term > $o ) > term > term ).
thf(func_def_560,type,
sK418: ( subst > term > subst > term > $o ) > term > term ).
thf(func_def_561,type,
sK419: term > ( subst > term > subst > term > term ) > term ).
thf(func_def_562,type,
sK420: term > ( subst > term > subst > term > term ) > term ).
thf(func_def_563,type,
sK421: term > ( subst > term > subst > term > term ) > term ).
thf(func_def_564,type,
sK422: ( term > term > $o ) > term ).
thf(func_def_565,type,
sK423: ( term > term > $o ) > term ).
thf(func_def_566,type,
sK424: ( term > term > term ) > term ).
thf(func_def_567,type,
sK425: term > ( subst > term > subst > subst > term > subst > subst > term > subst > $o ) > subst ).
thf(func_def_568,type,
sK426: term > ( subst > term > subst > subst > term > subst > subst > term > subst > $o ) > term ).
thf(func_def_569,type,
sK427: term > ( subst > term > subst > subst > term > subst > subst > term > subst > $o ) > term ).
thf(f5,axiom,
( axclos
= ( ! [X0: term,X1: subst,X2: subst] :
( ( sub @ ( sub @ X0 @ X1 ) @ X2 )
= ( sub @ X0 @ ( comp @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',axclos) ).
thf(f7,axiom,
( axshiftcons
= ( ! [X0: term,X1: subst] :
( ( comp @ sh @ ( push @ X0 @ X1 ) )
= X1 ) ) ),
file('/export/starexec/sandbox2/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] :
( ( X3 @ X4 )
<=> ( X2 @ ( sub @ X4 @ ( push @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',pushprop_p_and_p_prime) ).
thf(f34,axiom,
( pushprop_lem2v2
= ( ! [X0: term > $o,X1: 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 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',pushprop_lem2v2) ).
thf(f36,axiom,
( ( pushprop_lem2v2_lthm = axclos )
=> ( axshiftcons
=> pushprop_lem2v2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/ALG003^0.ax',pushprop_lem2v2_lthm) ).
thf(f114,conjecture,
pushprop_lem2v2_lthm,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ pushprop_lem2v2_lthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f120,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f122,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f143,plain,
( pushprop_p_and_p_prime
= ( ^ [X0: term,X1: subst,X2: term > $o,X3: term > $o] :
! [X4: term] :
( ( X3 @ X4 )
<=> ( X2 @ ( sub @ X4 @ ( push @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f144,plain,
( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f143]) ).
thf(f161,plain,
( pushprop_lem2v2
= ( ! [X0: term > $o,X1: 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 ) ) ) ) ) ) ) ),
inference(rectify,[],[f34]) ).
thf(f162,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 @ Y3 @ Y2 )
=> ( ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y3 @ ( sub @ Y4 @ Y0 ) ) ) )
=> ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( ( Y2 @ Y4 )
=> ( Y2 @ ( sub @ Y4 @ sh ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f161]) ).
thf(f165,plain,
( ( pushprop_lem2v2_lthm = axclos )
=> ( axshiftcons
=> pushprop_lem2v2 ) ),
inference(rectify,[],[f36]) ).
thf(f166,plain,
( pushprop_lem2v2_lthm
= ( axclos
=> ( axshiftcons
=> pushprop_lem2v2 ) ) ),
inference(fool_elimination,[],[f165]) ).
thf(f306,plain,
~ pushprop_lem2v2_lthm,
inference(rectify,[],[f115]) ).
thf(f307,plain,
pushprop_lem2v2_lthm != $true,
inference(fool_elimination,[],[f306]) ).
thf(f308,plain,
pushprop_lem2v2_lthm != $true,
inference(flattening,[],[f307]) ).
thf(f313,plain,
( axclos
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f120]) ).
thf(f315,plain,
( axshiftcons
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) ) ),
inference(cnf_transformation,[],[f122]) ).
thf(f332,plain,
( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y3 @ Y4 )
= ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f144]) ).
thf(f342,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 @ Y3 @ Y2 )
=> ( ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y3 @ ( sub @ Y4 @ Y0 ) ) ) )
=> ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( ( Y2 @ Y4 )
=> ( Y2 @ ( sub @ Y4 @ sh ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f162]) ).
thf(f344,plain,
( pushprop_lem2v2_lthm
= ( axclos
=> ( axshiftcons
=> pushprop_lem2v2 ) ) ),
inference(cnf_transformation,[],[f166]) ).
thf(f422,plain,
pushprop_lem2v2_lthm != $true,
inference(cnf_transformation,[],[f308]) ).
thf(f428,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] :
( ( Y7 @ Y8 )
= ( Y6 @ ( sub @ Y8 @ ( push @ Y4 @ Y5 ) ) ) ) )
@ Y1
@ Y0
@ Y3
@ Y2 )
=> ( ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y3 @ ( sub @ Y4 @ Y0 ) ) ) )
=> ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( ( Y2 @ Y4 )
=> ( Y2 @ ( sub @ Y4 @ sh ) ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f342,f332]) ).
thf(f4954,plain,
( ( pushprop_lem2v2_lthm = $true )
| ( ( axclos
=> ( axshiftcons
=> pushprop_lem2v2 ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f344]) ).
thf(f4958,plain,
( ( pushprop_lem2v2_lthm = $true )
| ( ( axshiftcons
=> pushprop_lem2v2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f4954]) ).
thf(f4959,plain,
( ( pushprop_lem2v2_lthm = $true )
| ( axclos = $true ) ),
inference(imp_proxy_clausification,[],[f4954]) ).
thf(f4960,plain,
( ( pushprop_lem2v2_lthm = $true )
| ( pushprop_lem2v2 = $false ) ),
inference(imp_proxy_clausification,[],[f4958]) ).
thf(f4961,plain,
( ( pushprop_lem2v2_lthm = $true )
| ( axshiftcons = $true ) ),
inference(imp_proxy_clausification,[],[f4958]) ).
thf(f5033,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( !! @ 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] :
( ( Y7 @ Y8 )
= ( Y6 @ ( sub @ Y8 @ ( push @ Y4 @ Y5 ) ) ) ) )
@ Y1
@ Y0
@ Y3
@ Y2 )
=> ( ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y3 @ ( sub @ Y4 @ Y0 ) ) ) )
=> ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( ( Y2 @ Y4 )
=> ( Y2 @ ( sub @ Y4 @ sh ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f428]) ).
thf(f5061,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( ^ [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] :
( ( Y7 @ Y8 )
= ( Y6 @ ( sub @ Y8 @ ( push @ Y4 @ Y5 ) ) ) ) )
@ Y1
@ Y0
@ Y3
@ Y2 )
=> ( ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( Y3 @ ( sub @ Y4 @ Y0 ) ) ) )
=> ( !! @ term
@ ^ [Y4: term] :
( ( var @ Y4 )
=> ( ( Y2 @ Y4 )
=> ( Y2 @ ( sub @ Y4 @ sh ) ) ) ) ) ) ) ) ) )
@ sK341 ) ) ),
inference(sigma_proxy_clausification,[],[f5033]) ).
thf(f5062,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ Y3 )
= ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ sK341 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ sK341 ) ) ) )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( ( Y1 @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ sh ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f5061]) ).
thf(f5063,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( ^ [Y0: term] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( !! @ ( term > $o )
@ ^ [Y2: term > $o] :
( ( !! @ term
@ ^ [Y3: term] :
( ( Y1 @ Y3 )
= ( Y2 @ ( sub @ Y3 @ ( push @ Y0 @ sK341 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( Y2 @ ( sub @ Y3 @ sK341 ) ) ) )
=> ( !! @ term
@ ^ [Y3: term] :
( ( var @ Y3 )
=> ( ( Y1 @ Y3 )
=> ( Y1 @ ( sub @ Y3 @ sh ) ) ) ) ) ) ) ) )
@ sK342 ) ) ),
inference(sigma_proxy_clausification,[],[f5062]) ).
thf(f5064,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
= ( Y1 @ ( sub @ Y2 @ ( push @ sK342 @ sK341 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y1 @ ( sub @ Y2 @ sK341 ) ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y2 @ sh ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f5063]) ).
thf(f5065,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( ^ [Y0: term > $o] :
( !! @ ( term > $o )
@ ^ [Y1: term > $o] :
( ( !! @ term
@ ^ [Y2: term] :
( ( Y0 @ Y2 )
= ( Y1 @ ( sub @ Y2 @ ( push @ sK342 @ sK341 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( Y1 @ ( sub @ Y2 @ sK341 ) ) ) )
=> ( !! @ term
@ ^ [Y2: term] :
( ( var @ Y2 )
=> ( ( Y0 @ Y2 )
=> ( Y0 @ ( sub @ Y2 @ sh ) ) ) ) ) ) ) )
@ sK343 ) ) ),
inference(sigma_proxy_clausification,[],[f5064]) ).
thf(f5066,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( !! @ ( term > $o )
@ ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK343 @ Y1 )
= ( Y0 @ ( sub @ Y1 @ ( push @ sK342 @ sK341 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sK341 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( sK343 @ Y1 )
=> ( sK343 @ ( sub @ Y1 @ sh ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f5065]) ).
thf(f5067,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( ^ [Y0: term > $o] :
( ( !! @ term
@ ^ [Y1: term] :
( ( sK343 @ Y1 )
= ( Y0 @ ( sub @ Y1 @ ( push @ sK342 @ sK341 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( Y0 @ ( sub @ Y1 @ sK341 ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( ( var @ Y1 )
=> ( ( sK343 @ Y1 )
=> ( sK343 @ ( sub @ Y1 @ sh ) ) ) ) ) ) )
@ sK344 ) ) ),
inference(sigma_proxy_clausification,[],[f5066]) ).
thf(f5068,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( sK343 @ Y0 )
= ( sK344 @ ( sub @ Y0 @ ( push @ sK342 @ sK341 ) ) ) ) )
=> ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK344 @ ( sub @ Y0 @ sK341 ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( sK343 @ Y0 )
=> ( sK343 @ ( sub @ Y0 @ sh ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f5067]) ).
thf(f5069,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK344 @ ( sub @ Y0 @ sK341 ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( sK343 @ Y0 )
=> ( sK343 @ ( sub @ Y0 @ sh ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f5068]) ).
thf(f5070,plain,
( ( pushprop_lem2v2 = $true )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sK343 @ Y0 )
= ( sK344 @ ( sub @ Y0 @ ( push @ sK342 @ sK341 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f5068]) ).
thf(f5071,plain,
! [X1: term] :
( ( pushprop_lem2v2 = $true )
| ( $true
= ( ^ [Y0: term] :
( ( sK343 @ Y0 )
= ( sK344 @ ( sub @ Y0 @ ( push @ sK342 @ sK341 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f5070]) ).
thf(f5072,plain,
! [X1: term] :
( ( pushprop_lem2v2 = $true )
| ( $true
= ( ( sK343 @ X1 )
= ( sK344 @ ( sub @ X1 @ ( push @ sK342 @ sK341 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f5071]) ).
thf(f5073,plain,
! [X1: term] :
( ( pushprop_lem2v2 = $true )
| ( ( sK343 @ X1 )
= ( sK344 @ ( sub @ X1 @ ( push @ sK342 @ sK341 ) ) ) ) ),
inference(iff_proxy_clausification,[],[f5072]) ).
thf(f5074,plain,
! [X1: term] :
( ( pushprop_lem2v2 = $true )
| ( $true
= ( sK343 @ X1 ) )
| ( $false
= ( sK344 @ ( sub @ X1 @ ( push @ sK342 @ sK341 ) ) ) ) ),
inference(iff_proxy_clausification,[],[f5073]) ).
thf(f5076,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( sK343 @ Y0 )
=> ( sK343 @ ( sub @ Y0 @ sh ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f5069]) ).
thf(f5077,plain,
( ( pushprop_lem2v2 = $true )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK344 @ ( sub @ Y0 @ sK341 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f5069]) ).
thf(f5078,plain,
! [X1: term] :
( ( pushprop_lem2v2 = $true )
| ( $true
= ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( sK344 @ ( sub @ Y0 @ sK341 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f5077]) ).
thf(f5079,plain,
! [X1: term] :
( ( pushprop_lem2v2 = $true )
| ( $true
= ( ( var @ X1 )
=> ( sK344 @ ( sub @ X1 @ sK341 ) ) ) ) ),
inference(beta-eta_normalization,[],[f5078]) ).
thf(f5080,plain,
! [X1: term] :
( ( pushprop_lem2v2 = $true )
| ( ( var @ X1 )
= $false )
| ( $true
= ( sK344 @ ( sub @ X1 @ sK341 ) ) ) ),
inference(imp_proxy_clausification,[],[f5079]) ).
thf(f5081,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( ^ [Y0: term] :
( ( var @ Y0 )
=> ( ( sK343 @ Y0 )
=> ( sK343 @ ( sub @ Y0 @ sh ) ) ) )
@ sK345 ) ) ),
inference(sigma_proxy_clausification,[],[f5076]) ).
thf(f5082,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( ( var @ sK345 )
=> ( ( sK343 @ sK345 )
=> ( sK343 @ ( sub @ sK345 @ sh ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f5081]) ).
thf(f5083,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( ( sK343 @ sK345 )
=> ( sK343 @ ( sub @ sK345 @ sh ) ) ) ) ),
inference(imp_proxy_clausification,[],[f5082]) ).
thf(f5084,plain,
( ( pushprop_lem2v2 = $true )
| ( $true
= ( var @ sK345 ) ) ),
inference(imp_proxy_clausification,[],[f5082]) ).
thf(f5085,plain,
( ( pushprop_lem2v2 = $true )
| ( $false
= ( sK343 @ ( sub @ sK345 @ sh ) ) ) ),
inference(imp_proxy_clausification,[],[f5083]) ).
thf(f5683,plain,
( ( axshiftcons = $false )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f315]) ).
thf(f5684,plain,
! [X1: subst] :
( ( axshiftcons = $false )
| ( $true
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( comp @ sh @ ( push @ Y1 @ Y0 ) )
= Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f5683]) ).
thf(f5685,plain,
! [X1: subst] :
( ( axshiftcons = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( comp @ sh @ ( push @ Y0 @ X1 ) )
= X1 ) ) ) ),
inference(beta-eta_normalization,[],[f5684]) ).
thf(f5686,plain,
! [X2: term,X1: subst] :
( ( axshiftcons = $false )
| ( $true
= ( ^ [Y0: term] :
( ( comp @ sh @ ( push @ Y0 @ X1 ) )
= X1 )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f5685]) ).
thf(f5687,plain,
! [X2: term,X1: subst] :
( ( axshiftcons = $false )
| ( $true
= ( ( comp @ sh @ ( push @ X2 @ X1 ) )
= X1 ) ) ),
inference(beta-eta_normalization,[],[f5686]) ).
thf(f5688,plain,
! [X2: term,X1: subst] :
( ( axshiftcons = $false )
| ( ( comp @ sh @ ( push @ X2 @ X1 ) )
= X1 ) ),
inference(equality_proxy_clausification,[],[f5687]) ).
thf(f5703,plain,
( ( axclos = $false )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f313]) ).
thf(f5704,plain,
! [X1: subst] :
( ( axclos = $false )
| ( $true
= ( ^ [Y0: subst] :
( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( sub @ Y2 @ Y1 ) @ Y0 )
= ( sub @ Y2 @ ( comp @ Y1 @ Y0 ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f5703]) ).
thf(f5705,plain,
! [X1: subst] :
( ( axclos = $false )
| ( $true
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( sub @ Y1 @ Y0 ) @ X1 )
= ( sub @ Y1 @ ( comp @ Y0 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f5704]) ).
thf(f5706,plain,
! [X2: subst,X1: subst] :
( ( axclos = $false )
| ( $true
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( sub @ Y1 @ Y0 ) @ X1 )
= ( sub @ Y1 @ ( comp @ Y0 @ X1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f5705]) ).
thf(f5707,plain,
! [X2: subst,X1: subst] :
( ( axclos = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ ( sub @ Y0 @ X2 ) @ X1 )
= ( sub @ Y0 @ ( comp @ X2 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f5706]) ).
thf(f5708,plain,
! [X2: subst,X3: term,X1: subst] :
( ( axclos = $false )
| ( $true
= ( ^ [Y0: term] :
( ( sub @ ( sub @ Y0 @ X2 ) @ X1 )
= ( sub @ Y0 @ ( comp @ X2 @ X1 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f5707]) ).
thf(f5709,plain,
! [X2: subst,X3: term,X1: subst] :
( ( axclos = $false )
| ( $true
= ( ( sub @ ( sub @ X3 @ X2 ) @ X1 )
= ( sub @ X3 @ ( comp @ X2 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f5708]) ).
thf(f5710,plain,
! [X2: subst,X3: term,X1: subst] :
( ( axclos = $false )
| ( ( sub @ ( sub @ X3 @ X2 ) @ X1 )
= ( sub @ X3 @ ( comp @ X2 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f5709]) ).
thf(f5768,plain,
pushprop_lem2v2 = $false,
inference(global_subsumption,[],[f4960,f422]) ).
thf(f5784,plain,
axshiftcons = $true,
inference(global_subsumption,[],[f4961,f422]) ).
thf(f5785,plain,
axclos = $true,
inference(global_subsumption,[],[f4959,f422]) ).
thf(f6351,plain,
( ( $true = $false )
| ( $true
= ( var @ sK345 ) ) ),
inference(forward_demodulation,[],[f5084,f5768]) ).
thf(f6352,plain,
( $true
= ( var @ sK345 ) ),
inference(trivial_inequality_removal,[],[f6351]) ).
thf(f6710,plain,
( ( $true = $false )
| ( $false
= ( sK343 @ ( sub @ sK345 @ sh ) ) ) ),
inference(forward_demodulation,[],[f5085,f5768]) ).
thf(f6711,plain,
( $false
= ( sK343 @ ( sub @ sK345 @ sh ) ) ),
inference(trivial_inequality_removal,[],[f6710]) ).
thf(f6755,plain,
! [X2: term,X1: subst] :
( ( $true = $false )
| ( ( comp @ sh @ ( push @ X2 @ X1 ) )
= X1 ) ),
inference(forward_demodulation,[],[f5688,f5784]) ).
thf(f6756,plain,
! [X2: term,X1: subst] :
( ( comp @ sh @ ( push @ X2 @ X1 ) )
= X1 ),
inference(trivial_inequality_removal,[],[f6755]) ).
thf(f6793,plain,
! [X1: term] :
( ( $true = $false )
| ( ( var @ X1 )
= $false )
| ( $true
= ( sK344 @ ( sub @ X1 @ sK341 ) ) ) ),
inference(forward_demodulation,[],[f5080,f5768]) ).
thf(f6794,plain,
! [X1: term] :
( ( $true
= ( sK344 @ ( sub @ X1 @ sK341 ) ) )
| ( ( var @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f6793]) ).
thf(f9765,plain,
! [X1: term] :
( ( $true = $false )
| ( $true
= ( sK343 @ X1 ) )
| ( $false
= ( sK344 @ ( sub @ X1 @ ( push @ sK342 @ sK341 ) ) ) ) ),
inference(forward_demodulation,[],[f5074,f5768]) ).
thf(f9766,plain,
! [X1: term] :
( ( $false
= ( sK344 @ ( sub @ X1 @ ( push @ sK342 @ sK341 ) ) ) )
| ( $true
= ( sK343 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f9765]) ).
thf(f146658,plain,
! [X2: subst,X3: term,X1: subst] :
( ( $true = $false )
| ( ( sub @ ( sub @ X3 @ X2 ) @ X1 )
= ( sub @ X3 @ ( comp @ X2 @ X1 ) ) ) ),
inference(forward_demodulation,[],[f5710,f5785]) ).
thf(f146659,plain,
! [X2: subst,X3: term,X1: subst] :
( ( sub @ ( sub @ X3 @ X2 ) @ X1 )
= ( sub @ X3 @ ( comp @ X2 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f146658]) ).
thf(f146668,plain,
! [X0: term,X1: subst] :
( ( $false
= ( sK344 @ ( sub @ X0 @ ( comp @ X1 @ ( push @ sK342 @ sK341 ) ) ) ) )
| ( $true
= ( sK343 @ ( sub @ X0 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f9766,f146659]) ).
thf(f151482,plain,
! [X0: term] :
( ( $false
= ( sK344 @ ( sub @ X0 @ sK341 ) ) )
| ( $true
= ( sK343 @ ( sub @ X0 @ sh ) ) ) ),
inference(constrained_superposition,[],[f146668,f6756]) ).
thf(f151778,plain,
! [X0: term] :
( ( $true = $false )
| ( ( var @ X0 )
= $false )
| ( $true
= ( sK343 @ ( sub @ X0 @ sh ) ) ) ),
inference(constrained_superposition,[],[f6794,f151482]) ).
thf(f151779,plain,
! [X0: term] :
( ( $true
= ( sK343 @ ( sub @ X0 @ sh ) ) )
| ( ( var @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f151778]) ).
thf(f152009,plain,
( ( $true = $false )
| ( $false
= ( var @ sK345 ) ) ),
inference(constrained_superposition,[],[f6711,f151779]) ).
thf(f152012,plain,
( $false
= ( var @ sK345 ) ),
inference(trivial_inequality_removal,[],[f152009]) ).
thf(f152075,plain,
$true = $false,
inference(constrained_superposition,[],[f6352,f152012]) ).
thf(f152076,plain,
$false,
inference(trivial_inequality_removal,[],[f152075]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 % Computer : n007.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 17:30:11 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.25 Running first-order model finding
% 0.10/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.71/1.45 % (3688063)Will run a generic schedule for satisfiability detection.
% 6.71/1.45 % (3688070)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1030404670:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.71/1.45 % (3688068)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2379488714_2999 on theBenchmark for (2999ds/0Mi)
% 6.71/1.45 % (3688072)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4017259591:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.71/1.45 % (3688069)% WARNING: option uhcvi not known.
% 6.71/1.45 % (3688071)dis+10_1_sil=32000:sp=arity:random_seed=2902188433:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.71/1.45 % (3688069)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=363058205:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.71/1.45 % (3688073)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=617002911:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.71/1.45 % (3688074)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2555662534:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.71/1.45 % (3688072)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.71/1.45 % Exception at run slice level
% 6.71/1.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.71/1.45 % (3688069)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.71/1.45 % (3688072)Instruction limit reached!
% 6.71/1.45 % (3688072)------------------------------
% 6.71/1.45 % (3688072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.71/1.45 % (3688072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.45 % (3688072)CaDiCaL version: 2.1.3
% 6.71/1.45 % (3688072)Termination reason: Instruction limit
% 6.71/1.45 % (3688072)Termination phase: Saturation
% 6.71/1.45 % (3688072)Time elapsed: 0.049 s
% 6.71/1.45 % (3688072)Peak memory usage: 12 MB
% 6.71/1.45 % (3688072)Instructions burned: 118 (million)
% 6.71/1.45 % (3688083)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3803328268:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.71/1.45 % (3688069)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.71/1.45 % (3688082)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=416857615:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.71/1.45 % (3688071)Instruction limit reached!
% 6.71/1.45 % (3688071)------------------------------
% 6.71/1.45 % (3688071)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.71/1.45 % (3688071)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.45 % (3688071)CaDiCaL version: 2.1.3
% 6.71/1.45 % (3688071)Termination reason: Instruction limit
% 6.71/1.45 % (3688071)Termination phase: Saturation
% 6.71/1.45 % (3688071)Time elapsed: 0.081 s
% 6.71/1.45 % (3688071)Peak memory usage: 12 MB
% 6.71/1.45 % (3688071)Instructions burned: 103 (million)
% 6.71/1.45 % (3688073)Instruction limit reached!
% 6.71/1.45 % (3688073)------------------------------
% 6.71/1.45 % (3688073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.71/1.45 % (3688073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.45 % (3688073)CaDiCaL version: 2.1.3
% 6.71/1.45 % (3688073)Termination reason: Instruction limit
% 6.71/1.45 % (3688073)Termination phase: Saturation
% 6.71/1.45 % (3688073)Time elapsed: 0.103 s
% 6.71/1.45 % (3688073)Peak memory usage: 12 MB
% 6.71/1.45 % (3688073)Instructions burned: 131 (million)
% 6.71/1.45 % Exception at run slice level
% 6.71/1.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.71/1.45 % (3688086)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2564374028:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 6.71/1.45 % (3688083)Instruction limit reached!
% 6.71/1.45 % (3688083)------------------------------
% 6.71/1.45 % (3688083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.71/1.45 % (3688083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.71/1.45 % (3688083)CaDiCaL version: 2.1.3
% 6.71/1.45 % (3688083)Termination reason: Instruction limit
% 27.68/4.35 % (3688083)Termination phase: Saturation
% 27.68/4.35 % (3688083)Time elapsed: 0.064 s
% 27.68/4.35 % (3688083)Peak memory usage: 12 MB
% 27.68/4.35 % (3688083)Instructions burned: 131 (million)
% 27.68/4.35 % (3688087)ott-21_1_sil=16000:fs=off:random_seed=144484124:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 27.68/4.35 % (3688074)Instruction limit reached!
% 27.68/4.35 % (3688074)------------------------------
% 27.68/4.35 % (3688074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.68/4.35 % (3688074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.68/4.35 % (3688074)CaDiCaL version: 2.1.3
% 27.68/4.35 % (3688074)Termination reason: Instruction limit
% 27.68/4.35 % (3688074)Termination phase: Saturation
% 27.68/4.35 % (3688074)Time elapsed: 0.126 s
% 27.68/4.35 % (3688074)Peak memory usage: 13 MB
% 27.68/4.35 % (3688074)Instructions burned: 160 (million)
% 27.68/4.35 % (3688088)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1924780624:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 27.68/4.35 % (3688086)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 27.68/4.35 % (3688092)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=373118959:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 27.68/4.35 % (3688090)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=890351152:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 27.68/4.35 % (3688086)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 27.68/4.35 % Exception at run slice level
% 27.68/4.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 27.68/4.35 % (3688087)Instruction limit reached!
% 27.68/4.35 % (3688087)------------------------------
% 27.68/4.35 % (3688087)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.68/4.35 % (3688087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.68/4.35 % (3688087)CaDiCaL version: 2.1.3
% 27.68/4.35 % (3688087)Termination reason: Instruction limit
% 27.68/4.35 % (3688087)Termination phase: Saturation
% 27.68/4.35 % (3688087)Time elapsed: 0.144 s
% 27.68/4.35 % (3688087)Peak memory usage: 13 MB
% 27.68/4.35 % (3688087)Instructions burned: 180 (million)
% 27.68/4.35 % (3688096)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=715683926:i=889:ins=1_2996 on theBenchmark for (2996ds/889Mi)
% 27.68/4.35 % (3688097)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3877264112:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2996 on theBenchmark for (2996ds/692Mi)
% 27.68/4.35 % (3688097)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 27.68/4.35 % Exception at run slice level
% 27.68/4.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 27.68/4.35 % (3688100)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1155531328:i=879:kws=inv_precedence:fsr=off_2995 on theBenchmark for (2995ds/879Mi)
% 27.68/4.35 % (3688100)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 27.68/4.35 % (3688088)Instruction limit reached!
% 27.68/4.35 % (3688088)------------------------------
% 27.68/4.35 % (3688088)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.68/4.35 % (3688088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.68/4.35 % (3688088)CaDiCaL version: 2.1.3
% 27.68/4.35 % (3688088)Termination reason: Instruction limit
% 27.68/4.35 % (3688088)Termination phase: Saturation
% 27.68/4.35 % (3688088)Time elapsed: 0.428 s
% 27.68/4.35 % (3688088)Peak memory usage: 16 MB
% 27.68/4.35 % (3688088)Instructions burned: 478 (million)
% 27.68/4.35 % (3688102)fmb+10_1_sil=64000:random_seed=3893970808:i=22061:nm=2:gsp=on_2993 on theBenchmark for (2993ds/22061Mi)
% 27.68/4.35 % (3688102)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 27.68/4.35 % Exception at run slice level
% 27.68/4.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 27.68/4.35 % (3688104)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=1664456743:i=9515:nm=5_2993 on theBenchmark for (2993ds/9515Mi)
% 27.68/4.35 % Exception at run slice level
% 27.68/4.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.35/5.08 % (3688086)Instruction limit reached!
% 33.35/5.08 % (3688086)------------------------------
% 33.35/5.08 % (3688086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.35/5.08 % (3688086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.35/5.08 % (3688086)CaDiCaL version: 2.1.3
% 33.35/5.08 % (3688086)Termination reason: Instruction limit
% 33.35/5.08 % (3688086)Termination phase: Saturation
% 33.35/5.08 % (3688086)Time elapsed: 0.574 s
% 33.35/5.08 % (3688086)Peak memory usage: 19 MB
% 33.35/5.08 % (3688086)Instructions burned: 684 (million)
% 33.35/5.08 % (3688106)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3489846971:fmbsr=1.7:i=920_2992 on theBenchmark for (2992ds/920Mi)
% 33.35/5.08 % (3688107)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1455522962:i=5131_2992 on theBenchmark for (2992ds/5131Mi)
% 33.35/5.08 % (3688107)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 33.35/5.08 % Exception at run slice level
% 33.35/5.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.35/5.08 % (3688111)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=448359577:i=1472:ins=7:fdi=8:gsp=on_2991 on theBenchmark for (2991ds/1472Mi)
% 33.35/5.08 % (3688111)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 33.35/5.08 % (3688111)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 33.35/5.08 % (3688092)Instruction limit reached!
% 33.35/5.08 % (3688092)------------------------------
% 33.35/5.08 % (3688092)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.35/5.08 % (3688092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.35/5.08 % (3688092)CaDiCaL version: 2.1.3
% 33.35/5.08 % (3688092)Termination reason: Instruction limit
% 33.35/5.08 % (3688092)Termination phase: Saturation
% 33.35/5.08 % (3688092)Time elapsed: 0.646 s
% 33.35/5.08 % (3688092)Peak memory usage: 24 MB
% 33.35/5.08 % (3688092)Instructions burned: 1179 (million)
% 33.35/5.08 % (3688113)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2425490146:i=6324_2991 on theBenchmark for (2991ds/6324Mi)
% 33.35/5.08 % Exception at run slice level
% 33.35/5.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.35/5.08 % (3688115)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1834028893:fmbsr=2.30978:i=2174_2990 on theBenchmark for (2990ds/2174Mi)
% 33.35/5.08 % (3688097)Instruction limit reached!
% 33.35/5.08 % (3688097)------------------------------
% 33.35/5.08 % (3688097)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.35/5.08 % (3688097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.35/5.08 % (3688097)CaDiCaL version: 2.1.3
% 33.35/5.08 % (3688097)Termination reason: Instruction limit
% 33.35/5.08 % (3688097)Termination phase: Saturation
% 33.35/5.08 % (3688097)Time elapsed: 0.578 s
% 33.35/5.08 % (3688097)Peak memory usage: 20 MB
% 33.35/5.08 % (3688097)Instructions burned: 692 (million)
% 33.35/5.08 % Exception at run slice level
% 33.35/5.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.35/5.08 % (3688117)ott-2_1_sil=16000:newcnf=on:random_seed=1407716878:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2990 on theBenchmark for (2990ds/869Mi)
% 33.35/5.08 % (3688118)ott+10_1_sil=32000:tgt=ground:random_seed=322982641:i=5114:av=off_2990 on theBenchmark for (2990ds/5114Mi)
% 33.35/5.08 % (3688117)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 33.35/5.08 % (3688100)Instruction limit reached!
% 33.35/5.08 % (3688100)------------------------------
% 33.35/5.08 % (3688100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.35/5.08 % (3688100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.35/5.08 % (3688100)CaDiCaL version: 2.1.3
% 33.35/5.08 % (3688100)Termination reason: Instruction limit
% 33.35/5.08 % (3688100)Termination phase: Saturation
% 33.35/5.08 % (3688100)Time elapsed: 0.611 s
% 33.35/5.08 % (3688100)Peak memory usage: 20 MB
% 33.35/5.08 % (3688100)Instructions burned: 879 (million)
% 33.35/5.08 % (3688121)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3140314950:i=54282_2989 on theBenchmark for (2989ds/54282Mi)
% 33.35/5.08 % Exception at run slice level
% 33.35/5.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.35/5.08 % (3688123)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3161153197:i=3512:aac=none_2988 on theBenchmark for (2988ds/3512Mi)
% 33.35/5.08 % (3688123)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 33.35/5.08 % (3688117)Instruction limit reached!
% 33.35/5.08 % (3688117)------------------------------
% 33.35/5.08 % (3688117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.35/5.08 % (3688117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.35/5.08 % (3688117)CaDiCaL version: 2.1.3
% 33.35/5.08 % (3688117)Termination reason: Instruction limit
% 33.35/5.08 % (3688117)Termination phase: Saturation
% 33.35/5.08 % (3688117)Time elapsed: 0.655 s
% 33.35/5.08 % (3688117)Peak memory usage: 21 MB
% 33.35/5.08 % (3688117)Instructions burned: 869 (million)
% 33.35/5.08 % (3688125)dis+21_1_sil=32000:sas=cadical:random_seed=2900383293:i=3773:amm=off_2983 on theBenchmark for (2983ds/3773Mi)
% 33.35/5.08 % (3688111)Instruction limit reached!
% 33.35/5.08 % (3688111)------------------------------
% 33.35/5.08 % (3688111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.35/5.08 % (3688111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.35/5.08 % (3688111)CaDiCaL version: 2.1.3
% 33.35/5.08 % (3688111)Termination reason: Instruction limit
% 33.35/5.08 % (3688111)Termination phase: Saturation
% 33.35/5.08 % (3688111)Time elapsed: 1.200 s
% 33.35/5.08 % (3688111)Peak memory usage: 23 MB
% 33.35/5.08 % (3688111)Instructions burned: 1472 (million)
% 33.35/5.08 % (3688127)ott+11_1_sil=16000:gs=on:random_seed=1160047783:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2979 on theBenchmark for (2979ds/2251Mi)
% 33.35/5.08 % (3688127)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 33.35/5.08 % (3688107)Instruction limit reached!
% 33.35/5.08 % (3688107)------------------------------
% 33.35/5.08 % (3688107)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.35/5.08 % (3688107)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.35/5.08 % (3688107)CaDiCaL version: 2.1.3
% 33.35/5.08 % (3688107)Termination reason: Instruction limit
% 33.35/5.08 % (3688107)Termination phase: Saturation
% 33.35/5.08 % (3688107)Time elapsed: 3.036 s
% 33.35/5.08 % (3688107)Peak memory usage: 33 MB
% 33.35/5.08 % (3688107)Instructions burned: 5133 (million)
% 33.35/5.08 % (3688118)Instruction limit reached!
% 33.35/5.08 % (3688118)------------------------------
% 33.35/5.08 % (3688118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.35/5.08 % (3688118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.35/5.08 % (3688118)CaDiCaL version: 2.1.3
% 33.35/5.08 % (3688118)Termination reason: Instruction limit
% 33.35/5.08 % (3688118)Termination phase: Saturation
% 33.35/5.08 % (3688118)Time elapsed: 2.832 s
% 33.35/5.08 % (3688118)Peak memory usage: 38 MB
% 33.35/5.08 % (3688118)Instructions burned: 5115 (million)
% 33.35/5.08 % (3688129)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=3719364490:fmbsr=1.6:i=67534_2961 on theBenchmark for (2961ds/67534Mi)
% 33.35/5.08 % (3688131)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=1755728830:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2961 on theBenchmark for (2961ds/4591Mi)
% 33.35/5.08 % Exception at run slice level
% 33.35/5.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.35/5.08 % (3688133)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=3719848083:i=29340_2961 on theBenchmark for (2961ds/29340Mi)
% 33.35/5.08 % (3688127)Instruction limit reached!
% 33.35/5.08 % (3688127)------------------------------
% 33.35/5.08 % (3688127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.35/5.08 % (3688127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.35/5.08 % (3688127)CaDiCaL version: 2.1.3
% 33.35/5.08 % (3688127)Termination reason: Instruction limit
% 33.35/5.08 % (3688127)Termination phase: Saturation
% 33.35/5.08 % (3688127)Time elapsed: 1.930 s
% 33.35/5.08 % (3688127)Peak memory usage: 28 MB
% 33.35/5.08 % (3688127)Instructions burned: 2251 (million)
% 33.35/5.08 % (3688135)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=1178653899:i=5211_2959 on theBenchmark for (2959ds/5211Mi)
% 33.35/5.08 % (3688123)Instruction limit reached!
% 33.35/5.08 % (3688123)------------------------------
% 33.35/5.08 % (3688123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.35/5.08 % (3688123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.35/5.08 % (3688123)CaDiCaL version: 2.1.3
% 33.35/5.08 % (3688123)Termination reason: Instruction limit
% 33.35/5.08 % (3688123)Termination phase: Saturation
% 33.35/5.08 % (3688123)Time elapsed: 3.017 s
% 33.35/5.08 % (3688123)Peak memory usage: 32 MB
% 33.35/5.08 % (3688123)Instructions burned: 3513 (million)
% 33.35/5.08 % (3688137)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=2559338482:i=5497:nm=2_2957 on theBenchmark for (2957ds/5497Mi)
% 33.35/5.08 % Exception at run slice level
% 33.35/5.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.35/5.08 % (3688139)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=683704822:fmbsr=2:i=46332_2956 on theBenchmark for (2956ds/46332Mi)
% 33.35/5.08 % Exception at run slice level
% 33.35/5.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.35/5.08 % (3688141)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=3188278424:i=14071_2955 on theBenchmark for (2955ds/14071Mi)
% 33.35/5.08 % Exception at run slice level
% 33.35/5.08 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 33.35/5.08 % (3688143)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3122429067:i=22565:add=on:rawr=on_2955 on theBenchmark for (2955ds/22565Mi)
% 33.35/5.08 % (3688125)Instruction limit reached!
% 33.35/5.08 % (3688125)------------------------------
% 33.35/5.08 % (3688125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.35/5.08 % (3688125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.35/5.08 % (3688125)CaDiCaL version: 2.1.3
% 33.35/5.08 % (3688125)Termination reason: Instruction limit
% 33.35/5.08 % (3688125)Termination phase: Saturation
% 33.35/5.08 % (3688125)Time elapsed: 2.996 s
% 33.35/5.08 % (3688125)Peak memory usage: 32 MB
% 33.35/5.08 % (3688125)Instructions burned: 3774 (million)
% 33.35/5.08 % (3688145)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=106907310:i=8173:av=off_2953 on theBenchmark for (2953ds/8173Mi)
% 33.35/5.08 % (3688070) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3688063-3688070"...
% 33.35/5.08 % (3688070)...printing done.
% 33.35/5.08 % (3688070)Refutation found. Thanks to Tanya!
% 33.35/5.08 % SZS status Theorem for theBenchmark
% 33.35/5.08 % SZS output start Proof for theBenchmark
% See solution above
% 33.35/5.09 % (3688070)------------------------------
% 33.35/5.09 % (3688070)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 33.35/5.09 % (3688070)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 33.35/5.09 % (3688070)CaDiCaL version: 2.1.3
% 33.35/5.09 % (3688070)Termination reason: Refutation
% 33.35/5.09 % (3688070)Time elapsed: 4.759 s
% 33.35/5.09 % (3688070)Peak memory usage: 58 MB
% 33.35/5.09 % (3688070)Instructions burned: 12537 (million)
% 33.35/5.09 % (3688063)Success in time 4.816 s
% 33.35/5.09 % Vampire exiting
%------------------------------------------------------------------------------