%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG259^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 07:45:26 AM UTC 2026
% Result : Theorem 1.63s 0.49s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 20
% Syntax : Number of formulae : 173 ( 50 unt; 0 typ; 12 def)
% Number of atoms : 1369 ( 248 equ; 0 cnn)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 1650 ( 97 ~; 126 |; 0 &; 711 @)
% ( 12 <=>; 628 =>; 0 <=; 0 <~>)
% Maximal formula depth : 32 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 566 ( 562 usr; 227 con; 0-4 aty)
% ( 76 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 219 ( 12 sgn 82 !; 0 ?; 219 :)
% 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(f1,axiom,
( axapp
= ( ! [X0: term,X1: term,X2: subst] :
( ( sub @ ( ap @ X0 @ X1 ) @ X2 )
= ( ap @ ( sub @ X0 @ X2 ) @ ( sub @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axapp) ).
thf(f4,axiom,
( axabs
= ( ! [X0: term,X1: subst] :
( ( sub @ ( lam @ X0 ) @ X1 )
= ( lam @ ( sub @ X0 @ ( push @ one @ ( comp @ X1 @ sh ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',axabs) ).
thf(f20,axiom,
( lamnotap
= ( ! [X0: term,X1: term,X2: term] :
( ( lam @ X0 )
!= ( ap @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',lamnotap) ).
thf(f55,axiom,
( hoasap
= ( ^ [X0: subst,X1: term,X2: subst,X3: term] : ( ap @ ( sub @ X1 @ X2 ) @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoasap) ).
thf(f56,axiom,
( hoaslam
= ( ^ [X0: subst,X1: subst > term > term] : ( lam @ ( X1 @ sh @ one ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoaslam) ).
thf(f67,axiom,
( hoaslamnotap
= ( ! [X0: subst > term > term] :
( ! [X1: subst,X2: term,X3: subst] :
( ( sub @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
=> ! [X2: term,X4: term] :
( ( hoaslam @ id
@ ^ [X1: subst,X5: term] : ( X0 @ X1 @ X5 ) )
!= ( hoasap @ id @ X2 @ id @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoaslamnotap) ).
thf(f68,axiom,
( ( hoaslamnotap_gthm = axapp )
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ALG003^0.ax',hoaslamnotap_gthm) ).
thf(f114,conjecture,
hoaslamnotap_gthm,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f115,negated_conjecture,
~ hoaslamnotap_gthm,
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f116,plain,
( axapp
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y1 ) @ Y0 )
= ( ap @ ( sub @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f119,plain,
( axabs
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( lam @ Y1 ) @ Y0 )
= ( lam @ ( sub @ Y1 @ ( push @ one @ ( comp @ Y0 @ sh ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f136,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y1 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f201,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f202,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f220,plain,
( hoaslamnotap
= ( ! [X0: subst > term > term] :
( ! [X1: subst,X2: term,X3: subst] :
( ( sub @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ ( comp @ X1 @ X3 ) @ ( sub @ X2 @ X3 ) ) )
=> ! [X4: term,X5: term] :
( ( hoaslam @ id
@ ^ [X6: subst,X7: term] : ( X0 @ X6 @ X7 ) )
!= ( hoasap @ id @ X4 @ id @ X5 ) ) ) ) ),
inference(rectify,[],[f67]) ).
thf(f221,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) )
!= ( hoasap @ id @ Y2 @ id @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f220]) ).
thf(f222,plain,
( ( hoaslamnotap_gthm = axapp )
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f68]) ).
thf(f223,plain,
( hoaslamnotap_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f222]) ).
thf(f306,plain,
~ hoaslamnotap_gthm,
inference(rectify,[],[f115]) ).
thf(f307,plain,
hoaslamnotap_gthm != $true,
inference(fool_elimination,[],[f306]) ).
thf(f308,plain,
hoaslamnotap_gthm != $true,
inference(flattening,[],[f307]) ).
thf(f309,plain,
( axapp
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y1 ) @ Y0 )
= ( ap @ ( sub @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f116]) ).
thf(f312,plain,
( axabs
= ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( lam @ Y1 ) @ Y0 )
= ( lam @ ( sub @ Y1 @ ( push @ one @ ( comp @ Y0 @ sh ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f119]) ).
thf(f328,plain,
( lamnotap
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f136]) ).
thf(f363,plain,
( hoasap
= ( ^ [Y0: subst,Y1: term,Y2: subst,Y3: term] : ( ap @ ( sub @ Y1 @ Y2 ) @ Y3 ) ) ),
inference(cnf_transformation,[],[f201]) ).
thf(f364,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( lam @ ( Y1 @ sh @ one ) ) ) ),
inference(cnf_transformation,[],[f202]) ).
thf(f375,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( hoaslam @ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) )
!= ( hoasap @ id @ Y2 @ id @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f221]) ).
thf(f376,plain,
( hoaslamnotap_gthm
= ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f223]) ).
thf(f422,plain,
hoaslamnotap_gthm != $true,
inference(cnf_transformation,[],[f308]) ).
thf(f434,plain,
( hoaslamnotap
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) )
!= ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f375,f364,f363]) ).
thf(f3650,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( axapp
=> ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f376]) ).
thf(f3683,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( axvarcons
=> ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3650]) ).
thf(f3684,plain,
( ( hoaslamnotap_gthm = $true )
| ( axapp = $true ) ),
inference(imp_proxy_clausification,[],[f3650]) ).
thf(f3685,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( axvarid
=> ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3683]) ).
thf(f3687,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( axabs
=> ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3685]) ).
thf(f3689,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( axclos
=> ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3687]) ).
thf(f3690,plain,
( ( hoaslamnotap_gthm = $true )
| ( axabs = $true ) ),
inference(imp_proxy_clausification,[],[f3687]) ).
thf(f3691,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( axidl
=> ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3689]) ).
thf(f3693,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( axshiftcons
=> ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3691]) ).
thf(f3695,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( axassoc
=> ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3693]) ).
thf(f3697,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( axmap
=> ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3695]) ).
thf(f3699,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( axidr
=> ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3697]) ).
thf(f3701,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( axvarshift
=> ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3699]) ).
thf(f3703,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( axscons
=> ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3701]) ).
thf(f3705,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( ulamvar1
=> ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3703]) ).
thf(f3707,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( ulamvarsh
=> ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3705]) ).
thf(f3709,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( ulamvarind
=> ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3707]) ).
thf(f3711,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( apinj1
=> ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3709]) ).
thf(f3713,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( apinj2
=> ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3711]) ).
thf(f3715,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( laminj
=> ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3713]) ).
thf(f3717,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( shinj
=> ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3715]) ).
thf(f3719,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( lamnotap
=> ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3717]) ).
thf(f3721,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( apnotvar
=> ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3719]) ).
thf(f3722,plain,
( ( hoaslamnotap_gthm = $true )
| ( lamnotap = $true ) ),
inference(imp_proxy_clausification,[],[f3719]) ).
thf(f3723,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( lamnotvar
=> ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3721]) ).
thf(f3725,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( induction
=> ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3723]) ).
thf(f3727,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( pushprop
=> ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3725]) ).
thf(f3729,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( induction2lem
=> ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3727]) ).
thf(f3731,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( induction2
=> ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3729]) ).
thf(f3733,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( substmonoid
=> ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3731]) ).
thf(f3735,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( termmset
=> ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3733]) ).
thf(f3737,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( hoasapinj1
=> ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3735]) ).
thf(f3739,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( hoasapinj2
=> ( hoaslaminj
=> hoaslamnotap ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f3737]) ).
thf(f3741,plain,
( ( hoaslamnotap_gthm = $true )
| ( ( hoaslaminj
=> hoaslamnotap )
= $false ) ),
inference(imp_proxy_clausification,[],[f3739]) ).
thf(f3743,plain,
( ( hoaslamnotap_gthm = $true )
| ( hoaslamnotap = $false ) ),
inference(imp_proxy_clausification,[],[f3741]) ).
thf(f3745,plain,
( ( hoaslamnotap = $true )
| ( $false
= ( !! @ ( subst > term > term )
@ ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) )
!= ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ Y1 ) ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f434]) ).
thf(f3761,plain,
( ( hoaslamnotap = $true )
| ( $false
= ( ^ [Y0: subst > term > term] :
( ( !! @ subst
@ ^ [Y1: subst] :
( !! @ term
@ ^ [Y2: term] :
( !! @ subst
@ ^ [Y3: subst] :
( ( sub @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ ( comp @ Y3 @ Y1 ) @ ( sub @ Y2 @ Y1 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( ^ [Y3: subst,Y4: subst > term > term] : ( lam @ ( Y4 @ sh @ one ) )
@ id
@ ^ [Y3: subst,Y4: term] : ( Y0 @ Y3 @ Y4 ) )
!= ( ^ [Y3: subst,Y4: term,Y5: subst,Y6: term] : ( ap @ ( sub @ Y4 @ Y5 ) @ Y6 )
@ id
@ Y2
@ id
@ Y1 ) ) ) ) )
@ sK276 ) ) ),
inference(sigma_proxy_clausification,[],[f3745]) ).
thf(f3762,plain,
( ( hoaslamnotap = $true )
| ( $false
= ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ subst
@ ^ [Y2: subst] :
( ( sub @ ( sK276 @ Y2 @ Y1 ) @ Y0 )
= ( sK276 @ ( comp @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) )
=> ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( lam @ ( sK276 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f3761]) ).
thf(f3763,plain,
( ( hoaslamnotap = $true )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( lam @ ( sK276 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f3762]) ).
thf(f3772,plain,
( ( hoaslamnotap = $true )
| ( $false
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( lam @ ( sK276 @ sh @ one ) )
!= ( ap @ ( sub @ Y1 @ id ) @ Y0 ) ) )
@ sK277 ) ) ),
inference(sigma_proxy_clausification,[],[f3763]) ).
thf(f3773,plain,
( ( hoaslamnotap = $true )
| ( $false
= ( !! @ term
@ ^ [Y0: term] :
( ( lam @ ( sK276 @ sh @ one ) )
!= ( ap @ ( sub @ Y0 @ id ) @ sK277 ) ) ) ) ),
inference(beta-eta_normalization,[],[f3772]) ).
thf(f3774,plain,
( ( hoaslamnotap = $true )
| ( $false
= ( ^ [Y0: term] :
( ( lam @ ( sK276 @ sh @ one ) )
!= ( ap @ ( sub @ Y0 @ id ) @ sK277 ) )
@ sK278 ) ) ),
inference(sigma_proxy_clausification,[],[f3773]) ).
thf(f3775,plain,
( ( hoaslamnotap = $true )
| ( $false
= ( ( lam @ ( sK276 @ sh @ one ) )
!= ( ap @ ( sub @ sK278 @ id ) @ sK277 ) ) ) ),
inference(beta-eta_normalization,[],[f3774]) ).
thf(f3776,plain,
( ( hoaslamnotap = $true )
| ( $true
= ( ( lam @ ( sK276 @ sh @ one ) )
= ( ap @ ( sub @ sK278 @ id ) @ sK277 ) ) ) ),
inference(not_proxy_clausification,[],[f3775]) ).
thf(f3777,plain,
( ( hoaslamnotap = $true )
| ( ( lam @ ( sK276 @ sh @ one ) )
= ( ap @ ( sub @ sK278 @ id ) @ sK277 ) ) ),
inference(equality_proxy_clausification,[],[f3776]) ).
thf(f5488,plain,
( ( lamnotap = $false )
| ( ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y1 @ Y0 ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f328]) ).
thf(f5489,plain,
! [X1: term] :
( ( lamnotap = $false )
| ( $true
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( lam @ Y2 )
!= ( ap @ Y1 @ Y0 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f5488]) ).
thf(f5490,plain,
! [X1: term] :
( ( lamnotap = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f5489]) ).
thf(f5491,plain,
! [X2: term,X1: term] :
( ( lamnotap = $false )
| ( $true
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( lam @ Y1 )
!= ( ap @ Y0 @ X1 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f5490]) ).
thf(f5492,plain,
! [X2: term,X1: term] :
( ( lamnotap = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( lam @ Y0 )
!= ( ap @ X2 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f5491]) ).
thf(f5493,plain,
! [X2: term,X3: term,X1: term] :
( ( lamnotap = $false )
| ( $true
= ( ^ [Y0: term] :
( ( lam @ Y0 )
!= ( ap @ X2 @ X1 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f5492]) ).
thf(f5494,plain,
! [X2: term,X3: term,X1: term] :
( ( lamnotap = $false )
| ( $true
= ( ( lam @ X3 )
!= ( ap @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f5493]) ).
thf(f5495,plain,
! [X2: term,X3: term,X1: term] :
( ( lamnotap = $false )
| ( $false
= ( ( lam @ X3 )
= ( ap @ X2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f5494]) ).
thf(f5496,plain,
! [X2: term,X3: term,X1: term] :
( ( lamnotap = $false )
| ( ( lam @ X3 )
!= ( ap @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f5495]) ).
thf(f5719,plain,
( ( axabs = $false )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( lam @ Y1 ) @ Y0 )
= ( lam @ ( sub @ Y1 @ ( push @ one @ ( comp @ Y0 @ sh ) ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f312]) ).
thf(f5720,plain,
! [X1: subst] :
( ( axabs = $false )
| ( $true
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( lam @ Y1 ) @ Y0 )
= ( lam @ ( sub @ Y1 @ ( push @ one @ ( comp @ Y0 @ sh ) ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f5719]) ).
thf(f5721,plain,
! [X1: subst] :
( ( axabs = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ ( lam @ Y0 ) @ X1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ X1 @ sh ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f5720]) ).
thf(f5722,plain,
! [X2: term,X1: subst] :
( ( axabs = $false )
| ( $true
= ( ^ [Y0: term] :
( ( sub @ ( lam @ Y0 ) @ X1 )
= ( lam @ ( sub @ Y0 @ ( push @ one @ ( comp @ X1 @ sh ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f5721]) ).
thf(f5723,plain,
! [X2: term,X1: subst] :
( ( axabs = $false )
| ( $true
= ( ( sub @ ( lam @ X2 ) @ X1 )
= ( lam @ ( sub @ X2 @ ( push @ one @ ( comp @ X1 @ sh ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f5722]) ).
thf(f5724,plain,
! [X2: term,X1: subst] :
( ( axabs = $false )
| ( ( sub @ ( lam @ X2 ) @ X1 )
= ( lam @ ( sub @ X2 @ ( push @ one @ ( comp @ X1 @ sh ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f5723]) ).
thf(f5751,plain,
( ( axapp = $false )
| ( ( !! @ subst
@ ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y1 ) @ Y0 )
= ( ap @ ( sub @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f309]) ).
thf(f5752,plain,
! [X1: subst] :
( ( axapp = $false )
| ( $true
= ( ^ [Y0: subst] :
( !! @ term
@ ^ [Y1: term] :
( !! @ term
@ ^ [Y2: term] :
( ( sub @ ( ap @ Y2 @ Y1 ) @ Y0 )
= ( ap @ ( sub @ Y2 @ Y0 ) @ ( sub @ Y1 @ Y0 ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f5751]) ).
thf(f5753,plain,
! [X1: subst] :
( ( axapp = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( ap @ Y1 @ Y0 ) @ X1 )
= ( ap @ ( sub @ Y1 @ X1 ) @ ( sub @ Y0 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f5752]) ).
thf(f5754,plain,
! [X2: term,X1: subst] :
( ( axapp = $false )
| ( $true
= ( ^ [Y0: term] :
( !! @ term
@ ^ [Y1: term] :
( ( sub @ ( ap @ Y1 @ Y0 ) @ X1 )
= ( ap @ ( sub @ Y1 @ X1 ) @ ( sub @ Y0 @ X1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f5753]) ).
thf(f5755,plain,
! [X2: term,X1: subst] :
( ( axapp = $false )
| ( $true
= ( !! @ term
@ ^ [Y0: term] :
( ( sub @ ( ap @ Y0 @ X2 ) @ X1 )
= ( ap @ ( sub @ Y0 @ X1 ) @ ( sub @ X2 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f5754]) ).
thf(f5756,plain,
! [X2: term,X3: term,X1: subst] :
( ( axapp = $false )
| ( $true
= ( ^ [Y0: term] :
( ( sub @ ( ap @ Y0 @ X2 ) @ X1 )
= ( ap @ ( sub @ Y0 @ X1 ) @ ( sub @ X2 @ X1 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f5755]) ).
thf(f5757,plain,
! [X2: term,X3: term,X1: subst] :
( ( axapp = $false )
| ( $true
= ( ( sub @ ( ap @ X3 @ X2 ) @ X1 )
= ( ap @ ( sub @ X3 @ X1 ) @ ( sub @ X2 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f5756]) ).
thf(f5758,plain,
! [X2: term,X3: term,X1: subst] :
( ( axapp = $false )
| ( ( sub @ ( ap @ X3 @ X2 ) @ X1 )
= ( ap @ ( sub @ X3 @ X1 ) @ ( sub @ X2 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f5757]) ).
thf(f5942,definition,
( spl412_40
<=> ( hoaslamnotap = $false ) ),
introduced(definition,[new_symbols(definition,[spl412_40])],[avatar_definition]) ).
thf(f5944,plain,
( ( hoaslamnotap = $false )
| ~ spl412_40 ),
inference(avatar_component_clause,[],[f5942]) ).
thf(f5986,definition,
( spl412_51
<=> ( lamnotap = $false ) ),
introduced(definition,[new_symbols(definition,[spl412_51])],[avatar_definition]) ).
thf(f5988,plain,
( ( lamnotap = $false )
| ~ spl412_51 ),
inference(avatar_component_clause,[],[f5986]) ).
thf(f6050,definition,
( spl412_67
<=> ( axabs = $false ) ),
introduced(definition,[new_symbols(definition,[spl412_67])],[avatar_definition]) ).
thf(f6052,plain,
( ( axabs = $false )
| ~ spl412_67 ),
inference(avatar_component_clause,[],[f6050]) ).
thf(f6058,definition,
( spl412_69
<=> ( axapp = $false ) ),
introduced(definition,[new_symbols(definition,[spl412_69])],[avatar_definition]) ).
thf(f6060,plain,
( ( axapp = $false )
| ~ spl412_69 ),
inference(avatar_component_clause,[],[f6058]) ).
thf(f6067,definition,
( spl412_71
<=> ( axapp = $true ) ),
introduced(definition,[new_symbols(definition,[spl412_71])],[avatar_definition]) ).
thf(f6069,plain,
( ( axapp = $true )
| ~ spl412_71 ),
inference(avatar_component_clause,[],[f6067]) ).
thf(f6082,definition,
( spl412_74
<=> ( axabs = $true ) ),
introduced(definition,[new_symbols(definition,[spl412_74])],[avatar_definition]) ).
thf(f6084,plain,
( ( axabs = $true )
| ~ spl412_74 ),
inference(avatar_component_clause,[],[f6082]) ).
thf(f6162,definition,
( spl412_90
<=> ( lamnotap = $true ) ),
introduced(definition,[new_symbols(definition,[spl412_90])],[avatar_definition]) ).
thf(f6164,plain,
( ( lamnotap = $true )
| ~ spl412_90 ),
inference(avatar_component_clause,[],[f6162]) ).
thf(f6218,definition,
( spl412_101
<=> ( hoaslamnotap = $true ) ),
introduced(definition,[new_symbols(definition,[spl412_101])],[avatar_definition]) ).
thf(f6220,plain,
( ( hoaslamnotap = $true )
| ~ spl412_101 ),
inference(avatar_component_clause,[],[f6218]) ).
thf(f8213,plain,
axapp = $true,
inference(forward_subsumption_resolution,[],[f3684,f422]) ).
thf(f8216,plain,
axabs = $true,
inference(forward_subsumption_resolution,[],[f3690,f422]) ).
thf(f8232,plain,
lamnotap = $true,
inference(forward_subsumption_resolution,[],[f3722,f422]) ).
thf(f8244,plain,
hoaslamnotap = $false,
inference(forward_subsumption_resolution,[],[f3743,f422]) ).
thf(f8254,definition,
( spl412_477
<=> ( ( lam @ ( sK276 @ sh @ one ) )
= ( ap @ ( sub @ sK278 @ id ) @ sK277 ) ) ),
introduced(definition,[new_symbols(definition,[spl412_477])],[avatar_definition]) ).
thf(f8256,plain,
( ( ( lam @ ( sK276 @ sh @ one ) )
= ( ap @ ( sub @ sK278 @ id ) @ sK277 ) )
| ~ spl412_477 ),
inference(avatar_component_clause,[],[f8254]) ).
thf(f8257,plain,
( spl412_477
| spl412_101 ),
inference(avatar_split_clause,[],[f3777,f6218,f8254]) ).
thf(f9361,definition,
( spl412_649
<=> ! [X2: term,X1: term,X3: term] :
( ( lam @ X3 )
!= ( ap @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl412_649])],[avatar_definition]) ).
thf(f9362,plain,
( ! [X2: term,X3: term,X1: term] :
( ( lam @ X3 )
!= ( ap @ X2 @ X1 ) )
| ~ spl412_649 ),
inference(avatar_component_clause,[],[f9361]) ).
thf(f9363,plain,
( spl412_649
| spl412_51 ),
inference(avatar_split_clause,[],[f5496,f5986,f9361]) ).
thf(f9538,definition,
( spl412_686
<=> ! [X2: term,X1: subst] :
( ( sub @ ( lam @ X2 ) @ X1 )
= ( lam @ ( sub @ X2 @ ( push @ one @ ( comp @ X1 @ sh ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl412_686])],[avatar_definition]) ).
thf(f9539,plain,
( ! [X2: term,X1: subst] :
( ( sub @ ( lam @ X2 ) @ X1 )
= ( lam @ ( sub @ X2 @ ( push @ one @ ( comp @ X1 @ sh ) ) ) ) )
| ~ spl412_686 ),
inference(avatar_component_clause,[],[f9538]) ).
thf(f9540,plain,
( spl412_686
| spl412_67 ),
inference(avatar_split_clause,[],[f5724,f6050,f9538]) ).
thf(f9562,definition,
( spl412_691
<=> ! [X2: term,X1: subst,X3: term] :
( ( sub @ ( ap @ X3 @ X2 ) @ X1 )
= ( ap @ ( sub @ X3 @ X1 ) @ ( sub @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl412_691])],[avatar_definition]) ).
thf(f9563,plain,
( ! [X2: term,X3: term,X1: subst] :
( ( sub @ ( ap @ X3 @ X2 ) @ X1 )
= ( ap @ ( sub @ X3 @ X1 ) @ ( sub @ X2 @ X1 ) ) )
| ~ spl412_691 ),
inference(avatar_component_clause,[],[f9562]) ).
thf(f9564,plain,
( spl412_691
| spl412_69 ),
inference(avatar_split_clause,[],[f5758,f6058,f9562]) ).
thf(f9570,plain,
spl412_71,
inference(avatar_split_clause,[],[f8213,f6067]) ).
thf(f9573,plain,
spl412_74,
inference(avatar_split_clause,[],[f8216,f6082]) ).
thf(f9589,plain,
spl412_90,
inference(avatar_split_clause,[],[f8232,f6162]) ).
thf(f9601,plain,
spl412_40,
inference(avatar_split_clause,[],[f8244,f5942]) ).
thf(f9623,plain,
( ( $true = $false )
| ~ spl412_69
| ~ spl412_71 ),
inference(forward_demodulation,[],[f6069,f6060]) ).
thf(f9624,plain,
( $false
| ~ spl412_69
| ~ spl412_71 ),
inference(trivial_inequality_removal,[],[f9623]) ).
thf(f9625,plain,
( ~ spl412_69
| ~ spl412_71 ),
inference(avatar_contradiction_clause,[],[f9624]) ).
thf(f9629,plain,
( ( $true = $false )
| ~ spl412_67
| ~ spl412_74 ),
inference(forward_demodulation,[],[f6084,f6052]) ).
thf(f9630,plain,
( $false
| ~ spl412_67
| ~ spl412_74 ),
inference(trivial_inequality_removal,[],[f9629]) ).
thf(f9631,plain,
( ~ spl412_67
| ~ spl412_74 ),
inference(avatar_contradiction_clause,[],[f9630]) ).
thf(f9677,plain,
( ( $true = $false )
| ~ spl412_51
| ~ spl412_90 ),
inference(forward_demodulation,[],[f6164,f5988]) ).
thf(f9678,plain,
( $false
| ~ spl412_51
| ~ spl412_90 ),
inference(trivial_inequality_removal,[],[f9677]) ).
thf(f9679,plain,
( ~ spl412_51
| ~ spl412_90 ),
inference(avatar_contradiction_clause,[],[f9678]) ).
thf(f9710,plain,
( ( $true = $false )
| ~ spl412_40
| ~ spl412_101 ),
inference(forward_demodulation,[],[f6220,f5944]) ).
thf(f9711,plain,
( $false
| ~ spl412_40
| ~ spl412_101 ),
inference(trivial_inequality_removal,[],[f9710]) ).
thf(f9712,plain,
( ~ spl412_40
| ~ spl412_101 ),
inference(avatar_contradiction_clause,[],[f9711]) ).
thf(f9832,plain,
( ! [X2: term,X3: term,X0: term,X1: subst] :
( ( sub @ ( lam @ X0 ) @ X1 )
!= ( ap @ X2 @ X3 ) )
| ~ spl412_649
| ~ spl412_686 ),
inference(constrained_superposition,[],[f9362,f9539]) ).
thf(f10328,plain,
( ! [X0: subst] :
( ( ap @ ( sub @ ( sub @ sK278 @ id ) @ X0 ) @ ( sub @ sK277 @ X0 ) )
= ( sub @ ( lam @ ( sK276 @ sh @ one ) ) @ X0 ) )
| ~ spl412_477
| ~ spl412_691 ),
inference(constrained_superposition,[],[f9563,f8256]) ).
thf(f10340,plain,
( $false
| ~ spl412_477
| ~ spl412_649
| ~ spl412_686
| ~ spl412_691 ),
inference(forward_subsumption_resolution,[],[f10328,f9832]) ).
thf(f10341,plain,
( ~ spl412_477
| ~ spl412_649
| ~ spl412_686
| ~ spl412_691 ),
inference(avatar_contradiction_clause,[],[f10340]) ).
cnf(s861,plain,
( spl412_101
| spl412_477 ),
inference(sat_conversion,[],[f8257]) ).
cnf(s1365,plain,
( spl412_51
| spl412_649 ),
inference(sat_conversion,[],[f9363]) ).
cnf(s1407,plain,
( spl412_67
| spl412_686 ),
inference(sat_conversion,[],[f9540]) ).
cnf(s1413,plain,
( spl412_69
| spl412_691 ),
inference(sat_conversion,[],[f9564]) ).
cnf(s1415,plain,
spl412_71,
inference(sat_conversion,[],[f9570]) ).
cnf(s1418,plain,
spl412_74,
inference(sat_conversion,[],[f9573]) ).
cnf(s1434,plain,
spl412_90,
inference(sat_conversion,[],[f9589]) ).
cnf(s1446,plain,
spl412_40,
inference(sat_conversion,[],[f9601]) ).
cnf(s1454,plain,
( ~ spl412_69
| ~ spl412_71 ),
inference(sat_conversion,[],[f9625]) ).
cnf(s1456,plain,
( ~ spl412_67
| ~ spl412_74 ),
inference(sat_conversion,[],[f9631]) ).
cnf(s1472,plain,
( ~ spl412_51
| ~ spl412_90 ),
inference(sat_conversion,[],[f9679]) ).
cnf(s1483,plain,
( ~ spl412_40
| ~ spl412_101 ),
inference(sat_conversion,[],[f9712]) ).
cnf(s1504,plain,
( ~ spl412_477
| ~ spl412_649
| ~ spl412_686
| ~ spl412_691 ),
inference(sat_conversion,[],[f10341]) ).
cnf(s1506,plain,
~ spl412_101,
inference(rat,[],[s1483,s1446]) ).
cnf(s1518,plain,
~ spl412_51,
inference(rat,[],[s1472,s1434]) ).
cnf(s1534,plain,
~ spl412_67,
inference(rat,[],[s1456,s1418]) ).
cnf(s1537,plain,
~ spl412_69,
inference(rat,[],[s1454,s1415]) ).
cnf(s1538,plain,
spl412_691,
inference(rat,[],[s1413,s1537]) ).
cnf(s1541,plain,
spl412_686,
inference(rat,[],[s1407,s1534]) ).
cnf(s1559,plain,
spl412_649,
inference(rat,[],[s1365,s1518]) ).
cnf(s1560,plain,
~ spl412_477,
inference(rat,[],[s1504,s1538,s1541,s1559]) ).
cnf(s1628,plain,
$false,
inference(rat,[],[s861,s1560,s1506]) ).
thf(f10344,plain,
$false,
inference(avatar_sat_refutation,[],[s1628]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG259^1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n016.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 17:38:47 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.63/0.49 % (667545)Will run a generic schedule for satisfiability detection.
% 1.63/0.49 % (667554)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2493433359:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.63/0.49 % (667551)% WARNING: option uhcvi not known.
% 1.63/0.49 % (667550)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1181934885_2999 on theBenchmark for (2999ds/0Mi)
% 1.63/0.49 % (667551)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1608813805:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.63/0.49 % (667552)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1772749864:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.63/0.49 % (667553)dis+10_1_sil=32000:sp=arity:random_seed=751128473:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.63/0.49 % (667555)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1600807213:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.63/0.49 % (667556)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1729260746:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.63/0.49 % (667554)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.63/0.49 % (667551)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.63/0.49 % (667554)Instruction limit reached!
% 1.63/0.49 % (667554)------------------------------
% 1.63/0.49 % (667554)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.63/0.49 % (667554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/0.49 % (667554)CaDiCaL version: 2.1.3
% 1.63/0.49 % (667554)Termination reason: Instruction limit
% 1.63/0.49 % (667554)Termination phase: Saturation
% 1.63/0.49 % (667554)Time elapsed: 0.026 s
% 1.63/0.49 % (667554)Peak memory usage: 12 MB
% 1.63/0.49 % (667554)Instructions burned: 118 (million)
% 1.63/0.49 % (667564)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3282866505:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.63/0.49 % Exception at run slice level
% 1.63/0.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.63/0.49 % (667551)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.63/0.49 % (667553)Instruction limit reached!
% 1.63/0.49 % (667553)------------------------------
% 1.63/0.49 % (667553)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.63/0.49 % (667553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/0.49 % (667553)CaDiCaL version: 2.1.3
% 1.63/0.49 % (667553)Termination reason: Instruction limit
% 1.63/0.49 % (667553)Termination phase: Saturation
% 1.63/0.49 % (667553)Time elapsed: 0.042 s
% 1.63/0.49 % (667553)Peak memory usage: 12 MB
% 1.63/0.49 % (667553)Instructions burned: 103 (million)
% 1.63/0.49 % Exception at run slice level
% 1.63/0.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.63/0.49 % (667566)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2100074:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.63/0.49 % (667555)Instruction limit reached!
% 1.63/0.49 % (667555)------------------------------
% 1.63/0.49 % (667555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.63/0.49 % (667555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/0.49 % (667555)CaDiCaL version: 2.1.3
% 1.63/0.49 % (667555)Termination reason: Instruction limit
% 1.63/0.49 % (667555)Termination phase: Saturation
% 1.63/0.49 % (667555)Time elapsed: 0.055 s
% 1.63/0.49 % (667555)Peak memory usage: 12 MB
% 1.63/0.49 % (667555)Instructions burned: 132 (million)
% 1.63/0.49 % (667568)ott-21_1_sil=16000:fs=off:random_seed=1508781411:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.63/0.49 % (667567)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=2994666577:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.63/0.49 % (667556)Instruction limit reached!
% 1.63/0.49 % (667556)------------------------------
% 1.63/0.49 % (667556)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.63/0.49 % (667556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/0.49 % (667556)CaDiCaL version: 2.1.3
% 1.63/0.49 % (667556)Termination reason: Instruction limit
% 1.63/0.49 % (667556)Termination phase: Saturation
% 1.63/0.49 % (667556)Time elapsed: 0.066 s
% 1.63/0.49 % (667556)Peak memory usage: 13 MB
% 1.63/0.49 % (667556)Instructions burned: 159 (million)
% 1.63/0.49 % (667570)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3579457946:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 1.63/0.49 % (667567)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.63/0.49 % (667573)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1093331426:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.63/0.49 % (667568)Instruction limit reached!
% 1.63/0.49 % (667568)------------------------------
% 1.63/0.49 % (667568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.63/0.49 % (667568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/0.49 % (667568)CaDiCaL version: 2.1.3
% 1.63/0.49 % (667568)Termination reason: Instruction limit
% 1.63/0.49 % (667568)Termination phase: Saturation
% 1.63/0.49 % (667568)Time elapsed: 0.039 s
% 1.63/0.49 % (667568)Peak memory usage: 13 MB
% 1.63/0.49 % (667568)Instructions burned: 182 (million)
% 1.63/0.49 % (667567)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.63/0.49 % (667566)Instruction limit reached!
% 1.63/0.49 % (667566)------------------------------
% 1.63/0.49 % (667566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.63/0.49 % (667566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/0.49 % (667566)CaDiCaL version: 2.1.3
% 1.63/0.49 % (667566)Termination reason: Instruction limit
% 1.63/0.49 % (667566)Termination phase: Saturation
% 1.63/0.49 % (667566)Time elapsed: 0.055 s
% 1.63/0.49 % (667566)Peak memory usage: 13 MB
% 1.63/0.49 % (667566)Instructions burned: 133 (million)
% 1.63/0.49 % (667576)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3812110660:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.63/0.49 % Exception at run slice level
% 1.63/0.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.63/0.49 % (667578)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1112826896:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.63/0.49 % (667579)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=257363492:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 1.63/0.49 % (667579)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.63/0.49 % Exception at run slice level
% 1.63/0.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.63/0.49 % (667582)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3194803925:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 1.63/0.49 % (667582)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.63/0.49 % (667576) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-667545-667576"...
% 1.63/0.49 % (667576)...printing done.
% 1.63/0.49 % (667576)Refutation found. Thanks to Tanya!
% 1.63/0.49 % SZS status Theorem for theBenchmark
% 1.63/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 1.63/0.50 % (667576)------------------------------
% 1.63/0.50 % (667576)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.63/0.50 % (667576)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.63/0.50 % (667576)CaDiCaL version: 2.1.3
% 1.63/0.50 % (667576)Termination reason: Refutation
% 1.63/0.50 % (667576)Time elapsed: 0.114 s
% 1.63/0.50 % (667576)Peak memory usage: 20 MB
% 1.63/0.50 % (667576)Instructions burned: 484 (million)
% 1.63/0.50 % (667545)Success in time 0.268 s
% 1.63/0.50 % Vampire exiting
%------------------------------------------------------------------------------