%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP185^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:56:14 AM UTC 2026
% Result : Theorem 3.22s 1.86s
% Output : Refutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 129 ( 37 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 451 ( 26 ~; 16 |; 0 &; 400 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 17 ( 16 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 220 ( 217 usr; 15 con; 0-11 aty)
% Number of variables : 45 ( 0 ^; 45 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
pi: $tType ).
thf(type_def_7,type,
name: $tType ).
thf(type_def_8,type,
set_name: $tType ).
thf(type_def_9,type,
late_freeRes: $tType ).
thf(type_def_10,type,
late_subject: $tType ).
thf(type_def_11,type,
late_residual: $tType ).
thf(type_def_12,type,
noptio354675977ion_pi: $tType ).
thf(type_def_13,type,
noption_name: $tType ).
thf(type_def_14,type,
noption_pi: $tType ).
thf(type_def_15,type,
noptio1926134715n_name: $tType ).
thf(type_def_16,type,
noption_Late_freeRes: $tType ).
thf(type_def_17,type,
noptio435234344reeRes: $tType ).
thf(type_def_18,type,
noption_Late_subject: $tType ).
thf(type_def_19,type,
noptio570777408ubject: $tType ).
thf(type_def_20,type,
noptio930204083reeRes: $tType ).
thf(type_def_21,type,
noptio1065747147ubject: $tType ).
thf(func_def_0,type,
noptio1065747147ubject: $tType ).
thf(func_def_1,type,
noptio930204083reeRes: $tType ).
thf(func_def_2,type,
noptio570777408ubject: $tType ).
thf(func_def_3,type,
noptio435234344reeRes: $tType ).
thf(func_def_4,type,
noptio1926134715n_name: $tType ).
thf(func_def_5,type,
noptio354675977ion_pi: $tType ).
thf(func_def_6,type,
noption_Late_subject: $tType ).
thf(func_def_7,type,
noption_Late_freeRes: $tType ).
thf(func_def_8,type,
noption_name: $tType ).
thf(func_def_9,type,
noption_pi: $tType ).
thf(func_def_10,type,
set_name: $tType ).
thf(func_def_11,type,
late_residual: $tType ).
thf(func_def_12,type,
late_subject: $tType ).
thf(func_def_13,type,
late_freeRes: $tType ).
thf(func_def_14,type,
name: $tType ).
thf(func_def_15,type,
pi: $tType ).
thf(func_def_16,type,
bang: pi > pi ).
thf(func_def_17,type,
input: name > name > pi > pi ).
thf(func_def_18,type,
match: name > name > pi > pi ).
thf(func_def_19,type,
mismatch: name > name > pi > pi ).
thf(func_def_20,type,
output: name > name > pi > pi ).
thf(func_def_21,type,
par: pi > pi > pi ).
thf(func_def_22,type,
piNil: pi ).
thf(func_def_23,type,
res: name > pi > pi ).
thf(func_def_24,type,
sum: pi > pi > pi ).
thf(func_def_25,type,
tau: pi > pi ).
thf(func_def_26,type,
pi_rec_pi: pi > ( name > name > pi > pi > pi ) > ( pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( pi > pi > pi > pi > pi ) > ( pi > pi > pi > pi > pi ) > ( name > pi > pi > pi ) > ( pi > pi > pi ) > pi > pi ).
thf(func_def_27,type,
subs: pi > name > name > pi ).
thf(func_def_28,type,
subst_name: name > name > name > name ).
thf(func_def_29,type,
finite_finite_name: set_name > $o ).
thf(func_def_30,type,
if_name: $o > name > name > name ).
thf(func_def_31,type,
late_bangPred: pi > pi > $o ).
thf(func_def_32,type,
late_OutputR: name > name > late_freeRes ).
thf(func_def_33,type,
late_TauR: late_freeRes ).
thf(func_def_34,type,
late_BoundR: late_subject > name > pi > late_residual ).
thf(func_def_35,type,
late_FreeR: late_freeRes > pi > late_residual ).
thf(func_def_36,type,
late_r1174711868c_name: ( late_subject > name > pi > name ) > ( late_freeRes > pi > name ) > late_residual > name ).
thf(func_def_37,type,
late_residual_rec_pi: ( late_subject > name > pi > pi ) > ( late_freeRes > pi > pi ) > late_residual > pi ).
thf(func_def_38,type,
late_r124702629reeRes: ( late_subject > name > pi > late_freeRes ) > ( late_freeRes > pi > late_freeRes ) > late_residual > late_freeRes ).
thf(func_def_39,type,
late_r1347955901ubject: ( late_subject > name > pi > late_subject ) > ( late_freeRes > pi > late_subject ) > late_residual > late_subject ).
thf(func_def_40,type,
late_r1558248490ion_pi: ( late_subject > name > pi > name > noptio354675977ion_pi ) > ( late_freeRes > pi > name > noptio354675977ion_pi ) > late_residual > ( name > noptio354675977ion_pi ) > $o ).
thf(func_def_41,type,
late_r303715378n_name: ( late_subject > name > pi > name > noption_name ) > ( late_freeRes > pi > name > noption_name ) > late_residual > ( name > noption_name ) > $o ).
thf(func_def_42,type,
late_r750878080ion_pi: ( late_subject > name > pi > name > noption_pi ) > ( late_freeRes > pi > name > noption_pi ) > late_residual > ( name > noption_pi ) > $o ).
thf(func_def_43,type,
late_r1742481968t_name: ( late_subject > name > pi > name ) > ( late_freeRes > pi > name ) > late_residual > name > $o ).
thf(func_def_44,type,
late_r1261898622set_pi: ( late_subject > name > pi > pi ) > ( late_freeRes > pi > pi ) > late_residual > pi > $o ).
thf(func_def_45,type,
late_r1613948593reeRes: ( late_subject > name > pi > late_freeRes ) > ( late_freeRes > pi > late_freeRes ) > late_residual > late_freeRes > $o ).
thf(func_def_46,type,
late_r689718217ubject: ( late_subject > name > pi > late_subject ) > ( late_freeRes > pi > late_subject ) > late_residual > late_subject > $o ).
thf(func_def_47,type,
late_BoundOutputS: name > late_subject ).
thf(func_def_48,type,
late_InputS: name > late_subject ).
thf(func_def_49,type,
late_transitions: pi > late_residual > $o ).
thf(func_def_50,type,
sup_sup_set_name: set_name > set_name > set_name ).
thf(func_def_51,type,
abs_fu1394407909n_name: name > ( name > noption_name ) > name > noptio1926134715n_name ).
thf(func_def_52,type,
abs_fu1614711987ion_pi: name > ( name > noption_pi ) > name > noptio354675977ion_pi ).
thf(func_def_53,type,
abs_fu1763130856reeRes: name > ( name > noption_Late_freeRes ) > name > noptio435234344reeRes ).
thf(func_def_54,type,
abs_fu1705804544ubject: name > ( name > noption_Late_subject ) > name > noptio570777408ubject ).
thf(func_def_55,type,
abs_fu946147443reeRes: name > ( late_freeRes > pi > late_freeRes ) > name > noptio930204083reeRes ).
thf(func_def_56,type,
abs_fu888821131ubject: name > ( late_freeRes > pi > late_subject ) > name > noptio1065747147ubject ).
thf(func_def_57,type,
abs_fun_name_name: name > name > name > noption_name ).
thf(func_def_58,type,
abs_fun_name_pi: name > pi > name > noption_pi ).
thf(func_def_59,type,
abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes ).
thf(func_def_60,type,
abs_fu1904601852ubject: name > late_subject > name > noption_Late_subject ).
thf(func_def_61,type,
fresh_1742414570n_name: name > ( name > noptio1926134715n_name ) > $o ).
thf(func_def_62,type,
fresh_92802872ion_pi: name > ( name > noptio354675977ion_pi ) > $o ).
thf(func_def_63,type,
fresh_1215331279reeRes: name > ( name > noptio435234344reeRes ) > $o ).
thf(func_def_64,type,
fresh_600418535ubject: name > ( name > noptio570777408ubject ) > $o ).
thf(func_def_65,type,
fresh_111433690reeRes: name > ( name > noptio930204083reeRes ) > $o ).
thf(func_def_66,type,
fresh_1644004594ubject: name > ( name > noptio1065747147ubject ) > $o ).
thf(func_def_67,type,
fresh_1093033124n_name: name > ( name > noption_name ) > $o ).
thf(func_def_68,type,
fresh_543891186ion_pi: name > ( name > noption_pi ) > $o ).
thf(func_def_69,type,
fresh_785364841reeRes: name > ( name > noption_Late_freeRes ) > $o ).
thf(func_def_70,type,
fresh_728038529ubject: name > ( name > noption_Late_subject ) > $o ).
thf(func_def_71,type,
fresh_2081817683ion_pi: name > ( late_freeRes > pi > name > noptio354675977ion_pi ) > $o ).
thf(func_def_72,type,
fresh_808662133n_name: name > ( late_freeRes > pi > name > noption_name ) > $o ).
thf(func_def_73,type,
fresh_7927363ion_pi: name > ( late_freeRes > pi > name > noption_pi ) > $o ).
thf(func_def_74,type,
fresh_1030632537i_name: name > ( late_freeRes > pi > name ) > $o ).
thf(func_def_75,type,
fresh_1011532071_pi_pi: name > ( late_freeRes > pi > pi ) > $o ).
thf(func_def_76,type,
fresh_256112244reeRes: name > ( late_freeRes > pi > late_freeRes ) > $o ).
thf(func_def_77,type,
fresh_198785932ubject: name > ( late_freeRes > pi > late_subject ) > $o ).
thf(func_def_78,type,
fresh_876421558ion_pi: name > ( late_subject > name > pi > name > noptio354675977ion_pi ) > $o ).
thf(func_def_79,type,
fresh_62885992n_name: name > ( late_subject > name > pi > name > noption_name ) > $o ).
thf(func_def_80,type,
fresh_747777846ion_pi: name > ( late_subject > name > pi > name > noption_pi ) > $o ).
thf(func_def_81,type,
fresh_621211324i_name: name > ( late_subject > name > pi > name ) > $o ).
thf(func_def_82,type,
fresh_1438126218_pi_pi: name > ( late_subject > name > pi > pi ) > $o ).
thf(func_def_83,type,
fresh_660367079reeRes: name > ( late_subject > name > pi > late_freeRes ) > $o ).
thf(func_def_84,type,
fresh_795910143ubject: name > ( late_subject > name > pi > late_subject ) > $o ).
thf(func_def_85,type,
fresh_name_name: name > name > $o ).
thf(func_def_86,type,
fresh_name_pi: name > pi > $o ).
thf(func_def_87,type,
fresh_1641682979reeRes: name > late_freeRes > $o ).
thf(func_def_88,type,
fresh_81631222sidual: name > late_residual > $o ).
thf(func_def_89,type,
fresh_717452603ubject: name > late_subject > $o ).
thf(func_def_90,type,
supp_n352473082e_name: ( name > noption_name ) > set_name ).
thf(func_def_91,type,
supp_n468628396i_name: ( name > noption_pi ) > set_name ).
thf(func_def_92,type,
supp_n252280103s_name: ( name > noption_Late_freeRes ) > set_name ).
thf(func_def_93,type,
supp_n1630792207t_name: ( name > noption_Late_subject ) > set_name ).
thf(func_def_94,type,
supp_L979396363i_name: ( late_freeRes > pi > name > noptio354675977ion_pi ) > set_name ).
thf(func_def_95,type,
supp_L473926939e_name: ( late_freeRes > pi > name > noption_name ) > set_name ).
thf(func_def_96,type,
supp_L635439693i_name: ( late_freeRes > pi > name > noption_pi ) > set_name ).
thf(func_def_97,type,
supp_L926407557e_name: ( late_freeRes > pi > name ) > set_name ).
thf(func_def_98,type,
supp_L2052723895i_name: ( late_freeRes > pi > pi ) > set_name ).
thf(func_def_99,type,
supp_L381160156s_name: ( late_freeRes > pi > late_freeRes ) > set_name ).
thf(func_def_100,type,
supp_L1759672260t_name: ( late_freeRes > pi > late_subject ) > set_name ).
thf(func_def_101,type,
supp_L1512088218i_name: ( late_subject > name > pi > name > noptio354675977ion_pi ) > set_name ).
thf(func_def_102,type,
supp_L14705974e_name: ( late_subject > name > pi > name > noption_name ) > set_name ).
thf(func_def_103,type,
supp_L3230824i_name: ( late_subject > name > pi > name > noption_pi ) > set_name ).
thf(func_def_104,type,
supp_L538372628e_name: ( late_subject > name > pi > name ) > set_name ).
thf(func_def_105,type,
supp_L729745222i_name: ( late_subject > name > pi > pi ) > set_name ).
thf(func_def_106,type,
supp_L1178477943s_name: ( late_subject > name > pi > late_freeRes ) > set_name ).
thf(func_def_107,type,
supp_L1144036959t_name: ( late_subject > name > pi > late_subject ) > set_name ).
thf(func_def_108,type,
supp_name_name: name > set_name ).
thf(func_def_109,type,
supp_pi_name: pi > set_name ).
thf(func_def_110,type,
supp_L1228270395s_name: late_freeRes > set_name ).
thf(func_def_111,type,
supp_L1174042202l_name: late_residual > set_name ).
thf(func_def_112,type,
supp_L1174290467t_name: late_subject > set_name ).
thf(func_def_113,type,
collect_name: ( name > $o ) > set_name ).
thf(func_def_114,type,
member_name: name > set_name > $o ).
thf(func_def_115,type,
p: pi ).
thf(func_def_116,type,
pqr: pi ).
thf(func_def_117,type,
q: pi ).
thf(func_def_118,type,
qr: pi ).
thf(func_def_119,type,
q2: pi ).
thf(func_def_120,type,
r: pi ).
thf(func_def_121,type,
r2: pi ).
thf(func_def_122,type,
alpha: late_freeRes ).
thf(func_def_123,type,
a: name ).
thf(func_def_124,type,
x: name ).
thf(func_def_125,type,
y: name ).
thf(func_def_140,type,
sP0: late_subject > name > pi > name > pi > $o ).
thf(func_def_141,type,
sP1: late_subject > name > pi > pi > pi > $o ).
thf(func_def_142,type,
sP2: name > pi > late_residual > $o ).
thf(func_def_143,type,
sP3: late_residual > name > pi > $o ).
thf(func_def_144,type,
sK4: ( late_subject > $o ) > name ).
thf(func_def_145,type,
sK5: ( late_subject > $o ) > name ).
thf(func_def_146,type,
sK6: ( pi > late_residual > $o ) > late_freeRes ).
thf(func_def_147,type,
sK7: ( pi > late_residual > $o ) > pi ).
thf(func_def_148,type,
sK8: ( pi > late_residual > $o ) > pi ).
thf(func_def_149,type,
sK9: ( pi > late_residual > $o ) > name ).
thf(func_def_150,type,
sK10: ( pi > late_residual > $o ) > pi ).
thf(func_def_151,type,
sK11: ( pi > late_residual > $o ) > pi ).
thf(func_def_152,type,
sK12: ( pi > late_residual > $o ) > late_subject ).
thf(func_def_153,type,
sK13: ( late_freeRes > $o ) > name ).
thf(func_def_154,type,
sK14: ( late_freeRes > $o ) > name ).
thf(func_def_155,type,
sK15: ( late_freeRes > late_residual > $o ) > pi ).
thf(func_def_156,type,
sK16: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_157,type,
sK17: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_158,type,
sK18: ( late_freeRes > late_residual > $o ) > name ).
thf(func_def_159,type,
sK19: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_160,type,
sK20: ( late_freeRes > late_residual > $o ) > pi ).
thf(func_def_161,type,
sK21: ( late_freeRes > late_residual > $o ) > late_subject ).
thf(func_def_162,type,
sK22: late_freeRes > name ).
thf(func_def_163,type,
sK23: ( late_freeRes > late_residual > $o ) > pi ).
thf(func_def_164,type,
sK24: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_165,type,
sK25: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_166,type,
sK26: ( late_freeRes > late_residual > $o ) > late_subject ).
thf(func_def_167,type,
sK27: ( late_freeRes > late_residual > $o ) > pi ).
thf(func_def_168,type,
sK28: ( late_freeRes > late_residual > $o ) > late_freeRes ).
thf(func_def_169,type,
sK29: ( late_freeRes > late_residual > $o ) > name ).
thf(func_def_170,type,
sK30: late_subject > name > pi > name > pi > pi ).
thf(func_def_171,type,
sK31: late_subject > name > pi > name > pi > name ).
thf(func_def_172,type,
sK32: late_subject > name > pi > name > pi > pi ).
thf(func_def_173,type,
sK33: late_subject > name > pi > name > pi > late_subject ).
thf(func_def_174,type,
sK34: late_subject > name > pi > name > pi > name ).
thf(func_def_175,type,
sK35: pi > pi > name > name > late_subject > pi ).
thf(func_def_176,type,
sK36: pi > pi > name > name > late_subject > name ).
thf(func_def_177,type,
sK37: pi > pi > name > name > late_subject > name ).
thf(func_def_178,type,
sK38: pi > pi > name > name > late_subject > pi ).
thf(func_def_179,type,
sK39: late_subject > name ).
thf(func_def_180,type,
sK40: late_residual > pi > name > name > pi ).
thf(func_def_181,type,
sK41: late_residual > pi > name > name > name ).
thf(func_def_182,type,
sK42: late_residual > pi > name > name > name ).
thf(func_def_183,type,
sK43: late_subject > name > pi > pi > pi > pi ).
thf(func_def_184,type,
sK44: late_subject > name > pi > pi > pi > name ).
thf(func_def_185,type,
sK45: late_subject > name > pi > pi > pi > pi ).
thf(func_def_186,type,
sK46: late_subject > name > pi > pi > pi > late_subject ).
thf(func_def_187,type,
sK47: late_subject > name > pi > pi > pi > pi ).
thf(func_def_188,type,
sK48: pi > name > late_subject > pi > pi > pi ).
thf(func_def_189,type,
sK49: pi > name > late_subject > pi > pi > pi ).
thf(func_def_190,type,
sK50: pi > name > late_subject > pi > pi > late_subject ).
thf(func_def_191,type,
sK51: pi > name > late_subject > pi > pi > name ).
thf(func_def_192,type,
sK52: pi > name > late_subject > pi > pi > pi ).
thf(func_def_193,type,
sK53: late_subject > name ).
thf(func_def_194,type,
sK54: late_subject > name ).
thf(func_def_195,type,
sK55: pi > late_residual > pi ).
thf(func_def_196,type,
sK56: ( late_subject > late_residual > $o ) > pi ).
thf(func_def_197,type,
sK57: ( late_subject > late_residual > $o ) > late_freeRes ).
thf(func_def_198,type,
sK58: ( late_subject > late_residual > $o ) > late_subject ).
thf(func_def_199,type,
sK59: ( late_subject > late_residual > $o ) > late_subject ).
thf(func_def_200,type,
sK60: ( late_subject > late_residual > $o ) > late_subject ).
thf(func_def_201,type,
sK61: ( late_subject > late_residual > $o ) > name ).
thf(func_def_202,type,
sK62: ( late_subject > late_residual > $o ) > pi ).
thf(func_def_203,type,
sK63: ( pi > late_residual > $o ) > pi ).
thf(func_def_204,type,
sK64: ( pi > late_residual > $o ) > late_freeRes ).
thf(func_def_205,type,
sK65: ( pi > late_residual > $o ) > pi ).
thf(func_def_206,type,
sK66: ( pi > late_residual > $o ) > pi ).
thf(func_def_207,type,
sK67: ( pi > late_residual > $o ) > late_subject ).
thf(func_def_208,type,
sK68: ( pi > late_residual > $o ) > pi ).
thf(func_def_209,type,
sK69: ( pi > late_residual > $o ) > name ).
thf(func_def_210,type,
sK70: ( late_subject > late_residual > $o ) > pi ).
thf(func_def_211,type,
sK71: ( late_subject > late_residual > $o ) > late_subject ).
thf(func_def_212,type,
sK72: ( late_subject > late_residual > $o ) > late_freeRes ).
thf(func_def_213,type,
sK73: ( late_subject > late_residual > $o ) > late_subject ).
thf(func_def_214,type,
sK74: ( late_subject > late_residual > $o ) > late_subject ).
thf(func_def_215,type,
sK75: ( late_subject > late_residual > $o ) > pi ).
thf(func_def_216,type,
sK76: ( late_subject > late_residual > $o ) > name ).
thf(func_def_217,type,
sK77: name > ( pi > $o ) > late_freeRes > pi > pi ).
thf(func_def_218,type,
sK78: pi > late_residual > pi ).
thf(func_def_219,type,
sK79: late_freeRes > name ).
thf(func_def_220,type,
sK80: late_freeRes > name ).
thf(func_def_221,type,
sK81: late_residual > name > pi > pi ).
thf(func_def_222,type,
sK82: late_residual > name > pi > name ).
thf(func_def_223,type,
sK83: late_residual > name > pi > name ).
thf(func_def_224,type,
sK84: late_residual > name > pi > pi ).
thf(func_def_225,type,
sK85: name > pi > late_residual > name ).
thf(func_def_226,type,
sK86: name > pi > late_residual > pi ).
thf(func_def_227,type,
sK87: name > pi > late_residual > name ).
thf(func_def_228,type,
sK88: name > pi > late_residual > late_subject ).
thf(func_def_229,type,
sK89: name > pi > late_residual > pi ).
thf(func_def_230,type,
sK90: pi > late_residual > name > name ).
thf(func_def_231,type,
sK91: pi > late_residual > name > late_freeRes ).
thf(func_def_232,type,
sK92: pi > late_residual > name > pi ).
thf(func_def_233,type,
sK93: pi > late_residual > name > pi ).
thf(func_def_234,type,
sK94: pi > name ).
thf(func_def_235,type,
sK95: late_subject > name > pi > ( pi > $o ) > pi > pi ).
thf(func_def_236,type,
sK96: late_subject > name > pi > ( pi > $o ) > pi > pi ).
thf(func_def_237,type,
sK97: ( late_residual > $o ) > name ).
thf(func_def_238,type,
sK98: ( late_residual > $o ) > late_subject ).
thf(func_def_239,type,
sK99: ( late_residual > $o ) > pi ).
thf(func_def_240,type,
sK100: ( late_residual > $o ) > pi ).
thf(func_def_241,type,
sK101: ( late_residual > $o ) > late_freeRes ).
thf(func_def_242,type,
sK102: name > late_freeRes > pi > pi > pi ).
thf(func_def_243,type,
sK103: name > late_freeRes > pi > pi > late_freeRes ).
thf(func_def_244,type,
sK104: name > late_freeRes > pi > pi > name ).
thf(func_def_245,type,
sK105: name > late_freeRes > pi > pi > pi ).
thf(func_def_247,type,
ph107:
!>[X0: $tType] : X0 ).
thf(f1405,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1404,f1158]) ).
thf(f1158,plain,
( ( late_transitions @ r @ ( late_BoundR @ ( late_InputS @ a ) @ x @ r2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f721]) ).
thf(f721,plain,
( ( late_transitions @ r @ ( late_BoundR @ ( late_InputS @ a ) @ x @ r2 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f720]) ).
thf(f720,plain,
late_transitions @ r @ ( late_BoundR @ ( late_InputS @ a ) @ x @ r2 ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
late_transitions @ r @ ( late_BoundR @ ( late_InputS @ a ) @ x @ r2 ),
file('/export/starexec/sandbox2/tmp/tmp.etxS7Hgr06/DTF2THF_17125.p',fact_12_cClose2_Ohyps_I2_J) ).
thf(f1404,plain,
( ( late_transitions @ r @ ( late_BoundR @ ( late_InputS @ a ) @ x @ r2 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f1399]) ).
thf(f1399,plain,
( ( $true != $true )
| ( ( late_transitions @ r @ ( late_BoundR @ ( late_InputS @ a ) @ x @ r2 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f1398,f1366]) ).
thf(f1366,plain,
( ( late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ ( par @ p @ q2 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f801]) ).
thf(f801,plain,
( ( late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ ( par @ p @ q2 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f800]) ).
thf(f800,plain,
late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ ( par @ p @ q2 ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ ( par @ p @ q2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.etxS7Hgr06/DTF2THF_17125.p',fact_13__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_Aa_060_092_060nu_062y_062_A_092_060prec_062_AP_A_092_060parallel_062_AQ_H_092_060close_062) ).
thf(f1398,plain,
! [X0: name] :
( ( $true
!= ( late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ X0 ) @ y @ ( par @ p @ q2 ) ) ) )
| ( ( late_transitions @ r @ ( late_BoundR @ ( late_InputS @ X0 ) @ x @ r2 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f1388,f1169]) ).
thf(f1169,plain,
( ( fresh_name_pi @ y @ r )
= $true ),
inference(cnf_transformation,[status(thm)],[f569]) ).
thf(f569,plain,
( ( fresh_name_pi @ y @ r )
= $true ),
inference(fool_elimination,[status(thm)],[f568]) ).
thf(f568,plain,
fresh_name_pi @ y @ r,
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
fresh_name_pi @ y @ r,
file('/export/starexec/sandbox2/tmp/tmp.etxS7Hgr06/DTF2THF_17125.p',fact_3_cClose2_Ohyps_I9_J) ).
thf(f1388,plain,
! [X0: name] :
( ( $true
!= ( late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ X0 ) @ y @ ( par @ p @ q2 ) ) ) )
| ( ( fresh_name_pi @ y @ r )
!= $true )
| ( ( late_transitions @ r @ ( late_BoundR @ ( late_InputS @ X0 ) @ x @ r2 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1386]) ).
thf(f1386,plain,
! [X0: name] :
( ( $true != $true )
| ( ( late_transitions @ r @ ( late_BoundR @ ( late_InputS @ X0 ) @ x @ r2 ) )
!= $true )
| ( ( fresh_name_pi @ y @ r )
!= $true )
| ( $true
!= ( late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ X0 ) @ y @ ( par @ p @ q2 ) ) ) ) ),
inference(superposition,[status(thm)],[f1154,f1277]) ).
thf(f1277,plain,
! [X2: name,X3: name,X0: pi,X1: name,X6: pi,X4: pi,X5: pi] :
( ( ( late_transitions @ ( par @ X6 @ X5 ) @ ( late_FreeR @ late_TauR @ ( res @ X2 @ ( par @ X0 @ ( subs @ X4 @ X1 @ X2 ) ) ) ) )
= $true )
| ( ( fresh_name_pi @ X2 @ X5 )
!= $true )
| ( ( late_transitions @ X5 @ ( late_BoundR @ ( late_InputS @ X3 ) @ X1 @ X4 ) )
!= $true )
| ( ( late_transitions @ X6 @ ( late_BoundR @ ( late_BoundOutputS @ X3 ) @ X2 @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f947]) ).
thf(f947,plain,
! [X0: pi,X1: name,X2: name,X3: name,X4: pi,X5: pi,X6: pi] :
( ( ( late_transitions @ X5 @ ( late_BoundR @ ( late_InputS @ X3 ) @ X1 @ X4 ) )
!= $true )
| ( ( late_transitions @ X6 @ ( late_BoundR @ ( late_BoundOutputS @ X3 ) @ X2 @ X0 ) )
!= $true )
| ( ( late_transitions @ ( par @ X6 @ X5 ) @ ( late_FreeR @ late_TauR @ ( res @ X2 @ ( par @ X0 @ ( subs @ X4 @ X1 @ X2 ) ) ) ) )
= $true )
| ( ( fresh_name_pi @ X2 @ X5 )
!= $true ) ),
inference(flattening,[status(thm)],[f946]) ).
thf(f946,plain,
! [X0: pi,X1: name,X2: name,X3: name,X4: pi,X5: pi,X6: pi] :
( ( ( late_transitions @ ( par @ X6 @ X5 ) @ ( late_FreeR @ late_TauR @ ( res @ X2 @ ( par @ X0 @ ( subs @ X4 @ X1 @ X2 ) ) ) ) )
= $true )
| ( ( fresh_name_pi @ X2 @ X5 )
!= $true )
| ( ( late_transitions @ X5 @ ( late_BoundR @ ( late_InputS @ X3 ) @ X1 @ X4 ) )
!= $true )
| ( ( late_transitions @ X6 @ ( late_BoundR @ ( late_BoundOutputS @ X3 ) @ X2 @ X0 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f541]) ).
thf(f541,plain,
! [X0: pi,X1: name,X2: name,X3: name,X4: pi,X5: pi,X6: pi] :
( ( ( late_transitions @ X6 @ ( late_BoundR @ ( late_BoundOutputS @ X3 ) @ X2 @ X0 ) )
= $true )
=> ( ( ( late_transitions @ X5 @ ( late_BoundR @ ( late_InputS @ X3 ) @ X1 @ X4 ) )
= $true )
=> ( ( ( fresh_name_pi @ X2 @ X5 )
= $true )
=> ( ( late_transitions @ ( par @ X6 @ X5 ) @ ( late_FreeR @ late_TauR @ ( res @ X2 @ ( par @ X0 @ ( subs @ X4 @ X1 @ X2 ) ) ) ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f540]) ).
thf(f540,plain,
! [X0: pi,X1: name,X2: name,X3: name,X4: pi,X5: pi,X6: pi] :
( ( late_transitions @ X6 @ ( late_BoundR @ ( late_BoundOutputS @ X3 ) @ X2 @ X0 ) )
=> ( ( late_transitions @ X5 @ ( late_BoundR @ ( late_InputS @ X3 ) @ X1 @ X4 ) )
=> ( ( fresh_name_pi @ X2 @ X5 )
=> ( late_transitions @ ( par @ X6 @ X5 ) @ ( late_FreeR @ late_TauR @ ( res @ X2 @ ( par @ X0 @ ( subs @ X4 @ X1 @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,axiom,
! [X6: pi,X0: name,X13: name,X8: name,X7: pi,X4: pi,X3: pi] :
( ( late_transitions @ X3 @ ( late_BoundR @ ( late_BoundOutputS @ X8 ) @ X13 @ X6 ) )
=> ( ( late_transitions @ X4 @ ( late_BoundR @ ( late_InputS @ X8 ) @ X0 @ X7 ) )
=> ( ( fresh_name_pi @ X13 @ X4 )
=> ( late_transitions @ ( par @ X3 @ X4 ) @ ( late_FreeR @ late_TauR @ ( res @ X13 @ ( par @ X6 @ ( subs @ X7 @ X0 @ X13 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.etxS7Hgr06/DTF2THF_17125.p',fact_24_Late__Semantics_OClose2) ).
thf(f1154,plain,
( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ ( par @ p @ q2 ) @ ( subs @ r2 @ x @ y ) ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f888]) ).
thf(f888,plain,
( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ ( par @ p @ q2 ) @ ( subs @ r2 @ x @ y ) ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f791]) ).
thf(f791,plain,
( ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ ( par @ p @ q2 ) @ ( subs @ r2 @ x @ y ) ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f790]) ).
thf(f790,plain,
~ ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ ( par @ p @ q2 ) @ ( subs @ r2 @ x @ y ) ) ) ) ),
inference(rectify,[status(thm)],[f354]) ).
thf(f354,negated_conjecture,
~ ( late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ ( par @ p @ q2 ) @ ( subs @ r2 @ x @ y ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f353]) ).
thf(f353,conjecture,
late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ ( par @ p @ q2 ) @ ( subs @ r2 @ x @ y ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.etxS7Hgr06/DTF2THF_17125.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP185^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n006.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 08:29:00 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : ITP185^1 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.46 % Domain : Interactive Theorem Proving
% 0.19/0.46 % Problem : Sledgehammer Strong_Late_Sim_SC problem prob_529__3413750_1
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Des21]
% 0.19/0.46 % Names : Strong_Late_Sim_SC/prob_529__3413750_1 [Des21]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.67 v9.1.0, 0.50 v9.0.0, 0.60 v8.2.0, 0.62 v8.1.0, 0.64 v7.5.0
% 0.19/0.46 % Syntax : Number of formulae : 479 ( 196 unt; 126 typ; 0 def)
% 0.19/0.46 % Number of atoms : 1123 ( 360 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 16 ( 3 avg)
% 0.19/0.46 % Number of connectives : 5344 ( 181 ~; 22 |; 43 &;4203 @)
% 0.19/0.46 % ( 0 <=>; 895 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 27 ( 9 avg)
% 0.19/0.46 % Number of types : 17 ( 16 usr)
% 0.19/0.46 % Number of type conns : 758 ( 758 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 113 ( 110 usr; 15 con; 0-11 aty)
% 0.19/0.46 % Number of variables : 1964 ( 71 ^;1871 !; 22 ?;1964 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 15:31:28.483
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % Could-be-implicit typings (16)
% 0.19/0.46 thf(ty_n_t__Nominal__Onoption_I_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_Mt__Late____Semantics__Osubject_J_J_J,type,
% 0.19/0.46 noptio1065747147ubject: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Nominal__Onoption_I_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_Mt__Late____Semantics__OfreeRes_J_J_J,type,
% 0.19/0.46 noptio930204083reeRes: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__Osubject_J_J_J,type,
% 0.19/0.46 noptio570777408ubject: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__OfreeRes_J_J_J,type,
% 0.19/0.46 noptio435234344reeRes: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Oname_J_J_J,type,
% 0.19/0.46 noptio1926134715n_name: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 0.19/0.46 noptio354675977ion_pi: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__Osubject_J,type,
% 0.19/0.46 noption_Late_subject: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__OfreeRes_J,type,
% 0.19/0.46 noption_Late_freeRes: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Nominal__Onoption_It__Agent__Oname_J,type,
% 0.19/0.46 noption_name: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Nominal__Onoption_It__Agent__Opi_J,type,
% 0.19/0.46 noption_pi: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Set__Oset_It__Agent__Oname_J,type,
% 0.19/0.46 set_name: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Late____Semantics__Oresidual,type,
% 0.19/0.46 late_residual: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Late____Semantics__Osubject,type,
% 0.19/0.46 late_subject: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Late____Semantics__OfreeRes,type,
% 0.19/0.46 late_freeRes: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Agent__Oname,type,
% 0.19/0.46 name: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Agent__Opi,type,
% 0.19/0.46 pi: $tType ).
% 0.19/0.46
% 0.19/0.46 % Explicit typings (110)
% 0.19/0.46 thf(sy_c_Agent_Opi_OBang,type,
% 0.19/0.46 bang: pi > pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Agent_Opi_OInput,type,
% 0.19/0.46 input: name > name > pi > pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Agent_Opi_OMatch,type,
% 0.19/0.46 match: name > name > pi > pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Agent_Opi_OMismatch,type,
% 0.19/0.46 mismatch: name > name > pi > pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Agent_Opi_OOutput,type,
% 0.19/0.46 output: name > name > pi > pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Agent_Opi_OPar,type,
% 0.19/0.46 par: pi > pi > pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Agent_Opi_OPiNil,type,
% 0.19/0.46 piNil: pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Agent_Opi_ORes,type,
% 0.19/0.46 res: name > pi > pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Agent_Opi_OSum,type,
% 0.19/0.46 sum: pi > pi > pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Agent_Opi_OTau,type,
% 0.19/0.46 tau: pi > pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Agent_Opi_Opi__rec_001t__Agent__Opi,type,
% 0.19/0.46 pi_rec_pi: pi > ( name > name > pi > pi > pi ) > ( pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( pi > pi > pi > pi > pi ) > ( pi > pi > pi > pi > pi ) > ( name > pi > pi > pi ) > ( pi > pi > pi ) > pi > pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Agent_Osubs,type,
% 0.19/0.46 subs: pi > name > name > pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Agent_Osubst__name,type,
% 0.19/0.46 subst_name: name > name > name > name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Finite__Set_Ofinite_001t__Agent__Oname,type,
% 0.19/0.46 finite_finite_name: set_name > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_If_001t__Agent__Oname,type,
% 0.19/0.46 if_name: $o > name > name > name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Late__Semantics_ObangPred,type,
% 0.19/0.46 late_bangPred: pi > pi > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 0.19/0.46 late_OutputR: name > name > late_freeRes ).
% 0.19/0.46
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% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_M_062_It__Agent__Oname_Mt__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J_J_J_J_001t__Agent__Oname,type,
% 0.19/0.46 supp_L1512088218i_name: ( late_subject > name > pi > name > noptio354675977ion_pi ) > set_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Oname_J_J_J_J_J_001t__Agent__Oname,type,
% 0.19/0.46 supp_L14705974e_name: ( late_subject > name > pi > name > noption_name ) > set_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_M_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J_J_001t__Agent__Oname,type,
% 0.19/0.46 supp_L3230824i_name: ( late_subject > name > pi > name > noption_pi ) > set_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_Mt__Agent__Oname_J_J_J_001t__Agent__Oname,type,
% 0.19/0.46 supp_L538372628e_name: ( late_subject > name > pi > name ) > set_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_Mt__Agent__Opi_J_J_J_001t__Agent__Oname,type,
% 0.19/0.46 supp_L729745222i_name: ( late_subject > name > pi > pi ) > set_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_Mt__Late____Semantics__OfreeRes_J_J_J_001t__Agent__Oname,type,
% 0.19/0.46 supp_L1178477943s_name: ( late_subject > name > pi > late_freeRes ) > set_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Osupp_001_062_It__Late____Semantics__Osubject_M_062_It__Agent__Oname_M_062_It__Agent__Opi_Mt__Late____Semantics__Osubject_J_J_J_001t__Agent__Oname,type,
% 0.19/0.46 supp_L1144036959t_name: ( late_subject > name > pi > late_subject ) > set_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Osupp_001t__Agent__Oname_001t__Agent__Oname,type,
% 0.19/0.46 supp_name_name: name > set_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Osupp_001t__Agent__Opi_001t__Agent__Oname,type,
% 0.19/0.46 supp_pi_name: pi > set_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Osupp_001t__Late____Semantics__OfreeRes_001t__Agent__Oname,type,
% 0.19/0.46 supp_L1228270395s_name: late_freeRes > set_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Osupp_001t__Late____Semantics__Oresidual_001t__Agent__Oname,type,
% 0.19/0.46 supp_L1174042202l_name: late_residual > set_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Nominal_Osupp_001t__Late____Semantics__Osubject_001t__Agent__Oname,type,
% 0.19/0.46 supp_L1174290467t_name: late_subject > set_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Set_OCollect_001t__Agent__Oname,type,
% 0.19/0.46 collect_name: ( name > $o ) > set_name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_member_001t__Agent__Oname,type,
% 0.19/0.46 member_name: name > set_name > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_P,type,
% 0.19/0.46 p: pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_PQR____,type,
% 0.19/0.46 pqr: pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_Q,type,
% 0.19/0.46 q: pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_QR____,type,
% 0.19/0.46 qr: pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_Q_H____,type,
% 0.19/0.46 q2: pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_R,type,
% 0.19/0.46 r: pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_R_H____,type,
% 0.19/0.46 r2: pi ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v__092_060alpha_062____,type,
% 0.19/0.46 alpha: late_freeRes ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_a____,type,
% 0.19/0.46 a: name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_x____,type,
% 0.19/0.46 x: name ).
% 0.19/0.46
% 0.19/0.46 thf(sy_v_y____,type,
% 0.19/0.46 y: name ).
% 0.19/0.46
% 0.19/0.46 % Relevant facts (349)
% 0.19/0.46 thf(fact_0_cClose2_Ohyps_I14_J,axiom,
% 0.19/0.46 alpha = late_TauR ).
% 0.19/0.46
% 0.19/0.46 % cClose2.hyps(14)
% 0.19/0.46 thf(fact_1_cClose2_Ohyps_I10_J,axiom,
% 0.19/0.46 y != a ).
% 0.19/0.46
% 0.19/0.46 % cClose2.hyps(10)
% 0.19/0.46 thf(fact_2_cClose2_Ohyps_I5_J,axiom,
% 0.19/0.46 x != a ).
% 0.19/0.46
% 0.19/0.46 % cClose2.hyps(5)
% 0.19/0.46 thf(fact_3_cClose2_Ohyps_I9_J,axiom,
% 0.19/0.46 fresh_name_pi @ y @ r ).
% 0.19/0.46
% 0.19/0.46 % cClose2.hyps(9)
% 0.19/0.46 thf(fact_4_cClose2_Ohyps_I6_J,axiom,
% 0.19/0.46 x != y ).
% 0.19/0.46
% 0.19/0.46 % cClose2.hyps(6)
% 0.19/0.46 thf(fact_5_cClose2_Ohyps_I8_J,axiom,
% 0.19/0.46 fresh_name_pi @ y @ q ).
% 0.19/0.46
% 0.19/0.46 % cClose2.hyps(8)
% 0.19/0.46 thf(fact_6_cClose2_Ohyps_I3_J,axiom,
% 0.19/0.46 fresh_name_pi @ x @ q ).
% 0.19/0.46
% 0.19/0.46 % cClose2.hyps(3)
% 0.19/0.46 thf(fact_7_cClose2_Ohyps_I13_J,axiom,
% 0.19/0.46 fresh_name_pi @ y @ p ).
% 0.19/0.46
% 0.19/0.46 % cClose2.hyps(13)
% 0.19/0.46 thf(fact_8_cClose2_Ohyps_I12_J,axiom,
% 0.19/0.46 fresh_name_pi @ x @ p ).
% 0.19/0.46
% 0.19/0.46 % cClose2.hyps(12)
% 0.19/0.46 thf(fact_9_cClose2_Ohyps_I4_J,axiom,
% 0.19/0.46 fresh_name_pi @ x @ r ).
% 0.19/0.46
% 0.19/0.46 % cClose2.hyps(4)
% 0.19/0.46 thf(fact_10_cClose2_Ohyps_I7_J,axiom,
% 0.19/0.46 fresh_name_pi @ x @ q2 ).
% 0.19/0.46
% 0.19/0.46 % cClose2.hyps(7)
% 0.19/0.46 thf(fact_11_cClose2_Ohyps_I11_J,axiom,
% 0.19/0.46 fresh_name_pi @ y @ r2 ).
% 0.19/0.46
% 0.19/0.46 % cClose2.hyps(11)
% 0.19/0.46 thf(fact_12_cClose2_Ohyps_I2_J,axiom,
% 0.19/0.46 late_transitions @ r @ ( late_BoundR @ ( late_InputS @ a ) @ x @ r2 ) ).
% 0.19/0.46
% 0.19/0.46 % cClose2.hyps(2)
% 0.19/0.46 thf(fact_13__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_Aa_060_092_060nu_062y_062_A_092_060prec_062_AP_A_092_060parallel_062_AQ_H_092_060close_062,axiom,
% 0.19/0.46 late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ ( par @ p @ q2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % \<open>P \<parallel> Q \<longmapsto> a<\<nu>y> \<prec> P \<parallel> Q'\<close>
% 0.19/0.46 thf(fact_14_cClose2_Ohyps_I1_J,axiom,
% 0.19/0.46 late_transitions @ q @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ q2 ) ).
% 0.19/0.46
% 0.19/0.46 % cClose2.hyps(1)
% 0.19/0.46 thf(fact_15_cPar2_Ohyps,axiom,
% 0.19/0.46 late_transitions @ ( par @ q @ r ) @ ( late_FreeR @ alpha @ qr ) ).
% 0.19/0.46
% 0.19/0.46 % cPar2.hyps
% 0.19/0.46 thf(fact_16_Free_Ohyps,axiom,
% 0.19/0.46 late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ) ).
% 0.19/0.46
% 0.19/0.46 % Free.hyps
% 0.19/0.46 thf(fact_17_simps_I9_J,axiom,
% 0.19/0.46 ! [X: name,C: name,D: name,P: pi] :
% 0.19/0.46 ( ( X != C )
% 0.19/0.46 => ( ( X != D )
% 0.19/0.46 => ( ( subs @ ( res @ X @ P ) @ C @ D )
% 0.19/0.46 = ( res @ X @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % simps(9)
% 0.19/0.46 thf(fact_18_simps_I8_J,axiom,
% 0.19/0.46 ! [P: pi,Q: pi,C: name,D: name] :
% 0.19/0.46 ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 0.19/0.47 = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simps(8)
% 0.19/0.47 thf(fact_19_Par1F,axiom,
% 0.19/0.47 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Par1F
% 0.19/0.47 thf(fact_20_Par2F,axiom,
% 0.19/0.47 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Par2F
% 0.19/0.47 thf(fact_21_subst__identity,axiom,
% 0.19/0.47 ! [P: pi,A: name] :
% 0.19/0.47 ( ( subs @ P @ A @ A )
% 0.19/0.47 = P ) ).
% 0.19/0.47
% 0.19/0.47 % subst_identity
% 0.19/0.47 thf(fact_22_pi_Odistinct_I85_J,axiom,
% 0.19/0.47 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.19/0.47 ( ( par @ Pi1 @ Pi2 )
% 0.19/0.47 != ( res @ Name @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(85)
% 0.19/0.47 thf(fact_23_Late__Semantics_OClose1,axiom,
% 0.19/0.47 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.Close1
% 0.19/0.47 thf(fact_24_Late__Semantics_OClose2,axiom,
% 0.19/0.47 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ Q )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.Close2
% 0.19/0.47 thf(fact_25_transitions_OClose1,axiom,
% 0.19/0.47 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ Q )
% 0.19/0.47 => ( ( X != A )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q2 )
% 0.19/0.47 => ( ( Y != A )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ P2 )
% 0.19/0.47 => ( ( X != Y )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transitions.Close1
% 0.19/0.47 thf(fact_26_transitions_OClose2,axiom,
% 0.19/0.47 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ Q )
% 0.19/0.47 => ( ( X != A )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P2 )
% 0.19/0.47 => ( ( Y != A )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ Q2 )
% 0.19/0.47 => ( ( X != Y )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transitions.Close2
% 0.19/0.47 thf(fact_27_substRes2,axiom,
% 0.19/0.47 ! [B: name,P: pi,A: name] :
% 0.19/0.47 ( ( fresh_name_pi @ B @ P )
% 0.19/0.47 => ( ( res @ A @ P )
% 0.19/0.47 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % substRes2
% 0.19/0.47 thf(fact_28_substRes3,axiom,
% 0.19/0.47 ! [B: name,P: pi,A: name] :
% 0.19/0.47 ( ( fresh_name_pi @ B @ P )
% 0.19/0.47 => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 0.19/0.47 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % substRes3
% 0.19/0.47 thf(fact_29_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 0.19/0.47 ! [X1: name,Y1: name] :
% 0.19/0.47 ( ( ( late_BoundOutputS @ X1 )
% 0.19/0.47 = ( late_BoundOutputS @ Y1 ) )
% 0.19/0.47 = ( X1 = Y1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.subject.inject(2)
% 0.19/0.47 thf(fact_30_pi_Ofresh_I8_J,axiom,
% 0.19/0.47 ! [A: name,X2: pi,X1: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 0.19/0.47 = ( ( fresh_name_pi @ A @ X2 )
% 0.19/0.47 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(8)
% 0.19/0.47 thf(fact_31_substTrans,axiom,
% 0.19/0.47 ! [B: name,P: pi,A: name,C: name] :
% 0.19/0.47 ( ( fresh_name_pi @ B @ P )
% 0.19/0.47 => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C )
% 0.19/0.47 = ( subs @ P @ A @ C ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % substTrans
% 0.19/0.47 thf(fact_32_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 0.19/0.47 ! [Name2: name,Name: name] :
% 0.19/0.47 ( ( late_InputS @ Name2 )
% 0.19/0.47 != ( late_BoundOutputS @ Name ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.subject.distinct(1)
% 0.19/0.47 thf(fact_33_name__exists__fresh,axiom,
% 0.19/0.47 ! [X: late_subject] :
% 0.19/0.47 ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_717452603ubject @ C2 @ X ) ).
% 0.19/0.47
% 0.19/0.47 % name_exists_fresh
% 0.19/0.47 thf(fact_34_name__exists__fresh,axiom,
% 0.19/0.47 ! [X: late_freeRes] :
% 0.19/0.47 ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_1641682979reeRes @ C2 @ X ) ).
% 0.19/0.47
% 0.19/0.47 % name_exists_fresh
% 0.19/0.47 thf(fact_35_name__exists__fresh,axiom,
% 0.19/0.47 ! [X: name] :
% 0.19/0.47 ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_name_name @ C2 @ X ) ).
% 0.19/0.47
% 0.19/0.47 % name_exists_fresh
% 0.19/0.47 thf(fact_36_name__exists__fresh,axiom,
% 0.19/0.47 ! [X: pi] :
% 0.19/0.47 ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_name_pi @ C2 @ X ) ).
% 0.19/0.47
% 0.19/0.47 % name_exists_fresh
% 0.19/0.47 thf(fact_37_subject_Oinducts,axiom,
% 0.19/0.47 ! [P: late_subject > $o,Subject: late_subject] :
% 0.19/0.47 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 0.19/0.47 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 0.19/0.47 => ( P @ Subject ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % subject.inducts
% 0.19/0.47 thf(fact_38_residual_Ostrong__inducts,axiom,
% 0.19/0.47 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.19/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.19/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.strong_inducts
% 0.19/0.47 thf(fact_39_residual_Ostrong__inducts,axiom,
% 0.19/0.47 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.19/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.19/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.strong_inducts
% 0.19/0.47 thf(fact_40_residual_Ostrong__inducts,axiom,
% 0.19/0.47 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ( fresh_name_name @ Name3 @ Z2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.19/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.19/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.strong_inducts
% 0.19/0.47 thf(fact_41_residual_Ostrong__inducts,axiom,
% 0.19/0.47 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ Name3 @ Z2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.19/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.19/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.strong_inducts
% 0.19/0.47 thf(fact_42_residual_Ostrong__induct,axiom,
% 0.19/0.47 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.19/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.19/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.strong_induct
% 0.19/0.47 thf(fact_43_residual_Ostrong__induct,axiom,
% 0.19/0.47 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.19/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.19/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.strong_induct
% 0.19/0.47 thf(fact_44_residual_Ostrong__induct,axiom,
% 0.19/0.47 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ( fresh_name_name @ Name3 @ Z2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.19/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.19/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.strong_induct
% 0.19/0.47 thf(fact_45_residual_Ostrong__induct,axiom,
% 0.19/0.47 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ Name3 @ Z2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 0.19/0.47 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.19/0.47 => ( P @ Z @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.strong_induct
% 0.19/0.47 thf(fact_46_freshBoundDerivative_I2_J,axiom,
% 0.19/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.47 => ( ( Y != X )
% 0.19/0.47 => ( fresh_name_pi @ Y @ P2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % freshBoundDerivative(2)
% 0.19/0.47 thf(fact_47_freshRes,axiom,
% 0.19/0.47 ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 0.19/0.47
% 0.19/0.47 % freshRes
% 0.19/0.47 thf(fact_48_residual_Oinducts,axiom,
% 0.19/0.47 ! [P: late_residual > $o,Residual: late_residual] :
% 0.19/0.47 ( ! [Subject2: late_subject,Name3: name,Pi3: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) )
% 0.19/0.47 => ( ! [FreeRes: late_freeRes,Pi3: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 0.19/0.47 => ( P @ Residual ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.inducts
% 0.19/0.47 thf(fact_49_residual_Odistinct_I1_J,axiom,
% 0.19/0.47 ! [Subject: late_subject,Name2: name,Pi4: pi,FreeRes2: late_freeRes,Pi: pi] :
% 0.19/0.47 ( ( late_BoundR @ Subject @ Name2 @ Pi4 )
% 0.19/0.47 != ( late_FreeR @ FreeRes2 @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.distinct(1)
% 0.19/0.47 thf(fact_50_fresh__fact2,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi] :
% 0.19/0.47 ( ( A != B )
% 0.19/0.47 => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_fact2
% 0.19/0.47 thf(fact_51_fresh__fact1,axiom,
% 0.19/0.47 ! [A: name,P: pi,C: name,B: name] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ P )
% 0.19/0.47 => ( ( A != C )
% 0.19/0.47 => ( fresh_name_pi @ A @ ( subs @ P @ B @ C ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_fact1
% 0.19/0.47 thf(fact_52_mem__Collect__eq,axiom,
% 0.19/0.47 ! [A: name,P: name > $o] :
% 0.19/0.47 ( ( member_name @ A @ ( collect_name @ P ) )
% 0.19/0.47 = ( P @ A ) ) ).
% 0.19/0.47
% 0.19/0.47 % mem_Collect_eq
% 0.19/0.47 thf(fact_53_Collect__mem__eq,axiom,
% 0.19/0.47 ! [A2: set_name] :
% 0.19/0.47 ( ( collect_name
% 0.19/0.47 @ ^ [X3: name] : ( member_name @ X3 @ A2 ) )
% 0.19/0.47 = A2 ) ).
% 0.19/0.47
% 0.19/0.47 % Collect_mem_eq
% 0.19/0.47 thf(fact_54_Collect__cong,axiom,
% 0.19/0.47 ! [P: name > $o,Q: name > $o] :
% 0.19/0.47 ( ! [X4: name] :
% 0.19/0.47 ( ( P @ X4 )
% 0.19/0.47 = ( Q @ X4 ) )
% 0.19/0.47 => ( ( collect_name @ P )
% 0.19/0.47 = ( collect_name @ Q ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Collect_cong
% 0.19/0.47 thf(fact_55_forget,axiom,
% 0.19/0.47 ! [A: name,P: pi,B: name] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ P )
% 0.19/0.47 => ( ( subs @ P @ A @ B )
% 0.19/0.47 = P ) ) ).
% 0.19/0.47
% 0.19/0.47 % forget
% 0.19/0.47 thf(fact_56_parCasesB,axiom,
% 0.19/0.47 ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 0.19/0.47 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.47 => ( ! [P3: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 0.19/0.47 => ( Prop @ ( par @ P3 @ Q ) ) )
% 0.19/0.47 => ( ! [Q3: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 0.19/0.47 => ( Prop @ ( par @ P @ Q3 ) ) )
% 0.19/0.47 => ( Prop @ PQ ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % parCasesB
% 0.19/0.47 thf(fact_57_Late__Semantics_OPar2B,axiom,
% 0.19/0.47 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.Par2B
% 0.19/0.47 thf(fact_58_Late__Semantics_OPar1B,axiom,
% 0.19/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.Par1B
% 0.19/0.47 thf(fact_59_pi_Oinject_I7_J,axiom,
% 0.19/0.47 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.19/0.47 ( ( ( par @ X2 @ X1 )
% 0.19/0.47 = ( par @ Y2 @ Y1 ) )
% 0.19/0.47 = ( ( X2 = Y2 )
% 0.19/0.47 & ( X1 = Y1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inject(7)
% 0.19/0.47 thf(fact_60_freshFreeDerivative_I2_J,axiom,
% 0.19/0.47 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.47 => ( fresh_name_pi @ Y @ P2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % freshFreeDerivative(2)
% 0.19/0.47 thf(fact_61_residual_Oinject_I2_J,axiom,
% 0.19/0.47 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 0.19/0.47 ( ( ( late_FreeR @ X2 @ X1 )
% 0.19/0.47 = ( late_FreeR @ Y2 @ Y1 ) )
% 0.19/0.47 = ( ( X2 = Y2 )
% 0.19/0.47 & ( X1 = Y1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.inject(2)
% 0.19/0.47 thf(fact_62_transitions_OComm2,axiom,
% 0.19/0.47 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.47 => ( ( X != A )
% 0.19/0.47 => ( ( X != B )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P2 )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transitions.Comm2
% 0.19/0.47 thf(fact_63_transitions_OComm1,axiom,
% 0.19/0.47 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.47 => ( ( X != A )
% 0.19/0.47 => ( ( X != B )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q2 )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transitions.Comm1
% 0.19/0.47 thf(fact_64_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 0.19/0.47 ! [X1: name,Y1: name] :
% 0.19/0.47 ( ( ( late_InputS @ X1 )
% 0.19/0.47 = ( late_InputS @ Y1 ) )
% 0.19/0.47 = ( X1 = Y1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics1.subject.inject(1)
% 0.19/0.47 thf(fact_65_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 0.19/0.47 ! [X2: name,Y2: name] :
% 0.19/0.47 ( ( ( late_BoundOutputS @ X2 )
% 0.19/0.47 = ( late_BoundOutputS @ Y2 ) )
% 0.19/0.47 = ( X2 = Y2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics1.subject.inject(2)
% 0.19/0.47 thf(fact_66_Late__Semantics_OComm2,axiom,
% 0.19/0.47 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.Comm2
% 0.19/0.47 thf(fact_67_Late__Semantics_OComm1,axiom,
% 0.19/0.47 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 0.19/0.47 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.Comm1
% 0.19/0.47 thf(fact_68_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 0.19/0.47 ! [X1: name,X2: name] :
% 0.19/0.47 ( ( late_InputS @ X1 )
% 0.19/0.47 != ( late_BoundOutputS @ X2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics1.subject.distinct(1)
% 0.19/0.47 thf(fact_69_subject_Oexhaust,axiom,
% 0.19/0.47 ! [Y: late_subject] :
% 0.19/0.47 ( ! [X12: name] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( late_InputS @ X12 ) )
% 0.19/0.47 => ~ ! [X22: name] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( late_BoundOutputS @ X22 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % subject.exhaust
% 0.19/0.47 thf(fact_70_Open,axiom,
% 0.19/0.47 ! [P: pi,A: name,B: name,P2: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 0.19/0.47 => ( ( A != B )
% 0.19/0.47 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Open
% 0.19/0.47 thf(fact_71_freeRes_Ofresh_I1_J,axiom,
% 0.19/0.47 ! [A: name,X2: name,X1: name] :
% 0.19/0.47 ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 0.19/0.47 = ( ( fresh_name_name @ A @ X2 )
% 0.19/0.47 & ( fresh_name_name @ A @ X1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % freeRes.fresh(1)
% 0.19/0.47 thf(fact_72_Late__Semantics_OfreeRes_Oinject,axiom,
% 0.19/0.47 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 0.19/0.47 ( ( ( late_OutputR @ X2 @ X1 )
% 0.19/0.47 = ( late_OutputR @ Y2 @ Y1 ) )
% 0.19/0.47 = ( ( X2 = Y2 )
% 0.19/0.47 & ( X1 = Y1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.freeRes.inject
% 0.19/0.47 thf(fact_73_Late__Semantics1_OfreeRes_Oinject,axiom,
% 0.19/0.47 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 0.19/0.47 ( ( ( late_OutputR @ X11 @ X122 )
% 0.19/0.47 = ( late_OutputR @ Y11 @ Y12 ) )
% 0.19/0.47 = ( ( X11 = Y11 )
% 0.19/0.47 & ( X122 = Y12 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics1.freeRes.inject
% 0.19/0.47 thf(fact_74_freeRes_Ofresh_I2_J,axiom,
% 0.19/0.47 ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 0.19/0.47
% 0.19/0.47 % freeRes.fresh(2)
% 0.19/0.47 thf(fact_75_residual_Ofresh_I2_J,axiom,
% 0.19/0.47 ! [A: name,X2: late_freeRes,X1: pi] :
% 0.19/0.47 ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 0.19/0.47 = ( ( fresh_1641682979reeRes @ A @ X2 )
% 0.19/0.47 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.fresh(2)
% 0.19/0.47 thf(fact_76_subject_Ofresh_I2_J,axiom,
% 0.19/0.47 ! [A: name,X1: name] :
% 0.19/0.47 ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 0.19/0.47 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % subject.fresh(2)
% 0.19/0.47 thf(fact_77_subject_Ofresh_I1_J,axiom,
% 0.19/0.47 ! [A: name,X1: name] :
% 0.19/0.47 ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 0.19/0.47 = ( fresh_name_name @ A @ X1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % subject.fresh(1)
% 0.19/0.47 thf(fact_78_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 0.19/0.47 ! [X11: name,X122: name] :
% 0.19/0.47 ( ( late_OutputR @ X11 @ X122 )
% 0.19/0.47 != late_TauR ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics1.freeRes.distinct(1)
% 0.19/0.47 thf(fact_79_freeRes_Oexhaust,axiom,
% 0.19/0.47 ! [Y: late_freeRes] :
% 0.19/0.47 ( ! [X112: name,X123: name] :
% 0.19/0.47 ( Y
% 0.19/0.47 != ( late_OutputR @ X112 @ X123 ) )
% 0.19/0.47 => ( Y = late_TauR ) ) ).
% 0.19/0.47
% 0.19/0.47 % freeRes.exhaust
% 0.19/0.47 thf(fact_80_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name] :
% 0.19/0.47 ( ( late_OutputR @ Name1 @ Name22 )
% 0.19/0.47 != late_TauR ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.freeRes.distinct(1)
% 0.19/0.47 thf(fact_81_freeRes_Oinducts,axiom,
% 0.19/0.47 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 0.19/0.47 ( ! [Name12: name,Name23: name] : ( P @ ( late_OutputR @ Name12 @ Name23 ) )
% 0.19/0.47 => ( ( P @ late_TauR )
% 0.19/0.47 => ( P @ FreeRes3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % freeRes.inducts
% 0.19/0.47 thf(fact_82_resCases_H,axiom,
% 0.19/0.47 ! [X: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 0.19/0.47 => ( ! [P4: pi,A3: name,B2: name] :
% 0.19/0.47 ( ( ( res @ X @ P )
% 0.19/0.47 = ( res @ B2 @ P4 ) )
% 0.19/0.47 => ! [P3: pi] :
% 0.19/0.47 ( ( Rs
% 0.19/0.47 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B2 @ P3 ) )
% 0.19/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B2 ) @ P3 ) )
% 0.19/0.47 => ( A3 = B2 ) ) ) )
% 0.19/0.47 => ( ! [P4: pi,A3: late_subject,X4: name,P3: pi,Y3: name] :
% 0.19/0.47 ( ( ( res @ X @ P )
% 0.19/0.47 = ( res @ Y3 @ P4 ) )
% 0.19/0.47 => ( ( Rs
% 0.19/0.47 = ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P3 ) ) )
% 0.19/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X4 @ P3 ) )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 0.19/0.47 => ( ( Y3 != X4 )
% 0.19/0.47 => ( ( fresh_name_pi @ X4 @ P4 )
% 0.19/0.47 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) )
% 0.19/0.47 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y3: name] :
% 0.19/0.47 ( ( ( res @ X @ P )
% 0.19/0.47 = ( res @ Y3 @ P4 ) )
% 0.19/0.47 => ( ( Rs
% 0.19/0.47 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P3 ) ) )
% 0.19/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.19/0.47 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % resCases'
% 0.19/0.47 thf(fact_83_freshResidual,axiom,
% 0.19/0.47 ! [P: pi,Rs: late_residual,X: name] :
% 0.19/0.47 ( ( late_transitions @ P @ Rs )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % freshResidual
% 0.19/0.47 thf(fact_84_resCasesF,axiom,
% 0.19/0.47 ! [X: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
% 0.19/0.47 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 0.19/0.47 => ( ! [P3: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 0.19/0.47 => ( F @ ( res @ X @ P3 ) ) ) )
% 0.19/0.47 => ( F @ XP ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % resCasesF
% 0.19/0.47 thf(fact_85_resCasesF_H,axiom,
% 0.19/0.47 ! [X: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.19/0.47 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.19/0.47 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y3: name] :
% 0.19/0.47 ( ( ( res @ X @ P )
% 0.19/0.47 = ( res @ Y3 @ P4 ) )
% 0.19/0.47 => ( ( ( late_FreeR @ Alpha @ P2 )
% 0.19/0.47 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P3 ) ) )
% 0.19/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 0.19/0.47 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % resCasesF'
% 0.19/0.47 thf(fact_86_ResF,axiom,
% 0.19/0.47 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ Y @ Alpha )
% 0.19/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % ResF
% 0.19/0.47 thf(fact_87_Late__Semantics_OResB,axiom,
% 0.19/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Y @ A )
% 0.19/0.47 => ( ( Y != X )
% 0.19/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.ResB
% 0.19/0.47 thf(fact_88_freshFreeDerivative_I1_J,axiom,
% 0.19/0.47 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.47 => ( fresh_1641682979reeRes @ Y @ Alpha ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % freshFreeDerivative(1)
% 0.19/0.47 thf(fact_89_freshBoundDerivative_I1_J,axiom,
% 0.19/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ Y @ P )
% 0.19/0.47 => ( fresh_717452603ubject @ Y @ A ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % freshBoundDerivative(1)
% 0.19/0.47 thf(fact_90_resCasesB_H,axiom,
% 0.19/0.47 ! [X5: name,P: pi,A: late_subject,Y4: name,P2: pi] :
% 0.19/0.47 ( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A @ Y4 @ P2 ) )
% 0.19/0.47 => ( ! [P4: pi,A3: name,B2: name] :
% 0.19/0.47 ( ( ( res @ X5 @ P )
% 0.19/0.47 = ( res @ B2 @ P4 ) )
% 0.19/0.47 => ! [P3: pi] :
% 0.19/0.47 ( ( ( late_BoundR @ A @ Y4 @ P2 )
% 0.19/0.47 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B2 @ P3 ) )
% 0.19/0.47 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B2 ) @ P3 ) )
% 0.19/0.47 => ( A3 = B2 ) ) ) )
% 0.19/0.47 => ~ ! [P4: pi,A3: late_subject,X4: name,P3: pi,Y3: name] :
% 0.19/0.47 ( ( ( res @ X5 @ P )
% 0.19/0.47 = ( res @ Y3 @ P4 ) )
% 0.19/0.47 => ( ( ( late_BoundR @ A @ Y4 @ P2 )
% 0.19/0.47 = ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P3 ) ) )
% 0.19/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X4 @ P3 ) )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 0.19/0.47 => ( ( Y3 != X4 )
% 0.19/0.47 => ( ( fresh_name_pi @ X4 @ P4 )
% 0.19/0.47 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % resCasesB'
% 0.19/0.47 thf(fact_91_parCasesB_H,axiom,
% 0.19/0.47 ! [P: pi,Q: pi,B: late_subject,Y: name,P2: pi] :
% 0.19/0.47 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 0.19/0.47 => ( ! [P4: pi,A3: late_subject,X4: name,P3: pi,Q4: pi] :
% 0.19/0.47 ( ( ( par @ P @ Q )
% 0.19/0.47 = ( par @ P4 @ Q4 ) )
% 0.19/0.47 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 0.19/0.47 = ( late_BoundR @ A3 @ X4 @ ( par @ P3 @ Q4 ) ) )
% 0.19/0.47 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X4 @ P3 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X4 @ P4 )
% 0.19/0.47 => ( ( fresh_name_pi @ X4 @ Q4 )
% 0.19/0.47 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) )
% 0.19/0.47 => ~ ! [Q4: pi,A3: late_subject,X4: name,Q3: pi,P4: pi] :
% 0.19/0.47 ( ( ( par @ P @ Q )
% 0.19/0.47 = ( par @ P4 @ Q4 ) )
% 0.19/0.47 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 0.19/0.47 = ( late_BoundR @ A3 @ X4 @ ( par @ P4 @ Q3 ) ) )
% 0.19/0.47 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A3 @ X4 @ Q3 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X4 @ P4 )
% 0.19/0.47 => ( ( fresh_name_pi @ X4 @ Q4 )
% 0.19/0.47 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % parCasesB'
% 0.19/0.47 thf(fact_92_transitions_OPar1B,axiom,
% 0.19/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X @ A )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transitions.Par1B
% 0.19/0.47 thf(fact_93_transitions_OPar2B,axiom,
% 0.19/0.47 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ Q )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X @ A )
% 0.19/0.47 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transitions.Par2B
% 0.19/0.47 thf(fact_94_transitions_OResB,axiom,
% 0.19/0.47 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 0.19/0.47 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Y @ A )
% 0.19/0.47 => ( ( Y != X )
% 0.19/0.47 => ( ( fresh_name_pi @ X @ P )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X @ A )
% 0.19/0.47 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transitions.ResB
% 0.19/0.47 thf(fact_95_resTauOutputTrans,axiom,
% 0.19/0.47 ! [X: name,P: pi,A: name,B: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % resTauOutputTrans
% 0.19/0.47 thf(fact_96_resOutputTauTrans,axiom,
% 0.19/0.47 ! [X: name,A: name,B: name,P: pi,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % resOutputTauTrans
% 0.19/0.47 thf(fact_97_resOutputInputTrans,axiom,
% 0.19/0.47 ! [X: name,A: name,B: name,P: pi,C: name,Y: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C ) @ Y @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % resOutputInputTrans
% 0.19/0.47 thf(fact_98_name__fresh,axiom,
% 0.19/0.47 ( fresh_name_name
% 0.19/0.47 = ( ^ [A4: name,B3: name] : ( A4 != B3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % name_fresh
% 0.19/0.47 thf(fact_99_pi_Ofresh_I3_J,axiom,
% 0.19/0.47 ! [A: name,X1: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ ( tau @ X1 ) )
% 0.19/0.47 = ( fresh_name_pi @ A @ X1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(3)
% 0.19/0.47 thf(fact_100_simps_I2_J,axiom,
% 0.19/0.47 ! [P: pi,C: name,D: name] :
% 0.19/0.47 ( ( subs @ ( tau @ P ) @ C @ D )
% 0.19/0.47 = ( tau @ ( subs @ P @ C @ D ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simps(2)
% 0.19/0.47 thf(fact_101_pi_Ofresh_I2_J,axiom,
% 0.19/0.47 ! [A: name,X32: name,X2: name,X1: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ ( output @ X32 @ X2 @ X1 ) )
% 0.19/0.47 = ( ( fresh_name_name @ A @ X32 )
% 0.19/0.47 & ( fresh_name_name @ A @ X2 )
% 0.19/0.47 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(2)
% 0.19/0.47 thf(fact_102_pi_Odistinct_I19_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 0.19/0.47 ( ( output @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( tau @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(19)
% 0.19/0.47 thf(fact_103_pi_Oinject_I1_J,axiom,
% 0.19/0.47 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.19/0.47 ( ( ( output @ X32 @ X2 @ X1 )
% 0.19/0.47 = ( output @ Y32 @ Y2 @ Y1 ) )
% 0.19/0.47 = ( ( X32 = Y32 )
% 0.19/0.47 & ( X2 = Y2 )
% 0.19/0.47 & ( X1 = Y1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inject(1)
% 0.19/0.47 thf(fact_104_pi_Oinject_I2_J,axiom,
% 0.19/0.47 ! [X1: pi,Y1: pi] :
% 0.19/0.47 ( ( ( tau @ X1 )
% 0.19/0.47 = ( tau @ Y1 ) )
% 0.19/0.47 = ( X1 = Y1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inject(2)
% 0.19/0.47 thf(fact_105_pi_Odistinct_I29_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.19/0.47 ( ( output @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(29)
% 0.19/0.47 thf(fact_106_pi_Odistinct_I31_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name: name,Pi: pi] :
% 0.19/0.47 ( ( output @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( res @ Name @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(31)
% 0.19/0.47 thf(fact_107_pi_Odistinct_I43_J,axiom,
% 0.19/0.47 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.19/0.47 ( ( tau @ Pi4 )
% 0.19/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(43)
% 0.19/0.47 thf(fact_108_pi_Odistinct_I45_J,axiom,
% 0.19/0.47 ! [Pi4: pi,Name: name,Pi: pi] :
% 0.19/0.47 ( ( tau @ Pi4 )
% 0.19/0.47 != ( res @ Name @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(45)
% 0.19/0.47 thf(fact_109_resTrans_I1_J,axiom,
% 0.19/0.47 ! [X: name,B: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( output @ X @ B @ P ) ) @ Rs ) ).
% 0.19/0.47
% 0.19/0.47 % resTrans(1)
% 0.19/0.47 thf(fact_110_outputBoundTrans,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,C: late_subject,X: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_BoundR @ C @ X @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % outputBoundTrans
% 0.19/0.47 thf(fact_111_outputFreshTrans,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.19/0.47 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.19/0.47 => ~ ( ( fresh_1641682979reeRes @ A @ Alpha )
% 0.19/0.47 | ( fresh_1641682979reeRes @ B @ Alpha ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % outputFreshTrans
% 0.19/0.47 thf(fact_112_tauBoundTrans,axiom,
% 0.19/0.47 ! [P: pi,A: late_subject,X: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A @ X @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % tauBoundTrans
% 0.19/0.47 thf(fact_113_resTauBoundTrans,axiom,
% 0.19/0.47 ! [X: name,P: pi,A: late_subject,Y: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_BoundR @ A @ Y @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % resTauBoundTrans
% 0.19/0.47 thf(fact_114_Output,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi] : ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P ) ) ).
% 0.19/0.47
% 0.19/0.47 % Output
% 0.19/0.47 thf(fact_115_outputIneqTrans,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,C: name,D: name,P2: pi] :
% 0.19/0.47 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ P2 ) )
% 0.19/0.47 => ~ ( ( A != C )
% 0.19/0.47 | ( B != D ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % outputIneqTrans
% 0.19/0.47 thf(fact_116_outputCases_H,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( output @ A @ B @ P ) @ Rs )
% 0.19/0.47 => ~ ! [A3: name,B2: name,P4: pi] :
% 0.19/0.47 ( ( ( A = A3 )
% 0.19/0.47 & ( B = B2 )
% 0.19/0.47 & ( P = P4 ) )
% 0.19/0.47 => ( Rs
% 0.19/0.47 != ( late_FreeR @ ( late_OutputR @ A3 @ B2 ) @ P4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % outputCases'
% 0.19/0.47 thf(fact_117_outputCases,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.19/0.47 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.19/0.47 => ( ( ( Alpha
% 0.19/0.47 = ( late_OutputR @ A @ B ) )
% 0.19/0.47 => ( ( P = P2 )
% 0.19/0.47 => ( Prop @ ( late_OutputR @ A @ B ) @ P ) ) )
% 0.19/0.47 => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % outputCases
% 0.19/0.47 thf(fact_118_outputTauTrans,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % outputTauTrans
% 0.19/0.47 thf(fact_119_tauOutputTrans,axiom,
% 0.19/0.47 ! [P: pi,A: name,B: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % tauOutputTrans
% 0.19/0.47 thf(fact_120_Tau,axiom,
% 0.19/0.47 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 0.19/0.47
% 0.19/0.47 % Tau
% 0.19/0.47 thf(fact_121_tauCases_H,axiom,
% 0.19/0.47 ! [P: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 0.19/0.47 => ~ ! [P4: pi] :
% 0.19/0.47 ( ( ( tau @ P )
% 0.19/0.47 = ( tau @ P4 ) )
% 0.19/0.47 => ( Rs
% 0.19/0.47 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % tauCases'
% 0.19/0.47 thf(fact_122_tauCases,axiom,
% 0.19/0.47 ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 0.19/0.47 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 0.19/0.47 => ( ( ( Alpha = late_TauR )
% 0.19/0.47 => ( ( P = P2 )
% 0.19/0.47 => ( Prop @ late_TauR @ P ) ) )
% 0.19/0.47 => ( Prop @ Alpha @ P2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % tauCases
% 0.19/0.47 thf(fact_123_resOutputOutputTrans,axiom,
% 0.19/0.47 ! [X: name,A: name,P: pi,B: name,Y: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( output @ A @ X @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % resOutputOutputTrans
% 0.19/0.47 thf(fact_124_resInputBoundOutputTrans,axiom,
% 0.19/0.47 ! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % resInputBoundOutputTrans
% 0.19/0.47 thf(fact_125_residual_Ofresh_I1_J,axiom,
% 0.19/0.47 ! [A: name,X32: late_subject,X1: name,X2: pi] :
% 0.19/0.47 ( ( fresh_81631222sidual @ A @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 0.19/0.47 = ( ( fresh_717452603ubject @ A @ X32 )
% 0.19/0.47 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.fresh(1)
% 0.19/0.47 thf(fact_126_simps_I3_J,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,C: name,D: name] :
% 0.19/0.47 ( ( subs @ ( output @ A @ B @ P ) @ C @ D )
% 0.19/0.47 = ( output @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simps(3)
% 0.19/0.47 thf(fact_127_inputIneqTrans,axiom,
% 0.19/0.47 ! [A: name,X: name,P: pi,B: late_subject,Y: name,P2: pi] :
% 0.19/0.47 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 0.19/0.47 => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 0.19/0.47
% 0.19/0.47 % inputIneqTrans
% 0.19/0.47 thf(fact_128_transitions_OInput,axiom,
% 0.19/0.47 ! [X: name,A: name,P: pi] :
% 0.19/0.47 ( ( X != A )
% 0.19/0.47 => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % transitions.Input
% 0.19/0.47 thf(fact_129_substInput,axiom,
% 0.19/0.47 ! [X: name,B: name,C: name,A: name,P: pi] :
% 0.19/0.47 ( ( X != B )
% 0.19/0.47 => ( ( X != C )
% 0.19/0.47 => ( ( subs @ ( input @ A @ X @ P ) @ B @ C )
% 0.19/0.47 = ( input @ ( subst_name @ A @ B @ C ) @ X @ ( subs @ P @ B @ C ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % substInput
% 0.19/0.47 thf(fact_130_simps_I4_J,axiom,
% 0.19/0.47 ! [X: name,A: name,C: name,D: name,P: pi] :
% 0.19/0.47 ( ( X != A )
% 0.19/0.47 => ( ( X != C )
% 0.19/0.47 => ( ( X != D )
% 0.19/0.47 => ( ( subs @ ( input @ A @ X @ P ) @ C @ D )
% 0.19/0.47 = ( input @ ( subst_name @ A @ C @ D ) @ X @ ( subs @ P @ C @ D ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simps(4)
% 0.19/0.47 thf(fact_131_pi_Ofresh_I9_J,axiom,
% 0.19/0.47 ! [A: name,X1: name,X2: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 0.19/0.47 = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(9)
% 0.19/0.47 thf(fact_132_pi_Ofresh_I4_J,axiom,
% 0.19/0.47 ! [A: name,X32: name,X1: name,X2: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ ( input @ X32 @ X1 @ X2 ) )
% 0.19/0.47 = ( ( fresh_name_name @ A @ X32 )
% 0.19/0.47 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(4)
% 0.19/0.47 thf(fact_133_pi_Oinject_I3_J,axiom,
% 0.19/0.47 ! [X32: name,X1: name,X2: pi,Y32: name,Y1: name,Y2: pi] :
% 0.19/0.47 ( ( ( input @ X32 @ X1 @ X2 )
% 0.19/0.47 = ( input @ Y32 @ Y1 @ Y2 ) )
% 0.19/0.47 = ( ( X32 = Y32 )
% 0.19/0.47 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.19/0.47 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inject(3)
% 0.19/0.47 thf(fact_134_subst__name__def,axiom,
% 0.19/0.47 ( subst_name
% 0.19/0.47 = ( ^ [A4: name,B3: name,C3: name] : ( if_name @ ( A4 = B3 ) @ C3 @ A4 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % subst_name_def
% 0.19/0.47 thf(fact_135_pi_Oinject_I8_J,axiom,
% 0.19/0.47 ! [X1: name,X2: pi,Y1: name,Y2: pi] :
% 0.19/0.47 ( ( ( res @ X1 @ X2 )
% 0.19/0.47 = ( res @ Y1 @ Y2 ) )
% 0.19/0.47 = ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.19/0.47 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inject(8)
% 0.19/0.47 thf(fact_136_residual_Oinject_I1_J,axiom,
% 0.19/0.47 ! [X32: late_subject,X1: name,X2: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 0.19/0.47 ( ( ( late_BoundR @ X32 @ X1 @ X2 )
% 0.19/0.47 = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 0.19/0.47 = ( ( X32 = Y32 )
% 0.19/0.47 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 0.19/0.47 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.inject(1)
% 0.19/0.47 thf(fact_137_name__fresh__abs,axiom,
% 0.19/0.47 ! [B: name,A: name,X: late_subject] :
% 0.19/0.47 ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_717452603ubject @ B @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % name_fresh_abs
% 0.19/0.47 thf(fact_138_name__fresh__abs,axiom,
% 0.19/0.47 ! [B: name,A: name,X: late_freeRes] :
% 0.19/0.47 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % name_fresh_abs
% 0.19/0.47 thf(fact_139_name__fresh__abs,axiom,
% 0.19/0.47 ! [B: name,A: name,X: name] :
% 0.19/0.47 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_name_name @ B @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % name_fresh_abs
% 0.19/0.47 thf(fact_140_name__fresh__abs,axiom,
% 0.19/0.47 ! [B: name,A: name,X: pi] :
% 0.19/0.47 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_name_pi @ B @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % name_fresh_abs
% 0.19/0.47 thf(fact_141_abs__fresh_I1_J,axiom,
% 0.19/0.47 ! [B: name,A: name,X: late_subject] :
% 0.19/0.47 ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_717452603ubject @ B @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(1)
% 0.19/0.47 thf(fact_142_abs__fresh_I1_J,axiom,
% 0.19/0.47 ! [B: name,A: name,X: late_freeRes] :
% 0.19/0.47 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(1)
% 0.19/0.47 thf(fact_143_abs__fresh_I1_J,axiom,
% 0.19/0.47 ! [B: name,A: name,X: name] :
% 0.19/0.47 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_name_name @ B @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(1)
% 0.19/0.47 thf(fact_144_abs__fresh_I1_J,axiom,
% 0.19/0.47 ! [B: name,A: name,X: pi] :
% 0.19/0.47 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_name_pi @ B @ X ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(1)
% 0.19/0.47 thf(fact_145_pi_Odistinct_I55_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.19/0.47 ( ( input @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(55)
% 0.19/0.47 thf(fact_146_pi_Odistinct_I57_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name: name,Pi: pi] :
% 0.19/0.47 ( ( input @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( res @ Name @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(57)
% 0.19/0.47 thf(fact_147_pi_Odistinct_I21_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.19/0.47 ( ( output @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(21)
% 0.19/0.47 thf(fact_148_pi_Odistinct_I35_J,axiom,
% 0.19/0.47 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.19/0.47 ( ( tau @ Pi4 )
% 0.19/0.47 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(35)
% 0.19/0.47 thf(fact_149_inputCases_H,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( input @ A @ B @ P ) @ Rs )
% 0.19/0.47 => ~ ! [X4: name,A3: name,P4: pi] :
% 0.19/0.47 ( ( ( A = A3 )
% 0.19/0.47 & ( ( abs_fun_name_pi @ B @ P )
% 0.19/0.47 = ( abs_fun_name_pi @ X4 @ P4 ) ) )
% 0.19/0.47 => ( ( Rs
% 0.19/0.47 = ( late_BoundR @ ( late_InputS @ A3 ) @ X4 @ P4 ) )
% 0.19/0.47 => ( X4 = A3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % inputCases'
% 0.19/0.47 thf(fact_150_resTrans_I2_J,axiom,
% 0.19/0.47 ! [X: name,Y: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% 0.19/0.47
% 0.19/0.47 % resTrans(2)
% 0.19/0.47 thf(fact_151_inputFreeTrans,axiom,
% 0.19/0.47 ! [A: name,X: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % inputFreeTrans
% 0.19/0.47 thf(fact_152_resInputFreeTrans,axiom,
% 0.19/0.47 ! [X: name,A: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % resInputFreeTrans
% 0.19/0.47 thf(fact_153_inputBoundOutputTrans,axiom,
% 0.19/0.47 ! [A: name,X: name,P: pi,B: name,Y: name,P2: pi] :
% 0.19/0.47 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P2 ) ) ).
% 0.19/0.47
% 0.19/0.47 % inputBoundOutputTrans
% 0.19/0.47 thf(fact_154_Late__Semantics_OInput,axiom,
% 0.19/0.47 ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 0.19/0.47
% 0.19/0.47 % Late_Semantics.Input
% 0.19/0.47 thf(fact_155_simps_I5_J,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,C: name,D: name] :
% 0.19/0.47 ( ( subs @ ( match @ A @ B @ P ) @ C @ D )
% 0.19/0.47 = ( match @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simps(5)
% 0.19/0.47 thf(fact_156_simps_I6_J,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,C: name,D: name] :
% 0.19/0.47 ( ( subs @ ( mismatch @ A @ B @ P ) @ C @ D )
% 0.19/0.47 = ( mismatch @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simps(6)
% 0.19/0.47 thf(fact_157_pi_Ofresh_I5_J,axiom,
% 0.19/0.47 ! [A: name,X32: name,X2: name,X1: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ ( match @ X32 @ X2 @ X1 ) )
% 0.19/0.47 = ( ( fresh_name_name @ A @ X32 )
% 0.19/0.47 & ( fresh_name_name @ A @ X2 )
% 0.19/0.47 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(5)
% 0.19/0.47 thf(fact_158_pi_Ofresh_I6_J,axiom,
% 0.19/0.47 ! [A: name,X32: name,X2: name,X1: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ ( mismatch @ X32 @ X2 @ X1 ) )
% 0.19/0.47 = ( ( fresh_name_name @ A @ X32 )
% 0.19/0.47 & ( fresh_name_name @ A @ X2 )
% 0.19/0.47 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(6)
% 0.19/0.47 thf(fact_159_pi_Odistinct_I61_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.19/0.47 ( ( match @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(61)
% 0.19/0.47 thf(fact_160_pi_Oinject_I4_J,axiom,
% 0.19/0.47 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.19/0.47 ( ( ( match @ X32 @ X2 @ X1 )
% 0.19/0.47 = ( match @ Y32 @ Y2 @ Y1 ) )
% 0.19/0.47 = ( ( X32 = Y32 )
% 0.19/0.47 & ( X2 = Y2 )
% 0.19/0.47 & ( X1 = Y1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inject(4)
% 0.19/0.47 thf(fact_161_pi_Oinject_I5_J,axiom,
% 0.19/0.47 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 0.19/0.47 ( ( ( mismatch @ X32 @ X2 @ X1 )
% 0.19/0.47 = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 0.19/0.47 = ( ( X32 = Y32 )
% 0.19/0.47 & ( X2 = Y2 )
% 0.19/0.47 & ( X1 = Y1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inject(5)
% 0.19/0.47 thf(fact_162_Mismatch,axiom,
% 0.19/0.47 ! [P: pi,Rs: late_residual,A: name,B: name] :
% 0.19/0.47 ( ( late_transitions @ P @ Rs )
% 0.19/0.47 => ( ( A != B )
% 0.19/0.47 => ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Mismatch
% 0.19/0.47 thf(fact_163_Match,axiom,
% 0.19/0.47 ! [P: pi,Rs: late_residual,B: name] :
% 0.19/0.47 ( ( late_transitions @ P @ Rs )
% 0.19/0.47 => ( late_transitions @ ( match @ B @ B @ P ) @ Rs ) ) ).
% 0.19/0.47
% 0.19/0.47 % Match
% 0.19/0.47 thf(fact_164_mismatchCases_H,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 0.19/0.47 => ~ ! [P4: pi,A3: name,B2: name] :
% 0.19/0.47 ( ( ( A = A3 )
% 0.19/0.47 & ( B = B2 )
% 0.19/0.47 & ( P = P4 ) )
% 0.19/0.47 => ( ( late_transitions @ P4 @ Rs )
% 0.19/0.47 => ( A3 = B2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % mismatchCases'
% 0.19/0.47 thf(fact_165_mismatchTrans,axiom,
% 0.19/0.47 ! [A: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ~ ( late_transitions @ ( mismatch @ A @ A @ P ) @ Rs ) ).
% 0.19/0.47
% 0.19/0.47 % mismatchTrans
% 0.19/0.47 thf(fact_166_mismatchCases,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 0.19/0.47 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 0.19/0.47 => ( ( ( late_transitions @ P @ Rs )
% 0.19/0.47 => ( ( A != B )
% 0.19/0.47 => ( F @ A @ B ) ) )
% 0.19/0.47 => ( F @ A @ B ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % mismatchCases
% 0.19/0.47 thf(fact_167_matchCases_H,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 0.19/0.47 => ~ ! [P4: pi] :
% 0.19/0.47 ( ( ( B = A )
% 0.19/0.47 & ( P = P4 ) )
% 0.19/0.47 => ~ ( late_transitions @ P4 @ Rs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % matchCases'
% 0.19/0.47 thf(fact_168_matchTrans,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 0.19/0.47 => ( A = B ) ) ).
% 0.19/0.47
% 0.19/0.47 % matchTrans
% 0.19/0.47 thf(fact_169_matchCases,axiom,
% 0.19/0.47 ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 0.19/0.47 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 0.19/0.47 => ( ( ( late_transitions @ P @ Rs )
% 0.19/0.47 => ( ( A = B )
% 0.19/0.47 => ( F @ A @ A ) ) )
% 0.19/0.47 => ( F @ A @ B ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % matchCases
% 0.19/0.47 thf(fact_170_pi_Odistinct_I65_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.19/0.47 ( ( match @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(65)
% 0.19/0.47 thf(fact_171_pi_Odistinct_I73_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.19/0.47 ( ( mismatch @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(73)
% 0.19/0.47 thf(fact_172_pi_Odistinct_I67_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name: name,Pi: pi] :
% 0.19/0.47 ( ( match @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( res @ Name @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(67)
% 0.19/0.47 thf(fact_173_pi_Odistinct_I75_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name: name,Pi: pi] :
% 0.19/0.47 ( ( mismatch @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( res @ Name @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(75)
% 0.19/0.47 thf(fact_174_pi_Odistinct_I49_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.19/0.47 ( ( input @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(49)
% 0.19/0.47 thf(fact_175_pi_Odistinct_I51_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.19/0.47 ( ( input @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(51)
% 0.19/0.47 thf(fact_176_pi_Odistinct_I23_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.19/0.47 ( ( output @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(23)
% 0.19/0.47 thf(fact_177_pi_Odistinct_I25_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.19/0.47 ( ( output @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(25)
% 0.19/0.47 thf(fact_178_pi_Odistinct_I37_J,axiom,
% 0.19/0.47 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.19/0.47 ( ( tau @ Pi4 )
% 0.19/0.47 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(37)
% 0.19/0.47 thf(fact_179_pi_Odistinct_I39_J,axiom,
% 0.19/0.47 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 0.19/0.47 ( ( tau @ Pi4 )
% 0.19/0.47 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(39)
% 0.19/0.47 thf(fact_180_abs__fun__eq1,axiom,
% 0.19/0.47 ! [A: name,X: name,Y: name] :
% 0.19/0.47 ( ( ( abs_fun_name_name @ A @ X )
% 0.19/0.47 = ( abs_fun_name_name @ A @ Y ) )
% 0.19/0.47 = ( X = Y ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fun_eq1
% 0.19/0.47 thf(fact_181_abs__fun__eq1,axiom,
% 0.19/0.47 ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 0.19/0.47 ( ( ( abs_fu681348580reeRes @ A @ X )
% 0.19/0.47 = ( abs_fu681348580reeRes @ A @ Y ) )
% 0.19/0.47 = ( X = Y ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fun_eq1
% 0.19/0.47 thf(fact_182_abs__fun__eq1,axiom,
% 0.19/0.47 ! [A: name,X: late_subject,Y: late_subject] :
% 0.19/0.47 ( ( ( abs_fu1904601852ubject @ A @ X )
% 0.19/0.47 = ( abs_fu1904601852ubject @ A @ Y ) )
% 0.19/0.47 = ( X = Y ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fun_eq1
% 0.19/0.47 thf(fact_183_abs__fun__eq1,axiom,
% 0.19/0.47 ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 0.19/0.47 ( ( ( abs_fu1614711987ion_pi @ A @ X )
% 0.19/0.47 = ( abs_fu1614711987ion_pi @ A @ Y ) )
% 0.19/0.47 = ( X = Y ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fun_eq1
% 0.19/0.47 thf(fact_184_abs__fun__eq1,axiom,
% 0.19/0.47 ! [A: name,X: pi,Y: pi] :
% 0.19/0.47 ( ( ( abs_fun_name_pi @ A @ X )
% 0.19/0.47 = ( abs_fun_name_pi @ A @ Y ) )
% 0.19/0.47 = ( X = Y ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fun_eq1
% 0.19/0.47 thf(fact_185_pi_Ostrong__inducts,axiom,
% 0.19/0.47 ! [P: late_subject > pi > $o,Z: late_subject,Pi4: pi] :
% 0.19/0.47 ( ! [Z2: late_subject] : ( P @ Z2 @ piNil )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ( fresh_717452603ubject @ Name23 @ Z2 )
% 0.19/0.47 => ( ( fresh_name_name @ Name23 @ Name12 )
% 0.19/0.47 => ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
% 0.19/0.47 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
% 0.19/0.47 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Name3: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 0.19/0.47 => ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.19/0.47 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.strong_inducts
% 0.19/0.47 thf(fact_186_pi_Ostrong__inducts,axiom,
% 0.19/0.47 ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi4: pi] :
% 0.19/0.47 ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 0.19/0.47 => ( ( fresh_name_name @ Name23 @ Name12 )
% 0.19/0.47 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 0.19/0.47 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 0.19/0.47 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Name3: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 0.19/0.47 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.19/0.47 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.strong_inducts
% 0.19/0.47 thf(fact_187_pi_Ostrong__inducts,axiom,
% 0.19/0.47 ! [P: name > pi > $o,Z: name,Pi4: pi] :
% 0.19/0.47 ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ( fresh_name_name @ Name23 @ Z2 )
% 0.19/0.47 => ( ( fresh_name_name @ Name23 @ Name12 )
% 0.19/0.47 => ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 0.19/0.47 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 0.19/0.47 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Name3: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ( fresh_name_name @ Name3 @ Z2 )
% 0.19/0.47 => ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.19/0.47 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.strong_inducts
% 0.19/0.47 thf(fact_188_pi_Ostrong__inducts,axiom,
% 0.19/0.47 ! [P: pi > pi > $o,Z: pi,Pi4: pi] :
% 0.19/0.47 ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ Name23 @ Z2 )
% 0.19/0.47 => ( ( fresh_name_name @ Name23 @ Name12 )
% 0.19/0.47 => ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 0.19/0.47 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 0.19/0.47 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 0.19/0.47 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 0.19/0.47 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Name3: name,Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ Name3 @ Z2 )
% 0.19/0.47 => ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.19/0.47 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.strong_inducts
% 0.19/0.47 thf(fact_189_pi_Ostrong__induct,axiom,
% 0.19/0.47 ! [P: late_subject > pi > $o,Z: late_subject,Pi4: pi] :
% 0.19/0.47 ( ! [Z2: late_subject] : ( P @ Z2 @ piNil )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ( fresh_717452603ubject @ Name23 @ Z2 )
% 0.19/0.47 => ( ( fresh_name_name @ Name23 @ Name12 )
% 0.19/0.47 => ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
% 0.19/0.47 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
% 0.19/0.47 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Name3: name,Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 0.19/0.47 => ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: late_subject] :
% 0.19/0.47 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.19/0.47 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.strong_induct
% 0.19/0.47 thf(fact_190_pi_Ostrong__induct,axiom,
% 0.19/0.47 ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi4: pi] :
% 0.19/0.47 ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 0.19/0.47 => ( ( fresh_name_name @ Name23 @ Name12 )
% 0.19/0.47 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 0.19/0.47 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 0.19/0.47 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Name3: name,Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 0.19/0.47 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: late_freeRes] :
% 0.19/0.47 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.19/0.47 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.strong_induct
% 0.19/0.47 thf(fact_191_pi_Ostrong__induct,axiom,
% 0.19/0.47 ! [P: name > pi > $o,Z: name,Pi4: pi] :
% 0.19/0.47 ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ( fresh_name_name @ Name23 @ Z2 )
% 0.19/0.47 => ( ( fresh_name_name @ Name23 @ Name12 )
% 0.19/0.47 => ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 0.19/0.47 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 0.19/0.47 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Name3: name,Pi3: pi,Z2: name] :
% 0.19/0.47 ( ( fresh_name_name @ Name3 @ Z2 )
% 0.19/0.47 => ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: name] :
% 0.19/0.47 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.19/0.47 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.strong_induct
% 0.19/0.47 thf(fact_192_pi_Ostrong__induct,axiom,
% 0.19/0.47 ! [P: pi > pi > $o,Z: pi,Pi4: pi] :
% 0.19/0.47 ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ Name23 @ Z2 )
% 0.19/0.47 => ( ( fresh_name_name @ Name23 @ Name12 )
% 0.19/0.47 => ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 0.19/0.47 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 0.19/0.47 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 0.19/0.47 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 0.19/0.47 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 0.19/0.47 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Name3: name,Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ Name3 @ Z2 )
% 0.19/0.47 => ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 0.19/0.47 => ( ! [Pi3: pi,Z2: pi] :
% 0.19/0.47 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 0.19/0.47 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 0.19/0.47 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.strong_induct
% 0.19/0.47 thf(fact_193_pi_Ofresh_I10_J,axiom,
% 0.19/0.47 ! [A: name,X1: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ ( bang @ X1 ) )
% 0.19/0.47 = ( fresh_name_pi @ A @ X1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(10)
% 0.19/0.47 thf(fact_194_pi_Ofresh_I7_J,axiom,
% 0.19/0.47 ! [A: name,X2: pi,X1: pi] :
% 0.19/0.47 ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
% 0.19/0.47 = ( ( fresh_name_pi @ A @ X2 )
% 0.19/0.47 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(7)
% 0.19/0.47 thf(fact_195_pi_Ofresh_I1_J,axiom,
% 0.19/0.47 ! [A: name] : ( fresh_name_pi @ A @ piNil ) ).
% 0.19/0.47
% 0.19/0.47 % pi.fresh(1)
% 0.19/0.47 thf(fact_196_simps_I10_J,axiom,
% 0.19/0.47 ! [P: pi,C: name,D: name] :
% 0.19/0.47 ( ( subs @ ( bang @ P ) @ C @ D )
% 0.19/0.47 = ( bang @ ( subs @ P @ C @ D ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simps(10)
% 0.19/0.47 thf(fact_197_simps_I7_J,axiom,
% 0.19/0.47 ! [P: pi,Q: pi,C: name,D: name] :
% 0.19/0.47 ( ( subs @ ( sum @ P @ Q ) @ C @ D )
% 0.19/0.47 = ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % simps(7)
% 0.19/0.47 thf(fact_198_simps_I1_J,axiom,
% 0.19/0.47 ! [C: name,D: name] :
% 0.19/0.47 ( ( subs @ piNil @ C @ D )
% 0.19/0.47 = piNil ) ).
% 0.19/0.47
% 0.19/0.47 % simps(1)
% 0.19/0.47 thf(fact_199_pi_Odistinct_I59_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 0.19/0.47 ( ( input @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( bang @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(59)
% 0.19/0.47 thf(fact_200_pi_Odistinct_I53_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.19/0.47 ( ( input @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(53)
% 0.19/0.47 thf(fact_201_pi_Odistinct_I87_J,axiom,
% 0.19/0.47 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 0.19/0.47 ( ( par @ Pi1 @ Pi2 )
% 0.19/0.47 != ( bang @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(87)
% 0.19/0.47 thf(fact_202_pi_Odistinct_I89_J,axiom,
% 0.19/0.47 ! [Name2: name,Pi4: pi,Pi: pi] :
% 0.19/0.47 ( ( res @ Name2 @ Pi4 )
% 0.19/0.47 != ( bang @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(89)
% 0.19/0.47 thf(fact_203_pi_Odistinct_I33_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 0.19/0.47 ( ( output @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( bang @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(33)
% 0.19/0.47 thf(fact_204_sumCases,axiom,
% 0.19/0.47 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.19/0.47 => ( ~ ( late_transitions @ P @ Rs )
% 0.19/0.47 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % sumCases
% 0.19/0.47 thf(fact_205_sumCases_H,axiom,
% 0.19/0.47 ! [P: pi,Q: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 0.19/0.47 => ( ~ ( late_transitions @ P @ Rs )
% 0.19/0.47 => ( late_transitions @ Q @ Rs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % sumCases'
% 0.19/0.47 thf(fact_206_Sum1,axiom,
% 0.19/0.47 ! [P: pi,Rs: late_residual,Q: pi] :
% 0.19/0.47 ( ( late_transitions @ P @ Rs )
% 0.19/0.47 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.19/0.47
% 0.19/0.47 % Sum1
% 0.19/0.47 thf(fact_207_Sum2,axiom,
% 0.19/0.47 ! [Q: pi,Rs: late_residual,P: pi] :
% 0.19/0.47 ( ( late_transitions @ Q @ Rs )
% 0.19/0.47 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 0.19/0.47
% 0.19/0.47 % Sum2
% 0.19/0.47 thf(fact_208_pi_Odistinct_I47_J,axiom,
% 0.19/0.47 ! [Pi4: pi,Pi: pi] :
% 0.19/0.47 ( ( tau @ Pi4 )
% 0.19/0.47 != ( bang @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(47)
% 0.19/0.47 thf(fact_209_pi_Odistinct_I79_J,axiom,
% 0.19/0.47 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 0.19/0.47 ( ( sum @ Pi1 @ Pi2 )
% 0.19/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(79)
% 0.19/0.47 thf(fact_210_pi_Odistinct_I81_J,axiom,
% 0.19/0.47 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 0.19/0.47 ( ( sum @ Pi1 @ Pi2 )
% 0.19/0.47 != ( res @ Name @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(81)
% 0.19/0.47 thf(fact_211_pi_Odistinct_I11_J,axiom,
% 0.19/0.47 ! [Pi12: pi,Pi22: pi] :
% 0.19/0.47 ( piNil
% 0.19/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(11)
% 0.19/0.47 thf(fact_212_pi_Odistinct_I17_J,axiom,
% 0.19/0.47 ! [Pi: pi] :
% 0.19/0.47 ( piNil
% 0.19/0.47 != ( bang @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(17)
% 0.19/0.47 thf(fact_213_pi_Odistinct_I83_J,axiom,
% 0.19/0.47 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 0.19/0.47 ( ( sum @ Pi1 @ Pi2 )
% 0.19/0.47 != ( bang @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(83)
% 0.19/0.47 thf(fact_214_pi_Oinject_I6_J,axiom,
% 0.19/0.47 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 0.19/0.47 ( ( ( sum @ X2 @ X1 )
% 0.19/0.47 = ( sum @ Y2 @ Y1 ) )
% 0.19/0.47 = ( ( X2 = Y2 )
% 0.19/0.47 & ( X1 = Y1 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inject(6)
% 0.19/0.47 thf(fact_215_pi_Oinject_I9_J,axiom,
% 0.19/0.47 ! [X1: pi,Y1: pi] :
% 0.19/0.47 ( ( ( bang @ X1 )
% 0.19/0.47 = ( bang @ Y1 ) )
% 0.19/0.47 = ( X1 = Y1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inject(9)
% 0.19/0.47 thf(fact_216_pi_Odistinct_I3_J,axiom,
% 0.19/0.47 ! [Pi: pi] :
% 0.19/0.47 ( piNil
% 0.19/0.47 != ( tau @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(3)
% 0.19/0.47 thf(fact_217_pi_Odistinct_I1_J,axiom,
% 0.19/0.47 ! [Name13: name,Name24: name,Pi: pi] :
% 0.19/0.47 ( piNil
% 0.19/0.47 != ( output @ Name13 @ Name24 @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(1)
% 0.19/0.47 thf(fact_218_pi_Odistinct_I5_J,axiom,
% 0.19/0.47 ! [Name13: name,Name24: name,Pi: pi] :
% 0.19/0.47 ( piNil
% 0.19/0.47 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(5)
% 0.19/0.47 thf(fact_219_pi_Odistinct_I15_J,axiom,
% 0.19/0.47 ! [Name: name,Pi: pi] :
% 0.19/0.47 ( piNil
% 0.19/0.47 != ( res @ Name @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(15)
% 0.19/0.47 thf(fact_220_pi_Odistinct_I13_J,axiom,
% 0.19/0.47 ! [Pi12: pi,Pi22: pi] :
% 0.19/0.47 ( piNil
% 0.19/0.47 != ( par @ Pi12 @ Pi22 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(13)
% 0.19/0.47 thf(fact_221_nilCases_H,axiom,
% 0.19/0.47 ! [Rs: late_residual] :
% 0.19/0.47 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.19/0.47
% 0.19/0.47 % nilCases'
% 0.19/0.47 thf(fact_222_zeroTrans,axiom,
% 0.19/0.47 ! [Rs: late_residual] :
% 0.19/0.47 ~ ( late_transitions @ piNil @ Rs ) ).
% 0.19/0.47
% 0.19/0.47 % zeroTrans
% 0.19/0.47 thf(fact_223_pi_Odistinct_I41_J,axiom,
% 0.19/0.47 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.19/0.47 ( ( tau @ Pi4 )
% 0.19/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(41)
% 0.19/0.47 thf(fact_224_pi_Odistinct_I27_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.19/0.47 ( ( output @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(27)
% 0.19/0.47 thf(fact_225_pi_Odistinct_I77_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 0.19/0.47 ( ( mismatch @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( bang @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(77)
% 0.19/0.47 thf(fact_226_pi_Odistinct_I71_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.19/0.47 ( ( mismatch @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(71)
% 0.19/0.47 thf(fact_227_pi_Odistinct_I69_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 0.19/0.47 ( ( match @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( bang @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(69)
% 0.19/0.47 thf(fact_228_pi_Odistinct_I63_J,axiom,
% 0.19/0.47 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 0.19/0.47 ( ( match @ Name1 @ Name22 @ Pi4 )
% 0.19/0.47 != ( sum @ Pi12 @ Pi22 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(63)
% 0.19/0.47 thf(fact_229_pi_Odistinct_I9_J,axiom,
% 0.19/0.47 ! [Name13: name,Name24: name,Pi: pi] :
% 0.19/0.47 ( piNil
% 0.19/0.47 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(9)
% 0.19/0.47 thf(fact_230_pi_Odistinct_I7_J,axiom,
% 0.19/0.47 ! [Name13: name,Name24: name,Pi: pi] :
% 0.19/0.47 ( piNil
% 0.19/0.47 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.distinct(7)
% 0.19/0.47 thf(fact_231_Bang,axiom,
% 0.19/0.47 ! [P: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( par @ P @ ( bang @ P ) ) @ Rs )
% 0.19/0.47 => ( late_transitions @ ( bang @ P ) @ Rs ) ) ).
% 0.19/0.47
% 0.19/0.47 % Bang
% 0.19/0.47 thf(fact_232_bangCases,axiom,
% 0.19/0.47 ! [P: pi,Rs: late_residual] :
% 0.19/0.47 ( ( late_transitions @ ( bang @ P ) @ Rs )
% 0.19/0.47 => ~ ! [P4: pi] :
% 0.19/0.47 ( ( ( bang @ P )
% 0.19/0.47 = ( bang @ P4 ) )
% 0.19/0.47 => ~ ( late_transitions @ ( par @ P4 @ ( bang @ P4 ) ) @ Rs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % bangCases
% 0.19/0.47 thf(fact_233_resZeroTrans,axiom,
% 0.19/0.47 ! [X: name,Rs: late_residual] :
% 0.19/0.47 ~ ( late_transitions @ ( res @ X @ piNil ) @ Rs ) ).
% 0.19/0.47
% 0.19/0.47 % resZeroTrans
% 0.19/0.47 thf(fact_234_pi_Oinducts,axiom,
% 0.19/0.47 ! [P: pi > $o,Pi4: pi] :
% 0.19/0.47 ( ( P @ piNil )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi] :
% 0.19/0.47 ( ( P @ Pi3 )
% 0.19/0.47 => ( P @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi3: pi] :
% 0.19/0.47 ( ( P @ Pi3 )
% 0.19/0.47 => ( P @ ( tau @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi] :
% 0.19/0.47 ( ( P @ Pi3 )
% 0.19/0.47 => ( P @ ( input @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi] :
% 0.19/0.47 ( ( P @ Pi3 )
% 0.19/0.47 => ( P @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Name12: name,Name23: name,Pi3: pi] :
% 0.19/0.47 ( ( P @ Pi3 )
% 0.19/0.47 => ( P @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi] :
% 0.19/0.47 ( ( P @ Pi13 )
% 0.19/0.47 => ( ( P @ Pi23 )
% 0.19/0.47 => ( P @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Pi13: pi,Pi23: pi] :
% 0.19/0.47 ( ( P @ Pi13 )
% 0.19/0.47 => ( ( P @ Pi23 )
% 0.19/0.47 => ( P @ ( par @ Pi13 @ Pi23 ) ) ) )
% 0.19/0.47 => ( ! [Name3: name,Pi3: pi] :
% 0.19/0.47 ( ( P @ Pi3 )
% 0.19/0.47 => ( P @ ( res @ Name3 @ Pi3 ) ) )
% 0.19/0.47 => ( ! [Pi3: pi] :
% 0.19/0.47 ( ( P @ Pi3 )
% 0.19/0.47 => ( P @ ( bang @ Pi3 ) ) )
% 0.19/0.47 => ( P @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.inducts
% 0.19/0.47 thf(fact_235_aux2,axiom,
% 0.19/0.47 ! [P: pi] : ( late_bangPred @ P @ ( par @ P @ ( bang @ P ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % aux2
% 0.19/0.47 thf(fact_236_bangPred_Ocases,axiom,
% 0.19/0.47 ! [A1: pi,A22: pi] :
% 0.19/0.47 ( ( late_bangPred @ A1 @ A22 )
% 0.19/0.47 => ( ( A22
% 0.19/0.47 != ( bang @ A1 ) )
% 0.19/0.47 => ( A22
% 0.19/0.47 = ( par @ A1 @ ( bang @ A1 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % bangPred.cases
% 0.19/0.47 thf(fact_237_bangPred_Osimps,axiom,
% 0.19/0.47 ( late_bangPred
% 0.19/0.47 = ( ^ [A12: pi,A23: pi] :
% 0.19/0.47 ( ? [P5: pi] :
% 0.19/0.47 ( ( A12 = P5 )
% 0.19/0.47 & ( A23
% 0.19/0.47 = ( bang @ P5 ) ) )
% 0.19/0.47 | ? [P5: pi] :
% 0.19/0.47 ( ( A12 = P5 )
% 0.19/0.47 & ( A23
% 0.19/0.47 = ( par @ P5 @ ( bang @ P5 ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % bangPred.simps
% 0.19/0.47 thf(fact_238_aux1,axiom,
% 0.19/0.47 ! [P: pi] : ( late_bangPred @ P @ ( bang @ P ) ) ).
% 0.19/0.47
% 0.19/0.47 % aux1
% 0.19/0.47 thf(fact_239_bangPred_Oinducts,axiom,
% 0.19/0.47 ! [X1: pi,X2: pi,P: pi > pi > $o] :
% 0.19/0.47 ( ( late_bangPred @ X1 @ X2 )
% 0.19/0.47 => ( ! [P4: pi] : ( P @ P4 @ ( bang @ P4 ) )
% 0.19/0.47 => ( ! [P4: pi] : ( P @ P4 @ ( par @ P4 @ ( bang @ P4 ) ) )
% 0.19/0.47 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % bangPred.inducts
% 0.19/0.47 thf(fact_240_subs__def,axiom,
% 0.19/0.47 ( subs
% 0.19/0.47 = ( ^ [X3: pi,C3: name,D2: name] :
% 0.19/0.47 ( pi_rec_pi @ piNil
% 0.19/0.47 @ ^ [A4: name,B3: name,P5: pi] : ( output @ ( subst_name @ A4 @ C3 @ D2 ) @ ( subst_name @ B3 @ C3 @ D2 ) )
% 0.19/0.47 @ ^ [P5: pi] : tau
% 0.19/0.47 @ ^ [A4: name,Y5: name,P5: pi] : ( input @ ( subst_name @ A4 @ C3 @ D2 ) @ Y5 )
% 0.19/0.47 @ ^ [A4: name,B3: name,P5: pi] : ( match @ ( subst_name @ A4 @ C3 @ D2 ) @ ( subst_name @ B3 @ C3 @ D2 ) )
% 0.19/0.47 @ ^ [A4: name,B3: name,P5: pi] : ( mismatch @ ( subst_name @ A4 @ C3 @ D2 ) @ ( subst_name @ B3 @ C3 @ D2 ) )
% 0.19/0.47 @ ^ [P5: pi,Q5: pi] : sum
% 0.19/0.47 @ ^ [P5: pi,Q5: pi] : par
% 0.19/0.47 @ ^ [Y5: name,P5: pi] : ( res @ Y5 )
% 0.19/0.47 @ ^ [P5: pi] : bang
% 0.19/0.47 @ X3 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % subs_def
% 0.19/0.47 thf(fact_241_abs__fresh_I2_J,axiom,
% 0.19/0.47 ! [X: late_subject,B: name,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1174290467t_name @ X ) )
% 0.19/0.47 => ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_717452603ubject @ B @ X ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(2)
% 0.19/0.47 thf(fact_242_abs__fresh_I2_J,axiom,
% 0.19/0.47 ! [X: late_freeRes,B: name,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1228270395s_name @ X ) )
% 0.19/0.47 => ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_1641682979reeRes @ B @ X ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(2)
% 0.19/0.47 thf(fact_243_abs__fresh_I2_J,axiom,
% 0.19/0.47 ! [X: name,B: name,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_name_name @ X ) )
% 0.19/0.47 => ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_name_name @ B @ X ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(2)
% 0.19/0.47 thf(fact_244_abs__fresh_I2_J,axiom,
% 0.19/0.47 ! [X: pi,B: name,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_pi_name @ X ) )
% 0.19/0.47 => ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_name_pi @ B @ X ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(2)
% 0.19/0.47 thf(fact_245_abs__fresh_I2_J,axiom,
% 0.19/0.47 ! [X: name > noption_pi,B: name,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_n468628396i_name @ X ) )
% 0.19/0.47 => ( ( fresh_92802872ion_pi @ B @ ( abs_fu1614711987ion_pi @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_543891186ion_pi @ B @ X ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(2)
% 0.19/0.47 thf(fact_246_abs__fresh_I2_J,axiom,
% 0.19/0.47 ! [X: name > noption_Late_subject,B: name,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_n1630792207t_name @ X ) )
% 0.19/0.47 => ( ( fresh_600418535ubject @ B @ ( abs_fu1705804544ubject @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_728038529ubject @ B @ X ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(2)
% 0.19/0.47 thf(fact_247_abs__fresh_I2_J,axiom,
% 0.19/0.47 ! [X: name > noption_Late_freeRes,B: name,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_n252280103s_name @ X ) )
% 0.19/0.47 => ( ( fresh_1215331279reeRes @ B @ ( abs_fu1763130856reeRes @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_785364841reeRes @ B @ X ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(2)
% 0.19/0.47 thf(fact_248_abs__fresh_I2_J,axiom,
% 0.19/0.47 ! [X: name > noption_name,B: name,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_n352473082e_name @ X ) )
% 0.19/0.47 => ( ( fresh_1742414570n_name @ B @ ( abs_fu1394407909n_name @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_1093033124n_name @ B @ X ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(2)
% 0.19/0.47 thf(fact_249_abs__fresh_I2_J,axiom,
% 0.19/0.47 ! [X: late_freeRes > pi > late_subject,B: name,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1759672260t_name @ X ) )
% 0.19/0.47 => ( ( fresh_1644004594ubject @ B @ ( abs_fu888821131ubject @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_198785932ubject @ B @ X ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(2)
% 0.19/0.47 thf(fact_250_abs__fresh_I2_J,axiom,
% 0.19/0.47 ! [X: late_freeRes > pi > late_freeRes,B: name,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L381160156s_name @ X ) )
% 0.19/0.47 => ( ( fresh_111433690reeRes @ B @ ( abs_fu946147443reeRes @ A @ X ) )
% 0.19/0.47 = ( ( B = A )
% 0.19/0.47 | ( fresh_256112244reeRes @ B @ X ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % abs_fresh(2)
% 0.19/0.47 thf(fact_251_exists__fresh,axiom,
% 0.19/0.47 ! [X: late_subject] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1174290467t_name @ X ) )
% 0.19/0.47 => ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_717452603ubject @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh
% 0.19/0.47 thf(fact_252_exists__fresh,axiom,
% 0.19/0.47 ! [X: late_freeRes] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1228270395s_name @ X ) )
% 0.19/0.47 => ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_1641682979reeRes @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh
% 0.19/0.47 thf(fact_253_exists__fresh,axiom,
% 0.19/0.47 ! [X: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_name_name @ X ) )
% 0.19/0.47 => ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_name_name @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh
% 0.19/0.47 thf(fact_254_exists__fresh,axiom,
% 0.19/0.47 ! [X: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_pi_name @ X ) )
% 0.19/0.47 => ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_name_pi @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh
% 0.19/0.47 thf(fact_255_exists__fresh,axiom,
% 0.19/0.47 ! [X: name > noption_pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_n468628396i_name @ X ) )
% 0.19/0.47 => ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_543891186ion_pi @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh
% 0.19/0.47 thf(fact_256_exists__fresh,axiom,
% 0.19/0.47 ! [X: name > noption_Late_subject] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_n1630792207t_name @ X ) )
% 0.19/0.47 => ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_728038529ubject @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh
% 0.19/0.47 thf(fact_257_exists__fresh,axiom,
% 0.19/0.47 ! [X: name > noption_Late_freeRes] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_n252280103s_name @ X ) )
% 0.19/0.47 => ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_785364841reeRes @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh
% 0.19/0.47 thf(fact_258_exists__fresh,axiom,
% 0.19/0.47 ! [X: name > noption_name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_n352473082e_name @ X ) )
% 0.19/0.47 => ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_1093033124n_name @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh
% 0.19/0.47 thf(fact_259_exists__fresh,axiom,
% 0.19/0.47 ! [X: late_freeRes > pi > late_subject] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1759672260t_name @ X ) )
% 0.19/0.47 => ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_198785932ubject @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh
% 0.19/0.47 thf(fact_260_exists__fresh,axiom,
% 0.19/0.47 ! [X: late_freeRes > pi > late_freeRes] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L381160156s_name @ X ) )
% 0.19/0.47 => ~ ! [C2: name] :
% 0.19/0.47 ~ ( fresh_256112244reeRes @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh
% 0.19/0.47 thf(fact_261_exists__fresh_H,axiom,
% 0.19/0.47 ! [X: late_subject] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1174290467t_name @ X ) )
% 0.19/0.47 => ? [C2: name] : ( fresh_717452603ubject @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh'
% 0.19/0.47 thf(fact_262_exists__fresh_H,axiom,
% 0.19/0.47 ! [X: late_freeRes] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1228270395s_name @ X ) )
% 0.19/0.47 => ? [C2: name] : ( fresh_1641682979reeRes @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh'
% 0.19/0.47 thf(fact_263_exists__fresh_H,axiom,
% 0.19/0.47 ! [X: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_name_name @ X ) )
% 0.19/0.47 => ? [C2: name] : ( fresh_name_name @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh'
% 0.19/0.47 thf(fact_264_exists__fresh_H,axiom,
% 0.19/0.47 ! [X: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_pi_name @ X ) )
% 0.19/0.47 => ? [C2: name] : ( fresh_name_pi @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh'
% 0.19/0.47 thf(fact_265_exists__fresh_H,axiom,
% 0.19/0.47 ! [X: name > noption_pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_n468628396i_name @ X ) )
% 0.19/0.47 => ? [C2: name] : ( fresh_543891186ion_pi @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh'
% 0.19/0.47 thf(fact_266_exists__fresh_H,axiom,
% 0.19/0.47 ! [X: name > noption_Late_subject] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_n1630792207t_name @ X ) )
% 0.19/0.47 => ? [C2: name] : ( fresh_728038529ubject @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh'
% 0.19/0.47 thf(fact_267_exists__fresh_H,axiom,
% 0.19/0.47 ! [X: name > noption_Late_freeRes] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_n252280103s_name @ X ) )
% 0.19/0.47 => ? [C2: name] : ( fresh_785364841reeRes @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh'
% 0.19/0.47 thf(fact_268_exists__fresh_H,axiom,
% 0.19/0.47 ! [X: name > noption_name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_n352473082e_name @ X ) )
% 0.19/0.47 => ? [C2: name] : ( fresh_1093033124n_name @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh'
% 0.19/0.47 thf(fact_269_exists__fresh_H,axiom,
% 0.19/0.47 ! [X: late_freeRes > pi > late_subject] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1759672260t_name @ X ) )
% 0.19/0.47 => ? [C2: name] : ( fresh_198785932ubject @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh'
% 0.19/0.47 thf(fact_270_exists__fresh_H,axiom,
% 0.19/0.47 ! [X: late_freeRes > pi > late_freeRes] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L381160156s_name @ X ) )
% 0.19/0.47 => ? [C2: name] : ( fresh_256112244reeRes @ C2 @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % exists_fresh'
% 0.19/0.47 thf(fact_271_supp__fresh__iff,axiom,
% 0.19/0.47 ( supp_L1174290467t_name
% 0.19/0.47 = ( ^ [X3: late_subject] :
% 0.19/0.47 ( collect_name
% 0.19/0.47 @ ^ [A4: name] :
% 0.19/0.47 ~ ( fresh_717452603ubject @ A4 @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % supp_fresh_iff
% 0.19/0.47 thf(fact_272_supp__fresh__iff,axiom,
% 0.19/0.47 ( supp_L1228270395s_name
% 0.19/0.47 = ( ^ [X3: late_freeRes] :
% 0.19/0.47 ( collect_name
% 0.19/0.47 @ ^ [A4: name] :
% 0.19/0.47 ~ ( fresh_1641682979reeRes @ A4 @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % supp_fresh_iff
% 0.19/0.47 thf(fact_273_supp__fresh__iff,axiom,
% 0.19/0.47 ( supp_name_name
% 0.19/0.47 = ( ^ [X3: name] :
% 0.19/0.47 ( collect_name
% 0.19/0.47 @ ^ [A4: name] :
% 0.19/0.47 ~ ( fresh_name_name @ A4 @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % supp_fresh_iff
% 0.19/0.47 thf(fact_274_supp__fresh__iff,axiom,
% 0.19/0.47 ( supp_pi_name
% 0.19/0.47 = ( ^ [X3: pi] :
% 0.19/0.47 ( collect_name
% 0.19/0.47 @ ^ [A4: name] :
% 0.19/0.47 ~ ( fresh_name_pi @ A4 @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % supp_fresh_iff
% 0.19/0.47 thf(fact_275_supp__fresh__iff,axiom,
% 0.19/0.47 ( supp_n468628396i_name
% 0.19/0.47 = ( ^ [X3: name > noption_pi] :
% 0.19/0.47 ( collect_name
% 0.19/0.47 @ ^ [A4: name] :
% 0.19/0.47 ~ ( fresh_543891186ion_pi @ A4 @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % supp_fresh_iff
% 0.19/0.47 thf(fact_276_supp__fresh__iff,axiom,
% 0.19/0.47 ( supp_n1630792207t_name
% 0.19/0.47 = ( ^ [X3: name > noption_Late_subject] :
% 0.19/0.47 ( collect_name
% 0.19/0.47 @ ^ [A4: name] :
% 0.19/0.47 ~ ( fresh_728038529ubject @ A4 @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % supp_fresh_iff
% 0.19/0.47 thf(fact_277_supp__fresh__iff,axiom,
% 0.19/0.47 ( supp_n252280103s_name
% 0.19/0.47 = ( ^ [X3: name > noption_Late_freeRes] :
% 0.19/0.47 ( collect_name
% 0.19/0.47 @ ^ [A4: name] :
% 0.19/0.47 ~ ( fresh_785364841reeRes @ A4 @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % supp_fresh_iff
% 0.19/0.47 thf(fact_278_supp__fresh__iff,axiom,
% 0.19/0.47 ( supp_n352473082e_name
% 0.19/0.47 = ( ^ [X3: name > noption_name] :
% 0.19/0.47 ( collect_name
% 0.19/0.47 @ ^ [A4: name] :
% 0.19/0.47 ~ ( fresh_1093033124n_name @ A4 @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % supp_fresh_iff
% 0.19/0.47 thf(fact_279_supp__fresh__iff,axiom,
% 0.19/0.47 ( supp_L1759672260t_name
% 0.19/0.47 = ( ^ [X3: late_freeRes > pi > late_subject] :
% 0.19/0.47 ( collect_name
% 0.19/0.47 @ ^ [A4: name] :
% 0.19/0.47 ~ ( fresh_198785932ubject @ A4 @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % supp_fresh_iff
% 0.19/0.47 thf(fact_280_supp__fresh__iff,axiom,
% 0.19/0.47 ( supp_L381160156s_name
% 0.19/0.47 = ( ^ [X3: late_freeRes > pi > late_freeRes] :
% 0.19/0.47 ( collect_name
% 0.19/0.47 @ ^ [A4: name] :
% 0.19/0.47 ~ ( fresh_256112244reeRes @ A4 @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % supp_fresh_iff
% 0.19/0.47 thf(fact_281_fresh__def,axiom,
% 0.19/0.47 ( fresh_717452603ubject
% 0.19/0.47 = ( ^ [A4: name,X3: late_subject] :
% 0.19/0.47 ~ ( member_name @ A4 @ ( supp_L1174290467t_name @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_def
% 0.19/0.47 thf(fact_282_fresh__def,axiom,
% 0.19/0.47 ( fresh_1641682979reeRes
% 0.19/0.47 = ( ^ [A4: name,X3: late_freeRes] :
% 0.19/0.47 ~ ( member_name @ A4 @ ( supp_L1228270395s_name @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_def
% 0.19/0.47 thf(fact_283_fresh__def,axiom,
% 0.19/0.47 ( fresh_name_name
% 0.19/0.47 = ( ^ [A4: name,X3: name] :
% 0.19/0.47 ~ ( member_name @ A4 @ ( supp_name_name @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_def
% 0.19/0.47 thf(fact_284_fresh__def,axiom,
% 0.19/0.47 ( fresh_name_pi
% 0.19/0.47 = ( ^ [A4: name,X3: pi] :
% 0.19/0.47 ~ ( member_name @ A4 @ ( supp_pi_name @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_def
% 0.19/0.47 thf(fact_285_fresh__def,axiom,
% 0.19/0.47 ( fresh_543891186ion_pi
% 0.19/0.47 = ( ^ [A4: name,X3: name > noption_pi] :
% 0.19/0.47 ~ ( member_name @ A4 @ ( supp_n468628396i_name @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_def
% 0.19/0.47 thf(fact_286_fresh__def,axiom,
% 0.19/0.47 ( fresh_728038529ubject
% 0.19/0.47 = ( ^ [A4: name,X3: name > noption_Late_subject] :
% 0.19/0.47 ~ ( member_name @ A4 @ ( supp_n1630792207t_name @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_def
% 0.19/0.47 thf(fact_287_fresh__def,axiom,
% 0.19/0.47 ( fresh_785364841reeRes
% 0.19/0.47 = ( ^ [A4: name,X3: name > noption_Late_freeRes] :
% 0.19/0.47 ~ ( member_name @ A4 @ ( supp_n252280103s_name @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_def
% 0.19/0.47 thf(fact_288_fresh__def,axiom,
% 0.19/0.47 ( fresh_1093033124n_name
% 0.19/0.47 = ( ^ [A4: name,X3: name > noption_name] :
% 0.19/0.47 ~ ( member_name @ A4 @ ( supp_n352473082e_name @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_def
% 0.19/0.47 thf(fact_289_fresh__def,axiom,
% 0.19/0.47 ( fresh_198785932ubject
% 0.19/0.47 = ( ^ [A4: name,X3: late_freeRes > pi > late_subject] :
% 0.19/0.47 ~ ( member_name @ A4 @ ( supp_L1759672260t_name @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_def
% 0.19/0.47 thf(fact_290_fresh__def,axiom,
% 0.19/0.47 ( fresh_256112244reeRes
% 0.19/0.47 = ( ^ [A4: name,X3: late_freeRes > pi > late_freeRes] :
% 0.19/0.47 ~ ( member_name @ A4 @ ( supp_L381160156s_name @ X3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % fresh_def
% 0.19/0.47 thf(fact_291_pi_Osupp_I9_J,axiom,
% 0.19/0.47 ! [X1: name,X2: pi] :
% 0.19/0.47 ( ( supp_pi_name @ ( res @ X1 @ X2 ) )
% 0.19/0.47 = ( supp_n468628396i_name @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.supp(9)
% 0.19/0.47 thf(fact_292_pi_Osupp_I3_J,axiom,
% 0.19/0.47 ! [X1: pi] :
% 0.19/0.47 ( ( supp_pi_name @ ( tau @ X1 ) )
% 0.19/0.47 = ( supp_pi_name @ X1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.supp(3)
% 0.19/0.47 thf(fact_293_subject_Osupp_I2_J,axiom,
% 0.19/0.47 ! [X1: name] :
% 0.19/0.47 ( ( supp_L1174290467t_name @ ( late_BoundOutputS @ X1 ) )
% 0.19/0.47 = ( supp_name_name @ X1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % subject.supp(2)
% 0.19/0.47 thf(fact_294_subject_Osupp_I1_J,axiom,
% 0.19/0.47 ! [X1: name] :
% 0.19/0.47 ( ( supp_L1174290467t_name @ ( late_InputS @ X1 ) )
% 0.19/0.47 = ( supp_name_name @ X1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % subject.supp(1)
% 0.19/0.47 thf(fact_295_pi_Osupp_I10_J,axiom,
% 0.19/0.47 ! [X1: pi] :
% 0.19/0.47 ( ( supp_pi_name @ ( bang @ X1 ) )
% 0.19/0.47 = ( supp_pi_name @ X1 ) ) ).
% 0.19/0.47
% 0.19/0.47 % pi.supp(10)
% 0.19/0.47 thf(fact_296_fs__name1,axiom,
% 0.19/0.47 ! [X: late_subject] : ( finite_finite_name @ ( supp_L1174290467t_name @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % fs_name1
% 0.19/0.47 thf(fact_297_fs__name1,axiom,
% 0.19/0.47 ! [X: late_freeRes] : ( finite_finite_name @ ( supp_L1228270395s_name @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % fs_name1
% 0.19/0.47 thf(fact_298_fs__name1,axiom,
% 0.19/0.47 ! [X: name] : ( finite_finite_name @ ( supp_name_name @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % fs_name1
% 0.19/0.47 thf(fact_299_fs__name1,axiom,
% 0.19/0.47 ! [X: pi] : ( finite_finite_name @ ( supp_pi_name @ X ) ) ).
% 0.19/0.47
% 0.19/0.47 % fs_name1
% 0.19/0.47 thf(fact_300_residual_Orecs_I2_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_subject,P: late_subject > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_795910143ubject @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.47 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(2)
% 0.19/0.47 thf(fact_301_residual_Orecs_I2_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_subject,P: late_freeRes > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.47 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(2)
% 0.19/0.47 thf(fact_302_residual_Orecs_I2_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_subject,P: name > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_621211324i_name @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_name_name @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( late_r1174711868c_name @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.47 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(2)
% 0.19/0.47 thf(fact_303_residual_Orecs_I2_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_subject,P: pi > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_name_pi @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( late_residual_rec_pi @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.47 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(2)
% 0.19/0.47 thf(fact_304_residual_Orecs_I2_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_freeRes,P: late_subject > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_795910143ubject @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.47 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(2)
% 0.19/0.47 thf(fact_305_residual_Orecs_I2_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_freeRes,P: late_freeRes > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.47 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(2)
% 0.19/0.47 thf(fact_306_residual_Orecs_I2_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_freeRes,P: name > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_621211324i_name @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_name_name @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( late_r1174711868c_name @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.47 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(2)
% 0.19/0.47 thf(fact_307_residual_Orecs_I2_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_freeRes,P: pi > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_name_pi @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( late_residual_rec_pi @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.47 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(2)
% 0.19/0.47 thf(fact_308_residual_Orecs_I2_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: name,P: late_subject > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_795910143ubject @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_name_name @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.47 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(2)
% 0.19/0.47 thf(fact_309_residual_Orecs_I2_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: name,P: late_freeRes > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_name_name @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 0.19/0.47 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(2)
% 0.19/0.47 thf(fact_310_residual_Orecs_I1_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_subject,P: late_subject > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_795910143ubject @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( fresh_795910143ubject @ Name2 @ F1 )
% 0.19/0.47 => ( ( fresh_198785932ubject @ Name2 @ F2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.19/0.47 => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 0.19/0.47 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(1)
% 0.19/0.47 thf(fact_311_residual_Orecs_I1_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_subject,P: late_freeRes > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( fresh_660367079reeRes @ Name2 @ F1 )
% 0.19/0.47 => ( ( fresh_256112244reeRes @ Name2 @ F2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.19/0.47 => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 0.19/0.47 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(1)
% 0.19/0.47 thf(fact_312_residual_Orecs_I1_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_subject,P: name > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_621211324i_name @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_name_name @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( fresh_621211324i_name @ Name2 @ F1 )
% 0.19/0.47 => ( ( fresh_1030632537i_name @ Name2 @ F2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.19/0.47 => ( ( late_r1174711868c_name @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 0.19/0.47 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(1)
% 0.19/0.47 thf(fact_313_residual_Orecs_I1_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_subject,P: pi > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_name_pi @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( fresh_1438126218_pi_pi @ Name2 @ F1 )
% 0.19/0.47 => ( ( fresh_1011532071_pi_pi @ Name2 @ F2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.19/0.47 => ( ( late_residual_rec_pi @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 0.19/0.47 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(1)
% 0.19/0.47 thf(fact_314_residual_Orecs_I1_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_freeRes,P: late_subject > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_795910143ubject @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( fresh_795910143ubject @ Name2 @ F1 )
% 0.19/0.47 => ( ( fresh_198785932ubject @ Name2 @ F2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.19/0.47 => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 0.19/0.47 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(1)
% 0.19/0.47 thf(fact_315_residual_Orecs_I1_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_freeRes,P: late_freeRes > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( fresh_660367079reeRes @ Name2 @ F1 )
% 0.19/0.47 => ( ( fresh_256112244reeRes @ Name2 @ F2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.19/0.47 => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 0.19/0.47 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(1)
% 0.19/0.47 thf(fact_316_residual_Orecs_I1_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_freeRes,P: name > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_621211324i_name @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_name_name @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( fresh_621211324i_name @ Name2 @ F1 )
% 0.19/0.47 => ( ( fresh_1030632537i_name @ Name2 @ F2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.19/0.47 => ( ( late_r1174711868c_name @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 0.19/0.47 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(1)
% 0.19/0.47 thf(fact_317_residual_Orecs_I1_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_freeRes,P: pi > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_name_pi @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( fresh_1438126218_pi_pi @ Name2 @ F1 )
% 0.19/0.47 => ( ( fresh_1011532071_pi_pi @ Name2 @ F2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.19/0.47 => ( ( late_residual_rec_pi @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 0.19/0.47 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(1)
% 0.19/0.47 thf(fact_318_residual_Orecs_I1_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: name,P: late_subject > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_795910143ubject @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_name_name @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( fresh_795910143ubject @ Name2 @ F1 )
% 0.19/0.47 => ( ( fresh_198785932ubject @ Name2 @ F2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.19/0.47 => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 0.19/0.47 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(1)
% 0.19/0.47 thf(fact_319_residual_Orecs_I1_J,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: name,P: late_freeRes > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 0.19/0.47 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_name_name @ X22 @ Z )
% 0.19/0.47 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ( ( fresh_660367079reeRes @ Name2 @ F1 )
% 0.19/0.47 => ( ( fresh_256112244reeRes @ Name2 @ F2 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 0.19/0.47 => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 0.19/0.47 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.recs(1)
% 0.19/0.47 thf(fact_320_residual_Orec__fresh,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > name > noption_name,F2: late_freeRes > pi > name > noption_name,X: late_residual,Y: name > noption_name,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L14705974e_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L473926939e_name @ F2 ) )
% 0.19/0.47 => ( ( late_r303715378n_name @ F1 @ F2 @ X @ Y )
% 0.19/0.47 => ( ! [Y6: name > noption_name] :
% 0.19/0.47 ( ( late_r303715378n_name @ F1 @ F2 @ X @ Y6 )
% 0.19/0.47 => ( Y6 = Y ) )
% 0.19/0.47 => ( ( fresh_81631222sidual @ A @ X )
% 0.19/0.47 => ( ( fresh_62885992n_name @ A @ F1 )
% 0.19/0.47 => ( ( fresh_808662133n_name @ A @ F2 )
% 0.19/0.47 => ( fresh_1093033124n_name @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.rec_fresh
% 0.19/0.47 thf(fact_321_residual_Orec__fresh,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > name > noptio354675977ion_pi,F2: late_freeRes > pi > name > noptio354675977ion_pi,X: late_residual,Y: name > noptio354675977ion_pi,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1512088218i_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L979396363i_name @ F2 ) )
% 0.19/0.47 => ( ( late_r1558248490ion_pi @ F1 @ F2 @ X @ Y )
% 0.19/0.47 => ( ! [Y6: name > noptio354675977ion_pi] :
% 0.19/0.47 ( ( late_r1558248490ion_pi @ F1 @ F2 @ X @ Y6 )
% 0.19/0.47 => ( Y6 = Y ) )
% 0.19/0.47 => ( ( fresh_81631222sidual @ A @ X )
% 0.19/0.47 => ( ( fresh_876421558ion_pi @ A @ F1 )
% 0.19/0.47 => ( ( fresh_2081817683ion_pi @ A @ F2 )
% 0.19/0.47 => ( fresh_92802872ion_pi @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.rec_fresh
% 0.19/0.47 thf(fact_322_residual_Orec__fresh,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,X: late_residual,Y: late_subject,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 0.19/0.47 => ( ( late_r689718217ubject @ F1 @ F2 @ X @ Y )
% 0.19/0.47 => ( ! [Y6: late_subject] :
% 0.19/0.47 ( ( late_r689718217ubject @ F1 @ F2 @ X @ Y6 )
% 0.19/0.47 => ( Y6 = Y ) )
% 0.19/0.47 => ( ( fresh_81631222sidual @ A @ X )
% 0.19/0.47 => ( ( fresh_795910143ubject @ A @ F1 )
% 0.19/0.47 => ( ( fresh_198785932ubject @ A @ F2 )
% 0.19/0.47 => ( fresh_717452603ubject @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.rec_fresh
% 0.19/0.47 thf(fact_323_residual_Orec__fresh,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,X: late_residual,Y: late_freeRes,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 0.19/0.47 => ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ Y )
% 0.19/0.47 => ( ! [Y6: late_freeRes] :
% 0.19/0.47 ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ Y6 )
% 0.19/0.47 => ( Y6 = Y ) )
% 0.19/0.47 => ( ( fresh_81631222sidual @ A @ X )
% 0.19/0.47 => ( ( fresh_660367079reeRes @ A @ F1 )
% 0.19/0.47 => ( ( fresh_256112244reeRes @ A @ F2 )
% 0.19/0.47 => ( fresh_1641682979reeRes @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.rec_fresh
% 0.19/0.47 thf(fact_324_residual_Orec__fresh,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,X: late_residual,Y: name,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
% 0.19/0.47 => ( ( late_r1742481968t_name @ F1 @ F2 @ X @ Y )
% 0.19/0.47 => ( ! [Y6: name] :
% 0.19/0.47 ( ( late_r1742481968t_name @ F1 @ F2 @ X @ Y6 )
% 0.19/0.47 => ( Y6 = Y ) )
% 0.19/0.47 => ( ( fresh_81631222sidual @ A @ X )
% 0.19/0.47 => ( ( fresh_621211324i_name @ A @ F1 )
% 0.19/0.47 => ( ( fresh_1030632537i_name @ A @ F2 )
% 0.19/0.47 => ( fresh_name_name @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.rec_fresh
% 0.19/0.47 thf(fact_325_residual_Orec__fresh,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,X: late_residual,Y: pi,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
% 0.19/0.47 => ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ Y )
% 0.19/0.47 => ( ! [Y6: pi] :
% 0.19/0.47 ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ Y6 )
% 0.19/0.47 => ( Y6 = Y ) )
% 0.19/0.47 => ( ( fresh_81631222sidual @ A @ X )
% 0.19/0.47 => ( ( fresh_1438126218_pi_pi @ A @ F1 )
% 0.19/0.47 => ( ( fresh_1011532071_pi_pi @ A @ F2 )
% 0.19/0.47 => ( fresh_name_pi @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.rec_fresh
% 0.19/0.47 thf(fact_326_residual_Orec__fresh,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > name > noption_pi,F2: late_freeRes > pi > name > noption_pi,X: late_residual,Y: name > noption_pi,A: name] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L3230824i_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L635439693i_name @ F2 ) )
% 0.19/0.47 => ( ( late_r750878080ion_pi @ F1 @ F2 @ X @ Y )
% 0.19/0.47 => ( ! [Y6: name > noption_pi] :
% 0.19/0.47 ( ( late_r750878080ion_pi @ F1 @ F2 @ X @ Y6 )
% 0.19/0.47 => ( Y6 = Y ) )
% 0.19/0.47 => ( ( fresh_81631222sidual @ A @ X )
% 0.19/0.47 => ( ( fresh_747777846ion_pi @ A @ F1 )
% 0.19/0.47 => ( ( fresh_7927363ion_pi @ A @ F2 )
% 0.19/0.47 => ( fresh_543891186ion_pi @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.rec_fresh
% 0.19/0.47 thf(fact_327_residual_Orec__unique,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_subject,P: late_subject > $o,X: late_residual] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name] :
% 0.19/0.47 ( ( fresh_795910143ubject @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ Z )
% 0.19/0.47 => ! [X33: pi] :
% 0.19/0.47 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ? [X4: late_subject] :
% 0.19/0.47 ( ( late_r689718217ubject @ F1 @ F2 @ X @ X4 )
% 0.19/0.47 & ! [Y7: late_subject] :
% 0.19/0.47 ( ( late_r689718217ubject @ F1 @ F2 @ X @ Y7 )
% 0.19/0.47 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.rec_unique
% 0.19/0.47 thf(fact_328_residual_Orec__unique,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_subject,P: late_freeRes > $o,X: late_residual] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name] :
% 0.19/0.47 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ Z )
% 0.19/0.47 => ! [X33: pi] :
% 0.19/0.47 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ? [X4: late_freeRes] :
% 0.19/0.47 ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ X4 )
% 0.19/0.47 & ! [Y7: late_freeRes] :
% 0.19/0.47 ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ Y7 )
% 0.19/0.47 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.rec_unique
% 0.19/0.47 thf(fact_329_residual_Orec__unique,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_subject,P: name > $o,X: late_residual] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name] :
% 0.19/0.47 ( ( fresh_621211324i_name @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ Z )
% 0.19/0.47 => ! [X33: pi] :
% 0.19/0.47 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_name_name @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ? [X4: name] :
% 0.19/0.47 ( ( late_r1742481968t_name @ F1 @ F2 @ X @ X4 )
% 0.19/0.47 & ! [Y7: name] :
% 0.19/0.47 ( ( late_r1742481968t_name @ F1 @ F2 @ X @ Y7 )
% 0.19/0.47 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.rec_unique
% 0.19/0.47 thf(fact_330_residual_Orec__unique,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_subject,P: pi > $o,X: late_residual] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name] :
% 0.19/0.47 ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ Z )
% 0.19/0.47 => ! [X33: pi] :
% 0.19/0.47 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_name_pi @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ? [X4: pi] :
% 0.19/0.47 ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ X4 )
% 0.19/0.47 & ! [Y7: pi] :
% 0.19/0.47 ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ Y7 )
% 0.19/0.47 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.rec_unique
% 0.19/0.47 thf(fact_331_residual_Orec__unique,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_freeRes,P: late_subject > $o,X: late_residual] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name] :
% 0.19/0.47 ( ( fresh_795910143ubject @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 0.19/0.47 => ! [X33: pi] :
% 0.19/0.47 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ? [X4: late_subject] :
% 0.19/0.47 ( ( late_r689718217ubject @ F1 @ F2 @ X @ X4 )
% 0.19/0.47 & ! [Y7: late_subject] :
% 0.19/0.47 ( ( late_r689718217ubject @ F1 @ F2 @ X @ Y7 )
% 0.19/0.47 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.rec_unique
% 0.19/0.47 thf(fact_332_residual_Orec__unique,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_freeRes,P: late_freeRes > $o,X: late_residual] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name] :
% 0.19/0.47 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 0.19/0.47 => ! [X33: pi] :
% 0.19/0.47 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ? [X4: late_freeRes] :
% 0.19/0.47 ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ X4 )
% 0.19/0.47 & ! [Y7: late_freeRes] :
% 0.19/0.47 ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ Y7 )
% 0.19/0.47 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.rec_unique
% 0.19/0.47 thf(fact_333_residual_Orec__unique,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_freeRes,P: name > $o,X: late_residual] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name] :
% 0.19/0.47 ( ( fresh_621211324i_name @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 0.19/0.47 => ! [X33: pi] :
% 0.19/0.47 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_name_name @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ? [X4: name] :
% 0.19/0.47 ( ( late_r1742481968t_name @ F1 @ F2 @ X @ X4 )
% 0.19/0.47 & ! [Y7: name] :
% 0.19/0.47 ( ( late_r1742481968t_name @ F1 @ F2 @ X @ Y7 )
% 0.19/0.47 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.rec_unique
% 0.19/0.47 thf(fact_334_residual_Orec__unique,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_freeRes,P: pi > $o,X: late_residual] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name] :
% 0.19/0.47 ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 0.19/0.47 => ! [X33: pi] :
% 0.19/0.47 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_name_pi @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ? [X4: pi] :
% 0.19/0.47 ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ X4 )
% 0.19/0.47 & ! [Y7: pi] :
% 0.19/0.47 ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ Y7 )
% 0.19/0.47 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.rec_unique
% 0.19/0.47 thf(fact_335_residual_Orec__unique,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: name,P: late_subject > $o,X: late_residual] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name] :
% 0.19/0.47 ( ( fresh_795910143ubject @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_name_name @ X22 @ Z )
% 0.19/0.47 => ! [X33: pi] :
% 0.19/0.47 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.47 => ? [X4: late_subject] :
% 0.19/0.47 ( ( late_r689718217ubject @ F1 @ F2 @ X @ X4 )
% 0.19/0.47 & ! [Y7: late_subject] :
% 0.19/0.47 ( ( late_r689718217ubject @ F1 @ F2 @ X @ Y7 )
% 0.19/0.47 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % residual.rec_unique
% 0.19/0.47 thf(fact_336_residual_Orec__unique,axiom,
% 0.19/0.47 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: name,P: late_freeRes > $o,X: late_residual] :
% 0.19/0.47 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 0.19/0.47 => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.47 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 0.19/0.47 => ( ! [X12: late_subject,X22: name] :
% 0.19/0.47 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 0.19/0.47 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 0.19/0.47 => ( ( fresh_name_name @ X22 @ Z )
% 0.19/0.47 => ! [X33: pi] :
% 0.19/0.47 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 0.19/0.48 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 0.19/0.48 => ? [X4: late_freeRes] :
% 0.19/0.48 ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ X4 )
% 0.19/0.48 & ! [Y7: late_freeRes] :
% 0.19/0.48 ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ Y7 )
% 0.19/0.48 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % residual.rec_unique
% 0.19/0.48 thf(fact_337_residual_Orec__fin__supp,axiom,
% 0.19/0.48 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,X1: late_residual,Y1: late_subject] :
% 0.19/0.48 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 0.19/0.48 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 0.19/0.48 => ( ( late_r689718217ubject @ F1 @ F2 @ X1 @ Y1 )
% 0.19/0.48 => ( finite_finite_name @ ( supp_L1174290467t_name @ Y1 ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % residual.rec_fin_supp
% 0.19/0.48 thf(fact_338_residual_Orec__fin__supp,axiom,
% 0.19/0.48 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,X1: late_residual,Y1: late_freeRes] :
% 0.19/0.48 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 0.19/0.48 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 0.19/0.48 => ( ( late_r1613948593reeRes @ F1 @ F2 @ X1 @ Y1 )
% 0.19/0.48 => ( finite_finite_name @ ( supp_L1228270395s_name @ Y1 ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % residual.rec_fin_supp
% 0.19/0.48 thf(fact_339_residual_Orec__fin__supp,axiom,
% 0.19/0.48 ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,X1: late_residual,Y1: name] :
% 0.19/0.48 ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
% 0.19/0.48 => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
% 0.19/0.48 => ( ( late_r1742481968t_name @ F1 @ F2 @ X1 @ Y1 )
% 0.19/0.48 => ( finite_finite_name @ ( supp_name_name @ Y1 ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % residual.rec_fin_supp
% 0.19/0.48 thf(fact_340_residual_Orec__fin__supp,axiom,
% 0.19/0.48 ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,X1: late_residual,Y1: pi] :
% 0.19/0.48 ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
% 0.19/0.48 => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
% 0.19/0.48 => ( ( late_r1261898622set_pi @ F1 @ F2 @ X1 @ Y1 )
% 0.19/0.48 => ( finite_finite_name @ ( supp_pi_name @ Y1 ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % residual.rec_fin_supp
% 0.19/0.48 thf(fact_341_residual_Orec__fin__supp,axiom,
% 0.19/0.48 ! [F1: late_subject > name > pi > name > noption_pi,F2: late_freeRes > pi > name > noption_pi,X1: late_residual,Y1: name > noption_pi] :
% 0.19/0.48 ( ( finite_finite_name @ ( supp_L3230824i_name @ F1 ) )
% 0.19/0.48 => ( ( finite_finite_name @ ( supp_L635439693i_name @ F2 ) )
% 0.19/0.48 => ( ( late_r750878080ion_pi @ F1 @ F2 @ X1 @ Y1 )
% 0.19/0.48 => ( finite_finite_name @ ( supp_n468628396i_name @ Y1 ) ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % residual.rec_fin_supp
% 0.19/0.48 thf(fact_342_pi_Osupp_I4_J,axiom,
% 0.19/0.48 ! [X32: name,X1: name,X2: pi] :
% 0.19/0.48 ( ( supp_pi_name @ ( input @ X32 @ X1 @ X2 ) )
% 0.19/0.48 = ( sup_sup_set_name @ ( supp_name_name @ X32 ) @ ( supp_n468628396i_name @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.supp(4)
% 0.19/0.48 thf(fact_343_residual_Osupp_I1_J,axiom,
% 0.19/0.48 ! [X32: late_subject,X1: name,X2: pi] :
% 0.19/0.48 ( ( supp_L1174042202l_name @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 0.19/0.48 = ( sup_sup_set_name @ ( supp_L1174290467t_name @ X32 ) @ ( supp_n468628396i_name @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % residual.supp(1)
% 0.19/0.48 thf(fact_344_pi_Osupp_I7_J,axiom,
% 0.19/0.48 ! [X2: pi,X1: pi] :
% 0.19/0.48 ( ( supp_pi_name @ ( sum @ X2 @ X1 ) )
% 0.19/0.48 = ( sup_sup_set_name @ ( supp_pi_name @ X2 ) @ ( supp_pi_name @ X1 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.supp(7)
% 0.19/0.48 thf(fact_345_pi_Osupp_I8_J,axiom,
% 0.19/0.48 ! [X2: pi,X1: pi] :
% 0.19/0.48 ( ( supp_pi_name @ ( par @ X2 @ X1 ) )
% 0.19/0.48 = ( sup_sup_set_name @ ( supp_pi_name @ X2 ) @ ( supp_pi_name @ X1 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.supp(8)
% 0.19/0.48 thf(fact_346_residual_Osupp_I2_J,axiom,
% 0.19/0.48 ! [X2: late_freeRes,X1: pi] :
% 0.19/0.48 ( ( supp_L1174042202l_name @ ( late_FreeR @ X2 @ X1 ) )
% 0.19/0.48 = ( sup_sup_set_name @ ( supp_L1228270395s_name @ X2 ) @ ( supp_pi_name @ X1 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % residual.supp(2)
% 0.19/0.48 thf(fact_347_freeRes_Osupp_I1_J,axiom,
% 0.19/0.48 ! [X2: name,X1: name] :
% 0.19/0.48 ( ( supp_L1228270395s_name @ ( late_OutputR @ X2 @ X1 ) )
% 0.19/0.48 = ( sup_sup_set_name @ ( supp_name_name @ X2 ) @ ( supp_name_name @ X1 ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % freeRes.supp(1)
% 0.19/0.48 thf(fact_348_pi_Osupp_I2_J,axiom,
% 0.19/0.48 ! [X32: name,X2: name,X1: pi] :
% 0.19/0.48 ( ( supp_pi_name @ ( output @ X32 @ X2 @ X1 ) )
% 0.19/0.48 = ( sup_sup_set_name @ ( supp_name_name @ X32 ) @ ( sup_sup_set_name @ ( supp_name_name @ X2 ) @ ( supp_pi_name @ X1 ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 % pi.supp(2)
% 0.19/0.48
% 0.19/0.48 % Helper facts (3)
% 0.19/0.48 thf(help_If_3_1_If_001t__Agent__Oname_T,axiom,
% 0.19/0.48 ! [P: $o] :
% 0.19/0.48 ( ( P = $true )
% 0.19/0.48 | ( P = $false ) ) ).
% 0.19/0.48
% 0.19/0.48 thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
% 0.19/0.48 ! [X: name,Y: name] :
% 0.19/0.48 ( ( if_name @ $false @ X @ Y )
% 0.19/0.48 = Y ) ).
% 0.19/0.48
% 0.19/0.48 thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
% 0.19/0.48 ! [X: name,Y: name] :
% 0.19/0.48 ( ( if_name @ $true @ X @ Y )
% 0.19/0.48 = X ) ).
% 0.19/0.48
% 0.19/0.48 % Conjectures (1)
% 0.19/0.48 thf(conj_0,conjecture,
% 0.19/0.48 late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ ( par @ p @ q2 ) @ ( subs @ r2 @ x @ y ) ) ) ) ).
% 0.19/0.48
% 0.19/0.48 %------------------------------------------------------------------------------
% 0.19/0.48 ------------------------
% 3.04/1.66 ---- Embedded in THF ---
% 3.04/1.66 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.04/1.66 %%% Generated on Tue Feb 24 08:29:01 EST 2026
% 3.04/1.66 %%% using '$$dhol' embedding, version 1.3.0.
% 3.04/1.66 %%% Logic specification used:
% 3.04/1.66 %%% thf(spec, logic, $$dhol).
% 3.04/1.66
% 3.04/1.66 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.etxS7Hgr06/DTF2DTF17125.p
% See solution above
% 3.04/1.66 ------------------------
% 3.18/1.71 ---- Cleaned THF ---
% 3.18/1.71 thf(ty_n_t__Nominal__Onoption_I_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_Mt__Late____Semantics__Osubject_J_J_J,type,
% 3.18/1.71 noptio1065747147ubject: $tType ).
% 3.18/1.71
% 3.18/1.71 thf(ty_n_t__Nominal__Onoption_I_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_Mt__Late____Semantics__OfreeRes_J_J_J,type,
% 3.18/1.71 noptio930204083reeRes: $tType ).
% 3.18/1.71
% 3.18/1.71 thf(ty_n_t__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__Osubject_J_J_J,type,
% 3.18/1.71 noptio570777408ubject: $tType ).
% 3.18/1.71
% 3.18/1.71 thf(ty_n_t__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__OfreeRes_J_J_J,type,
% 3.18/1.71 noptio435234344reeRes: $tType ).
% 3.18/1.71
% 3.18/1.71 thf(ty_n_t__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Oname_J_J_J,type,
% 3.18/1.71 noptio1926134715n_name: $tType ).
% 3.18/1.71
% 3.18/1.71 thf(ty_n_t__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J,type,
% 3.18/1.71 noptio354675977ion_pi: $tType ).
% 3.18/1.71
% 3.18/1.71 thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__Osubject_J,type,
% 3.18/1.71 noption_Late_subject: $tType ).
% 3.18/1.71
% 3.18/1.71 thf(ty_n_t__Nominal__Onoption_It__Late____Semantics__OfreeRes_J,type,
% 3.18/1.71 noption_Late_freeRes: $tType ).
% 3.18/1.71
% 3.18/1.71 thf(ty_n_t__Nominal__Onoption_It__Agent__Oname_J,type,
% 3.18/1.71 noption_name: $tType ).
% 3.18/1.71
% 3.18/1.71 thf(ty_n_t__Nominal__Onoption_It__Agent__Opi_J,type,
% 3.18/1.71 noption_pi: $tType ).
% 3.18/1.71
% 3.18/1.71 thf(ty_n_t__Set__Oset_It__Agent__Oname_J,type,
% 3.18/1.71 set_name: $tType ).
% 3.18/1.71
% 3.18/1.71 thf(ty_n_t__Late____Semantics__Oresidual,type,
% 3.18/1.71 late_residual: $tType ).
% 3.18/1.71
% 3.18/1.71 thf(ty_n_t__Late____Semantics__Osubject,type,
% 3.18/1.71 late_subject: $tType ).
% 3.18/1.71
% 3.18/1.71 thf(ty_n_t__Late____Semantics__OfreeRes,type,
% 3.18/1.71 late_freeRes: $tType ).
% 3.18/1.71
% 3.18/1.71 thf(ty_n_t__Agent__Oname,type,
% 3.18/1.71 name: $tType ).
% 3.18/1.71
% 3.18/1.71 thf(ty_n_t__Agent__Opi,type,
% 3.18/1.71 pi: $tType ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Agent_Opi_OBang,type,
% 3.18/1.71 bang: pi > pi ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Agent_Opi_OInput,type,
% 3.18/1.71 input: name > name > pi > pi ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Agent_Opi_OMatch,type,
% 3.18/1.71 match: name > name > pi > pi ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Agent_Opi_OMismatch,type,
% 3.18/1.71 mismatch: name > name > pi > pi ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Agent_Opi_OOutput,type,
% 3.18/1.71 output: name > name > pi > pi ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Agent_Opi_OPar,type,
% 3.18/1.71 par: pi > pi > pi ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Agent_Opi_OPiNil,type,
% 3.18/1.71 piNil: pi ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Agent_Opi_ORes,type,
% 3.18/1.71 res: name > pi > pi ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Agent_Opi_OSum,type,
% 3.18/1.71 sum: pi > pi > pi ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Agent_Opi_OTau,type,
% 3.18/1.71 tau: pi > pi ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Agent_Opi_Opi__rec_001t__Agent__Opi,type,
% 3.18/1.71 pi_rec_pi: pi > ( name > name > pi > pi > pi ) > ( pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( name > name > pi > pi > pi ) > ( pi > pi > pi > pi > pi ) > ( pi > pi > pi > pi > pi ) > ( name > pi > pi > pi ) > ( pi > pi > pi ) > pi > pi ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Agent_Osubs,type,
% 3.18/1.71 subs: pi > name > name > pi ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Agent_Osubst__name,type,
% 3.18/1.71 subst_name: name > name > name > name ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Finite__Set_Ofinite_001t__Agent__Oname,type,
% 3.18/1.71 finite_finite_name: set_name > $o ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_If_001t__Agent__Oname,type,
% 3.18/1.71 if_name: $o > name > name > name ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_ObangPred,type,
% 3.18/1.71 late_bangPred: pi > pi > $o ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_OfreeRes_OOutputR,type,
% 3.18/1.71 late_OutputR: name > name > late_freeRes ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_OfreeRes_OTauR,type,
% 3.18/1.71 late_TauR: late_freeRes ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_Oresidual_OBoundR,type,
% 3.18/1.71 late_BoundR: late_subject > name > pi > late_residual ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_Oresidual_OFreeR,type,
% 3.18/1.71 late_FreeR: late_freeRes > pi > late_residual ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec_001t__Agent__Oname,type,
% 3.18/1.71 late_r1174711868c_name: ( late_subject > name > pi > name ) > ( late_freeRes > pi > name ) > late_residual > name ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec_001t__Agent__Opi,type,
% 3.18/1.71 late_residual_rec_pi: ( late_subject > name > pi > pi ) > ( late_freeRes > pi > pi ) > late_residual > pi ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec_001t__Late____Semantics__OfreeRes,type,
% 3.18/1.71 late_r124702629reeRes: ( late_subject > name > pi > late_freeRes ) > ( late_freeRes > pi > late_freeRes ) > late_residual > late_freeRes ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec_001t__Late____Semantics__Osubject,type,
% 3.18/1.71 late_r1347955901ubject: ( late_subject > name > pi > late_subject ) > ( late_freeRes > pi > late_subject ) > late_residual > late_subject ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set_001_062_It__Agent__Oname_Mt__Nominal__Onoption_I_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J_J_J,type,
% 3.18/1.71 late_r1558248490ion_pi: ( late_subject > name > pi > name > noptio354675977ion_pi ) > ( late_freeRes > pi > name > noptio354675977ion_pi ) > late_residual > ( name > noptio354675977ion_pi ) > $o ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Oname_J_J,type,
% 3.18/1.71 late_r303715378n_name: ( late_subject > name > pi > name > noption_name ) > ( late_freeRes > pi > name > noption_name ) > late_residual > ( name > noption_name ) > $o ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
% 3.18/1.71 late_r750878080ion_pi: ( late_subject > name > pi > name > noption_pi ) > ( late_freeRes > pi > name > noption_pi ) > late_residual > ( name > noption_pi ) > $o ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set_001t__Agent__Oname,type,
% 3.18/1.71 late_r1742481968t_name: ( late_subject > name > pi > name ) > ( late_freeRes > pi > name ) > late_residual > name > $o ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set_001t__Agent__Opi,type,
% 3.18/1.71 late_r1261898622set_pi: ( late_subject > name > pi > pi ) > ( late_freeRes > pi > pi ) > late_residual > pi > $o ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set_001t__Late____Semantics__OfreeRes,type,
% 3.18/1.71 late_r1613948593reeRes: ( late_subject > name > pi > late_freeRes ) > ( late_freeRes > pi > late_freeRes ) > late_residual > late_freeRes > $o ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_Oresidual_Oresidual__rec__set_001t__Late____Semantics__Osubject,type,
% 3.18/1.71 late_r689718217ubject: ( late_subject > name > pi > late_subject ) > ( late_freeRes > pi > late_subject ) > late_residual > late_subject > $o ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_Osubject_OBoundOutputS,type,
% 3.18/1.71 late_BoundOutputS: name > late_subject ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_Osubject_OInputS,type,
% 3.18/1.71 late_InputS: name > late_subject ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Late__Semantics_Otransitions,type,
% 3.18/1.71 late_transitions: pi > late_residual > $o ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Agent__Oname_J,type,
% 3.18/1.71 sup_sup_set_name: set_name > set_name > set_name ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Oname_J_J,type,
% 3.18/1.71 abs_fu1394407909n_name: name > ( name > noption_name ) > name > noptio1926134715n_name ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Agent__Opi_J_J,type,
% 3.18/1.71 abs_fu1614711987ion_pi: name > ( name > noption_pi ) > name > noptio354675977ion_pi ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__OfreeRes_J_J,type,
% 3.18/1.71 abs_fu1763130856reeRes: name > ( name > noption_Late_freeRes ) > name > noptio435234344reeRes ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001_062_It__Agent__Oname_Mt__Nominal__Onoption_It__Late____Semantics__Osubject_J_J,type,
% 3.18/1.71 abs_fu1705804544ubject: name > ( name > noption_Late_subject ) > name > noptio570777408ubject ).
% 3.18/1.71
% 3.18/1.71 thf(sy_c_Nominal_Oabs__fun_001t__Agent__Oname_001_062_It__Late____Semantics__OfreeRes_M_062_It__Agent__Opi_Mt__Late____Semantics__OfreeRes_J_J,type,
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% 3.18/1.71 fresh_name_pi @ x @ q ).
% 3.18/1.71
% 3.18/1.71 thf(fact_7_cClose2_Ohyps_I13_J,axiom,
% 3.18/1.71 fresh_name_pi @ y @ p ).
% 3.18/1.71
% 3.18/1.71 thf(fact_8_cClose2_Ohyps_I12_J,axiom,
% 3.18/1.71 fresh_name_pi @ x @ p ).
% 3.18/1.71
% 3.18/1.71 thf(fact_9_cClose2_Ohyps_I4_J,axiom,
% 3.18/1.71 fresh_name_pi @ x @ r ).
% 3.18/1.71
% 3.18/1.71 thf(fact_10_cClose2_Ohyps_I7_J,axiom,
% 3.18/1.71 fresh_name_pi @ x @ q2 ).
% 3.18/1.71
% 3.18/1.71 thf(fact_11_cClose2_Ohyps_I11_J,axiom,
% 3.18/1.71 fresh_name_pi @ y @ r2 ).
% 3.18/1.71
% 3.18/1.71 thf(fact_12_cClose2_Ohyps_I2_J,axiom,
% 3.18/1.71 late_transitions @ r @ ( late_BoundR @ ( late_InputS @ a ) @ x @ r2 ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_13__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_Aa_060_092_060nu_062y_062_A_092_060prec_062_AP_A_092_060parallel_062_AQ_H_092_060close_062,axiom,
% 3.18/1.71 late_transitions @ ( par @ p @ q ) @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ ( par @ p @ q2 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_14_cClose2_Ohyps_I1_J,axiom,
% 3.18/1.71 late_transitions @ q @ ( late_BoundR @ ( late_BoundOutputS @ a ) @ y @ q2 ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_15_cPar2_Ohyps,axiom,
% 3.18/1.71 late_transitions @ ( par @ q @ r ) @ ( late_FreeR @ alpha @ qr ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_16_Free_Ohyps,axiom,
% 3.18/1.71 late_transitions @ ( par @ p @ ( par @ q @ r ) ) @ ( late_FreeR @ alpha @ pqr ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_17_simps_I9_J,axiom,
% 3.18/1.71 ! [X: name,C: name,D: name,P: pi] :
% 3.18/1.71 ( ( X != C )
% 3.18/1.71 => ( ( X != D )
% 3.18/1.71 => ( ( subs @ ( res @ X @ P ) @ C @ D )
% 3.18/1.71 = ( res @ X @ ( subs @ P @ C @ D ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_18_simps_I8_J,axiom,
% 3.18/1.71 ! [P: pi,Q: pi,C: name,D: name] :
% 3.18/1.71 ( ( subs @ ( par @ P @ Q ) @ C @ D )
% 3.18/1.71 = ( par @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_19_Par1F,axiom,
% 3.18/1.71 ! [P: pi,Alpha: late_freeRes,P2: pi,Q: pi] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.18/1.71 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P2 @ Q ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_20_Par2F,axiom,
% 3.18/1.71 ! [Q: pi,Alpha: late_freeRes,Q2: pi,P: pi] :
% 3.18/1.71 ( ( late_transitions @ Q @ ( late_FreeR @ Alpha @ Q2 ) )
% 3.18/1.71 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ Alpha @ ( par @ P @ Q2 ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_21_subst__identity,axiom,
% 3.18/1.71 ! [P: pi,A: name] :
% 3.18/1.71 ( ( subs @ P @ A @ A )
% 3.18/1.71 = P ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_22_pi_Odistinct_I85_J,axiom,
% 3.18/1.71 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 3.18/1.71 ( ( par @ Pi1 @ Pi2 )
% 3.18/1.71 != ( res @ Name @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_23_Late__Semantics_OClose1,axiom,
% 3.18/1.71 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 3.18/1.71 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 3.18/1.71 => ( ( fresh_name_pi @ Y @ P )
% 3.18/1.71 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_24_Late__Semantics_OClose2,axiom,
% 3.18/1.71 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 3.18/1.71 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 3.18/1.71 => ( ( fresh_name_pi @ Y @ Q )
% 3.18/1.71 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_25_transitions_OClose1,axiom,
% 3.18/1.71 ! [P: pi,A: name,X: name,P2: pi,Q: pi,Y: name,Q2: pi] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 3.18/1.71 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ Q2 ) )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ P )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ Q )
% 3.18/1.71 => ( ( fresh_name_pi @ Y @ P )
% 3.18/1.71 => ( ( fresh_name_pi @ Y @ Q )
% 3.18/1.71 => ( ( X != A )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ Q2 )
% 3.18/1.71 => ( ( Y != A )
% 3.18/1.71 => ( ( fresh_name_pi @ Y @ P2 )
% 3.18/1.71 => ( ( X != Y )
% 3.18/1.71 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ ( subs @ P2 @ X @ Y ) @ Q2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_26_transitions_OClose2,axiom,
% 3.18/1.71 ! [P: pi,A: name,Y: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ Y @ P2 ) )
% 3.18/1.71 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ P )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ Q )
% 3.18/1.71 => ( ( fresh_name_pi @ Y @ P )
% 3.18/1.71 => ( ( fresh_name_pi @ Y @ Q )
% 3.18/1.71 => ( ( X != A )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ P2 )
% 3.18/1.71 => ( ( Y != A )
% 3.18/1.71 => ( ( fresh_name_pi @ Y @ Q2 )
% 3.18/1.71 => ( ( X != Y )
% 3.18/1.71 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( res @ Y @ ( par @ P2 @ ( subs @ Q2 @ X @ Y ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_27_substRes2,axiom,
% 3.18/1.71 ! [B: name,P: pi,A: name] :
% 3.18/1.71 ( ( fresh_name_pi @ B @ P )
% 3.18/1.71 => ( ( res @ A @ P )
% 3.18/1.71 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_28_substRes3,axiom,
% 3.18/1.71 ! [B: name,P: pi,A: name] :
% 3.18/1.71 ( ( fresh_name_pi @ B @ P )
% 3.18/1.71 => ( ( subs @ ( res @ A @ P ) @ A @ B )
% 3.18/1.71 = ( res @ B @ ( subs @ P @ A @ B ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_29_Late__Semantics_Osubject_Oinject_I2_J,axiom,
% 3.18/1.71 ! [X1: name,Y1: name] :
% 3.18/1.71 ( ( ( late_BoundOutputS @ X1 )
% 3.18/1.71 = ( late_BoundOutputS @ Y1 ) )
% 3.18/1.71 = ( X1 = Y1 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_30_pi_Ofresh_I8_J,axiom,
% 3.18/1.71 ! [A: name,X2: pi,X1: pi] :
% 3.18/1.71 ( ( fresh_name_pi @ A @ ( par @ X2 @ X1 ) )
% 3.18/1.71 = ( ( fresh_name_pi @ A @ X2 )
% 3.18/1.71 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_31_substTrans,axiom,
% 3.18/1.71 ! [B: name,P: pi,A: name,C: name] :
% 3.18/1.71 ( ( fresh_name_pi @ B @ P )
% 3.18/1.71 => ( ( subs @ ( subs @ P @ A @ B ) @ B @ C )
% 3.18/1.71 = ( subs @ P @ A @ C ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_32_Late__Semantics_Osubject_Odistinct_I1_J,axiom,
% 3.18/1.71 ! [Name2: name,Name: name] :
% 3.18/1.71 ( ( late_InputS @ Name2 )
% 3.18/1.71 != ( late_BoundOutputS @ Name ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_33_name__exists__fresh,axiom,
% 3.18/1.71 ! [X: late_subject] :
% 3.18/1.71 ~ ! [C2: name] :
% 3.18/1.71 ~ ( fresh_717452603ubject @ C2 @ X ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_34_name__exists__fresh,axiom,
% 3.18/1.71 ! [X: late_freeRes] :
% 3.18/1.71 ~ ! [C2: name] :
% 3.18/1.71 ~ ( fresh_1641682979reeRes @ C2 @ X ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_35_name__exists__fresh,axiom,
% 3.18/1.71 ! [X: name] :
% 3.18/1.71 ~ ! [C2: name] :
% 3.18/1.71 ~ ( fresh_name_name @ C2 @ X ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_36_name__exists__fresh,axiom,
% 3.18/1.71 ! [X: pi] :
% 3.18/1.71 ~ ! [C2: name] :
% 3.18/1.71 ~ ( fresh_name_pi @ C2 @ X ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_37_subject_Oinducts,axiom,
% 3.18/1.71 ! [P: late_subject > $o,Subject: late_subject] :
% 3.18/1.71 ( ! [Name3: name] : ( P @ ( late_InputS @ Name3 ) )
% 3.18/1.71 => ( ! [Name3: name] : ( P @ ( late_BoundOutputS @ Name3 ) )
% 3.18/1.71 => ( P @ Subject ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_38_residual_Ostrong__inducts,axiom,
% 3.18/1.71 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 3.18/1.71 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: late_subject] :
% 3.18/1.71 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 3.18/1.71 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 3.18/1.71 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 3.18/1.71 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 3.18/1.71 => ( P @ Z @ Residual ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_39_residual_Ostrong__inducts,axiom,
% 3.18/1.71 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 3.18/1.71 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 3.18/1.71 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 3.18/1.71 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 3.18/1.71 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 3.18/1.71 => ( P @ Z @ Residual ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_40_residual_Ostrong__inducts,axiom,
% 3.18/1.71 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 3.18/1.71 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: name] :
% 3.18/1.71 ( ( fresh_name_name @ Name3 @ Z2 )
% 3.18/1.71 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 3.18/1.71 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 3.18/1.71 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 3.18/1.71 => ( P @ Z @ Residual ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_41_residual_Ostrong__inducts,axiom,
% 3.18/1.71 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 3.18/1.71 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: pi] :
% 3.18/1.71 ( ( fresh_name_pi @ Name3 @ Z2 )
% 3.18/1.71 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 3.18/1.71 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 3.18/1.71 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 3.18/1.71 => ( P @ Z @ Residual ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_42_residual_Ostrong__induct,axiom,
% 3.18/1.71 ! [P: late_subject > late_residual > $o,Z: late_subject,Residual: late_residual] :
% 3.18/1.71 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: late_subject] :
% 3.18/1.71 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 3.18/1.71 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 3.18/1.71 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 3.18/1.71 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_subject] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 3.18/1.71 => ( P @ Z @ Residual ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_43_residual_Ostrong__induct,axiom,
% 3.18/1.71 ! [P: late_freeRes > late_residual > $o,Z: late_freeRes,Residual: late_residual] :
% 3.18/1.71 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 3.18/1.71 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 3.18/1.71 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 3.18/1.71 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: late_freeRes] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 3.18/1.71 => ( P @ Z @ Residual ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_44_residual_Ostrong__induct,axiom,
% 3.18/1.71 ! [P: name > late_residual > $o,Z: name,Residual: late_residual] :
% 3.18/1.71 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: name] :
% 3.18/1.71 ( ( fresh_name_name @ Name3 @ Z2 )
% 3.18/1.71 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 3.18/1.71 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 3.18/1.71 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: name] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 3.18/1.71 => ( P @ Z @ Residual ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_45_residual_Ostrong__induct,axiom,
% 3.18/1.71 ! [P: pi > late_residual > $o,Z: pi,Residual: late_residual] :
% 3.18/1.71 ( ! [Subject2: late_subject,Name3: name,Pi3: pi,Z2: pi] :
% 3.18/1.71 ( ( fresh_name_pi @ Name3 @ Z2 )
% 3.18/1.71 => ( ( fresh_717452603ubject @ Name3 @ Subject2 )
% 3.18/1.71 => ( P @ Z2 @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) ) ) )
% 3.18/1.71 => ( ! [FreeRes: late_freeRes,Pi3: pi,Z2: pi] : ( P @ Z2 @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 3.18/1.71 => ( P @ Z @ Residual ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_46_freshBoundDerivative_I2_J,axiom,
% 3.18/1.71 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 3.18/1.71 => ( ( fresh_name_pi @ Y @ P )
% 3.18/1.71 => ( ( Y != X )
% 3.18/1.71 => ( fresh_name_pi @ Y @ P2 ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_47_freshRes,axiom,
% 3.18/1.71 ! [A: name,P: pi] : ( fresh_name_pi @ A @ ( res @ A @ P ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_48_residual_Oinducts,axiom,
% 3.18/1.71 ! [P: late_residual > $o,Residual: late_residual] :
% 3.18/1.71 ( ! [Subject2: late_subject,Name3: name,Pi3: pi] : ( P @ ( late_BoundR @ Subject2 @ Name3 @ Pi3 ) )
% 3.18/1.71 => ( ! [FreeRes: late_freeRes,Pi3: pi] : ( P @ ( late_FreeR @ FreeRes @ Pi3 ) )
% 3.18/1.71 => ( P @ Residual ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_49_residual_Odistinct_I1_J,axiom,
% 3.18/1.71 ! [Subject: late_subject,Name2: name,Pi4: pi,FreeRes2: late_freeRes,Pi: pi] :
% 3.18/1.71 ( ( late_BoundR @ Subject @ Name2 @ Pi4 )
% 3.18/1.71 != ( late_FreeR @ FreeRes2 @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_50_fresh__fact2,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi] :
% 3.18/1.71 ( ( A != B )
% 3.18/1.71 => ( fresh_name_pi @ A @ ( subs @ P @ A @ B ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_51_fresh__fact1,axiom,
% 3.18/1.71 ! [A: name,P: pi,C: name,B: name] :
% 3.18/1.71 ( ( fresh_name_pi @ A @ P )
% 3.18/1.71 => ( ( A != C )
% 3.18/1.71 => ( fresh_name_pi @ A @ ( subs @ P @ B @ C ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_52_mem__Collect__eq,axiom,
% 3.18/1.71 ! [A: name,P: name > $o] :
% 3.18/1.71 ( ( member_name @ A @ ( collect_name @ P ) )
% 3.18/1.71 = ( P @ A ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_53_Collect__mem__eq,axiom,
% 3.18/1.71 ! [A2: set_name] :
% 3.18/1.71 ( ( collect_name
% 3.18/1.71 @ ^ [X3: name] : ( member_name @ X3 @ A2 ) )
% 3.18/1.71 = A2 ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_54_Collect__cong,axiom,
% 3.18/1.71 ! [P: name > $o,Q: name > $o] :
% 3.18/1.71 ( ! [X4: name] :
% 3.18/1.71 ( ( P @ X4 )
% 3.18/1.71 = ( Q @ X4 ) )
% 3.18/1.71 => ( ( collect_name @ P )
% 3.18/1.71 = ( collect_name @ Q ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_55_forget,axiom,
% 3.18/1.71 ! [A: name,P: pi,B: name] :
% 3.18/1.71 ( ( fresh_name_pi @ A @ P )
% 3.18/1.71 => ( ( subs @ P @ A @ B )
% 3.18/1.71 = P ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_56_parCasesB,axiom,
% 3.18/1.71 ! [P: pi,Q: pi,A: late_subject,X: name,PQ: pi,Prop: pi > $o] :
% 3.18/1.71 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ PQ ) )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ P )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ Q )
% 3.18/1.71 => ( ! [P3: pi] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P3 ) )
% 3.18/1.71 => ( Prop @ ( par @ P3 @ Q ) ) )
% 3.18/1.71 => ( ! [Q3: pi] :
% 3.18/1.71 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q3 ) )
% 3.18/1.71 => ( Prop @ ( par @ P @ Q3 ) ) )
% 3.18/1.71 => ( Prop @ PQ ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_57_Late__Semantics_OPar2B,axiom,
% 3.18/1.71 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 3.18/1.71 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ P )
% 3.18/1.71 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_58_Late__Semantics_OPar1B,axiom,
% 3.18/1.71 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ Q )
% 3.18/1.71 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_59_pi_Oinject_I7_J,axiom,
% 3.18/1.71 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 3.18/1.71 ( ( ( par @ X2 @ X1 )
% 3.18/1.71 = ( par @ Y2 @ Y1 ) )
% 3.18/1.71 = ( ( X2 = Y2 )
% 3.18/1.71 & ( X1 = Y1 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_60_freshFreeDerivative_I2_J,axiom,
% 3.18/1.71 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.18/1.71 => ( ( fresh_name_pi @ Y @ P )
% 3.18/1.71 => ( fresh_name_pi @ Y @ P2 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_61_residual_Oinject_I2_J,axiom,
% 3.18/1.71 ! [X2: late_freeRes,X1: pi,Y2: late_freeRes,Y1: pi] :
% 3.18/1.71 ( ( ( late_FreeR @ X2 @ X1 )
% 3.18/1.71 = ( late_FreeR @ Y2 @ Y1 ) )
% 3.18/1.71 = ( ( X2 = Y2 )
% 3.18/1.71 & ( X1 = Y1 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_62_transitions_OComm2,axiom,
% 3.18/1.71 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 3.18/1.71 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ P )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ Q )
% 3.18/1.71 => ( ( X != A )
% 3.18/1.71 => ( ( X != B )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ P2 )
% 3.18/1.71 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_63_transitions_OComm1,axiom,
% 3.18/1.71 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 3.18/1.71 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ P )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ Q )
% 3.18/1.71 => ( ( X != A )
% 3.18/1.71 => ( ( X != B )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ Q2 )
% 3.18/1.71 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_64_Late__Semantics1_Osubject_Oinject_I1_J,axiom,
% 3.18/1.71 ! [X1: name,Y1: name] :
% 3.18/1.71 ( ( ( late_InputS @ X1 )
% 3.18/1.71 = ( late_InputS @ Y1 ) )
% 3.18/1.71 = ( X1 = Y1 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_65_Late__Semantics1_Osubject_Oinject_I2_J,axiom,
% 3.18/1.71 ! [X2: name,Y2: name] :
% 3.18/1.71 ( ( ( late_BoundOutputS @ X2 )
% 3.18/1.71 = ( late_BoundOutputS @ Y2 ) )
% 3.18/1.71 = ( X2 = Y2 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_66_Late__Semantics_OComm2,axiom,
% 3.18/1.71 ! [P: pi,A: name,B: name,P2: pi,Q: pi,X: name,Q2: pi] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 3.18/1.71 => ( ( late_transitions @ Q @ ( late_BoundR @ ( late_InputS @ A ) @ X @ Q2 ) )
% 3.18/1.71 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ P2 @ ( subs @ Q2 @ X @ B ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_67_Late__Semantics_OComm1,axiom,
% 3.18/1.71 ! [P: pi,A: name,X: name,P2: pi,Q: pi,B: name,Q2: pi] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P2 ) )
% 3.18/1.71 => ( ( late_transitions @ Q @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ Q2 ) )
% 3.18/1.71 => ( late_transitions @ ( par @ P @ Q ) @ ( late_FreeR @ late_TauR @ ( par @ ( subs @ P2 @ X @ B ) @ Q2 ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_68_Late__Semantics1_Osubject_Odistinct_I1_J,axiom,
% 3.18/1.71 ! [X1: name,X2: name] :
% 3.18/1.71 ( ( late_InputS @ X1 )
% 3.18/1.71 != ( late_BoundOutputS @ X2 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_69_subject_Oexhaust,axiom,
% 3.18/1.71 ! [Y: late_subject] :
% 3.18/1.71 ( ! [X12: name] :
% 3.18/1.71 ( Y
% 3.18/1.71 != ( late_InputS @ X12 ) )
% 3.18/1.71 => ~ ! [X22: name] :
% 3.18/1.71 ( Y
% 3.18/1.71 != ( late_BoundOutputS @ X22 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_70_Open,axiom,
% 3.18/1.71 ! [P: pi,A: name,B: name,P2: pi] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) )
% 3.18/1.71 => ( ( A != B )
% 3.18/1.71 => ( late_transitions @ ( res @ B @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ A ) @ B @ P2 ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_71_freeRes_Ofresh_I1_J,axiom,
% 3.18/1.71 ! [A: name,X2: name,X1: name] :
% 3.18/1.71 ( ( fresh_1641682979reeRes @ A @ ( late_OutputR @ X2 @ X1 ) )
% 3.18/1.71 = ( ( fresh_name_name @ A @ X2 )
% 3.18/1.71 & ( fresh_name_name @ A @ X1 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_72_Late__Semantics_OfreeRes_Oinject,axiom,
% 3.18/1.71 ! [X2: name,X1: name,Y2: name,Y1: name] :
% 3.18/1.71 ( ( ( late_OutputR @ X2 @ X1 )
% 3.18/1.71 = ( late_OutputR @ Y2 @ Y1 ) )
% 3.18/1.71 = ( ( X2 = Y2 )
% 3.18/1.71 & ( X1 = Y1 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_73_Late__Semantics1_OfreeRes_Oinject,axiom,
% 3.18/1.71 ! [X11: name,X122: name,Y11: name,Y12: name] :
% 3.18/1.71 ( ( ( late_OutputR @ X11 @ X122 )
% 3.18/1.71 = ( late_OutputR @ Y11 @ Y12 ) )
% 3.18/1.71 = ( ( X11 = Y11 )
% 3.18/1.71 & ( X122 = Y12 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_74_freeRes_Ofresh_I2_J,axiom,
% 3.18/1.71 ! [A: name] : ( fresh_1641682979reeRes @ A @ late_TauR ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_75_residual_Ofresh_I2_J,axiom,
% 3.18/1.71 ! [A: name,X2: late_freeRes,X1: pi] :
% 3.18/1.71 ( ( fresh_81631222sidual @ A @ ( late_FreeR @ X2 @ X1 ) )
% 3.18/1.71 = ( ( fresh_1641682979reeRes @ A @ X2 )
% 3.18/1.71 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_76_subject_Ofresh_I2_J,axiom,
% 3.18/1.71 ! [A: name,X1: name] :
% 3.18/1.71 ( ( fresh_717452603ubject @ A @ ( late_BoundOutputS @ X1 ) )
% 3.18/1.71 = ( fresh_name_name @ A @ X1 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_77_subject_Ofresh_I1_J,axiom,
% 3.18/1.71 ! [A: name,X1: name] :
% 3.18/1.71 ( ( fresh_717452603ubject @ A @ ( late_InputS @ X1 ) )
% 3.18/1.71 = ( fresh_name_name @ A @ X1 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_78_Late__Semantics1_OfreeRes_Odistinct_I1_J,axiom,
% 3.18/1.71 ! [X11: name,X122: name] :
% 3.18/1.71 ( ( late_OutputR @ X11 @ X122 )
% 3.18/1.71 != late_TauR ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_79_freeRes_Oexhaust,axiom,
% 3.18/1.71 ! [Y: late_freeRes] :
% 3.18/1.71 ( ! [X112: name,X123: name] :
% 3.18/1.71 ( Y
% 3.18/1.71 != ( late_OutputR @ X112 @ X123 ) )
% 3.18/1.71 => ( Y = late_TauR ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_80_Late__Semantics_OfreeRes_Odistinct_I1_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name] :
% 3.18/1.71 ( ( late_OutputR @ Name1 @ Name22 )
% 3.18/1.71 != late_TauR ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_81_freeRes_Oinducts,axiom,
% 3.18/1.71 ! [P: late_freeRes > $o,FreeRes3: late_freeRes] :
% 3.18/1.71 ( ! [Name12: name,Name23: name] : ( P @ ( late_OutputR @ Name12 @ Name23 ) )
% 3.18/1.71 => ( ( P @ late_TauR )
% 3.18/1.71 => ( P @ FreeRes3 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_82_resCases_H,axiom,
% 3.18/1.71 ! [X: name,P: pi,Rs: late_residual] :
% 3.18/1.71 ( ( late_transitions @ ( res @ X @ P ) @ Rs )
% 3.18/1.71 => ( ! [P4: pi,A3: name,B2: name] :
% 3.18/1.71 ( ( ( res @ X @ P )
% 3.18/1.71 = ( res @ B2 @ P4 ) )
% 3.18/1.71 => ! [P3: pi] :
% 3.18/1.71 ( ( Rs
% 3.18/1.71 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B2 @ P3 ) )
% 3.18/1.71 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B2 ) @ P3 ) )
% 3.18/1.71 => ( A3 = B2 ) ) ) )
% 3.18/1.71 => ( ! [P4: pi,A3: late_subject,X4: name,P3: pi,Y3: name] :
% 3.18/1.71 ( ( ( res @ X @ P )
% 3.18/1.71 = ( res @ Y3 @ P4 ) )
% 3.18/1.71 => ( ( Rs
% 3.18/1.71 = ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P3 ) ) )
% 3.18/1.71 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X4 @ P3 ) )
% 3.18/1.71 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 3.18/1.71 => ( ( Y3 != X4 )
% 3.18/1.71 => ( ( fresh_name_pi @ X4 @ P4 )
% 3.18/1.71 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) )
% 3.18/1.71 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y3: name] :
% 3.18/1.71 ( ( ( res @ X @ P )
% 3.18/1.71 = ( res @ Y3 @ P4 ) )
% 3.18/1.71 => ( ( Rs
% 3.18/1.71 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P3 ) ) )
% 3.18/1.71 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 3.18/1.71 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_83_freshResidual,axiom,
% 3.18/1.71 ! [P: pi,Rs: late_residual,X: name] :
% 3.18/1.71 ( ( late_transitions @ P @ Rs )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ P )
% 3.18/1.71 => ( fresh_81631222sidual @ X @ Rs ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_84_resCasesF,axiom,
% 3.18/1.71 ! [X: name,P: pi,Alpha: late_freeRes,XP: pi,F: pi > $o] :
% 3.18/1.71 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ XP ) )
% 3.18/1.71 => ( ! [P3: pi] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P3 ) )
% 3.18/1.71 => ( ( fresh_1641682979reeRes @ X @ Alpha )
% 3.18/1.71 => ( F @ ( res @ X @ P3 ) ) ) )
% 3.18/1.71 => ( F @ XP ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_85_resCasesF_H,axiom,
% 3.18/1.71 ! [X: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 3.18/1.71 ( ( late_transitions @ ( res @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 3.18/1.71 => ~ ! [P4: pi,Alpha2: late_freeRes,P3: pi,Y3: name] :
% 3.18/1.71 ( ( ( res @ X @ P )
% 3.18/1.71 = ( res @ Y3 @ P4 ) )
% 3.18/1.71 => ( ( ( late_FreeR @ Alpha @ P2 )
% 3.18/1.71 = ( late_FreeR @ Alpha2 @ ( res @ Y3 @ P3 ) ) )
% 3.18/1.71 => ( ( late_transitions @ P4 @ ( late_FreeR @ Alpha2 @ P3 ) )
% 3.18/1.71 => ~ ( fresh_1641682979reeRes @ Y3 @ Alpha2 ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_86_ResF,axiom,
% 3.18/1.71 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.18/1.71 => ( ( fresh_1641682979reeRes @ Y @ Alpha )
% 3.18/1.71 => ( late_transitions @ ( res @ Y @ P ) @ ( late_FreeR @ Alpha @ ( res @ Y @ P2 ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_87_Late__Semantics_OResB,axiom,
% 3.18/1.71 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 3.18/1.71 => ( ( fresh_717452603ubject @ Y @ A )
% 3.18/1.71 => ( ( Y != X )
% 3.18/1.71 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_88_freshFreeDerivative_I1_J,axiom,
% 3.18/1.71 ! [P: pi,Alpha: late_freeRes,P2: pi,Y: name] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_FreeR @ Alpha @ P2 ) )
% 3.18/1.71 => ( ( fresh_name_pi @ Y @ P )
% 3.18/1.71 => ( fresh_1641682979reeRes @ Y @ Alpha ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_89_freshBoundDerivative_I1_J,axiom,
% 3.18/1.71 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 3.18/1.71 => ( ( fresh_name_pi @ Y @ P )
% 3.18/1.71 => ( fresh_717452603ubject @ Y @ A ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_90_resCasesB_H,axiom,
% 3.18/1.71 ! [X5: name,P: pi,A: late_subject,Y4: name,P2: pi] :
% 3.18/1.71 ( ( late_transitions @ ( res @ X5 @ P ) @ ( late_BoundR @ A @ Y4 @ P2 ) )
% 3.18/1.71 => ( ! [P4: pi,A3: name,B2: name] :
% 3.18/1.71 ( ( ( res @ X5 @ P )
% 3.18/1.71 = ( res @ B2 @ P4 ) )
% 3.18/1.71 => ! [P3: pi] :
% 3.18/1.71 ( ( ( late_BoundR @ A @ Y4 @ P2 )
% 3.18/1.71 = ( late_BoundR @ ( late_BoundOutputS @ A3 ) @ B2 @ P3 ) )
% 3.18/1.71 => ( ( late_transitions @ P4 @ ( late_FreeR @ ( late_OutputR @ A3 @ B2 ) @ P3 ) )
% 3.18/1.71 => ( A3 = B2 ) ) ) )
% 3.18/1.71 => ~ ! [P4: pi,A3: late_subject,X4: name,P3: pi,Y3: name] :
% 3.18/1.71 ( ( ( res @ X5 @ P )
% 3.18/1.71 = ( res @ Y3 @ P4 ) )
% 3.18/1.71 => ( ( ( late_BoundR @ A @ Y4 @ P2 )
% 3.18/1.71 = ( late_BoundR @ A3 @ X4 @ ( res @ Y3 @ P3 ) ) )
% 3.18/1.71 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X4 @ P3 ) )
% 3.18/1.71 => ( ( fresh_717452603ubject @ Y3 @ A3 )
% 3.18/1.71 => ( ( Y3 != X4 )
% 3.18/1.71 => ( ( fresh_name_pi @ X4 @ P4 )
% 3.18/1.71 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_91_parCasesB_H,axiom,
% 3.18/1.71 ! [P: pi,Q: pi,B: late_subject,Y: name,P2: pi] :
% 3.18/1.71 ( ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 3.18/1.71 => ( ! [P4: pi,A3: late_subject,X4: name,P3: pi,Q4: pi] :
% 3.18/1.71 ( ( ( par @ P @ Q )
% 3.18/1.71 = ( par @ P4 @ Q4 ) )
% 3.18/1.71 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 3.18/1.71 = ( late_BoundR @ A3 @ X4 @ ( par @ P3 @ Q4 ) ) )
% 3.18/1.71 => ( ( late_transitions @ P4 @ ( late_BoundR @ A3 @ X4 @ P3 ) )
% 3.18/1.71 => ( ( fresh_name_pi @ X4 @ P4 )
% 3.18/1.71 => ( ( fresh_name_pi @ X4 @ Q4 )
% 3.18/1.71 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) )
% 3.18/1.71 => ~ ! [Q4: pi,A3: late_subject,X4: name,Q3: pi,P4: pi] :
% 3.18/1.71 ( ( ( par @ P @ Q )
% 3.18/1.71 = ( par @ P4 @ Q4 ) )
% 3.18/1.71 => ( ( ( late_BoundR @ B @ Y @ P2 )
% 3.18/1.71 = ( late_BoundR @ A3 @ X4 @ ( par @ P4 @ Q3 ) ) )
% 3.18/1.71 => ( ( late_transitions @ Q4 @ ( late_BoundR @ A3 @ X4 @ Q3 ) )
% 3.18/1.71 => ( ( fresh_name_pi @ X4 @ P4 )
% 3.18/1.71 => ( ( fresh_name_pi @ X4 @ Q4 )
% 3.18/1.71 => ~ ( fresh_717452603ubject @ X4 @ A3 ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_92_transitions_OPar1B,axiom,
% 3.18/1.71 ! [P: pi,A: late_subject,X: name,P2: pi,Q: pi] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ P )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ Q )
% 3.18/1.71 => ( ( fresh_717452603ubject @ X @ A )
% 3.18/1.71 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P2 @ Q ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_93_transitions_OPar2B,axiom,
% 3.18/1.71 ! [Q: pi,A: late_subject,X: name,Q2: pi,P: pi] :
% 3.18/1.71 ( ( late_transitions @ Q @ ( late_BoundR @ A @ X @ Q2 ) )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ P )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ Q )
% 3.18/1.71 => ( ( fresh_717452603ubject @ X @ A )
% 3.18/1.71 => ( late_transitions @ ( par @ P @ Q ) @ ( late_BoundR @ A @ X @ ( par @ P @ Q2 ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_94_transitions_OResB,axiom,
% 3.18/1.71 ! [P: pi,A: late_subject,X: name,P2: pi,Y: name] :
% 3.18/1.71 ( ( late_transitions @ P @ ( late_BoundR @ A @ X @ P2 ) )
% 3.18/1.71 => ( ( fresh_717452603ubject @ Y @ A )
% 3.18/1.71 => ( ( Y != X )
% 3.18/1.71 => ( ( fresh_name_pi @ X @ P )
% 3.18/1.71 => ( ( fresh_717452603ubject @ X @ A )
% 3.18/1.71 => ( late_transitions @ ( res @ Y @ P ) @ ( late_BoundR @ A @ X @ ( res @ Y @ P2 ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_95_resTauOutputTrans,axiom,
% 3.18/1.71 ! [X: name,P: pi,A: name,B: name,P2: pi] :
% 3.18/1.71 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_96_resOutputTauTrans,axiom,
% 3.18/1.71 ! [X: name,A: name,B: name,P: pi,P2: pi] :
% 3.18/1.71 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_97_resOutputInputTrans,axiom,
% 3.18/1.71 ! [X: name,A: name,B: name,P: pi,C: name,Y: name,P2: pi] :
% 3.18/1.71 ~ ( late_transitions @ ( res @ X @ ( output @ A @ B @ P ) ) @ ( late_BoundR @ ( late_InputS @ C ) @ Y @ P2 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_98_name__fresh,axiom,
% 3.18/1.71 ( fresh_name_name
% 3.18/1.71 = ( ^ [A4: name,B3: name] : ( A4 != B3 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_99_pi_Ofresh_I3_J,axiom,
% 3.18/1.71 ! [A: name,X1: pi] :
% 3.18/1.71 ( ( fresh_name_pi @ A @ ( tau @ X1 ) )
% 3.18/1.71 = ( fresh_name_pi @ A @ X1 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_100_simps_I2_J,axiom,
% 3.18/1.71 ! [P: pi,C: name,D: name] :
% 3.18/1.71 ( ( subs @ ( tau @ P ) @ C @ D )
% 3.18/1.71 = ( tau @ ( subs @ P @ C @ D ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_101_pi_Ofresh_I2_J,axiom,
% 3.18/1.71 ! [A: name,X32: name,X2: name,X1: pi] :
% 3.18/1.71 ( ( fresh_name_pi @ A @ ( output @ X32 @ X2 @ X1 ) )
% 3.18/1.71 = ( ( fresh_name_name @ A @ X32 )
% 3.18/1.71 & ( fresh_name_name @ A @ X2 )
% 3.18/1.71 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_102_pi_Odistinct_I19_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 3.18/1.71 ( ( output @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( tau @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_103_pi_Oinject_I1_J,axiom,
% 3.18/1.71 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 3.18/1.71 ( ( ( output @ X32 @ X2 @ X1 )
% 3.18/1.71 = ( output @ Y32 @ Y2 @ Y1 ) )
% 3.18/1.71 = ( ( X32 = Y32 )
% 3.18/1.71 & ( X2 = Y2 )
% 3.18/1.71 & ( X1 = Y1 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_104_pi_Oinject_I2_J,axiom,
% 3.18/1.71 ! [X1: pi,Y1: pi] :
% 3.18/1.71 ( ( ( tau @ X1 )
% 3.18/1.71 = ( tau @ Y1 ) )
% 3.18/1.71 = ( X1 = Y1 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_105_pi_Odistinct_I29_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.18/1.71 ( ( output @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_106_pi_Odistinct_I31_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Name: name,Pi: pi] :
% 3.18/1.71 ( ( output @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( res @ Name @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_107_pi_Odistinct_I43_J,axiom,
% 3.18/1.71 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.18/1.71 ( ( tau @ Pi4 )
% 3.18/1.71 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_108_pi_Odistinct_I45_J,axiom,
% 3.18/1.71 ! [Pi4: pi,Name: name,Pi: pi] :
% 3.18/1.71 ( ( tau @ Pi4 )
% 3.18/1.71 != ( res @ Name @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_109_resTrans_I1_J,axiom,
% 3.18/1.71 ! [X: name,B: name,P: pi,Rs: late_residual] :
% 3.18/1.71 ~ ( late_transitions @ ( res @ X @ ( output @ X @ B @ P ) ) @ Rs ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_110_outputBoundTrans,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi,C: late_subject,X: name,P2: pi] :
% 3.18/1.71 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_BoundR @ C @ X @ P2 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_111_outputFreshTrans,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 3.18/1.71 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 3.18/1.71 => ~ ( ( fresh_1641682979reeRes @ A @ Alpha )
% 3.18/1.71 | ( fresh_1641682979reeRes @ B @ Alpha ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_112_tauBoundTrans,axiom,
% 3.18/1.71 ! [P: pi,A: late_subject,X: name,P2: pi] :
% 3.18/1.71 ~ ( late_transitions @ ( tau @ P ) @ ( late_BoundR @ A @ X @ P2 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_113_resTauBoundTrans,axiom,
% 3.18/1.71 ! [X: name,P: pi,A: late_subject,Y: name,P2: pi] :
% 3.18/1.71 ~ ( late_transitions @ ( res @ X @ ( tau @ P ) ) @ ( late_BoundR @ A @ Y @ P2 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_114_Output,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi] : ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_115_outputIneqTrans,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi,C: name,D: name,P2: pi] :
% 3.18/1.71 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ ( late_OutputR @ C @ D ) @ P2 ) )
% 3.18/1.71 => ~ ( ( A != C )
% 3.18/1.71 | ( B != D ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_116_outputCases_H,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 3.18/1.71 ( ( late_transitions @ ( output @ A @ B @ P ) @ Rs )
% 3.18/1.71 => ~ ! [A3: name,B2: name,P4: pi] :
% 3.18/1.71 ( ( ( A = A3 )
% 3.18/1.71 & ( B = B2 )
% 3.18/1.71 & ( P = P4 ) )
% 3.18/1.71 => ( Rs
% 3.18/1.71 != ( late_FreeR @ ( late_OutputR @ A3 @ B2 ) @ P4 ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_117_outputCases,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 3.18/1.71 ( ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 3.18/1.71 => ( ( ( Alpha
% 3.18/1.71 = ( late_OutputR @ A @ B ) )
% 3.18/1.71 => ( ( P = P2 )
% 3.18/1.71 => ( Prop @ ( late_OutputR @ A @ B ) @ P ) ) )
% 3.18/1.71 => ( Prop @ Alpha @ P2 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_118_outputTauTrans,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi,P2: pi] :
% 3.18/1.71 ~ ( late_transitions @ ( output @ A @ B @ P ) @ ( late_FreeR @ late_TauR @ P2 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_119_tauOutputTrans,axiom,
% 3.18/1.71 ! [P: pi,A: name,B: name,P2: pi] :
% 3.18/1.71 ~ ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ ( late_OutputR @ A @ B ) @ P2 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_120_Tau,axiom,
% 3.18/1.71 ! [P: pi] : ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ late_TauR @ P ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_121_tauCases_H,axiom,
% 3.18/1.71 ! [P: pi,Rs: late_residual] :
% 3.18/1.71 ( ( late_transitions @ ( tau @ P ) @ Rs )
% 3.18/1.71 => ~ ! [P4: pi] :
% 3.18/1.71 ( ( ( tau @ P )
% 3.18/1.71 = ( tau @ P4 ) )
% 3.18/1.71 => ( Rs
% 3.18/1.71 != ( late_FreeR @ late_TauR @ P4 ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_122_tauCases,axiom,
% 3.18/1.71 ! [P: pi,Alpha: late_freeRes,P2: pi,Prop: late_freeRes > pi > $o] :
% 3.18/1.71 ( ( late_transitions @ ( tau @ P ) @ ( late_FreeR @ Alpha @ P2 ) )
% 3.18/1.71 => ( ( ( Alpha = late_TauR )
% 3.18/1.71 => ( ( P = P2 )
% 3.18/1.71 => ( Prop @ late_TauR @ P ) ) )
% 3.18/1.71 => ( Prop @ Alpha @ P2 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_123_resOutputOutputTrans,axiom,
% 3.18/1.71 ! [X: name,A: name,P: pi,B: name,Y: name,P2: pi] :
% 3.18/1.71 ~ ( late_transitions @ ( res @ X @ ( output @ A @ X @ P ) ) @ ( late_FreeR @ ( late_OutputR @ B @ Y ) @ P2 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_124_resInputBoundOutputTrans,axiom,
% 3.18/1.71 ! [X: name,A: name,Y: name,P: pi,B: name,Z: name,P2: pi] :
% 3.18/1.71 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Z @ P2 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_125_residual_Ofresh_I1_J,axiom,
% 3.18/1.71 ! [A: name,X32: late_subject,X1: name,X2: pi] :
% 3.18/1.71 ( ( fresh_81631222sidual @ A @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 3.18/1.71 = ( ( fresh_717452603ubject @ A @ X32 )
% 3.18/1.71 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_126_simps_I3_J,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi,C: name,D: name] :
% 3.18/1.71 ( ( subs @ ( output @ A @ B @ P ) @ C @ D )
% 3.18/1.71 = ( output @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_127_inputIneqTrans,axiom,
% 3.18/1.71 ! [A: name,X: name,P: pi,B: late_subject,Y: name,P2: pi] :
% 3.18/1.71 ( ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ B @ Y @ P2 ) )
% 3.18/1.71 => ~ ( fresh_717452603ubject @ A @ B ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_128_transitions_OInput,axiom,
% 3.18/1.71 ! [X: name,A: name,P: pi] :
% 3.18/1.71 ( ( X != A )
% 3.18/1.71 => ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_129_substInput,axiom,
% 3.18/1.71 ! [X: name,B: name,C: name,A: name,P: pi] :
% 3.18/1.71 ( ( X != B )
% 3.18/1.71 => ( ( X != C )
% 3.18/1.71 => ( ( subs @ ( input @ A @ X @ P ) @ B @ C )
% 3.18/1.71 = ( input @ ( subst_name @ A @ B @ C ) @ X @ ( subs @ P @ B @ C ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_130_simps_I4_J,axiom,
% 3.18/1.71 ! [X: name,A: name,C: name,D: name,P: pi] :
% 3.18/1.71 ( ( X != A )
% 3.18/1.71 => ( ( X != C )
% 3.18/1.71 => ( ( X != D )
% 3.18/1.71 => ( ( subs @ ( input @ A @ X @ P ) @ C @ D )
% 3.18/1.71 = ( input @ ( subst_name @ A @ C @ D ) @ X @ ( subs @ P @ C @ D ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_131_pi_Ofresh_I9_J,axiom,
% 3.18/1.71 ! [A: name,X1: name,X2: pi] :
% 3.18/1.71 ( ( fresh_name_pi @ A @ ( res @ X1 @ X2 ) )
% 3.18/1.71 = ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_132_pi_Ofresh_I4_J,axiom,
% 3.18/1.71 ! [A: name,X32: name,X1: name,X2: pi] :
% 3.18/1.71 ( ( fresh_name_pi @ A @ ( input @ X32 @ X1 @ X2 ) )
% 3.18/1.71 = ( ( fresh_name_name @ A @ X32 )
% 3.18/1.71 & ( fresh_543891186ion_pi @ A @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_133_pi_Oinject_I3_J,axiom,
% 3.18/1.71 ! [X32: name,X1: name,X2: pi,Y32: name,Y1: name,Y2: pi] :
% 3.18/1.71 ( ( ( input @ X32 @ X1 @ X2 )
% 3.18/1.71 = ( input @ Y32 @ Y1 @ Y2 ) )
% 3.18/1.71 = ( ( X32 = Y32 )
% 3.18/1.71 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 3.18/1.71 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_134_subst__name__def,axiom,
% 3.18/1.71 ( subst_name
% 3.18/1.71 = ( ^ [A4: name,B3: name,C3: name] : ( if_name @ ( A4 = B3 ) @ C3 @ A4 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_135_pi_Oinject_I8_J,axiom,
% 3.18/1.71 ! [X1: name,X2: pi,Y1: name,Y2: pi] :
% 3.18/1.71 ( ( ( res @ X1 @ X2 )
% 3.18/1.71 = ( res @ Y1 @ Y2 ) )
% 3.18/1.71 = ( ( abs_fun_name_pi @ X1 @ X2 )
% 3.18/1.71 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_136_residual_Oinject_I1_J,axiom,
% 3.18/1.71 ! [X32: late_subject,X1: name,X2: pi,Y32: late_subject,Y1: name,Y2: pi] :
% 3.18/1.71 ( ( ( late_BoundR @ X32 @ X1 @ X2 )
% 3.18/1.71 = ( late_BoundR @ Y32 @ Y1 @ Y2 ) )
% 3.18/1.71 = ( ( X32 = Y32 )
% 3.18/1.71 & ( ( abs_fun_name_pi @ X1 @ X2 )
% 3.18/1.71 = ( abs_fun_name_pi @ Y1 @ Y2 ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_137_name__fresh__abs,axiom,
% 3.18/1.71 ! [B: name,A: name,X: late_subject] :
% 3.18/1.71 ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_717452603ubject @ B @ X ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_138_name__fresh__abs,axiom,
% 3.18/1.71 ! [B: name,A: name,X: late_freeRes] :
% 3.18/1.71 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_139_name__fresh__abs,axiom,
% 3.18/1.71 ! [B: name,A: name,X: name] :
% 3.18/1.71 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_name_name @ B @ X ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_140_name__fresh__abs,axiom,
% 3.18/1.71 ! [B: name,A: name,X: pi] :
% 3.18/1.71 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_name_pi @ B @ X ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_141_abs__fresh_I1_J,axiom,
% 3.18/1.71 ! [B: name,A: name,X: late_subject] :
% 3.18/1.71 ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_717452603ubject @ B @ X ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_142_abs__fresh_I1_J,axiom,
% 3.18/1.71 ! [B: name,A: name,X: late_freeRes] :
% 3.18/1.71 ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_1641682979reeRes @ B @ X ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_143_abs__fresh_I1_J,axiom,
% 3.18/1.71 ! [B: name,A: name,X: name] :
% 3.18/1.71 ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_name_name @ B @ X ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_144_abs__fresh_I1_J,axiom,
% 3.18/1.71 ! [B: name,A: name,X: pi] :
% 3.18/1.71 ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_name_pi @ B @ X ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_145_pi_Odistinct_I55_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.18/1.71 ( ( input @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_146_pi_Odistinct_I57_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Name: name,Pi: pi] :
% 3.18/1.71 ( ( input @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( res @ Name @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_147_pi_Odistinct_I21_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.18/1.71 ( ( output @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_148_pi_Odistinct_I35_J,axiom,
% 3.18/1.71 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.18/1.71 ( ( tau @ Pi4 )
% 3.18/1.71 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_149_inputCases_H,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 3.18/1.71 ( ( late_transitions @ ( input @ A @ B @ P ) @ Rs )
% 3.18/1.71 => ~ ! [X4: name,A3: name,P4: pi] :
% 3.18/1.71 ( ( ( A = A3 )
% 3.18/1.71 & ( ( abs_fun_name_pi @ B @ P )
% 3.18/1.71 = ( abs_fun_name_pi @ X4 @ P4 ) ) )
% 3.18/1.71 => ( ( Rs
% 3.18/1.71 = ( late_BoundR @ ( late_InputS @ A3 ) @ X4 @ P4 ) )
% 3.18/1.71 => ( X4 = A3 ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_150_resTrans_I2_J,axiom,
% 3.18/1.71 ! [X: name,Y: name,P: pi,Rs: late_residual] :
% 3.18/1.71 ~ ( late_transitions @ ( res @ X @ ( input @ X @ Y @ P ) ) @ Rs ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_151_inputFreeTrans,axiom,
% 3.18/1.71 ! [A: name,X: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 3.18/1.71 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_152_resInputFreeTrans,axiom,
% 3.18/1.71 ! [X: name,A: name,Y: name,P: pi,Alpha: late_freeRes,P2: pi] :
% 3.18/1.71 ~ ( late_transitions @ ( res @ X @ ( input @ A @ Y @ P ) ) @ ( late_FreeR @ Alpha @ P2 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_153_inputBoundOutputTrans,axiom,
% 3.18/1.71 ! [A: name,X: name,P: pi,B: name,Y: name,P2: pi] :
% 3.18/1.71 ~ ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_BoundOutputS @ B ) @ Y @ P2 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_154_Late__Semantics_OInput,axiom,
% 3.18/1.71 ! [A: name,X: name,P: pi] : ( late_transitions @ ( input @ A @ X @ P ) @ ( late_BoundR @ ( late_InputS @ A ) @ X @ P ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_155_simps_I5_J,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi,C: name,D: name] :
% 3.18/1.71 ( ( subs @ ( match @ A @ B @ P ) @ C @ D )
% 3.18/1.71 = ( match @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_156_simps_I6_J,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi,C: name,D: name] :
% 3.18/1.71 ( ( subs @ ( mismatch @ A @ B @ P ) @ C @ D )
% 3.18/1.71 = ( mismatch @ ( subst_name @ A @ C @ D ) @ ( subst_name @ B @ C @ D ) @ ( subs @ P @ C @ D ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_157_pi_Ofresh_I5_J,axiom,
% 3.18/1.71 ! [A: name,X32: name,X2: name,X1: pi] :
% 3.18/1.71 ( ( fresh_name_pi @ A @ ( match @ X32 @ X2 @ X1 ) )
% 3.18/1.71 = ( ( fresh_name_name @ A @ X32 )
% 3.18/1.71 & ( fresh_name_name @ A @ X2 )
% 3.18/1.71 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_158_pi_Ofresh_I6_J,axiom,
% 3.18/1.71 ! [A: name,X32: name,X2: name,X1: pi] :
% 3.18/1.71 ( ( fresh_name_pi @ A @ ( mismatch @ X32 @ X2 @ X1 ) )
% 3.18/1.71 = ( ( fresh_name_name @ A @ X32 )
% 3.18/1.71 & ( fresh_name_name @ A @ X2 )
% 3.18/1.71 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_159_pi_Odistinct_I61_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.18/1.71 ( ( match @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_160_pi_Oinject_I4_J,axiom,
% 3.18/1.71 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 3.18/1.71 ( ( ( match @ X32 @ X2 @ X1 )
% 3.18/1.71 = ( match @ Y32 @ Y2 @ Y1 ) )
% 3.18/1.71 = ( ( X32 = Y32 )
% 3.18/1.71 & ( X2 = Y2 )
% 3.18/1.71 & ( X1 = Y1 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_161_pi_Oinject_I5_J,axiom,
% 3.18/1.71 ! [X32: name,X2: name,X1: pi,Y32: name,Y2: name,Y1: pi] :
% 3.18/1.71 ( ( ( mismatch @ X32 @ X2 @ X1 )
% 3.18/1.71 = ( mismatch @ Y32 @ Y2 @ Y1 ) )
% 3.18/1.71 = ( ( X32 = Y32 )
% 3.18/1.71 & ( X2 = Y2 )
% 3.18/1.71 & ( X1 = Y1 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_162_Mismatch,axiom,
% 3.18/1.71 ! [P: pi,Rs: late_residual,A: name,B: name] :
% 3.18/1.71 ( ( late_transitions @ P @ Rs )
% 3.18/1.71 => ( ( A != B )
% 3.18/1.71 => ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_163_Match,axiom,
% 3.18/1.71 ! [P: pi,Rs: late_residual,B: name] :
% 3.18/1.71 ( ( late_transitions @ P @ Rs )
% 3.18/1.71 => ( late_transitions @ ( match @ B @ B @ P ) @ Rs ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_164_mismatchCases_H,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 3.18/1.71 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 3.18/1.71 => ~ ! [P4: pi,A3: name,B2: name] :
% 3.18/1.71 ( ( ( A = A3 )
% 3.18/1.71 & ( B = B2 )
% 3.18/1.71 & ( P = P4 ) )
% 3.18/1.71 => ( ( late_transitions @ P4 @ Rs )
% 3.18/1.71 => ( A3 = B2 ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_165_mismatchTrans,axiom,
% 3.18/1.71 ! [A: name,P: pi,Rs: late_residual] :
% 3.18/1.71 ~ ( late_transitions @ ( mismatch @ A @ A @ P ) @ Rs ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_166_mismatchCases,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 3.18/1.71 ( ( late_transitions @ ( mismatch @ A @ B @ P ) @ Rs )
% 3.18/1.71 => ( ( ( late_transitions @ P @ Rs )
% 3.18/1.71 => ( ( A != B )
% 3.18/1.71 => ( F @ A @ B ) ) )
% 3.18/1.71 => ( F @ A @ B ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_167_matchCases_H,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 3.18/1.71 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 3.18/1.71 => ~ ! [P4: pi] :
% 3.18/1.71 ( ( ( B = A )
% 3.18/1.71 & ( P = P4 ) )
% 3.18/1.71 => ~ ( late_transitions @ P4 @ Rs ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_168_matchTrans,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi,Rs: late_residual] :
% 3.18/1.71 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 3.18/1.71 => ( A = B ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_169_matchCases,axiom,
% 3.18/1.71 ! [A: name,B: name,P: pi,Rs: late_residual,F: name > name > $o] :
% 3.18/1.71 ( ( late_transitions @ ( match @ A @ B @ P ) @ Rs )
% 3.18/1.71 => ( ( ( late_transitions @ P @ Rs )
% 3.18/1.71 => ( ( A = B )
% 3.18/1.71 => ( F @ A @ A ) ) )
% 3.18/1.71 => ( F @ A @ B ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_170_pi_Odistinct_I65_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.18/1.71 ( ( match @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_171_pi_Odistinct_I73_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.18/1.71 ( ( mismatch @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_172_pi_Odistinct_I67_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Name: name,Pi: pi] :
% 3.18/1.71 ( ( match @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( res @ Name @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_173_pi_Odistinct_I75_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Name: name,Pi: pi] :
% 3.18/1.71 ( ( mismatch @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( res @ Name @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_174_pi_Odistinct_I49_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.18/1.71 ( ( input @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_175_pi_Odistinct_I51_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.18/1.71 ( ( input @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_176_pi_Odistinct_I23_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.18/1.71 ( ( output @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_177_pi_Odistinct_I25_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.18/1.71 ( ( output @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_178_pi_Odistinct_I37_J,axiom,
% 3.18/1.71 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.18/1.71 ( ( tau @ Pi4 )
% 3.18/1.71 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_179_pi_Odistinct_I39_J,axiom,
% 3.18/1.71 ! [Pi4: pi,Name13: name,Name24: name,Pi: pi] :
% 3.18/1.71 ( ( tau @ Pi4 )
% 3.18/1.71 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_180_abs__fun__eq1,axiom,
% 3.18/1.71 ! [A: name,X: name,Y: name] :
% 3.18/1.71 ( ( ( abs_fun_name_name @ A @ X )
% 3.18/1.71 = ( abs_fun_name_name @ A @ Y ) )
% 3.18/1.71 = ( X = Y ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_181_abs__fun__eq1,axiom,
% 3.18/1.71 ! [A: name,X: late_freeRes,Y: late_freeRes] :
% 3.18/1.71 ( ( ( abs_fu681348580reeRes @ A @ X )
% 3.18/1.71 = ( abs_fu681348580reeRes @ A @ Y ) )
% 3.18/1.71 = ( X = Y ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_182_abs__fun__eq1,axiom,
% 3.18/1.71 ! [A: name,X: late_subject,Y: late_subject] :
% 3.18/1.71 ( ( ( abs_fu1904601852ubject @ A @ X )
% 3.18/1.71 = ( abs_fu1904601852ubject @ A @ Y ) )
% 3.18/1.71 = ( X = Y ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_183_abs__fun__eq1,axiom,
% 3.18/1.71 ! [A: name,X: name > noption_pi,Y: name > noption_pi] :
% 3.18/1.71 ( ( ( abs_fu1614711987ion_pi @ A @ X )
% 3.18/1.71 = ( abs_fu1614711987ion_pi @ A @ Y ) )
% 3.18/1.71 = ( X = Y ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_184_abs__fun__eq1,axiom,
% 3.18/1.71 ! [A: name,X: pi,Y: pi] :
% 3.18/1.71 ( ( ( abs_fun_name_pi @ A @ X )
% 3.18/1.71 = ( abs_fun_name_pi @ A @ Y ) )
% 3.18/1.71 = ( X = Y ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_185_pi_Ostrong__inducts,axiom,
% 3.18/1.71 ! [P: late_subject > pi > $o,Z: late_subject,Pi4: pi] :
% 3.18/1.71 ( ! [Z2: late_subject] : ( P @ Z2 @ piNil )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 3.18/1.71 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi3: pi,Z2: late_subject] :
% 3.18/1.71 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 3.18/1.71 ( ( fresh_717452603ubject @ Name23 @ Z2 )
% 3.18/1.71 => ( ( fresh_name_name @ Name23 @ Name12 )
% 3.18/1.71 => ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 3.18/1.71 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 3.18/1.71 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
% 3.18/1.71 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 3.18/1.71 => ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
% 3.18/1.71 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
% 3.18/1.71 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 3.18/1.71 => ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
% 3.18/1.71 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Name3: name,Pi3: pi,Z2: late_subject] :
% 3.18/1.71 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 3.18/1.71 => ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 3.18/1.71 => ( ! [Pi3: pi,Z2: late_subject] :
% 3.18/1.71 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 3.18/1.71 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_186_pi_Ostrong__inducts,axiom,
% 3.18/1.71 ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi4: pi] :
% 3.18/1.71 ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi3: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 3.18/1.71 => ( ( fresh_name_name @ Name23 @ Name12 )
% 3.18/1.71 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 3.18/1.71 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 3.18/1.71 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 3.18/1.71 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 3.18/1.71 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Name3: name,Pi3: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 3.18/1.71 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 3.18/1.71 => ( ! [Pi3: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 3.18/1.71 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_187_pi_Ostrong__inducts,axiom,
% 3.18/1.71 ! [P: name > pi > $o,Z: name,Pi4: pi] :
% 3.18/1.71 ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: name] :
% 3.18/1.71 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi3: pi,Z2: name] :
% 3.18/1.71 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: name] :
% 3.18/1.71 ( ( fresh_name_name @ Name23 @ Z2 )
% 3.18/1.71 => ( ( fresh_name_name @ Name23 @ Name12 )
% 3.18/1.71 => ( ! [Za: name] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: name] :
% 3.18/1.71 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: name] :
% 3.18/1.71 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 3.18/1.71 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 3.18/1.71 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 3.18/1.71 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 3.18/1.71 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 3.18/1.71 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 3.18/1.71 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Name3: name,Pi3: pi,Z2: name] :
% 3.18/1.71 ( ( fresh_name_name @ Name3 @ Z2 )
% 3.18/1.71 => ( ! [Za: name] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 3.18/1.71 => ( ! [Pi3: pi,Z2: name] :
% 3.18/1.71 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 3.18/1.71 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_188_pi_Ostrong__inducts,axiom,
% 3.18/1.71 ! [P: pi > pi > $o,Z: pi,Pi4: pi] :
% 3.18/1.71 ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: pi] :
% 3.18/1.71 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi3: pi,Z2: pi] :
% 3.18/1.71 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: pi] :
% 3.18/1.71 ( ( fresh_name_pi @ Name23 @ Z2 )
% 3.18/1.71 => ( ( fresh_name_name @ Name23 @ Name12 )
% 3.18/1.71 => ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: pi] :
% 3.18/1.71 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: pi] :
% 3.18/1.71 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 3.18/1.71 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 3.18/1.71 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 3.18/1.71 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 3.18/1.71 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 3.18/1.71 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 3.18/1.71 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Name3: name,Pi3: pi,Z2: pi] :
% 3.18/1.71 ( ( fresh_name_pi @ Name3 @ Z2 )
% 3.18/1.71 => ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 3.18/1.71 => ( ! [Pi3: pi,Z2: pi] :
% 3.18/1.71 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 3.18/1.71 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_189_pi_Ostrong__induct,axiom,
% 3.18/1.71 ! [P: late_subject > pi > $o,Z: late_subject,Pi4: pi] :
% 3.18/1.71 ( ! [Z2: late_subject] : ( P @ Z2 @ piNil )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 3.18/1.71 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi3: pi,Z2: late_subject] :
% 3.18/1.71 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 3.18/1.71 ( ( fresh_717452603ubject @ Name23 @ Z2 )
% 3.18/1.71 => ( ( fresh_name_name @ Name23 @ Name12 )
% 3.18/1.71 => ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 3.18/1.71 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_subject] :
% 3.18/1.71 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
% 3.18/1.71 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 3.18/1.71 => ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
% 3.18/1.71 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi,Z2: late_subject] :
% 3.18/1.71 ( ! [Za: late_subject] : ( P @ Za @ Pi13 )
% 3.18/1.71 => ( ! [Za: late_subject] : ( P @ Za @ Pi23 )
% 3.18/1.71 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Name3: name,Pi3: pi,Z2: late_subject] :
% 3.18/1.71 ( ( fresh_717452603ubject @ Name3 @ Z2 )
% 3.18/1.71 => ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 3.18/1.71 => ( ! [Pi3: pi,Z2: late_subject] :
% 3.18/1.71 ( ! [Za: late_subject] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 3.18/1.71 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_190_pi_Ostrong__induct,axiom,
% 3.18/1.71 ! [P: late_freeRes > pi > $o,Z: late_freeRes,Pi4: pi] :
% 3.18/1.71 ( ! [Z2: late_freeRes] : ( P @ Z2 @ piNil )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi3: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ( fresh_1641682979reeRes @ Name23 @ Z2 )
% 3.18/1.71 => ( ( fresh_name_name @ Name23 @ Name12 )
% 3.18/1.71 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 3.18/1.71 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 3.18/1.71 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ! [Za: late_freeRes] : ( P @ Za @ Pi13 )
% 3.18/1.71 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi23 )
% 3.18/1.71 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Name3: name,Pi3: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ( fresh_1641682979reeRes @ Name3 @ Z2 )
% 3.18/1.71 => ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 3.18/1.71 => ( ! [Pi3: pi,Z2: late_freeRes] :
% 3.18/1.71 ( ! [Za: late_freeRes] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 3.18/1.71 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_191_pi_Ostrong__induct,axiom,
% 3.18/1.71 ! [P: name > pi > $o,Z: name,Pi4: pi] :
% 3.18/1.71 ( ! [Z2: name] : ( P @ Z2 @ piNil )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: name] :
% 3.18/1.71 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi3: pi,Z2: name] :
% 3.18/1.71 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: name] :
% 3.18/1.71 ( ( fresh_name_name @ Name23 @ Z2 )
% 3.18/1.71 => ( ( fresh_name_name @ Name23 @ Name12 )
% 3.18/1.71 => ( ! [Za: name] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: name] :
% 3.18/1.71 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: name] :
% 3.18/1.71 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 3.18/1.71 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 3.18/1.71 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 3.18/1.71 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi,Z2: name] :
% 3.18/1.71 ( ! [Za: name] : ( P @ Za @ Pi13 )
% 3.18/1.71 => ( ! [Za: name] : ( P @ Za @ Pi23 )
% 3.18/1.71 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Name3: name,Pi3: pi,Z2: name] :
% 3.18/1.71 ( ( fresh_name_name @ Name3 @ Z2 )
% 3.18/1.71 => ( ! [Za: name] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 3.18/1.71 => ( ! [Pi3: pi,Z2: name] :
% 3.18/1.71 ( ! [Za: name] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 3.18/1.71 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_192_pi_Ostrong__induct,axiom,
% 3.18/1.71 ! [P: pi > pi > $o,Z: pi,Pi4: pi] :
% 3.18/1.71 ( ! [Z2: pi] : ( P @ Z2 @ piNil )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: pi] :
% 3.18/1.71 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi3: pi,Z2: pi] :
% 3.18/1.71 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( tau @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: pi] :
% 3.18/1.71 ( ( fresh_name_pi @ Name23 @ Z2 )
% 3.18/1.71 => ( ( fresh_name_name @ Name23 @ Name12 )
% 3.18/1.71 => ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( input @ Name12 @ Name23 @ Pi3 ) ) ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: pi] :
% 3.18/1.71 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi,Z2: pi] :
% 3.18/1.71 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 3.18/1.71 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 3.18/1.71 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 3.18/1.71 => ( P @ Z2 @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi,Z2: pi] :
% 3.18/1.71 ( ! [Za: pi] : ( P @ Za @ Pi13 )
% 3.18/1.71 => ( ! [Za: pi] : ( P @ Za @ Pi23 )
% 3.18/1.71 => ( P @ Z2 @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Name3: name,Pi3: pi,Z2: pi] :
% 3.18/1.71 ( ( fresh_name_pi @ Name3 @ Z2 )
% 3.18/1.71 => ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( res @ Name3 @ Pi3 ) ) ) )
% 3.18/1.71 => ( ! [Pi3: pi,Z2: pi] :
% 3.18/1.71 ( ! [Za: pi] : ( P @ Za @ Pi3 )
% 3.18/1.71 => ( P @ Z2 @ ( bang @ Pi3 ) ) )
% 3.18/1.71 => ( P @ Z @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_193_pi_Ofresh_I10_J,axiom,
% 3.18/1.71 ! [A: name,X1: pi] :
% 3.18/1.71 ( ( fresh_name_pi @ A @ ( bang @ X1 ) )
% 3.18/1.71 = ( fresh_name_pi @ A @ X1 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_194_pi_Ofresh_I7_J,axiom,
% 3.18/1.71 ! [A: name,X2: pi,X1: pi] :
% 3.18/1.71 ( ( fresh_name_pi @ A @ ( sum @ X2 @ X1 ) )
% 3.18/1.71 = ( ( fresh_name_pi @ A @ X2 )
% 3.18/1.71 & ( fresh_name_pi @ A @ X1 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_195_pi_Ofresh_I1_J,axiom,
% 3.18/1.71 ! [A: name] : ( fresh_name_pi @ A @ piNil ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_196_simps_I10_J,axiom,
% 3.18/1.71 ! [P: pi,C: name,D: name] :
% 3.18/1.71 ( ( subs @ ( bang @ P ) @ C @ D )
% 3.18/1.71 = ( bang @ ( subs @ P @ C @ D ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_197_simps_I7_J,axiom,
% 3.18/1.71 ! [P: pi,Q: pi,C: name,D: name] :
% 3.18/1.71 ( ( subs @ ( sum @ P @ Q ) @ C @ D )
% 3.18/1.71 = ( sum @ ( subs @ P @ C @ D ) @ ( subs @ Q @ C @ D ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_198_simps_I1_J,axiom,
% 3.18/1.71 ! [C: name,D: name] :
% 3.18/1.71 ( ( subs @ piNil @ C @ D )
% 3.18/1.71 = piNil ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_199_pi_Odistinct_I59_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 3.18/1.71 ( ( input @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( bang @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_200_pi_Odistinct_I53_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.18/1.71 ( ( input @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_201_pi_Odistinct_I87_J,axiom,
% 3.18/1.71 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 3.18/1.71 ( ( par @ Pi1 @ Pi2 )
% 3.18/1.71 != ( bang @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_202_pi_Odistinct_I89_J,axiom,
% 3.18/1.71 ! [Name2: name,Pi4: pi,Pi: pi] :
% 3.18/1.71 ( ( res @ Name2 @ Pi4 )
% 3.18/1.71 != ( bang @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_203_pi_Odistinct_I33_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 3.18/1.71 ( ( output @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( bang @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_204_sumCases,axiom,
% 3.18/1.71 ! [P: pi,Q: pi,Rs: late_residual] :
% 3.18/1.71 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 3.18/1.71 => ( ~ ( late_transitions @ P @ Rs )
% 3.18/1.71 => ( late_transitions @ Q @ Rs ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_205_sumCases_H,axiom,
% 3.18/1.71 ! [P: pi,Q: pi,Rs: late_residual] :
% 3.18/1.71 ( ( late_transitions @ ( sum @ P @ Q ) @ Rs )
% 3.18/1.71 => ( ~ ( late_transitions @ P @ Rs )
% 3.18/1.71 => ( late_transitions @ Q @ Rs ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_206_Sum1,axiom,
% 3.18/1.71 ! [P: pi,Rs: late_residual,Q: pi] :
% 3.18/1.71 ( ( late_transitions @ P @ Rs )
% 3.18/1.71 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_207_Sum2,axiom,
% 3.18/1.71 ! [Q: pi,Rs: late_residual,P: pi] :
% 3.18/1.71 ( ( late_transitions @ Q @ Rs )
% 3.18/1.71 => ( late_transitions @ ( sum @ P @ Q ) @ Rs ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_208_pi_Odistinct_I47_J,axiom,
% 3.18/1.71 ! [Pi4: pi,Pi: pi] :
% 3.18/1.71 ( ( tau @ Pi4 )
% 3.18/1.71 != ( bang @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_209_pi_Odistinct_I79_J,axiom,
% 3.18/1.71 ! [Pi1: pi,Pi2: pi,Pi12: pi,Pi22: pi] :
% 3.18/1.71 ( ( sum @ Pi1 @ Pi2 )
% 3.18/1.71 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_210_pi_Odistinct_I81_J,axiom,
% 3.18/1.71 ! [Pi1: pi,Pi2: pi,Name: name,Pi: pi] :
% 3.18/1.71 ( ( sum @ Pi1 @ Pi2 )
% 3.18/1.71 != ( res @ Name @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_211_pi_Odistinct_I11_J,axiom,
% 3.18/1.71 ! [Pi12: pi,Pi22: pi] :
% 3.18/1.71 ( piNil
% 3.18/1.71 != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_212_pi_Odistinct_I17_J,axiom,
% 3.18/1.71 ! [Pi: pi] :
% 3.18/1.71 ( piNil
% 3.18/1.71 != ( bang @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_213_pi_Odistinct_I83_J,axiom,
% 3.18/1.71 ! [Pi1: pi,Pi2: pi,Pi: pi] :
% 3.18/1.71 ( ( sum @ Pi1 @ Pi2 )
% 3.18/1.71 != ( bang @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_214_pi_Oinject_I6_J,axiom,
% 3.18/1.71 ! [X2: pi,X1: pi,Y2: pi,Y1: pi] :
% 3.18/1.71 ( ( ( sum @ X2 @ X1 )
% 3.18/1.71 = ( sum @ Y2 @ Y1 ) )
% 3.18/1.71 = ( ( X2 = Y2 )
% 3.18/1.71 & ( X1 = Y1 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_215_pi_Oinject_I9_J,axiom,
% 3.18/1.71 ! [X1: pi,Y1: pi] :
% 3.18/1.71 ( ( ( bang @ X1 )
% 3.18/1.71 = ( bang @ Y1 ) )
% 3.18/1.71 = ( X1 = Y1 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_216_pi_Odistinct_I3_J,axiom,
% 3.18/1.71 ! [Pi: pi] :
% 3.18/1.71 ( piNil
% 3.18/1.71 != ( tau @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_217_pi_Odistinct_I1_J,axiom,
% 3.18/1.71 ! [Name13: name,Name24: name,Pi: pi] :
% 3.18/1.71 ( piNil
% 3.18/1.71 != ( output @ Name13 @ Name24 @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_218_pi_Odistinct_I5_J,axiom,
% 3.18/1.71 ! [Name13: name,Name24: name,Pi: pi] :
% 3.18/1.71 ( piNil
% 3.18/1.71 != ( input @ Name13 @ Name24 @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_219_pi_Odistinct_I15_J,axiom,
% 3.18/1.71 ! [Name: name,Pi: pi] :
% 3.18/1.71 ( piNil
% 3.18/1.71 != ( res @ Name @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_220_pi_Odistinct_I13_J,axiom,
% 3.18/1.71 ! [Pi12: pi,Pi22: pi] :
% 3.18/1.71 ( piNil
% 3.18/1.71 != ( par @ Pi12 @ Pi22 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_221_nilCases_H,axiom,
% 3.18/1.71 ! [Rs: late_residual] :
% 3.18/1.71 ~ ( late_transitions @ piNil @ Rs ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_222_zeroTrans,axiom,
% 3.18/1.71 ! [Rs: late_residual] :
% 3.18/1.71 ~ ( late_transitions @ piNil @ Rs ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_223_pi_Odistinct_I41_J,axiom,
% 3.18/1.71 ! [Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.18/1.71 ( ( tau @ Pi4 )
% 3.18/1.71 != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_224_pi_Odistinct_I27_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.18/1.71 ( ( output @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_225_pi_Odistinct_I77_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 3.18/1.71 ( ( mismatch @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( bang @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_226_pi_Odistinct_I71_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.18/1.71 ( ( mismatch @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_227_pi_Odistinct_I69_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Pi: pi] :
% 3.18/1.71 ( ( match @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( bang @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_228_pi_Odistinct_I63_J,axiom,
% 3.18/1.71 ! [Name1: name,Name22: name,Pi4: pi,Pi12: pi,Pi22: pi] :
% 3.18/1.71 ( ( match @ Name1 @ Name22 @ Pi4 )
% 3.18/1.71 != ( sum @ Pi12 @ Pi22 ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_229_pi_Odistinct_I9_J,axiom,
% 3.18/1.71 ! [Name13: name,Name24: name,Pi: pi] :
% 3.18/1.71 ( piNil
% 3.18/1.71 != ( mismatch @ Name13 @ Name24 @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_230_pi_Odistinct_I7_J,axiom,
% 3.18/1.71 ! [Name13: name,Name24: name,Pi: pi] :
% 3.18/1.71 ( piNil
% 3.18/1.71 != ( match @ Name13 @ Name24 @ Pi ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_231_Bang,axiom,
% 3.18/1.71 ! [P: pi,Rs: late_residual] :
% 3.18/1.71 ( ( late_transitions @ ( par @ P @ ( bang @ P ) ) @ Rs )
% 3.18/1.71 => ( late_transitions @ ( bang @ P ) @ Rs ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_232_bangCases,axiom,
% 3.18/1.71 ! [P: pi,Rs: late_residual] :
% 3.18/1.71 ( ( late_transitions @ ( bang @ P ) @ Rs )
% 3.18/1.71 => ~ ! [P4: pi] :
% 3.18/1.71 ( ( ( bang @ P )
% 3.18/1.71 = ( bang @ P4 ) )
% 3.18/1.71 => ~ ( late_transitions @ ( par @ P4 @ ( bang @ P4 ) ) @ Rs ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_233_resZeroTrans,axiom,
% 3.18/1.71 ! [X: name,Rs: late_residual] :
% 3.18/1.71 ~ ( late_transitions @ ( res @ X @ piNil ) @ Rs ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_234_pi_Oinducts,axiom,
% 3.18/1.71 ! [P: pi > $o,Pi4: pi] :
% 3.18/1.71 ( ( P @ piNil )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi] :
% 3.18/1.71 ( ( P @ Pi3 )
% 3.18/1.71 => ( P @ ( output @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi3: pi] :
% 3.18/1.71 ( ( P @ Pi3 )
% 3.18/1.71 => ( P @ ( tau @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi] :
% 3.18/1.71 ( ( P @ Pi3 )
% 3.18/1.71 => ( P @ ( input @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi] :
% 3.18/1.71 ( ( P @ Pi3 )
% 3.18/1.71 => ( P @ ( match @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Name12: name,Name23: name,Pi3: pi] :
% 3.18/1.71 ( ( P @ Pi3 )
% 3.18/1.71 => ( P @ ( mismatch @ Name12 @ Name23 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi] :
% 3.18/1.71 ( ( P @ Pi13 )
% 3.18/1.71 => ( ( P @ Pi23 )
% 3.18/1.71 => ( P @ ( sum @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Pi13: pi,Pi23: pi] :
% 3.18/1.71 ( ( P @ Pi13 )
% 3.18/1.71 => ( ( P @ Pi23 )
% 3.18/1.71 => ( P @ ( par @ Pi13 @ Pi23 ) ) ) )
% 3.18/1.71 => ( ! [Name3: name,Pi3: pi] :
% 3.18/1.71 ( ( P @ Pi3 )
% 3.18/1.71 => ( P @ ( res @ Name3 @ Pi3 ) ) )
% 3.18/1.71 => ( ! [Pi3: pi] :
% 3.18/1.71 ( ( P @ Pi3 )
% 3.18/1.71 => ( P @ ( bang @ Pi3 ) ) )
% 3.18/1.71 => ( P @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_235_aux2,axiom,
% 3.18/1.71 ! [P: pi] : ( late_bangPred @ P @ ( par @ P @ ( bang @ P ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_236_bangPred_Ocases,axiom,
% 3.18/1.71 ! [A1: pi,A22: pi] :
% 3.18/1.71 ( ( late_bangPred @ A1 @ A22 )
% 3.18/1.71 => ( ( A22
% 3.18/1.71 != ( bang @ A1 ) )
% 3.18/1.71 => ( A22
% 3.18/1.71 = ( par @ A1 @ ( bang @ A1 ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_237_bangPred_Osimps,axiom,
% 3.18/1.71 ( late_bangPred
% 3.18/1.71 = ( ^ [A12: pi,A23: pi] :
% 3.18/1.71 ( ? [P5: pi] :
% 3.18/1.71 ( ( A12 = P5 )
% 3.18/1.71 & ( A23
% 3.18/1.71 = ( bang @ P5 ) ) )
% 3.18/1.71 | ? [P5: pi] :
% 3.18/1.71 ( ( A12 = P5 )
% 3.18/1.71 & ( A23
% 3.18/1.71 = ( par @ P5 @ ( bang @ P5 ) ) ) ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_238_aux1,axiom,
% 3.18/1.71 ! [P: pi] : ( late_bangPred @ P @ ( bang @ P ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_239_bangPred_Oinducts,axiom,
% 3.18/1.71 ! [X1: pi,X2: pi,P: pi > pi > $o] :
% 3.18/1.71 ( ( late_bangPred @ X1 @ X2 )
% 3.18/1.71 => ( ! [P4: pi] : ( P @ P4 @ ( bang @ P4 ) )
% 3.18/1.71 => ( ! [P4: pi] : ( P @ P4 @ ( par @ P4 @ ( bang @ P4 ) ) )
% 3.18/1.71 => ( P @ X1 @ X2 ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_240_subs__def,axiom,
% 3.18/1.71 ( subs
% 3.18/1.71 = ( ^ [X3: pi,C3: name,D2: name] :
% 3.18/1.71 ( pi_rec_pi @ piNil
% 3.18/1.71 @ ^ [A4: name,B3: name,P5: pi] : ( output @ ( subst_name @ A4 @ C3 @ D2 ) @ ( subst_name @ B3 @ C3 @ D2 ) )
% 3.18/1.71 @ ^ [P5: pi] : tau
% 3.18/1.71 @ ^ [A4: name,Y5: name,P5: pi] : ( input @ ( subst_name @ A4 @ C3 @ D2 ) @ Y5 )
% 3.18/1.71 @ ^ [A4: name,B3: name,P5: pi] : ( match @ ( subst_name @ A4 @ C3 @ D2 ) @ ( subst_name @ B3 @ C3 @ D2 ) )
% 3.18/1.71 @ ^ [A4: name,B3: name,P5: pi] : ( mismatch @ ( subst_name @ A4 @ C3 @ D2 ) @ ( subst_name @ B3 @ C3 @ D2 ) )
% 3.18/1.71 @ ^ [P5: pi,Q5: pi] : sum
% 3.18/1.71 @ ^ [P5: pi,Q5: pi] : par
% 3.18/1.71 @ ^ [Y5: name,P5: pi] : ( res @ Y5 )
% 3.18/1.71 @ ^ [P5: pi] : bang
% 3.18/1.71 @ X3 ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_241_abs__fresh_I2_J,axiom,
% 3.18/1.71 ! [X: late_subject,B: name,A: name] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_L1174290467t_name @ X ) )
% 3.18/1.71 => ( ( fresh_728038529ubject @ B @ ( abs_fu1904601852ubject @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_717452603ubject @ B @ X ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_242_abs__fresh_I2_J,axiom,
% 3.18/1.71 ! [X: late_freeRes,B: name,A: name] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_L1228270395s_name @ X ) )
% 3.18/1.71 => ( ( fresh_785364841reeRes @ B @ ( abs_fu681348580reeRes @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_1641682979reeRes @ B @ X ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_243_abs__fresh_I2_J,axiom,
% 3.18/1.71 ! [X: name,B: name,A: name] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_name_name @ X ) )
% 3.18/1.71 => ( ( fresh_1093033124n_name @ B @ ( abs_fun_name_name @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_name_name @ B @ X ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_244_abs__fresh_I2_J,axiom,
% 3.18/1.71 ! [X: pi,B: name,A: name] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_pi_name @ X ) )
% 3.18/1.71 => ( ( fresh_543891186ion_pi @ B @ ( abs_fun_name_pi @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_name_pi @ B @ X ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_245_abs__fresh_I2_J,axiom,
% 3.18/1.71 ! [X: name > noption_pi,B: name,A: name] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_n468628396i_name @ X ) )
% 3.18/1.71 => ( ( fresh_92802872ion_pi @ B @ ( abs_fu1614711987ion_pi @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_543891186ion_pi @ B @ X ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_246_abs__fresh_I2_J,axiom,
% 3.18/1.71 ! [X: name > noption_Late_subject,B: name,A: name] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_n1630792207t_name @ X ) )
% 3.18/1.71 => ( ( fresh_600418535ubject @ B @ ( abs_fu1705804544ubject @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_728038529ubject @ B @ X ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_247_abs__fresh_I2_J,axiom,
% 3.18/1.71 ! [X: name > noption_Late_freeRes,B: name,A: name] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_n252280103s_name @ X ) )
% 3.18/1.71 => ( ( fresh_1215331279reeRes @ B @ ( abs_fu1763130856reeRes @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_785364841reeRes @ B @ X ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_248_abs__fresh_I2_J,axiom,
% 3.18/1.71 ! [X: name > noption_name,B: name,A: name] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_n352473082e_name @ X ) )
% 3.18/1.71 => ( ( fresh_1742414570n_name @ B @ ( abs_fu1394407909n_name @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_1093033124n_name @ B @ X ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_249_abs__fresh_I2_J,axiom,
% 3.18/1.71 ! [X: late_freeRes > pi > late_subject,B: name,A: name] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_L1759672260t_name @ X ) )
% 3.18/1.71 => ( ( fresh_1644004594ubject @ B @ ( abs_fu888821131ubject @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_198785932ubject @ B @ X ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_250_abs__fresh_I2_J,axiom,
% 3.18/1.71 ! [X: late_freeRes > pi > late_freeRes,B: name,A: name] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_L381160156s_name @ X ) )
% 3.18/1.71 => ( ( fresh_111433690reeRes @ B @ ( abs_fu946147443reeRes @ A @ X ) )
% 3.18/1.71 = ( ( B = A )
% 3.18/1.71 | ( fresh_256112244reeRes @ B @ X ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_251_exists__fresh,axiom,
% 3.18/1.71 ! [X: late_subject] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_L1174290467t_name @ X ) )
% 3.18/1.71 => ~ ! [C2: name] :
% 3.18/1.71 ~ ( fresh_717452603ubject @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_252_exists__fresh,axiom,
% 3.18/1.71 ! [X: late_freeRes] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_L1228270395s_name @ X ) )
% 3.18/1.71 => ~ ! [C2: name] :
% 3.18/1.71 ~ ( fresh_1641682979reeRes @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_253_exists__fresh,axiom,
% 3.18/1.71 ! [X: name] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_name_name @ X ) )
% 3.18/1.71 => ~ ! [C2: name] :
% 3.18/1.71 ~ ( fresh_name_name @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_254_exists__fresh,axiom,
% 3.18/1.71 ! [X: pi] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_pi_name @ X ) )
% 3.18/1.71 => ~ ! [C2: name] :
% 3.18/1.71 ~ ( fresh_name_pi @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_255_exists__fresh,axiom,
% 3.18/1.71 ! [X: name > noption_pi] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_n468628396i_name @ X ) )
% 3.18/1.71 => ~ ! [C2: name] :
% 3.18/1.71 ~ ( fresh_543891186ion_pi @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_256_exists__fresh,axiom,
% 3.18/1.71 ! [X: name > noption_Late_subject] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_n1630792207t_name @ X ) )
% 3.18/1.71 => ~ ! [C2: name] :
% 3.18/1.71 ~ ( fresh_728038529ubject @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_257_exists__fresh,axiom,
% 3.18/1.71 ! [X: name > noption_Late_freeRes] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_n252280103s_name @ X ) )
% 3.18/1.71 => ~ ! [C2: name] :
% 3.18/1.71 ~ ( fresh_785364841reeRes @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_258_exists__fresh,axiom,
% 3.18/1.71 ! [X: name > noption_name] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_n352473082e_name @ X ) )
% 3.18/1.71 => ~ ! [C2: name] :
% 3.18/1.71 ~ ( fresh_1093033124n_name @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_259_exists__fresh,axiom,
% 3.18/1.71 ! [X: late_freeRes > pi > late_subject] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_L1759672260t_name @ X ) )
% 3.18/1.71 => ~ ! [C2: name] :
% 3.18/1.71 ~ ( fresh_198785932ubject @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_260_exists__fresh,axiom,
% 3.18/1.71 ! [X: late_freeRes > pi > late_freeRes] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_L381160156s_name @ X ) )
% 3.18/1.71 => ~ ! [C2: name] :
% 3.18/1.71 ~ ( fresh_256112244reeRes @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_261_exists__fresh_H,axiom,
% 3.18/1.71 ! [X: late_subject] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_L1174290467t_name @ X ) )
% 3.18/1.71 => ? [C2: name] : ( fresh_717452603ubject @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_262_exists__fresh_H,axiom,
% 3.18/1.71 ! [X: late_freeRes] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_L1228270395s_name @ X ) )
% 3.18/1.71 => ? [C2: name] : ( fresh_1641682979reeRes @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_263_exists__fresh_H,axiom,
% 3.18/1.71 ! [X: name] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_name_name @ X ) )
% 3.18/1.71 => ? [C2: name] : ( fresh_name_name @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_264_exists__fresh_H,axiom,
% 3.18/1.71 ! [X: pi] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_pi_name @ X ) )
% 3.18/1.71 => ? [C2: name] : ( fresh_name_pi @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_265_exists__fresh_H,axiom,
% 3.18/1.71 ! [X: name > noption_pi] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_n468628396i_name @ X ) )
% 3.18/1.71 => ? [C2: name] : ( fresh_543891186ion_pi @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_266_exists__fresh_H,axiom,
% 3.18/1.71 ! [X: name > noption_Late_subject] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_n1630792207t_name @ X ) )
% 3.18/1.71 => ? [C2: name] : ( fresh_728038529ubject @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_267_exists__fresh_H,axiom,
% 3.18/1.71 ! [X: name > noption_Late_freeRes] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_n252280103s_name @ X ) )
% 3.18/1.71 => ? [C2: name] : ( fresh_785364841reeRes @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_268_exists__fresh_H,axiom,
% 3.18/1.71 ! [X: name > noption_name] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_n352473082e_name @ X ) )
% 3.18/1.71 => ? [C2: name] : ( fresh_1093033124n_name @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_269_exists__fresh_H,axiom,
% 3.18/1.71 ! [X: late_freeRes > pi > late_subject] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_L1759672260t_name @ X ) )
% 3.18/1.71 => ? [C2: name] : ( fresh_198785932ubject @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_270_exists__fresh_H,axiom,
% 3.18/1.71 ! [X: late_freeRes > pi > late_freeRes] :
% 3.18/1.71 ( ( finite_finite_name @ ( supp_L381160156s_name @ X ) )
% 3.18/1.71 => ? [C2: name] : ( fresh_256112244reeRes @ C2 @ X ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_271_supp__fresh__iff,axiom,
% 3.18/1.71 ( supp_L1174290467t_name
% 3.18/1.71 = ( ^ [X3: late_subject] :
% 3.18/1.71 ( collect_name
% 3.18/1.71 @ ^ [A4: name] :
% 3.18/1.71 ~ ( fresh_717452603ubject @ A4 @ X3 ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_272_supp__fresh__iff,axiom,
% 3.18/1.71 ( supp_L1228270395s_name
% 3.18/1.71 = ( ^ [X3: late_freeRes] :
% 3.18/1.71 ( collect_name
% 3.18/1.71 @ ^ [A4: name] :
% 3.18/1.71 ~ ( fresh_1641682979reeRes @ A4 @ X3 ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_273_supp__fresh__iff,axiom,
% 3.18/1.71 ( supp_name_name
% 3.18/1.71 = ( ^ [X3: name] :
% 3.18/1.71 ( collect_name
% 3.18/1.71 @ ^ [A4: name] :
% 3.18/1.71 ~ ( fresh_name_name @ A4 @ X3 ) ) ) ) ).
% 3.18/1.71
% 3.18/1.71 thf(fact_274_supp__fresh__iff,axiom,
% 3.18/1.72 ( supp_pi_name
% 3.18/1.72 = ( ^ [X3: pi] :
% 3.18/1.72 ( collect_name
% 3.18/1.72 @ ^ [A4: name] :
% 3.18/1.72 ~ ( fresh_name_pi @ A4 @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_275_supp__fresh__iff,axiom,
% 3.18/1.72 ( supp_n468628396i_name
% 3.18/1.72 = ( ^ [X3: name > noption_pi] :
% 3.18/1.72 ( collect_name
% 3.18/1.72 @ ^ [A4: name] :
% 3.18/1.72 ~ ( fresh_543891186ion_pi @ A4 @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_276_supp__fresh__iff,axiom,
% 3.18/1.72 ( supp_n1630792207t_name
% 3.18/1.72 = ( ^ [X3: name > noption_Late_subject] :
% 3.18/1.72 ( collect_name
% 3.18/1.72 @ ^ [A4: name] :
% 3.18/1.72 ~ ( fresh_728038529ubject @ A4 @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_277_supp__fresh__iff,axiom,
% 3.18/1.72 ( supp_n252280103s_name
% 3.18/1.72 = ( ^ [X3: name > noption_Late_freeRes] :
% 3.18/1.72 ( collect_name
% 3.18/1.72 @ ^ [A4: name] :
% 3.18/1.72 ~ ( fresh_785364841reeRes @ A4 @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_278_supp__fresh__iff,axiom,
% 3.18/1.72 ( supp_n352473082e_name
% 3.18/1.72 = ( ^ [X3: name > noption_name] :
% 3.18/1.72 ( collect_name
% 3.18/1.72 @ ^ [A4: name] :
% 3.18/1.72 ~ ( fresh_1093033124n_name @ A4 @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_279_supp__fresh__iff,axiom,
% 3.18/1.72 ( supp_L1759672260t_name
% 3.18/1.72 = ( ^ [X3: late_freeRes > pi > late_subject] :
% 3.18/1.72 ( collect_name
% 3.18/1.72 @ ^ [A4: name] :
% 3.18/1.72 ~ ( fresh_198785932ubject @ A4 @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_280_supp__fresh__iff,axiom,
% 3.18/1.72 ( supp_L381160156s_name
% 3.18/1.72 = ( ^ [X3: late_freeRes > pi > late_freeRes] :
% 3.18/1.72 ( collect_name
% 3.18/1.72 @ ^ [A4: name] :
% 3.18/1.72 ~ ( fresh_256112244reeRes @ A4 @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_281_fresh__def,axiom,
% 3.18/1.72 ( fresh_717452603ubject
% 3.18/1.72 = ( ^ [A4: name,X3: late_subject] :
% 3.18/1.72 ~ ( member_name @ A4 @ ( supp_L1174290467t_name @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_282_fresh__def,axiom,
% 3.18/1.72 ( fresh_1641682979reeRes
% 3.18/1.72 = ( ^ [A4: name,X3: late_freeRes] :
% 3.18/1.72 ~ ( member_name @ A4 @ ( supp_L1228270395s_name @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_283_fresh__def,axiom,
% 3.18/1.72 ( fresh_name_name
% 3.18/1.72 = ( ^ [A4: name,X3: name] :
% 3.18/1.72 ~ ( member_name @ A4 @ ( supp_name_name @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_284_fresh__def,axiom,
% 3.18/1.72 ( fresh_name_pi
% 3.18/1.72 = ( ^ [A4: name,X3: pi] :
% 3.18/1.72 ~ ( member_name @ A4 @ ( supp_pi_name @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_285_fresh__def,axiom,
% 3.18/1.72 ( fresh_543891186ion_pi
% 3.18/1.72 = ( ^ [A4: name,X3: name > noption_pi] :
% 3.18/1.72 ~ ( member_name @ A4 @ ( supp_n468628396i_name @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_286_fresh__def,axiom,
% 3.18/1.72 ( fresh_728038529ubject
% 3.18/1.72 = ( ^ [A4: name,X3: name > noption_Late_subject] :
% 3.18/1.72 ~ ( member_name @ A4 @ ( supp_n1630792207t_name @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_287_fresh__def,axiom,
% 3.18/1.72 ( fresh_785364841reeRes
% 3.18/1.72 = ( ^ [A4: name,X3: name > noption_Late_freeRes] :
% 3.18/1.72 ~ ( member_name @ A4 @ ( supp_n252280103s_name @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_288_fresh__def,axiom,
% 3.18/1.72 ( fresh_1093033124n_name
% 3.18/1.72 = ( ^ [A4: name,X3: name > noption_name] :
% 3.18/1.72 ~ ( member_name @ A4 @ ( supp_n352473082e_name @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_289_fresh__def,axiom,
% 3.18/1.72 ( fresh_198785932ubject
% 3.18/1.72 = ( ^ [A4: name,X3: late_freeRes > pi > late_subject] :
% 3.18/1.72 ~ ( member_name @ A4 @ ( supp_L1759672260t_name @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_290_fresh__def,axiom,
% 3.18/1.72 ( fresh_256112244reeRes
% 3.18/1.72 = ( ^ [A4: name,X3: late_freeRes > pi > late_freeRes] :
% 3.18/1.72 ~ ( member_name @ A4 @ ( supp_L381160156s_name @ X3 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_291_pi_Osupp_I9_J,axiom,
% 3.18/1.72 ! [X1: name,X2: pi] :
% 3.18/1.72 ( ( supp_pi_name @ ( res @ X1 @ X2 ) )
% 3.18/1.72 = ( supp_n468628396i_name @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_292_pi_Osupp_I3_J,axiom,
% 3.18/1.72 ! [X1: pi] :
% 3.18/1.72 ( ( supp_pi_name @ ( tau @ X1 ) )
% 3.18/1.72 = ( supp_pi_name @ X1 ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_293_subject_Osupp_I2_J,axiom,
% 3.18/1.72 ! [X1: name] :
% 3.18/1.72 ( ( supp_L1174290467t_name @ ( late_BoundOutputS @ X1 ) )
% 3.18/1.72 = ( supp_name_name @ X1 ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_294_subject_Osupp_I1_J,axiom,
% 3.18/1.72 ! [X1: name] :
% 3.18/1.72 ( ( supp_L1174290467t_name @ ( late_InputS @ X1 ) )
% 3.18/1.72 = ( supp_name_name @ X1 ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_295_pi_Osupp_I10_J,axiom,
% 3.18/1.72 ! [X1: pi] :
% 3.18/1.72 ( ( supp_pi_name @ ( bang @ X1 ) )
% 3.18/1.72 = ( supp_pi_name @ X1 ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_296_fs__name1,axiom,
% 3.18/1.72 ! [X: late_subject] : ( finite_finite_name @ ( supp_L1174290467t_name @ X ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_297_fs__name1,axiom,
% 3.18/1.72 ! [X: late_freeRes] : ( finite_finite_name @ ( supp_L1228270395s_name @ X ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_298_fs__name1,axiom,
% 3.18/1.72 ! [X: name] : ( finite_finite_name @ ( supp_name_name @ X ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_299_fs__name1,axiom,
% 3.18/1.72 ! [X: pi] : ( finite_finite_name @ ( supp_pi_name @ X ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_300_residual_Orecs_I2_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_subject,P: late_subject > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_795910143ubject @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.18/1.72 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_301_residual_Orecs_I2_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_subject,P: late_freeRes > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.18/1.72 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_302_residual_Orecs_I2_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_subject,P: name > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_621211324i_name @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_name_name @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( late_r1174711868c_name @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.18/1.72 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_303_residual_Orecs_I2_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_subject,P: pi > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_name_pi @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( late_residual_rec_pi @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.18/1.72 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_304_residual_Orecs_I2_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_freeRes,P: late_subject > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_795910143ubject @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.18/1.72 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_305_residual_Orecs_I2_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_freeRes,P: late_freeRes > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.18/1.72 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_306_residual_Orecs_I2_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_freeRes,P: name > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_621211324i_name @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_name_name @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( late_r1174711868c_name @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.18/1.72 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_307_residual_Orecs_I2_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_freeRes,P: pi > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_name_pi @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( late_residual_rec_pi @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.18/1.72 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_308_residual_Orecs_I2_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: name,P: late_subject > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_795910143ubject @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_name_name @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.18/1.72 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_309_residual_Orecs_I2_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: name,P: late_freeRes > $o,FreeRes3: late_freeRes,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_name_name @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_FreeR @ FreeRes3 @ Pi4 ) )
% 3.18/1.72 = ( F2 @ FreeRes3 @ Pi4 ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_310_residual_Orecs_I1_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_subject,P: late_subject > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_795910143ubject @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( fresh_795910143ubject @ Name2 @ F1 )
% 3.18/1.72 => ( ( fresh_198785932ubject @ Name2 @ F2 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 3.18/1.72 => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 3.18/1.72 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_311_residual_Orecs_I1_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_subject,P: late_freeRes > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( fresh_660367079reeRes @ Name2 @ F1 )
% 3.18/1.72 => ( ( fresh_256112244reeRes @ Name2 @ F2 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 3.18/1.72 => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 3.18/1.72 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_312_residual_Orecs_I1_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_subject,P: name > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_621211324i_name @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_name_name @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( fresh_621211324i_name @ Name2 @ F1 )
% 3.18/1.72 => ( ( fresh_1030632537i_name @ Name2 @ F2 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 3.18/1.72 => ( ( late_r1174711868c_name @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 3.18/1.72 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_313_residual_Orecs_I1_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_subject,P: pi > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_name_pi @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( fresh_1438126218_pi_pi @ Name2 @ F1 )
% 3.18/1.72 => ( ( fresh_1011532071_pi_pi @ Name2 @ F2 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 3.18/1.72 => ( ( late_residual_rec_pi @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 3.18/1.72 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_314_residual_Orecs_I1_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_freeRes,P: late_subject > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_795910143ubject @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( fresh_795910143ubject @ Name2 @ F1 )
% 3.18/1.72 => ( ( fresh_198785932ubject @ Name2 @ F2 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 3.18/1.72 => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 3.18/1.72 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_315_residual_Orecs_I1_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_freeRes,P: late_freeRes > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( fresh_660367079reeRes @ Name2 @ F1 )
% 3.18/1.72 => ( ( fresh_256112244reeRes @ Name2 @ F2 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 3.18/1.72 => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 3.18/1.72 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_316_residual_Orecs_I1_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_freeRes,P: name > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_621211324i_name @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_name_name @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( fresh_621211324i_name @ Name2 @ F1 )
% 3.18/1.72 => ( ( fresh_1030632537i_name @ Name2 @ F2 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 3.18/1.72 => ( ( late_r1174711868c_name @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 3.18/1.72 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_317_residual_Orecs_I1_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_freeRes,P: pi > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_name_pi @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( fresh_1438126218_pi_pi @ Name2 @ F1 )
% 3.18/1.72 => ( ( fresh_1011532071_pi_pi @ Name2 @ F2 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 3.18/1.72 => ( ( late_residual_rec_pi @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 3.18/1.72 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_318_residual_Orecs_I1_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: name,P: late_subject > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_795910143ubject @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_name_name @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( fresh_795910143ubject @ Name2 @ F1 )
% 3.18/1.72 => ( ( fresh_198785932ubject @ Name2 @ F2 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 3.18/1.72 => ( ( late_r1347955901ubject @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 3.18/1.72 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_319_residual_Orecs_I1_J,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: name,P: late_freeRes > $o,Name2: name,Subject: late_subject,Pi4: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] :
% 3.18/1.72 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_name_name @ X22 @ Z )
% 3.18/1.72 => ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ( ( fresh_660367079reeRes @ Name2 @ F1 )
% 3.18/1.72 => ( ( fresh_256112244reeRes @ Name2 @ F2 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ Name2 @ Subject )
% 3.18/1.72 => ( ( late_r124702629reeRes @ F1 @ F2 @ ( late_BoundR @ Subject @ Name2 @ Pi4 ) )
% 3.18/1.72 = ( F1 @ Subject @ Name2 @ Pi4 ) ) ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_320_residual_Orec__fresh,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > name > noption_name,F2: late_freeRes > pi > name > noption_name,X: late_residual,Y: name > noption_name,A: name] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L14705974e_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L473926939e_name @ F2 ) )
% 3.18/1.72 => ( ( late_r303715378n_name @ F1 @ F2 @ X @ Y )
% 3.18/1.72 => ( ! [Y6: name > noption_name] :
% 3.18/1.72 ( ( late_r303715378n_name @ F1 @ F2 @ X @ Y6 )
% 3.18/1.72 => ( Y6 = Y ) )
% 3.18/1.72 => ( ( fresh_81631222sidual @ A @ X )
% 3.18/1.72 => ( ( fresh_62885992n_name @ A @ F1 )
% 3.18/1.72 => ( ( fresh_808662133n_name @ A @ F2 )
% 3.18/1.72 => ( fresh_1093033124n_name @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_321_residual_Orec__fresh,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > name > noptio354675977ion_pi,F2: late_freeRes > pi > name > noptio354675977ion_pi,X: late_residual,Y: name > noptio354675977ion_pi,A: name] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1512088218i_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L979396363i_name @ F2 ) )
% 3.18/1.72 => ( ( late_r1558248490ion_pi @ F1 @ F2 @ X @ Y )
% 3.18/1.72 => ( ! [Y6: name > noptio354675977ion_pi] :
% 3.18/1.72 ( ( late_r1558248490ion_pi @ F1 @ F2 @ X @ Y6 )
% 3.18/1.72 => ( Y6 = Y ) )
% 3.18/1.72 => ( ( fresh_81631222sidual @ A @ X )
% 3.18/1.72 => ( ( fresh_876421558ion_pi @ A @ F1 )
% 3.18/1.72 => ( ( fresh_2081817683ion_pi @ A @ F2 )
% 3.18/1.72 => ( fresh_92802872ion_pi @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_322_residual_Orec__fresh,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,X: late_residual,Y: late_subject,A: name] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 3.18/1.72 => ( ( late_r689718217ubject @ F1 @ F2 @ X @ Y )
% 3.18/1.72 => ( ! [Y6: late_subject] :
% 3.18/1.72 ( ( late_r689718217ubject @ F1 @ F2 @ X @ Y6 )
% 3.18/1.72 => ( Y6 = Y ) )
% 3.18/1.72 => ( ( fresh_81631222sidual @ A @ X )
% 3.18/1.72 => ( ( fresh_795910143ubject @ A @ F1 )
% 3.18/1.72 => ( ( fresh_198785932ubject @ A @ F2 )
% 3.18/1.72 => ( fresh_717452603ubject @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_323_residual_Orec__fresh,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,X: late_residual,Y: late_freeRes,A: name] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 3.18/1.72 => ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ Y )
% 3.18/1.72 => ( ! [Y6: late_freeRes] :
% 3.18/1.72 ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ Y6 )
% 3.18/1.72 => ( Y6 = Y ) )
% 3.18/1.72 => ( ( fresh_81631222sidual @ A @ X )
% 3.18/1.72 => ( ( fresh_660367079reeRes @ A @ F1 )
% 3.18/1.72 => ( ( fresh_256112244reeRes @ A @ F2 )
% 3.18/1.72 => ( fresh_1641682979reeRes @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_324_residual_Orec__fresh,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,X: late_residual,Y: name,A: name] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
% 3.18/1.72 => ( ( late_r1742481968t_name @ F1 @ F2 @ X @ Y )
% 3.18/1.72 => ( ! [Y6: name] :
% 3.18/1.72 ( ( late_r1742481968t_name @ F1 @ F2 @ X @ Y6 )
% 3.18/1.72 => ( Y6 = Y ) )
% 3.18/1.72 => ( ( fresh_81631222sidual @ A @ X )
% 3.18/1.72 => ( ( fresh_621211324i_name @ A @ F1 )
% 3.18/1.72 => ( ( fresh_1030632537i_name @ A @ F2 )
% 3.18/1.72 => ( fresh_name_name @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_325_residual_Orec__fresh,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,X: late_residual,Y: pi,A: name] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
% 3.18/1.72 => ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ Y )
% 3.18/1.72 => ( ! [Y6: pi] :
% 3.18/1.72 ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ Y6 )
% 3.18/1.72 => ( Y6 = Y ) )
% 3.18/1.72 => ( ( fresh_81631222sidual @ A @ X )
% 3.18/1.72 => ( ( fresh_1438126218_pi_pi @ A @ F1 )
% 3.18/1.72 => ( ( fresh_1011532071_pi_pi @ A @ F2 )
% 3.18/1.72 => ( fresh_name_pi @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_326_residual_Orec__fresh,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > name > noption_pi,F2: late_freeRes > pi > name > noption_pi,X: late_residual,Y: name > noption_pi,A: name] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L3230824i_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L635439693i_name @ F2 ) )
% 3.18/1.72 => ( ( late_r750878080ion_pi @ F1 @ F2 @ X @ Y )
% 3.18/1.72 => ( ! [Y6: name > noption_pi] :
% 3.18/1.72 ( ( late_r750878080ion_pi @ F1 @ F2 @ X @ Y6 )
% 3.18/1.72 => ( Y6 = Y ) )
% 3.18/1.72 => ( ( fresh_81631222sidual @ A @ X )
% 3.18/1.72 => ( ( fresh_747777846ion_pi @ A @ F1 )
% 3.18/1.72 => ( ( fresh_7927363ion_pi @ A @ F2 )
% 3.18/1.72 => ( fresh_543891186ion_pi @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_327_residual_Orec__unique,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_subject,P: late_subject > $o,X: late_residual] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name] :
% 3.18/1.72 ( ( fresh_795910143ubject @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ Z )
% 3.18/1.72 => ! [X33: pi] :
% 3.18/1.72 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ? [X4: late_subject] :
% 3.18/1.72 ( ( late_r689718217ubject @ F1 @ F2 @ X @ X4 )
% 3.18/1.72 & ! [Y7: late_subject] :
% 3.18/1.72 ( ( late_r689718217ubject @ F1 @ F2 @ X @ Y7 )
% 3.18/1.72 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_328_residual_Orec__unique,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_subject,P: late_freeRes > $o,X: late_residual] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name] :
% 3.18/1.72 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ Z )
% 3.18/1.72 => ! [X33: pi] :
% 3.18/1.72 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ? [X4: late_freeRes] :
% 3.18/1.72 ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ X4 )
% 3.18/1.72 & ! [Y7: late_freeRes] :
% 3.18/1.72 ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ Y7 )
% 3.18/1.72 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_329_residual_Orec__unique,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_subject,P: name > $o,X: late_residual] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name] :
% 3.18/1.72 ( ( fresh_621211324i_name @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ Z )
% 3.18/1.72 => ! [X33: pi] :
% 3.18/1.72 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_name_name @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ? [X4: name] :
% 3.18/1.72 ( ( late_r1742481968t_name @ F1 @ F2 @ X @ X4 )
% 3.18/1.72 & ! [Y7: name] :
% 3.18/1.72 ( ( late_r1742481968t_name @ F1 @ F2 @ X @ Y7 )
% 3.18/1.72 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_330_residual_Orec__unique,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_subject,P: pi > $o,X: late_residual] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1174290467t_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name] :
% 3.18/1.72 ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ Z )
% 3.18/1.72 => ! [X33: pi] :
% 3.18/1.72 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_name_pi @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ? [X4: pi] :
% 3.18/1.72 ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ X4 )
% 3.18/1.72 & ! [Y7: pi] :
% 3.18/1.72 ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ Y7 )
% 3.18/1.72 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_331_residual_Orec__unique,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: late_freeRes,P: late_subject > $o,X: late_residual] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name] :
% 3.18/1.72 ( ( fresh_795910143ubject @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 3.18/1.72 => ! [X33: pi] :
% 3.18/1.72 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ? [X4: late_subject] :
% 3.18/1.72 ( ( late_r689718217ubject @ F1 @ F2 @ X @ X4 )
% 3.18/1.72 & ! [Y7: late_subject] :
% 3.18/1.72 ( ( late_r689718217ubject @ F1 @ F2 @ X @ Y7 )
% 3.18/1.72 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_332_residual_Orec__unique,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: late_freeRes,P: late_freeRes > $o,X: late_residual] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name] :
% 3.18/1.72 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 3.18/1.72 => ! [X33: pi] :
% 3.18/1.72 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ? [X4: late_freeRes] :
% 3.18/1.72 ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ X4 )
% 3.18/1.72 & ! [Y7: late_freeRes] :
% 3.18/1.72 ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ Y7 )
% 3.18/1.72 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_333_residual_Orec__unique,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,Z: late_freeRes,P: name > $o,X: late_residual] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name] :
% 3.18/1.72 ( ( fresh_621211324i_name @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 3.18/1.72 => ! [X33: pi] :
% 3.18/1.72 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_name_name @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ? [X4: name] :
% 3.18/1.72 ( ( late_r1742481968t_name @ F1 @ F2 @ X @ X4 )
% 3.18/1.72 & ! [Y7: name] :
% 3.18/1.72 ( ( late_r1742481968t_name @ F1 @ F2 @ X @ Y7 )
% 3.18/1.72 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_334_residual_Orec__unique,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,Z: late_freeRes,P: pi > $o,X: late_residual] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1228270395s_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name] :
% 3.18/1.72 ( ( fresh_1438126218_pi_pi @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_1641682979reeRes @ X22 @ Z )
% 3.18/1.72 => ! [X33: pi] :
% 3.18/1.72 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_name_pi @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ? [X4: pi] :
% 3.18/1.72 ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ X4 )
% 3.18/1.72 & ! [Y7: pi] :
% 3.18/1.72 ( ( late_r1261898622set_pi @ F1 @ F2 @ X @ Y7 )
% 3.18/1.72 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_335_residual_Orec__unique,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,Z: name,P: late_subject > $o,X: late_residual] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name] :
% 3.18/1.72 ( ( fresh_795910143ubject @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_name_name @ X22 @ Z )
% 3.18/1.72 => ! [X33: pi] :
% 3.18/1.72 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_717452603ubject @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ? [X4: late_subject] :
% 3.18/1.72 ( ( late_r689718217ubject @ F1 @ F2 @ X @ X4 )
% 3.18/1.72 & ! [Y7: late_subject] :
% 3.18/1.72 ( ( late_r689718217ubject @ F1 @ F2 @ X @ Y7 )
% 3.18/1.72 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_336_residual_Orec__unique,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,Z: name,P: late_freeRes > $o,X: late_residual] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_name_name @ Z ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name,X33: pi] : ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( ! [X12: late_freeRes,X22: pi] : ( P @ ( F2 @ X12 @ X22 ) )
% 3.18/1.72 => ( ! [X12: late_subject,X22: name] :
% 3.18/1.72 ( ( fresh_660367079reeRes @ X22 @ F1 )
% 3.18/1.72 => ( ( fresh_717452603ubject @ X22 @ X12 )
% 3.18/1.72 => ( ( fresh_name_name @ X22 @ Z )
% 3.18/1.72 => ! [X33: pi] :
% 3.18/1.72 ( ( P @ ( F1 @ X12 @ X22 @ X33 ) )
% 3.18/1.72 => ( fresh_1641682979reeRes @ X22 @ ( F1 @ X12 @ X22 @ X33 ) ) ) ) ) )
% 3.18/1.72 => ? [X4: late_freeRes] :
% 3.18/1.72 ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ X4 )
% 3.18/1.72 & ! [Y7: late_freeRes] :
% 3.18/1.72 ( ( late_r1613948593reeRes @ F1 @ F2 @ X @ Y7 )
% 3.18/1.72 => ( Y7 = X4 ) ) ) ) ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_337_residual_Orec__fin__supp,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_subject,F2: late_freeRes > pi > late_subject,X1: late_residual,Y1: late_subject] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1144036959t_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L1759672260t_name @ F2 ) )
% 3.18/1.72 => ( ( late_r689718217ubject @ F1 @ F2 @ X1 @ Y1 )
% 3.18/1.72 => ( finite_finite_name @ ( supp_L1174290467t_name @ Y1 ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_338_residual_Orec__fin__supp,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > late_freeRes,F2: late_freeRes > pi > late_freeRes,X1: late_residual,Y1: late_freeRes] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L1178477943s_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L381160156s_name @ F2 ) )
% 3.18/1.72 => ( ( late_r1613948593reeRes @ F1 @ F2 @ X1 @ Y1 )
% 3.18/1.72 => ( finite_finite_name @ ( supp_L1228270395s_name @ Y1 ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_339_residual_Orec__fin__supp,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > name,F2: late_freeRes > pi > name,X1: late_residual,Y1: name] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L538372628e_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L926407557e_name @ F2 ) )
% 3.18/1.72 => ( ( late_r1742481968t_name @ F1 @ F2 @ X1 @ Y1 )
% 3.18/1.72 => ( finite_finite_name @ ( supp_name_name @ Y1 ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_340_residual_Orec__fin__supp,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > pi,F2: late_freeRes > pi > pi,X1: late_residual,Y1: pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L729745222i_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L2052723895i_name @ F2 ) )
% 3.18/1.72 => ( ( late_r1261898622set_pi @ F1 @ F2 @ X1 @ Y1 )
% 3.18/1.72 => ( finite_finite_name @ ( supp_pi_name @ Y1 ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_341_residual_Orec__fin__supp,axiom,
% 3.18/1.72 ! [F1: late_subject > name > pi > name > noption_pi,F2: late_freeRes > pi > name > noption_pi,X1: late_residual,Y1: name > noption_pi] :
% 3.18/1.72 ( ( finite_finite_name @ ( supp_L3230824i_name @ F1 ) )
% 3.18/1.72 => ( ( finite_finite_name @ ( supp_L635439693i_name @ F2 ) )
% 3.18/1.72 => ( ( late_r750878080ion_pi @ F1 @ F2 @ X1 @ Y1 )
% 3.18/1.72 => ( finite_finite_name @ ( supp_n468628396i_name @ Y1 ) ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_342_pi_Osupp_I4_J,axiom,
% 3.18/1.72 ! [X32: name,X1: name,X2: pi] :
% 3.18/1.72 ( ( supp_pi_name @ ( input @ X32 @ X1 @ X2 ) )
% 3.18/1.72 = ( sup_sup_set_name @ ( supp_name_name @ X32 ) @ ( supp_n468628396i_name @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_343_residual_Osupp_I1_J,axiom,
% 3.18/1.72 ! [X32: late_subject,X1: name,X2: pi] :
% 3.18/1.72 ( ( supp_L1174042202l_name @ ( late_BoundR @ X32 @ X1 @ X2 ) )
% 3.18/1.72 = ( sup_sup_set_name @ ( supp_L1174290467t_name @ X32 ) @ ( supp_n468628396i_name @ ( abs_fun_name_pi @ X1 @ X2 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_344_pi_Osupp_I7_J,axiom,
% 3.18/1.72 ! [X2: pi,X1: pi] :
% 3.18/1.72 ( ( supp_pi_name @ ( sum @ X2 @ X1 ) )
% 3.18/1.72 = ( sup_sup_set_name @ ( supp_pi_name @ X2 ) @ ( supp_pi_name @ X1 ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_345_pi_Osupp_I8_J,axiom,
% 3.18/1.72 ! [X2: pi,X1: pi] :
% 3.18/1.72 ( ( supp_pi_name @ ( par @ X2 @ X1 ) )
% 3.18/1.72 = ( sup_sup_set_name @ ( supp_pi_name @ X2 ) @ ( supp_pi_name @ X1 ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_346_residual_Osupp_I2_J,axiom,
% 3.18/1.72 ! [X2: late_freeRes,X1: pi] :
% 3.18/1.72 ( ( supp_L1174042202l_name @ ( late_FreeR @ X2 @ X1 ) )
% 3.18/1.72 = ( sup_sup_set_name @ ( supp_L1228270395s_name @ X2 ) @ ( supp_pi_name @ X1 ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_347_freeRes_Osupp_I1_J,axiom,
% 3.18/1.72 ! [X2: name,X1: name] :
% 3.18/1.72 ( ( supp_L1228270395s_name @ ( late_OutputR @ X2 @ X1 ) )
% 3.18/1.72 = ( sup_sup_set_name @ ( supp_name_name @ X2 ) @ ( supp_name_name @ X1 ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(fact_348_pi_Osupp_I2_J,axiom,
% 3.18/1.72 ! [X32: name,X2: name,X1: pi] :
% 3.18/1.72 ( ( supp_pi_name @ ( output @ X32 @ X2 @ X1 ) )
% 3.18/1.72 = ( sup_sup_set_name @ ( supp_name_name @ X32 ) @ ( sup_sup_set_name @ ( supp_name_name @ X2 ) @ ( supp_pi_name @ X1 ) ) ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(help_If_3_1_If_001t__Agent__Oname_T,axiom,
% 3.18/1.72 ! [P: $o] :
% 3.18/1.72 ( ( P = $true )
% 3.18/1.72 | ( P = $false ) ) ).
% 3.18/1.72
% 3.18/1.72 thf(help_If_2_1_If_001t__Agent__Oname_T,axiom,
% 3.18/1.72 ! [X: name,Y: name] :
% 3.18/1.72 ( ( if_name @ $false @ X @ Y )
% 3.18/1.72 = Y ) ).
% 3.18/1.72
% 3.18/1.72 thf(help_If_1_1_If_001t__Agent__Oname_T,axiom,
% 3.18/1.72 ! [X: name,Y: name] :
% 3.18/1.72 ( ( if_name @ $true @ X @ Y )
% 3.18/1.72 = X ) ).
% 3.18/1.72
% 3.18/1.72 thf(conj_0,conjecture,
% 3.18/1.72 late_transitions @ ( par @ ( par @ p @ q ) @ r ) @ ( late_FreeR @ late_TauR @ ( res @ y @ ( par @ ( par @ p @ q2 ) @ ( subs @ r2 @ x @ y ) ) ) ) ).
% 3.18/1.72 ------------------------
% 3.18/1.76 % (17321)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/183Mi)
% 3.18/1.76 % (17325)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/2Mi)
% 3.18/1.77 % (17325)Instruction limit reached!
% 3.18/1.77 % (17325)------------------------------
% 3.18/1.77 % (17325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.77 % (17325)Termination reason: Unknown
% 3.18/1.77 % (17325)Termination phase: shuffling
% 3.18/1.77
% 3.18/1.77 % (17325)Memory used [KB]: 1535
% 3.18/1.77 % (17325)Time elapsed: 0.002 s
% 3.18/1.77 % (17325)Instructions burned: 2 (million)
% 3.18/1.77 % (17325)------------------------------
% 3.18/1.77 % (17325)------------------------------
% 3.18/1.77 % (17323)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/27Mi)
% 3.18/1.77 % (17324)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/2Mi)
% 3.18/1.77 % (17327)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/18Mi)
% 3.18/1.77 % (17326)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/275Mi)
% 3.18/1.77 % (17324)Instruction limit reached!
% 3.18/1.77 % (17324)------------------------------
% 3.18/1.77 % (17324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.77 % (17324)Termination reason: Unknown
% 3.18/1.77 % (17324)Termination phase: shuffling
% 3.18/1.77
% 3.18/1.77 % (17324)Memory used [KB]: 1535
% 3.18/1.77 % (17324)Time elapsed: 0.004 s
% 3.18/1.77 % (17324)Instructions burned: 2 (million)
% 3.18/1.77 % (17324)------------------------------
% 3.18/1.77 % (17324)------------------------------
% 3.18/1.77 % (17322)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/4Mi)
% 3.18/1.78 % (17329)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/3Mi)
% 3.18/1.78 % (17322)Instruction limit reached!
% 3.18/1.78 % (17322)------------------------------
% 3.18/1.78 % (17322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.78 % (17322)Termination reason: Unknown
% 3.18/1.78 % (17322)Termination phase: shuffling
% 3.18/1.78
% 3.18/1.78 % (17322)Memory used [KB]: 1663
% 3.18/1.78 % (17322)Time elapsed: 0.004 s
% 3.18/1.78 % (17322)Instructions burned: 4 (million)
% 3.18/1.78 % (17322)------------------------------
% 3.18/1.78 % (17322)------------------------------
% 3.18/1.78 % (17329)Instruction limit reached!
% 3.18/1.78 % (17329)------------------------------
% 3.18/1.78 % (17329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.78 % (17329)Termination reason: Unknown
% 3.18/1.78 % (17329)Termination phase: shuffling
% 3.18/1.78
% 3.18/1.78 % (17329)Memory used [KB]: 1535
% 3.18/1.78 % (17329)Time elapsed: 0.003 s
% 3.18/1.78 % (17329)Instructions burned: 3 (million)
% 3.18/1.78 % (17329)------------------------------
% 3.18/1.78 % (17329)------------------------------
% 3.18/1.78 % (17327)Instruction limit reached!
% 3.18/1.78 % (17327)------------------------------
% 3.18/1.78 % (17327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.78 % (17327)Termination reason: Unknown
% 3.18/1.78 % (17327)Termination phase: shuffling
% 3.18/1.78
% 3.18/1.78 % (17327)Memory used [KB]: 1918
% 3.18/1.78 % (17327)Time elapsed: 0.014 s
% 3.18/1.78 % (17327)Instructions burned: 19 (million)
% 3.18/1.78 % (17327)------------------------------
% 3.18/1.78 % (17327)------------------------------
% 3.18/1.79 % (17337)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/3Mi)
% 3.18/1.79 % (17337)Instruction limit reached!
% 3.18/1.79 % (17337)------------------------------
% 3.18/1.79 % (17337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.79 % (17337)Termination reason: Unknown
% 3.18/1.79 % (17337)Termination phase: shuffling
% 3.18/1.79
% 3.18/1.79 % (17337)Memory used [KB]: 1663
% 3.18/1.79 % (17323)Instruction limit reached!
% 3.18/1.79 % (17323)------------------------------
% 3.18/1.79 % (17323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.79 % (17337)Time elapsed: 0.003 s
% 3.18/1.79 % (17337)Instructions burned: 5 (million)
% 3.18/1.79 % (17337)------------------------------
% 3.18/1.79 % (17337)------------------------------
% 3.18/1.79 % (17323)Termination reason: Unknown
% 3.18/1.79 % (17323)Termination phase: shuffling
% 3.18/1.79
% 3.18/1.79 % (17323)Memory used [KB]: 2046
% 3.18/1.79 % (17323)Time elapsed: 0.019 s
% 3.18/1.79 % (17323)Instructions burned: 27 (million)
% 3.18/1.79 % (17323)------------------------------
% 3.18/1.79 % (17323)------------------------------
% 3.18/1.79 % (17336)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/15Mi)
% 3.18/1.79 % (17334)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/37Mi)
% 3.18/1.80 % (17336)Instruction limit reached!
% 3.18/1.80 % (17336)------------------------------
% 3.18/1.80 % (17336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.80 % (17336)Termination reason: Unknown
% 3.18/1.80 % (17336)Termination phase: shuffling
% 3.18/1.80
% 3.18/1.80 % (17336)Memory used [KB]: 1918
% 3.18/1.80 % (17336)Time elapsed: 0.007 s
% 3.18/1.80 % (17336)Instructions burned: 17 (million)
% 3.18/1.80 % (17336)------------------------------
% 3.18/1.80 % (17336)------------------------------
% 3.22/1.80 % (17344)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/7Mi)
% 3.22/1.80 % (17344)Instruction limit reached!
% 3.22/1.80 % (17344)------------------------------
% 3.22/1.80 % (17344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.80 % (17344)Termination reason: Unknown
% 3.22/1.80 % (17344)Termination phase: shuffling
% 3.22/1.80
% 3.22/1.80 % (17344)Memory used [KB]: 1791
% 3.22/1.80 % (17344)Time elapsed: 0.004 s
% 3.22/1.80 % (17344)Instructions burned: 8 (million)
% 3.22/1.80 % (17344)------------------------------
% 3.22/1.80 % (17344)------------------------------
% 3.22/1.80 % (17340)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/1041Mi)
% 3.22/1.81 % (17348)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/3Mi)
% 3.22/1.81 % (17348)Instruction limit reached!
% 3.22/1.81 % (17348)------------------------------
% 3.22/1.81 % (17348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.81 % (17348)Termination reason: Unknown
% 3.22/1.81 % (17348)Termination phase: shuffling
% 3.22/1.81
% 3.22/1.81 % (17348)Memory used [KB]: 1535
% 3.22/1.81 % (17348)Time elapsed: 0.003 s
% 3.22/1.81 % (17348)Instructions burned: 3 (million)
% 3.22/1.81 % (17348)------------------------------
% 3.22/1.81 % (17348)------------------------------
% 3.22/1.81 % (17345)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/16Mi)
% 3.22/1.81 % (17351)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/3Mi)
% 3.22/1.81 % (17334)Instruction limit reached!
% 3.22/1.81 % (17334)------------------------------
% 3.22/1.81 % (17334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.81 % (17334)Termination reason: Unknown
% 3.22/1.81 % (17334)Termination phase: shuffling
% 3.22/1.81
% 3.22/1.81 % (17334)Memory used [KB]: 2302
% 3.22/1.81 % (17334)Time elapsed: 0.022 s
% 3.22/1.81 % (17334)Instructions burned: 38 (million)
% 3.22/1.81 % (17334)------------------------------
% 3.22/1.81 % (17334)------------------------------
% 3.22/1.81 % (17351)Instruction limit reached!
% 3.22/1.81 % (17351)------------------------------
% 3.22/1.81 % (17351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.81 % (17351)Termination reason: Unknown
% 3.22/1.81 % (17351)Termination phase: shuffling
% 3.22/1.81
% 3.22/1.81 % (17351)Memory used [KB]: 1663
% 3.22/1.81 % (17351)Time elapsed: 0.003 s
% 3.22/1.81 % (17351)Instructions burned: 5 (million)
% 3.22/1.81 % (17351)------------------------------
% 3.22/1.81 % (17351)------------------------------
% 3.22/1.82 % (17345)Instruction limit reached!
% 3.22/1.82 % (17345)------------------------------
% 3.22/1.82 % (17345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.82 % (17345)Termination reason: Unknown
% 3.22/1.82 % (17345)Termination phase: shuffling
% 3.22/1.82
% 3.22/1.82 % (17345)Memory used [KB]: 1918
% 3.22/1.82 % (17345)Time elapsed: 0.012 s
% 3.22/1.82 % (17345)Instructions burned: 16 (million)
% 3.22/1.82 % (17345)------------------------------
% 3.22/1.82 % (17345)------------------------------
% 3.22/1.82 % (17321)Instruction limit reached!
% 3.22/1.82 % (17321)------------------------------
% 3.22/1.82 % (17321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.82 % (17321)Termination reason: Unknown
% 3.22/1.82 % (17321)Termination phase: Property scanning
% 3.22/1.82
% 3.22/1.82 % (17321)Memory used [KB]: 4093
% 3.22/1.82 % (17321)Time elapsed: 0.054 s
% 3.22/1.82 % (17321)Instructions burned: 184 (million)
% 3.22/1.82 % (17321)------------------------------
% 3.22/1.82 % (17321)------------------------------
% 3.22/1.82 % (17354)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/7Mi)
% 3.22/1.82 % (17354)Instruction limit reached!
% 3.22/1.82 % (17354)------------------------------
% 3.22/1.82 % (17354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.82 % (17354)Termination reason: Unknown
% 3.22/1.82 % (17354)Termination phase: shuffling
% 3.22/1.82
% 3.22/1.82 % (17354)Memory used [KB]: 1791
% 3.22/1.82 % (17354)Time elapsed: 0.005 s
% 3.22/1.82 % (17354)Instructions burned: 9 (million)
% 3.22/1.82 % (17354)------------------------------
% 3.22/1.82 % (17354)------------------------------
% 3.22/1.82 % (17357)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/4Mi)
% 3.22/1.82 % (17357)Instruction limit reached!
% 3.22/1.82 % (17357)------------------------------
% 3.22/1.82 % (17357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.82 % (17357)Termination reason: Unknown
% 3.22/1.82 % (17357)Termination phase: shuffling
% 3.22/1.82
% 3.22/1.82 % (17357)Memory used [KB]: 1663
% 3.22/1.82 % (17357)Time elapsed: 0.003 s
% 3.22/1.82 % (17357)Instructions burned: 6 (million)
% 3.22/1.82 % (17357)------------------------------
% 3.22/1.82 % (17357)------------------------------
% 3.22/1.83 % (17359)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/710Mi)
% 3.22/1.83 % (17356)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/3Mi)
% 3.22/1.83 % (17361)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/6Mi)
% 3.22/1.83 % (17358)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/18Mi)
% 3.22/1.83 % (17356)Instruction limit reached!
% 3.22/1.83 % (17356)------------------------------
% 3.22/1.83 % (17356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.83 % (17356)Termination reason: Unknown
% 3.22/1.83 % (17356)Termination phase: shuffling
% 3.22/1.83
% 3.22/1.83 % (17356)Memory used [KB]: 1535
% 3.22/1.83 % (17356)Time elapsed: 0.004 s
% 3.22/1.83 % (17356)Instructions burned: 3 (million)
% 3.22/1.83 % (17356)------------------------------
% 3.22/1.83 % (17356)------------------------------
% 3.22/1.83 % (17361)Instruction limit reached!
% 3.22/1.83 % (17361)------------------------------
% 3.22/1.83 % (17361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.83 % (17361)Termination reason: Unknown
% 3.22/1.83 % (17361)Termination phase: shuffling
% 3.22/1.83
% 3.22/1.83 % (17361)Memory used [KB]: 1663
% 3.22/1.83 % (17361)Time elapsed: 0.004 s
% 3.22/1.83 % (17361)Instructions burned: 6 (million)
% 3.22/1.83 % (17361)------------------------------
% 3.22/1.83 % (17361)------------------------------
% 3.22/1.83 % (17364)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_17125 for (2999ds/902Mi)
% 3.22/1.84 % (17358)Instruction limit reached!
% 3.22/1.84 % (17358)------------------------------
% 3.22/1.84 % (17358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.84 % (17358)Termination reason: Unknown
% 3.22/1.84 % (17358)Termination phase: shuffling
% 3.22/1.84
% 3.22/1.84 % (17358)Memory used [KB]: 1918
% 3.22/1.84 % (17358)Time elapsed: 0.010 s
% 3.22/1.84 % (17358)Instructions burned: 19 (million)
% 3.22/1.84 % (17358)------------------------------
% 3.22/1.84 % (17358)------------------------------
% 3.22/1.84 % (17372)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_17125 for (2998ds/5Mi)
% 3.22/1.84 % (17372)Instruction limit reached!
% 3.22/1.84 % (17372)------------------------------
% 3.22/1.84 % (17372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.84 % (17372)Termination reason: Unknown
% 3.22/1.84 % (17372)Termination phase: shuffling
% 3.22/1.84
% 3.22/1.84 % (17372)Memory used [KB]: 1663
% 3.22/1.84 % (17372)Time elapsed: 0.003 s
% 3.22/1.84 % (17372)Instructions burned: 6 (million)
% 3.22/1.84 % (17372)------------------------------
% 3.22/1.84 % (17372)------------------------------
% 3.22/1.85 % (17369)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_17125 for (2998ds/21Mi)
% 3.22/1.85 % (17373)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_17125 for (2998ds/6Mi)
% 3.22/1.85 % (17373)Instruction limit reached!
% 3.22/1.85 % (17373)------------------------------
% 3.22/1.85 % (17373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.85 % (17373)Termination reason: Unknown
% 3.22/1.85 % (17373)Termination phase: shuffling
% 3.22/1.85
% 3.22/1.85 % (17373)Memory used [KB]: 1663
% 3.22/1.85 % (17373)Time elapsed: 0.004 s
% 3.22/1.85 % (17373)Instructions burned: 7 (million)
% 3.22/1.85 % (17373)------------------------------
% 3.22/1.85 % (17373)------------------------------
% 3.22/1.85 % (17374)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_17125 for (2998ds/377Mi)
% 3.22/1.86 % (17326)First to succeed.
% 3.22/1.86 % (17369)Instruction limit reached!
% 3.22/1.86 % (17369)------------------------------
% 3.22/1.86 % (17369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.86 % (17369)Termination reason: Unknown
% 3.22/1.86 % (17369)Termination phase: shuffling
% 3.22/1.86
% 3.22/1.86 % (17369)Memory used [KB]: 1918
% 3.22/1.86 % (17369)Time elapsed: 0.015 s
% 3.22/1.86 % (17369)Instructions burned: 21 (million)
% 3.22/1.86 % (17369)------------------------------
% 3.22/1.86 % (17369)------------------------------
% 3.22/1.86 % (17377)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_17125 for (2998ds/779Mi)
% 3.22/1.86 % (17326)Refutation found. Thanks to Tanya!
% 3.22/1.86 % SZS status Theorem for DTF2THF_17125
% 3.22/1.86 % SZS output start Proof for DTF2THF_17125
% 3.22/1.86 thf(type_def_5, type, pi: $tType).
% 3.22/1.86 thf(type_def_7, type, name: $tType).
% 3.22/1.86 thf(type_def_8, type, set_name: $tType).
% 3.22/1.86 thf(type_def_9, type, late_freeRes: $tType).
% 3.22/1.86 thf(type_def_10, type, late_subject: $tType).
% 3.22/1.86 thf(type_def_11, type, late_residual: $tType).
% 3.22/1.86 thf(type_def_12, type, noptio354675977ion_pi: $tType).
% 3.22/1.86 thf(type_def_13, type, noption_name: $tType).
% 3.22/1.86 thf(type_def_14, type, noption_pi: $tType).
% 3.22/1.86 thf(type_def_15, type, noptio1926134715n_name: $tType).
% 3.22/1.86 thf(type_def_16, type, noption_Late_freeRes: $tType).
% 3.22/1.86 thf(type_def_17, type, noptio435234344reeRes: $tType).
% 3.22/1.86 thf(type_def_18, type, noption_Late_subject: $tType).
% 3.22/1.86 thf(type_def_19, type, noptio570777408ubject: $tType).
% 3.22/1.86 thf(type_def_20, type, noptio930204083reeRes: $tType).
% 3.22/1.86 thf(type_def_21, type, noptio1065747147ubject: $tType).
% 3.22/1.86 thf(func_def_0, type, noptio1065747147ubject: $tType).
% 3.22/1.86 thf(func_def_1, type, noptio930204083reeRes: $tType).
% 3.22/1.86 thf(func_def_2, type, noptio570777408ubject: $tType).
% 3.22/1.86 thf(func_def_3, type, noptio435234344reeRes: $tType).
% 3.22/1.86 thf(func_def_4, type, noptio1926134715n_name: $tType).
% 3.22/1.86 thf(func_def_5, type, noptio354675977ion_pi: $tType).
% 3.22/1.86 thf(func_def_6, type, noption_Late_subject: $tType).
% 3.22/1.86 thf(func_def_7, type, noption_Late_freeRes: $tType).
% 3.22/1.86 thf(func_def_8, type, noption_name: $tType).
% 3.22/1.86 thf(func_def_9, type, noption_pi: $tType).
% 3.22/1.86 thf(func_def_10, type, set_name: $tType).
% 3.22/1.86 thf(func_def_11, type, late_residual: $tType).
% 3.22/1.86 thf(func_def_12, type, late_subject: $tType).
% 3.22/1.86 thf(func_def_13, type, late_freeRes: $tType).
% 3.22/1.86 thf(func_def_14, type, name: $tType).
% 3.22/1.86 thf(func_def_15, type, pi: $tType).
% 3.22/1.86 thf(func_def_16, type, bang: pi > pi).
% 3.22/1.86 thf(func_def_17, type, input: name > name > pi > pi).
% 3.22/1.86 thf(func_def_18, type, match: name > name > pi > pi).
% 3.22/1.86 thf(func_def_19, type, mismatch: name > name > pi > pi).
% 3.22/1.86 thf(func_def_20, type, output: name > name > pi > pi).
% 3.22/1.86 thf(func_def_21, type, par: pi > pi > pi).
% 3.22/1.86 thf(func_def_22, type, piNil: pi).
% 3.22/1.86 thf(func_def_23, type, res: name > pi > pi).
% 3.22/1.86 thf(func_def_24, type, sum: pi > pi > pi).
% 3.22/1.86 thf(func_def_25, type, tau: pi > pi).
% 3.22/1.86 thf(func_def_26, type, pi_rec_pi: pi > (name > name > pi > pi > pi) > (pi > pi > pi) > (name > name > pi > pi > pi) > (name > name > pi > pi > pi) > (name > name > pi > pi > pi) > (pi > pi > pi > pi > pi) > (pi > pi > pi > pi > pi) > (name > pi > pi > pi) > (pi > pi > pi) > pi > pi).
% 3.22/1.86 thf(func_def_27, type, subs: pi > name > name > pi).
% 3.22/1.86 thf(func_def_28, type, subst_name: name > name > name > name).
% 3.22/1.86 thf(func_def_29, type, finite_finite_name: set_name > $o).
% 3.22/1.86 thf(func_def_30, type, if_name: $o > name > name > name).
% 3.22/1.86 thf(func_def_31, type, late_bangPred: pi > pi > $o).
% 3.22/1.86 thf(func_def_32, type, late_OutputR: name > name > late_freeRes).
% 3.22/1.86 thf(func_def_33, type, late_TauR: late_freeRes).
% 3.22/1.86 thf(func_def_34, type, late_BoundR: late_subject > name > pi > late_residual).
% 3.22/1.86 thf(func_def_35, type, late_FreeR: late_freeRes > pi > late_residual).
% 3.22/1.86 thf(func_def_36, type, late_r1174711868c_name: (late_subject > name > pi > name) > (late_freeRes > pi > name) > late_residual > name).
% 3.22/1.86 thf(func_def_37, type, late_residual_rec_pi: (late_subject > name > pi > pi) > (late_freeRes > pi > pi) > late_residual > pi).
% 3.22/1.86 thf(func_def_38, type, late_r124702629reeRes: (late_subject > name > pi > late_freeRes) > (late_freeRes > pi > late_freeRes) > late_residual > late_freeRes).
% 3.22/1.86 thf(func_def_39, type, late_r1347955901ubject: (late_subject > name > pi > late_subject) > (late_freeRes > pi > late_subject) > late_residual > late_subject).
% 3.22/1.86 thf(func_def_40, type, late_r1558248490ion_pi: (late_subject > name > pi > name > noptio354675977ion_pi) > (late_freeRes > pi > name > noptio354675977ion_pi) > late_residual > (name > noptio354675977ion_pi) > $o).
% 3.22/1.86 thf(func_def_41, type, late_r303715378n_name: (late_subject > name > pi > name > noption_name) > (late_freeRes > pi > name > noption_name) > late_residual > (name > noption_name) > $o).
% 3.22/1.86 thf(func_def_42, type, late_r750878080ion_pi: (late_subject > name > pi > name > noption_pi) > (late_freeRes > pi > name > noption_pi) > late_residual > (name > noption_pi) > $o).
% 3.22/1.86 thf(func_def_43, type, late_r1742481968t_name: (late_subject > name > pi > name) > (late_freeRes > pi > name) > late_residual > name > $o).
% 3.22/1.86 thf(func_def_44, type, late_r1261898622set_pi: (late_subject > name > pi > pi) > (late_freeRes > pi > pi) > late_residual > pi > $o).
% 3.22/1.86 thf(func_def_45, type, late_r1613948593reeRes: (late_subject > name > pi > late_freeRes) > (late_freeRes > pi > late_freeRes) > late_residual > late_freeRes > $o).
% 3.22/1.86 thf(func_def_46, type, late_r689718217ubject: (late_subject > name > pi > late_subject) > (late_freeRes > pi > late_subject) > late_residual > late_subject > $o).
% 3.22/1.86 thf(func_def_47, type, late_BoundOutputS: name > late_subject).
% 3.22/1.86 thf(func_def_48, type, late_InputS: name > late_subject).
% 3.22/1.86 thf(func_def_49, type, late_transitions: pi > late_residual > $o).
% 3.22/1.86 thf(func_def_50, type, sup_sup_set_name: set_name > set_name > set_name).
% 3.22/1.86 thf(func_def_51, type, abs_fu1394407909n_name: name > (name > noption_name) > name > noptio1926134715n_name).
% 3.22/1.86 thf(func_def_52, type, abs_fu1614711987ion_pi: name > (name > noption_pi) > name > noptio354675977ion_pi).
% 3.22/1.86 thf(func_def_53, type, abs_fu1763130856reeRes: name > (name > noption_Late_freeRes) > name > noptio435234344reeRes).
% 3.22/1.86 thf(func_def_54, type, abs_fu1705804544ubject: name > (name > noption_Late_subject) > name > noptio570777408ubject).
% 3.22/1.86 thf(func_def_55, type, abs_fu946147443reeRes: name > (late_freeRes > pi > late_freeRes) > name > noptio930204083reeRes).
% 3.22/1.86 thf(func_def_56, type, abs_fu888821131ubject: name > (late_freeRes > pi > late_subject) > name > noptio1065747147ubject).
% 3.22/1.86 thf(func_def_57, type, abs_fun_name_name: name > name > name > noption_name).
% 3.22/1.86 thf(func_def_58, type, abs_fun_name_pi: name > pi > name > noption_pi).
% 3.22/1.86 thf(func_def_59, type, abs_fu681348580reeRes: name > late_freeRes > name > noption_Late_freeRes).
% 3.22/1.86 thf(func_def_60, type, abs_fu1904601852ubject: name > late_subject > name > noption_Late_subject).
% 3.22/1.86 thf(func_def_61, type, fresh_1742414570n_name: name > (name > noptio1926134715n_name) > $o).
% 3.22/1.86 thf(func_def_62, type, fresh_92802872ion_pi: name > (name > noptio354675977ion_pi) > $o).
% 3.22/1.86 thf(func_def_63, type, fresh_1215331279reeRes: name > (name > noptio435234344reeRes) > $o).
% 3.22/1.86 thf(func_def_64, type, fresh_600418535ubject: name > (name > noptio570777408ubject) > $o).
% 3.22/1.86 thf(func_def_65, type, fresh_111433690reeRes: name > (name > noptio930204083reeRes) > $o).
% 3.22/1.86 thf(func_def_66, type, fresh_1644004594ubject: name > (name > noptio1065747147ubject) > $o).
% 3.22/1.86 thf(func_def_67, type, fresh_1093033124n_name: name > (name > noption_name) > $o).
% 3.22/1.86 thf(func_def_68, type, fresh_543891186ion_pi: name > (name > noption_pi) > $o).
% 3.22/1.86 thf(func_def_69, type, fresh_785364841reeRes: name > (name > noption_Late_freeRes) > $o).
% 3.22/1.86 thf(func_def_70, type, fresh_728038529ubject: name > (name > noption_Late_subject) > $o).
% 3.22/1.86 thf(func_def_71, type, fresh_2081817683ion_pi: name > (late_freeRes > pi > name > noptio354675977ion_pi) > $o).
% 3.22/1.86 thf(func_def_72, type, fresh_808662133n_name: name > (late_freeRes > pi > name > noption_name) > $o).
% 3.22/1.86 thf(func_def_73, type, fresh_7927363ion_pi: name > (late_freeRes > pi > name > noption_pi) > $o).
% 3.22/1.86 thf(func_def_74, type, fresh_1030632537i_name: name > (late_freeRes > pi > name) > $o).
% 3.22/1.86 thf(func_def_75, type, fresh_1011532071_pi_pi: name > (late_freeRes > pi > pi) > $o).
% 3.22/1.86 thf(func_def_76, type, fresh_256112244reeRes: name > (late_freeRes > pi > late_freeRes) > $o).
% 3.22/1.86 thf(func_def_77, type, fresh_198785932ubject: name > (late_freeRes > pi > late_subject) > $o).
% 3.22/1.86 thf(func_def_78, type, fresh_876421558ion_pi: name > (late_subject > name > pi > name > noptio354675977ion_pi) > $o).
% 3.22/1.86 thf(func_def_79, type, fresh_62885992n_name: name > (late_subject > name > pi > name > noption_name) > $o).
% 3.22/1.86 thf(func_def_80, type, fresh_747777846ion_pi: name > (late_subject > name > pi > name > noption_pi) > $o).
% 3.22/1.86 thf(func_def_81, type, fresh_621211324i_name: name > (late_subject > name > pi > name) > $o).
% 3.22/1.86 thf(func_def_82, type, fresh_1438126218_pi_pi: name > (late_subject > name > pi > pi) > $o).
% 3.22/1.86 thf(func_def_83, type, fresh_660367079reeRes: name > (late_subject > name > pi > late_freeRes) > $o).
% 3.22/1.86 thf(func_def_84, type, fresh_795910143ubject: name > (late_subject > name > pi > late_subject) > $o).
% 3.22/1.86 thf(func_def_85, type, fresh_name_name: name > name > $o).
% 3.22/1.86 thf(func_def_86, type, fresh_name_pi: name > pi > $o).
% 3.22/1.86 thf(func_def_87, type, fresh_1641682979reeRes: name > late_freeRes > $o).
% 3.22/1.86 thf(func_def_88, type, fresh_81631222sidual: name > late_residual > $o).
% 3.22/1.86 thf(func_def_89, type, fresh_717452603ubject: name > late_subject > $o).
% 3.22/1.86 thf(func_def_90, type, supp_n352473082e_name: (name > noption_name) > set_name).
% 3.22/1.86 thf(func_def_91, type, supp_n468628396i_name: (name > noption_pi) > set_name).
% 3.22/1.86 thf(func_def_92, type, supp_n252280103s_name: (name > noption_Late_freeRes) > set_name).
% 3.22/1.86 thf(func_def_93, type, supp_n1630792207t_name: (name > noption_Late_subject) > set_name).
% 3.22/1.86 thf(func_def_94, type, supp_L979396363i_name: (late_freeRes > pi > name > noptio354675977ion_pi) > set_name).
% 3.22/1.86 thf(func_def_95, type, supp_L473926939e_name: (late_freeRes > pi > name > noption_name) > set_name).
% 3.22/1.86 thf(func_def_96, type, supp_L635439693i_name: (late_freeRes > pi > name > noption_pi) > set_name).
% 3.22/1.86 thf(func_def_97, type, supp_L926407557e_name: (late_freeRes > pi > name) > set_name).
% 3.22/1.86 thf(func_def_98, type, supp_L2052723895i_name: (late_freeRes > pi > pi) > set_name).
% 3.22/1.86 thf(func_def_99, type, supp_L381160156s_name: (late_freeRes > pi > late_freeRes) > set_name).
% 3.22/1.86 thf(func_def_100, type, supp_L1759672260t_name: (late_freeRes > pi > late_subject) > set_name).
% 3.22/1.86 thf(func_def_101, type, supp_L1512088218i_name: (late_subject > name > pi > name > noptio354675977ion_pi) > set_name).
% 3.22/1.86 thf(func_def_102, type, supp_L14705974e_name: (late_subject > name > pi > name > noption_name) > set_name).
% 3.22/1.86 thf(func_def_103, type, supp_L3230824i_name: (late_subject > name > pi > name > noption_pi) > set_name).
% 3.22/1.86 thf(func_def_104, type, supp_L538372628e_name: (late_subject > name > pi > name) > set_name).
% 3.22/1.86 thf(func_def_105, type, supp_L729745222i_name: (late_subject > name > pi > pi) > set_name).
% 3.22/1.86 thf(func_def_106, type, supp_L1178477943s_name: (late_subject > name > pi > late_freeRes) > set_name).
% 3.22/1.86 thf(func_def_107, type, supp_L1144036959t_name: (late_subject > name > pi > late_subject) > set_name).
% 3.22/1.86 thf(func_def_108, type, supp_name_name: name > set_name).
% 3.22/1.86 thf(func_def_109, type, supp_pi_name: pi > set_name).
% 3.22/1.86 thf(func_def_110, type, supp_L1228270395s_name: late_freeRes > set_name).
% 3.22/1.86 thf(func_def_111, type, supp_L1174042202l_name: late_residual > set_name).
% 3.22/1.86 thf(func_def_112, type, supp_L1174290467t_name: late_subject > set_name).
% 3.22/1.86 thf(func_def_113, type, collect_name: (name > $o) > set_name).
% 3.22/1.86 thf(func_def_114, type, member_name: name > set_name > $o).
% 3.22/1.86 thf(func_def_115, type, p: pi).
% 3.22/1.86 thf(func_def_116, type, pqr: pi).
% 3.22/1.86 thf(func_def_117, type, q: pi).
% 3.22/1.86 thf(func_def_118, type, qr: pi).
% 3.22/1.86 thf(func_def_119, type, q2: pi).
% 3.22/1.86 thf(func_def_120, type, r: pi).
% 3.22/1.86 thf(func_def_121, type, r2: pi).
% 3.22/1.86 thf(func_def_122, type, alpha: late_freeRes).
% 3.22/1.86 thf(func_def_123, type, a: name).
% 3.22/1.86 thf(func_def_124, type, x: name).
% 3.22/1.86 thf(func_def_125, type, y: name).
% 3.22/1.86 thf(func_def_140, type, sP0: late_subject > name > pi > name > pi > $o).
% 3.22/1.86 thf(func_def_141, type, sP1: late_subject > name > pi > pi > pi > $o).
% 3.22/1.86 thf(func_def_142, type, sP2: name > pi > late_residual > $o).
% 3.22/1.86 thf(func_def_143, type, sP3: late_residual > name > pi > $o).
% 3.22/1.86 thf(func_def_144, type, sK4: (late_subject > $o) > name).
% 3.22/1.86 thf(func_def_145, type, sK5: (late_subject > $o) > name).
% 3.22/1.86 thf(func_def_146, type, sK6: (pi > late_residual > $o) > late_freeRes).
% 3.22/1.86 thf(func_def_147, type, sK7: (pi > late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_148, type, sK8: (pi > late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_149, type, sK9: (pi > late_residual > $o) > name).
% 3.22/1.86 thf(func_def_150, type, sK10: (pi > late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_151, type, sK11: (pi > late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_152, type, sK12: (pi > late_residual > $o) > late_subject).
% 3.22/1.86 thf(func_def_153, type, sK13: (late_freeRes > $o) > name).
% 3.22/1.86 thf(func_def_154, type, sK14: (late_freeRes > $o) > name).
% 3.22/1.86 thf(func_def_155, type, sK15: (late_freeRes > late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_156, type, sK16: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.22/1.86 thf(func_def_157, type, sK17: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.22/1.86 thf(func_def_158, type, sK18: (late_freeRes > late_residual > $o) > name).
% 3.22/1.86 thf(func_def_159, type, sK19: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.22/1.86 thf(func_def_160, type, sK20: (late_freeRes > late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_161, type, sK21: (late_freeRes > late_residual > $o) > late_subject).
% 3.22/1.86 thf(func_def_162, type, sK22: late_freeRes > name).
% 3.22/1.86 thf(func_def_163, type, sK23: (late_freeRes > late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_164, type, sK24: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.22/1.86 thf(func_def_165, type, sK25: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.22/1.86 thf(func_def_166, type, sK26: (late_freeRes > late_residual > $o) > late_subject).
% 3.22/1.86 thf(func_def_167, type, sK27: (late_freeRes > late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_168, type, sK28: (late_freeRes > late_residual > $o) > late_freeRes).
% 3.22/1.86 thf(func_def_169, type, sK29: (late_freeRes > late_residual > $o) > name).
% 3.22/1.86 thf(func_def_170, type, sK30: late_subject > name > pi > name > pi > pi).
% 3.22/1.86 thf(func_def_171, type, sK31: late_subject > name > pi > name > pi > name).
% 3.22/1.86 thf(func_def_172, type, sK32: late_subject > name > pi > name > pi > pi).
% 3.22/1.86 thf(func_def_173, type, sK33: late_subject > name > pi > name > pi > late_subject).
% 3.22/1.86 thf(func_def_174, type, sK34: late_subject > name > pi > name > pi > name).
% 3.22/1.86 thf(func_def_175, type, sK35: pi > pi > name > name > late_subject > pi).
% 3.22/1.86 thf(func_def_176, type, sK36: pi > pi > name > name > late_subject > name).
% 3.22/1.86 thf(func_def_177, type, sK37: pi > pi > name > name > late_subject > name).
% 3.22/1.86 thf(func_def_178, type, sK38: pi > pi > name > name > late_subject > pi).
% 3.22/1.86 thf(func_def_179, type, sK39: late_subject > name).
% 3.22/1.86 thf(func_def_180, type, sK40: late_residual > pi > name > name > pi).
% 3.22/1.86 thf(func_def_181, type, sK41: late_residual > pi > name > name > name).
% 3.22/1.86 thf(func_def_182, type, sK42: late_residual > pi > name > name > name).
% 3.22/1.86 thf(func_def_183, type, sK43: late_subject > name > pi > pi > pi > pi).
% 3.22/1.86 thf(func_def_184, type, sK44: late_subject > name > pi > pi > pi > name).
% 3.22/1.86 thf(func_def_185, type, sK45: late_subject > name > pi > pi > pi > pi).
% 3.22/1.86 thf(func_def_186, type, sK46: late_subject > name > pi > pi > pi > late_subject).
% 3.22/1.86 thf(func_def_187, type, sK47: late_subject > name > pi > pi > pi > pi).
% 3.22/1.86 thf(func_def_188, type, sK48: pi > name > late_subject > pi > pi > pi).
% 3.22/1.86 thf(func_def_189, type, sK49: pi > name > late_subject > pi > pi > pi).
% 3.22/1.86 thf(func_def_190, type, sK50: pi > name > late_subject > pi > pi > late_subject).
% 3.22/1.86 thf(func_def_191, type, sK51: pi > name > late_subject > pi > pi > name).
% 3.22/1.86 thf(func_def_192, type, sK52: pi > name > late_subject > pi > pi > pi).
% 3.22/1.86 thf(func_def_193, type, sK53: late_subject > name).
% 3.22/1.86 thf(func_def_194, type, sK54: late_subject > name).
% 3.22/1.86 thf(func_def_195, type, sK55: pi > late_residual > pi).
% 3.22/1.86 thf(func_def_196, type, sK56: (late_subject > late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_197, type, sK57: (late_subject > late_residual > $o) > late_freeRes).
% 3.22/1.86 thf(func_def_198, type, sK58: (late_subject > late_residual > $o) > late_subject).
% 3.22/1.86 thf(func_def_199, type, sK59: (late_subject > late_residual > $o) > late_subject).
% 3.22/1.86 thf(func_def_200, type, sK60: (late_subject > late_residual > $o) > late_subject).
% 3.22/1.86 thf(func_def_201, type, sK61: (late_subject > late_residual > $o) > name).
% 3.22/1.86 thf(func_def_202, type, sK62: (late_subject > late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_203, type, sK63: (pi > late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_204, type, sK64: (pi > late_residual > $o) > late_freeRes).
% 3.22/1.86 thf(func_def_205, type, sK65: (pi > late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_206, type, sK66: (pi > late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_207, type, sK67: (pi > late_residual > $o) > late_subject).
% 3.22/1.86 thf(func_def_208, type, sK68: (pi > late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_209, type, sK69: (pi > late_residual > $o) > name).
% 3.22/1.86 thf(func_def_210, type, sK70: (late_subject > late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_211, type, sK71: (late_subject > late_residual > $o) > late_subject).
% 3.22/1.86 thf(func_def_212, type, sK72: (late_subject > late_residual > $o) > late_freeRes).
% 3.22/1.86 thf(func_def_213, type, sK73: (late_subject > late_residual > $o) > late_subject).
% 3.22/1.86 thf(func_def_214, type, sK74: (late_subject > late_residual > $o) > late_subject).
% 3.22/1.86 thf(func_def_215, type, sK75: (late_subject > late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_216, type, sK76: (late_subject > late_residual > $o) > name).
% 3.22/1.86 thf(func_def_217, type, sK77: name > (pi > $o) > late_freeRes > pi > pi).
% 3.22/1.86 thf(func_def_218, type, sK78: pi > late_residual > pi).
% 3.22/1.86 thf(func_def_219, type, sK79: late_freeRes > name).
% 3.22/1.86 thf(func_def_220, type, sK80: late_freeRes > name).
% 3.22/1.86 thf(func_def_221, type, sK81: late_residual > name > pi > pi).
% 3.22/1.86 thf(func_def_222, type, sK82: late_residual > name > pi > name).
% 3.22/1.86 thf(func_def_223, type, sK83: late_residual > name > pi > name).
% 3.22/1.86 thf(func_def_224, type, sK84: late_residual > name > pi > pi).
% 3.22/1.86 thf(func_def_225, type, sK85: name > pi > late_residual > name).
% 3.22/1.86 thf(func_def_226, type, sK86: name > pi > late_residual > pi).
% 3.22/1.86 thf(func_def_227, type, sK87: name > pi > late_residual > name).
% 3.22/1.86 thf(func_def_228, type, sK88: name > pi > late_residual > late_subject).
% 3.22/1.86 thf(func_def_229, type, sK89: name > pi > late_residual > pi).
% 3.22/1.86 thf(func_def_230, type, sK90: pi > late_residual > name > name).
% 3.22/1.86 thf(func_def_231, type, sK91: pi > late_residual > name > late_freeRes).
% 3.22/1.86 thf(func_def_232, type, sK92: pi > late_residual > name > pi).
% 3.22/1.86 thf(func_def_233, type, sK93: pi > late_residual > name > pi).
% 3.22/1.86 thf(func_def_234, type, sK94: pi > name).
% 3.22/1.86 thf(func_def_235, type, sK95: late_subject > name > pi > (pi > $o) > pi > pi).
% 3.22/1.86 thf(func_def_236, type, sK96: late_subject > name > pi > (pi > $o) > pi > pi).
% 3.22/1.86 thf(func_def_237, type, sK97: (late_residual > $o) > name).
% 3.22/1.86 thf(func_def_238, type, sK98: (late_residual > $o) > late_subject).
% 3.22/1.86 thf(func_def_239, type, sK99: (late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_240, type, sK100: (late_residual > $o) > pi).
% 3.22/1.86 thf(func_def_241, type, sK101: (late_residual > $o) > late_freeRes).
% 3.22/1.86 thf(func_def_242, type, sK102: name > late_freeRes > pi > pi > pi).
% 3.22/1.86 thf(func_def_243, type, sK103: name > late_freeRes > pi > pi > late_freeRes).
% 3.22/1.86 thf(func_def_244, type, sK104: name > late_freeRes > pi > pi > name).
% 3.22/1.86 thf(func_def_245, type, sK105: name > late_freeRes > pi > pi > pi).
% 3.22/1.86 thf(func_def_247, type, ph107: !>[X0: $tType]:(X0)).
% 3.22/1.86 thf(f1405,plain,(
% 3.22/1.86 $false),
% 3.22/1.86 inference(subsumption_resolution,[status(thm)],[f1404,f1158])).
% 3.22/1.86 thf(f1158,plain,(
% 3.22/1.86 ((late_transitions @ r @ (late_BoundR @ (late_InputS @ a) @ x @ r2)) = $true)),
% 3.22/1.86 inference(cnf_transformation,[status(thm)],[f721])).
% 3.22/1.86 thf(f721,plain,(
% 3.22/1.86 ((late_transitions @ r @ (late_BoundR @ (late_InputS @ a) @ x @ r2)) = $true)),
% 3.22/1.86 inference(fool_elimination,[status(thm)],[f720])).
% 3.22/1.86 thf(f720,plain,(
% 3.22/1.86 (late_transitions @ r @ (late_BoundR @ (late_InputS @ a) @ x @ r2))),
% 3.22/1.86 inference(rectify,[status(thm)],[f13])).
% 3.22/1.86 thf(f13,axiom,(
% 3.22/1.86 (late_transitions @ r @ (late_BoundR @ (late_InputS @ a) @ x @ r2))),
% 3.22/1.86 file('/export/starexec/sandbox2/tmp/tmp.etxS7Hgr06/DTF2THF_17125.p',fact_12_cClose2_Ohyps_I2_J)).
% 3.22/1.86 thf(f1404,plain,(
% 3.22/1.86 ((late_transitions @ r @ (late_BoundR @ (late_InputS @ a) @ x @ r2)) != $true)),
% 3.22/1.86 inference(trivial_inequality_removal,[status(thm)],[f1399])).
% 3.22/1.86 thf(f1399,plain,(
% 3.22/1.86 ($true != $true) | ((late_transitions @ r @ (late_BoundR @ (late_InputS @ a) @ x @ r2)) != $true)),
% 3.22/1.86 inference(superposition,[status(thm)],[f1398,f1366])).
% 3.22/1.86 thf(f1366,plain,(
% 3.22/1.86 ((late_transitions @ (par @ p @ q) @ (late_BoundR @ (late_BoundOutputS @ a) @ y @ (par @ p @ q2))) = $true)),
% 3.22/1.86 inference(cnf_transformation,[status(thm)],[f801])).
% 3.22/1.86 thf(f801,plain,(
% 3.22/1.86 ((late_transitions @ (par @ p @ q) @ (late_BoundR @ (late_BoundOutputS @ a) @ y @ (par @ p @ q2))) = $true)),
% 3.22/1.86 inference(fool_elimination,[status(thm)],[f800])).
% 3.22/1.86 thf(f800,plain,(
% 3.22/1.86 (late_transitions @ (par @ p @ q) @ (late_BoundR @ (late_BoundOutputS @ a) @ y @ (par @ p @ q2)))),
% 3.22/1.86 inference(rectify,[status(thm)],[f14])).
% 3.22/1.86 thf(f14,axiom,(
% 3.22/1.86 (late_transitions @ (par @ p @ q) @ (late_BoundR @ (late_BoundOutputS @ a) @ y @ (par @ p @ q2)))),
% 3.22/1.86 file('/export/starexec/sandbox2/tmp/tmp.etxS7Hgr06/DTF2THF_17125.p',fact_13__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_Aa_060_092_060nu_062y_062_A_092_060prec_062_AP_A_092_060parallel_062_AQ_H_092_060close_062)).
% 3.22/1.86 thf(f1398,plain,(
% 3.22/1.86 ( ! [X0 : name] : (($true != (late_transitions @ (par @ p @ q) @ (late_BoundR @ (late_BoundOutputS @ X0) @ y @ (par @ p @ q2)))) | ((late_transitions @ r @ (late_BoundR @ (late_InputS @ X0) @ x @ r2)) != $true)) )),
% 3.22/1.86 inference(subsumption_resolution,[status(thm)],[f1388,f1169])).
% 3.22/1.86 thf(f1169,plain,(
% 3.22/1.86 ((fresh_name_pi @ y @ r) = $true)),
% 3.22/1.86 inference(cnf_transformation,[status(thm)],[f569])).
% 3.22/1.86 thf(f569,plain,(
% 3.22/1.86 ((fresh_name_pi @ y @ r) = $true)),
% 3.22/1.86 inference(fool_elimination,[status(thm)],[f568])).
% 3.22/1.86 thf(f568,plain,(
% 3.22/1.86 (fresh_name_pi @ y @ r)),
% 3.22/1.86 inference(rectify,[status(thm)],[f4])).
% 3.22/1.86 thf(f4,axiom,(
% 3.22/1.86 (fresh_name_pi @ y @ r)),
% 3.22/1.86 file('/export/starexec/sandbox2/tmp/tmp.etxS7Hgr06/DTF2THF_17125.p',fact_3_cClose2_Ohyps_I9_J)).
% 3.22/1.86 thf(f1388,plain,(
% 3.22/1.86 ( ! [X0 : name] : (($true != (late_transitions @ (par @ p @ q) @ (late_BoundR @ (late_BoundOutputS @ X0) @ y @ (par @ p @ q2)))) | ((fresh_name_pi @ y @ r) != $true) | ((late_transitions @ r @ (late_BoundR @ (late_InputS @ X0) @ x @ r2)) != $true)) )),
% 3.22/1.86 inference(trivial_inequality_removal,[status(thm)],[f1386])).
% 3.22/1.86 thf(f1386,plain,(
% 3.22/1.86 ( ! [X0 : name] : (($true != $true) | ((late_transitions @ r @ (late_BoundR @ (late_InputS @ X0) @ x @ r2)) != $true) | ((fresh_name_pi @ y @ r) != $true) | ($true != (late_transitions @ (par @ p @ q) @ (late_BoundR @ (late_BoundOutputS @ X0) @ y @ (par @ p @ q2))))) )),
% 3.22/1.86 inference(superposition,[status(thm)],[f1154,f1277])).
% 3.22/1.86 thf(f1277,plain,(
% 3.22/1.86 ( ! [X2 : name,X3 : name,X0 : pi,X1 : name,X6 : pi,X4 : pi,X5 : pi] : (((late_transitions @ (par @ X6 @ X5) @ (late_FreeR @ late_TauR @ (res @ X2 @ (par @ X0 @ (subs @ X4 @ X1 @ X2))))) = $true) | ((fresh_name_pi @ X2 @ X5) != $true) | ((late_transitions @ X5 @ (late_BoundR @ (late_InputS @ X3) @ X1 @ X4)) != $true) | ((late_transitions @ X6 @ (late_BoundR @ (late_BoundOutputS @ X3) @ X2 @ X0)) != $true)) )),
% 3.22/1.86 inference(cnf_transformation,[status(thm)],[f947])).
% 3.22/1.86 thf(f947,plain,(
% 3.22/1.86 ! [X0 : pi,X1 : name,X2 : name,X3 : name,X4 : pi,X5 : pi,X6 : pi] : (((late_transitions @ X5 @ (late_BoundR @ (late_InputS @ X3) @ X1 @ X4)) != $true) | ((late_transitions @ X6 @ (late_BoundR @ (late_BoundOutputS @ X3) @ X2 @ X0)) != $true) | ((late_transitions @ (par @ X6 @ X5) @ (late_FreeR @ late_TauR @ (res @ X2 @ (par @ X0 @ (subs @ X4 @ X1 @ X2))))) = $true) | ((fresh_name_pi @ X2 @ X5) != $true))),
% 3.22/1.86 inference(flattening,[status(thm)],[f946])).
% 3.22/1.86 thf(f946,plain,(
% 3.22/1.86 ! [X0 : pi,X1 : name,X2 : name,X3 : name,X4 : pi,X5 : pi,X6 : pi] : (((((late_transitions @ (par @ X6 @ X5) @ (late_FreeR @ late_TauR @ (res @ X2 @ (par @ X0 @ (subs @ X4 @ X1 @ X2))))) = $true) | ((fresh_name_pi @ X2 @ X5) != $true)) | ((late_transitions @ X5 @ (late_BoundR @ (late_InputS @ X3) @ X1 @ X4)) != $true)) | ((late_transitions @ X6 @ (late_BoundR @ (late_BoundOutputS @ X3) @ X2 @ X0)) != $true))),
% 3.22/1.86 inference(ennf_transformation,[status(thm)],[f541])).
% 3.22/1.86 thf(f541,plain,(
% 3.22/1.86 ! [X0 : pi,X1 : name,X2 : name,X3 : name,X4 : pi,X5 : pi,X6 : pi] : (((late_transitions @ X6 @ (late_BoundR @ (late_BoundOutputS @ X3) @ X2 @ X0)) = $true) => (((late_transitions @ X5 @ (late_BoundR @ (late_InputS @ X3) @ X1 @ X4)) = $true) => (((fresh_name_pi @ X2 @ X5) = $true) => ((late_transitions @ (par @ X6 @ X5) @ (late_FreeR @ late_TauR @ (res @ X2 @ (par @ X0 @ (subs @ X4 @ X1 @ X2))))) = $true))))),
% 3.22/1.86 inference(fool_elimination,[status(thm)],[f540])).
% 3.22/1.86 thf(f540,plain,(
% 3.22/1.86 ! [X0 : pi,X1 : name,X2 : name,X3 : name,X4 : pi,X5 : pi,X6 : pi] : ((late_transitions @ X6 @ (late_BoundR @ (late_BoundOutputS @ X3) @ X2 @ X0)) => ((late_transitions @ X5 @ (late_BoundR @ (late_InputS @ X3) @ X1 @ X4)) => ((fresh_name_pi @ X2 @ X5) => (late_transitions @ (par @ X6 @ X5) @ (late_FreeR @ late_TauR @ (res @ X2 @ (par @ X0 @ (subs @ X4 @ X1 @ X2))))))))),
% 3.22/1.86 inference(rectify,[status(thm)],[f25])).
% 3.22/1.86 thf(f25,axiom,(
% 3.22/1.86 ! [X6 : pi,X0 : name,X13 : name,X8 : name,X7 : pi,X4 : pi,X3 : pi] : ((late_transitions @ X3 @ (late_BoundR @ (late_BoundOutputS @ X8) @ X13 @ X6)) => ((late_transitions @ X4 @ (late_BoundR @ (late_InputS @ X8) @ X0 @ X7)) => ((fresh_name_pi @ X13 @ X4) => (late_transitions @ (par @ X3 @ X4) @ (late_FreeR @ late_TauR @ (res @ X13 @ (par @ X6 @ (subs @ X7 @ X0 @ X13))))))))),
% 3.22/1.86 file('/export/starexec/sandbox2/tmp/tmp.etxS7Hgr06/DTF2THF_17125.p',fact_24_Late__Semantics_OClose2)).
% 3.22/1.86 thf(f1154,plain,(
% 3.22/1.86 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (res @ y @ (par @ (par @ p @ q2) @ (subs @ r2 @ x @ y))))) != $true)),
% 3.22/1.86 inference(cnf_transformation,[status(thm)],[f888])).
% 3.22/1.86 thf(f888,plain,(
% 3.22/1.86 ((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (res @ y @ (par @ (par @ p @ q2) @ (subs @ r2 @ x @ y))))) != $true)),
% 3.22/1.86 inference(flattening,[status(thm)],[f791])).
% 3.22/1.86 thf(f791,plain,(
% 3.22/1.86 ~((late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (res @ y @ (par @ (par @ p @ q2) @ (subs @ r2 @ x @ y))))) = $true)),
% 3.22/1.86 inference(fool_elimination,[status(thm)],[f790])).
% 3.22/1.86 thf(f790,plain,(
% 3.22/1.86 ~(late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (res @ y @ (par @ (par @ p @ q2) @ (subs @ r2 @ x @ y)))))),
% 3.22/1.86 inference(rectify,[status(thm)],[f354])).
% 3.22/1.86 thf(f354,negated_conjecture,(
% 3.22/1.86 ~(late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (res @ y @ (par @ (par @ p @ q2) @ (subs @ r2 @ x @ y)))))),
% 3.22/1.86 inference(negated_conjecture,[status(cth)],[f353])).
% 3.22/1.86 thf(f353,conjecture,(
% 3.22/1.86 (late_transitions @ (par @ (par @ p @ q) @ r) @ (late_FreeR @ late_TauR @ (res @ y @ (par @ (par @ p @ q2) @ (subs @ r2 @ x @ y)))))),
% 3.22/1.86 file('/export/starexec/sandbox2/tmp/tmp.etxS7Hgr06/DTF2THF_17125.p',conj_0)).
% 3.22/1.86 % SZS output end Proof for DTF2THF_17125
% 3.22/1.86 % (17326)------------------------------
% 3.22/1.86 % (17326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.22/1.86 % (17326)Termination reason: Refutation
% 3.22/1.86
% 3.22/1.86 % (17326)Memory used [KB]: 7931
% 3.22/1.86 % (17326)Time elapsed: 0.091 s
% 3.22/1.86 % (17326)Instructions burned: 156 (million)
% 3.22/1.86 % (17326)------------------------------
% 3.22/1.86 % (17326)------------------------------
% 3.22/1.86 % (17302)Success in time 0.133 s
%------------------------------------------------------------------------------