%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP080^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 08:55:23 AM UTC 2026
% Result : Theorem 44.75s 7.93s
% Output : Refutation 44.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 139 ( 39 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 301 ( 24 ~; 9 |; 0 &; 258 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 16 ( 15 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 367 ( 364 usr; 20 con; 0-9 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_node: $tType ).
thf(type_def_7,type,
set_val: $tType ).
thf(type_def_8,type,
g: $tType ).
thf(type_def_9,type,
list_node: $tType ).
thf(type_def_10,type,
node: $tType ).
thf(type_def_11,type,
list_P561207620_edgeD: $tType ).
thf(type_def_12,type,
list_P738500740D_node: $tType ).
thf(type_def_13,type,
list_val: $tType ).
thf(type_def_14,type,
list_l1129649930D_node: $tType ).
thf(type_def_15,type,
list_list_node: $tType ).
thf(type_def_16,type,
produc1453890942D_node: $tType ).
thf(type_def_17,type,
val: $tType ).
thf(type_def_18,type,
set_Pr1040144478D_node: $tType ).
thf(type_def_19,type,
produc1432036078de_val: $tType ).
thf(type_def_20,type,
option_list_val: $tType ).
thf(func_def_0,type,
list_l1129649930D_node: $tType ).
thf(func_def_1,type,
list_P738500740D_node: $tType ).
thf(func_def_2,type,
set_Pr1040144478D_node: $tType ).
thf(func_def_3,type,
produc1453890942D_node: $tType ).
thf(func_def_4,type,
list_P561207620_edgeD: $tType ).
thf(func_def_5,type,
option_list_val: $tType ).
thf(func_def_6,type,
produc1432036078de_val: $tType ).
thf(func_def_7,type,
list_list_node: $tType ).
thf(func_def_8,type,
list_node: $tType ).
thf(func_def_9,type,
list_val: $tType ).
thf(func_def_10,type,
set_node: $tType ).
thf(func_def_11,type,
set_val: $tType ).
thf(func_def_12,type,
node: $tType ).
thf(func_def_13,type,
val: $tType ).
thf(func_def_14,type,
g: $tType ).
thf(func_def_15,type,
finite_finite_node: set_node > $o ).
thf(func_def_16,type,
finite_finite_val: set_val > $o ).
thf(func_def_17,type,
graph_1994935542_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > list_node > $o ).
thf(func_def_18,type,
graph_1670286392_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > node > node > $o ).
thf(func_def_19,type,
graph_436675702_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > node > node > $o ).
thf(func_def_20,type,
graph_1947481694_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_P738500740D_node ).
thf(func_def_21,type,
graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
thf(func_def_22,type,
graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
thf(func_def_23,type,
append2096883353D_node: list_P738500740D_node > list_P738500740D_node > list_P738500740D_node ).
thf(func_def_24,type,
append_node: list_node > list_node > list_node ).
thf(func_def_25,type,
append_val: list_val > list_val > list_val ).
thf(func_def_26,type,
distin1098566007D_node: list_P738500740D_node > $o ).
thf(func_def_27,type,
distinct_node: list_node > $o ).
thf(func_def_28,type,
distinct_val: list_val > $o ).
thf(func_def_29,type,
cons_l1288865338D_node: list_P738500740D_node > list_l1129649930D_node > list_l1129649930D_node ).
thf(func_def_30,type,
cons_list_node: list_node > list_list_node > list_list_node ).
thf(func_def_31,type,
cons_P1018517044D_node: produc1453890942D_node > list_P738500740D_node > list_P738500740D_node ).
thf(func_def_32,type,
cons_node: node > list_node > list_node ).
thf(func_def_33,type,
cons_val: val > list_val > list_val ).
thf(func_def_34,type,
nil_li1626782346D_node: list_l1129649930D_node ).
thf(func_def_35,type,
nil_list_node: list_list_node ).
thf(func_def_36,type,
nil_Pr1769730692D_node: list_P738500740D_node ).
thf(func_def_37,type,
nil_node: list_node ).
thf(func_def_38,type,
nil_val: list_val ).
thf(func_def_39,type,
hd_Pro1395892457D_node: list_P738500740D_node > produc1453890942D_node ).
thf(func_def_40,type,
hd_node: list_node > node ).
thf(func_def_41,type,
hd_val: list_val > val ).
thf(func_def_42,type,
set_Pr1238794387D_node: list_P738500740D_node > set_Pr1040144478D_node ).
thf(func_def_43,type,
set_node2: list_node > set_node ).
thf(func_def_44,type,
set_val2: list_val > set_val ).
thf(func_def_45,type,
tl_Pro1633633005D_node: list_P738500740D_node > list_P738500740D_node ).
thf(func_def_46,type,
tl_node: list_node > list_node ).
thf(func_def_47,type,
tl_val: list_val > list_val ).
thf(func_def_48,type,
graph_589078910_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > $o ).
thf(func_def_49,type,
sSA_CF139593942de_val: ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(func_def_50,type,
sSA_CF1156973626eD_val: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > node > val > $o ).
thf(func_def_51,type,
sSA_CF370335846de_val: ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(func_def_52,type,
sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
thf(func_def_53,type,
sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
thf(func_def_54,type,
sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
thf(func_def_55,type,
sSA_CF1558836456eD_val: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > ( g > node > set_val ) > g > node > val > $o ).
thf(func_def_56,type,
collect_node: ( node > $o ) > set_node ).
thf(func_def_57,type,
collect_val: ( val > $o ) > set_val ).
thf(func_def_58,type,
suffix1143830554D_node: list_P738500740D_node > list_P738500740D_node > $o ).
thf(func_def_59,type,
suffix_node: list_node > list_node > $o ).
thf(func_def_60,type,
member1797643303D_node: produc1453890942D_node > set_Pr1040144478D_node > $o ).
thf(func_def_61,type,
member_node: node > set_node > $o ).
thf(func_def_62,type,
member_val: val > set_val > $o ).
thf(func_def_63,type,
entry: g > node ).
thf(func_def_64,type,
alpha_n: g > list_node ).
thf(func_def_65,type,
phi_r: val ).
thf(func_def_66,type,
defs: g > node > set_val ).
thf(func_def_67,type,
g2: g ).
thf(func_def_68,type,
inEdges: g > node > list_P561207620_edgeD ).
thf(func_def_69,type,
invar: g > $o ).
thf(func_def_70,type,
m: node ).
thf(func_def_71,type,
ms: list_node ).
thf(func_def_72,type,
n: node ).
thf(func_def_73,type,
ns: list_node ).
thf(func_def_74,type,
phis: g > produc1432036078de_val > option_list_val ).
thf(func_def_75,type,
pred_phi_r: node ).
thf(func_def_76,type,
r: val ).
thf(func_def_77,type,
rs: list_node ).
thf(func_def_78,type,
rs2: list_node ).
thf(func_def_79,type,
s: val ).
thf(func_def_95,type,
sP0: list_node > list_node > list_node > list_node > node > node > $o ).
thf(func_def_96,type,
sP1: ( list_node > list_node > $o ) > $o ).
thf(func_def_97,type,
sP2: ( list_node > list_node > $o ) > ( node > node > $o ) > $o ).
thf(func_def_98,type,
sP3: list_node > list_node > $o ).
thf(func_def_99,type,
sK4: list_node > node ).
thf(func_def_100,type,
sK5: list_node > list_node ).
thf(func_def_101,type,
sK6: list_node > node ).
thf(func_def_102,type,
sK7: list_node > node ).
thf(func_def_103,type,
sK8: node > list_node > node > list_node > list_node > list_node > list_node ).
thf(func_def_104,type,
sK9: node > list_node > node > list_node > list_node > list_node > list_node ).
thf(func_def_105,type,
sK10: ( node > list_node > node > $o ) > node > g > node ).
thf(func_def_106,type,
sK11: ( node > list_node > node > $o ) > node > g > list_node ).
thf(func_def_107,type,
sK12: ( node > list_node > node > $o ) > node > g > node ).
thf(func_def_108,type,
sK13: list_node > node > node ).
thf(func_def_109,type,
sK14: list_node > node > list_node ).
thf(func_def_110,type,
sK15: list_node > node > list_node ).
thf(func_def_111,type,
sK16: g > node > node ).
thf(func_def_112,type,
sK17: list_node > list_node ).
thf(func_def_113,type,
sK18: list_node > node ).
thf(func_def_114,type,
sK19: ( ( node > node > $o ) > list_node > $o ) > node > node > $o ).
thf(func_def_115,type,
sK20: ( ( node > node > $o ) > list_node > $o ) > node > node > $o ).
thf(func_def_116,type,
sK21: ( ( node > node > $o ) > list_node > $o ) > list_node ).
thf(func_def_117,type,
sK22: ( ( node > node > $o ) > list_node > $o ) > node ).
thf(func_def_118,type,
sK23: ( list_node > $o ) > node ).
thf(func_def_119,type,
sK24: ( list_node > $o ) > list_node ).
thf(func_def_120,type,
sK25: list_node > list_node > node > list_node > list_node ).
thf(func_def_121,type,
sK26: ( list_node > $o ) > list_node ).
thf(func_def_122,type,
sK27: ( list_node > $o ) > node ).
thf(func_def_123,type,
sK28: node > list_node > list_node ).
thf(func_def_124,type,
sK29: node > list_node > list_node ).
thf(func_def_125,type,
sK30: ( list_node > list_node > $o ) > list_node ).
thf(func_def_126,type,
sK31: ( list_node > list_node > $o ) > list_node ).
thf(func_def_127,type,
sK32: ( list_node > list_node > $o ) > node ).
thf(func_def_128,type,
sK33: ( list_node > list_node > $o ) > list_node ).
thf(func_def_129,type,
sK34: ( list_node > list_node > $o ) > list_node ).
thf(func_def_130,type,
sK35: ( list_node > list_node > $o ) > node ).
thf(func_def_131,type,
sK36: ( list_node > list_node > $o ) > node ).
thf(func_def_132,type,
sK37: ( list_node > list_node > $o ) > list_node ).
thf(func_def_133,type,
sK38: ( list_node > list_node > $o ) > list_node ).
thf(func_def_134,type,
sK39: ( list_node > list_node > $o ) > list_node ).
thf(func_def_135,type,
sK40: ( list_node > list_node > $o ) > node ).
thf(func_def_136,type,
sK41: ( list_node > list_node > $o ) > list_node ).
thf(func_def_137,type,
sK42: ( list_node > list_node > $o ) > list_node ).
thf(func_def_138,type,
sK43: ( list_node > list_node > $o ) > node ).
thf(func_def_139,type,
sK44: ( list_node > list_node > $o ) > node ).
thf(func_def_140,type,
sK45: ( list_node > list_node > $o ) > list_node ).
thf(func_def_141,type,
sK46: ( list_node > list_node > $o ) > node ).
thf(func_def_142,type,
sK47: ( list_node > list_node > $o ) > node ).
thf(func_def_143,type,
sK48: ( list_node > list_node > $o ) > node ).
thf(func_def_144,type,
sK49: ( list_node > list_node > $o ) > node ).
thf(func_def_145,type,
sK50: ( list_node > list_node > $o ) > node ).
thf(func_def_146,type,
sK51: ( list_node > list_node > $o ) > list_node ).
thf(func_def_147,type,
sK52: ( node > list_node > node > $o ) > g > node > list_node ).
thf(func_def_148,type,
sK53: ( node > list_node > node > $o ) > g > node > node ).
thf(func_def_149,type,
sK54: ( node > list_node > node > $o ) > g > node > node ).
thf(func_def_150,type,
sK55: ( list_node > list_node > $o ) > list_node ).
thf(func_def_151,type,
sK56: ( list_node > list_node > $o ) > list_node ).
thf(func_def_152,type,
sK57: ( list_node > list_node > $o ) > node ).
thf(func_def_153,type,
sK58: ( list_node > list_node > $o ) > list_node ).
thf(func_def_154,type,
sK59: list_node > node ).
thf(func_def_155,type,
sK60: list_node > list_node ).
thf(func_def_156,type,
sK61: ( ( node > node > $o ) > list_node > $o ) > node > node > $o ).
thf(func_def_157,type,
sK62: ( ( node > node > $o ) > list_node > $o ) > node > node > $o ).
thf(func_def_158,type,
sK63: ( ( node > node > $o ) > list_node > $o ) > node ).
thf(func_def_159,type,
sK64: ( ( node > node > $o ) > list_node > $o ) > list_node ).
thf(func_def_160,type,
sK65: ( ( node > node > $o ) > list_node > $o ) > node ).
thf(func_def_161,type,
sK66: ( ( node > node > $o ) > list_node > $o ) > node > node > $o ).
thf(func_def_162,type,
sK67: ( ( node > node > $o ) > list_node > $o ) > node ).
thf(func_def_163,type,
sK68: set_val > list_val ).
thf(func_def_164,type,
sK69: list_node > node ).
thf(func_def_165,type,
sK70: list_node > list_node ).
thf(func_def_166,type,
sK71: list_node > node ).
thf(func_def_167,type,
sK72: val > list_node > g > node ).
thf(func_def_168,type,
sK73: list_node > list_node ).
thf(func_def_169,type,
sK74: list_node > node ).
thf(func_def_170,type,
sK75: ( node > $o ) > list_node > node ).
thf(func_def_171,type,
sK76: ( node > $o ) > list_node > list_node ).
thf(func_def_172,type,
sK77: ( node > $o ) > list_node > list_node ).
thf(func_def_173,type,
sK78: ( list_node > list_node > $o ) > list_node ).
thf(func_def_174,type,
sK79: ( list_node > list_node > $o ) > node ).
thf(func_def_175,type,
sK80: ( list_node > list_node > $o ) > list_node ).
thf(func_def_176,type,
sK81: ( list_node > list_node > $o ) > node ).
thf(func_def_177,type,
sK82: ( list_node > list_node > $o ) > node ).
thf(func_def_178,type,
sK83: ( list_node > list_node > $o ) > list_node ).
thf(func_def_179,type,
sK84: ( list_node > list_node > $o ) > node ).
thf(func_def_180,type,
sK85: ( list_node > list_node > $o ) > list_node ).
thf(func_def_181,type,
sK86: ( list_node > list_node > $o ) > list_node ).
thf(func_def_182,type,
sK87: ( list_node > list_node > $o ) > node ).
thf(func_def_183,type,
sK88: ( list_node > $o ) > node ).
thf(func_def_184,type,
sK89: ( list_node > $o ) > node ).
thf(func_def_185,type,
sK90: ( list_node > $o ) > list_node ).
thf(func_def_186,type,
sK91: ( list_node > $o ) > node ).
thf(func_def_187,type,
sK92: list_node > node > list_node ).
thf(func_def_188,type,
sK93: list_node > node > list_node ).
thf(func_def_189,type,
sK94: ( list_node > $o ) > node ).
thf(func_def_190,type,
sK95: ( list_node > $o ) > node ).
thf(func_def_191,type,
sK96: ( list_node > $o ) > list_node ).
thf(func_def_192,type,
sK97: node > g > node > list_node ).
thf(func_def_193,type,
sK98: list_node > list_node ).
thf(func_def_194,type,
sK99: list_node > node ).
thf(func_def_195,type,
sK100: list_node > list_node ).
thf(func_def_196,type,
sK101: list_node > list_node ).
thf(func_def_197,type,
sK102: list_node > node ).
thf(func_def_198,type,
sK103: list_node > list_node ).
thf(func_def_199,type,
sK104: list_node > val > g > node ).
thf(func_def_200,type,
sK105: node > g > val > list_node ).
thf(func_def_201,type,
sK106: ( ( node > node ) > list_node > list_node > $o ) > list_node ).
thf(func_def_202,type,
sK107: ( ( node > node ) > list_node > list_node > $o ) > node > node ).
thf(func_def_203,type,
sK108: ( ( node > node ) > list_node > list_node > $o ) > node ).
thf(func_def_204,type,
sK109: ( ( node > node ) > list_node > list_node > $o ) > list_node ).
thf(func_def_205,type,
sK110: ( ( node > node ) > list_node > list_node > $o ) > node > node ).
thf(func_def_206,type,
sK111: ( ( node > node ) > list_node > list_node > $o ) > list_node ).
thf(func_def_207,type,
sK112: list_node > list_node > list_node > node > list_node ).
thf(func_def_208,type,
sK113: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(func_def_209,type,
sK114: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(func_def_210,type,
sK115: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(func_def_211,type,
sK116: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(func_def_212,type,
sK117: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(func_def_213,type,
sK118: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(func_def_214,type,
sK119: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(func_def_215,type,
sK120: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(func_def_216,type,
sK121: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(func_def_217,type,
sK122: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(func_def_218,type,
sK123: g > node > val > list_node ).
thf(func_def_219,type,
sK124: ( list_node > $o ) > list_node ).
thf(func_def_220,type,
sK125: ( list_node > $o ) > node ).
thf(func_def_221,type,
sK126: ( list_node > $o ) > node ).
thf(func_def_222,type,
sK127: ( list_node > $o ) > node ).
thf(func_def_223,type,
sK128: node > list_node > list_node ).
thf(func_def_224,type,
sK129: node > list_node > list_node ).
thf(func_def_225,type,
sK130: ( node > $o ) > list_node > node ).
thf(func_def_226,type,
sK131: ( node > $o ) > list_node > list_node ).
thf(func_def_227,type,
sK132: ( node > $o ) > list_node > list_node ).
thf(func_def_228,type,
sK133: ( list_node > $o ) > list_node ).
thf(func_def_229,type,
sK134: ( list_node > $o ) > node ).
thf(func_def_230,type,
sK135: ( node > $o ) > list_node > node ).
thf(func_def_231,type,
sK136: ( node > $o ) > list_node > list_node ).
thf(func_def_232,type,
sK137: ( node > $o ) > list_node > list_node ).
thf(func_def_233,type,
sK138: list_node > node > list_node ).
thf(func_def_234,type,
sK139: list_node > node > list_node ).
thf(func_def_235,type,
sK140: list_node > g > val > node ).
thf(func_def_236,type,
sK141: val > g > list_node > node ).
thf(func_def_237,type,
sK142: list_node > list_node ).
thf(func_def_238,type,
sK143: list_node > node ).
thf(func_def_239,type,
sK144: list_node > list_node ).
thf(func_def_240,type,
sK145: ( list_node > list_node > $o ) > ( node > node > $o ) > node ).
thf(func_def_241,type,
sK146: ( list_node > list_node > $o ) > ( node > node > $o ) > list_node ).
thf(func_def_242,type,
sK147: ( list_node > list_node > $o ) > ( node > node > $o ) > list_node ).
thf(func_def_243,type,
sK148: ( list_node > list_node > $o ) > ( node > node > $o ) > node ).
thf(func_def_244,type,
sK149: ( list_node > list_node > $o ) > list_node ).
thf(func_def_245,type,
sK150: ( list_node > list_node > $o ) > list_node ).
thf(func_def_246,type,
sK151: ( list_node > list_node > $o ) > ( node > node > $o ) > list_node ).
thf(func_def_247,type,
sK152: ( list_node > list_node > $o ) > ( node > node > $o ) > node ).
thf(func_def_248,type,
sK153: ( list_node > list_node > $o ) > ( node > node > $o ) > list_node ).
thf(func_def_249,type,
sK154: ( list_node > list_node > $o ) > ( node > node > $o ) > node ).
thf(func_def_250,type,
sK155: ( list_node > $o ) > node ).
thf(func_def_251,type,
sK156: ( list_node > $o ) > list_node ).
thf(func_def_252,type,
sK157: ( list_node > $o ) > node ).
thf(func_def_253,type,
sK158: ( list_node > $o ) > list_node ).
thf(func_def_254,type,
sK159: ( list_node > $o ) > node ).
thf(func_def_255,type,
sK160: list_node > ( node > $o ) > node > g > list_node ).
thf(func_def_256,type,
sK161: list_node > ( node > $o ) > node > g > node ).
thf(func_def_257,type,
sK162: ( node > $o ) > list_node > list_node ).
thf(func_def_258,type,
sK163: ( node > $o ) > list_node > node ).
thf(func_def_259,type,
sK164: ( node > $o ) > list_node > list_node ).
thf(func_def_260,type,
sK165: list_node > ( node > $o ) > list_node ).
thf(func_def_261,type,
sK166: list_node > ( node > $o ) > list_node ).
thf(func_def_262,type,
sK167: list_node > ( node > $o ) > node ).
thf(func_def_263,type,
sK168: ( list_node > list_node > $o ) > list_node ).
thf(func_def_264,type,
sK169: ( list_node > list_node > $o ) > node ).
thf(func_def_265,type,
sK170: ( list_node > list_node > $o ) > node ).
thf(func_def_266,type,
sK171: ( list_node > list_node > $o ) > list_node ).
thf(func_def_267,type,
sK172: ( list_node > list_node > $o ) > list_node ).
thf(func_def_268,type,
sK173: ( list_node > list_node > $o ) > node ).
thf(func_def_269,type,
sK174: ( list_node > list_node > $o ) > list_node ).
thf(func_def_270,type,
sK175: ( list_node > list_node > $o ) > node ).
thf(func_def_271,type,
sK176: ( node > $o ) > list_node > list_node ).
thf(func_def_272,type,
sK177: ( node > $o ) > list_node > node ).
thf(func_def_273,type,
sK178: ( node > $o ) > list_node > list_node ).
thf(func_def_274,type,
sK179: node > g > list_node ).
thf(func_def_275,type,
sK180: node > list_node > node ).
thf(func_def_276,type,
sK181: ( list_node > list_node > $o ) > node ).
thf(func_def_277,type,
sK182: ( list_node > list_node > $o ) > list_node ).
thf(func_def_278,type,
sK183: ( list_node > list_node > $o ) > list_node ).
thf(func_def_279,type,
sK184: ( list_node > list_node > $o ) > list_node ).
thf(func_def_280,type,
sK185: ( list_node > list_node > $o ) > list_node ).
thf(func_def_281,type,
sK186: ( list_node > list_node > $o ) > node ).
thf(func_def_282,type,
sK187: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(func_def_283,type,
sK188: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(func_def_284,type,
sK189: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(func_def_285,type,
sK190: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(func_def_286,type,
sK191: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(func_def_287,type,
sK192: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(func_def_288,type,
sK193: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(func_def_289,type,
sK194: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(func_def_290,type,
sK195: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(func_def_291,type,
sK196: ( ( node > node > $o ) > list_node > list_node > $o ) > node ).
thf(func_def_292,type,
sK197: ( ( node > node > $o ) > list_node > list_node > $o ) > list_node ).
thf(func_def_293,type,
sK198: ( ( node > node > $o ) > list_node > list_node > $o ) > node > node > $o ).
thf(func_def_294,type,
sK199: ( list_node > $o ) > node ).
thf(func_def_295,type,
sK200: ( list_node > $o ) > node ).
thf(func_def_296,type,
sK201: ( list_node > $o ) > list_node ).
thf(func_def_297,type,
sK202: ( list_node > $o ) > node ).
thf(func_def_298,type,
sK203: node > g > node > list_node ).
thf(func_def_299,type,
sK204: ( list_node > list_node > $o ) > list_node ).
thf(func_def_300,type,
sK205: ( list_node > list_node > $o ) > list_node ).
thf(func_def_301,type,
sK206: ( list_node > list_node > $o ) > node ).
thf(func_def_302,type,
sK207: ( list_node > list_node > $o ) > node ).
thf(func_def_303,type,
sK208: ( list_node > list_node > $o ) > list_node ).
thf(func_def_304,type,
sK209: ( list_node > list_node > $o ) > list_node ).
thf(func_def_305,type,
sK210: list_node ).
thf(func_def_306,type,
sK211: node ).
thf(func_def_307,type,
sK212: list_node > list_node > list_node ).
thf(func_def_308,type,
sK213: list_node > list_node > node ).
thf(func_def_309,type,
sK214: list_node > list_node > list_node ).
thf(func_def_310,type,
sK215: list_node > list_node > node ).
thf(func_def_311,type,
sK216: list_node > list_node > node ).
thf(func_def_312,type,
sK217: list_node > list_node > node ).
thf(func_def_313,type,
sK218: list_node > list_node > list_node ).
thf(func_def_314,type,
sK219: list_node > list_node > list_node ).
thf(func_def_315,type,
sK220: ( list_node > list_node > $o ) > node ).
thf(func_def_316,type,
sK221: ( list_node > list_node > $o ) > list_node ).
thf(func_def_317,type,
sK222: ( list_node > list_node > $o ) > node ).
thf(func_def_318,type,
sK223: ( list_node > list_node > $o ) > list_node ).
thf(func_def_319,type,
sK224: ( list_node > list_node > $o ) > list_node ).
thf(func_def_320,type,
sK225: ( list_node > list_node > $o ) > node ).
thf(func_def_321,type,
sK226: ( list_node > list_node > $o ) > list_node ).
thf(func_def_322,type,
sK227: ( list_node > list_node > $o ) > node ).
thf(func_def_323,type,
sK228: list_node > node > list_node ).
thf(func_def_324,type,
sK229: list_node > node > list_node ).
thf(func_def_325,type,
sK230: node > list_node > node > list_node ).
thf(func_def_326,type,
sK231: node > list_node > node > list_node ).
thf(func_def_327,type,
sK232: node > list_node > node > list_node ).
thf(func_def_328,type,
sK233: node > list_node > node > list_node ).
thf(func_def_329,type,
sK234: node > list_node > node > list_node ).
thf(func_def_330,type,
sK235: node > list_node > node > list_node ).
thf(func_def_331,type,
sK236: node > g > list_node ).
thf(func_def_333,type,
sK238: list_node > ( node > $o ) > list_node ).
thf(func_def_334,type,
sK239: list_node > ( node > $o ) > node ).
thf(func_def_335,type,
sK240: list_node > ( node > $o ) > list_node ).
thf(func_def_336,type,
sK241: list_node > ( node > $o ) > node ).
thf(func_def_337,type,
sK242: ( node > $o ) > list_node > node ).
thf(func_def_338,type,
sK243: ( node > $o ) > list_node > node ).
thf(func_def_339,type,
sK244: list_node > node > list_node ).
thf(func_def_340,type,
sK245: list_node > node > list_node ).
thf(func_def_341,type,
sK246: list_P738500740D_node > produc1453890942D_node ).
thf(func_def_342,type,
sK247: g > list_node > node ).
thf(func_def_343,type,
sK248: g > node ).
thf(func_def_344,type,
sK249: g > list_node ).
thf(func_def_345,type,
sK250: node > g > node ).
thf(func_def_346,type,
sK251: node > list_node > list_node ).
thf(func_def_347,type,
sK252: node > list_node > list_node ).
thf(func_def_348,type,
sK253: list_P738500740D_node > produc1453890942D_node ).
thf(func_def_349,type,
sK254: list_P738500740D_node > list_P738500740D_node ).
thf(func_def_350,type,
sK255: val > list_val > list_val ).
thf(func_def_351,type,
sK256: val > list_val > list_val ).
thf(func_def_352,type,
sK257: list_P738500740D_node > produc1453890942D_node ).
thf(func_def_353,type,
sK258: node > list_node > list_node > list_node > list_node ).
thf(func_def_354,type,
sK259: node > list_node > list_node > list_node > list_node ).
thf(func_def_355,type,
sK260: list_node > list_node > list_node > list_node > list_node ).
thf(func_def_356,type,
sK261: val > list_val > list_val ).
thf(func_def_357,type,
sK262: val > list_val > list_val ).
thf(func_def_358,type,
sK263: g > node > node > node ).
thf(func_def_359,type,
sK264: list_node > node ).
thf(func_def_360,type,
sK265: list_node > list_node ).
thf(func_def_361,type,
sK266: list_node > list_node ).
thf(func_def_362,type,
sK267: val > list_val > list_val ).
thf(func_def_363,type,
sK268: val > list_val > list_val ).
thf(func_def_364,type,
sK269: produc1453890942D_node > list_P738500740D_node > list_P738500740D_node > list_P738500740D_node > list_P738500740D_node ).
thf(func_def_365,type,
sK270: list_node > node > list_node > list_node > list_node ).
thf(func_def_366,type,
sK271: list_node > node > list_node ).
thf(func_def_367,type,
sK272: list_node > node > list_node ).
thf(func_def_368,type,
sK273: val > list_node > g > node ).
thf(func_def_369,type,
sK274: node > g > val > list_node ).
thf(func_def_370,type,
sK275: node > node > g > list_node ).
thf(func_def_371,type,
sK276: list_P738500740D_node > produc1453890942D_node > list_P738500740D_node > list_P738500740D_node > list_P738500740D_node ).
thf(func_def_372,type,
sK277: list_node > list_node > node > list_node ).
thf(func_def_373,type,
sK278: list_P738500740D_node > produc1453890942D_node ).
thf(func_def_374,type,
sK279: list_P738500740D_node > list_P738500740D_node ).
thf(func_def_375,type,
sK280: g > node > val > node ).
thf(func_def_376,type,
sK281: list_val > list_val ).
thf(func_def_377,type,
sK282: list_val > val ).
thf(func_def_378,type,
sK283: list_val > list_val ).
thf(func_def_379,type,
sK284: list_node > list_node ).
thf(func_def_380,type,
sK285: list_node > node ).
thf(func_def_381,type,
sK286: list_node > node ).
thf(func_def_382,type,
sK287: list_node > node ).
thf(func_def_383,type,
sK288: ( node > $o ) > list_node > list_node ).
thf(func_def_384,type,
sK289: ( node > $o ) > list_node > node ).
thf(func_def_385,type,
sK290: ( node > $o ) > list_node > list_node ).
thf(func_def_386,type,
sK291: ( node > $o ) > list_node > node ).
thf(func_def_387,type,
sK292: ( node > $o ) > list_node > node ).
thf(func_def_388,type,
sK293: ( node > $o ) > list_node > node ).
thf(func_def_389,type,
sK294: list_P738500740D_node > produc1453890942D_node > list_P738500740D_node > list_P738500740D_node ).
thf(func_def_390,type,
sK295: list_node > node ).
thf(func_def_391,type,
sK296: list_node > list_node ).
thf(func_def_392,type,
sK297: val > list_node > g > node ).
thf(func_def_393,type,
sK298: val > node > g > list_node ).
thf(func_def_394,type,
ph299:
!>[X0: $tType] : X0 ).
thf(f7344,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f7332,f6897]) ).
thf(f6897,plain,
( $true
= ( distinct_node @ rs ) ),
inference(trivial_inequality_removal,[status(thm)],[f6895]) ).
thf(f6895,plain,
( ( $true != $true )
| ( $true
= ( distinct_node @ rs ) ) ),
inference(superposition,[status(thm)],[f1729,f1645]) ).
thf(f1645,plain,
( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs )
= $true ),
inference(cnf_transformation,[status(thm)],[f894]) ).
thf(f894,plain,
( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs )
= $true ),
inference(fool_elimination,[status(thm)],[f893]) ).
thf(f893,plain,
graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs,
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs,
file('/export/starexec/sandbox/tmp/tmp.zlt6T4WObL/DTF2THF_2101.p',fact_3_rs_H__props_I2_J) ).
thf(f1729,plain,
! [X0: g,X1: list_node] :
( ( $true
!= ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ X0 @ X1 ) )
| ( ( distinct_node @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f1089]) ).
thf(f1089,plain,
! [X0: g,X1: list_node] :
( ( $true
!= ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ X0 @ X1 ) )
| ( ( distinct_node @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f360]) ).
thf(f360,plain,
! [X0: g,X1: list_node] :
( ( $true
= ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ X0 @ X1 ) )
=> ( ( distinct_node @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f359]) ).
thf(f359,plain,
! [X0: g,X1: list_node] :
( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ X0 @ X1 )
=> ( distinct_node @ X1 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X0: g,X2: list_node] :
( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ X0 @ X2 )
=> ( distinct_node @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.zlt6T4WObL/DTF2THF_2101.p',fact_5_old_OEntryPath__distinct) ).
thf(f7332,plain,
( $true
!= ( distinct_node @ rs ) ),
inference(trivial_inequality_removal,[status(thm)],[f7302]) ).
thf(f7302,plain,
( ( $true
!= ( distinct_node @ rs ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1667,f7286]) ).
thf(f7286,plain,
( ( member_node @ ( hd_node @ rs ) @ ( set_node2 @ ( tl_node @ rs ) ) )
= $true ),
inference(backward_demodulation,[status(thm)],[f1575,f7282]) ).
thf(f7282,plain,
( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r )
= ( hd_node @ rs ) ),
inference(trivial_inequality_removal,[status(thm)],[f7279]) ).
thf(f7279,plain,
( ( $true != $true )
| ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r )
= ( hd_node @ rs ) ) ),
inference(superposition,[status(thm)],[f1587,f1766]) ).
thf(f1766,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r )
= $true ),
inference(cnf_transformation,[status(thm)],[f604]) ).
thf(f604,plain,
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r )
= $true ),
inference(fool_elimination,[status(thm)],[f603]) ).
thf(f603,plain,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r,
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r,
file('/export/starexec/sandbox/tmp/tmp.zlt6T4WObL/DTF2THF_2101.p',fact_4_rs_H__props_I1_J) ).
thf(f1587,plain,
! [X2: node,X3: g,X0: node,X1: list_node] :
( ( $true
!= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X3 @ X0 @ X1 @ X2 ) )
| ( ( hd_node @ X1 )
= X0 ) ),
inference(cnf_transformation,[status(thm)],[f1233]) ).
thf(f1233,plain,
! [X0: node,X1: list_node,X2: node,X3: g] :
( ( $true
!= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X3 @ X0 @ X1 @ X2 ) )
| ( ( hd_node @ X1 )
= X0 ) ),
inference(ennf_transformation,[status(thm)],[f586]) ).
thf(f586,plain,
! [X0: node,X1: list_node,X2: node,X3: g] :
( ( $true
= ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X3 @ X0 @ X1 @ X2 ) )
=> ( ( hd_node @ X1 )
= X0 ) ),
inference(fool_elimination,[status(thm)],[f585]) ).
thf(f585,plain,
! [X0: node,X1: list_node,X2: node,X3: g] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X3 @ X0 @ X1 @ X2 )
=> ( ( hd_node @ X1 )
= X0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X1: node,X2: list_node,X3: node,X0: g] :
( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ X2 @ X3 )
=> ( ( hd_node @ X2 )
= X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.zlt6T4WObL/DTF2THF_2101.p',fact_0_old_Opath2__hd) ).
thf(f1575,plain,
( ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f937]) ).
thf(f937,plain,
( ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) )
= $true ),
inference(flattening,[status(thm)],[f644]) ).
thf(f644,plain,
~ ( ( ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f643]) ).
thf(f643,plain,
~ ~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ),
inference(rectify,[status(thm)],[f353]) ).
thf(f353,negated_conjecture,
~ ~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ),
inference(negated_conjecture,[status(cth)],[f352]) ).
thf(f352,conjecture,
~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zlt6T4WObL/DTF2THF_2101.p',conj_0) ).
thf(f1667,plain,
! [X0: list_node] :
( ( $true
!= ( member_node @ ( hd_node @ X0 ) @ ( set_node2 @ ( tl_node @ X0 ) ) ) )
| ( ( distinct_node @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1209]) ).
thf(f1209,plain,
! [X0: list_node] :
( ( $true
!= ( member_node @ ( hd_node @ X0 ) @ ( set_node2 @ ( tl_node @ X0 ) ) ) )
| ( ( distinct_node @ X0 )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f955]) ).
thf(f955,plain,
! [X0: list_node] :
( ( ( distinct_node @ X0 )
= $true )
=> ( $true
!= ( member_node @ ( hd_node @ X0 ) @ ( set_node2 @ ( tl_node @ X0 ) ) ) ) ),
inference(flattening,[status(thm)],[f756]) ).
thf(f756,plain,
! [X0: list_node] :
( ( ( distinct_node @ X0 )
= $true )
=> ( $true
!= ( member_node @ ( hd_node @ X0 ) @ ( set_node2 @ ( tl_node @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f755]) ).
thf(f755,plain,
! [X0: list_node] :
( ( distinct_node @ X0 )
=> ~ ( member_node @ ( hd_node @ X0 ) @ ( set_node2 @ ( tl_node @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f31]) ).
thf(f31,axiom,
! [X6: list_node] :
( ( distinct_node @ X6 )
=> ~ ( member_node @ ( hd_node @ X6 ) @ ( set_node2 @ ( tl_node @ X6 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zlt6T4WObL/DTF2THF_2101.p',fact_30_FormalSSA__Misc_Odistinct__hd__tl) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP080^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:25:42 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 : ITP080^1 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.46 % Domain : Interactive Theorem Proving
% 0.19/0.46 % Problem : Sledgehammer Irreducible problem prob_414__6626236_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 : Irreducible/prob_414__6626236_1 [Des21]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0
% 0.19/0.46 % Syntax : Number of formulae : 432 ( 123 unt; 80 typ; 0 def)
% 0.19/0.46 % Number of atoms : 1081 ( 546 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 10 ( 3 avg)
% 0.19/0.46 % Number of connectives : 4835 ( 250 ~; 18 |; 109 &;3799 @)
% 0.19/0.46 % ( 0 <=>; 659 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 22 ( 9 avg)
% 0.19/0.46 % Number of types : 16 ( 15 usr)
% 0.19/0.46 % Number of type conns : 441 ( 441 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 66 ( 65 usr; 16 con; 0-9 aty)
% 0.19/0.46 % Number of variables : 1493 ( 16 ^;1379 !; 98 ?;1493 :)
% 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 15:39:25.169
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % Could-be-implicit typings (15)
% 0.19/0.46 thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J_J_J,type,
% 0.19/0.46 list_l1129649930D_node: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J_J,type,
% 0.19/0.46 list_P738500740D_node: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J_J,type,
% 0.19/0.46 set_Pr1040144478D_node: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 0.19/0.46 produc1453890942D_node: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mtf__edgeD_J_J,type,
% 0.19/0.46 list_P561207620_edgeD: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Option__Ooption_It__List__Olist_Itf__val_J_J,type,
% 0.19/0.46 option_list_val: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Product____Type__Oprod_Itf__node_Mtf__val_J,type,
% 0.19/0.46 produc1432036078de_val: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_It__List__Olist_Itf__node_J_J,type,
% 0.19/0.46 list_list_node: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_Itf__node_J,type,
% 0.19/0.46 list_node: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__List__Olist_Itf__val_J,type,
% 0.19/0.46 list_val: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Set__Oset_Itf__node_J,type,
% 0.19/0.46 set_node: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_t__Set__Oset_Itf__val_J,type,
% 0.19/0.46 set_val: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_tf__node,type,
% 0.19/0.46 node: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_tf__val,type,
% 0.19/0.46 val: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(ty_n_tf__g,type,
% 0.19/0.46 g: $tType ).
% 0.19/0.46
% 0.19/0.46 % Explicit typings (65)
% 0.19/0.46 thf(sy_c_Finite__Set_Ofinite_001tf__node,type,
% 0.19/0.46 finite_finite_node: set_node > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Finite__Set_Ofinite_001tf__val,type,
% 0.19/0.46 finite_finite_val: set_val > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Graph__path_Ograph__Entry_OEntryPath_001tf__g_001tf__node_001tf__edgeD,type,
% 0.19/0.46 graph_1994935542_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > list_node > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Graph__path_Ograph__Entry_OisIdom_001tf__g_001tf__node_001tf__edgeD,type,
% 0.19/0.46 graph_1670286392_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > node > node > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Graph__path_Ograph__Entry__base_Odominates_001tf__g_001tf__node_001tf__edgeD,type,
% 0.19/0.46 graph_436675702_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > node > node > $o ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Graph__path_Ograph__path__base_OinEdges_001tf__g_001tf__node_001tf__edgeD,type,
% 0.19/0.46 graph_1947481694_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_P738500740D_node ).
% 0.19/0.46
% 0.19/0.46 thf(sy_c_Graph__path_Ograph__path__base_Opath2_001tf__g_001tf__node_001tf__edgeD,type,
% 0.19/0.47 graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors_001tf__g_001tf__node_001tf__edgeD,type,
% 0.19/0.47 graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Oappend_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 0.19/0.47 append2096883353D_node: list_P738500740D_node > list_P738500740D_node > list_P738500740D_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Oappend_001tf__node,type,
% 0.19/0.47 append_node: list_node > list_node > list_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Oappend_001tf__val,type,
% 0.19/0.47 append_val: list_val > list_val > list_val ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Odistinct_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 0.19/0.47 distin1098566007D_node: list_P738500740D_node > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Odistinct_001tf__node,type,
% 0.19/0.47 distinct_node: list_node > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Odistinct_001tf__val,type,
% 0.19/0.47 distinct_val: list_val > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J_J,type,
% 0.19/0.47 cons_l1288865338D_node: list_P738500740D_node > list_l1129649930D_node > list_l1129649930D_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_OCons_001t__List__Olist_Itf__node_J,type,
% 0.19/0.47 cons_list_node: list_node > list_list_node > list_list_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 0.19/0.47 cons_P1018517044D_node: produc1453890942D_node > list_P738500740D_node > list_P738500740D_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_OCons_001tf__node,type,
% 0.19/0.47 cons_node: node > list_node > list_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_OCons_001tf__val,type,
% 0.19/0.47 cons_val: val > list_val > list_val ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J_J,type,
% 0.19/0.47 nil_li1626782346D_node: list_l1129649930D_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_ONil_001t__List__Olist_Itf__node_J,type,
% 0.19/0.47 nil_list_node: list_list_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 0.19/0.47 nil_Pr1769730692D_node: list_P738500740D_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_ONil_001tf__node,type,
% 0.19/0.47 nil_node: list_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_ONil_001tf__val,type,
% 0.19/0.47 nil_val: list_val ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_Ohd_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 0.19/0.47 hd_Pro1395892457D_node: list_P738500740D_node > produc1453890942D_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_Ohd_001tf__node,type,
% 0.19/0.47 hd_node: list_node > node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_Ohd_001tf__val,type,
% 0.19/0.47 hd_val: list_val > val ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 0.19/0.47 set_Pr1238794387D_node: list_P738500740D_node > set_Pr1040144478D_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_Oset_001tf__node,type,
% 0.19/0.47 set_node2: list_node > set_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_Oset_001tf__val,type,
% 0.19/0.47 set_val2: list_val > set_val ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_Otl_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 0.19/0.47 tl_Pro1633633005D_node: list_P738500740D_node > list_P738500740D_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_Otl_001tf__node,type,
% 0.19/0.47 tl_node: list_node > list_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_List_Olist_Otl_001tf__val,type,
% 0.19/0.47 tl_val: list_val > list_val ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Minimality_Ograph__Entry_Oreducible_001tf__g_001tf__node_001tf__edgeD,type,
% 0.19/0.47 graph_589078910_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallDefs_001tf__g_001tf__node_001tf__val,type,
% 0.19/0.47 sSA_CF139593942de_val: ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__base_OdefAss_001tf__g_001tf__node_001tf__edgeD_001tf__val,type,
% 0.19/0.47 sSA_CF1156973626eD_val: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > node > val > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiDefs_001tf__g_001tf__node_001tf__val,type,
% 0.19/0.47 sSA_CF370335846de_val: ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses_001tf__g_001tf__node_001tf__edgeD_001tf__val,type,
% 0.19/0.47 sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode_001tf__g_001tf__node_001tf__val,type,
% 0.19/0.47 sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg_001tf__g_001tf__node_001tf__val,type,
% 0.19/0.47 sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_SSA__CFG_OCFG__base_OdefAss_H_001tf__g_001tf__node_001tf__edgeD_001tf__val,type,
% 0.19/0.47 sSA_CF1558836456eD_val: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > ( g > node > set_val ) > g > node > val > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Set_OCollect_001tf__node,type,
% 0.19/0.47 collect_node: ( node > $o ) > set_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Set_OCollect_001tf__val,type,
% 0.19/0.47 collect_val: ( val > $o ) > set_val ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Sublist_Osuffix_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 0.19/0.47 suffix1143830554D_node: list_P738500740D_node > list_P738500740D_node > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_Sublist_Osuffix_001tf__node,type,
% 0.19/0.47 suffix_node: list_node > list_node > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_member_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 0.19/0.47 member1797643303D_node: produc1453890942D_node > set_Pr1040144478D_node > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_member_001tf__node,type,
% 0.19/0.47 member_node: node > set_node > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_c_member_001tf__val,type,
% 0.19/0.47 member_val: val > set_val > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_Entry,type,
% 0.19/0.47 entry: g > node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v__092_060alpha_062n,type,
% 0.19/0.47 alpha_n: g > list_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v__092_060phi_062_092_060_094sub_062r,type,
% 0.19/0.47 phi_r: val ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_defs,type,
% 0.19/0.47 defs: g > node > set_val ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_g,type,
% 0.19/0.47 g2: g ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_inEdges_H,type,
% 0.19/0.47 inEdges: g > node > list_P561207620_edgeD ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_invar,type,
% 0.19/0.47 invar: g > $o ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_m,type,
% 0.19/0.47 m: node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_ms,type,
% 0.19/0.47 ms: list_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_n,type,
% 0.19/0.47 n: node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_ns,type,
% 0.19/0.47 ns: list_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_phis,type,
% 0.19/0.47 phis: g > produc1432036078de_val > option_list_val ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r____,type,
% 0.19/0.47 pred_phi_r: node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_r,type,
% 0.19/0.47 r: val ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_rs_H____,type,
% 0.19/0.47 rs: list_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_rs____,type,
% 0.19/0.47 rs2: list_node ).
% 0.19/0.47
% 0.19/0.47 thf(sy_v_s,type,
% 0.19/0.47 s: val ).
% 0.19/0.47
% 0.19/0.47 % Relevant facts (351)
% 0.19/0.47 thf(fact_0_old_Opath2__hd,axiom,
% 0.19/0.47 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( N
% 0.19/0.47 = ( hd_node @ Ns ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.path2_hd
% 0.19/0.47 thf(fact_1_False,axiom,
% 0.19/0.47 r != phi_r ).
% 0.19/0.47
% 0.19/0.47 % False
% 0.19/0.47 thf(fact_2_old_OEntry__in__graph,axiom,
% 0.19/0.47 ! [G: g] : ( member_node @ ( entry @ G ) @ ( set_node2 @ ( alpha_n @ G ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.Entry_in_graph
% 0.19/0.47 thf(fact_3_rs_H__props_I2_J,axiom,
% 0.19/0.47 graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs ).
% 0.19/0.47
% 0.19/0.47 % rs'_props(2)
% 0.19/0.47 thf(fact_4_rs_H__props_I1_J,axiom,
% 0.19/0.47 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r ).
% 0.19/0.47
% 0.19/0.47 % rs'_props(1)
% 0.19/0.47 thf(fact_5_old_OEntryPath__distinct,axiom,
% 0.19/0.47 ! [G: g,Ns: list_node] :
% 0.19/0.47 ( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ Ns )
% 0.19/0.47 => ( distinct_node @ Ns ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.EntryPath_distinct
% 0.19/0.47 thf(fact_6_old_O_092_060alpha_062n__distinct,axiom,
% 0.19/0.47 ! [G: g] :
% 0.19/0.47 ( ( invar @ G )
% 0.19/0.47 => ( distinct_node @ ( alpha_n @ G ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.\<alpha>n_distinct
% 0.19/0.47 thf(fact_7_rs_H__props_I3_J,axiom,
% 0.19/0.47 member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ) ).
% 0.19/0.47
% 0.19/0.47 % rs'_props(3)
% 0.19/0.47 thf(fact_8_assms_I10_J,axiom,
% 0.19/0.47 sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r ).
% 0.19/0.47
% 0.19/0.47 % assms(10)
% 0.19/0.47 thf(fact_9_allDefs__disjoint_H,axiom,
% 0.19/0.47 ! [N: node,G: g,M: node,V: val] :
% 0.19/0.47 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 0.19/0.47 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ M ) )
% 0.19/0.47 => ( N = M ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % allDefs_disjoint'
% 0.19/0.47 thf(fact_10_assms_I7_J,axiom,
% 0.19/0.47 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) ).
% 0.19/0.47
% 0.19/0.47 % assms(7)
% 0.19/0.47 thf(fact_11_defNode__eq,axiom,
% 0.19/0.47 ! [N: node,G: g,V: val] :
% 0.19/0.47 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 0.19/0.47 => ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V )
% 0.19/0.47 = N ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % defNode_eq
% 0.19/0.47 thf(fact_12_rs_H__props_I4_J,axiom,
% 0.19/0.47 member_node @ pred_phi_r @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % rs'_props(4)
% 0.19/0.47 thf(fact_13_defs__in__allDefs,axiom,
% 0.19/0.47 ! [V: val,G: g,N: node] :
% 0.19/0.47 ( ( member_val @ V @ ( defs @ G @ N ) )
% 0.19/0.47 => ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % defs_in_allDefs
% 0.19/0.47 thf(fact_14_FormalSSA__Misc_Oin__set__tlD,axiom,
% 0.19/0.47 ! [X: val,Xs: list_val] :
% 0.19/0.47 ( ( member_val @ X @ ( set_val2 @ ( tl_val @ Xs ) ) )
% 0.19/0.47 => ( member_val @ X @ ( set_val2 @ Xs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % FormalSSA_Misc.in_set_tlD
% 0.19/0.47 thf(fact_15_FormalSSA__Misc_Oin__set__tlD,axiom,
% 0.19/0.47 ! [X: node,Xs: list_node] :
% 0.19/0.47 ( ( member_node @ X @ ( set_node2 @ ( tl_node @ Xs ) ) )
% 0.19/0.47 => ( member_node @ X @ ( set_node2 @ Xs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % FormalSSA_Misc.in_set_tlD
% 0.19/0.47 thf(fact_16_old_Opath2__hd__in___092_060alpha_062n,axiom,
% 0.19/0.47 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.path2_hd_in_\<alpha>n
% 0.19/0.47 thf(fact_17_old_Opath2__hd__in__ns,axiom,
% 0.19/0.47 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( member_node @ N @ ( set_node2 @ Ns ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.path2_hd_in_ns
% 0.19/0.47 thf(fact_18_old_Opath2__in___092_060alpha_062n,axiom,
% 0.19/0.47 ! [G: g,N: node,Ns: list_node,M: node,L: node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( ( member_node @ L @ ( set_node2 @ Ns ) )
% 0.19/0.47 => ( member_node @ L @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.path2_in_\<alpha>n
% 0.19/0.47 thf(fact_19_old_Oinvar,axiom,
% 0.19/0.47 ! [G: g] : ( invar @ G ) ).
% 0.19/0.47
% 0.19/0.47 % old.invar
% 0.19/0.47 thf(fact_20_old_Opath2__tl__in___092_060alpha_062n,axiom,
% 0.19/0.47 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.path2_tl_in_\<alpha>n
% 0.19/0.47 thf(fact_21_old_Opath2__last__in__ns,axiom,
% 0.19/0.47 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( member_node @ M @ ( set_node2 @ Ns ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.path2_last_in_ns
% 0.19/0.47 thf(fact_22_old_Osuccessor__is__node,axiom,
% 0.19/0.47 ! [N: node,G: g,N2: node] :
% 0.19/0.47 ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N2 ) ) )
% 0.19/0.47 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( ( invar @ G )
% 0.19/0.47 => ( member_node @ N2 @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.successor_is_node
% 0.19/0.47 thf(fact_23_old_Opredecessor__is__node,axiom,
% 0.19/0.47 ! [N: node,G: g,N2: node] :
% 0.19/0.47 ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N2 ) ) )
% 0.19/0.47 => ( ( invar @ G )
% 0.19/0.47 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.predecessor_is_node
% 0.19/0.47 thf(fact_24_old_Opath2__forget__hd,axiom,
% 0.19/0.47 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( hd_node @ Ns ) @ Ns @ M ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.path2_forget_hd
% 0.19/0.47 thf(fact_25_old_OEntry__reachesE,axiom,
% 0.19/0.47 ! [N: node,G: g] :
% 0.19/0.47 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( ( invar @ G )
% 0.19/0.47 => ~ ! [Ns2: list_node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns2 @ N )
% 0.19/0.47 => ~ ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ Ns2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.Entry_reachesE
% 0.19/0.47 thf(fact_26__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nrs_H_092_060rightarrow_062pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Aold_OEntryPath_Ag_Ars_H_059_Ar_A_092_060in_062_AphiUses_Ag_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_A_092_060in_062_Aset_A_Iold_Opredecessors_Ag_A_IdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_J_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.19/0.47 ~ ! [Rs: list_node,Pred_phi_r: node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ Rs @ Pred_phi_r )
% 0.19/0.47 => ( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ Rs )
% 0.19/0.47 => ( ( member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ Pred_phi_r ) )
% 0.19/0.47 => ~ ( member_node @ Pred_phi_r @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % \<open>\<And>thesis. (\<And>rs' pred\<^sub>\<phi>\<^sub>r. \<lbrakk>g \<turnstile> defNode g r-rs'\<rightarrow>pred\<^sub>\<phi>\<^sub>r; old.EntryPath g rs'; r \<in> phiUses g pred\<^sub>\<phi>\<^sub>r; pred\<^sub>\<phi>\<^sub>r \<in> set (old.predecessors g (defNode g \<phi>\<^sub>r))\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.19/0.47 thf(fact_27_old_OEntry__reaches,axiom,
% 0.19/0.47 ! [N: node,G: g] :
% 0.19/0.47 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( ( invar @ G )
% 0.19/0.47 => ? [Ns2: list_node] : ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns2 @ N ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.Entry_reaches
% 0.19/0.47 thf(fact_28_old_Oidom__ex,axiom,
% 0.19/0.47 ! [G: g,N: node] :
% 0.19/0.47 ( ( invar @ G )
% 0.19/0.47 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( ( N
% 0.19/0.47 != ( entry @ G ) )
% 0.19/0.47 => ? [X2: node] :
% 0.19/0.47 ( ( graph_1670286392_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ X2 )
% 0.19/0.47 & ! [Y: node] :
% 0.19/0.47 ( ( graph_1670286392_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ Y )
% 0.19/0.47 => ( Y = X2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.idom_ex
% 0.19/0.47 thf(fact_29_FormalSSA__Misc_Odistinct__hd__tl,axiom,
% 0.19/0.47 ! [Xs: list_val] :
% 0.19/0.47 ( ( distinct_val @ Xs )
% 0.19/0.47 => ~ ( member_val @ ( hd_val @ Xs ) @ ( set_val2 @ ( tl_val @ Xs ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % FormalSSA_Misc.distinct_hd_tl
% 0.19/0.47 thf(fact_30_FormalSSA__Misc_Odistinct__hd__tl,axiom,
% 0.19/0.47 ! [Xs: list_node] :
% 0.19/0.47 ( ( distinct_node @ Xs )
% 0.19/0.47 => ~ ( member_node @ ( hd_node @ Xs ) @ ( set_node2 @ ( tl_node @ Xs ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % FormalSSA_Misc.distinct_hd_tl
% 0.19/0.47 thf(fact_31_defAss_H__extend,axiom,
% 0.19/0.47 ! [G: g,M: node,V: val,N: node,Ns: list_node] :
% 0.19/0.47 ( ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ G @ M @ V )
% 0.19/0.47 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( ! [X2: node] :
% 0.19/0.47 ( ( member_node @ X2 @ ( set_node2 @ ( tl_node @ Ns ) ) )
% 0.19/0.47 => ~ ( member_val @ V @ ( defs @ G @ X2 ) ) )
% 0.19/0.47 => ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ G @ N @ V ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % defAss'_extend
% 0.19/0.47 thf(fact_32_defAss_H__def,axiom,
% 0.19/0.47 ! [G: g,M: node,V: val] :
% 0.19/0.47 ( ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ G @ M @ V )
% 0.19/0.47 = ( ! [Ns3: list_node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns3 @ M )
% 0.19/0.47 => ? [X3: node] :
% 0.19/0.47 ( ( member_node @ X3 @ ( set_node2 @ Ns3 ) )
% 0.19/0.47 & ( member_val @ V @ ( defs @ G @ X3 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % defAss'_def
% 0.19/0.47 thf(fact_33_defAss_HI,axiom,
% 0.19/0.47 ! [G: g,M: node,V: val] :
% 0.19/0.47 ( ! [Ns2: list_node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns2 @ M )
% 0.19/0.47 => ? [X4: node] :
% 0.19/0.47 ( ( member_node @ X4 @ ( set_node2 @ Ns2 ) )
% 0.19/0.47 & ( member_val @ V @ ( defs @ G @ X4 ) ) ) )
% 0.19/0.47 => ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ G @ M @ V ) ) ).
% 0.19/0.47
% 0.19/0.47 % defAss'I
% 0.19/0.47 thf(fact_34_defAss_HE,axiom,
% 0.19/0.47 ! [G: g,M: node,V: val,Ns: list_node] :
% 0.19/0.47 ( ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ G @ M @ V )
% 0.19/0.47 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns @ M )
% 0.19/0.47 => ~ ! [N3: node] :
% 0.19/0.47 ( ( member_node @ N3 @ ( set_node2 @ Ns ) )
% 0.19/0.47 => ~ ( member_val @ V @ ( defs @ G @ N3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % defAss'E
% 0.19/0.47 thf(fact_35_defAss__extend,axiom,
% 0.19/0.47 ! [G: g,M: node,V: val,N: node,Ns: list_node] :
% 0.19/0.47 ( ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G @ M @ V )
% 0.19/0.47 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( ! [X2: node] :
% 0.19/0.47 ( ( member_node @ X2 @ ( set_node2 @ ( tl_node @ Ns ) ) )
% 0.19/0.47 => ~ ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ X2 ) ) )
% 0.19/0.47 => ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G @ N @ V ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % defAss_extend
% 0.19/0.47 thf(fact_36_assms_I8_J,axiom,
% 0.19/0.47 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ).
% 0.19/0.47
% 0.19/0.47 % assms(8)
% 0.19/0.47 thf(fact_37_defAss__def,axiom,
% 0.19/0.47 ! [G: g,M: node,V: val] :
% 0.19/0.47 ( ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G @ M @ V )
% 0.19/0.47 = ( ! [Ns3: list_node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns3 @ M )
% 0.19/0.47 => ? [X3: node] :
% 0.19/0.47 ( ( member_node @ X3 @ ( set_node2 @ Ns3 ) )
% 0.19/0.47 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ X3 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % defAss_def
% 0.19/0.47 thf(fact_38_defAssI,axiom,
% 0.19/0.47 ! [G: g,M: node,V: val] :
% 0.19/0.47 ( ! [Ns2: list_node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns2 @ M )
% 0.19/0.47 => ? [X4: node] :
% 0.19/0.47 ( ( member_node @ X4 @ ( set_node2 @ Ns2 ) )
% 0.19/0.47 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ X4 ) ) ) )
% 0.19/0.47 => ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G @ M @ V ) ) ).
% 0.19/0.47
% 0.19/0.47 % defAssI
% 0.19/0.47 thf(fact_39_defAssD,axiom,
% 0.19/0.47 ! [G: g,M: node,V: val,Ns: list_node] :
% 0.19/0.47 ( ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G @ M @ V )
% 0.19/0.47 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns @ M )
% 0.19/0.47 => ? [X2: node] :
% 0.19/0.47 ( ( member_node @ X2 @ ( set_node2 @ Ns ) )
% 0.19/0.47 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ X2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % defAssD
% 0.19/0.47 thf(fact_40_phiDefs__in__allDefs,axiom,
% 0.19/0.47 ! [V: val,G: g,N: node] :
% 0.19/0.47 ( ( member_val @ V @ ( sSA_CF370335846de_val @ phis @ G @ N ) )
% 0.19/0.47 => ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % phiDefs_in_allDefs
% 0.19/0.47 thf(fact_41_defAss__dominating,axiom,
% 0.19/0.47 ! [N: node,G: g,V: val] :
% 0.19/0.47 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G @ N @ V )
% 0.19/0.47 = ( ? [X3: node] :
% 0.19/0.47 ( ( member_node @ X3 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ X3 @ N )
% 0.19/0.47 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ X3 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % defAss_dominating
% 0.19/0.47 thf(fact_42_old_Osuccessor__in___092_060alpha_062n,axiom,
% 0.19/0.47 ! [G: g,N: node] :
% 0.19/0.47 ( ( ( graph_272749361_edgeD @ inEdges @ G @ N )
% 0.19/0.47 != nil_node )
% 0.19/0.47 => ( ( invar @ G )
% 0.19/0.47 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.successor_in_\<alpha>n
% 0.19/0.47 thf(fact_43_phiUses__finite,axiom,
% 0.19/0.47 ! [N: node,G: g] :
% 0.19/0.47 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( finite_finite_val @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % phiUses_finite
% 0.19/0.47 thf(fact_44_old_Opath2__split__last__prop,axiom,
% 0.19/0.47 ! [G: g,N: node,Ns: list_node,M: node,P: node > $o] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( ? [X4: node] :
% 0.19/0.47 ( ( member_node @ X4 @ ( set_node2 @ Ns ) )
% 0.19/0.47 & ( P @ X4 ) )
% 0.19/0.47 => ~ ! [N4: node,Ns4: list_node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N4 @ Ns4 @ M )
% 0.19/0.47 => ( ( P @ N4 )
% 0.19/0.47 => ( ! [X4: node] :
% 0.19/0.47 ( ( member_node @ X4 @ ( set_node2 @ ( tl_node @ Ns4 ) ) )
% 0.19/0.47 => ~ ( P @ X4 ) )
% 0.19/0.47 => ~ ( suffix_node @ Ns4 @ Ns ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.path2_split_last_prop
% 0.19/0.47 thf(fact_45_allDefs__finite,axiom,
% 0.19/0.47 ! [N: node,G: g] :
% 0.19/0.47 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( finite_finite_val @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % allDefs_finite
% 0.19/0.47 thf(fact_46_old_Opath2__not__Nil,axiom,
% 0.19/0.47 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( Ns != nil_node ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.path2_not_Nil
% 0.19/0.47 thf(fact_47_mem__Collect__eq,axiom,
% 0.19/0.47 ! [A: node,P: node > $o] :
% 0.19/0.47 ( ( member_node @ A @ ( collect_node @ P ) )
% 0.19/0.47 = ( P @ A ) ) ).
% 0.19/0.47
% 0.19/0.47 % mem_Collect_eq
% 0.19/0.47 thf(fact_48_mem__Collect__eq,axiom,
% 0.19/0.47 ! [A: val,P: val > $o] :
% 0.19/0.47 ( ( member_val @ A @ ( collect_val @ P ) )
% 0.19/0.47 = ( P @ A ) ) ).
% 0.19/0.47
% 0.19/0.47 % mem_Collect_eq
% 0.19/0.47 thf(fact_49_Collect__mem__eq,axiom,
% 0.19/0.47 ! [A2: set_node] :
% 0.19/0.47 ( ( collect_node
% 0.19/0.47 @ ^ [X3: node] : ( member_node @ X3 @ A2 ) )
% 0.19/0.47 = A2 ) ).
% 0.19/0.47
% 0.19/0.47 % Collect_mem_eq
% 0.19/0.47 thf(fact_50_Collect__mem__eq,axiom,
% 0.19/0.47 ! [A2: set_val] :
% 0.19/0.47 ( ( collect_val
% 0.19/0.47 @ ^ [X3: val] : ( member_val @ X3 @ A2 ) )
% 0.19/0.47 = A2 ) ).
% 0.19/0.47
% 0.19/0.47 % Collect_mem_eq
% 0.19/0.47 thf(fact_51_old_Opath2__not__Nil2,axiom,
% 0.19/0.47 ! [G: g,N: node,M: node] :
% 0.19/0.47 ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ nil_node @ M ) ).
% 0.19/0.47
% 0.19/0.47 % old.path2_not_Nil2
% 0.19/0.47 thf(fact_52_old_Opath2__app,axiom,
% 0.19/0.47 ! [G: g,N: node,Ns: list_node,M: node,Ms: list_node,L: node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ M @ Ms @ L )
% 0.19/0.47 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( tl_node @ Ms ) ) @ L ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.path2_app
% 0.19/0.47 thf(fact_53_defs__finite,axiom,
% 0.19/0.47 ! [G: g,N: node] : ( finite_finite_val @ ( defs @ G @ N ) ) ).
% 0.19/0.47
% 0.19/0.47 % defs_finite
% 0.19/0.47 thf(fact_54_phiDefs__finite,axiom,
% 0.19/0.47 ! [G: g,N: node] : ( finite_finite_val @ ( sSA_CF370335846de_val @ phis @ G @ N ) ) ).
% 0.19/0.47
% 0.19/0.47 % phiDefs_finite
% 0.19/0.47 thf(fact_55_strict__dom__trans_H,axiom,
% 0.19/0.47 ! [N: node,M: node,G: g,M2: node] :
% 0.19/0.47 ( ( ( N != M )
% 0.19/0.47 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M ) )
% 0.19/0.47 => ( ( ( M != M2 )
% 0.19/0.47 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ M @ M2 ) )
% 0.19/0.47 => ( ( N != M2 )
% 0.19/0.47 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % strict_dom_trans'
% 0.19/0.47 thf(fact_56_old_Ostrict__dom__trans,axiom,
% 0.19/0.47 ! [G: g,N: node,M: node,M2: node] :
% 0.19/0.47 ( ( invar @ G )
% 0.19/0.47 => ( ( ( N != M )
% 0.19/0.47 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M ) )
% 0.19/0.47 => ( ( ( M != M2 )
% 0.19/0.47 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ M @ M2 ) )
% 0.19/0.47 => ( ( N != M2 )
% 0.19/0.47 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.strict_dom_trans
% 0.19/0.47 thf(fact_57_old_Odominates__trans,axiom,
% 0.19/0.47 ! [G: g,N: node,N2: node,N5: node] :
% 0.19/0.47 ( ( invar @ G )
% 0.19/0.47 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ N2 )
% 0.19/0.47 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N2 @ N5 )
% 0.19/0.47 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ N5 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.dominates_trans
% 0.19/0.47 thf(fact_58_old_Odominates__antitrans,axiom,
% 0.19/0.47 ! [G: g,N_1: node,M: node,N_2: node] :
% 0.19/0.47 ( ( invar @ G )
% 0.19/0.47 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N_1 @ M )
% 0.19/0.47 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N_2 @ M )
% 0.19/0.47 => ( ~ ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N_1 @ N_2 )
% 0.19/0.47 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N_2 @ N_1 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.dominates_antitrans
% 0.19/0.47 thf(fact_59_old_Odominates__antisymm,axiom,
% 0.19/0.47 ! [G: g,N: node,N2: node] :
% 0.19/0.47 ( ( invar @ G )
% 0.19/0.47 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ N2 )
% 0.19/0.47 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N2 @ N )
% 0.19/0.47 => ( N = N2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.dominates_antisymm
% 0.19/0.47 thf(fact_60_dominates__trans_H,axiom,
% 0.19/0.47 ! [G: g,N: node,N2: node,N5: node] :
% 0.19/0.47 ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ N2 )
% 0.19/0.47 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N2 @ N5 )
% 0.19/0.47 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ N5 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % dominates_trans'
% 0.19/0.47 thf(fact_61_dominates__antisymm_H,axiom,
% 0.19/0.47 ! [G: g,N: node,N2: node] :
% 0.19/0.47 ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ N2 )
% 0.19/0.47 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N2 @ N )
% 0.19/0.47 => ( N = N2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % dominates_antisymm'
% 0.19/0.47 thf(fact_62_dominates__refl_H,axiom,
% 0.19/0.47 ! [N: node,G: g] :
% 0.19/0.47 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ N ) ) ).
% 0.19/0.47
% 0.19/0.47 % dominates_refl'
% 0.19/0.47 thf(fact_63_old_Odominates__path,axiom,
% 0.19/0.47 ! [G: g,N: node,M: node] :
% 0.19/0.47 ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M )
% 0.19/0.47 => ( ( invar @ G )
% 0.19/0.47 => ~ ! [Ns2: list_node] :
% 0.19/0.47 ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns2 @ M ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.dominates_path
% 0.19/0.47 thf(fact_64_old_Odominates__mid,axiom,
% 0.19/0.47 ! [G: g,N: node,X: node,M: node,Ns: list_node] :
% 0.19/0.47 ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ X )
% 0.19/0.47 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ X @ M )
% 0.19/0.47 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( ( invar @ G )
% 0.19/0.47 => ( member_node @ X @ ( set_node2 @ Ns ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.dominates_mid
% 0.19/0.47 thf(fact_65_old_Odominates__def,axiom,
% 0.19/0.47 ! [G: g,N: node,M: node] :
% 0.19/0.47 ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M )
% 0.19/0.47 = ( ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 & ! [Ns3: list_node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns3 @ M )
% 0.19/0.47 => ( member_node @ N @ ( set_node2 @ Ns3 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.dominates_def
% 0.19/0.47 thf(fact_66_old_OdominatesE,axiom,
% 0.19/0.47 ! [G: g,N: node,M: node] :
% 0.19/0.47 ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M )
% 0.19/0.47 => ~ ( ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ~ ! [Ns5: list_node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns5 @ M )
% 0.19/0.47 => ( member_node @ N @ ( set_node2 @ Ns5 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.dominatesE
% 0.19/0.47 thf(fact_67_old_Odominates__unsnoc,axiom,
% 0.19/0.47 ! [G: g,N: node,M: node,M2: node] :
% 0.19/0.47 ( ( invar @ G )
% 0.19/0.47 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M )
% 0.19/0.47 => ( ( member_node @ M2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M ) ) )
% 0.19/0.47 => ( ( N != M )
% 0.19/0.47 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.dominates_unsnoc
% 0.19/0.47 thf(fact_68_non__dominated__predecessor,axiom,
% 0.19/0.47 ! [N: node,G: g] :
% 0.19/0.47 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( ( N
% 0.19/0.47 != ( entry @ G ) )
% 0.19/0.47 => ~ ! [M3: node] :
% 0.19/0.47 ( ( member_node @ M3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N ) ) )
% 0.19/0.47 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M3 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % non_dominated_predecessor
% 0.19/0.47 thf(fact_69_old_OisIdom__def,axiom,
% 0.19/0.47 ! [G: g,N: node,M: node] :
% 0.19/0.47 ( ( graph_1670286392_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M )
% 0.19/0.47 = ( ( M != N )
% 0.19/0.47 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ M @ N )
% 0.19/0.47 & ! [X3: node] :
% 0.19/0.47 ( ( member_node @ X3 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( ( ( X3 != N )
% 0.19/0.47 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ X3 @ N ) )
% 0.19/0.47 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ X3 @ M ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.isIdom_def
% 0.19/0.47 thf(fact_70_old_OEntryPath__suffix,axiom,
% 0.19/0.47 ! [G: g,Ns: list_node,Ns6: list_node] :
% 0.19/0.47 ( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ Ns )
% 0.19/0.47 => ( ( suffix_node @ Ns6 @ Ns )
% 0.19/0.47 => ( ( Ns6 != nil_node )
% 0.19/0.47 => ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ Ns6 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.EntryPath_suffix
% 0.19/0.47 thf(fact_71_old_Odominates__unsnoc_H,axiom,
% 0.19/0.47 ! [G: g,N: node,M: node,M2: node,Ms: list_node] :
% 0.19/0.47 ( ( invar @ G )
% 0.19/0.47 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M )
% 0.19/0.47 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ M2 @ Ms @ M )
% 0.19/0.47 => ( ! [X2: node] :
% 0.19/0.47 ( ( member_node @ X2 @ ( set_node2 @ ( tl_node @ Ms ) ) )
% 0.19/0.47 => ( X2 != N ) )
% 0.19/0.47 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M2 ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.dominates_unsnoc'
% 0.19/0.47 thf(fact_72_old_Odominates__extend,axiom,
% 0.19/0.47 ! [G: g,N: node,M: node,M2: node,Ms: list_node] :
% 0.19/0.47 ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M )
% 0.19/0.47 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ M2 @ Ms @ M )
% 0.19/0.47 => ( ~ ( member_node @ N @ ( set_node2 @ ( tl_node @ Ms ) ) )
% 0.19/0.47 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M2 ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.dominates_extend
% 0.19/0.47 thf(fact_73_old_OEntry__no__predecessor,axiom,
% 0.19/0.47 ! [G: g] :
% 0.19/0.47 ( ( graph_272749361_edgeD @ inEdges @ G @ ( entry @ G ) )
% 0.19/0.47 = nil_node ) ).
% 0.19/0.47
% 0.19/0.47 % old.Entry_no_predecessor
% 0.19/0.47 thf(fact_74_old_Odominates__refl,axiom,
% 0.19/0.47 ! [G: g,N: node] :
% 0.19/0.47 ( ( invar @ G )
% 0.19/0.47 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ N ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.dominates_refl
% 0.19/0.47 thf(fact_75_old_OEntry__dominates,axiom,
% 0.19/0.47 ! [G: g,N: node] :
% 0.19/0.47 ( ( invar @ G )
% 0.19/0.47 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ ( entry @ G ) @ N ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.Entry_dominates
% 0.19/0.47 thf(fact_76_old_OdominatesI,axiom,
% 0.19/0.47 ! [M: node,G: g,N: node] :
% 0.19/0.47 ( ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( ! [Ns2: list_node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns2 @ M )
% 0.19/0.47 => ( member_node @ N @ ( set_node2 @ Ns2 ) ) )
% 0.19/0.47 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.dominatesI
% 0.19/0.47 thf(fact_77_old_OEntry__iff__unreachable,axiom,
% 0.19/0.47 ! [G: g,N: node] :
% 0.19/0.47 ( ( invar @ G )
% 0.19/0.47 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( ( ( graph_272749361_edgeD @ inEdges @ G @ N )
% 0.19/0.47 = nil_node )
% 0.19/0.47 = ( N
% 0.19/0.47 = ( entry @ G ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.Entry_iff_unreachable
% 0.19/0.47 thf(fact_78_old_Oreducible__def,axiom,
% 0.19/0.47 ! [G: g] :
% 0.19/0.47 ( ( graph_589078910_edgeD @ alpha_n @ invar @ inEdges @ entry @ G )
% 0.19/0.47 = ( ! [N6: node,Ns3: list_node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N6 @ Ns3 @ N6 )
% 0.19/0.47 => ? [X3: node] :
% 0.19/0.47 ( ( member_node @ X3 @ ( set_node2 @ Ns3 ) )
% 0.19/0.47 & ! [Y2: node] :
% 0.19/0.47 ( ( member_node @ Y2 @ ( set_node2 @ Ns3 ) )
% 0.19/0.47 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ X3 @ Y2 ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.reducible_def
% 0.19/0.47 thf(fact_79_in__hd__or__tl__conv,axiom,
% 0.19/0.47 ! [L: list_val,X: val] :
% 0.19/0.47 ( ( L != nil_val )
% 0.19/0.47 => ( ( ( X
% 0.19/0.47 = ( hd_val @ L ) )
% 0.19/0.47 | ( member_val @ X @ ( set_val2 @ ( tl_val @ L ) ) ) )
% 0.19/0.47 = ( member_val @ X @ ( set_val2 @ L ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % in_hd_or_tl_conv
% 0.19/0.47 thf(fact_80_in__hd__or__tl__conv,axiom,
% 0.19/0.47 ! [L: list_P738500740D_node,X: produc1453890942D_node] :
% 0.19/0.47 ( ( L != nil_Pr1769730692D_node )
% 0.19/0.47 => ( ( ( X
% 0.19/0.47 = ( hd_Pro1395892457D_node @ L ) )
% 0.19/0.47 | ( member1797643303D_node @ X @ ( set_Pr1238794387D_node @ ( tl_Pro1633633005D_node @ L ) ) ) )
% 0.19/0.47 = ( member1797643303D_node @ X @ ( set_Pr1238794387D_node @ L ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % in_hd_or_tl_conv
% 0.19/0.47 thf(fact_81_in__hd__or__tl__conv,axiom,
% 0.19/0.47 ! [L: list_node,X: node] :
% 0.19/0.47 ( ( L != nil_node )
% 0.19/0.47 => ( ( ( X
% 0.19/0.47 = ( hd_node @ L ) )
% 0.19/0.47 | ( member_node @ X @ ( set_node2 @ ( tl_node @ L ) ) ) )
% 0.19/0.47 = ( member_node @ X @ ( set_node2 @ L ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % in_hd_or_tl_conv
% 0.19/0.47 thf(fact_82_old_Opath2__cases,axiom,
% 0.19/0.47 ! [G: g,N: node,Ns: list_node,M: node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( ( ( Ns
% 0.19/0.47 = ( cons_node @ N @ nil_node ) )
% 0.19/0.47 => ( M != N ) )
% 0.19/0.47 => ~ ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( hd_node @ ( tl_node @ Ns ) ) @ ( tl_node @ Ns ) @ M )
% 0.19/0.47 => ~ ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ ( tl_node @ Ns ) ) ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.path2_cases
% 0.19/0.47 thf(fact_83_old_Opath2__snoc,axiom,
% 0.19/0.47 ! [G: g,N: node,Ns: list_node,M: node,M2: node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( ( member_node @ M @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M2 ) ) )
% 0.19/0.47 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ M2 @ nil_node ) ) @ M2 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.path2_snoc
% 0.19/0.47 thf(fact_84_old_Opath2__rev__induct,axiom,
% 0.19/0.47 ! [G: g,N: node,Ns: list_node,M: node,P: node > list_node > node > $o] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.19/0.47 => ( P @ N @ ( cons_node @ N @ nil_node ) @ N ) )
% 0.19/0.47 => ( ! [Ns2: list_node,M4: node,M3: node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns2 @ M4 )
% 0.19/0.47 => ( ( P @ N @ Ns2 @ M4 )
% 0.19/0.47 => ( ( member_node @ M4 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M3 ) ) )
% 0.19/0.47 => ( P @ N @ ( append_node @ Ns2 @ ( cons_node @ M3 @ nil_node ) ) @ M3 ) ) ) )
% 0.19/0.47 => ( P @ N @ Ns @ M ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.path2_rev_induct
% 0.19/0.47 thf(fact_85_tl__append2,axiom,
% 0.19/0.47 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.47 ( ( Xs != nil_node )
% 0.19/0.47 => ( ( tl_node @ ( append_node @ Xs @ Ys ) )
% 0.19/0.47 = ( append_node @ ( tl_node @ Xs ) @ Ys ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % tl_append2
% 0.19/0.47 thf(fact_86_tl__append2,axiom,
% 0.19/0.47 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 0.19/0.47 ( ( Xs != nil_Pr1769730692D_node )
% 0.19/0.47 => ( ( tl_Pro1633633005D_node @ ( append2096883353D_node @ Xs @ Ys ) )
% 0.19/0.47 = ( append2096883353D_node @ ( tl_Pro1633633005D_node @ Xs ) @ Ys ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % tl_append2
% 0.19/0.47 thf(fact_87_hd__append2,axiom,
% 0.19/0.47 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.47 ( ( Xs != nil_node )
% 0.19/0.47 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 0.19/0.47 = ( hd_node @ Xs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % hd_append2
% 0.19/0.47 thf(fact_88_hd__append2,axiom,
% 0.19/0.47 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 0.19/0.47 ( ( Xs != nil_Pr1769730692D_node )
% 0.19/0.47 => ( ( hd_Pro1395892457D_node @ ( append2096883353D_node @ Xs @ Ys ) )
% 0.19/0.47 = ( hd_Pro1395892457D_node @ Xs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % hd_append2
% 0.19/0.47 thf(fact_89_same__suffix__nil,axiom,
% 0.19/0.47 ! [Ys: list_P738500740D_node,Xs: list_P738500740D_node] :
% 0.19/0.47 ( ( suffix1143830554D_node @ ( append2096883353D_node @ Ys @ Xs ) @ Xs )
% 0.19/0.47 = ( Ys = nil_Pr1769730692D_node ) ) ).
% 0.19/0.47
% 0.19/0.47 % same_suffix_nil
% 0.19/0.47 thf(fact_90_same__suffix__nil,axiom,
% 0.19/0.47 ! [Ys: list_node,Xs: list_node] :
% 0.19/0.47 ( ( suffix_node @ ( append_node @ Ys @ Xs ) @ Xs )
% 0.19/0.47 = ( Ys = nil_node ) ) ).
% 0.19/0.47
% 0.19/0.47 % same_suffix_nil
% 0.19/0.47 thf(fact_91_old_Opath2__induct,axiom,
% 0.19/0.47 ! [G: g,N: node,Ns: list_node,M: node,P: node > list_node > node > $o] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.19/0.47 => ( ( ( invar @ G )
% 0.19/0.47 => ( P @ M @ ( cons_node @ M @ nil_node ) @ M ) )
% 0.19/0.47 => ( ! [Ns2: list_node,N4: node,N3: node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N3 @ Ns2 @ M )
% 0.19/0.47 => ( ( P @ N3 @ Ns2 @ M )
% 0.19/0.47 => ( ( member_node @ N4 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N3 ) ) )
% 0.19/0.47 => ( P @ N4 @ ( cons_node @ N4 @ Ns2 ) @ M ) ) ) )
% 0.19/0.47 => ( P @ N @ Ns @ M ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.path2_induct
% 0.19/0.47 thf(fact_92_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 0.19/0.47 ! [X: val,Xs: list_val,Ys: list_val,Y3: val] :
% 0.19/0.47 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.19/0.47 => ( member_val @ X @ ( set_val2 @ ( tl_val @ ( append_val @ Ys @ ( cons_val @ Y3 @ Xs ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.elem_set_implies_elem_tl_app_cons
% 0.19/0.47 thf(fact_93_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 0.19/0.47 ! [X: node,Xs: list_node,Ys: list_node,Y3: node] :
% 0.19/0.47 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.19/0.47 => ( member_node @ X @ ( set_node2 @ ( tl_node @ ( append_node @ Ys @ ( cons_node @ Y3 @ Xs ) ) ) ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.elem_set_implies_elem_tl_app_cons
% 0.19/0.47 thf(fact_94_list_Oinject,axiom,
% 0.19/0.47 ! [X21: node,X22: list_node,Y21: node,Y22: list_node] :
% 0.19/0.47 ( ( ( cons_node @ X21 @ X22 )
% 0.19/0.47 = ( cons_node @ Y21 @ Y22 ) )
% 0.19/0.47 = ( ( X21 = Y21 )
% 0.19/0.47 & ( X22 = Y22 ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % list.inject
% 0.19/0.47 thf(fact_95_same__append__eq,axiom,
% 0.19/0.47 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.19/0.47 ( ( ( append_node @ Xs @ Ys )
% 0.19/0.47 = ( append_node @ Xs @ Zs ) )
% 0.19/0.47 = ( Ys = Zs ) ) ).
% 0.19/0.47
% 0.19/0.47 % same_append_eq
% 0.19/0.47 thf(fact_96_append__same__eq,axiom,
% 0.19/0.47 ! [Ys: list_node,Xs: list_node,Zs: list_node] :
% 0.19/0.47 ( ( ( append_node @ Ys @ Xs )
% 0.19/0.47 = ( append_node @ Zs @ Xs ) )
% 0.19/0.47 = ( Ys = Zs ) ) ).
% 0.19/0.47
% 0.19/0.47 % append_same_eq
% 0.19/0.47 thf(fact_97_append__assoc,axiom,
% 0.19/0.47 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.19/0.47 ( ( append_node @ ( append_node @ Xs @ Ys ) @ Zs )
% 0.19/0.47 = ( append_node @ Xs @ ( append_node @ Ys @ Zs ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % append_assoc
% 0.19/0.47 thf(fact_98_append_Oassoc,axiom,
% 0.19/0.47 ! [A: list_node,B: list_node,C: list_node] :
% 0.19/0.47 ( ( append_node @ ( append_node @ A @ B ) @ C )
% 0.19/0.47 = ( append_node @ A @ ( append_node @ B @ C ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % append.assoc
% 0.19/0.47 thf(fact_99_suffix__order_Odual__order_Orefl,axiom,
% 0.19/0.47 ! [A: list_node] : ( suffix_node @ A @ A ) ).
% 0.19/0.47
% 0.19/0.47 % suffix_order.dual_order.refl
% 0.19/0.47 thf(fact_100_suffix__order_Oorder__refl,axiom,
% 0.19/0.47 ! [X: list_node] : ( suffix_node @ X @ X ) ).
% 0.19/0.47
% 0.19/0.47 % suffix_order.order_refl
% 0.19/0.47 thf(fact_101_old_Opath2__split_I2_J,axiom,
% 0.19/0.47 ! [G: g,N: node,Ns: list_node,N2: node,Ns6: list_node,M: node] :
% 0.19/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ Ns6 ) ) @ M )
% 0.19/0.47 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N2 @ ( cons_node @ N2 @ Ns6 ) @ M ) ) ).
% 0.19/0.47
% 0.19/0.47 % old.path2_split(2)
% 0.19/0.47 thf(fact_102_List_Ofinite__set,axiom,
% 0.19/0.47 ! [Xs: list_node] : ( finite_finite_node @ ( set_node2 @ Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % List.finite_set
% 0.19/0.47 thf(fact_103_List_Ofinite__set,axiom,
% 0.19/0.47 ! [Xs: list_val] : ( finite_finite_val @ ( set_val2 @ Xs ) ) ).
% 0.19/0.47
% 0.19/0.47 % List.finite_set
% 0.19/0.47 thf(fact_104_append_Oright__neutral,axiom,
% 0.19/0.47 ! [A: list_node] :
% 0.19/0.47 ( ( append_node @ A @ nil_node )
% 0.19/0.47 = A ) ).
% 0.19/0.47
% 0.19/0.47 % append.right_neutral
% 0.19/0.47 thf(fact_105_append_Oright__neutral,axiom,
% 0.19/0.47 ! [A: list_P738500740D_node] :
% 0.19/0.47 ( ( append2096883353D_node @ A @ nil_Pr1769730692D_node )
% 0.19/0.47 = A ) ).
% 0.19/0.47
% 0.19/0.47 % append.right_neutral
% 0.19/0.47 thf(fact_106_empty__append__eq__id,axiom,
% 0.19/0.47 ( ( append_node @ nil_node )
% 0.19/0.47 = ( ^ [X3: list_node] : X3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % empty_append_eq_id
% 0.19/0.47 thf(fact_107_empty__append__eq__id,axiom,
% 0.19/0.47 ( ( append2096883353D_node @ nil_Pr1769730692D_node )
% 0.19/0.47 = ( ^ [X3: list_P738500740D_node] : X3 ) ) ).
% 0.19/0.47
% 0.19/0.47 % empty_append_eq_id
% 0.19/0.47 thf(fact_108_append__is__Nil__conv,axiom,
% 0.19/0.47 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.47 ( ( ( append_node @ Xs @ Ys )
% 0.19/0.47 = nil_node )
% 0.19/0.47 = ( ( Xs = nil_node )
% 0.19/0.47 & ( Ys = nil_node ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % append_is_Nil_conv
% 0.19/0.47 thf(fact_109_append__is__Nil__conv,axiom,
% 0.19/0.47 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 0.19/0.47 ( ( ( append2096883353D_node @ Xs @ Ys )
% 0.19/0.47 = nil_Pr1769730692D_node )
% 0.19/0.47 = ( ( Xs = nil_Pr1769730692D_node )
% 0.19/0.47 & ( Ys = nil_Pr1769730692D_node ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % append_is_Nil_conv
% 0.19/0.47 thf(fact_110_Nil__is__append__conv,axiom,
% 0.19/0.47 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.47 ( ( nil_node
% 0.19/0.47 = ( append_node @ Xs @ Ys ) )
% 0.19/0.47 = ( ( Xs = nil_node )
% 0.19/0.47 & ( Ys = nil_node ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Nil_is_append_conv
% 0.19/0.47 thf(fact_111_Nil__is__append__conv,axiom,
% 0.19/0.47 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 0.19/0.47 ( ( nil_Pr1769730692D_node
% 0.19/0.47 = ( append2096883353D_node @ Xs @ Ys ) )
% 0.19/0.47 = ( ( Xs = nil_Pr1769730692D_node )
% 0.19/0.47 & ( Ys = nil_Pr1769730692D_node ) ) ) ).
% 0.19/0.47
% 0.19/0.47 % Nil_is_append_conv
% 0.19/0.47 thf(fact_112_self__append__conv2,axiom,
% 0.19/0.47 ! [Ys: list_node,Xs: list_node] :
% 0.19/0.47 ( ( Ys
% 0.19/0.47 = ( append_node @ Xs @ Ys ) )
% 0.19/0.47 = ( Xs = nil_node ) ) ).
% 0.19/0.47
% 0.19/0.47 % self_append_conv2
% 0.19/0.47 thf(fact_113_self__append__conv2,axiom,
% 0.19/0.47 ! [Ys: list_P738500740D_node,Xs: list_P738500740D_node] :
% 0.19/0.47 ( ( Ys
% 0.19/0.47 = ( append2096883353D_node @ Xs @ Ys ) )
% 0.19/0.47 = ( Xs = nil_Pr1769730692D_node ) ) ).
% 0.19/0.47
% 0.19/0.47 % self_append_conv2
% 0.19/0.47 thf(fact_114_append__self__conv2,axiom,
% 0.19/0.47 ! [Xs: list_node,Ys: list_node] :
% 0.19/0.47 ( ( ( append_node @ Xs @ Ys )
% 0.19/0.47 = Ys )
% 0.19/0.47 = ( Xs = nil_node ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_self_conv2
% 0.31/0.47 thf(fact_115_append__self__conv2,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 0.31/0.47 ( ( ( append2096883353D_node @ Xs @ Ys )
% 0.31/0.47 = Ys )
% 0.31/0.47 = ( Xs = nil_Pr1769730692D_node ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_self_conv2
% 0.31/0.47 thf(fact_116_self__append__conv,axiom,
% 0.31/0.47 ! [Xs: list_node,Ys: list_node] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append_node @ Xs @ Ys ) )
% 0.31/0.47 = ( Ys = nil_node ) ) ).
% 0.31/0.47
% 0.31/0.47 % self_append_conv
% 0.31/0.47 thf(fact_117_self__append__conv,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append2096883353D_node @ Xs @ Ys ) )
% 0.31/0.47 = ( Ys = nil_Pr1769730692D_node ) ) ).
% 0.31/0.47
% 0.31/0.47 % self_append_conv
% 0.31/0.47 thf(fact_118_append__self__conv,axiom,
% 0.31/0.47 ! [Xs: list_node,Ys: list_node] :
% 0.31/0.47 ( ( ( append_node @ Xs @ Ys )
% 0.31/0.47 = Xs )
% 0.31/0.47 = ( Ys = nil_node ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_self_conv
% 0.31/0.47 thf(fact_119_append__self__conv,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 0.31/0.47 ( ( ( append2096883353D_node @ Xs @ Ys )
% 0.31/0.47 = Xs )
% 0.31/0.47 = ( Ys = nil_Pr1769730692D_node ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_self_conv
% 0.31/0.47 thf(fact_120_append__Nil2,axiom,
% 0.31/0.47 ! [Xs: list_node] :
% 0.31/0.47 ( ( append_node @ Xs @ nil_node )
% 0.31/0.47 = Xs ) ).
% 0.31/0.47
% 0.31/0.47 % append_Nil2
% 0.31/0.47 thf(fact_121_append__Nil2,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node] :
% 0.31/0.47 ( ( append2096883353D_node @ Xs @ nil_Pr1769730692D_node )
% 0.31/0.47 = Xs ) ).
% 0.31/0.47
% 0.31/0.47 % append_Nil2
% 0.31/0.47 thf(fact_122_suffix__bot_Obot_Oextremum__unique,axiom,
% 0.31/0.47 ! [A: list_P738500740D_node] :
% 0.31/0.47 ( ( suffix1143830554D_node @ A @ nil_Pr1769730692D_node )
% 0.31/0.47 = ( A = nil_Pr1769730692D_node ) ) ).
% 0.31/0.47
% 0.31/0.47 % suffix_bot.bot.extremum_unique
% 0.31/0.47 thf(fact_123_suffix__bot_Obot_Oextremum__unique,axiom,
% 0.31/0.47 ! [A: list_node] :
% 0.31/0.47 ( ( suffix_node @ A @ nil_node )
% 0.31/0.47 = ( A = nil_node ) ) ).
% 0.31/0.47
% 0.31/0.47 % suffix_bot.bot.extremum_unique
% 0.31/0.47 thf(fact_124_suffix__Nil,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node] :
% 0.31/0.47 ( ( suffix1143830554D_node @ Xs @ nil_Pr1769730692D_node )
% 0.31/0.47 = ( Xs = nil_Pr1769730692D_node ) ) ).
% 0.31/0.47
% 0.31/0.47 % suffix_Nil
% 0.31/0.47 thf(fact_125_suffix__Nil,axiom,
% 0.31/0.47 ! [Xs: list_node] :
% 0.31/0.47 ( ( suffix_node @ Xs @ nil_node )
% 0.31/0.47 = ( Xs = nil_node ) ) ).
% 0.31/0.47
% 0.31/0.47 % suffix_Nil
% 0.31/0.47 thf(fact_126_same__suffix__suffix,axiom,
% 0.31/0.47 ! [Ys: list_node,Xs: list_node,Zs: list_node] :
% 0.31/0.47 ( ( suffix_node @ ( append_node @ Ys @ Xs ) @ ( append_node @ Zs @ Xs ) )
% 0.31/0.47 = ( suffix_node @ Ys @ Zs ) ) ).
% 0.31/0.47
% 0.31/0.47 % same_suffix_suffix
% 0.31/0.47 thf(fact_127_old_Opath2__split_I1_J,axiom,
% 0.31/0.47 ! [G: g,N: node,Ns: list_node,N2: node,Ns6: list_node,M: node] :
% 0.31/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ Ns6 ) ) @ M )
% 0.31/0.47 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ nil_node ) ) @ N2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.path2_split(1)
% 0.31/0.47 thf(fact_128_old_OEntry__loop,axiom,
% 0.31/0.47 ! [G: g,Ns: list_node] :
% 0.31/0.47 ( ( invar @ G )
% 0.31/0.47 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns @ ( entry @ G ) )
% 0.31/0.47 => ( Ns
% 0.31/0.47 = ( cons_node @ ( entry @ G ) @ nil_node ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.Entry_loop
% 0.31/0.47 thf(fact_129_old_OEntryPath__triv,axiom,
% 0.31/0.47 ! [G: g,N: node] : ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ ( cons_node @ N @ nil_node ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.EntryPath_triv
% 0.31/0.47 thf(fact_130_append1__eq__conv,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node,X: produc1453890942D_node,Ys: list_P738500740D_node,Y3: produc1453890942D_node] :
% 0.31/0.47 ( ( ( append2096883353D_node @ Xs @ ( cons_P1018517044D_node @ X @ nil_Pr1769730692D_node ) )
% 0.31/0.47 = ( append2096883353D_node @ Ys @ ( cons_P1018517044D_node @ Y3 @ nil_Pr1769730692D_node ) ) )
% 0.31/0.47 = ( ( Xs = Ys )
% 0.31/0.47 & ( X = Y3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % append1_eq_conv
% 0.31/0.47 thf(fact_131_append1__eq__conv,axiom,
% 0.31/0.47 ! [Xs: list_node,X: node,Ys: list_node,Y3: node] :
% 0.31/0.47 ( ( ( append_node @ Xs @ ( cons_node @ X @ nil_node ) )
% 0.31/0.47 = ( append_node @ Ys @ ( cons_node @ Y3 @ nil_node ) ) )
% 0.31/0.47 = ( ( Xs = Ys )
% 0.31/0.47 & ( X = Y3 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % append1_eq_conv
% 0.31/0.47 thf(fact_132_list__ee__eq__leel_I1_J,axiom,
% 0.31/0.47 ! [E1: produc1453890942D_node,E2: produc1453890942D_node,L1: list_P738500740D_node,E12: produc1453890942D_node,E22: produc1453890942D_node,L2: list_P738500740D_node] :
% 0.31/0.47 ( ( ( cons_P1018517044D_node @ E1 @ ( cons_P1018517044D_node @ E2 @ nil_Pr1769730692D_node ) )
% 0.31/0.47 = ( append2096883353D_node @ L1 @ ( cons_P1018517044D_node @ E12 @ ( cons_P1018517044D_node @ E22 @ L2 ) ) ) )
% 0.31/0.47 = ( ( L1 = nil_Pr1769730692D_node )
% 0.31/0.47 & ( E1 = E12 )
% 0.31/0.47 & ( E2 = E22 )
% 0.31/0.47 & ( L2 = nil_Pr1769730692D_node ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_ee_eq_leel(1)
% 0.31/0.47 thf(fact_133_list__ee__eq__leel_I1_J,axiom,
% 0.31/0.47 ! [E1: node,E2: node,L1: list_node,E12: node,E22: node,L2: list_node] :
% 0.31/0.47 ( ( ( cons_node @ E1 @ ( cons_node @ E2 @ nil_node ) )
% 0.31/0.47 = ( append_node @ L1 @ ( cons_node @ E12 @ ( cons_node @ E22 @ L2 ) ) ) )
% 0.31/0.47 = ( ( L1 = nil_node )
% 0.31/0.47 & ( E1 = E12 )
% 0.31/0.47 & ( E2 = E22 )
% 0.31/0.47 & ( L2 = nil_node ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_ee_eq_leel(1)
% 0.31/0.47 thf(fact_134_list__ee__eq__leel_I2_J,axiom,
% 0.31/0.47 ! [L1: list_P738500740D_node,E12: produc1453890942D_node,E22: produc1453890942D_node,L2: list_P738500740D_node,E1: produc1453890942D_node,E2: produc1453890942D_node] :
% 0.31/0.47 ( ( ( append2096883353D_node @ L1 @ ( cons_P1018517044D_node @ E12 @ ( cons_P1018517044D_node @ E22 @ L2 ) ) )
% 0.31/0.47 = ( cons_P1018517044D_node @ E1 @ ( cons_P1018517044D_node @ E2 @ nil_Pr1769730692D_node ) ) )
% 0.31/0.47 = ( ( L1 = nil_Pr1769730692D_node )
% 0.31/0.47 & ( E1 = E12 )
% 0.31/0.47 & ( E2 = E22 )
% 0.31/0.47 & ( L2 = nil_Pr1769730692D_node ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_ee_eq_leel(2)
% 0.31/0.47 thf(fact_135_list__ee__eq__leel_I2_J,axiom,
% 0.31/0.47 ! [L1: list_node,E12: node,E22: node,L2: list_node,E1: node,E2: node] :
% 0.31/0.47 ( ( ( append_node @ L1 @ ( cons_node @ E12 @ ( cons_node @ E22 @ L2 ) ) )
% 0.31/0.47 = ( cons_node @ E1 @ ( cons_node @ E2 @ nil_node ) ) )
% 0.31/0.47 = ( ( L1 = nil_node )
% 0.31/0.47 & ( E1 = E12 )
% 0.31/0.47 & ( E2 = E22 )
% 0.31/0.47 & ( L2 = nil_node ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_ee_eq_leel(2)
% 0.31/0.47 thf(fact_136_list__se__match_I1_J,axiom,
% 0.31/0.47 ! [L1: list_P738500740D_node,L2: list_P738500740D_node,A: produc1453890942D_node] :
% 0.31/0.47 ( ( L1 != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ( ( append2096883353D_node @ L1 @ L2 )
% 0.31/0.47 = ( cons_P1018517044D_node @ A @ nil_Pr1769730692D_node ) )
% 0.31/0.47 = ( ( L1
% 0.31/0.47 = ( cons_P1018517044D_node @ A @ nil_Pr1769730692D_node ) )
% 0.31/0.47 & ( L2 = nil_Pr1769730692D_node ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_se_match(1)
% 0.31/0.47 thf(fact_137_list__se__match_I1_J,axiom,
% 0.31/0.47 ! [L1: list_node,L2: list_node,A: node] :
% 0.31/0.47 ( ( L1 != nil_node )
% 0.31/0.47 => ( ( ( append_node @ L1 @ L2 )
% 0.31/0.47 = ( cons_node @ A @ nil_node ) )
% 0.31/0.47 = ( ( L1
% 0.31/0.47 = ( cons_node @ A @ nil_node ) )
% 0.31/0.47 & ( L2 = nil_node ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_se_match(1)
% 0.31/0.47 thf(fact_138_list__se__match_I2_J,axiom,
% 0.31/0.47 ! [L2: list_P738500740D_node,L1: list_P738500740D_node,A: produc1453890942D_node] :
% 0.31/0.47 ( ( L2 != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ( ( append2096883353D_node @ L1 @ L2 )
% 0.31/0.47 = ( cons_P1018517044D_node @ A @ nil_Pr1769730692D_node ) )
% 0.31/0.47 = ( ( L1 = nil_Pr1769730692D_node )
% 0.31/0.47 & ( L2
% 0.31/0.47 = ( cons_P1018517044D_node @ A @ nil_Pr1769730692D_node ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_se_match(2)
% 0.31/0.47 thf(fact_139_list__se__match_I2_J,axiom,
% 0.31/0.47 ! [L2: list_node,L1: list_node,A: node] :
% 0.31/0.47 ( ( L2 != nil_node )
% 0.31/0.47 => ( ( ( append_node @ L1 @ L2 )
% 0.31/0.47 = ( cons_node @ A @ nil_node ) )
% 0.31/0.47 = ( ( L1 = nil_node )
% 0.31/0.47 & ( L2
% 0.31/0.47 = ( cons_node @ A @ nil_node ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_se_match(2)
% 0.31/0.47 thf(fact_140_list__se__match_I3_J,axiom,
% 0.31/0.47 ! [L1: list_P738500740D_node,A: produc1453890942D_node,L2: list_P738500740D_node] :
% 0.31/0.47 ( ( L1 != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ( ( cons_P1018517044D_node @ A @ nil_Pr1769730692D_node )
% 0.31/0.47 = ( append2096883353D_node @ L1 @ L2 ) )
% 0.31/0.47 = ( ( L1
% 0.31/0.47 = ( cons_P1018517044D_node @ A @ nil_Pr1769730692D_node ) )
% 0.31/0.47 & ( L2 = nil_Pr1769730692D_node ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_se_match(3)
% 0.31/0.47 thf(fact_141_list__se__match_I3_J,axiom,
% 0.31/0.47 ! [L1: list_node,A: node,L2: list_node] :
% 0.31/0.47 ( ( L1 != nil_node )
% 0.31/0.47 => ( ( ( cons_node @ A @ nil_node )
% 0.31/0.47 = ( append_node @ L1 @ L2 ) )
% 0.31/0.47 = ( ( L1
% 0.31/0.47 = ( cons_node @ A @ nil_node ) )
% 0.31/0.47 & ( L2 = nil_node ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_se_match(3)
% 0.31/0.47 thf(fact_142_list__se__match_I4_J,axiom,
% 0.31/0.47 ! [L2: list_P738500740D_node,A: produc1453890942D_node,L1: list_P738500740D_node] :
% 0.31/0.47 ( ( L2 != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ( ( cons_P1018517044D_node @ A @ nil_Pr1769730692D_node )
% 0.31/0.47 = ( append2096883353D_node @ L1 @ L2 ) )
% 0.31/0.47 = ( ( L1 = nil_Pr1769730692D_node )
% 0.31/0.47 & ( L2
% 0.31/0.47 = ( cons_P1018517044D_node @ A @ nil_Pr1769730692D_node ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_se_match(4)
% 0.31/0.47 thf(fact_143_list__se__match_I4_J,axiom,
% 0.31/0.47 ! [L2: list_node,A: node,L1: list_node] :
% 0.31/0.47 ( ( L2 != nil_node )
% 0.31/0.47 => ( ( ( cons_node @ A @ nil_node )
% 0.31/0.47 = ( append_node @ L1 @ L2 ) )
% 0.31/0.47 = ( ( L1 = nil_node )
% 0.31/0.47 & ( L2
% 0.31/0.47 = ( cons_node @ A @ nil_node ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_se_match(4)
% 0.31/0.47 thf(fact_144_list__e__eq__lel_I1_J,axiom,
% 0.31/0.47 ! [E: produc1453890942D_node,L1: list_P738500740D_node,E3: produc1453890942D_node,L2: list_P738500740D_node] :
% 0.31/0.47 ( ( ( cons_P1018517044D_node @ E @ nil_Pr1769730692D_node )
% 0.31/0.47 = ( append2096883353D_node @ L1 @ ( cons_P1018517044D_node @ E3 @ L2 ) ) )
% 0.31/0.47 = ( ( L1 = nil_Pr1769730692D_node )
% 0.31/0.47 & ( E3 = E )
% 0.31/0.47 & ( L2 = nil_Pr1769730692D_node ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_e_eq_lel(1)
% 0.31/0.47 thf(fact_145_list__e__eq__lel_I1_J,axiom,
% 0.31/0.47 ! [E: node,L1: list_node,E3: node,L2: list_node] :
% 0.31/0.47 ( ( ( cons_node @ E @ nil_node )
% 0.31/0.47 = ( append_node @ L1 @ ( cons_node @ E3 @ L2 ) ) )
% 0.31/0.47 = ( ( L1 = nil_node )
% 0.31/0.47 & ( E3 = E )
% 0.31/0.47 & ( L2 = nil_node ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_e_eq_lel(1)
% 0.31/0.47 thf(fact_146_list__e__eq__lel_I2_J,axiom,
% 0.31/0.47 ! [L1: list_P738500740D_node,E3: produc1453890942D_node,L2: list_P738500740D_node,E: produc1453890942D_node] :
% 0.31/0.47 ( ( ( append2096883353D_node @ L1 @ ( cons_P1018517044D_node @ E3 @ L2 ) )
% 0.31/0.47 = ( cons_P1018517044D_node @ E @ nil_Pr1769730692D_node ) )
% 0.31/0.47 = ( ( L1 = nil_Pr1769730692D_node )
% 0.31/0.47 & ( E3 = E )
% 0.31/0.47 & ( L2 = nil_Pr1769730692D_node ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_e_eq_lel(2)
% 0.31/0.47 thf(fact_147_list__e__eq__lel_I2_J,axiom,
% 0.31/0.47 ! [L1: list_node,E3: node,L2: list_node,E: node] :
% 0.31/0.47 ( ( ( append_node @ L1 @ ( cons_node @ E3 @ L2 ) )
% 0.31/0.47 = ( cons_node @ E @ nil_node ) )
% 0.31/0.47 = ( ( L1 = nil_node )
% 0.31/0.47 & ( E3 = E )
% 0.31/0.47 & ( L2 = nil_node ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_e_eq_lel(2)
% 0.31/0.47 thf(fact_148_snoc__suffix__snoc,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node,X: produc1453890942D_node,Ys: list_P738500740D_node,Y3: produc1453890942D_node] :
% 0.31/0.47 ( ( suffix1143830554D_node @ ( append2096883353D_node @ Xs @ ( cons_P1018517044D_node @ X @ nil_Pr1769730692D_node ) ) @ ( append2096883353D_node @ Ys @ ( cons_P1018517044D_node @ Y3 @ nil_Pr1769730692D_node ) ) )
% 0.31/0.47 = ( ( X = Y3 )
% 0.31/0.47 & ( suffix1143830554D_node @ Xs @ Ys ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % snoc_suffix_snoc
% 0.31/0.47 thf(fact_149_snoc__suffix__snoc,axiom,
% 0.31/0.47 ! [Xs: list_node,X: node,Ys: list_node,Y3: node] :
% 0.31/0.47 ( ( suffix_node @ ( append_node @ Xs @ ( cons_node @ X @ nil_node ) ) @ ( append_node @ Ys @ ( cons_node @ Y3 @ nil_node ) ) )
% 0.31/0.47 = ( ( X = Y3 )
% 0.31/0.47 & ( suffix_node @ Xs @ Ys ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % snoc_suffix_snoc
% 0.31/0.47 thf(fact_150_suffix__snoc,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node,Y3: produc1453890942D_node] :
% 0.31/0.47 ( ( suffix1143830554D_node @ Xs @ ( append2096883353D_node @ Ys @ ( cons_P1018517044D_node @ Y3 @ nil_Pr1769730692D_node ) ) )
% 0.31/0.47 = ( ( Xs = nil_Pr1769730692D_node )
% 0.31/0.47 | ? [Zs2: list_P738500740D_node] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append2096883353D_node @ Zs2 @ ( cons_P1018517044D_node @ Y3 @ nil_Pr1769730692D_node ) ) )
% 0.31/0.47 & ( suffix1143830554D_node @ Zs2 @ Ys ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % suffix_snoc
% 0.31/0.47 thf(fact_151_suffix__snoc,axiom,
% 0.31/0.47 ! [Xs: list_node,Ys: list_node,Y3: node] :
% 0.31/0.47 ( ( suffix_node @ Xs @ ( append_node @ Ys @ ( cons_node @ Y3 @ nil_node ) ) )
% 0.31/0.47 = ( ( Xs = nil_node )
% 0.31/0.47 | ? [Zs2: list_node] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append_node @ Zs2 @ ( cons_node @ Y3 @ nil_node ) ) )
% 0.31/0.47 & ( suffix_node @ Zs2 @ Ys ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % suffix_snoc
% 0.31/0.47 thf(fact_152_list_Ocollapse,axiom,
% 0.31/0.47 ! [List: list_P738500740D_node] :
% 0.31/0.47 ( ( List != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ( cons_P1018517044D_node @ ( hd_Pro1395892457D_node @ List ) @ ( tl_Pro1633633005D_node @ List ) )
% 0.31/0.47 = List ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.collapse
% 0.31/0.47 thf(fact_153_list_Ocollapse,axiom,
% 0.31/0.47 ! [List: list_node] :
% 0.31/0.47 ( ( List != nil_node )
% 0.31/0.47 => ( ( cons_node @ ( hd_node @ List ) @ ( tl_node @ List ) )
% 0.31/0.47 = List ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.collapse
% 0.31/0.47 thf(fact_154_hd__Cons__tl,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node] :
% 0.31/0.47 ( ( Xs != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ( cons_P1018517044D_node @ ( hd_Pro1395892457D_node @ Xs ) @ ( tl_Pro1633633005D_node @ Xs ) )
% 0.31/0.47 = Xs ) ) ).
% 0.31/0.47
% 0.31/0.47 % hd_Cons_tl
% 0.31/0.47 thf(fact_155_hd__Cons__tl,axiom,
% 0.31/0.47 ! [Xs: list_node] :
% 0.31/0.47 ( ( Xs != nil_node )
% 0.31/0.47 => ( ( cons_node @ ( hd_node @ Xs ) @ ( tl_node @ Xs ) )
% 0.31/0.47 = Xs ) ) ).
% 0.31/0.47
% 0.31/0.47 % hd_Cons_tl
% 0.31/0.47 thf(fact_156_rs__def,axiom,
% 0.31/0.47 ( rs2
% 0.31/0.47 = ( append_node @ rs @ ( cons_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ nil_node ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rs_def
% 0.31/0.47 thf(fact_157_old_Oempty__path2,axiom,
% 0.31/0.47 ! [N: node,G: g] :
% 0.31/0.47 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 0.31/0.47 => ( ( invar @ G )
% 0.31/0.47 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( cons_node @ N @ nil_node ) @ N ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.empty_path2
% 0.31/0.47 thf(fact_158_old_OCons__path2,axiom,
% 0.31/0.47 ! [G: g,N: node,Ns: list_node,M: node,N2: node] :
% 0.31/0.47 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 0.31/0.47 => ( ( member_node @ N2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N ) ) )
% 0.31/0.47 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N2 @ ( cons_node @ N2 @ Ns ) @ M ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % old.Cons_path2
% 0.31/0.47 thf(fact_159_list_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X21: produc1453890942D_node,X22: list_P738500740D_node] :
% 0.31/0.47 ( nil_Pr1769730692D_node
% 0.31/0.47 != ( cons_P1018517044D_node @ X21 @ X22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.distinct(1)
% 0.31/0.47 thf(fact_160_list_Odistinct_I1_J,axiom,
% 0.31/0.47 ! [X21: node,X22: list_node] :
% 0.31/0.47 ( nil_node
% 0.31/0.47 != ( cons_node @ X21 @ X22 ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.distinct(1)
% 0.31/0.47 thf(fact_161_neq__NilE,axiom,
% 0.31/0.47 ! [L: list_P738500740D_node] :
% 0.31/0.47 ( ( L != nil_Pr1769730692D_node )
% 0.31/0.47 => ~ ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 0.31/0.47 ( L
% 0.31/0.47 != ( cons_P1018517044D_node @ X2 @ Xs2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_NilE
% 0.31/0.47 thf(fact_162_neq__NilE,axiom,
% 0.31/0.47 ! [L: list_node] :
% 0.31/0.47 ( ( L != nil_node )
% 0.31/0.47 => ~ ! [X2: node,Xs2: list_node] :
% 0.31/0.47 ( L
% 0.31/0.47 != ( cons_node @ X2 @ Xs2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_NilE
% 0.31/0.47 thf(fact_163_list_OdiscI,axiom,
% 0.31/0.47 ! [List: list_P738500740D_node,X21: produc1453890942D_node,X22: list_P738500740D_node] :
% 0.31/0.47 ( ( List
% 0.31/0.47 = ( cons_P1018517044D_node @ X21 @ X22 ) )
% 0.31/0.47 => ( List != nil_Pr1769730692D_node ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.discI
% 0.31/0.47 thf(fact_164_list_OdiscI,axiom,
% 0.31/0.47 ! [List: list_node,X21: node,X22: list_node] :
% 0.31/0.47 ( ( List
% 0.31/0.47 = ( cons_node @ X21 @ X22 ) )
% 0.31/0.47 => ( List != nil_node ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.discI
% 0.31/0.47 thf(fact_165_revg_Oinduct,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > list_P738500740D_node > $o,A0: list_P738500740D_node,A1: list_P738500740D_node] :
% 0.31/0.47 ( ! [X_1: list_P738500740D_node] : ( P @ nil_Pr1769730692D_node @ X_1 )
% 0.31/0.47 => ( ! [A3: produc1453890942D_node,As: list_P738500740D_node,B2: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ As @ ( cons_P1018517044D_node @ A3 @ B2 ) )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ A3 @ As ) @ B2 ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revg.induct
% 0.31/0.47 thf(fact_166_revg_Oinduct,axiom,
% 0.31/0.47 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 0.31/0.47 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.31/0.47 => ( ! [A3: node,As: list_node,B2: list_node] :
% 0.31/0.47 ( ( P @ As @ ( cons_node @ A3 @ B2 ) )
% 0.31/0.47 => ( P @ ( cons_node @ A3 @ As ) @ B2 ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % revg.induct
% 0.31/0.47 thf(fact_167_list_Oexhaust,axiom,
% 0.31/0.47 ! [Y3: list_P738500740D_node] :
% 0.31/0.47 ( ( Y3 != nil_Pr1769730692D_node )
% 0.31/0.47 => ~ ! [X212: produc1453890942D_node,X222: list_P738500740D_node] :
% 0.31/0.47 ( Y3
% 0.31/0.47 != ( cons_P1018517044D_node @ X212 @ X222 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.exhaust
% 0.31/0.47 thf(fact_168_list_Oexhaust,axiom,
% 0.31/0.47 ! [Y3: list_node] :
% 0.31/0.47 ( ( Y3 != nil_node )
% 0.31/0.47 => ~ ! [X212: node,X222: list_node] :
% 0.31/0.47 ( Y3
% 0.31/0.47 != ( cons_node @ X212 @ X222 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.exhaust
% 0.31/0.47 thf(fact_169_list_Oinducts,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > $o,List: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X1: produc1453890942D_node,X23: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ X23 )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X1 @ X23 ) ) )
% 0.31/0.47 => ( P @ List ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.inducts
% 0.31/0.47 thf(fact_170_list_Oinducts,axiom,
% 0.31/0.47 ! [P: list_node > $o,List: list_node] :
% 0.31/0.47 ( ( P @ nil_node )
% 0.31/0.47 => ( ! [X1: node,X23: list_node] :
% 0.31/0.47 ( ( P @ X23 )
% 0.31/0.47 => ( P @ ( cons_node @ X1 @ X23 ) ) )
% 0.31/0.47 => ( P @ List ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.inducts
% 0.31/0.47 thf(fact_171_neq__Nil__conv,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node] :
% 0.31/0.47 ( ( Xs != nil_Pr1769730692D_node )
% 0.31/0.47 = ( ? [Y2: produc1453890942D_node,Ys2: list_P738500740D_node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( cons_P1018517044D_node @ Y2 @ Ys2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_Nil_conv
% 0.31/0.47 thf(fact_172_neq__Nil__conv,axiom,
% 0.31/0.47 ! [Xs: list_node] :
% 0.31/0.47 ( ( Xs != nil_node )
% 0.31/0.47 = ( ? [Y2: node,Ys2: list_node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( cons_node @ Y2 @ Ys2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_Nil_conv
% 0.31/0.47 thf(fact_173_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > list_P738500740D_node > $o,Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ nil_Pr1769730692D_node @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] : ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [Y4: produc1453890942D_node,Ys3: list_P738500740D_node] : ( P @ nil_Pr1769730692D_node @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_174_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > list_node > $o,Xs: list_P738500740D_node,Ys: list_node] :
% 0.31/0.47 ( ( P @ nil_Pr1769730692D_node @ nil_node )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] : ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ nil_node )
% 0.31/0.47 => ( ! [Y4: node,Ys3: list_node] : ( P @ nil_Pr1769730692D_node @ ( cons_node @ Y4 @ Ys3 ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_175_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_node > list_P738500740D_node > $o,Xs: list_node,Ys: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ nil_node @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node] : ( P @ ( cons_node @ X2 @ Xs2 ) @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [Y4: produc1453890942D_node,Ys3: list_P738500740D_node] : ( P @ nil_node @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_176_list__induct2_H,axiom,
% 0.31/0.47 ! [P: list_node > list_node > $o,Xs: list_node,Ys: list_node] :
% 0.31/0.47 ( ( P @ nil_node @ nil_node )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node] : ( P @ ( cons_node @ X2 @ Xs2 ) @ nil_node )
% 0.31/0.47 => ( ! [Y4: node,Ys3: list_node] : ( P @ nil_node @ ( cons_node @ Y4 @ Ys3 ) )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct2'
% 0.31/0.47 thf(fact_177_splice_Oinduct,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > list_P738500740D_node > $o,A0: list_P738500740D_node,A1: list_P738500740D_node] :
% 0.31/0.47 ( ! [X_1: list_P738500740D_node] : ( P @ nil_Pr1769730692D_node @ X_1 )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ Ys3 @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ Ys3 ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % splice.induct
% 0.31/0.47 thf(fact_178_splice_Oinduct,axiom,
% 0.31/0.47 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 0.31/0.47 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node,Ys3: list_node] :
% 0.31/0.47 ( ( P @ Ys3 @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ Xs2 ) @ Ys3 ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % splice.induct
% 0.31/0.47 thf(fact_179_induct__list012,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > $o,Xs: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node] : ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Y4: produc1453890942D_node,Zs3: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ Zs3 )
% 0.31/0.47 => ( ( P @ ( cons_P1018517044D_node @ Y4 @ Zs3 ) )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X2 @ ( cons_P1018517044D_node @ Y4 @ Zs3 ) ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % induct_list012
% 0.31/0.47 thf(fact_180_induct__list012,axiom,
% 0.31/0.47 ! [P: list_node > $o,Xs: list_node] :
% 0.31/0.47 ( ( P @ nil_node )
% 0.31/0.47 => ( ! [X2: node] : ( P @ ( cons_node @ X2 @ nil_node ) )
% 0.31/0.47 => ( ! [X2: node,Y4: node,Zs3: list_node] :
% 0.31/0.47 ( ( P @ Zs3 )
% 0.31/0.47 => ( ( P @ ( cons_node @ Y4 @ Zs3 ) )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ ( cons_node @ Y4 @ Zs3 ) ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % induct_list012
% 0.31/0.47 thf(fact_181_min__list_Ocases,axiom,
% 0.31/0.47 ! [X: list_node] :
% 0.31/0.47 ( ! [X2: node,Xs2: list_node] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_node @ X2 @ Xs2 ) )
% 0.31/0.47 => ( X = nil_node ) ) ).
% 0.31/0.47
% 0.31/0.47 % min_list.cases
% 0.31/0.47 thf(fact_182_suffix__Cons,axiom,
% 0.31/0.47 ! [Xs: list_node,Y3: node,Ys: list_node] :
% 0.31/0.47 ( ( suffix_node @ Xs @ ( cons_node @ Y3 @ Ys ) )
% 0.31/0.47 = ( ( Xs
% 0.31/0.47 = ( cons_node @ Y3 @ Ys ) )
% 0.31/0.47 | ( suffix_node @ Xs @ Ys ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % suffix_Cons
% 0.31/0.47 thf(fact_183_Cons__eq__appendI,axiom,
% 0.31/0.47 ! [X: node,Xs1: list_node,Ys: list_node,Xs: list_node,Zs: list_node] :
% 0.31/0.47 ( ( ( cons_node @ X @ Xs1 )
% 0.31/0.47 = Ys )
% 0.31/0.47 => ( ( Xs
% 0.31/0.47 = ( append_node @ Xs1 @ Zs ) )
% 0.31/0.47 => ( ( cons_node @ X @ Xs )
% 0.31/0.47 = ( append_node @ Ys @ Zs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Cons_eq_appendI
% 0.31/0.47 thf(fact_184_min__list_Oinduct,axiom,
% 0.31/0.47 ! [P: list_node > $o,A0: list_node] :
% 0.31/0.47 ( ! [X2: node,Xs2: list_node] :
% 0.31/0.47 ( ! [X213: node,X223: list_node] :
% 0.31/0.47 ( ( Xs2
% 0.31/0.47 = ( cons_node @ X213 @ X223 ) )
% 0.31/0.47 => ( P @ Xs2 ) )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ Xs2 ) ) )
% 0.31/0.47 => ( ( P @ nil_node )
% 0.31/0.47 => ( P @ A0 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % min_list.induct
% 0.31/0.47 thf(fact_185_shuffles_Oinduct,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > list_P738500740D_node > $o,A0: list_P738500740D_node,A1: list_P738500740D_node] :
% 0.31/0.47 ( ! [X_1: list_P738500740D_node] : ( P @ nil_Pr1769730692D_node @ X_1 )
% 0.31/0.47 => ( ! [Xs2: list_P738500740D_node] : ( P @ Xs2 @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ Xs2 @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) )
% 0.31/0.47 => ( ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % shuffles.induct
% 0.31/0.47 thf(fact_186_shuffles_Oinduct,axiom,
% 0.31/0.47 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 0.31/0.47 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.31/0.47 => ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_node )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ( P @ Xs2 @ ( cons_node @ Y4 @ Ys3 ) )
% 0.31/0.47 => ( ( P @ ( cons_node @ X2 @ Xs2 ) @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % shuffles.induct
% 0.31/0.47 thf(fact_187_transpose_Ocases,axiom,
% 0.31/0.47 ! [X: list_l1129649930D_node] :
% 0.31/0.47 ( ( X != nil_li1626782346D_node )
% 0.31/0.47 => ( ! [Xss: list_l1129649930D_node] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_l1288865338D_node @ nil_Pr1769730692D_node @ Xss ) )
% 0.31/0.47 => ~ ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Xss: list_l1129649930D_node] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_l1288865338D_node @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % transpose.cases
% 0.31/0.47 thf(fact_188_transpose_Ocases,axiom,
% 0.31/0.47 ! [X: list_list_node] :
% 0.31/0.47 ( ( X != nil_list_node )
% 0.31/0.47 => ( ! [Xss: list_list_node] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_list_node @ nil_node @ Xss ) )
% 0.31/0.47 => ~ ! [X2: node,Xs2: list_node,Xss: list_list_node] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_list_node @ ( cons_node @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % transpose.cases
% 0.31/0.47 thf(fact_189_suffix__ConsD,axiom,
% 0.31/0.47 ! [X: node,Xs: list_node,Ys: list_node] :
% 0.31/0.47 ( ( suffix_node @ ( cons_node @ X @ Xs ) @ Ys )
% 0.31/0.47 => ( suffix_node @ Xs @ Ys ) ) ).
% 0.31/0.47
% 0.31/0.47 % suffix_ConsD
% 0.31/0.47 thf(fact_190_suffix__ConsI,axiom,
% 0.31/0.47 ! [Xs: list_node,Ys: list_node,Y3: node] :
% 0.31/0.47 ( ( suffix_node @ Xs @ Ys )
% 0.31/0.47 => ( suffix_node @ Xs @ ( cons_node @ Y3 @ Ys ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % suffix_ConsI
% 0.31/0.47 thf(fact_191_list__2pre__induct,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > list_P738500740D_node > $o,W1: list_P738500740D_node,W2: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ nil_Pr1769730692D_node @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [E4: produc1453890942D_node,W12: list_P738500740D_node,W22: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ W12 @ W22 )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ E4 @ W12 ) @ W22 ) )
% 0.31/0.47 => ( ! [E4: produc1453890942D_node,W13: list_P738500740D_node,W23: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ W13 @ W23 )
% 0.31/0.47 => ( P @ W13 @ ( cons_P1018517044D_node @ E4 @ W23 ) ) )
% 0.31/0.47 => ( P @ W1 @ W2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_2pre_induct
% 0.31/0.47 thf(fact_192_list__2pre__induct,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > list_node > $o,W1: list_P738500740D_node,W2: list_node] :
% 0.31/0.47 ( ( P @ nil_Pr1769730692D_node @ nil_node )
% 0.31/0.47 => ( ! [E4: produc1453890942D_node,W12: list_P738500740D_node,W22: list_node] :
% 0.31/0.47 ( ( P @ W12 @ W22 )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ E4 @ W12 ) @ W22 ) )
% 0.31/0.47 => ( ! [E4: node,W13: list_P738500740D_node,W23: list_node] :
% 0.31/0.47 ( ( P @ W13 @ W23 )
% 0.31/0.47 => ( P @ W13 @ ( cons_node @ E4 @ W23 ) ) )
% 0.31/0.47 => ( P @ W1 @ W2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_2pre_induct
% 0.31/0.47 thf(fact_193_list__2pre__induct,axiom,
% 0.31/0.47 ! [P: list_node > list_P738500740D_node > $o,W1: list_node,W2: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ nil_node @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [E4: node,W12: list_node,W22: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ W12 @ W22 )
% 0.31/0.47 => ( P @ ( cons_node @ E4 @ W12 ) @ W22 ) )
% 0.31/0.47 => ( ! [E4: produc1453890942D_node,W13: list_node,W23: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ W13 @ W23 )
% 0.31/0.47 => ( P @ W13 @ ( cons_P1018517044D_node @ E4 @ W23 ) ) )
% 0.31/0.47 => ( P @ W1 @ W2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_2pre_induct
% 0.31/0.47 thf(fact_194_list__2pre__induct,axiom,
% 0.31/0.47 ! [P: list_node > list_node > $o,W1: list_node,W2: list_node] :
% 0.31/0.47 ( ( P @ nil_node @ nil_node )
% 0.31/0.47 => ( ! [E4: node,W12: list_node,W22: list_node] :
% 0.31/0.47 ( ( P @ W12 @ W22 )
% 0.31/0.47 => ( P @ ( cons_node @ E4 @ W12 ) @ W22 ) )
% 0.31/0.47 => ( ! [E4: node,W13: list_node,W23: list_node] :
% 0.31/0.47 ( ( P @ W13 @ W23 )
% 0.31/0.47 => ( P @ W13 @ ( cons_node @ E4 @ W23 ) ) )
% 0.31/0.47 => ( P @ W1 @ W2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_2pre_induct
% 0.31/0.47 thf(fact_195_suffix__ConsD2,axiom,
% 0.31/0.47 ! [X: node,Xs: list_node,Y3: node,Ys: list_node] :
% 0.31/0.47 ( ( suffix_node @ ( cons_node @ X @ Xs ) @ ( cons_node @ Y3 @ Ys ) )
% 0.31/0.47 => ( suffix_node @ Xs @ Ys ) ) ).
% 0.31/0.47
% 0.31/0.47 % suffix_ConsD2
% 0.31/0.47 thf(fact_196_remdups__adj_Ocases,axiom,
% 0.31/0.47 ! [X: list_P738500740D_node] :
% 0.31/0.47 ( ( X != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) )
% 0.31/0.47 => ~ ! [X2: produc1453890942D_node,Y4: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_P1018517044D_node @ X2 @ ( cons_P1018517044D_node @ Y4 @ Xs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.cases
% 0.31/0.47 thf(fact_197_remdups__adj_Ocases,axiom,
% 0.31/0.47 ! [X: list_node] :
% 0.31/0.47 ( ( X != nil_node )
% 0.31/0.47 => ( ! [X2: node] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_node @ X2 @ nil_node ) )
% 0.31/0.47 => ~ ! [X2: node,Y4: node,Xs2: list_node] :
% 0.31/0.47 ( X
% 0.31/0.47 != ( cons_node @ X2 @ ( cons_node @ Y4 @ Xs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.cases
% 0.31/0.47 thf(fact_198_sorted__wrt_Oinduct,axiom,
% 0.31/0.47 ! [P: ( produc1453890942D_node > produc1453890942D_node > $o ) > list_P738500740D_node > $o,A0: produc1453890942D_node > produc1453890942D_node > $o,A1: list_P738500740D_node] :
% 0.31/0.47 ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o] : ( P @ P2 @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o,X2: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ P2 @ Ys3 )
% 0.31/0.47 => ( P @ P2 @ ( cons_P1018517044D_node @ X2 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sorted_wrt.induct
% 0.31/0.47 thf(fact_199_sorted__wrt_Oinduct,axiom,
% 0.31/0.47 ! [P: ( node > node > $o ) > list_node > $o,A0: node > node > $o,A1: list_node] :
% 0.31/0.47 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node )
% 0.31/0.47 => ( ! [P2: node > node > $o,X2: node,Ys3: list_node] :
% 0.31/0.47 ( ( P @ P2 @ Ys3 )
% 0.31/0.47 => ( P @ P2 @ ( cons_node @ X2 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sorted_wrt.induct
% 0.31/0.47 thf(fact_200_append__Cons,axiom,
% 0.31/0.47 ! [X: node,Xs: list_node,Ys: list_node] :
% 0.31/0.47 ( ( append_node @ ( cons_node @ X @ Xs ) @ Ys )
% 0.31/0.47 = ( cons_node @ X @ ( append_node @ Xs @ Ys ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_Cons
% 0.31/0.47 thf(fact_201_remdups__adj_Oinduct,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > $o,A0: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node] : ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Y4: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 0.31/0.47 ( ( ( X2 = Y4 )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) ) )
% 0.31/0.47 => ( ( ( X2 != Y4 )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ Y4 @ Xs2 ) ) )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X2 @ ( cons_P1018517044D_node @ Y4 @ Xs2 ) ) ) ) )
% 0.31/0.47 => ( P @ A0 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.induct
% 0.31/0.47 thf(fact_202_remdups__adj_Oinduct,axiom,
% 0.31/0.47 ! [P: list_node > $o,A0: list_node] :
% 0.31/0.47 ( ( P @ nil_node )
% 0.31/0.47 => ( ! [X2: node] : ( P @ ( cons_node @ X2 @ nil_node ) )
% 0.31/0.47 => ( ! [X2: node,Y4: node,Xs2: list_node] :
% 0.31/0.47 ( ( ( X2 = Y4 )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ Xs2 ) ) )
% 0.31/0.47 => ( ( ( X2 != Y4 )
% 0.31/0.47 => ( P @ ( cons_node @ Y4 @ Xs2 ) ) )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ ( cons_node @ Y4 @ Xs2 ) ) ) ) )
% 0.31/0.47 => ( P @ A0 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % remdups_adj.induct
% 0.31/0.47 thf(fact_203_list__induct__first2,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > $o,Xs: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node] : ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) )
% 0.31/0.47 => ( ! [X1: produc1453890942D_node,X23: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X1 @ ( cons_P1018517044D_node @ X23 @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct_first2
% 0.31/0.47 thf(fact_204_list__induct__first2,axiom,
% 0.31/0.47 ! [P: list_node > $o,Xs: list_node] :
% 0.31/0.47 ( ( P @ nil_node )
% 0.31/0.47 => ( ! [X2: node] : ( P @ ( cons_node @ X2 @ nil_node ) )
% 0.31/0.47 => ( ! [X1: node,X23: node,Xs2: list_node] :
% 0.31/0.47 ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_node @ X1 @ ( cons_node @ X23 @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_induct_first2
% 0.31/0.47 thf(fact_205_list__match__lel__lel,axiom,
% 0.31/0.47 ! [C1: list_node,Qs: node,C2: list_node,C12: list_node,Qs2: node,C22: list_node] :
% 0.31/0.47 ( ( ( append_node @ C1 @ ( cons_node @ Qs @ C2 ) )
% 0.31/0.47 = ( append_node @ C12 @ ( cons_node @ Qs2 @ C22 ) ) )
% 0.31/0.47 => ( ! [C21: list_node] :
% 0.31/0.47 ( ( C1
% 0.31/0.47 = ( append_node @ C12 @ ( cons_node @ Qs2 @ C21 ) ) )
% 0.31/0.47 => ( C22
% 0.31/0.47 != ( append_node @ C21 @ ( cons_node @ Qs @ C2 ) ) ) )
% 0.31/0.47 => ( ( ( C12 = C1 )
% 0.31/0.47 => ( ( Qs2 = Qs )
% 0.31/0.47 => ( C22 != C2 ) ) )
% 0.31/0.47 => ~ ! [C212: list_node] :
% 0.31/0.47 ( ( C12
% 0.31/0.47 = ( append_node @ C1 @ ( cons_node @ Qs @ C212 ) ) )
% 0.31/0.47 => ( C2
% 0.31/0.47 != ( append_node @ C212 @ ( cons_node @ Qs2 @ C22 ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_match_lel_lel
% 0.31/0.47 thf(fact_206_successively_Oinduct,axiom,
% 0.31/0.47 ! [P: ( produc1453890942D_node > produc1453890942D_node > $o ) > list_P738500740D_node > $o,A0: produc1453890942D_node > produc1453890942D_node > $o,A1: list_P738500740D_node] :
% 0.31/0.47 ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o] : ( P @ P2 @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o,X2: produc1453890942D_node] : ( P @ P2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) )
% 0.31/0.47 => ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o,X2: produc1453890942D_node,Y4: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ P2 @ ( cons_P1018517044D_node @ Y4 @ Xs2 ) )
% 0.31/0.47 => ( P @ P2 @ ( cons_P1018517044D_node @ X2 @ ( cons_P1018517044D_node @ Y4 @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % successively.induct
% 0.31/0.47 thf(fact_207_successively_Oinduct,axiom,
% 0.31/0.47 ! [P: ( node > node > $o ) > list_node > $o,A0: node > node > $o,A1: list_node] :
% 0.31/0.47 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node )
% 0.31/0.47 => ( ! [P2: node > node > $o,X2: node] : ( P @ P2 @ ( cons_node @ X2 @ nil_node ) )
% 0.31/0.47 => ( ! [P2: node > node > $o,X2: node,Y4: node,Xs2: list_node] :
% 0.31/0.47 ( ( P @ P2 @ ( cons_node @ Y4 @ Xs2 ) )
% 0.31/0.47 => ( P @ P2 @ ( cons_node @ X2 @ ( cons_node @ Y4 @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % successively.induct
% 0.31/0.47 thf(fact_208_list__all__zip_Oinduct,axiom,
% 0.31/0.47 ! [P: ( produc1453890942D_node > produc1453890942D_node > $o ) > list_P738500740D_node > list_P738500740D_node > $o,A0: produc1453890942D_node > produc1453890942D_node > $o,A1: list_P738500740D_node,A22: list_P738500740D_node] :
% 0.31/0.47 ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o] : ( P @ P2 @ nil_Pr1769730692D_node @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o,A3: produc1453890942D_node,As: list_P738500740D_node,B2: produc1453890942D_node,Bs: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ P2 @ As @ Bs )
% 0.31/0.47 => ( P @ P2 @ ( cons_P1018517044D_node @ A3 @ As ) @ ( cons_P1018517044D_node @ B2 @ Bs ) ) )
% 0.31/0.47 => ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o,V2: produc1453890942D_node,Va: list_P738500740D_node] : ( P @ P2 @ ( cons_P1018517044D_node @ V2 @ Va ) @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o,V2: produc1453890942D_node,Va: list_P738500740D_node] : ( P @ P2 @ nil_Pr1769730692D_node @ ( cons_P1018517044D_node @ V2 @ Va ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_all_zip.induct
% 0.31/0.47 thf(fact_209_list__all__zip_Oinduct,axiom,
% 0.31/0.47 ! [P: ( produc1453890942D_node > node > $o ) > list_P738500740D_node > list_node > $o,A0: produc1453890942D_node > node > $o,A1: list_P738500740D_node,A22: list_node] :
% 0.31/0.47 ( ! [P2: produc1453890942D_node > node > $o] : ( P @ P2 @ nil_Pr1769730692D_node @ nil_node )
% 0.31/0.47 => ( ! [P2: produc1453890942D_node > node > $o,A3: produc1453890942D_node,As: list_P738500740D_node,B2: node,Bs: list_node] :
% 0.31/0.47 ( ( P @ P2 @ As @ Bs )
% 0.31/0.47 => ( P @ P2 @ ( cons_P1018517044D_node @ A3 @ As ) @ ( cons_node @ B2 @ Bs ) ) )
% 0.31/0.47 => ( ! [P2: produc1453890942D_node > node > $o,V2: produc1453890942D_node,Va: list_P738500740D_node] : ( P @ P2 @ ( cons_P1018517044D_node @ V2 @ Va ) @ nil_node )
% 0.31/0.47 => ( ! [P2: produc1453890942D_node > node > $o,V2: node,Va: list_node] : ( P @ P2 @ nil_Pr1769730692D_node @ ( cons_node @ V2 @ Va ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_all_zip.induct
% 0.31/0.47 thf(fact_210_list__all__zip_Oinduct,axiom,
% 0.31/0.47 ! [P: ( node > produc1453890942D_node > $o ) > list_node > list_P738500740D_node > $o,A0: node > produc1453890942D_node > $o,A1: list_node,A22: list_P738500740D_node] :
% 0.31/0.47 ( ! [P2: node > produc1453890942D_node > $o] : ( P @ P2 @ nil_node @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [P2: node > produc1453890942D_node > $o,A3: node,As: list_node,B2: produc1453890942D_node,Bs: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ P2 @ As @ Bs )
% 0.31/0.47 => ( P @ P2 @ ( cons_node @ A3 @ As ) @ ( cons_P1018517044D_node @ B2 @ Bs ) ) )
% 0.31/0.47 => ( ! [P2: node > produc1453890942D_node > $o,V2: node,Va: list_node] : ( P @ P2 @ ( cons_node @ V2 @ Va ) @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [P2: node > produc1453890942D_node > $o,V2: produc1453890942D_node,Va: list_P738500740D_node] : ( P @ P2 @ nil_node @ ( cons_P1018517044D_node @ V2 @ Va ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_all_zip.induct
% 0.31/0.47 thf(fact_211_list__all__zip_Oinduct,axiom,
% 0.31/0.47 ! [P: ( node > node > $o ) > list_node > list_node > $o,A0: node > node > $o,A1: list_node,A22: list_node] :
% 0.31/0.47 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node @ nil_node )
% 0.31/0.47 => ( ! [P2: node > node > $o,A3: node,As: list_node,B2: node,Bs: list_node] :
% 0.31/0.47 ( ( P @ P2 @ As @ Bs )
% 0.31/0.47 => ( P @ P2 @ ( cons_node @ A3 @ As ) @ ( cons_node @ B2 @ Bs ) ) )
% 0.31/0.47 => ( ! [P2: node > node > $o,V2: node,Va: list_node] : ( P @ P2 @ ( cons_node @ V2 @ Va ) @ nil_node )
% 0.31/0.47 => ( ! [P2: node > node > $o,V2: node,Va: list_node] : ( P @ P2 @ nil_node @ ( cons_node @ V2 @ Va ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_all_zip.induct
% 0.31/0.47 thf(fact_212_list__nonempty__induct,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node,P: list_P738500740D_node > $o] :
% 0.31/0.47 ( ( Xs != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node] : ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 0.31/0.47 ( ( Xs2 != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_nonempty_induct
% 0.31/0.47 thf(fact_213_list__nonempty__induct,axiom,
% 0.31/0.47 ! [Xs: list_node,P: list_node > $o] :
% 0.31/0.47 ( ( Xs != nil_node )
% 0.31/0.47 => ( ! [X2: node] : ( P @ ( cons_node @ X2 @ nil_node ) )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node] :
% 0.31/0.47 ( ( Xs2 != nil_node )
% 0.31/0.47 => ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ Xs2 ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_nonempty_induct
% 0.31/0.47 thf(fact_214_map__tailrec__rev_Oinduct,axiom,
% 0.31/0.47 ! [P: ( produc1453890942D_node > node ) > list_P738500740D_node > list_node > $o,A0: produc1453890942D_node > node,A1: list_P738500740D_node,A22: list_node] :
% 0.31/0.47 ( ! [F: produc1453890942D_node > node,X_1: list_node] : ( P @ F @ nil_Pr1769730692D_node @ X_1 )
% 0.31/0.47 => ( ! [F: produc1453890942D_node > node,A3: produc1453890942D_node,As: list_P738500740D_node,Bs: list_node] :
% 0.31/0.47 ( ( P @ F @ As @ ( cons_node @ ( F @ A3 ) @ Bs ) )
% 0.31/0.47 => ( P @ F @ ( cons_P1018517044D_node @ A3 @ As ) @ Bs ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.induct
% 0.31/0.47 thf(fact_215_map__tailrec__rev_Oinduct,axiom,
% 0.31/0.47 ! [P: ( node > node ) > list_node > list_node > $o,A0: node > node,A1: list_node,A22: list_node] :
% 0.31/0.47 ( ! [F: node > node,X_1: list_node] : ( P @ F @ nil_node @ X_1 )
% 0.31/0.47 => ( ! [F: node > node,A3: node,As: list_node,Bs: list_node] :
% 0.31/0.47 ( ( P @ F @ As @ ( cons_node @ ( F @ A3 ) @ Bs ) )
% 0.31/0.47 => ( P @ F @ ( cons_node @ A3 @ As ) @ Bs ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % map_tailrec_rev.induct
% 0.31/0.47 thf(fact_216_mergesort__by__rel__merge_Oinduct,axiom,
% 0.31/0.47 ! [P: ( produc1453890942D_node > produc1453890942D_node > $o ) > list_P738500740D_node > list_P738500740D_node > $o,A0: produc1453890942D_node > produc1453890942D_node > $o,A1: list_P738500740D_node,A22: list_P738500740D_node] :
% 0.31/0.47 ( ! [R: produc1453890942D_node > produc1453890942D_node > $o,X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( ( R @ X2 @ Y4 )
% 0.31/0.47 => ( P @ R @ Xs2 @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) )
% 0.31/0.47 => ( ( ~ ( R @ X2 @ Y4 )
% 0.31/0.47 => ( P @ R @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ Ys3 ) )
% 0.31/0.47 => ( P @ R @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) ) )
% 0.31/0.47 => ( ! [R: produc1453890942D_node > produc1453890942D_node > $o,Xs2: list_P738500740D_node] : ( P @ R @ Xs2 @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [R: produc1453890942D_node > produc1453890942D_node > $o,V2: produc1453890942D_node,Va: list_P738500740D_node] : ( P @ R @ nil_Pr1769730692D_node @ ( cons_P1018517044D_node @ V2 @ Va ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A22 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mergesort_by_rel_merge.induct
% 0.31/0.47 thf(fact_217_mergesort__by__rel__merge_Oinduct,axiom,
% 0.31/0.47 ! [P: ( node > node > $o ) > list_node > list_node > $o,A0: node > node > $o,A1: list_node,A22: list_node] :
% 0.31/0.47 ( ! [R: node > node > $o,X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ( ( R @ X2 @ Y4 )
% 0.31/0.47 => ( P @ R @ Xs2 @ ( cons_node @ Y4 @ Ys3 ) ) )
% 0.31/0.47 => ( ( ~ ( R @ X2 @ Y4 )
% 0.31/0.47 => ( P @ R @ ( cons_node @ X2 @ Xs2 ) @ Ys3 ) )
% 0.31/0.47 => ( P @ R @ ( cons_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) ) )
% 0.31/0.47 => ( ! [R: node > node > $o,Xs2: list_node] : ( P @ R @ Xs2 @ nil_node )
% 0.31/0.47 => ( ! [R: node > node > $o,V2: node,Va: list_node] : ( P @ R @ nil_node @ ( cons_node @ V2 @ Va ) )
% 0.31/0.47 => ( P @ A0 @ A1 @ A22 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mergesort_by_rel_merge.induct
% 0.31/0.47 thf(fact_218_mergesort__by__rel__merge__induct,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > list_P738500740D_node > $o,R2: produc1453890942D_node > produc1453890942D_node > $o,Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 0.31/0.47 ( ! [Xs2: list_P738500740D_node] : ( P @ Xs2 @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X_1: list_P738500740D_node] : ( P @ nil_Pr1769730692D_node @ X_1 )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( R2 @ X2 @ Y4 )
% 0.31/0.47 => ( ( P @ Xs2 @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ~ ( R2 @ X2 @ Y4 )
% 0.31/0.47 => ( ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mergesort_by_rel_merge_induct
% 0.31/0.47 thf(fact_219_mergesort__by__rel__merge__induct,axiom,
% 0.31/0.47 ! [P: list_node > list_P738500740D_node > $o,R2: node > produc1453890942D_node > $o,Xs: list_node,Ys: list_P738500740D_node] :
% 0.31/0.47 ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X_1: list_P738500740D_node] : ( P @ nil_node @ X_1 )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( R2 @ X2 @ Y4 )
% 0.31/0.47 => ( ( P @ Xs2 @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) ) )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ~ ( R2 @ X2 @ Y4 )
% 0.31/0.47 => ( ( P @ ( cons_node @ X2 @ Xs2 ) @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mergesort_by_rel_merge_induct
% 0.31/0.47 thf(fact_220_mergesort__by__rel__merge__induct,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > list_node > $o,R2: produc1453890942D_node > node > $o,Xs: list_P738500740D_node,Ys: list_node] :
% 0.31/0.47 ( ! [Xs2: list_P738500740D_node] : ( P @ Xs2 @ nil_node )
% 0.31/0.47 => ( ! [X_1: list_node] : ( P @ nil_Pr1769730692D_node @ X_1 )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ( R2 @ X2 @ Y4 )
% 0.31/0.47 => ( ( P @ Xs2 @ ( cons_node @ Y4 @ Ys3 ) )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ~ ( R2 @ X2 @ Y4 )
% 0.31/0.47 => ( ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mergesort_by_rel_merge_induct
% 0.31/0.47 thf(fact_221_mergesort__by__rel__merge__induct,axiom,
% 0.31/0.47 ! [P: list_node > list_node > $o,R2: node > node > $o,Xs: list_node,Ys: list_node] :
% 0.31/0.47 ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_node )
% 0.31/0.47 => ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ( R2 @ X2 @ Y4 )
% 0.31/0.47 => ( ( P @ Xs2 @ ( cons_node @ Y4 @ Ys3 ) )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) ) )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ~ ( R2 @ X2 @ Y4 )
% 0.31/0.47 => ( ( P @ ( cons_node @ X2 @ Xs2 ) @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % mergesort_by_rel_merge_induct
% 0.31/0.47 thf(fact_222_longest__common__prefix_Oinduct,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > list_P738500740D_node > $o,A0: list_P738500740D_node,A1: list_P738500740D_node] :
% 0.31/0.47 ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( ( X2 = Y4 )
% 0.31/0.47 => ( P @ Xs2 @ Ys3 ) )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) )
% 0.31/0.47 => ( ! [X_1: list_P738500740D_node] : ( P @ nil_Pr1769730692D_node @ X_1 )
% 0.31/0.47 => ( ! [Uu: list_P738500740D_node] : ( P @ Uu @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % longest_common_prefix.induct
% 0.31/0.47 thf(fact_223_longest__common__prefix_Oinduct,axiom,
% 0.31/0.47 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 0.31/0.47 ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ( ( X2 = Y4 )
% 0.31/0.47 => ( P @ Xs2 @ Ys3 ) )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) )
% 0.31/0.47 => ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 0.31/0.47 => ( ! [Uu: list_node] : ( P @ Uu @ nil_node )
% 0.31/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % longest_common_prefix.induct
% 0.31/0.47 thf(fact_224_strict__sorted_Oinduct,axiom,
% 0.31/0.47 ! [P: list_node > $o,A0: list_node] :
% 0.31/0.47 ( ( P @ nil_node )
% 0.31/0.47 => ( ! [X2: node,Ys3: list_node] :
% 0.31/0.47 ( ( P @ Ys3 )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ Ys3 ) ) )
% 0.31/0.47 => ( P @ A0 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % strict_sorted.induct
% 0.31/0.47 thf(fact_225_list_Osel_I1_J,axiom,
% 0.31/0.47 ! [X21: node,X22: list_node] :
% 0.31/0.47 ( ( hd_node @ ( cons_node @ X21 @ X22 ) )
% 0.31/0.47 = X21 ) ).
% 0.31/0.47
% 0.31/0.47 % list.sel(1)
% 0.31/0.47 thf(fact_226_list_Osel_I3_J,axiom,
% 0.31/0.47 ! [X21: node,X22: list_node] :
% 0.31/0.47 ( ( tl_node @ ( cons_node @ X21 @ X22 ) )
% 0.31/0.47 = X22 ) ).
% 0.31/0.47
% 0.31/0.47 % list.sel(3)
% 0.31/0.47 thf(fact_227_list__tail__coinc,axiom,
% 0.31/0.47 ! [N1: node,R1: list_node,N22: node,R22: list_node] :
% 0.31/0.47 ( ( ( cons_node @ N1 @ R1 )
% 0.31/0.47 = ( cons_node @ N22 @ R22 ) )
% 0.31/0.47 => ( ( N1 = N22 )
% 0.31/0.47 & ( R1 = R22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_tail_coinc
% 0.31/0.47 thf(fact_228_not__Cons__self2,axiom,
% 0.31/0.47 ! [X: node,Xs: list_node] :
% 0.31/0.47 ( ( cons_node @ X @ Xs )
% 0.31/0.47 != Xs ) ).
% 0.31/0.47
% 0.31/0.47 % not_Cons_self2
% 0.31/0.47 thf(fact_229_distinct__length__2__or__more,axiom,
% 0.31/0.47 ! [A: node,B: node,Xs: list_node] :
% 0.31/0.47 ( ( distinct_node @ ( cons_node @ A @ ( cons_node @ B @ Xs ) ) )
% 0.31/0.47 = ( ( A != B )
% 0.31/0.47 & ( distinct_node @ ( cons_node @ A @ Xs ) )
% 0.31/0.47 & ( distinct_node @ ( cons_node @ B @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % distinct_length_2_or_more
% 0.31/0.47 thf(fact_230_list_Oset__cases,axiom,
% 0.31/0.47 ! [E: val,A: list_val] :
% 0.31/0.47 ( ( member_val @ E @ ( set_val2 @ A ) )
% 0.31/0.47 => ( ! [Z2: list_val] :
% 0.31/0.47 ( A
% 0.31/0.47 != ( cons_val @ E @ Z2 ) )
% 0.31/0.47 => ~ ! [Z1: val,Z2: list_val] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( cons_val @ Z1 @ Z2 ) )
% 0.31/0.47 => ~ ( member_val @ E @ ( set_val2 @ Z2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.set_cases
% 0.31/0.47 thf(fact_231_list_Oset__cases,axiom,
% 0.31/0.47 ! [E: node,A: list_node] :
% 0.31/0.47 ( ( member_node @ E @ ( set_node2 @ A ) )
% 0.31/0.47 => ( ! [Z2: list_node] :
% 0.31/0.47 ( A
% 0.31/0.47 != ( cons_node @ E @ Z2 ) )
% 0.31/0.47 => ~ ! [Z1: node,Z2: list_node] :
% 0.31/0.47 ( ( A
% 0.31/0.47 = ( cons_node @ Z1 @ Z2 ) )
% 0.31/0.47 => ~ ( member_node @ E @ ( set_node2 @ Z2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.set_cases
% 0.31/0.47 thf(fact_232_set__ConsD,axiom,
% 0.31/0.47 ! [Y3: val,X: val,Xs: list_val] :
% 0.31/0.47 ( ( member_val @ Y3 @ ( set_val2 @ ( cons_val @ X @ Xs ) ) )
% 0.31/0.47 => ( ( Y3 = X )
% 0.31/0.47 | ( member_val @ Y3 @ ( set_val2 @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % set_ConsD
% 0.31/0.47 thf(fact_233_set__ConsD,axiom,
% 0.31/0.47 ! [Y3: node,X: node,Xs: list_node] :
% 0.31/0.47 ( ( member_node @ Y3 @ ( set_node2 @ ( cons_node @ X @ Xs ) ) )
% 0.31/0.47 => ( ( Y3 = X )
% 0.31/0.47 | ( member_node @ Y3 @ ( set_node2 @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % set_ConsD
% 0.31/0.47 thf(fact_234_list_Oset__intros_I1_J,axiom,
% 0.31/0.47 ! [X21: val,X22: list_val] : ( member_val @ X21 @ ( set_val2 @ ( cons_val @ X21 @ X22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.set_intros(1)
% 0.31/0.47 thf(fact_235_list_Oset__intros_I1_J,axiom,
% 0.31/0.47 ! [X21: node,X22: list_node] : ( member_node @ X21 @ ( set_node2 @ ( cons_node @ X21 @ X22 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.set_intros(1)
% 0.31/0.47 thf(fact_236_list_Oset__intros_I2_J,axiom,
% 0.31/0.47 ! [Y3: val,X22: list_val,X21: val] :
% 0.31/0.47 ( ( member_val @ Y3 @ ( set_val2 @ X22 ) )
% 0.31/0.47 => ( member_val @ Y3 @ ( set_val2 @ ( cons_val @ X21 @ X22 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.set_intros(2)
% 0.31/0.47 thf(fact_237_list_Oset__intros_I2_J,axiom,
% 0.31/0.47 ! [Y3: node,X22: list_node,X21: node] :
% 0.31/0.47 ( ( member_node @ Y3 @ ( set_node2 @ X22 ) )
% 0.31/0.47 => ( member_node @ Y3 @ ( set_node2 @ ( cons_node @ X21 @ X22 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.set_intros(2)
% 0.31/0.47 thf(fact_238_list__append__eq__Cons__cases,axiom,
% 0.31/0.47 ! [Ys: list_P738500740D_node,Zs: list_P738500740D_node,X: produc1453890942D_node,Xs: list_P738500740D_node] :
% 0.31/0.47 ( ( ( append2096883353D_node @ Ys @ Zs )
% 0.31/0.47 = ( cons_P1018517044D_node @ X @ Xs ) )
% 0.31/0.47 => ( ( ( Ys = nil_Pr1769730692D_node )
% 0.31/0.47 => ( Zs
% 0.31/0.47 != ( cons_P1018517044D_node @ X @ Xs ) ) )
% 0.31/0.47 => ~ ! [Ys4: list_P738500740D_node] :
% 0.31/0.47 ( ( Ys
% 0.31/0.47 = ( cons_P1018517044D_node @ X @ Ys4 ) )
% 0.31/0.47 => ( ( append2096883353D_node @ Ys4 @ Zs )
% 0.31/0.47 != Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_append_eq_Cons_cases
% 0.31/0.47 thf(fact_239_list__append__eq__Cons__cases,axiom,
% 0.31/0.47 ! [Ys: list_node,Zs: list_node,X: node,Xs: list_node] :
% 0.31/0.47 ( ( ( append_node @ Ys @ Zs )
% 0.31/0.47 = ( cons_node @ X @ Xs ) )
% 0.31/0.47 => ( ( ( Ys = nil_node )
% 0.31/0.47 => ( Zs
% 0.31/0.47 != ( cons_node @ X @ Xs ) ) )
% 0.31/0.47 => ~ ! [Ys4: list_node] :
% 0.31/0.47 ( ( Ys
% 0.31/0.47 = ( cons_node @ X @ Ys4 ) )
% 0.31/0.47 => ( ( append_node @ Ys4 @ Zs )
% 0.31/0.47 != Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_append_eq_Cons_cases
% 0.31/0.47 thf(fact_240_list__Cons__eq__append__cases,axiom,
% 0.31/0.47 ! [X: produc1453890942D_node,Xs: list_P738500740D_node,Ys: list_P738500740D_node,Zs: list_P738500740D_node] :
% 0.31/0.47 ( ( ( cons_P1018517044D_node @ X @ Xs )
% 0.31/0.47 = ( append2096883353D_node @ Ys @ Zs ) )
% 0.31/0.47 => ( ( ( Ys = nil_Pr1769730692D_node )
% 0.31/0.47 => ( Zs
% 0.31/0.47 != ( cons_P1018517044D_node @ X @ Xs ) ) )
% 0.31/0.47 => ~ ! [Ys4: list_P738500740D_node] :
% 0.31/0.47 ( ( Ys
% 0.31/0.47 = ( cons_P1018517044D_node @ X @ Ys4 ) )
% 0.31/0.47 => ( ( append2096883353D_node @ Ys4 @ Zs )
% 0.31/0.47 != Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_Cons_eq_append_cases
% 0.31/0.47 thf(fact_241_list__Cons__eq__append__cases,axiom,
% 0.31/0.47 ! [X: node,Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.31/0.47 ( ( ( cons_node @ X @ Xs )
% 0.31/0.47 = ( append_node @ Ys @ Zs ) )
% 0.31/0.47 => ( ( ( Ys = nil_node )
% 0.31/0.47 => ( Zs
% 0.31/0.47 != ( cons_node @ X @ Xs ) ) )
% 0.31/0.47 => ~ ! [Ys4: list_node] :
% 0.31/0.47 ( ( Ys
% 0.31/0.47 = ( cons_node @ X @ Ys4 ) )
% 0.31/0.47 => ( ( append_node @ Ys4 @ Zs )
% 0.31/0.47 != Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list_Cons_eq_append_cases
% 0.31/0.47 thf(fact_242_rev__nonempty__induct2_H,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node,P: list_P738500740D_node > list_P738500740D_node > $o] :
% 0.31/0.47 ( ( Xs != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ( Ys != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Y4: produc1453890942D_node] : ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node] :
% 0.31/0.47 ( ( Xs2 != nil_Pr1769730692D_node )
% 0.31/0.47 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( Ys3 != nil_Pr1769730692D_node )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( ( Xs2 != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ( Ys3 != nil_Pr1769730692D_node )
% 0.31/0.47 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_nonempty_induct2'
% 0.31/0.47 thf(fact_243_rev__nonempty__induct2_H,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node,Ys: list_node,P: list_P738500740D_node > list_node > $o] :
% 0.31/0.47 ( ( Xs != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ( Ys != nil_node )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Y4: node] : ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) @ ( cons_node @ Y4 @ nil_node ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: node] :
% 0.31/0.47 ( ( Xs2 != nil_Pr1769730692D_node )
% 0.31/0.47 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ ( cons_node @ Y4 @ nil_node ) ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ( Ys3 != nil_node )
% 0.31/0.47 => ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( ( Xs2 != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ( Ys3 != nil_node )
% 0.31/0.47 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_nonempty_induct2'
% 0.31/0.47 thf(fact_244_rev__nonempty__induct2_H,axiom,
% 0.31/0.47 ! [Xs: list_node,Ys: list_P738500740D_node,P: list_node > list_P738500740D_node > $o] :
% 0.31/0.47 ( ( Xs != nil_node )
% 0.31/0.47 => ( ( Ys != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X2: node,Y4: produc1453890942D_node] : ( P @ ( cons_node @ X2 @ nil_node ) @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node,Y4: produc1453890942D_node] :
% 0.31/0.47 ( ( Xs2 != nil_node )
% 0.31/0.47 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) )
% 0.31/0.47 => ( ! [X2: node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( Ys3 != nil_Pr1769730692D_node )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ nil_node ) @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( ( Xs2 != nil_node )
% 0.31/0.47 => ( ( Ys3 != nil_Pr1769730692D_node )
% 0.31/0.47 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_nonempty_induct2'
% 0.31/0.47 thf(fact_245_rev__nonempty__induct2_H,axiom,
% 0.31/0.47 ! [Xs: list_node,Ys: list_node,P: list_node > list_node > $o] :
% 0.31/0.47 ( ( Xs != nil_node )
% 0.31/0.47 => ( ( Ys != nil_node )
% 0.31/0.47 => ( ! [X2: node,Y4: node] : ( P @ ( cons_node @ X2 @ nil_node ) @ ( cons_node @ Y4 @ nil_node ) )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node,Y4: node] :
% 0.31/0.47 ( ( Xs2 != nil_node )
% 0.31/0.47 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ ( cons_node @ Y4 @ nil_node ) ) )
% 0.31/0.47 => ( ! [X2: node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ( Ys3 != nil_node )
% 0.31/0.47 => ( P @ ( cons_node @ X2 @ nil_node ) @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( ( Xs2 != nil_node )
% 0.31/0.47 => ( ( Ys3 != nil_node )
% 0.31/0.47 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_nonempty_induct2'
% 0.31/0.47 thf(fact_246_rev__nonempty__induct,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node,P: list_P738500740D_node > $o] :
% 0.31/0.47 ( ( Xs != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node] : ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 0.31/0.47 ( ( Xs2 != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_nonempty_induct
% 0.31/0.47 thf(fact_247_rev__nonempty__induct,axiom,
% 0.31/0.47 ! [Xs: list_node,P: list_node > $o] :
% 0.31/0.47 ( ( Xs != nil_node )
% 0.31/0.47 => ( ! [X2: node] : ( P @ ( cons_node @ X2 @ nil_node ) )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node] :
% 0.31/0.47 ( ( Xs2 != nil_node )
% 0.31/0.47 => ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_nonempty_induct
% 0.31/0.47 thf(fact_248_append__eq__Cons__conv,axiom,
% 0.31/0.47 ! [Ys: list_P738500740D_node,Zs: list_P738500740D_node,X: produc1453890942D_node,Xs: list_P738500740D_node] :
% 0.31/0.47 ( ( ( append2096883353D_node @ Ys @ Zs )
% 0.31/0.47 = ( cons_P1018517044D_node @ X @ Xs ) )
% 0.31/0.47 = ( ( ( Ys = nil_Pr1769730692D_node )
% 0.31/0.47 & ( Zs
% 0.31/0.47 = ( cons_P1018517044D_node @ X @ Xs ) ) )
% 0.31/0.47 | ? [Ys5: list_P738500740D_node] :
% 0.31/0.47 ( ( Ys
% 0.31/0.47 = ( cons_P1018517044D_node @ X @ Ys5 ) )
% 0.31/0.47 & ( ( append2096883353D_node @ Ys5 @ Zs )
% 0.31/0.47 = Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_eq_Cons_conv
% 0.31/0.47 thf(fact_249_append__eq__Cons__conv,axiom,
% 0.31/0.47 ! [Ys: list_node,Zs: list_node,X: node,Xs: list_node] :
% 0.31/0.47 ( ( ( append_node @ Ys @ Zs )
% 0.31/0.47 = ( cons_node @ X @ Xs ) )
% 0.31/0.47 = ( ( ( Ys = nil_node )
% 0.31/0.47 & ( Zs
% 0.31/0.47 = ( cons_node @ X @ Xs ) ) )
% 0.31/0.47 | ? [Ys5: list_node] :
% 0.31/0.47 ( ( Ys
% 0.31/0.47 = ( cons_node @ X @ Ys5 ) )
% 0.31/0.47 & ( ( append_node @ Ys5 @ Zs )
% 0.31/0.47 = Xs ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_eq_Cons_conv
% 0.31/0.47 thf(fact_250_Cons__eq__append__conv,axiom,
% 0.31/0.47 ! [X: produc1453890942D_node,Xs: list_P738500740D_node,Ys: list_P738500740D_node,Zs: list_P738500740D_node] :
% 0.31/0.47 ( ( ( cons_P1018517044D_node @ X @ Xs )
% 0.31/0.47 = ( append2096883353D_node @ Ys @ Zs ) )
% 0.31/0.47 = ( ( ( Ys = nil_Pr1769730692D_node )
% 0.31/0.47 & ( ( cons_P1018517044D_node @ X @ Xs )
% 0.31/0.47 = Zs ) )
% 0.31/0.47 | ? [Ys5: list_P738500740D_node] :
% 0.31/0.47 ( ( ( cons_P1018517044D_node @ X @ Ys5 )
% 0.31/0.47 = Ys )
% 0.31/0.47 & ( Xs
% 0.31/0.47 = ( append2096883353D_node @ Ys5 @ Zs ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Cons_eq_append_conv
% 0.31/0.47 thf(fact_251_Cons__eq__append__conv,axiom,
% 0.31/0.47 ! [X: node,Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.31/0.47 ( ( ( cons_node @ X @ Xs )
% 0.31/0.47 = ( append_node @ Ys @ Zs ) )
% 0.31/0.47 = ( ( ( Ys = nil_node )
% 0.31/0.47 & ( ( cons_node @ X @ Xs )
% 0.31/0.47 = Zs ) )
% 0.31/0.47 | ? [Ys5: list_node] :
% 0.31/0.47 ( ( ( cons_node @ X @ Ys5 )
% 0.31/0.47 = Ys )
% 0.31/0.47 & ( Xs
% 0.31/0.47 = ( append_node @ Ys5 @ Zs ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Cons_eq_append_conv
% 0.31/0.47 thf(fact_252_neq__Nil__rev__conv,axiom,
% 0.31/0.47 ! [L: list_P738500740D_node] :
% 0.31/0.47 ( ( L != nil_Pr1769730692D_node )
% 0.31/0.47 = ( ? [Xs3: list_P738500740D_node,X3: produc1453890942D_node] :
% 0.31/0.47 ( L
% 0.31/0.47 = ( append2096883353D_node @ Xs3 @ ( cons_P1018517044D_node @ X3 @ nil_Pr1769730692D_node ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_Nil_rev_conv
% 0.31/0.47 thf(fact_253_neq__Nil__rev__conv,axiom,
% 0.31/0.47 ! [L: list_node] :
% 0.31/0.47 ( ( L != nil_node )
% 0.31/0.47 = ( ? [Xs3: list_node,X3: node] :
% 0.31/0.47 ( L
% 0.31/0.47 = ( append_node @ Xs3 @ ( cons_node @ X3 @ nil_node ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_Nil_rev_conv
% 0.31/0.47 thf(fact_254_rev__induct2_H,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > list_P738500740D_node > $o,Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ nil_Pr1769730692D_node @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] : ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [Y4: produc1453890942D_node,Ys3: list_P738500740D_node] : ( P @ nil_Pr1769730692D_node @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_induct2'
% 0.31/0.47 thf(fact_255_rev__induct2_H,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > list_node > $o,Xs: list_P738500740D_node,Ys: list_node] :
% 0.31/0.47 ( ( P @ nil_Pr1769730692D_node @ nil_node )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] : ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ nil_node )
% 0.31/0.47 => ( ! [Y4: node,Ys3: list_node] : ( P @ nil_Pr1769730692D_node @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_induct2'
% 0.31/0.47 thf(fact_256_rev__induct2_H,axiom,
% 0.31/0.47 ! [P: list_node > list_P738500740D_node > $o,Xs: list_node,Ys: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ nil_node @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node] : ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [Y4: produc1453890942D_node,Ys3: list_P738500740D_node] : ( P @ nil_node @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_induct2'
% 0.31/0.47 thf(fact_257_rev__induct2_H,axiom,
% 0.31/0.47 ! [P: list_node > list_node > $o,Xs: list_node,Ys: list_node] :
% 0.31/0.47 ( ( P @ nil_node @ nil_node )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node] : ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ nil_node )
% 0.31/0.47 => ( ! [Y4: node,Ys3: list_node] : ( P @ nil_node @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) )
% 0.31/0.47 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_induct2'
% 0.31/0.47 thf(fact_258_neq__Nil__revE,axiom,
% 0.31/0.47 ! [L: list_P738500740D_node] :
% 0.31/0.47 ( ( L != nil_Pr1769730692D_node )
% 0.31/0.47 => ~ ! [Ll: list_P738500740D_node,E4: produc1453890942D_node] :
% 0.31/0.47 ( L
% 0.31/0.47 != ( append2096883353D_node @ Ll @ ( cons_P1018517044D_node @ E4 @ nil_Pr1769730692D_node ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_Nil_revE
% 0.31/0.47 thf(fact_259_neq__Nil__revE,axiom,
% 0.31/0.47 ! [L: list_node] :
% 0.31/0.47 ( ( L != nil_node )
% 0.31/0.47 => ~ ! [Ll: list_node,E4: node] :
% 0.31/0.47 ( L
% 0.31/0.47 != ( append_node @ Ll @ ( cons_node @ E4 @ nil_node ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % neq_Nil_revE
% 0.31/0.47 thf(fact_260_rev__exhaust,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node] :
% 0.31/0.47 ( ( Xs != nil_Pr1769730692D_node )
% 0.31/0.47 => ~ ! [Ys3: list_P738500740D_node,Y4: produc1453890942D_node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 != ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_exhaust
% 0.31/0.47 thf(fact_261_rev__exhaust,axiom,
% 0.31/0.47 ! [Xs: list_node] :
% 0.31/0.47 ( ( Xs != nil_node )
% 0.31/0.47 => ~ ! [Ys3: list_node,Y4: node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 != ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_exhaust
% 0.31/0.47 thf(fact_262_rev__induct,axiom,
% 0.31/0.47 ! [P: list_P738500740D_node > $o,Xs: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 0.31/0.47 ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_induct
% 0.31/0.47 thf(fact_263_rev__induct,axiom,
% 0.31/0.47 ! [P: list_node > $o,Xs: list_node] :
% 0.31/0.47 ( ( P @ nil_node )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node] :
% 0.31/0.47 ( ( P @ Xs2 )
% 0.31/0.47 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) ) )
% 0.31/0.47 => ( P @ Xs ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % rev_induct
% 0.31/0.47 thf(fact_264_split__list,axiom,
% 0.31/0.47 ! [X: val,Xs: list_val] :
% 0.31/0.47 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.31/0.47 => ? [Ys3: list_val,Zs3: list_val] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_list
% 0.31/0.47 thf(fact_265_split__list,axiom,
% 0.31/0.47 ! [X: node,Xs: list_node] :
% 0.31/0.47 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.31/0.47 => ? [Ys3: list_node,Zs3: list_node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_list
% 0.31/0.47 thf(fact_266_split__list__last,axiom,
% 0.31/0.47 ! [X: val,Xs: list_val] :
% 0.31/0.47 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.31/0.47 => ? [Ys3: list_val,Zs3: list_val] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs3 ) ) )
% 0.31/0.47 & ~ ( member_val @ X @ ( set_val2 @ Zs3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_list_last
% 0.31/0.47 thf(fact_267_split__list__last,axiom,
% 0.31/0.47 ! [X: node,Xs: list_node] :
% 0.31/0.47 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.31/0.47 => ? [Ys3: list_node,Zs3: list_node] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs3 ) ) )
% 0.31/0.47 & ~ ( member_node @ X @ ( set_node2 @ Zs3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_list_last
% 0.31/0.47 thf(fact_268_split__list__prop,axiom,
% 0.31/0.47 ! [Xs: list_node,P: node > $o] :
% 0.31/0.47 ( ? [X4: node] :
% 0.31/0.47 ( ( member_node @ X4 @ ( set_node2 @ Xs ) )
% 0.31/0.47 & ( P @ X4 ) )
% 0.31/0.47 => ? [Ys3: list_node,X2: node] :
% 0.31/0.47 ( ? [Zs3: list_node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( append_node @ Ys3 @ ( cons_node @ X2 @ Zs3 ) ) )
% 0.31/0.47 & ( P @ X2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_list_prop
% 0.31/0.47 thf(fact_269_xy__in__set__cases,axiom,
% 0.31/0.47 ! [X: val,L: list_val,Y3: val] :
% 0.31/0.47 ( ( member_val @ X @ ( set_val2 @ L ) )
% 0.31/0.47 => ( ( member_val @ Y3 @ ( set_val2 @ L ) )
% 0.31/0.47 => ( ( ( X = Y3 )
% 0.31/0.47 => ! [L12: list_val,L22: list_val] :
% 0.31/0.47 ( L
% 0.31/0.47 != ( append_val @ L12 @ ( cons_val @ Y3 @ L22 ) ) ) )
% 0.31/0.47 => ( ( ( X != Y3 )
% 0.31/0.47 => ! [L12: list_val,L22: list_val,L3: list_val] :
% 0.31/0.47 ( L
% 0.31/0.47 != ( append_val @ L12 @ ( cons_val @ X @ ( append_val @ L22 @ ( cons_val @ Y3 @ L3 ) ) ) ) ) )
% 0.31/0.47 => ~ ( ( X != Y3 )
% 0.31/0.47 => ! [L12: list_val,L22: list_val,L3: list_val] :
% 0.31/0.47 ( L
% 0.31/0.47 != ( append_val @ L12 @ ( cons_val @ Y3 @ ( append_val @ L22 @ ( cons_val @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % xy_in_set_cases
% 0.31/0.47 thf(fact_270_xy__in__set__cases,axiom,
% 0.31/0.47 ! [X: node,L: list_node,Y3: node] :
% 0.31/0.47 ( ( member_node @ X @ ( set_node2 @ L ) )
% 0.31/0.47 => ( ( member_node @ Y3 @ ( set_node2 @ L ) )
% 0.31/0.47 => ( ( ( X = Y3 )
% 0.31/0.47 => ! [L12: list_node,L22: list_node] :
% 0.31/0.47 ( L
% 0.31/0.47 != ( append_node @ L12 @ ( cons_node @ Y3 @ L22 ) ) ) )
% 0.31/0.47 => ( ( ( X != Y3 )
% 0.31/0.47 => ! [L12: list_node,L22: list_node,L3: list_node] :
% 0.31/0.47 ( L
% 0.31/0.47 != ( append_node @ L12 @ ( cons_node @ X @ ( append_node @ L22 @ ( cons_node @ Y3 @ L3 ) ) ) ) ) )
% 0.31/0.47 => ~ ( ( X != Y3 )
% 0.31/0.47 => ! [L12: list_node,L22: list_node,L3: list_node] :
% 0.31/0.47 ( L
% 0.31/0.47 != ( append_node @ L12 @ ( cons_node @ Y3 @ ( append_node @ L22 @ ( cons_node @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % xy_in_set_cases
% 0.31/0.47 thf(fact_271_split__list__first,axiom,
% 0.31/0.47 ! [X: val,Xs: list_val] :
% 0.31/0.47 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.31/0.47 => ? [Ys3: list_val,Zs3: list_val] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs3 ) ) )
% 0.31/0.47 & ~ ( member_val @ X @ ( set_val2 @ Ys3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_list_first
% 0.31/0.47 thf(fact_272_split__list__first,axiom,
% 0.31/0.47 ! [X: node,Xs: list_node] :
% 0.31/0.47 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.31/0.47 => ? [Ys3: list_node,Zs3: list_node] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs3 ) ) )
% 0.31/0.47 & ~ ( member_node @ X @ ( set_node2 @ Ys3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_list_first
% 0.31/0.47 thf(fact_273_split__list__propE,axiom,
% 0.31/0.47 ! [Xs: list_node,P: node > $o] :
% 0.31/0.47 ( ? [X4: node] :
% 0.31/0.47 ( ( member_node @ X4 @ ( set_node2 @ Xs ) )
% 0.31/0.47 & ( P @ X4 ) )
% 0.31/0.47 => ~ ! [Ys3: list_node,X2: node] :
% 0.31/0.47 ( ? [Zs3: list_node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( append_node @ Ys3 @ ( cons_node @ X2 @ Zs3 ) ) )
% 0.31/0.47 => ~ ( P @ X2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_list_propE
% 0.31/0.47 thf(fact_274_append__Cons__eq__iff,axiom,
% 0.31/0.47 ! [X: val,Xs: list_val,Ys: list_val,Xs4: list_val,Ys6: list_val] :
% 0.31/0.47 ( ~ ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.31/0.47 => ( ~ ( member_val @ X @ ( set_val2 @ Ys ) )
% 0.31/0.47 => ( ( ( append_val @ Xs @ ( cons_val @ X @ Ys ) )
% 0.31/0.47 = ( append_val @ Xs4 @ ( cons_val @ X @ Ys6 ) ) )
% 0.31/0.47 = ( ( Xs = Xs4 )
% 0.31/0.47 & ( Ys = Ys6 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_Cons_eq_iff
% 0.31/0.47 thf(fact_275_append__Cons__eq__iff,axiom,
% 0.31/0.47 ! [X: node,Xs: list_node,Ys: list_node,Xs4: list_node,Ys6: list_node] :
% 0.31/0.47 ( ~ ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.31/0.47 => ( ~ ( member_node @ X @ ( set_node2 @ Ys ) )
% 0.31/0.47 => ( ( ( append_node @ Xs @ ( cons_node @ X @ Ys ) )
% 0.31/0.47 = ( append_node @ Xs4 @ ( cons_node @ X @ Ys6 ) ) )
% 0.31/0.47 = ( ( Xs = Xs4 )
% 0.31/0.47 & ( Ys = Ys6 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % append_Cons_eq_iff
% 0.31/0.47 thf(fact_276_in__set__conv__decomp,axiom,
% 0.31/0.47 ! [X: val,Xs: list_val] :
% 0.31/0.47 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.31/0.47 = ( ? [Ys2: list_val,Zs2: list_val] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_set_conv_decomp
% 0.31/0.47 thf(fact_277_in__set__conv__decomp,axiom,
% 0.31/0.47 ! [X: node,Xs: list_node] :
% 0.31/0.47 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.31/0.47 = ( ? [Ys2: list_node,Zs2: list_node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_set_conv_decomp
% 0.31/0.47 thf(fact_278_in__set__list__format,axiom,
% 0.31/0.47 ! [E: val,L: list_val] :
% 0.31/0.47 ( ( member_val @ E @ ( set_val2 @ L ) )
% 0.31/0.47 => ~ ! [L12: list_val,L22: list_val] :
% 0.31/0.47 ( L
% 0.31/0.47 != ( append_val @ L12 @ ( cons_val @ E @ L22 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_set_list_format
% 0.31/0.47 thf(fact_279_in__set__list__format,axiom,
% 0.31/0.47 ! [E: node,L: list_node] :
% 0.31/0.47 ( ( member_node @ E @ ( set_node2 @ L ) )
% 0.31/0.47 => ~ ! [L12: list_node,L22: list_node] :
% 0.31/0.47 ( L
% 0.31/0.47 != ( append_node @ L12 @ ( cons_node @ E @ L22 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_set_list_format
% 0.31/0.47 thf(fact_280_split__list__last__prop,axiom,
% 0.31/0.47 ! [Xs: list_node,P: node > $o] :
% 0.31/0.47 ( ? [X4: node] :
% 0.31/0.47 ( ( member_node @ X4 @ ( set_node2 @ Xs ) )
% 0.31/0.47 & ( P @ X4 ) )
% 0.31/0.47 => ? [Ys3: list_node,X2: node,Zs3: list_node] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append_node @ Ys3 @ ( cons_node @ X2 @ Zs3 ) ) )
% 0.31/0.47 & ( P @ X2 )
% 0.31/0.47 & ! [Xa: node] :
% 0.31/0.47 ( ( member_node @ Xa @ ( set_node2 @ Zs3 ) )
% 0.31/0.47 => ~ ( P @ Xa ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_list_last_prop
% 0.31/0.47 thf(fact_281_split__list__first__prop,axiom,
% 0.31/0.47 ! [Xs: list_node,P: node > $o] :
% 0.31/0.47 ( ? [X4: node] :
% 0.31/0.47 ( ( member_node @ X4 @ ( set_node2 @ Xs ) )
% 0.31/0.47 & ( P @ X4 ) )
% 0.31/0.47 => ? [Ys3: list_node,X2: node] :
% 0.31/0.47 ( ? [Zs3: list_node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( append_node @ Ys3 @ ( cons_node @ X2 @ Zs3 ) ) )
% 0.31/0.47 & ( P @ X2 )
% 0.31/0.47 & ! [Xa: node] :
% 0.31/0.47 ( ( member_node @ Xa @ ( set_node2 @ Ys3 ) )
% 0.31/0.47 => ~ ( P @ Xa ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_list_first_prop
% 0.31/0.47 thf(fact_282_split__list__last__propE,axiom,
% 0.31/0.47 ! [Xs: list_node,P: node > $o] :
% 0.31/0.47 ( ? [X4: node] :
% 0.31/0.47 ( ( member_node @ X4 @ ( set_node2 @ Xs ) )
% 0.31/0.47 & ( P @ X4 ) )
% 0.31/0.47 => ~ ! [Ys3: list_node,X2: node,Zs3: list_node] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append_node @ Ys3 @ ( cons_node @ X2 @ Zs3 ) ) )
% 0.31/0.47 => ( ( P @ X2 )
% 0.31/0.47 => ~ ! [Xa: node] :
% 0.31/0.47 ( ( member_node @ Xa @ ( set_node2 @ Zs3 ) )
% 0.31/0.47 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_list_last_propE
% 0.31/0.47 thf(fact_283_split__list__first__propE,axiom,
% 0.31/0.47 ! [Xs: list_node,P: node > $o] :
% 0.31/0.47 ( ? [X4: node] :
% 0.31/0.47 ( ( member_node @ X4 @ ( set_node2 @ Xs ) )
% 0.31/0.47 & ( P @ X4 ) )
% 0.31/0.47 => ~ ! [Ys3: list_node,X2: node] :
% 0.31/0.47 ( ? [Zs3: list_node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( append_node @ Ys3 @ ( cons_node @ X2 @ Zs3 ) ) )
% 0.31/0.47 => ( ( P @ X2 )
% 0.31/0.47 => ~ ! [Xa: node] :
% 0.31/0.47 ( ( member_node @ Xa @ ( set_node2 @ Ys3 ) )
% 0.31/0.47 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_list_first_propE
% 0.31/0.47 thf(fact_284_in__set__conv__decomp__last,axiom,
% 0.31/0.47 ! [X: val,Xs: list_val] :
% 0.31/0.47 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.31/0.47 = ( ? [Ys2: list_val,Zs2: list_val] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs2 ) ) )
% 0.31/0.47 & ~ ( member_val @ X @ ( set_val2 @ Zs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_set_conv_decomp_last
% 0.31/0.47 thf(fact_285_in__set__conv__decomp__last,axiom,
% 0.31/0.47 ! [X: node,Xs: list_node] :
% 0.31/0.47 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.31/0.47 = ( ? [Ys2: list_node,Zs2: list_node] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs2 ) ) )
% 0.31/0.47 & ~ ( member_node @ X @ ( set_node2 @ Zs2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_set_conv_decomp_last
% 0.31/0.47 thf(fact_286_in__set__conv__decomp__first,axiom,
% 0.31/0.47 ! [X: val,Xs: list_val] :
% 0.31/0.47 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.31/0.47 = ( ? [Ys2: list_val,Zs2: list_val] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs2 ) ) )
% 0.31/0.47 & ~ ( member_val @ X @ ( set_val2 @ Ys2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_set_conv_decomp_first
% 0.31/0.47 thf(fact_287_in__set__conv__decomp__first,axiom,
% 0.31/0.47 ! [X: node,Xs: list_node] :
% 0.31/0.47 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.31/0.47 = ( ? [Ys2: list_node,Zs2: list_node] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs2 ) ) )
% 0.31/0.47 & ~ ( member_node @ X @ ( set_node2 @ Ys2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % in_set_conv_decomp_first
% 0.31/0.47 thf(fact_288_split__list__last__prop__iff,axiom,
% 0.31/0.47 ! [Xs: list_node,P: node > $o] :
% 0.31/0.47 ( ( ? [X3: node] :
% 0.31/0.47 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 0.31/0.47 & ( P @ X3 ) ) )
% 0.31/0.47 = ( ? [Ys2: list_node,X3: node,Zs2: list_node] :
% 0.31/0.47 ( ( Xs
% 0.31/0.47 = ( append_node @ Ys2 @ ( cons_node @ X3 @ Zs2 ) ) )
% 0.31/0.47 & ( P @ X3 )
% 0.31/0.47 & ! [Y2: node] :
% 0.31/0.47 ( ( member_node @ Y2 @ ( set_node2 @ Zs2 ) )
% 0.31/0.47 => ~ ( P @ Y2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_list_last_prop_iff
% 0.31/0.47 thf(fact_289_split__list__first__prop__iff,axiom,
% 0.31/0.47 ! [Xs: list_node,P: node > $o] :
% 0.31/0.47 ( ( ? [X3: node] :
% 0.31/0.47 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 0.31/0.47 & ( P @ X3 ) ) )
% 0.31/0.47 = ( ? [Ys2: list_node,X3: node] :
% 0.31/0.47 ( ? [Zs2: list_node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( append_node @ Ys2 @ ( cons_node @ X3 @ Zs2 ) ) )
% 0.31/0.47 & ( P @ X3 )
% 0.31/0.47 & ! [Y2: node] :
% 0.31/0.47 ( ( member_node @ Y2 @ ( set_node2 @ Ys2 ) )
% 0.31/0.47 => ~ ( P @ Y2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % split_list_first_prop_iff
% 0.31/0.47 thf(fact_290_distinct__singleton,axiom,
% 0.31/0.47 ! [X: produc1453890942D_node] : ( distin1098566007D_node @ ( cons_P1018517044D_node @ X @ nil_Pr1769730692D_node ) ) ).
% 0.31/0.47
% 0.31/0.47 % distinct_singleton
% 0.31/0.47 thf(fact_291_distinct__singleton,axiom,
% 0.31/0.47 ! [X: node] : ( distinct_node @ ( cons_node @ X @ nil_node ) ) ).
% 0.31/0.47
% 0.31/0.47 % distinct_singleton
% 0.31/0.47 thf(fact_292_distinct_Osimps_I2_J,axiom,
% 0.31/0.47 ! [X: val,Xs: list_val] :
% 0.31/0.47 ( ( distinct_val @ ( cons_val @ X @ Xs ) )
% 0.31/0.47 = ( ~ ( member_val @ X @ ( set_val2 @ Xs ) )
% 0.31/0.47 & ( distinct_val @ Xs ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % distinct.simps(2)
% 0.31/0.47 thf(fact_293_distinct_Osimps_I2_J,axiom,
% 0.31/0.47 ! [X: node,Xs: list_node] :
% 0.31/0.47 ( ( distinct_node @ ( cons_node @ X @ Xs ) )
% 0.31/0.47 = ( ~ ( member_node @ X @ ( set_node2 @ Xs ) )
% 0.31/0.47 & ( distinct_node @ Xs ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % distinct.simps(2)
% 0.31/0.47 thf(fact_294_distinct__match,axiom,
% 0.31/0.47 ! [Al: list_node,E: node,Bl: list_node,Al2: list_node,Bl2: list_node] :
% 0.31/0.47 ( ( distinct_node @ ( append_node @ Al @ ( cons_node @ E @ Bl ) ) )
% 0.31/0.47 => ( ( ( append_node @ Al @ ( cons_node @ E @ Bl ) )
% 0.31/0.47 = ( append_node @ Al2 @ ( cons_node @ E @ Bl2 ) ) )
% 0.31/0.47 = ( ( Al = Al2 )
% 0.31/0.47 & ( Bl = Bl2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % distinct_match
% 0.31/0.47 thf(fact_295_Nil__tl,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node] :
% 0.31/0.47 ( ( nil_Pr1769730692D_node
% 0.31/0.47 = ( tl_Pro1633633005D_node @ Xs ) )
% 0.31/0.47 = ( ( Xs = nil_Pr1769730692D_node )
% 0.31/0.47 | ? [X3: produc1453890942D_node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( cons_P1018517044D_node @ X3 @ nil_Pr1769730692D_node ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Nil_tl
% 0.31/0.47 thf(fact_296_Nil__tl,axiom,
% 0.31/0.47 ! [Xs: list_node] :
% 0.31/0.47 ( ( nil_node
% 0.31/0.47 = ( tl_node @ Xs ) )
% 0.31/0.47 = ( ( Xs = nil_node )
% 0.31/0.47 | ? [X3: node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( cons_node @ X3 @ nil_node ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Nil_tl
% 0.31/0.47 thf(fact_297_tl__Nil,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node] :
% 0.31/0.47 ( ( ( tl_Pro1633633005D_node @ Xs )
% 0.31/0.47 = nil_Pr1769730692D_node )
% 0.31/0.47 = ( ( Xs = nil_Pr1769730692D_node )
% 0.31/0.47 | ? [X3: produc1453890942D_node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( cons_P1018517044D_node @ X3 @ nil_Pr1769730692D_node ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % tl_Nil
% 0.31/0.47 thf(fact_298_tl__Nil,axiom,
% 0.31/0.47 ! [Xs: list_node] :
% 0.31/0.47 ( ( ( tl_node @ Xs )
% 0.31/0.47 = nil_node )
% 0.31/0.47 = ( ( Xs = nil_node )
% 0.31/0.47 | ? [X3: node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 = ( cons_node @ X3 @ nil_node ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % tl_Nil
% 0.31/0.47 thf(fact_299_tl__obtain__elem,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node] :
% 0.31/0.47 ( ( Xs != nil_Pr1769730692D_node )
% 0.31/0.47 => ( ( ( tl_Pro1633633005D_node @ Xs )
% 0.31/0.47 = nil_Pr1769730692D_node )
% 0.31/0.47 => ~ ! [E4: produc1453890942D_node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 != ( cons_P1018517044D_node @ E4 @ nil_Pr1769730692D_node ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % tl_obtain_elem
% 0.31/0.47 thf(fact_300_tl__obtain__elem,axiom,
% 0.31/0.47 ! [Xs: list_node] :
% 0.31/0.47 ( ( Xs != nil_node )
% 0.31/0.47 => ( ( ( tl_node @ Xs )
% 0.31/0.47 = nil_node )
% 0.31/0.47 => ~ ! [E4: node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 != ( cons_node @ E4 @ nil_node ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % tl_obtain_elem
% 0.31/0.47 thf(fact_301_not__distinct__decomp,axiom,
% 0.31/0.47 ! [Ws: list_P738500740D_node] :
% 0.31/0.47 ( ~ ( distin1098566007D_node @ Ws )
% 0.31/0.47 => ? [Xs2: list_P738500740D_node,Ys3: list_P738500740D_node,Zs3: list_P738500740D_node,Y4: produc1453890942D_node] :
% 0.31/0.47 ( Ws
% 0.31/0.47 = ( append2096883353D_node @ Xs2 @ ( append2096883353D_node @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) @ ( append2096883353D_node @ Ys3 @ ( append2096883353D_node @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) @ Zs3 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_distinct_decomp
% 0.31/0.47 thf(fact_302_not__distinct__decomp,axiom,
% 0.31/0.47 ! [Ws: list_node] :
% 0.31/0.47 ( ~ ( distinct_node @ Ws )
% 0.31/0.47 => ? [Xs2: list_node,Ys3: list_node,Zs3: list_node,Y4: node] :
% 0.31/0.47 ( Ws
% 0.31/0.47 = ( append_node @ Xs2 @ ( append_node @ ( cons_node @ Y4 @ nil_node ) @ ( append_node @ Ys3 @ ( append_node @ ( cons_node @ Y4 @ nil_node ) @ Zs3 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_distinct_decomp
% 0.31/0.47 thf(fact_303_not__distinct__conv__prefix,axiom,
% 0.31/0.47 ! [As2: list_val] :
% 0.31/0.47 ( ( ~ ( distinct_val @ As2 ) )
% 0.31/0.47 = ( ? [Xs3: list_val,Y2: val,Ys2: list_val] :
% 0.31/0.47 ( ( member_val @ Y2 @ ( set_val2 @ Xs3 ) )
% 0.31/0.47 & ( distinct_val @ Xs3 )
% 0.31/0.47 & ( As2
% 0.31/0.47 = ( append_val @ Xs3 @ ( cons_val @ Y2 @ Ys2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_distinct_conv_prefix
% 0.31/0.47 thf(fact_304_not__distinct__conv__prefix,axiom,
% 0.31/0.47 ! [As2: list_node] :
% 0.31/0.47 ( ( ~ ( distinct_node @ As2 ) )
% 0.31/0.47 = ( ? [Xs3: list_node,Y2: node,Ys2: list_node] :
% 0.31/0.47 ( ( member_node @ Y2 @ ( set_node2 @ Xs3 ) )
% 0.31/0.47 & ( distinct_node @ Xs3 )
% 0.31/0.47 & ( As2
% 0.31/0.47 = ( append_node @ Xs3 @ ( cons_node @ Y2 @ Ys2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_distinct_conv_prefix
% 0.31/0.47 thf(fact_305_not__suffix__induct,axiom,
% 0.31/0.47 ! [Ps: list_P738500740D_node,Ls: list_P738500740D_node,P: list_P738500740D_node > list_P738500740D_node > $o] :
% 0.31/0.47 ( ~ ( suffix1143830554D_node @ Ps @ Ls )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] : ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ nil_Pr1769730692D_node )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( X2 != Y4 )
% 0.31/0.47 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) )
% 0.31/0.47 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( X2 = Y4 )
% 0.31/0.47 => ( ~ ( suffix1143830554D_node @ Xs2 @ Ys3 )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) ) ) )
% 0.31/0.47 => ( P @ Ps @ Ls ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_suffix_induct
% 0.31/0.47 thf(fact_306_not__suffix__induct,axiom,
% 0.31/0.47 ! [Ps: list_node,Ls: list_node,P: list_node > list_node > $o] :
% 0.31/0.47 ( ~ ( suffix_node @ Ps @ Ls )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node] : ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ nil_node )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ( X2 != Y4 )
% 0.31/0.47 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) )
% 0.31/0.47 => ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 0.31/0.47 ( ( X2 = Y4 )
% 0.31/0.47 => ( ~ ( suffix_node @ Xs2 @ Ys3 )
% 0.31/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.31/0.47 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) ) ) )
% 0.31/0.47 => ( P @ Ps @ Ls ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_suffix_induct
% 0.31/0.47 thf(fact_307_not__suffix__cases,axiom,
% 0.31/0.47 ! [Ps: list_P738500740D_node,Ls: list_P738500740D_node] :
% 0.31/0.47 ( ~ ( suffix1143830554D_node @ Ps @ Ls )
% 0.31/0.47 => ( ( ( Ps != nil_Pr1769730692D_node )
% 0.31/0.47 => ( Ls != nil_Pr1769730692D_node ) )
% 0.31/0.47 => ( ! [A3: produc1453890942D_node,As: list_P738500740D_node] :
% 0.31/0.47 ( ( Ps
% 0.31/0.47 = ( append2096883353D_node @ As @ ( cons_P1018517044D_node @ A3 @ nil_Pr1769730692D_node ) ) )
% 0.31/0.47 => ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 0.31/0.47 ( ( Ls
% 0.31/0.47 = ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) )
% 0.31/0.47 => ( ( X2 = A3 )
% 0.31/0.47 => ( suffix1143830554D_node @ As @ Xs2 ) ) ) )
% 0.31/0.47 => ~ ! [A3: produc1453890942D_node] :
% 0.31/0.47 ( ? [As: list_P738500740D_node] :
% 0.31/0.47 ( Ps
% 0.31/0.47 = ( append2096883353D_node @ As @ ( cons_P1018517044D_node @ A3 @ nil_Pr1769730692D_node ) ) )
% 0.31/0.47 => ! [X2: produc1453890942D_node] :
% 0.31/0.47 ( ? [Xs2: list_P738500740D_node] :
% 0.31/0.47 ( Ls
% 0.31/0.47 = ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) )
% 0.31/0.47 => ( X2 = A3 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_suffix_cases
% 0.31/0.47 thf(fact_308_not__suffix__cases,axiom,
% 0.31/0.47 ! [Ps: list_node,Ls: list_node] :
% 0.31/0.47 ( ~ ( suffix_node @ Ps @ Ls )
% 0.31/0.47 => ( ( ( Ps != nil_node )
% 0.31/0.47 => ( Ls != nil_node ) )
% 0.31/0.47 => ( ! [A3: node,As: list_node] :
% 0.31/0.47 ( ( Ps
% 0.31/0.47 = ( append_node @ As @ ( cons_node @ A3 @ nil_node ) ) )
% 0.31/0.47 => ! [X2: node,Xs2: list_node] :
% 0.31/0.47 ( ( Ls
% 0.31/0.47 = ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) )
% 0.31/0.47 => ( ( X2 = A3 )
% 0.31/0.47 => ( suffix_node @ As @ Xs2 ) ) ) )
% 0.31/0.47 => ~ ! [A3: node] :
% 0.31/0.47 ( ? [As: list_node] :
% 0.31/0.47 ( Ps
% 0.31/0.47 = ( append_node @ As @ ( cons_node @ A3 @ nil_node ) ) )
% 0.31/0.47 => ! [X2: node] :
% 0.31/0.47 ( ? [Xs2: list_node] :
% 0.31/0.47 ( Ls
% 0.31/0.47 = ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) )
% 0.31/0.47 => ( X2 = A3 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_suffix_cases
% 0.31/0.47 thf(fact_309_list_Oexhaust__sel,axiom,
% 0.31/0.47 ! [List: list_P738500740D_node] :
% 0.31/0.47 ( ( List != nil_Pr1769730692D_node )
% 0.31/0.47 => ( List
% 0.31/0.47 = ( cons_P1018517044D_node @ ( hd_Pro1395892457D_node @ List ) @ ( tl_Pro1633633005D_node @ List ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.exhaust_sel
% 0.31/0.47 thf(fact_310_list_Oexhaust__sel,axiom,
% 0.31/0.47 ! [List: list_node] :
% 0.31/0.47 ( ( List != nil_node )
% 0.31/0.47 => ( List
% 0.31/0.47 = ( cons_node @ ( hd_node @ List ) @ ( tl_node @ List ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % list.exhaust_sel
% 0.31/0.47 thf(fact_311_not__distinct__split__distinct,axiom,
% 0.31/0.47 ! [Xs: list_val] :
% 0.31/0.47 ( ~ ( distinct_val @ Xs )
% 0.31/0.47 => ~ ! [Y4: val,Ys3: list_val] :
% 0.31/0.47 ( ( distinct_val @ Ys3 )
% 0.31/0.47 => ( ( member_val @ Y4 @ ( set_val2 @ Ys3 ) )
% 0.31/0.47 => ! [Zs3: list_val] :
% 0.31/0.47 ( Xs
% 0.31/0.47 != ( append_val @ Ys3 @ ( append_val @ ( cons_val @ Y4 @ nil_val ) @ Zs3 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_distinct_split_distinct
% 0.31/0.47 thf(fact_312_not__distinct__split__distinct,axiom,
% 0.31/0.47 ! [Xs: list_P738500740D_node] :
% 0.31/0.47 ( ~ ( distin1098566007D_node @ Xs )
% 0.31/0.47 => ~ ! [Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 0.31/0.47 ( ( distin1098566007D_node @ Ys3 )
% 0.31/0.47 => ( ( member1797643303D_node @ Y4 @ ( set_Pr1238794387D_node @ Ys3 ) )
% 0.31/0.47 => ! [Zs3: list_P738500740D_node] :
% 0.31/0.47 ( Xs
% 0.31/0.47 != ( append2096883353D_node @ Ys3 @ ( append2096883353D_node @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) @ Zs3 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_distinct_split_distinct
% 0.31/0.47 thf(fact_313_not__distinct__split__distinct,axiom,
% 0.31/0.47 ! [Xs: list_node] :
% 0.31/0.47 ( ~ ( distinct_node @ Xs )
% 0.31/0.48 => ~ ! [Y4: node,Ys3: list_node] :
% 0.31/0.48 ( ( distinct_node @ Ys3 )
% 0.31/0.48 => ( ( member_node @ Y4 @ ( set_node2 @ Ys3 ) )
% 0.31/0.48 => ! [Zs3: list_node] :
% 0.31/0.48 ( Xs
% 0.31/0.48 != ( append_node @ Ys3 @ ( append_node @ ( cons_node @ Y4 @ nil_node ) @ Zs3 ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % not_distinct_split_distinct
% 0.31/0.48 thf(fact_314_append__eq__append__conv2,axiom,
% 0.31/0.48 ! [Xs: list_node,Ys: list_node,Zs: list_node,Ts: list_node] :
% 0.31/0.48 ( ( ( append_node @ Xs @ Ys )
% 0.31/0.48 = ( append_node @ Zs @ Ts ) )
% 0.31/0.48 = ( ? [Us: list_node] :
% 0.31/0.48 ( ( ( Xs
% 0.31/0.48 = ( append_node @ Zs @ Us ) )
% 0.31/0.48 & ( ( append_node @ Us @ Ys )
% 0.31/0.48 = Ts ) )
% 0.31/0.48 | ( ( ( append_node @ Xs @ Us )
% 0.31/0.48 = Zs )
% 0.31/0.48 & ( Ys
% 0.31/0.48 = ( append_node @ Us @ Ts ) ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % append_eq_append_conv2
% 0.31/0.48 thf(fact_315_append__eq__appendI,axiom,
% 0.31/0.48 ! [Xs: list_node,Xs1: list_node,Zs: list_node,Ys: list_node,Us2: list_node] :
% 0.31/0.48 ( ( ( append_node @ Xs @ Xs1 )
% 0.31/0.48 = Zs )
% 0.31/0.48 => ( ( Ys
% 0.31/0.48 = ( append_node @ Xs1 @ Us2 ) )
% 0.31/0.48 => ( ( append_node @ Xs @ Ys )
% 0.31/0.48 = ( append_node @ Zs @ Us2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % append_eq_appendI
% 0.31/0.48 thf(fact_316_suffix__order_Odual__order_Oantisym,axiom,
% 0.31/0.48 ! [B: list_node,A: list_node] :
% 0.31/0.48 ( ( suffix_node @ B @ A )
% 0.31/0.48 => ( ( suffix_node @ A @ B )
% 0.31/0.48 => ( A = B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_order.dual_order.antisym
% 0.31/0.48 thf(fact_317_suffix__order_Odual__order_Oeq__iff,axiom,
% 0.31/0.48 ( ( ^ [Y5: list_node,Z: list_node] : ( Y5 = Z ) )
% 0.31/0.48 = ( ^ [A4: list_node,B3: list_node] :
% 0.31/0.48 ( ( suffix_node @ B3 @ A4 )
% 0.31/0.48 & ( suffix_node @ A4 @ B3 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_order.dual_order.eq_iff
% 0.31/0.48 thf(fact_318_suffix__order_Odual__order_Otrans,axiom,
% 0.31/0.48 ! [B: list_node,A: list_node,C: list_node] :
% 0.31/0.48 ( ( suffix_node @ B @ A )
% 0.31/0.48 => ( ( suffix_node @ C @ B )
% 0.31/0.48 => ( suffix_node @ C @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_order.dual_order.trans
% 0.31/0.48 thf(fact_319_suffix__order_Oord__le__eq__trans,axiom,
% 0.31/0.48 ! [A: list_node,B: list_node,C: list_node] :
% 0.31/0.48 ( ( suffix_node @ A @ B )
% 0.31/0.48 => ( ( B = C )
% 0.31/0.48 => ( suffix_node @ A @ C ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_order.ord_le_eq_trans
% 0.31/0.48 thf(fact_320_suffix__order_Oord__eq__le__trans,axiom,
% 0.31/0.48 ! [A: list_node,B: list_node,C: list_node] :
% 0.31/0.48 ( ( A = B )
% 0.31/0.48 => ( ( suffix_node @ B @ C )
% 0.31/0.48 => ( suffix_node @ A @ C ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_order.ord_eq_le_trans
% 0.31/0.48 thf(fact_321_suffix__order_Oorder_Oantisym,axiom,
% 0.31/0.48 ! [A: list_node,B: list_node] :
% 0.31/0.48 ( ( suffix_node @ A @ B )
% 0.31/0.48 => ( ( suffix_node @ B @ A )
% 0.31/0.48 => ( A = B ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_order.order.antisym
% 0.31/0.48 thf(fact_322_suffix__order_Oorder_Oeq__iff,axiom,
% 0.31/0.48 ( ( ^ [Y5: list_node,Z: list_node] : ( Y5 = Z ) )
% 0.31/0.48 = ( ^ [A4: list_node,B3: list_node] :
% 0.31/0.48 ( ( suffix_node @ A4 @ B3 )
% 0.31/0.48 & ( suffix_node @ B3 @ A4 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_order.order.eq_iff
% 0.31/0.48 thf(fact_323_suffix__order_Oantisym__conv,axiom,
% 0.31/0.48 ! [Y3: list_node,X: list_node] :
% 0.31/0.48 ( ( suffix_node @ Y3 @ X )
% 0.31/0.48 => ( ( suffix_node @ X @ Y3 )
% 0.31/0.48 = ( X = Y3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_order.antisym_conv
% 0.31/0.48 thf(fact_324_suffix__order_Oorder__trans,axiom,
% 0.31/0.48 ! [X: list_node,Y3: list_node,Z3: list_node] :
% 0.31/0.48 ( ( suffix_node @ X @ Y3 )
% 0.31/0.48 => ( ( suffix_node @ Y3 @ Z3 )
% 0.31/0.48 => ( suffix_node @ X @ Z3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_order.order_trans
% 0.31/0.48 thf(fact_325_suffix__order_Oorder_Otrans,axiom,
% 0.31/0.48 ! [A: list_node,B: list_node,C: list_node] :
% 0.31/0.48 ( ( suffix_node @ A @ B )
% 0.31/0.48 => ( ( suffix_node @ B @ C )
% 0.31/0.48 => ( suffix_node @ A @ C ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_order.order.trans
% 0.31/0.48 thf(fact_326_suffix__order_Oeq__refl,axiom,
% 0.31/0.48 ! [X: list_node,Y3: list_node] :
% 0.31/0.48 ( ( X = Y3 )
% 0.31/0.48 => ( suffix_node @ X @ Y3 ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_order.eq_refl
% 0.31/0.48 thf(fact_327_suffix__order_Oantisym,axiom,
% 0.31/0.48 ! [X: list_node,Y3: list_node] :
% 0.31/0.48 ( ( suffix_node @ X @ Y3 )
% 0.31/0.48 => ( ( suffix_node @ Y3 @ X )
% 0.31/0.48 => ( X = Y3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_order.antisym
% 0.31/0.48 thf(fact_328_suffix__order_Oeq__iff,axiom,
% 0.31/0.48 ( ( ^ [Y5: list_node,Z: list_node] : ( Y5 = Z ) )
% 0.31/0.48 = ( ^ [X3: list_node,Y2: list_node] :
% 0.31/0.48 ( ( suffix_node @ X3 @ Y2 )
% 0.31/0.48 & ( suffix_node @ Y2 @ X3 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_order.eq_iff
% 0.31/0.48 thf(fact_329_suffix__same__cases,axiom,
% 0.31/0.48 ! [Xs_1: list_node,Ys: list_node,Xs_2: list_node] :
% 0.31/0.48 ( ( suffix_node @ Xs_1 @ Ys )
% 0.31/0.48 => ( ( suffix_node @ Xs_2 @ Ys )
% 0.31/0.48 => ( ( suffix_node @ Xs_1 @ Xs_2 )
% 0.31/0.48 | ( suffix_node @ Xs_2 @ Xs_1 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_same_cases
% 0.31/0.48 thf(fact_330_finite__list,axiom,
% 0.31/0.48 ! [A2: set_node] :
% 0.31/0.48 ( ( finite_finite_node @ A2 )
% 0.31/0.48 => ? [Xs2: list_node] :
% 0.31/0.48 ( ( set_node2 @ Xs2 )
% 0.31/0.48 = A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % finite_list
% 0.31/0.48 thf(fact_331_finite__list,axiom,
% 0.31/0.48 ! [A2: set_val] :
% 0.31/0.48 ( ( finite_finite_val @ A2 )
% 0.31/0.48 => ? [Xs2: list_val] :
% 0.31/0.48 ( ( set_val2 @ Xs2 )
% 0.31/0.48 = A2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % finite_list
% 0.31/0.48 thf(fact_332_append_Oleft__neutral,axiom,
% 0.31/0.48 ! [A: list_node] :
% 0.31/0.48 ( ( append_node @ nil_node @ A )
% 0.31/0.48 = A ) ).
% 0.31/0.48
% 0.31/0.48 % append.left_neutral
% 0.31/0.48 thf(fact_333_append_Oleft__neutral,axiom,
% 0.31/0.48 ! [A: list_P738500740D_node] :
% 0.31/0.48 ( ( append2096883353D_node @ nil_Pr1769730692D_node @ A )
% 0.31/0.48 = A ) ).
% 0.31/0.48
% 0.31/0.48 % append.left_neutral
% 0.31/0.48 thf(fact_334_append__Nil,axiom,
% 0.31/0.48 ! [Ys: list_node] :
% 0.31/0.48 ( ( append_node @ nil_node @ Ys )
% 0.31/0.48 = Ys ) ).
% 0.31/0.48
% 0.31/0.48 % append_Nil
% 0.31/0.48 thf(fact_335_append__Nil,axiom,
% 0.31/0.48 ! [Ys: list_P738500740D_node] :
% 0.31/0.48 ( ( append2096883353D_node @ nil_Pr1769730692D_node @ Ys )
% 0.31/0.48 = Ys ) ).
% 0.31/0.48
% 0.31/0.48 % append_Nil
% 0.31/0.48 thf(fact_336_eq__Nil__appendI,axiom,
% 0.31/0.48 ! [Xs: list_node,Ys: list_node] :
% 0.31/0.48 ( ( Xs = Ys )
% 0.31/0.48 => ( Xs
% 0.31/0.48 = ( append_node @ nil_node @ Ys ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % eq_Nil_appendI
% 0.31/0.48 thf(fact_337_eq__Nil__appendI,axiom,
% 0.31/0.48 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 0.31/0.48 ( ( Xs = Ys )
% 0.31/0.48 => ( Xs
% 0.31/0.48 = ( append2096883353D_node @ nil_Pr1769730692D_node @ Ys ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % eq_Nil_appendI
% 0.31/0.48 thf(fact_338_distinct_Osimps_I1_J,axiom,
% 0.31/0.48 distinct_node @ nil_node ).
% 0.31/0.48
% 0.31/0.48 % distinct.simps(1)
% 0.31/0.48 thf(fact_339_distinct_Osimps_I1_J,axiom,
% 0.31/0.48 distin1098566007D_node @ nil_Pr1769730692D_node ).
% 0.31/0.48
% 0.31/0.48 % distinct.simps(1)
% 0.31/0.48 thf(fact_340_suffix__bot_Obot_Oextremum__uniqueI,axiom,
% 0.31/0.48 ! [A: list_P738500740D_node] :
% 0.31/0.48 ( ( suffix1143830554D_node @ A @ nil_Pr1769730692D_node )
% 0.31/0.48 => ( A = nil_Pr1769730692D_node ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_bot.bot.extremum_uniqueI
% 0.31/0.48 thf(fact_341_suffix__bot_Obot_Oextremum__uniqueI,axiom,
% 0.31/0.48 ! [A: list_node] :
% 0.31/0.48 ( ( suffix_node @ A @ nil_node )
% 0.31/0.48 => ( A = nil_node ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_bot.bot.extremum_uniqueI
% 0.31/0.48 thf(fact_342_suffix__bot_Obot_Oextremum,axiom,
% 0.31/0.48 ! [A: list_P738500740D_node] : ( suffix1143830554D_node @ nil_Pr1769730692D_node @ A ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_bot.bot.extremum
% 0.31/0.48 thf(fact_343_suffix__bot_Obot_Oextremum,axiom,
% 0.31/0.48 ! [A: list_node] : ( suffix_node @ nil_node @ A ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_bot.bot.extremum
% 0.31/0.48 thf(fact_344_Nil__suffix,axiom,
% 0.31/0.48 ! [Xs: list_P738500740D_node] : ( suffix1143830554D_node @ nil_Pr1769730692D_node @ Xs ) ).
% 0.31/0.48
% 0.31/0.48 % Nil_suffix
% 0.31/0.48 thf(fact_345_Nil__suffix,axiom,
% 0.31/0.48 ! [Xs: list_node] : ( suffix_node @ nil_node @ Xs ) ).
% 0.31/0.48
% 0.31/0.48 % Nil_suffix
% 0.31/0.48 thf(fact_346_list_Osel_I2_J,axiom,
% 0.31/0.48 ( ( tl_node @ nil_node )
% 0.31/0.48 = nil_node ) ).
% 0.31/0.48
% 0.31/0.48 % list.sel(2)
% 0.31/0.48 thf(fact_347_list_Osel_I2_J,axiom,
% 0.31/0.48 ( ( tl_Pro1633633005D_node @ nil_Pr1769730692D_node )
% 0.31/0.48 = nil_Pr1769730692D_node ) ).
% 0.31/0.48
% 0.31/0.48 % list.sel(2)
% 0.31/0.48 thf(fact_348_suffix__appendI,axiom,
% 0.31/0.48 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 0.31/0.48 ( ( suffix_node @ Xs @ Ys )
% 0.31/0.48 => ( suffix_node @ Xs @ ( append_node @ Zs @ Ys ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_appendI
% 0.31/0.48 thf(fact_349_suffix__appendD,axiom,
% 0.31/0.48 ! [Zs: list_node,Xs: list_node,Ys: list_node] :
% 0.31/0.48 ( ( suffix_node @ ( append_node @ Zs @ Xs ) @ Ys )
% 0.31/0.48 => ( suffix_node @ Xs @ Ys ) ) ).
% 0.31/0.48
% 0.31/0.48 % suffix_appendD
% 0.31/0.48 thf(fact_350_old_OEntry__unreachable,axiom,
% 0.31/0.48 ! [G: g] :
% 0.31/0.48 ( ( invar @ G )
% 0.31/0.48 => ( ( graph_1947481694_edgeD @ inEdges @ G @ ( entry @ G ) )
% 0.31/0.48 = nil_Pr1769730692D_node ) ) ).
% 0.31/0.48
% 0.31/0.48 % old.Entry_unreachable
% 0.31/0.48
% 0.31/0.48 % Conjectures (1)
% 0.31/0.48 thf(conj_0,conjecture,
% 0.31/0.48 ~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ) ).
% 0.31/0.48
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 ------------------------
% 2.65/1.55 ---- Embedded in THF ---
% 2.65/1.55 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.65/1.55 %%% Generated on Tue Feb 24 08:25:43 EST 2026
% 2.65/1.55 %%% using '$$dhol' embedding, version 1.3.0.
% 2.65/1.55 %%% Logic specification used:
% 2.65/1.55 %%% thf(spec, logic, $$dhol).
% 2.65/1.55
% 2.65/1.55 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.zlt6T4WObL/DTF2DTF2101.p
% See solution above
% 2.65/1.55 ------------------------
% 2.65/1.59 ---- Cleaned THF ---
% 2.65/1.59 thf(ty_n_t__List__Olist_It__List__Olist_It__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J_J_J,type,
% 2.65/1.59 list_l1129649930D_node: $tType ).
% 2.65/1.59
% 2.65/1.59 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J_J,type,
% 2.65/1.59 list_P738500740D_node: $tType ).
% 2.65/1.59
% 2.65/1.59 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J_J,type,
% 2.65/1.59 set_Pr1040144478D_node: $tType ).
% 2.65/1.59
% 2.65/1.59 thf(ty_n_t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 2.65/1.59 produc1453890942D_node: $tType ).
% 2.65/1.59
% 2.65/1.59 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_Itf__node_Mtf__edgeD_J_J,type,
% 2.65/1.59 list_P561207620_edgeD: $tType ).
% 2.65/1.59
% 2.65/1.59 thf(ty_n_t__Option__Ooption_It__List__Olist_Itf__val_J_J,type,
% 2.65/1.59 option_list_val: $tType ).
% 2.65/1.59
% 2.65/1.59 thf(ty_n_t__Product____Type__Oprod_Itf__node_Mtf__val_J,type,
% 2.65/1.59 produc1432036078de_val: $tType ).
% 2.65/1.59
% 2.65/1.59 thf(ty_n_t__List__Olist_It__List__Olist_Itf__node_J_J,type,
% 2.65/1.59 list_list_node: $tType ).
% 2.65/1.59
% 2.65/1.59 thf(ty_n_t__List__Olist_Itf__node_J,type,
% 2.65/1.59 list_node: $tType ).
% 2.65/1.59
% 2.65/1.59 thf(ty_n_t__List__Olist_Itf__val_J,type,
% 2.65/1.59 list_val: $tType ).
% 2.65/1.59
% 2.65/1.59 thf(ty_n_t__Set__Oset_Itf__node_J,type,
% 2.65/1.59 set_node: $tType ).
% 2.65/1.59
% 2.65/1.59 thf(ty_n_t__Set__Oset_Itf__val_J,type,
% 2.65/1.59 set_val: $tType ).
% 2.65/1.59
% 2.65/1.59 thf(ty_n_tf__node,type,
% 2.65/1.59 node: $tType ).
% 2.65/1.59
% 2.65/1.59 thf(ty_n_tf__val,type,
% 2.65/1.59 val: $tType ).
% 2.65/1.59
% 2.65/1.59 thf(ty_n_tf__g,type,
% 2.65/1.59 g: $tType ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_Finite__Set_Ofinite_001tf__node,type,
% 2.65/1.59 finite_finite_node: set_node > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_Finite__Set_Ofinite_001tf__val,type,
% 2.65/1.59 finite_finite_val: set_val > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_Graph__path_Ograph__Entry_OEntryPath_001tf__g_001tf__node_001tf__edgeD,type,
% 2.65/1.59 graph_1994935542_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > list_node > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_Graph__path_Ograph__Entry_OisIdom_001tf__g_001tf__node_001tf__edgeD,type,
% 2.65/1.59 graph_1670286392_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > node > node > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_Graph__path_Ograph__Entry__base_Odominates_001tf__g_001tf__node_001tf__edgeD,type,
% 2.65/1.59 graph_436675702_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > node > node > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_Graph__path_Ograph__path__base_OinEdges_001tf__g_001tf__node_001tf__edgeD,type,
% 2.65/1.59 graph_1947481694_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_P738500740D_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_Graph__path_Ograph__path__base_Opath2_001tf__g_001tf__node_001tf__edgeD,type,
% 2.65/1.59 graph_1012773594_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > g > node > list_node > node > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_Graph__path_Ograph__path__base_Opredecessors_001tf__g_001tf__node_001tf__edgeD,type,
% 2.65/1.59 graph_272749361_edgeD: ( g > node > list_P561207620_edgeD ) > g > node > list_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Oappend_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 2.65/1.59 append2096883353D_node: list_P738500740D_node > list_P738500740D_node > list_P738500740D_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Oappend_001tf__node,type,
% 2.65/1.59 append_node: list_node > list_node > list_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Oappend_001tf__val,type,
% 2.65/1.59 append_val: list_val > list_val > list_val ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Odistinct_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 2.65/1.59 distin1098566007D_node: list_P738500740D_node > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Odistinct_001tf__node,type,
% 2.65/1.59 distinct_node: list_node > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Odistinct_001tf__val,type,
% 2.65/1.59 distinct_val: list_val > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J_J,type,
% 2.65/1.59 cons_l1288865338D_node: list_P738500740D_node > list_l1129649930D_node > list_l1129649930D_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_OCons_001t__List__Olist_Itf__node_J,type,
% 2.65/1.59 cons_list_node: list_node > list_list_node > list_list_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 2.65/1.59 cons_P1018517044D_node: produc1453890942D_node > list_P738500740D_node > list_P738500740D_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_OCons_001tf__node,type,
% 2.65/1.59 cons_node: node > list_node > list_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_OCons_001tf__val,type,
% 2.65/1.59 cons_val: val > list_val > list_val ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J_J,type,
% 2.65/1.59 nil_li1626782346D_node: list_l1129649930D_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_ONil_001t__List__Olist_Itf__node_J,type,
% 2.65/1.59 nil_list_node: list_list_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_ONil_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 2.65/1.59 nil_Pr1769730692D_node: list_P738500740D_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_ONil_001tf__node,type,
% 2.65/1.59 nil_node: list_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_ONil_001tf__val,type,
% 2.65/1.59 nil_val: list_val ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_Ohd_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 2.65/1.59 hd_Pro1395892457D_node: list_P738500740D_node > produc1453890942D_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_Ohd_001tf__node,type,
% 2.65/1.59 hd_node: list_node > node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_Ohd_001tf__val,type,
% 2.65/1.59 hd_val: list_val > val ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 2.65/1.59 set_Pr1238794387D_node: list_P738500740D_node > set_Pr1040144478D_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_Oset_001tf__node,type,
% 2.65/1.59 set_node2: list_node > set_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_Oset_001tf__val,type,
% 2.65/1.59 set_val2: list_val > set_val ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_Otl_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 2.65/1.59 tl_Pro1633633005D_node: list_P738500740D_node > list_P738500740D_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_Otl_001tf__node,type,
% 2.65/1.59 tl_node: list_node > list_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_List_Olist_Otl_001tf__val,type,
% 2.65/1.59 tl_val: list_val > list_val ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_Minimality_Ograph__Entry_Oreducible_001tf__g_001tf__node_001tf__edgeD,type,
% 2.65/1.59 graph_589078910_edgeD: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > g > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_SSA__CFG_OCFG__SSA__base_OallDefs_001tf__g_001tf__node_001tf__val,type,
% 2.65/1.59 sSA_CF139593942de_val: ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_SSA__CFG_OCFG__SSA__base_OdefAss_001tf__g_001tf__node_001tf__edgeD_001tf__val,type,
% 2.65/1.59 sSA_CF1156973626eD_val: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > node > val > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiDefs_001tf__g_001tf__node_001tf__val,type,
% 2.65/1.59 sSA_CF370335846de_val: ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_SSA__CFG_OCFG__SSA__base_OphiUses_001tf__g_001tf__node_001tf__edgeD_001tf__val,type,
% 2.65/1.59 sSA_CF848637139eD_val: ( g > list_node ) > ( g > node > list_P561207620_edgeD ) > ( g > produc1432036078de_val > option_list_val ) > g > node > set_val ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OdefNode_001tf__g_001tf__node_001tf__val,type,
% 2.65/1.59 sSA_CF551432799de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_SSA__CFG_OCFG__SSA__wf__base_OphiArg_001tf__g_001tf__node_001tf__val,type,
% 2.65/1.59 sSA_CF1252180629de_val: ( g > list_node ) > ( g > node > set_val ) > ( g > produc1432036078de_val > option_list_val ) > g > val > val > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_SSA__CFG_OCFG__base_OdefAss_H_001tf__g_001tf__node_001tf__edgeD_001tf__val,type,
% 2.65/1.59 sSA_CF1558836456eD_val: ( g > list_node ) > ( g > $o ) > ( g > node > list_P561207620_edgeD ) > ( g > node ) > ( g > node > set_val ) > g > node > val > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_Set_OCollect_001tf__node,type,
% 2.65/1.59 collect_node: ( node > $o ) > set_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_Set_OCollect_001tf__val,type,
% 2.65/1.59 collect_val: ( val > $o ) > set_val ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_Sublist_Osuffix_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 2.65/1.59 suffix1143830554D_node: list_P738500740D_node > list_P738500740D_node > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_Sublist_Osuffix_001tf__node,type,
% 2.65/1.59 suffix_node: list_node > list_node > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_member_001t__Product____Type__Oprod_Itf__node_Mt__Product____Type__Oprod_Itf__edgeD_Mtf__node_J_J,type,
% 2.65/1.59 member1797643303D_node: produc1453890942D_node > set_Pr1040144478D_node > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_member_001tf__node,type,
% 2.65/1.59 member_node: node > set_node > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_c_member_001tf__val,type,
% 2.65/1.59 member_val: val > set_val > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v_Entry,type,
% 2.65/1.59 entry: g > node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v__092_060alpha_062n,type,
% 2.65/1.59 alpha_n: g > list_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v__092_060phi_062_092_060_094sub_062r,type,
% 2.65/1.59 phi_r: val ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v_defs,type,
% 2.65/1.59 defs: g > node > set_val ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v_g,type,
% 2.65/1.59 g2: g ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v_inEdges_H,type,
% 2.65/1.59 inEdges: g > node > list_P561207620_edgeD ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v_invar,type,
% 2.65/1.59 invar: g > $o ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v_m,type,
% 2.65/1.59 m: node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v_ms,type,
% 2.65/1.59 ms: list_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v_n,type,
% 2.65/1.59 n: node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v_ns,type,
% 2.65/1.59 ns: list_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v_phis,type,
% 2.65/1.59 phis: g > produc1432036078de_val > option_list_val ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v_pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r____,type,
% 2.65/1.59 pred_phi_r: node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v_r,type,
% 2.65/1.59 r: val ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v_rs_H____,type,
% 2.65/1.59 rs: list_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v_rs____,type,
% 2.65/1.59 rs2: list_node ).
% 2.65/1.59
% 2.65/1.59 thf(sy_v_s,type,
% 2.65/1.59 s: val ).
% 2.65/1.59
% 2.65/1.59 thf(fact_0_old_Opath2__hd,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,M: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( N
% 2.65/1.59 = ( hd_node @ Ns ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_1_False,axiom,
% 2.65/1.59 r != phi_r ).
% 2.65/1.59
% 2.65/1.59 thf(fact_2_old_OEntry__in__graph,axiom,
% 2.65/1.59 ! [G: g] : ( member_node @ ( entry @ G ) @ ( set_node2 @ ( alpha_n @ G ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_3_rs_H__props_I2_J,axiom,
% 2.65/1.59 graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs ).
% 2.65/1.59
% 2.65/1.59 thf(fact_4_rs_H__props_I1_J,axiom,
% 2.65/1.59 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ rs @ pred_phi_r ).
% 2.65/1.59
% 2.65/1.59 thf(fact_5_old_OEntryPath__distinct,axiom,
% 2.65/1.59 ! [G: g,Ns: list_node] :
% 2.65/1.59 ( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ Ns )
% 2.65/1.59 => ( distinct_node @ Ns ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_6_old_O_092_060alpha_062n__distinct,axiom,
% 2.65/1.59 ! [G: g] :
% 2.65/1.59 ( ( invar @ G )
% 2.65/1.59 => ( distinct_node @ ( alpha_n @ G ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_7_rs_H__props_I3_J,axiom,
% 2.65/1.59 member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ pred_phi_r ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_8_assms_I10_J,axiom,
% 2.65/1.59 sSA_CF1252180629de_val @ alpha_n @ defs @ phis @ g2 @ phi_r @ r ).
% 2.65/1.59
% 2.65/1.59 thf(fact_9_allDefs__disjoint_H,axiom,
% 2.65/1.59 ! [N: node,G: g,M: node,V: val] :
% 2.65/1.59 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 2.65/1.59 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ M ) )
% 2.65/1.59 => ( N = M ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_10_assms_I7_J,axiom,
% 2.65/1.59 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ n @ ns @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_11_defNode__eq,axiom,
% 2.65/1.59 ! [N: node,G: g,V: val] :
% 2.65/1.59 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) )
% 2.65/1.59 => ( ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ G @ V )
% 2.65/1.59 = N ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_12_rs_H__props_I4_J,axiom,
% 2.65/1.59 member_node @ pred_phi_r @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_13_defs__in__allDefs,axiom,
% 2.65/1.59 ! [V: val,G: g,N: node] :
% 2.65/1.59 ( ( member_val @ V @ ( defs @ G @ N ) )
% 2.65/1.59 => ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_14_FormalSSA__Misc_Oin__set__tlD,axiom,
% 2.65/1.59 ! [X: val,Xs: list_val] :
% 2.65/1.59 ( ( member_val @ X @ ( set_val2 @ ( tl_val @ Xs ) ) )
% 2.65/1.59 => ( member_val @ X @ ( set_val2 @ Xs ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_15_FormalSSA__Misc_Oin__set__tlD,axiom,
% 2.65/1.59 ! [X: node,Xs: list_node] :
% 2.65/1.59 ( ( member_node @ X @ ( set_node2 @ ( tl_node @ Xs ) ) )
% 2.65/1.59 => ( member_node @ X @ ( set_node2 @ Xs ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_16_old_Opath2__hd__in___092_060alpha_062n,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,M: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_17_old_Opath2__hd__in__ns,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,M: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( member_node @ N @ ( set_node2 @ Ns ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_18_old_Opath2__in___092_060alpha_062n,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,M: node,L: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( ( member_node @ L @ ( set_node2 @ Ns ) )
% 2.65/1.59 => ( member_node @ L @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_19_old_Oinvar,axiom,
% 2.65/1.59 ! [G: g] : ( invar @ G ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_20_old_Opath2__tl__in___092_060alpha_062n,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,M: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_21_old_Opath2__last__in__ns,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,M: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( member_node @ M @ ( set_node2 @ Ns ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_22_old_Osuccessor__is__node,axiom,
% 2.65/1.59 ! [N: node,G: g,N2: node] :
% 2.65/1.59 ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N2 ) ) )
% 2.65/1.59 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( ( invar @ G )
% 2.65/1.59 => ( member_node @ N2 @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_23_old_Opredecessor__is__node,axiom,
% 2.65/1.59 ! [N: node,G: g,N2: node] :
% 2.65/1.59 ( ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N2 ) ) )
% 2.65/1.59 => ( ( invar @ G )
% 2.65/1.59 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_24_old_Opath2__forget__hd,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,M: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( hd_node @ Ns ) @ Ns @ M ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_25_old_OEntry__reachesE,axiom,
% 2.65/1.59 ! [N: node,G: g] :
% 2.65/1.59 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( ( invar @ G )
% 2.65/1.59 => ~ ! [Ns2: list_node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns2 @ N )
% 2.65/1.59 => ~ ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ Ns2 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_26__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062rs_H_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_O_A_092_060lbrakk_062g_A_092_060turnstile_062_AdefNode_Ag_Ar_Nrs_H_092_060rightarrow_062pred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Aold_OEntryPath_Ag_Ars_H_059_Ar_A_092_060in_062_AphiUses_Ag_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_059_Apred_092_060_094sub_062_092_060phi_062_092_060_094sub_062r_A_092_060in_062_Aset_A_Iold_Opredecessors_Ag_A_IdefNode_Ag_A_092_060phi_062_092_060_094sub_062r_J_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.65/1.59 ~ ! [Rs: list_node,Pred_phi_r: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ Rs @ Pred_phi_r )
% 2.65/1.59 => ( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ Rs )
% 2.65/1.59 => ( ( member_val @ r @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ g2 @ Pred_phi_r ) )
% 2.65/1.59 => ~ ( member_node @ Pred_phi_r @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ g2 @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_27_old_OEntry__reaches,axiom,
% 2.65/1.59 ! [N: node,G: g] :
% 2.65/1.59 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( ( invar @ G )
% 2.65/1.59 => ? [Ns2: list_node] : ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns2 @ N ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_28_old_Oidom__ex,axiom,
% 2.65/1.59 ! [G: g,N: node] :
% 2.65/1.59 ( ( invar @ G )
% 2.65/1.59 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( ( N
% 2.65/1.59 != ( entry @ G ) )
% 2.65/1.59 => ? [X2: node] :
% 2.65/1.59 ( ( graph_1670286392_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ X2 )
% 2.65/1.59 & ! [Y: node] :
% 2.65/1.59 ( ( graph_1670286392_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ Y )
% 2.65/1.59 => ( Y = X2 ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_29_FormalSSA__Misc_Odistinct__hd__tl,axiom,
% 2.65/1.59 ! [Xs: list_val] :
% 2.65/1.59 ( ( distinct_val @ Xs )
% 2.65/1.59 => ~ ( member_val @ ( hd_val @ Xs ) @ ( set_val2 @ ( tl_val @ Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_30_FormalSSA__Misc_Odistinct__hd__tl,axiom,
% 2.65/1.59 ! [Xs: list_node] :
% 2.65/1.59 ( ( distinct_node @ Xs )
% 2.65/1.59 => ~ ( member_node @ ( hd_node @ Xs ) @ ( set_node2 @ ( tl_node @ Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_31_defAss_H__extend,axiom,
% 2.65/1.59 ! [G: g,M: node,V: val,N: node,Ns: list_node] :
% 2.65/1.59 ( ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ G @ M @ V )
% 2.65/1.59 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( ! [X2: node] :
% 2.65/1.59 ( ( member_node @ X2 @ ( set_node2 @ ( tl_node @ Ns ) ) )
% 2.65/1.59 => ~ ( member_val @ V @ ( defs @ G @ X2 ) ) )
% 2.65/1.59 => ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ G @ N @ V ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_32_defAss_H__def,axiom,
% 2.65/1.59 ! [G: g,M: node,V: val] :
% 2.65/1.59 ( ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ G @ M @ V )
% 2.65/1.59 = ( ! [Ns3: list_node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns3 @ M )
% 2.65/1.59 => ? [X3: node] :
% 2.65/1.59 ( ( member_node @ X3 @ ( set_node2 @ Ns3 ) )
% 2.65/1.59 & ( member_val @ V @ ( defs @ G @ X3 ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_33_defAss_HI,axiom,
% 2.65/1.59 ! [G: g,M: node,V: val] :
% 2.65/1.59 ( ! [Ns2: list_node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns2 @ M )
% 2.65/1.59 => ? [X4: node] :
% 2.65/1.59 ( ( member_node @ X4 @ ( set_node2 @ Ns2 ) )
% 2.65/1.59 & ( member_val @ V @ ( defs @ G @ X4 ) ) ) )
% 2.65/1.59 => ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ G @ M @ V ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_34_defAss_HE,axiom,
% 2.65/1.59 ! [G: g,M: node,V: val,Ns: list_node] :
% 2.65/1.59 ( ( sSA_CF1558836456eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ G @ M @ V )
% 2.65/1.59 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns @ M )
% 2.65/1.59 => ~ ! [N3: node] :
% 2.65/1.59 ( ( member_node @ N3 @ ( set_node2 @ Ns ) )
% 2.65/1.59 => ~ ( member_val @ V @ ( defs @ G @ N3 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_35_defAss__extend,axiom,
% 2.65/1.59 ! [G: g,M: node,V: val,N: node,Ns: list_node] :
% 2.65/1.59 ( ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G @ M @ V )
% 2.65/1.59 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( ! [X2: node] :
% 2.65/1.59 ( ( member_node @ X2 @ ( set_node2 @ ( tl_node @ Ns ) ) )
% 2.65/1.59 => ~ ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ X2 ) ) )
% 2.65/1.59 => ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G @ N @ V ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_36_assms_I8_J,axiom,
% 2.65/1.59 graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ m @ ms @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ s ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_37_defAss__def,axiom,
% 2.65/1.59 ! [G: g,M: node,V: val] :
% 2.65/1.59 ( ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G @ M @ V )
% 2.65/1.59 = ( ! [Ns3: list_node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns3 @ M )
% 2.65/1.59 => ? [X3: node] :
% 2.65/1.59 ( ( member_node @ X3 @ ( set_node2 @ Ns3 ) )
% 2.65/1.59 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ X3 ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_38_defAssI,axiom,
% 2.65/1.59 ! [G: g,M: node,V: val] :
% 2.65/1.59 ( ! [Ns2: list_node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns2 @ M )
% 2.65/1.59 => ? [X4: node] :
% 2.65/1.59 ( ( member_node @ X4 @ ( set_node2 @ Ns2 ) )
% 2.65/1.59 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ X4 ) ) ) )
% 2.65/1.59 => ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G @ M @ V ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_39_defAssD,axiom,
% 2.65/1.59 ! [G: g,M: node,V: val,Ns: list_node] :
% 2.65/1.59 ( ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G @ M @ V )
% 2.65/1.59 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns @ M )
% 2.65/1.59 => ? [X2: node] :
% 2.65/1.59 ( ( member_node @ X2 @ ( set_node2 @ Ns ) )
% 2.65/1.59 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ X2 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_40_phiDefs__in__allDefs,axiom,
% 2.65/1.59 ! [V: val,G: g,N: node] :
% 2.65/1.59 ( ( member_val @ V @ ( sSA_CF370335846de_val @ phis @ G @ N ) )
% 2.65/1.59 => ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_41_defAss__dominating,axiom,
% 2.65/1.59 ! [N: node,G: g,V: val] :
% 2.65/1.59 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( ( sSA_CF1156973626eD_val @ alpha_n @ invar @ inEdges @ entry @ defs @ phis @ G @ N @ V )
% 2.65/1.59 = ( ? [X3: node] :
% 2.65/1.59 ( ( member_node @ X3 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ X3 @ N )
% 2.65/1.59 & ( member_val @ V @ ( sSA_CF139593942de_val @ defs @ phis @ G @ X3 ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_42_old_Osuccessor__in___092_060alpha_062n,axiom,
% 2.65/1.59 ! [G: g,N: node] :
% 2.65/1.59 ( ( ( graph_272749361_edgeD @ inEdges @ G @ N )
% 2.65/1.59 != nil_node )
% 2.65/1.59 => ( ( invar @ G )
% 2.65/1.59 => ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_43_phiUses__finite,axiom,
% 2.65/1.59 ! [N: node,G: g] :
% 2.65/1.59 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( finite_finite_val @ ( sSA_CF848637139eD_val @ alpha_n @ inEdges @ phis @ G @ N ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_44_old_Opath2__split__last__prop,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,M: node,P: node > $o] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( ? [X4: node] :
% 2.65/1.59 ( ( member_node @ X4 @ ( set_node2 @ Ns ) )
% 2.65/1.59 & ( P @ X4 ) )
% 2.65/1.59 => ~ ! [N4: node,Ns4: list_node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N4 @ Ns4 @ M )
% 2.65/1.59 => ( ( P @ N4 )
% 2.65/1.59 => ( ! [X4: node] :
% 2.65/1.59 ( ( member_node @ X4 @ ( set_node2 @ ( tl_node @ Ns4 ) ) )
% 2.65/1.59 => ~ ( P @ X4 ) )
% 2.65/1.59 => ~ ( suffix_node @ Ns4 @ Ns ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_45_allDefs__finite,axiom,
% 2.65/1.59 ! [N: node,G: g] :
% 2.65/1.59 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( finite_finite_val @ ( sSA_CF139593942de_val @ defs @ phis @ G @ N ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_46_old_Opath2__not__Nil,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,M: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( Ns != nil_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_47_mem__Collect__eq,axiom,
% 2.65/1.59 ! [A: node,P: node > $o] :
% 2.65/1.59 ( ( member_node @ A @ ( collect_node @ P ) )
% 2.65/1.59 = ( P @ A ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_48_mem__Collect__eq,axiom,
% 2.65/1.59 ! [A: val,P: val > $o] :
% 2.65/1.59 ( ( member_val @ A @ ( collect_val @ P ) )
% 2.65/1.59 = ( P @ A ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_49_Collect__mem__eq,axiom,
% 2.65/1.59 ! [A2: set_node] :
% 2.65/1.59 ( ( collect_node
% 2.65/1.59 @ ^ [X3: node] : ( member_node @ X3 @ A2 ) )
% 2.65/1.59 = A2 ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_50_Collect__mem__eq,axiom,
% 2.65/1.59 ! [A2: set_val] :
% 2.65/1.59 ( ( collect_val
% 2.65/1.59 @ ^ [X3: val] : ( member_val @ X3 @ A2 ) )
% 2.65/1.59 = A2 ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_51_old_Opath2__not__Nil2,axiom,
% 2.65/1.59 ! [G: g,N: node,M: node] :
% 2.65/1.59 ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ nil_node @ M ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_52_old_Opath2__app,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,M: node,Ms: list_node,L: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ M @ Ms @ L )
% 2.65/1.59 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( tl_node @ Ms ) ) @ L ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_53_defs__finite,axiom,
% 2.65/1.59 ! [G: g,N: node] : ( finite_finite_val @ ( defs @ G @ N ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_54_phiDefs__finite,axiom,
% 2.65/1.59 ! [G: g,N: node] : ( finite_finite_val @ ( sSA_CF370335846de_val @ phis @ G @ N ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_55_strict__dom__trans_H,axiom,
% 2.65/1.59 ! [N: node,M: node,G: g,M2: node] :
% 2.65/1.59 ( ( ( N != M )
% 2.65/1.59 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M ) )
% 2.65/1.59 => ( ( ( M != M2 )
% 2.65/1.59 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ M @ M2 ) )
% 2.65/1.59 => ( ( N != M2 )
% 2.65/1.59 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M2 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_56_old_Ostrict__dom__trans,axiom,
% 2.65/1.59 ! [G: g,N: node,M: node,M2: node] :
% 2.65/1.59 ( ( invar @ G )
% 2.65/1.59 => ( ( ( N != M )
% 2.65/1.59 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M ) )
% 2.65/1.59 => ( ( ( M != M2 )
% 2.65/1.59 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ M @ M2 ) )
% 2.65/1.59 => ( ( N != M2 )
% 2.65/1.59 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M2 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_57_old_Odominates__trans,axiom,
% 2.65/1.59 ! [G: g,N: node,N2: node,N5: node] :
% 2.65/1.59 ( ( invar @ G )
% 2.65/1.59 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ N2 )
% 2.65/1.59 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N2 @ N5 )
% 2.65/1.59 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ N5 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_58_old_Odominates__antitrans,axiom,
% 2.65/1.59 ! [G: g,N_1: node,M: node,N_2: node] :
% 2.65/1.59 ( ( invar @ G )
% 2.65/1.59 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N_1 @ M )
% 2.65/1.59 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N_2 @ M )
% 2.65/1.59 => ( ~ ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N_1 @ N_2 )
% 2.65/1.59 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N_2 @ N_1 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_59_old_Odominates__antisymm,axiom,
% 2.65/1.59 ! [G: g,N: node,N2: node] :
% 2.65/1.59 ( ( invar @ G )
% 2.65/1.59 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ N2 )
% 2.65/1.59 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N2 @ N )
% 2.65/1.59 => ( N = N2 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_60_dominates__trans_H,axiom,
% 2.65/1.59 ! [G: g,N: node,N2: node,N5: node] :
% 2.65/1.59 ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ N2 )
% 2.65/1.59 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N2 @ N5 )
% 2.65/1.59 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ N5 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_61_dominates__antisymm_H,axiom,
% 2.65/1.59 ! [G: g,N: node,N2: node] :
% 2.65/1.59 ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ N2 )
% 2.65/1.59 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N2 @ N )
% 2.65/1.59 => ( N = N2 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_62_dominates__refl_H,axiom,
% 2.65/1.59 ! [N: node,G: g] :
% 2.65/1.59 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ N ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_63_old_Odominates__path,axiom,
% 2.65/1.59 ! [G: g,N: node,M: node] :
% 2.65/1.59 ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M )
% 2.65/1.59 => ( ( invar @ G )
% 2.65/1.59 => ~ ! [Ns2: list_node] :
% 2.65/1.59 ~ ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns2 @ M ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_64_old_Odominates__mid,axiom,
% 2.65/1.59 ! [G: g,N: node,X: node,M: node,Ns: list_node] :
% 2.65/1.59 ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ X )
% 2.65/1.59 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ X @ M )
% 2.65/1.59 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( ( invar @ G )
% 2.65/1.59 => ( member_node @ X @ ( set_node2 @ Ns ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_65_old_Odominates__def,axiom,
% 2.65/1.59 ! [G: g,N: node,M: node] :
% 2.65/1.59 ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M )
% 2.65/1.59 = ( ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 & ! [Ns3: list_node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns3 @ M )
% 2.65/1.59 => ( member_node @ N @ ( set_node2 @ Ns3 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_66_old_OdominatesE,axiom,
% 2.65/1.59 ! [G: g,N: node,M: node] :
% 2.65/1.59 ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M )
% 2.65/1.59 => ~ ( ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ~ ! [Ns5: list_node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns5 @ M )
% 2.65/1.59 => ( member_node @ N @ ( set_node2 @ Ns5 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_67_old_Odominates__unsnoc,axiom,
% 2.65/1.59 ! [G: g,N: node,M: node,M2: node] :
% 2.65/1.59 ( ( invar @ G )
% 2.65/1.59 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M )
% 2.65/1.59 => ( ( member_node @ M2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M ) ) )
% 2.65/1.59 => ( ( N != M )
% 2.65/1.59 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M2 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_68_non__dominated__predecessor,axiom,
% 2.65/1.59 ! [N: node,G: g] :
% 2.65/1.59 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( ( N
% 2.65/1.59 != ( entry @ G ) )
% 2.65/1.59 => ~ ! [M3: node] :
% 2.65/1.59 ( ( member_node @ M3 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N ) ) )
% 2.65/1.59 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M3 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_69_old_OisIdom__def,axiom,
% 2.65/1.59 ! [G: g,N: node,M: node] :
% 2.65/1.59 ( ( graph_1670286392_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M )
% 2.65/1.59 = ( ( M != N )
% 2.65/1.59 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ M @ N )
% 2.65/1.59 & ! [X3: node] :
% 2.65/1.59 ( ( member_node @ X3 @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( ( ( X3 != N )
% 2.65/1.59 & ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ X3 @ N ) )
% 2.65/1.59 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ X3 @ M ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_70_old_OEntryPath__suffix,axiom,
% 2.65/1.59 ! [G: g,Ns: list_node,Ns6: list_node] :
% 2.65/1.59 ( ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ Ns )
% 2.65/1.59 => ( ( suffix_node @ Ns6 @ Ns )
% 2.65/1.59 => ( ( Ns6 != nil_node )
% 2.65/1.59 => ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ Ns6 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_71_old_Odominates__unsnoc_H,axiom,
% 2.65/1.59 ! [G: g,N: node,M: node,M2: node,Ms: list_node] :
% 2.65/1.59 ( ( invar @ G )
% 2.65/1.59 => ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M )
% 2.65/1.59 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ M2 @ Ms @ M )
% 2.65/1.59 => ( ! [X2: node] :
% 2.65/1.59 ( ( member_node @ X2 @ ( set_node2 @ ( tl_node @ Ms ) ) )
% 2.65/1.59 => ( X2 != N ) )
% 2.65/1.59 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M2 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_72_old_Odominates__extend,axiom,
% 2.65/1.59 ! [G: g,N: node,M: node,M2: node,Ms: list_node] :
% 2.65/1.59 ( ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M )
% 2.65/1.59 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ M2 @ Ms @ M )
% 2.65/1.59 => ( ~ ( member_node @ N @ ( set_node2 @ ( tl_node @ Ms ) ) )
% 2.65/1.59 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M2 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_73_old_OEntry__no__predecessor,axiom,
% 2.65/1.59 ! [G: g] :
% 2.65/1.59 ( ( graph_272749361_edgeD @ inEdges @ G @ ( entry @ G ) )
% 2.65/1.59 = nil_node ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_74_old_Odominates__refl,axiom,
% 2.65/1.59 ! [G: g,N: node] :
% 2.65/1.59 ( ( invar @ G )
% 2.65/1.59 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ N ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_75_old_OEntry__dominates,axiom,
% 2.65/1.59 ! [G: g,N: node] :
% 2.65/1.59 ( ( invar @ G )
% 2.65/1.59 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ ( entry @ G ) @ N ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_76_old_OdominatesI,axiom,
% 2.65/1.59 ! [M: node,G: g,N: node] :
% 2.65/1.59 ( ( member_node @ M @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( ! [Ns2: list_node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns2 @ M )
% 2.65/1.59 => ( member_node @ N @ ( set_node2 @ Ns2 ) ) )
% 2.65/1.59 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ N @ M ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_77_old_OEntry__iff__unreachable,axiom,
% 2.65/1.59 ! [G: g,N: node] :
% 2.65/1.59 ( ( invar @ G )
% 2.65/1.59 => ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( ( ( graph_272749361_edgeD @ inEdges @ G @ N )
% 2.65/1.59 = nil_node )
% 2.65/1.59 = ( N
% 2.65/1.59 = ( entry @ G ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_78_old_Oreducible__def,axiom,
% 2.65/1.59 ! [G: g] :
% 2.65/1.59 ( ( graph_589078910_edgeD @ alpha_n @ invar @ inEdges @ entry @ G )
% 2.65/1.59 = ( ! [N6: node,Ns3: list_node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N6 @ Ns3 @ N6 )
% 2.65/1.59 => ? [X3: node] :
% 2.65/1.59 ( ( member_node @ X3 @ ( set_node2 @ Ns3 ) )
% 2.65/1.59 & ! [Y2: node] :
% 2.65/1.59 ( ( member_node @ Y2 @ ( set_node2 @ Ns3 ) )
% 2.65/1.59 => ( graph_436675702_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ X3 @ Y2 ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_79_in__hd__or__tl__conv,axiom,
% 2.65/1.59 ! [L: list_val,X: val] :
% 2.65/1.59 ( ( L != nil_val )
% 2.65/1.59 => ( ( ( X
% 2.65/1.59 = ( hd_val @ L ) )
% 2.65/1.59 | ( member_val @ X @ ( set_val2 @ ( tl_val @ L ) ) ) )
% 2.65/1.59 = ( member_val @ X @ ( set_val2 @ L ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_80_in__hd__or__tl__conv,axiom,
% 2.65/1.59 ! [L: list_P738500740D_node,X: produc1453890942D_node] :
% 2.65/1.59 ( ( L != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ( ( X
% 2.65/1.59 = ( hd_Pro1395892457D_node @ L ) )
% 2.65/1.59 | ( member1797643303D_node @ X @ ( set_Pr1238794387D_node @ ( tl_Pro1633633005D_node @ L ) ) ) )
% 2.65/1.59 = ( member1797643303D_node @ X @ ( set_Pr1238794387D_node @ L ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_81_in__hd__or__tl__conv,axiom,
% 2.65/1.59 ! [L: list_node,X: node] :
% 2.65/1.59 ( ( L != nil_node )
% 2.65/1.59 => ( ( ( X
% 2.65/1.59 = ( hd_node @ L ) )
% 2.65/1.59 | ( member_node @ X @ ( set_node2 @ ( tl_node @ L ) ) ) )
% 2.65/1.59 = ( member_node @ X @ ( set_node2 @ L ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_82_old_Opath2__cases,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,M: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( ( ( Ns
% 2.65/1.59 = ( cons_node @ N @ nil_node ) )
% 2.65/1.59 => ( M != N ) )
% 2.65/1.59 => ~ ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( hd_node @ ( tl_node @ Ns ) ) @ ( tl_node @ Ns ) @ M )
% 2.65/1.59 => ~ ( member_node @ N @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ ( hd_node @ ( tl_node @ Ns ) ) ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_83_old_Opath2__snoc,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,M: node,M2: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( ( member_node @ M @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M2 ) ) )
% 2.65/1.59 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ M2 @ nil_node ) ) @ M2 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_84_old_Opath2__rev__induct,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,M: node,P: node > list_node > node > $o] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( P @ N @ ( cons_node @ N @ nil_node ) @ N ) )
% 2.65/1.59 => ( ! [Ns2: list_node,M4: node,M3: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns2 @ M4 )
% 2.65/1.59 => ( ( P @ N @ Ns2 @ M4 )
% 2.65/1.59 => ( ( member_node @ M4 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ M3 ) ) )
% 2.65/1.59 => ( P @ N @ ( append_node @ Ns2 @ ( cons_node @ M3 @ nil_node ) ) @ M3 ) ) ) )
% 2.65/1.59 => ( P @ N @ Ns @ M ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_85_tl__append2,axiom,
% 2.65/1.59 ! [Xs: list_node,Ys: list_node] :
% 2.65/1.59 ( ( Xs != nil_node )
% 2.65/1.59 => ( ( tl_node @ ( append_node @ Xs @ Ys ) )
% 2.65/1.59 = ( append_node @ ( tl_node @ Xs ) @ Ys ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_86_tl__append2,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 2.65/1.59 ( ( Xs != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ( tl_Pro1633633005D_node @ ( append2096883353D_node @ Xs @ Ys ) )
% 2.65/1.59 = ( append2096883353D_node @ ( tl_Pro1633633005D_node @ Xs ) @ Ys ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_87_hd__append2,axiom,
% 2.65/1.59 ! [Xs: list_node,Ys: list_node] :
% 2.65/1.59 ( ( Xs != nil_node )
% 2.65/1.59 => ( ( hd_node @ ( append_node @ Xs @ Ys ) )
% 2.65/1.59 = ( hd_node @ Xs ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_88_hd__append2,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 2.65/1.59 ( ( Xs != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ( hd_Pro1395892457D_node @ ( append2096883353D_node @ Xs @ Ys ) )
% 2.65/1.59 = ( hd_Pro1395892457D_node @ Xs ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_89_same__suffix__nil,axiom,
% 2.65/1.59 ! [Ys: list_P738500740D_node,Xs: list_P738500740D_node] :
% 2.65/1.59 ( ( suffix1143830554D_node @ ( append2096883353D_node @ Ys @ Xs ) @ Xs )
% 2.65/1.59 = ( Ys = nil_Pr1769730692D_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_90_same__suffix__nil,axiom,
% 2.65/1.59 ! [Ys: list_node,Xs: list_node] :
% 2.65/1.59 ( ( suffix_node @ ( append_node @ Ys @ Xs ) @ Xs )
% 2.65/1.59 = ( Ys = nil_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_91_old_Opath2__induct,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,M: node,P: node > list_node > node > $o] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( ( ( invar @ G )
% 2.65/1.59 => ( P @ M @ ( cons_node @ M @ nil_node ) @ M ) )
% 2.65/1.59 => ( ! [Ns2: list_node,N4: node,N3: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N3 @ Ns2 @ M )
% 2.65/1.59 => ( ( P @ N3 @ Ns2 @ M )
% 2.65/1.59 => ( ( member_node @ N4 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N3 ) ) )
% 2.65/1.59 => ( P @ N4 @ ( cons_node @ N4 @ Ns2 ) @ M ) ) ) )
% 2.65/1.59 => ( P @ N @ Ns @ M ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_92_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 2.65/1.59 ! [X: val,Xs: list_val,Ys: list_val,Y3: val] :
% 2.65/1.59 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.65/1.59 => ( member_val @ X @ ( set_val2 @ ( tl_val @ ( append_val @ Ys @ ( cons_val @ Y3 @ Xs ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_93_old_Oelem__set__implies__elem__tl__app__cons,axiom,
% 2.65/1.59 ! [X: node,Xs: list_node,Ys: list_node,Y3: node] :
% 2.65/1.59 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.65/1.59 => ( member_node @ X @ ( set_node2 @ ( tl_node @ ( append_node @ Ys @ ( cons_node @ Y3 @ Xs ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_94_list_Oinject,axiom,
% 2.65/1.59 ! [X21: node,X22: list_node,Y21: node,Y22: list_node] :
% 2.65/1.59 ( ( ( cons_node @ X21 @ X22 )
% 2.65/1.59 = ( cons_node @ Y21 @ Y22 ) )
% 2.65/1.59 = ( ( X21 = Y21 )
% 2.65/1.59 & ( X22 = Y22 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_95_same__append__eq,axiom,
% 2.65/1.59 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 2.65/1.59 ( ( ( append_node @ Xs @ Ys )
% 2.65/1.59 = ( append_node @ Xs @ Zs ) )
% 2.65/1.59 = ( Ys = Zs ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_96_append__same__eq,axiom,
% 2.65/1.59 ! [Ys: list_node,Xs: list_node,Zs: list_node] :
% 2.65/1.59 ( ( ( append_node @ Ys @ Xs )
% 2.65/1.59 = ( append_node @ Zs @ Xs ) )
% 2.65/1.59 = ( Ys = Zs ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_97_append__assoc,axiom,
% 2.65/1.59 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 2.65/1.59 ( ( append_node @ ( append_node @ Xs @ Ys ) @ Zs )
% 2.65/1.59 = ( append_node @ Xs @ ( append_node @ Ys @ Zs ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_98_append_Oassoc,axiom,
% 2.65/1.59 ! [A: list_node,B: list_node,C: list_node] :
% 2.65/1.59 ( ( append_node @ ( append_node @ A @ B ) @ C )
% 2.65/1.59 = ( append_node @ A @ ( append_node @ B @ C ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_99_suffix__order_Odual__order_Orefl,axiom,
% 2.65/1.59 ! [A: list_node] : ( suffix_node @ A @ A ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_100_suffix__order_Oorder__refl,axiom,
% 2.65/1.59 ! [X: list_node] : ( suffix_node @ X @ X ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_101_old_Opath2__split_I2_J,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,N2: node,Ns6: list_node,M: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ Ns6 ) ) @ M )
% 2.65/1.59 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N2 @ ( cons_node @ N2 @ Ns6 ) @ M ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_102_List_Ofinite__set,axiom,
% 2.65/1.59 ! [Xs: list_node] : ( finite_finite_node @ ( set_node2 @ Xs ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_103_List_Ofinite__set,axiom,
% 2.65/1.59 ! [Xs: list_val] : ( finite_finite_val @ ( set_val2 @ Xs ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_104_append_Oright__neutral,axiom,
% 2.65/1.59 ! [A: list_node] :
% 2.65/1.59 ( ( append_node @ A @ nil_node )
% 2.65/1.59 = A ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_105_append_Oright__neutral,axiom,
% 2.65/1.59 ! [A: list_P738500740D_node] :
% 2.65/1.59 ( ( append2096883353D_node @ A @ nil_Pr1769730692D_node )
% 2.65/1.59 = A ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_106_empty__append__eq__id,axiom,
% 2.65/1.59 ( ( append_node @ nil_node )
% 2.65/1.59 = ( ^ [X3: list_node] : X3 ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_107_empty__append__eq__id,axiom,
% 2.65/1.59 ( ( append2096883353D_node @ nil_Pr1769730692D_node )
% 2.65/1.59 = ( ^ [X3: list_P738500740D_node] : X3 ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_108_append__is__Nil__conv,axiom,
% 2.65/1.59 ! [Xs: list_node,Ys: list_node] :
% 2.65/1.59 ( ( ( append_node @ Xs @ Ys )
% 2.65/1.59 = nil_node )
% 2.65/1.59 = ( ( Xs = nil_node )
% 2.65/1.59 & ( Ys = nil_node ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_109_append__is__Nil__conv,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 2.65/1.59 ( ( ( append2096883353D_node @ Xs @ Ys )
% 2.65/1.59 = nil_Pr1769730692D_node )
% 2.65/1.59 = ( ( Xs = nil_Pr1769730692D_node )
% 2.65/1.59 & ( Ys = nil_Pr1769730692D_node ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_110_Nil__is__append__conv,axiom,
% 2.65/1.59 ! [Xs: list_node,Ys: list_node] :
% 2.65/1.59 ( ( nil_node
% 2.65/1.59 = ( append_node @ Xs @ Ys ) )
% 2.65/1.59 = ( ( Xs = nil_node )
% 2.65/1.59 & ( Ys = nil_node ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_111_Nil__is__append__conv,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 2.65/1.59 ( ( nil_Pr1769730692D_node
% 2.65/1.59 = ( append2096883353D_node @ Xs @ Ys ) )
% 2.65/1.59 = ( ( Xs = nil_Pr1769730692D_node )
% 2.65/1.59 & ( Ys = nil_Pr1769730692D_node ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_112_self__append__conv2,axiom,
% 2.65/1.59 ! [Ys: list_node,Xs: list_node] :
% 2.65/1.59 ( ( Ys
% 2.65/1.59 = ( append_node @ Xs @ Ys ) )
% 2.65/1.59 = ( Xs = nil_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_113_self__append__conv2,axiom,
% 2.65/1.59 ! [Ys: list_P738500740D_node,Xs: list_P738500740D_node] :
% 2.65/1.59 ( ( Ys
% 2.65/1.59 = ( append2096883353D_node @ Xs @ Ys ) )
% 2.65/1.59 = ( Xs = nil_Pr1769730692D_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_114_append__self__conv2,axiom,
% 2.65/1.59 ! [Xs: list_node,Ys: list_node] :
% 2.65/1.59 ( ( ( append_node @ Xs @ Ys )
% 2.65/1.59 = Ys )
% 2.65/1.59 = ( Xs = nil_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_115_append__self__conv2,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 2.65/1.59 ( ( ( append2096883353D_node @ Xs @ Ys )
% 2.65/1.59 = Ys )
% 2.65/1.59 = ( Xs = nil_Pr1769730692D_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_116_self__append__conv,axiom,
% 2.65/1.59 ! [Xs: list_node,Ys: list_node] :
% 2.65/1.59 ( ( Xs
% 2.65/1.59 = ( append_node @ Xs @ Ys ) )
% 2.65/1.59 = ( Ys = nil_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_117_self__append__conv,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 2.65/1.59 ( ( Xs
% 2.65/1.59 = ( append2096883353D_node @ Xs @ Ys ) )
% 2.65/1.59 = ( Ys = nil_Pr1769730692D_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_118_append__self__conv,axiom,
% 2.65/1.59 ! [Xs: list_node,Ys: list_node] :
% 2.65/1.59 ( ( ( append_node @ Xs @ Ys )
% 2.65/1.59 = Xs )
% 2.65/1.59 = ( Ys = nil_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_119_append__self__conv,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 2.65/1.59 ( ( ( append2096883353D_node @ Xs @ Ys )
% 2.65/1.59 = Xs )
% 2.65/1.59 = ( Ys = nil_Pr1769730692D_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_120_append__Nil2,axiom,
% 2.65/1.59 ! [Xs: list_node] :
% 2.65/1.59 ( ( append_node @ Xs @ nil_node )
% 2.65/1.59 = Xs ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_121_append__Nil2,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node] :
% 2.65/1.59 ( ( append2096883353D_node @ Xs @ nil_Pr1769730692D_node )
% 2.65/1.59 = Xs ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_122_suffix__bot_Obot_Oextremum__unique,axiom,
% 2.65/1.59 ! [A: list_P738500740D_node] :
% 2.65/1.59 ( ( suffix1143830554D_node @ A @ nil_Pr1769730692D_node )
% 2.65/1.59 = ( A = nil_Pr1769730692D_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_123_suffix__bot_Obot_Oextremum__unique,axiom,
% 2.65/1.59 ! [A: list_node] :
% 2.65/1.59 ( ( suffix_node @ A @ nil_node )
% 2.65/1.59 = ( A = nil_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_124_suffix__Nil,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node] :
% 2.65/1.59 ( ( suffix1143830554D_node @ Xs @ nil_Pr1769730692D_node )
% 2.65/1.59 = ( Xs = nil_Pr1769730692D_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_125_suffix__Nil,axiom,
% 2.65/1.59 ! [Xs: list_node] :
% 2.65/1.59 ( ( suffix_node @ Xs @ nil_node )
% 2.65/1.59 = ( Xs = nil_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_126_same__suffix__suffix,axiom,
% 2.65/1.59 ! [Ys: list_node,Xs: list_node,Zs: list_node] :
% 2.65/1.59 ( ( suffix_node @ ( append_node @ Ys @ Xs ) @ ( append_node @ Zs @ Xs ) )
% 2.65/1.59 = ( suffix_node @ Ys @ Zs ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_127_old_Opath2__split_I1_J,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,N2: node,Ns6: list_node,M: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ Ns6 ) ) @ M )
% 2.65/1.59 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( append_node @ Ns @ ( cons_node @ N2 @ nil_node ) ) @ N2 ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_128_old_OEntry__loop,axiom,
% 2.65/1.59 ! [G: g,Ns: list_node] :
% 2.65/1.59 ( ( invar @ G )
% 2.65/1.59 => ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ ( entry @ G ) @ Ns @ ( entry @ G ) )
% 2.65/1.59 => ( Ns
% 2.65/1.59 = ( cons_node @ ( entry @ G ) @ nil_node ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_129_old_OEntryPath__triv,axiom,
% 2.65/1.59 ! [G: g,N: node] : ( graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ G @ ( cons_node @ N @ nil_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_130_append1__eq__conv,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node,X: produc1453890942D_node,Ys: list_P738500740D_node,Y3: produc1453890942D_node] :
% 2.65/1.59 ( ( ( append2096883353D_node @ Xs @ ( cons_P1018517044D_node @ X @ nil_Pr1769730692D_node ) )
% 2.65/1.59 = ( append2096883353D_node @ Ys @ ( cons_P1018517044D_node @ Y3 @ nil_Pr1769730692D_node ) ) )
% 2.65/1.59 = ( ( Xs = Ys )
% 2.65/1.59 & ( X = Y3 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_131_append1__eq__conv,axiom,
% 2.65/1.59 ! [Xs: list_node,X: node,Ys: list_node,Y3: node] :
% 2.65/1.59 ( ( ( append_node @ Xs @ ( cons_node @ X @ nil_node ) )
% 2.65/1.59 = ( append_node @ Ys @ ( cons_node @ Y3 @ nil_node ) ) )
% 2.65/1.59 = ( ( Xs = Ys )
% 2.65/1.59 & ( X = Y3 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_132_list__ee__eq__leel_I1_J,axiom,
% 2.65/1.59 ! [E1: produc1453890942D_node,E2: produc1453890942D_node,L1: list_P738500740D_node,E12: produc1453890942D_node,E22: produc1453890942D_node,L2: list_P738500740D_node] :
% 2.65/1.59 ( ( ( cons_P1018517044D_node @ E1 @ ( cons_P1018517044D_node @ E2 @ nil_Pr1769730692D_node ) )
% 2.65/1.59 = ( append2096883353D_node @ L1 @ ( cons_P1018517044D_node @ E12 @ ( cons_P1018517044D_node @ E22 @ L2 ) ) ) )
% 2.65/1.59 = ( ( L1 = nil_Pr1769730692D_node )
% 2.65/1.59 & ( E1 = E12 )
% 2.65/1.59 & ( E2 = E22 )
% 2.65/1.59 & ( L2 = nil_Pr1769730692D_node ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_133_list__ee__eq__leel_I1_J,axiom,
% 2.65/1.59 ! [E1: node,E2: node,L1: list_node,E12: node,E22: node,L2: list_node] :
% 2.65/1.59 ( ( ( cons_node @ E1 @ ( cons_node @ E2 @ nil_node ) )
% 2.65/1.59 = ( append_node @ L1 @ ( cons_node @ E12 @ ( cons_node @ E22 @ L2 ) ) ) )
% 2.65/1.59 = ( ( L1 = nil_node )
% 2.65/1.59 & ( E1 = E12 )
% 2.65/1.59 & ( E2 = E22 )
% 2.65/1.59 & ( L2 = nil_node ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_134_list__ee__eq__leel_I2_J,axiom,
% 2.65/1.59 ! [L1: list_P738500740D_node,E12: produc1453890942D_node,E22: produc1453890942D_node,L2: list_P738500740D_node,E1: produc1453890942D_node,E2: produc1453890942D_node] :
% 2.65/1.59 ( ( ( append2096883353D_node @ L1 @ ( cons_P1018517044D_node @ E12 @ ( cons_P1018517044D_node @ E22 @ L2 ) ) )
% 2.65/1.59 = ( cons_P1018517044D_node @ E1 @ ( cons_P1018517044D_node @ E2 @ nil_Pr1769730692D_node ) ) )
% 2.65/1.59 = ( ( L1 = nil_Pr1769730692D_node )
% 2.65/1.59 & ( E1 = E12 )
% 2.65/1.59 & ( E2 = E22 )
% 2.65/1.59 & ( L2 = nil_Pr1769730692D_node ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_135_list__ee__eq__leel_I2_J,axiom,
% 2.65/1.59 ! [L1: list_node,E12: node,E22: node,L2: list_node,E1: node,E2: node] :
% 2.65/1.59 ( ( ( append_node @ L1 @ ( cons_node @ E12 @ ( cons_node @ E22 @ L2 ) ) )
% 2.65/1.59 = ( cons_node @ E1 @ ( cons_node @ E2 @ nil_node ) ) )
% 2.65/1.59 = ( ( L1 = nil_node )
% 2.65/1.59 & ( E1 = E12 )
% 2.65/1.59 & ( E2 = E22 )
% 2.65/1.59 & ( L2 = nil_node ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_136_list__se__match_I1_J,axiom,
% 2.65/1.59 ! [L1: list_P738500740D_node,L2: list_P738500740D_node,A: produc1453890942D_node] :
% 2.65/1.59 ( ( L1 != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ( ( append2096883353D_node @ L1 @ L2 )
% 2.65/1.59 = ( cons_P1018517044D_node @ A @ nil_Pr1769730692D_node ) )
% 2.65/1.59 = ( ( L1
% 2.65/1.59 = ( cons_P1018517044D_node @ A @ nil_Pr1769730692D_node ) )
% 2.65/1.59 & ( L2 = nil_Pr1769730692D_node ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_137_list__se__match_I1_J,axiom,
% 2.65/1.59 ! [L1: list_node,L2: list_node,A: node] :
% 2.65/1.59 ( ( L1 != nil_node )
% 2.65/1.59 => ( ( ( append_node @ L1 @ L2 )
% 2.65/1.59 = ( cons_node @ A @ nil_node ) )
% 2.65/1.59 = ( ( L1
% 2.65/1.59 = ( cons_node @ A @ nil_node ) )
% 2.65/1.59 & ( L2 = nil_node ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_138_list__se__match_I2_J,axiom,
% 2.65/1.59 ! [L2: list_P738500740D_node,L1: list_P738500740D_node,A: produc1453890942D_node] :
% 2.65/1.59 ( ( L2 != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ( ( append2096883353D_node @ L1 @ L2 )
% 2.65/1.59 = ( cons_P1018517044D_node @ A @ nil_Pr1769730692D_node ) )
% 2.65/1.59 = ( ( L1 = nil_Pr1769730692D_node )
% 2.65/1.59 & ( L2
% 2.65/1.59 = ( cons_P1018517044D_node @ A @ nil_Pr1769730692D_node ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_139_list__se__match_I2_J,axiom,
% 2.65/1.59 ! [L2: list_node,L1: list_node,A: node] :
% 2.65/1.59 ( ( L2 != nil_node )
% 2.65/1.59 => ( ( ( append_node @ L1 @ L2 )
% 2.65/1.59 = ( cons_node @ A @ nil_node ) )
% 2.65/1.59 = ( ( L1 = nil_node )
% 2.65/1.59 & ( L2
% 2.65/1.59 = ( cons_node @ A @ nil_node ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_140_list__se__match_I3_J,axiom,
% 2.65/1.59 ! [L1: list_P738500740D_node,A: produc1453890942D_node,L2: list_P738500740D_node] :
% 2.65/1.59 ( ( L1 != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ( ( cons_P1018517044D_node @ A @ nil_Pr1769730692D_node )
% 2.65/1.59 = ( append2096883353D_node @ L1 @ L2 ) )
% 2.65/1.59 = ( ( L1
% 2.65/1.59 = ( cons_P1018517044D_node @ A @ nil_Pr1769730692D_node ) )
% 2.65/1.59 & ( L2 = nil_Pr1769730692D_node ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_141_list__se__match_I3_J,axiom,
% 2.65/1.59 ! [L1: list_node,A: node,L2: list_node] :
% 2.65/1.59 ( ( L1 != nil_node )
% 2.65/1.59 => ( ( ( cons_node @ A @ nil_node )
% 2.65/1.59 = ( append_node @ L1 @ L2 ) )
% 2.65/1.59 = ( ( L1
% 2.65/1.59 = ( cons_node @ A @ nil_node ) )
% 2.65/1.59 & ( L2 = nil_node ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_142_list__se__match_I4_J,axiom,
% 2.65/1.59 ! [L2: list_P738500740D_node,A: produc1453890942D_node,L1: list_P738500740D_node] :
% 2.65/1.59 ( ( L2 != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ( ( cons_P1018517044D_node @ A @ nil_Pr1769730692D_node )
% 2.65/1.59 = ( append2096883353D_node @ L1 @ L2 ) )
% 2.65/1.59 = ( ( L1 = nil_Pr1769730692D_node )
% 2.65/1.59 & ( L2
% 2.65/1.59 = ( cons_P1018517044D_node @ A @ nil_Pr1769730692D_node ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_143_list__se__match_I4_J,axiom,
% 2.65/1.59 ! [L2: list_node,A: node,L1: list_node] :
% 2.65/1.59 ( ( L2 != nil_node )
% 2.65/1.59 => ( ( ( cons_node @ A @ nil_node )
% 2.65/1.59 = ( append_node @ L1 @ L2 ) )
% 2.65/1.59 = ( ( L1 = nil_node )
% 2.65/1.59 & ( L2
% 2.65/1.59 = ( cons_node @ A @ nil_node ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_144_list__e__eq__lel_I1_J,axiom,
% 2.65/1.59 ! [E: produc1453890942D_node,L1: list_P738500740D_node,E3: produc1453890942D_node,L2: list_P738500740D_node] :
% 2.65/1.59 ( ( ( cons_P1018517044D_node @ E @ nil_Pr1769730692D_node )
% 2.65/1.59 = ( append2096883353D_node @ L1 @ ( cons_P1018517044D_node @ E3 @ L2 ) ) )
% 2.65/1.59 = ( ( L1 = nil_Pr1769730692D_node )
% 2.65/1.59 & ( E3 = E )
% 2.65/1.59 & ( L2 = nil_Pr1769730692D_node ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_145_list__e__eq__lel_I1_J,axiom,
% 2.65/1.59 ! [E: node,L1: list_node,E3: node,L2: list_node] :
% 2.65/1.59 ( ( ( cons_node @ E @ nil_node )
% 2.65/1.59 = ( append_node @ L1 @ ( cons_node @ E3 @ L2 ) ) )
% 2.65/1.59 = ( ( L1 = nil_node )
% 2.65/1.59 & ( E3 = E )
% 2.65/1.59 & ( L2 = nil_node ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_146_list__e__eq__lel_I2_J,axiom,
% 2.65/1.59 ! [L1: list_P738500740D_node,E3: produc1453890942D_node,L2: list_P738500740D_node,E: produc1453890942D_node] :
% 2.65/1.59 ( ( ( append2096883353D_node @ L1 @ ( cons_P1018517044D_node @ E3 @ L2 ) )
% 2.65/1.59 = ( cons_P1018517044D_node @ E @ nil_Pr1769730692D_node ) )
% 2.65/1.59 = ( ( L1 = nil_Pr1769730692D_node )
% 2.65/1.59 & ( E3 = E )
% 2.65/1.59 & ( L2 = nil_Pr1769730692D_node ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_147_list__e__eq__lel_I2_J,axiom,
% 2.65/1.59 ! [L1: list_node,E3: node,L2: list_node,E: node] :
% 2.65/1.59 ( ( ( append_node @ L1 @ ( cons_node @ E3 @ L2 ) )
% 2.65/1.59 = ( cons_node @ E @ nil_node ) )
% 2.65/1.59 = ( ( L1 = nil_node )
% 2.65/1.59 & ( E3 = E )
% 2.65/1.59 & ( L2 = nil_node ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_148_snoc__suffix__snoc,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node,X: produc1453890942D_node,Ys: list_P738500740D_node,Y3: produc1453890942D_node] :
% 2.65/1.59 ( ( suffix1143830554D_node @ ( append2096883353D_node @ Xs @ ( cons_P1018517044D_node @ X @ nil_Pr1769730692D_node ) ) @ ( append2096883353D_node @ Ys @ ( cons_P1018517044D_node @ Y3 @ nil_Pr1769730692D_node ) ) )
% 2.65/1.59 = ( ( X = Y3 )
% 2.65/1.59 & ( suffix1143830554D_node @ Xs @ Ys ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_149_snoc__suffix__snoc,axiom,
% 2.65/1.59 ! [Xs: list_node,X: node,Ys: list_node,Y3: node] :
% 2.65/1.59 ( ( suffix_node @ ( append_node @ Xs @ ( cons_node @ X @ nil_node ) ) @ ( append_node @ Ys @ ( cons_node @ Y3 @ nil_node ) ) )
% 2.65/1.59 = ( ( X = Y3 )
% 2.65/1.59 & ( suffix_node @ Xs @ Ys ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_150_suffix__snoc,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node,Y3: produc1453890942D_node] :
% 2.65/1.59 ( ( suffix1143830554D_node @ Xs @ ( append2096883353D_node @ Ys @ ( cons_P1018517044D_node @ Y3 @ nil_Pr1769730692D_node ) ) )
% 2.65/1.59 = ( ( Xs = nil_Pr1769730692D_node )
% 2.65/1.59 | ? [Zs2: list_P738500740D_node] :
% 2.65/1.59 ( ( Xs
% 2.65/1.59 = ( append2096883353D_node @ Zs2 @ ( cons_P1018517044D_node @ Y3 @ nil_Pr1769730692D_node ) ) )
% 2.65/1.59 & ( suffix1143830554D_node @ Zs2 @ Ys ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_151_suffix__snoc,axiom,
% 2.65/1.59 ! [Xs: list_node,Ys: list_node,Y3: node] :
% 2.65/1.59 ( ( suffix_node @ Xs @ ( append_node @ Ys @ ( cons_node @ Y3 @ nil_node ) ) )
% 2.65/1.59 = ( ( Xs = nil_node )
% 2.65/1.59 | ? [Zs2: list_node] :
% 2.65/1.59 ( ( Xs
% 2.65/1.59 = ( append_node @ Zs2 @ ( cons_node @ Y3 @ nil_node ) ) )
% 2.65/1.59 & ( suffix_node @ Zs2 @ Ys ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_152_list_Ocollapse,axiom,
% 2.65/1.59 ! [List: list_P738500740D_node] :
% 2.65/1.59 ( ( List != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ( cons_P1018517044D_node @ ( hd_Pro1395892457D_node @ List ) @ ( tl_Pro1633633005D_node @ List ) )
% 2.65/1.59 = List ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_153_list_Ocollapse,axiom,
% 2.65/1.59 ! [List: list_node] :
% 2.65/1.59 ( ( List != nil_node )
% 2.65/1.59 => ( ( cons_node @ ( hd_node @ List ) @ ( tl_node @ List ) )
% 2.65/1.59 = List ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_154_hd__Cons__tl,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node] :
% 2.65/1.59 ( ( Xs != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ( cons_P1018517044D_node @ ( hd_Pro1395892457D_node @ Xs ) @ ( tl_Pro1633633005D_node @ Xs ) )
% 2.65/1.59 = Xs ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_155_hd__Cons__tl,axiom,
% 2.65/1.59 ! [Xs: list_node] :
% 2.65/1.59 ( ( Xs != nil_node )
% 2.65/1.59 => ( ( cons_node @ ( hd_node @ Xs ) @ ( tl_node @ Xs ) )
% 2.65/1.59 = Xs ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_156_rs__def,axiom,
% 2.65/1.59 ( rs2
% 2.65/1.59 = ( append_node @ rs @ ( cons_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ phi_r ) @ nil_node ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_157_old_Oempty__path2,axiom,
% 2.65/1.59 ! [N: node,G: g] :
% 2.65/1.59 ( ( member_node @ N @ ( set_node2 @ ( alpha_n @ G ) ) )
% 2.65/1.59 => ( ( invar @ G )
% 2.65/1.59 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ ( cons_node @ N @ nil_node ) @ N ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_158_old_OCons__path2,axiom,
% 2.65/1.59 ! [G: g,N: node,Ns: list_node,M: node,N2: node] :
% 2.65/1.59 ( ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N @ Ns @ M )
% 2.65/1.59 => ( ( member_node @ N2 @ ( set_node2 @ ( graph_272749361_edgeD @ inEdges @ G @ N ) ) )
% 2.65/1.59 => ( graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ G @ N2 @ ( cons_node @ N2 @ Ns ) @ M ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_159_list_Odistinct_I1_J,axiom,
% 2.65/1.59 ! [X21: produc1453890942D_node,X22: list_P738500740D_node] :
% 2.65/1.59 ( nil_Pr1769730692D_node
% 2.65/1.59 != ( cons_P1018517044D_node @ X21 @ X22 ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_160_list_Odistinct_I1_J,axiom,
% 2.65/1.59 ! [X21: node,X22: list_node] :
% 2.65/1.59 ( nil_node
% 2.65/1.59 != ( cons_node @ X21 @ X22 ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_161_neq__NilE,axiom,
% 2.65/1.59 ! [L: list_P738500740D_node] :
% 2.65/1.59 ( ( L != nil_Pr1769730692D_node )
% 2.65/1.59 => ~ ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 2.65/1.59 ( L
% 2.65/1.59 != ( cons_P1018517044D_node @ X2 @ Xs2 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_162_neq__NilE,axiom,
% 2.65/1.59 ! [L: list_node] :
% 2.65/1.59 ( ( L != nil_node )
% 2.65/1.59 => ~ ! [X2: node,Xs2: list_node] :
% 2.65/1.59 ( L
% 2.65/1.59 != ( cons_node @ X2 @ Xs2 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_163_list_OdiscI,axiom,
% 2.65/1.59 ! [List: list_P738500740D_node,X21: produc1453890942D_node,X22: list_P738500740D_node] :
% 2.65/1.59 ( ( List
% 2.65/1.59 = ( cons_P1018517044D_node @ X21 @ X22 ) )
% 2.65/1.59 => ( List != nil_Pr1769730692D_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_164_list_OdiscI,axiom,
% 2.65/1.59 ! [List: list_node,X21: node,X22: list_node] :
% 2.65/1.59 ( ( List
% 2.65/1.59 = ( cons_node @ X21 @ X22 ) )
% 2.65/1.59 => ( List != nil_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_165_revg_Oinduct,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > list_P738500740D_node > $o,A0: list_P738500740D_node,A1: list_P738500740D_node] :
% 2.65/1.59 ( ! [X_1: list_P738500740D_node] : ( P @ nil_Pr1769730692D_node @ X_1 )
% 2.65/1.59 => ( ! [A3: produc1453890942D_node,As: list_P738500740D_node,B2: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ As @ ( cons_P1018517044D_node @ A3 @ B2 ) )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ A3 @ As ) @ B2 ) )
% 2.65/1.59 => ( P @ A0 @ A1 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_166_revg_Oinduct,axiom,
% 2.65/1.59 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 2.65/1.59 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 2.65/1.59 => ( ! [A3: node,As: list_node,B2: list_node] :
% 2.65/1.59 ( ( P @ As @ ( cons_node @ A3 @ B2 ) )
% 2.65/1.59 => ( P @ ( cons_node @ A3 @ As ) @ B2 ) )
% 2.65/1.59 => ( P @ A0 @ A1 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_167_list_Oexhaust,axiom,
% 2.65/1.59 ! [Y3: list_P738500740D_node] :
% 2.65/1.59 ( ( Y3 != nil_Pr1769730692D_node )
% 2.65/1.59 => ~ ! [X212: produc1453890942D_node,X222: list_P738500740D_node] :
% 2.65/1.59 ( Y3
% 2.65/1.59 != ( cons_P1018517044D_node @ X212 @ X222 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_168_list_Oexhaust,axiom,
% 2.65/1.59 ! [Y3: list_node] :
% 2.65/1.59 ( ( Y3 != nil_node )
% 2.65/1.59 => ~ ! [X212: node,X222: list_node] :
% 2.65/1.59 ( Y3
% 2.65/1.59 != ( cons_node @ X212 @ X222 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_169_list_Oinducts,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > $o,List: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X1: produc1453890942D_node,X23: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ X23 )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X1 @ X23 ) ) )
% 2.65/1.59 => ( P @ List ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_170_list_Oinducts,axiom,
% 2.65/1.59 ! [P: list_node > $o,List: list_node] :
% 2.65/1.59 ( ( P @ nil_node )
% 2.65/1.59 => ( ! [X1: node,X23: list_node] :
% 2.65/1.59 ( ( P @ X23 )
% 2.65/1.59 => ( P @ ( cons_node @ X1 @ X23 ) ) )
% 2.65/1.59 => ( P @ List ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_171_neq__Nil__conv,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node] :
% 2.65/1.59 ( ( Xs != nil_Pr1769730692D_node )
% 2.65/1.59 = ( ? [Y2: produc1453890942D_node,Ys2: list_P738500740D_node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 = ( cons_P1018517044D_node @ Y2 @ Ys2 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_172_neq__Nil__conv,axiom,
% 2.65/1.59 ! [Xs: list_node] :
% 2.65/1.59 ( ( Xs != nil_node )
% 2.65/1.59 = ( ? [Y2: node,Ys2: list_node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 = ( cons_node @ Y2 @ Ys2 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_173_list__induct2_H,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > list_P738500740D_node > $o,Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ nil_Pr1769730692D_node @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] : ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [Y4: produc1453890942D_node,Ys3: list_P738500740D_node] : ( P @ nil_Pr1769730692D_node @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ Xs2 @ Ys3 )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) )
% 2.65/1.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_174_list__induct2_H,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > list_node > $o,Xs: list_P738500740D_node,Ys: list_node] :
% 2.65/1.59 ( ( P @ nil_Pr1769730692D_node @ nil_node )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] : ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ nil_node )
% 2.65/1.59 => ( ! [Y4: node,Ys3: list_node] : ( P @ nil_Pr1769730692D_node @ ( cons_node @ Y4 @ Ys3 ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ( P @ Xs2 @ Ys3 )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) )
% 2.65/1.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_175_list__induct2_H,axiom,
% 2.65/1.59 ! [P: list_node > list_P738500740D_node > $o,Xs: list_node,Ys: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ nil_node @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node] : ( P @ ( cons_node @ X2 @ Xs2 ) @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [Y4: produc1453890942D_node,Ys3: list_P738500740D_node] : ( P @ nil_node @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ Xs2 @ Ys3 )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) )
% 2.65/1.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_176_list__induct2_H,axiom,
% 2.65/1.59 ! [P: list_node > list_node > $o,Xs: list_node,Ys: list_node] :
% 2.65/1.59 ( ( P @ nil_node @ nil_node )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node] : ( P @ ( cons_node @ X2 @ Xs2 ) @ nil_node )
% 2.65/1.59 => ( ! [Y4: node,Ys3: list_node] : ( P @ nil_node @ ( cons_node @ Y4 @ Ys3 ) )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ( P @ Xs2 @ Ys3 )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) )
% 2.65/1.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_177_splice_Oinduct,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > list_P738500740D_node > $o,A0: list_P738500740D_node,A1: list_P738500740D_node] :
% 2.65/1.59 ( ! [X_1: list_P738500740D_node] : ( P @ nil_Pr1769730692D_node @ X_1 )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ Ys3 @ Xs2 )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ Ys3 ) )
% 2.65/1.59 => ( P @ A0 @ A1 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_178_splice_Oinduct,axiom,
% 2.65/1.59 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 2.65/1.59 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node,Ys3: list_node] :
% 2.65/1.59 ( ( P @ Ys3 @ Xs2 )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ Xs2 ) @ Ys3 ) )
% 2.65/1.59 => ( P @ A0 @ A1 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_179_induct__list012,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > $o,Xs: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node] : ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Y4: produc1453890942D_node,Zs3: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ Zs3 )
% 2.65/1.59 => ( ( P @ ( cons_P1018517044D_node @ Y4 @ Zs3 ) )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X2 @ ( cons_P1018517044D_node @ Y4 @ Zs3 ) ) ) ) )
% 2.65/1.59 => ( P @ Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_180_induct__list012,axiom,
% 2.65/1.59 ! [P: list_node > $o,Xs: list_node] :
% 2.65/1.59 ( ( P @ nil_node )
% 2.65/1.59 => ( ! [X2: node] : ( P @ ( cons_node @ X2 @ nil_node ) )
% 2.65/1.59 => ( ! [X2: node,Y4: node,Zs3: list_node] :
% 2.65/1.59 ( ( P @ Zs3 )
% 2.65/1.59 => ( ( P @ ( cons_node @ Y4 @ Zs3 ) )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ ( cons_node @ Y4 @ Zs3 ) ) ) ) )
% 2.65/1.59 => ( P @ Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_181_min__list_Ocases,axiom,
% 2.65/1.59 ! [X: list_node] :
% 2.65/1.59 ( ! [X2: node,Xs2: list_node] :
% 2.65/1.59 ( X
% 2.65/1.59 != ( cons_node @ X2 @ Xs2 ) )
% 2.65/1.59 => ( X = nil_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_182_suffix__Cons,axiom,
% 2.65/1.59 ! [Xs: list_node,Y3: node,Ys: list_node] :
% 2.65/1.59 ( ( suffix_node @ Xs @ ( cons_node @ Y3 @ Ys ) )
% 2.65/1.59 = ( ( Xs
% 2.65/1.59 = ( cons_node @ Y3 @ Ys ) )
% 2.65/1.59 | ( suffix_node @ Xs @ Ys ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_183_Cons__eq__appendI,axiom,
% 2.65/1.59 ! [X: node,Xs1: list_node,Ys: list_node,Xs: list_node,Zs: list_node] :
% 2.65/1.59 ( ( ( cons_node @ X @ Xs1 )
% 2.65/1.59 = Ys )
% 2.65/1.59 => ( ( Xs
% 2.65/1.59 = ( append_node @ Xs1 @ Zs ) )
% 2.65/1.59 => ( ( cons_node @ X @ Xs )
% 2.65/1.59 = ( append_node @ Ys @ Zs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_184_min__list_Oinduct,axiom,
% 2.65/1.59 ! [P: list_node > $o,A0: list_node] :
% 2.65/1.59 ( ! [X2: node,Xs2: list_node] :
% 2.65/1.59 ( ! [X213: node,X223: list_node] :
% 2.65/1.59 ( ( Xs2
% 2.65/1.59 = ( cons_node @ X213 @ X223 ) )
% 2.65/1.59 => ( P @ Xs2 ) )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ Xs2 ) ) )
% 2.65/1.59 => ( ( P @ nil_node )
% 2.65/1.59 => ( P @ A0 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_185_shuffles_Oinduct,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > list_P738500740D_node > $o,A0: list_P738500740D_node,A1: list_P738500740D_node] :
% 2.65/1.59 ( ! [X_1: list_P738500740D_node] : ( P @ nil_Pr1769730692D_node @ X_1 )
% 2.65/1.59 => ( ! [Xs2: list_P738500740D_node] : ( P @ Xs2 @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ Xs2 @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) )
% 2.65/1.59 => ( ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ Ys3 )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) ) )
% 2.65/1.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_186_shuffles_Oinduct,axiom,
% 2.65/1.59 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 2.65/1.59 ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 2.65/1.59 => ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_node )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ( P @ Xs2 @ ( cons_node @ Y4 @ Ys3 ) )
% 2.65/1.59 => ( ( P @ ( cons_node @ X2 @ Xs2 ) @ Ys3 )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) ) )
% 2.65/1.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_187_transpose_Ocases,axiom,
% 2.65/1.59 ! [X: list_l1129649930D_node] :
% 2.65/1.59 ( ( X != nil_li1626782346D_node )
% 2.65/1.59 => ( ! [Xss: list_l1129649930D_node] :
% 2.65/1.59 ( X
% 2.65/1.59 != ( cons_l1288865338D_node @ nil_Pr1769730692D_node @ Xss ) )
% 2.65/1.59 => ~ ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Xss: list_l1129649930D_node] :
% 2.65/1.59 ( X
% 2.65/1.59 != ( cons_l1288865338D_node @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_188_transpose_Ocases,axiom,
% 2.65/1.59 ! [X: list_list_node] :
% 2.65/1.59 ( ( X != nil_list_node )
% 2.65/1.59 => ( ! [Xss: list_list_node] :
% 2.65/1.59 ( X
% 2.65/1.59 != ( cons_list_node @ nil_node @ Xss ) )
% 2.65/1.59 => ~ ! [X2: node,Xs2: list_node,Xss: list_list_node] :
% 2.65/1.59 ( X
% 2.65/1.59 != ( cons_list_node @ ( cons_node @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_189_suffix__ConsD,axiom,
% 2.65/1.59 ! [X: node,Xs: list_node,Ys: list_node] :
% 2.65/1.59 ( ( suffix_node @ ( cons_node @ X @ Xs ) @ Ys )
% 2.65/1.59 => ( suffix_node @ Xs @ Ys ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_190_suffix__ConsI,axiom,
% 2.65/1.59 ! [Xs: list_node,Ys: list_node,Y3: node] :
% 2.65/1.59 ( ( suffix_node @ Xs @ Ys )
% 2.65/1.59 => ( suffix_node @ Xs @ ( cons_node @ Y3 @ Ys ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_191_list__2pre__induct,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > list_P738500740D_node > $o,W1: list_P738500740D_node,W2: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ nil_Pr1769730692D_node @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [E4: produc1453890942D_node,W12: list_P738500740D_node,W22: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ W12 @ W22 )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ E4 @ W12 ) @ W22 ) )
% 2.65/1.59 => ( ! [E4: produc1453890942D_node,W13: list_P738500740D_node,W23: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ W13 @ W23 )
% 2.65/1.59 => ( P @ W13 @ ( cons_P1018517044D_node @ E4 @ W23 ) ) )
% 2.65/1.59 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_192_list__2pre__induct,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > list_node > $o,W1: list_P738500740D_node,W2: list_node] :
% 2.65/1.59 ( ( P @ nil_Pr1769730692D_node @ nil_node )
% 2.65/1.59 => ( ! [E4: produc1453890942D_node,W12: list_P738500740D_node,W22: list_node] :
% 2.65/1.59 ( ( P @ W12 @ W22 )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ E4 @ W12 ) @ W22 ) )
% 2.65/1.59 => ( ! [E4: node,W13: list_P738500740D_node,W23: list_node] :
% 2.65/1.59 ( ( P @ W13 @ W23 )
% 2.65/1.59 => ( P @ W13 @ ( cons_node @ E4 @ W23 ) ) )
% 2.65/1.59 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_193_list__2pre__induct,axiom,
% 2.65/1.59 ! [P: list_node > list_P738500740D_node > $o,W1: list_node,W2: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ nil_node @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [E4: node,W12: list_node,W22: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ W12 @ W22 )
% 2.65/1.59 => ( P @ ( cons_node @ E4 @ W12 ) @ W22 ) )
% 2.65/1.59 => ( ! [E4: produc1453890942D_node,W13: list_node,W23: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ W13 @ W23 )
% 2.65/1.59 => ( P @ W13 @ ( cons_P1018517044D_node @ E4 @ W23 ) ) )
% 2.65/1.59 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_194_list__2pre__induct,axiom,
% 2.65/1.59 ! [P: list_node > list_node > $o,W1: list_node,W2: list_node] :
% 2.65/1.59 ( ( P @ nil_node @ nil_node )
% 2.65/1.59 => ( ! [E4: node,W12: list_node,W22: list_node] :
% 2.65/1.59 ( ( P @ W12 @ W22 )
% 2.65/1.59 => ( P @ ( cons_node @ E4 @ W12 ) @ W22 ) )
% 2.65/1.59 => ( ! [E4: node,W13: list_node,W23: list_node] :
% 2.65/1.59 ( ( P @ W13 @ W23 )
% 2.65/1.59 => ( P @ W13 @ ( cons_node @ E4 @ W23 ) ) )
% 2.65/1.59 => ( P @ W1 @ W2 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_195_suffix__ConsD2,axiom,
% 2.65/1.59 ! [X: node,Xs: list_node,Y3: node,Ys: list_node] :
% 2.65/1.59 ( ( suffix_node @ ( cons_node @ X @ Xs ) @ ( cons_node @ Y3 @ Ys ) )
% 2.65/1.59 => ( suffix_node @ Xs @ Ys ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_196_remdups__adj_Ocases,axiom,
% 2.65/1.59 ! [X: list_P738500740D_node] :
% 2.65/1.59 ( ( X != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node] :
% 2.65/1.59 ( X
% 2.65/1.59 != ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) )
% 2.65/1.59 => ~ ! [X2: produc1453890942D_node,Y4: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 2.65/1.59 ( X
% 2.65/1.59 != ( cons_P1018517044D_node @ X2 @ ( cons_P1018517044D_node @ Y4 @ Xs2 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_197_remdups__adj_Ocases,axiom,
% 2.65/1.59 ! [X: list_node] :
% 2.65/1.59 ( ( X != nil_node )
% 2.65/1.59 => ( ! [X2: node] :
% 2.65/1.59 ( X
% 2.65/1.59 != ( cons_node @ X2 @ nil_node ) )
% 2.65/1.59 => ~ ! [X2: node,Y4: node,Xs2: list_node] :
% 2.65/1.59 ( X
% 2.65/1.59 != ( cons_node @ X2 @ ( cons_node @ Y4 @ Xs2 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_198_sorted__wrt_Oinduct,axiom,
% 2.65/1.59 ! [P: ( produc1453890942D_node > produc1453890942D_node > $o ) > list_P738500740D_node > $o,A0: produc1453890942D_node > produc1453890942D_node > $o,A1: list_P738500740D_node] :
% 2.65/1.59 ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o] : ( P @ P2 @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o,X2: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ P2 @ Ys3 )
% 2.65/1.59 => ( P @ P2 @ ( cons_P1018517044D_node @ X2 @ Ys3 ) ) )
% 2.65/1.59 => ( P @ A0 @ A1 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_199_sorted__wrt_Oinduct,axiom,
% 2.65/1.59 ! [P: ( node > node > $o ) > list_node > $o,A0: node > node > $o,A1: list_node] :
% 2.65/1.59 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node )
% 2.65/1.59 => ( ! [P2: node > node > $o,X2: node,Ys3: list_node] :
% 2.65/1.59 ( ( P @ P2 @ Ys3 )
% 2.65/1.59 => ( P @ P2 @ ( cons_node @ X2 @ Ys3 ) ) )
% 2.65/1.59 => ( P @ A0 @ A1 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_200_append__Cons,axiom,
% 2.65/1.59 ! [X: node,Xs: list_node,Ys: list_node] :
% 2.65/1.59 ( ( append_node @ ( cons_node @ X @ Xs ) @ Ys )
% 2.65/1.59 = ( cons_node @ X @ ( append_node @ Xs @ Ys ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_201_remdups__adj_Oinduct,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > $o,A0: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node] : ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Y4: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 2.65/1.59 ( ( ( X2 = Y4 )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) ) )
% 2.65/1.59 => ( ( ( X2 != Y4 )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ Y4 @ Xs2 ) ) )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X2 @ ( cons_P1018517044D_node @ Y4 @ Xs2 ) ) ) ) )
% 2.65/1.59 => ( P @ A0 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_202_remdups__adj_Oinduct,axiom,
% 2.65/1.59 ! [P: list_node > $o,A0: list_node] :
% 2.65/1.59 ( ( P @ nil_node )
% 2.65/1.59 => ( ! [X2: node] : ( P @ ( cons_node @ X2 @ nil_node ) )
% 2.65/1.59 => ( ! [X2: node,Y4: node,Xs2: list_node] :
% 2.65/1.59 ( ( ( X2 = Y4 )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ Xs2 ) ) )
% 2.65/1.59 => ( ( ( X2 != Y4 )
% 2.65/1.59 => ( P @ ( cons_node @ Y4 @ Xs2 ) ) )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ ( cons_node @ Y4 @ Xs2 ) ) ) ) )
% 2.65/1.59 => ( P @ A0 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_203_list__induct__first2,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > $o,Xs: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node] : ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) )
% 2.65/1.59 => ( ! [X1: produc1453890942D_node,X23: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ Xs2 )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X1 @ ( cons_P1018517044D_node @ X23 @ Xs2 ) ) ) )
% 2.65/1.59 => ( P @ Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_204_list__induct__first2,axiom,
% 2.65/1.59 ! [P: list_node > $o,Xs: list_node] :
% 2.65/1.59 ( ( P @ nil_node )
% 2.65/1.59 => ( ! [X2: node] : ( P @ ( cons_node @ X2 @ nil_node ) )
% 2.65/1.59 => ( ! [X1: node,X23: node,Xs2: list_node] :
% 2.65/1.59 ( ( P @ Xs2 )
% 2.65/1.59 => ( P @ ( cons_node @ X1 @ ( cons_node @ X23 @ Xs2 ) ) ) )
% 2.65/1.59 => ( P @ Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_205_list__match__lel__lel,axiom,
% 2.65/1.59 ! [C1: list_node,Qs: node,C2: list_node,C12: list_node,Qs2: node,C22: list_node] :
% 2.65/1.59 ( ( ( append_node @ C1 @ ( cons_node @ Qs @ C2 ) )
% 2.65/1.59 = ( append_node @ C12 @ ( cons_node @ Qs2 @ C22 ) ) )
% 2.65/1.59 => ( ! [C21: list_node] :
% 2.65/1.59 ( ( C1
% 2.65/1.59 = ( append_node @ C12 @ ( cons_node @ Qs2 @ C21 ) ) )
% 2.65/1.59 => ( C22
% 2.65/1.59 != ( append_node @ C21 @ ( cons_node @ Qs @ C2 ) ) ) )
% 2.65/1.59 => ( ( ( C12 = C1 )
% 2.65/1.59 => ( ( Qs2 = Qs )
% 2.65/1.59 => ( C22 != C2 ) ) )
% 2.65/1.59 => ~ ! [C212: list_node] :
% 2.65/1.59 ( ( C12
% 2.65/1.59 = ( append_node @ C1 @ ( cons_node @ Qs @ C212 ) ) )
% 2.65/1.59 => ( C2
% 2.65/1.59 != ( append_node @ C212 @ ( cons_node @ Qs2 @ C22 ) ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_206_successively_Oinduct,axiom,
% 2.65/1.59 ! [P: ( produc1453890942D_node > produc1453890942D_node > $o ) > list_P738500740D_node > $o,A0: produc1453890942D_node > produc1453890942D_node > $o,A1: list_P738500740D_node] :
% 2.65/1.59 ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o] : ( P @ P2 @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o,X2: produc1453890942D_node] : ( P @ P2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) )
% 2.65/1.59 => ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o,X2: produc1453890942D_node,Y4: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ P2 @ ( cons_P1018517044D_node @ Y4 @ Xs2 ) )
% 2.65/1.59 => ( P @ P2 @ ( cons_P1018517044D_node @ X2 @ ( cons_P1018517044D_node @ Y4 @ Xs2 ) ) ) )
% 2.65/1.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_207_successively_Oinduct,axiom,
% 2.65/1.59 ! [P: ( node > node > $o ) > list_node > $o,A0: node > node > $o,A1: list_node] :
% 2.65/1.59 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node )
% 2.65/1.59 => ( ! [P2: node > node > $o,X2: node] : ( P @ P2 @ ( cons_node @ X2 @ nil_node ) )
% 2.65/1.59 => ( ! [P2: node > node > $o,X2: node,Y4: node,Xs2: list_node] :
% 2.65/1.59 ( ( P @ P2 @ ( cons_node @ Y4 @ Xs2 ) )
% 2.65/1.59 => ( P @ P2 @ ( cons_node @ X2 @ ( cons_node @ Y4 @ Xs2 ) ) ) )
% 2.65/1.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_208_list__all__zip_Oinduct,axiom,
% 2.65/1.59 ! [P: ( produc1453890942D_node > produc1453890942D_node > $o ) > list_P738500740D_node > list_P738500740D_node > $o,A0: produc1453890942D_node > produc1453890942D_node > $o,A1: list_P738500740D_node,A22: list_P738500740D_node] :
% 2.65/1.59 ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o] : ( P @ P2 @ nil_Pr1769730692D_node @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o,A3: produc1453890942D_node,As: list_P738500740D_node,B2: produc1453890942D_node,Bs: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ P2 @ As @ Bs )
% 2.65/1.59 => ( P @ P2 @ ( cons_P1018517044D_node @ A3 @ As ) @ ( cons_P1018517044D_node @ B2 @ Bs ) ) )
% 2.65/1.59 => ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o,V2: produc1453890942D_node,Va: list_P738500740D_node] : ( P @ P2 @ ( cons_P1018517044D_node @ V2 @ Va ) @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [P2: produc1453890942D_node > produc1453890942D_node > $o,V2: produc1453890942D_node,Va: list_P738500740D_node] : ( P @ P2 @ nil_Pr1769730692D_node @ ( cons_P1018517044D_node @ V2 @ Va ) )
% 2.65/1.59 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_209_list__all__zip_Oinduct,axiom,
% 2.65/1.59 ! [P: ( produc1453890942D_node > node > $o ) > list_P738500740D_node > list_node > $o,A0: produc1453890942D_node > node > $o,A1: list_P738500740D_node,A22: list_node] :
% 2.65/1.59 ( ! [P2: produc1453890942D_node > node > $o] : ( P @ P2 @ nil_Pr1769730692D_node @ nil_node )
% 2.65/1.59 => ( ! [P2: produc1453890942D_node > node > $o,A3: produc1453890942D_node,As: list_P738500740D_node,B2: node,Bs: list_node] :
% 2.65/1.59 ( ( P @ P2 @ As @ Bs )
% 2.65/1.59 => ( P @ P2 @ ( cons_P1018517044D_node @ A3 @ As ) @ ( cons_node @ B2 @ Bs ) ) )
% 2.65/1.59 => ( ! [P2: produc1453890942D_node > node > $o,V2: produc1453890942D_node,Va: list_P738500740D_node] : ( P @ P2 @ ( cons_P1018517044D_node @ V2 @ Va ) @ nil_node )
% 2.65/1.59 => ( ! [P2: produc1453890942D_node > node > $o,V2: node,Va: list_node] : ( P @ P2 @ nil_Pr1769730692D_node @ ( cons_node @ V2 @ Va ) )
% 2.65/1.59 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_210_list__all__zip_Oinduct,axiom,
% 2.65/1.59 ! [P: ( node > produc1453890942D_node > $o ) > list_node > list_P738500740D_node > $o,A0: node > produc1453890942D_node > $o,A1: list_node,A22: list_P738500740D_node] :
% 2.65/1.59 ( ! [P2: node > produc1453890942D_node > $o] : ( P @ P2 @ nil_node @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [P2: node > produc1453890942D_node > $o,A3: node,As: list_node,B2: produc1453890942D_node,Bs: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ P2 @ As @ Bs )
% 2.65/1.59 => ( P @ P2 @ ( cons_node @ A3 @ As ) @ ( cons_P1018517044D_node @ B2 @ Bs ) ) )
% 2.65/1.59 => ( ! [P2: node > produc1453890942D_node > $o,V2: node,Va: list_node] : ( P @ P2 @ ( cons_node @ V2 @ Va ) @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [P2: node > produc1453890942D_node > $o,V2: produc1453890942D_node,Va: list_P738500740D_node] : ( P @ P2 @ nil_node @ ( cons_P1018517044D_node @ V2 @ Va ) )
% 2.65/1.59 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_211_list__all__zip_Oinduct,axiom,
% 2.65/1.59 ! [P: ( node > node > $o ) > list_node > list_node > $o,A0: node > node > $o,A1: list_node,A22: list_node] :
% 2.65/1.59 ( ! [P2: node > node > $o] : ( P @ P2 @ nil_node @ nil_node )
% 2.65/1.59 => ( ! [P2: node > node > $o,A3: node,As: list_node,B2: node,Bs: list_node] :
% 2.65/1.59 ( ( P @ P2 @ As @ Bs )
% 2.65/1.59 => ( P @ P2 @ ( cons_node @ A3 @ As ) @ ( cons_node @ B2 @ Bs ) ) )
% 2.65/1.59 => ( ! [P2: node > node > $o,V2: node,Va: list_node] : ( P @ P2 @ ( cons_node @ V2 @ Va ) @ nil_node )
% 2.65/1.59 => ( ! [P2: node > node > $o,V2: node,Va: list_node] : ( P @ P2 @ nil_node @ ( cons_node @ V2 @ Va ) )
% 2.65/1.59 => ( P @ A0 @ A1 @ A22 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_212_list__nonempty__induct,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node,P: list_P738500740D_node > $o] :
% 2.65/1.59 ( ( Xs != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node] : ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 2.65/1.59 ( ( Xs2 != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ( P @ Xs2 )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) ) ) )
% 2.65/1.59 => ( P @ Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_213_list__nonempty__induct,axiom,
% 2.65/1.59 ! [Xs: list_node,P: list_node > $o] :
% 2.65/1.59 ( ( Xs != nil_node )
% 2.65/1.59 => ( ! [X2: node] : ( P @ ( cons_node @ X2 @ nil_node ) )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node] :
% 2.65/1.59 ( ( Xs2 != nil_node )
% 2.65/1.59 => ( ( P @ Xs2 )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ Xs2 ) ) ) )
% 2.65/1.59 => ( P @ Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_214_map__tailrec__rev_Oinduct,axiom,
% 2.65/1.59 ! [P: ( produc1453890942D_node > node ) > list_P738500740D_node > list_node > $o,A0: produc1453890942D_node > node,A1: list_P738500740D_node,A22: list_node] :
% 2.65/1.59 ( ! [F: produc1453890942D_node > node,X_1: list_node] : ( P @ F @ nil_Pr1769730692D_node @ X_1 )
% 2.65/1.59 => ( ! [F: produc1453890942D_node > node,A3: produc1453890942D_node,As: list_P738500740D_node,Bs: list_node] :
% 2.65/1.59 ( ( P @ F @ As @ ( cons_node @ ( F @ A3 ) @ Bs ) )
% 2.65/1.59 => ( P @ F @ ( cons_P1018517044D_node @ A3 @ As ) @ Bs ) )
% 2.65/1.59 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_215_map__tailrec__rev_Oinduct,axiom,
% 2.65/1.59 ! [P: ( node > node ) > list_node > list_node > $o,A0: node > node,A1: list_node,A22: list_node] :
% 2.65/1.59 ( ! [F: node > node,X_1: list_node] : ( P @ F @ nil_node @ X_1 )
% 2.65/1.59 => ( ! [F: node > node,A3: node,As: list_node,Bs: list_node] :
% 2.65/1.59 ( ( P @ F @ As @ ( cons_node @ ( F @ A3 ) @ Bs ) )
% 2.65/1.59 => ( P @ F @ ( cons_node @ A3 @ As ) @ Bs ) )
% 2.65/1.59 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_216_mergesort__by__rel__merge_Oinduct,axiom,
% 2.65/1.59 ! [P: ( produc1453890942D_node > produc1453890942D_node > $o ) > list_P738500740D_node > list_P738500740D_node > $o,A0: produc1453890942D_node > produc1453890942D_node > $o,A1: list_P738500740D_node,A22: list_P738500740D_node] :
% 2.65/1.59 ( ! [R: produc1453890942D_node > produc1453890942D_node > $o,X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( ( R @ X2 @ Y4 )
% 2.65/1.59 => ( P @ R @ Xs2 @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) )
% 2.65/1.59 => ( ( ~ ( R @ X2 @ Y4 )
% 2.65/1.59 => ( P @ R @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ Ys3 ) )
% 2.65/1.59 => ( P @ R @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) ) )
% 2.65/1.59 => ( ! [R: produc1453890942D_node > produc1453890942D_node > $o,Xs2: list_P738500740D_node] : ( P @ R @ Xs2 @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [R: produc1453890942D_node > produc1453890942D_node > $o,V2: produc1453890942D_node,Va: list_P738500740D_node] : ( P @ R @ nil_Pr1769730692D_node @ ( cons_P1018517044D_node @ V2 @ Va ) )
% 2.65/1.59 => ( P @ A0 @ A1 @ A22 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_217_mergesort__by__rel__merge_Oinduct,axiom,
% 2.65/1.59 ! [P: ( node > node > $o ) > list_node > list_node > $o,A0: node > node > $o,A1: list_node,A22: list_node] :
% 2.65/1.59 ( ! [R: node > node > $o,X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ( ( R @ X2 @ Y4 )
% 2.65/1.59 => ( P @ R @ Xs2 @ ( cons_node @ Y4 @ Ys3 ) ) )
% 2.65/1.59 => ( ( ~ ( R @ X2 @ Y4 )
% 2.65/1.59 => ( P @ R @ ( cons_node @ X2 @ Xs2 ) @ Ys3 ) )
% 2.65/1.59 => ( P @ R @ ( cons_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) ) )
% 2.65/1.59 => ( ! [R: node > node > $o,Xs2: list_node] : ( P @ R @ Xs2 @ nil_node )
% 2.65/1.59 => ( ! [R: node > node > $o,V2: node,Va: list_node] : ( P @ R @ nil_node @ ( cons_node @ V2 @ Va ) )
% 2.65/1.59 => ( P @ A0 @ A1 @ A22 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_218_mergesort__by__rel__merge__induct,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > list_P738500740D_node > $o,R2: produc1453890942D_node > produc1453890942D_node > $o,Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 2.65/1.59 ( ! [Xs2: list_P738500740D_node] : ( P @ Xs2 @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X_1: list_P738500740D_node] : ( P @ nil_Pr1769730692D_node @ X_1 )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( R2 @ X2 @ Y4 )
% 2.65/1.59 => ( ( P @ Xs2 @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ~ ( R2 @ X2 @ Y4 )
% 2.65/1.59 => ( ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ Ys3 )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) ) )
% 2.65/1.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_219_mergesort__by__rel__merge__induct,axiom,
% 2.65/1.59 ! [P: list_node > list_P738500740D_node > $o,R2: node > produc1453890942D_node > $o,Xs: list_node,Ys: list_P738500740D_node] :
% 2.65/1.59 ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X_1: list_P738500740D_node] : ( P @ nil_node @ X_1 )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( R2 @ X2 @ Y4 )
% 2.65/1.59 => ( ( P @ Xs2 @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) ) )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ~ ( R2 @ X2 @ Y4 )
% 2.65/1.59 => ( ( P @ ( cons_node @ X2 @ Xs2 ) @ Ys3 )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) ) )
% 2.65/1.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_220_mergesort__by__rel__merge__induct,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > list_node > $o,R2: produc1453890942D_node > node > $o,Xs: list_P738500740D_node,Ys: list_node] :
% 2.65/1.59 ( ! [Xs2: list_P738500740D_node] : ( P @ Xs2 @ nil_node )
% 2.65/1.59 => ( ! [X_1: list_node] : ( P @ nil_Pr1769730692D_node @ X_1 )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ( R2 @ X2 @ Y4 )
% 2.65/1.59 => ( ( P @ Xs2 @ ( cons_node @ Y4 @ Ys3 ) )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ~ ( R2 @ X2 @ Y4 )
% 2.65/1.59 => ( ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ Ys3 )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) ) )
% 2.65/1.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_221_mergesort__by__rel__merge__induct,axiom,
% 2.65/1.59 ! [P: list_node > list_node > $o,R2: node > node > $o,Xs: list_node,Ys: list_node] :
% 2.65/1.59 ( ! [Xs2: list_node] : ( P @ Xs2 @ nil_node )
% 2.65/1.59 => ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ( R2 @ X2 @ Y4 )
% 2.65/1.59 => ( ( P @ Xs2 @ ( cons_node @ Y4 @ Ys3 ) )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) ) )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ~ ( R2 @ X2 @ Y4 )
% 2.65/1.59 => ( ( P @ ( cons_node @ X2 @ Xs2 ) @ Ys3 )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) ) )
% 2.65/1.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_222_longest__common__prefix_Oinduct,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > list_P738500740D_node > $o,A0: list_P738500740D_node,A1: list_P738500740D_node] :
% 2.65/1.59 ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( ( X2 = Y4 )
% 2.65/1.59 => ( P @ Xs2 @ Ys3 ) )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X2 @ Xs2 ) @ ( cons_P1018517044D_node @ Y4 @ Ys3 ) ) )
% 2.65/1.59 => ( ! [X_1: list_P738500740D_node] : ( P @ nil_Pr1769730692D_node @ X_1 )
% 2.65/1.59 => ( ! [Uu: list_P738500740D_node] : ( P @ Uu @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_223_longest__common__prefix_Oinduct,axiom,
% 2.65/1.59 ! [P: list_node > list_node > $o,A0: list_node,A1: list_node] :
% 2.65/1.59 ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ( ( X2 = Y4 )
% 2.65/1.59 => ( P @ Xs2 @ Ys3 ) )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ Xs2 ) @ ( cons_node @ Y4 @ Ys3 ) ) )
% 2.65/1.59 => ( ! [X_1: list_node] : ( P @ nil_node @ X_1 )
% 2.65/1.59 => ( ! [Uu: list_node] : ( P @ Uu @ nil_node )
% 2.65/1.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_224_strict__sorted_Oinduct,axiom,
% 2.65/1.59 ! [P: list_node > $o,A0: list_node] :
% 2.65/1.59 ( ( P @ nil_node )
% 2.65/1.59 => ( ! [X2: node,Ys3: list_node] :
% 2.65/1.59 ( ( P @ Ys3 )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ Ys3 ) ) )
% 2.65/1.59 => ( P @ A0 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_225_list_Osel_I1_J,axiom,
% 2.65/1.59 ! [X21: node,X22: list_node] :
% 2.65/1.59 ( ( hd_node @ ( cons_node @ X21 @ X22 ) )
% 2.65/1.59 = X21 ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_226_list_Osel_I3_J,axiom,
% 2.65/1.59 ! [X21: node,X22: list_node] :
% 2.65/1.59 ( ( tl_node @ ( cons_node @ X21 @ X22 ) )
% 2.65/1.59 = X22 ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_227_list__tail__coinc,axiom,
% 2.65/1.59 ! [N1: node,R1: list_node,N22: node,R22: list_node] :
% 2.65/1.59 ( ( ( cons_node @ N1 @ R1 )
% 2.65/1.59 = ( cons_node @ N22 @ R22 ) )
% 2.65/1.59 => ( ( N1 = N22 )
% 2.65/1.59 & ( R1 = R22 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_228_not__Cons__self2,axiom,
% 2.65/1.59 ! [X: node,Xs: list_node] :
% 2.65/1.59 ( ( cons_node @ X @ Xs )
% 2.65/1.59 != Xs ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_229_distinct__length__2__or__more,axiom,
% 2.65/1.59 ! [A: node,B: node,Xs: list_node] :
% 2.65/1.59 ( ( distinct_node @ ( cons_node @ A @ ( cons_node @ B @ Xs ) ) )
% 2.65/1.59 = ( ( A != B )
% 2.65/1.59 & ( distinct_node @ ( cons_node @ A @ Xs ) )
% 2.65/1.59 & ( distinct_node @ ( cons_node @ B @ Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_230_list_Oset__cases,axiom,
% 2.65/1.59 ! [E: val,A: list_val] :
% 2.65/1.59 ( ( member_val @ E @ ( set_val2 @ A ) )
% 2.65/1.59 => ( ! [Z2: list_val] :
% 2.65/1.59 ( A
% 2.65/1.59 != ( cons_val @ E @ Z2 ) )
% 2.65/1.59 => ~ ! [Z1: val,Z2: list_val] :
% 2.65/1.59 ( ( A
% 2.65/1.59 = ( cons_val @ Z1 @ Z2 ) )
% 2.65/1.59 => ~ ( member_val @ E @ ( set_val2 @ Z2 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_231_list_Oset__cases,axiom,
% 2.65/1.59 ! [E: node,A: list_node] :
% 2.65/1.59 ( ( member_node @ E @ ( set_node2 @ A ) )
% 2.65/1.59 => ( ! [Z2: list_node] :
% 2.65/1.59 ( A
% 2.65/1.59 != ( cons_node @ E @ Z2 ) )
% 2.65/1.59 => ~ ! [Z1: node,Z2: list_node] :
% 2.65/1.59 ( ( A
% 2.65/1.59 = ( cons_node @ Z1 @ Z2 ) )
% 2.65/1.59 => ~ ( member_node @ E @ ( set_node2 @ Z2 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_232_set__ConsD,axiom,
% 2.65/1.59 ! [Y3: val,X: val,Xs: list_val] :
% 2.65/1.59 ( ( member_val @ Y3 @ ( set_val2 @ ( cons_val @ X @ Xs ) ) )
% 2.65/1.59 => ( ( Y3 = X )
% 2.65/1.59 | ( member_val @ Y3 @ ( set_val2 @ Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_233_set__ConsD,axiom,
% 2.65/1.59 ! [Y3: node,X: node,Xs: list_node] :
% 2.65/1.59 ( ( member_node @ Y3 @ ( set_node2 @ ( cons_node @ X @ Xs ) ) )
% 2.65/1.59 => ( ( Y3 = X )
% 2.65/1.59 | ( member_node @ Y3 @ ( set_node2 @ Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_234_list_Oset__intros_I1_J,axiom,
% 2.65/1.59 ! [X21: val,X22: list_val] : ( member_val @ X21 @ ( set_val2 @ ( cons_val @ X21 @ X22 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_235_list_Oset__intros_I1_J,axiom,
% 2.65/1.59 ! [X21: node,X22: list_node] : ( member_node @ X21 @ ( set_node2 @ ( cons_node @ X21 @ X22 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_236_list_Oset__intros_I2_J,axiom,
% 2.65/1.59 ! [Y3: val,X22: list_val,X21: val] :
% 2.65/1.59 ( ( member_val @ Y3 @ ( set_val2 @ X22 ) )
% 2.65/1.59 => ( member_val @ Y3 @ ( set_val2 @ ( cons_val @ X21 @ X22 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_237_list_Oset__intros_I2_J,axiom,
% 2.65/1.59 ! [Y3: node,X22: list_node,X21: node] :
% 2.65/1.59 ( ( member_node @ Y3 @ ( set_node2 @ X22 ) )
% 2.65/1.59 => ( member_node @ Y3 @ ( set_node2 @ ( cons_node @ X21 @ X22 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_238_list__append__eq__Cons__cases,axiom,
% 2.65/1.59 ! [Ys: list_P738500740D_node,Zs: list_P738500740D_node,X: produc1453890942D_node,Xs: list_P738500740D_node] :
% 2.65/1.59 ( ( ( append2096883353D_node @ Ys @ Zs )
% 2.65/1.59 = ( cons_P1018517044D_node @ X @ Xs ) )
% 2.65/1.59 => ( ( ( Ys = nil_Pr1769730692D_node )
% 2.65/1.59 => ( Zs
% 2.65/1.59 != ( cons_P1018517044D_node @ X @ Xs ) ) )
% 2.65/1.59 => ~ ! [Ys4: list_P738500740D_node] :
% 2.65/1.59 ( ( Ys
% 2.65/1.59 = ( cons_P1018517044D_node @ X @ Ys4 ) )
% 2.65/1.59 => ( ( append2096883353D_node @ Ys4 @ Zs )
% 2.65/1.59 != Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_239_list__append__eq__Cons__cases,axiom,
% 2.65/1.59 ! [Ys: list_node,Zs: list_node,X: node,Xs: list_node] :
% 2.65/1.59 ( ( ( append_node @ Ys @ Zs )
% 2.65/1.59 = ( cons_node @ X @ Xs ) )
% 2.65/1.59 => ( ( ( Ys = nil_node )
% 2.65/1.59 => ( Zs
% 2.65/1.59 != ( cons_node @ X @ Xs ) ) )
% 2.65/1.59 => ~ ! [Ys4: list_node] :
% 2.65/1.59 ( ( Ys
% 2.65/1.59 = ( cons_node @ X @ Ys4 ) )
% 2.65/1.59 => ( ( append_node @ Ys4 @ Zs )
% 2.65/1.59 != Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_240_list__Cons__eq__append__cases,axiom,
% 2.65/1.59 ! [X: produc1453890942D_node,Xs: list_P738500740D_node,Ys: list_P738500740D_node,Zs: list_P738500740D_node] :
% 2.65/1.59 ( ( ( cons_P1018517044D_node @ X @ Xs )
% 2.65/1.59 = ( append2096883353D_node @ Ys @ Zs ) )
% 2.65/1.59 => ( ( ( Ys = nil_Pr1769730692D_node )
% 2.65/1.59 => ( Zs
% 2.65/1.59 != ( cons_P1018517044D_node @ X @ Xs ) ) )
% 2.65/1.59 => ~ ! [Ys4: list_P738500740D_node] :
% 2.65/1.59 ( ( Ys
% 2.65/1.59 = ( cons_P1018517044D_node @ X @ Ys4 ) )
% 2.65/1.59 => ( ( append2096883353D_node @ Ys4 @ Zs )
% 2.65/1.59 != Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_241_list__Cons__eq__append__cases,axiom,
% 2.65/1.59 ! [X: node,Xs: list_node,Ys: list_node,Zs: list_node] :
% 2.65/1.59 ( ( ( cons_node @ X @ Xs )
% 2.65/1.59 = ( append_node @ Ys @ Zs ) )
% 2.65/1.59 => ( ( ( Ys = nil_node )
% 2.65/1.59 => ( Zs
% 2.65/1.59 != ( cons_node @ X @ Xs ) ) )
% 2.65/1.59 => ~ ! [Ys4: list_node] :
% 2.65/1.59 ( ( Ys
% 2.65/1.59 = ( cons_node @ X @ Ys4 ) )
% 2.65/1.59 => ( ( append_node @ Ys4 @ Zs )
% 2.65/1.59 != Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_242_rev__nonempty__induct2_H,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node,P: list_P738500740D_node > list_P738500740D_node > $o] :
% 2.65/1.59 ( ( Xs != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ( Ys != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Y4: produc1453890942D_node] : ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node] :
% 2.65/1.59 ( ( Xs2 != nil_Pr1769730692D_node )
% 2.65/1.59 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( Ys3 != nil_Pr1769730692D_node )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ Xs2 @ Ys3 )
% 2.65/1.59 => ( ( Xs2 != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ( Ys3 != nil_Pr1769730692D_node )
% 2.65/1.59 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) ) ) )
% 2.65/1.59 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_243_rev__nonempty__induct2_H,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node,Ys: list_node,P: list_P738500740D_node > list_node > $o] :
% 2.65/1.59 ( ( Xs != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ( Ys != nil_node )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Y4: node] : ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) @ ( cons_node @ Y4 @ nil_node ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: node] :
% 2.65/1.59 ( ( Xs2 != nil_Pr1769730692D_node )
% 2.65/1.59 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ ( cons_node @ Y4 @ nil_node ) ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ( Ys3 != nil_node )
% 2.65/1.59 => ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ( P @ Xs2 @ Ys3 )
% 2.65/1.59 => ( ( Xs2 != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ( Ys3 != nil_node )
% 2.65/1.59 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) ) ) )
% 2.65/1.59 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_244_rev__nonempty__induct2_H,axiom,
% 2.65/1.59 ! [Xs: list_node,Ys: list_P738500740D_node,P: list_node > list_P738500740D_node > $o] :
% 2.65/1.59 ( ( Xs != nil_node )
% 2.65/1.59 => ( ( Ys != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X2: node,Y4: produc1453890942D_node] : ( P @ ( cons_node @ X2 @ nil_node ) @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node,Y4: produc1453890942D_node] :
% 2.65/1.59 ( ( Xs2 != nil_node )
% 2.65/1.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) )
% 2.65/1.59 => ( ! [X2: node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( Ys3 != nil_Pr1769730692D_node )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ nil_node ) @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ Xs2 @ Ys3 )
% 2.65/1.59 => ( ( Xs2 != nil_node )
% 2.65/1.59 => ( ( Ys3 != nil_Pr1769730692D_node )
% 2.65/1.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) ) ) )
% 2.65/1.59 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_245_rev__nonempty__induct2_H,axiom,
% 2.65/1.59 ! [Xs: list_node,Ys: list_node,P: list_node > list_node > $o] :
% 2.65/1.59 ( ( Xs != nil_node )
% 2.65/1.59 => ( ( Ys != nil_node )
% 2.65/1.59 => ( ! [X2: node,Y4: node] : ( P @ ( cons_node @ X2 @ nil_node ) @ ( cons_node @ Y4 @ nil_node ) )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node,Y4: node] :
% 2.65/1.59 ( ( Xs2 != nil_node )
% 2.65/1.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ ( cons_node @ Y4 @ nil_node ) ) )
% 2.65/1.59 => ( ! [X2: node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ( Ys3 != nil_node )
% 2.65/1.59 => ( P @ ( cons_node @ X2 @ nil_node ) @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ( P @ Xs2 @ Ys3 )
% 2.65/1.59 => ( ( Xs2 != nil_node )
% 2.65/1.59 => ( ( Ys3 != nil_node )
% 2.65/1.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) ) ) )
% 2.65/1.59 => ( P @ Xs @ Ys ) ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_246_rev__nonempty__induct,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node,P: list_P738500740D_node > $o] :
% 2.65/1.59 ( ( Xs != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node] : ( P @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 2.65/1.59 ( ( Xs2 != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ( P @ Xs2 )
% 2.65/1.59 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) ) ) )
% 2.65/1.59 => ( P @ Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_247_rev__nonempty__induct,axiom,
% 2.65/1.59 ! [Xs: list_node,P: list_node > $o] :
% 2.65/1.59 ( ( Xs != nil_node )
% 2.65/1.59 => ( ! [X2: node] : ( P @ ( cons_node @ X2 @ nil_node ) )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node] :
% 2.65/1.59 ( ( Xs2 != nil_node )
% 2.65/1.59 => ( ( P @ Xs2 )
% 2.65/1.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) ) ) )
% 2.65/1.59 => ( P @ Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_248_append__eq__Cons__conv,axiom,
% 2.65/1.59 ! [Ys: list_P738500740D_node,Zs: list_P738500740D_node,X: produc1453890942D_node,Xs: list_P738500740D_node] :
% 2.65/1.59 ( ( ( append2096883353D_node @ Ys @ Zs )
% 2.65/1.59 = ( cons_P1018517044D_node @ X @ Xs ) )
% 2.65/1.59 = ( ( ( Ys = nil_Pr1769730692D_node )
% 2.65/1.59 & ( Zs
% 2.65/1.59 = ( cons_P1018517044D_node @ X @ Xs ) ) )
% 2.65/1.59 | ? [Ys5: list_P738500740D_node] :
% 2.65/1.59 ( ( Ys
% 2.65/1.59 = ( cons_P1018517044D_node @ X @ Ys5 ) )
% 2.65/1.59 & ( ( append2096883353D_node @ Ys5 @ Zs )
% 2.65/1.59 = Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_249_append__eq__Cons__conv,axiom,
% 2.65/1.59 ! [Ys: list_node,Zs: list_node,X: node,Xs: list_node] :
% 2.65/1.59 ( ( ( append_node @ Ys @ Zs )
% 2.65/1.59 = ( cons_node @ X @ Xs ) )
% 2.65/1.59 = ( ( ( Ys = nil_node )
% 2.65/1.59 & ( Zs
% 2.65/1.59 = ( cons_node @ X @ Xs ) ) )
% 2.65/1.59 | ? [Ys5: list_node] :
% 2.65/1.59 ( ( Ys
% 2.65/1.59 = ( cons_node @ X @ Ys5 ) )
% 2.65/1.59 & ( ( append_node @ Ys5 @ Zs )
% 2.65/1.59 = Xs ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_250_Cons__eq__append__conv,axiom,
% 2.65/1.59 ! [X: produc1453890942D_node,Xs: list_P738500740D_node,Ys: list_P738500740D_node,Zs: list_P738500740D_node] :
% 2.65/1.59 ( ( ( cons_P1018517044D_node @ X @ Xs )
% 2.65/1.59 = ( append2096883353D_node @ Ys @ Zs ) )
% 2.65/1.59 = ( ( ( Ys = nil_Pr1769730692D_node )
% 2.65/1.59 & ( ( cons_P1018517044D_node @ X @ Xs )
% 2.65/1.59 = Zs ) )
% 2.65/1.59 | ? [Ys5: list_P738500740D_node] :
% 2.65/1.59 ( ( ( cons_P1018517044D_node @ X @ Ys5 )
% 2.65/1.59 = Ys )
% 2.65/1.59 & ( Xs
% 2.65/1.59 = ( append2096883353D_node @ Ys5 @ Zs ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_251_Cons__eq__append__conv,axiom,
% 2.65/1.59 ! [X: node,Xs: list_node,Ys: list_node,Zs: list_node] :
% 2.65/1.59 ( ( ( cons_node @ X @ Xs )
% 2.65/1.59 = ( append_node @ Ys @ Zs ) )
% 2.65/1.59 = ( ( ( Ys = nil_node )
% 2.65/1.59 & ( ( cons_node @ X @ Xs )
% 2.65/1.59 = Zs ) )
% 2.65/1.59 | ? [Ys5: list_node] :
% 2.65/1.59 ( ( ( cons_node @ X @ Ys5 )
% 2.65/1.59 = Ys )
% 2.65/1.59 & ( Xs
% 2.65/1.59 = ( append_node @ Ys5 @ Zs ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_252_neq__Nil__rev__conv,axiom,
% 2.65/1.59 ! [L: list_P738500740D_node] :
% 2.65/1.59 ( ( L != nil_Pr1769730692D_node )
% 2.65/1.59 = ( ? [Xs3: list_P738500740D_node,X3: produc1453890942D_node] :
% 2.65/1.59 ( L
% 2.65/1.59 = ( append2096883353D_node @ Xs3 @ ( cons_P1018517044D_node @ X3 @ nil_Pr1769730692D_node ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_253_neq__Nil__rev__conv,axiom,
% 2.65/1.59 ! [L: list_node] :
% 2.65/1.59 ( ( L != nil_node )
% 2.65/1.59 = ( ? [Xs3: list_node,X3: node] :
% 2.65/1.59 ( L
% 2.65/1.59 = ( append_node @ Xs3 @ ( cons_node @ X3 @ nil_node ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_254_rev__induct2_H,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > list_P738500740D_node > $o,Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ nil_Pr1769730692D_node @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] : ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [Y4: produc1453890942D_node,Ys3: list_P738500740D_node] : ( P @ nil_Pr1769730692D_node @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ Xs2 @ Ys3 )
% 2.65/1.59 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) )
% 2.65/1.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_255_rev__induct2_H,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > list_node > $o,Xs: list_P738500740D_node,Ys: list_node] :
% 2.65/1.59 ( ( P @ nil_Pr1769730692D_node @ nil_node )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] : ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ nil_node )
% 2.65/1.59 => ( ! [Y4: node,Ys3: list_node] : ( P @ nil_Pr1769730692D_node @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ( P @ Xs2 @ Ys3 )
% 2.65/1.59 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) )
% 2.65/1.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_256_rev__induct2_H,axiom,
% 2.65/1.59 ! [P: list_node > list_P738500740D_node > $o,Xs: list_node,Ys: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ nil_node @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node] : ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [Y4: produc1453890942D_node,Ys3: list_P738500740D_node] : ( P @ nil_node @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ Xs2 @ Ys3 )
% 2.65/1.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) )
% 2.65/1.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_257_rev__induct2_H,axiom,
% 2.65/1.59 ! [P: list_node > list_node > $o,Xs: list_node,Ys: list_node] :
% 2.65/1.59 ( ( P @ nil_node @ nil_node )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node] : ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ nil_node )
% 2.65/1.59 => ( ! [Y4: node,Ys3: list_node] : ( P @ nil_node @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ( P @ Xs2 @ Ys3 )
% 2.65/1.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) )
% 2.65/1.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_258_neq__Nil__revE,axiom,
% 2.65/1.59 ! [L: list_P738500740D_node] :
% 2.65/1.59 ( ( L != nil_Pr1769730692D_node )
% 2.65/1.59 => ~ ! [Ll: list_P738500740D_node,E4: produc1453890942D_node] :
% 2.65/1.59 ( L
% 2.65/1.59 != ( append2096883353D_node @ Ll @ ( cons_P1018517044D_node @ E4 @ nil_Pr1769730692D_node ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_259_neq__Nil__revE,axiom,
% 2.65/1.59 ! [L: list_node] :
% 2.65/1.59 ( ( L != nil_node )
% 2.65/1.59 => ~ ! [Ll: list_node,E4: node] :
% 2.65/1.59 ( L
% 2.65/1.59 != ( append_node @ Ll @ ( cons_node @ E4 @ nil_node ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_260_rev__exhaust,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node] :
% 2.65/1.59 ( ( Xs != nil_Pr1769730692D_node )
% 2.65/1.59 => ~ ! [Ys3: list_P738500740D_node,Y4: produc1453890942D_node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 != ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_261_rev__exhaust,axiom,
% 2.65/1.59 ! [Xs: list_node] :
% 2.65/1.59 ( ( Xs != nil_node )
% 2.65/1.59 => ~ ! [Ys3: list_node,Y4: node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 != ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_262_rev__induct,axiom,
% 2.65/1.59 ! [P: list_P738500740D_node > $o,Xs: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 2.65/1.59 ( ( P @ Xs2 )
% 2.65/1.59 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) ) )
% 2.65/1.59 => ( P @ Xs ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_263_rev__induct,axiom,
% 2.65/1.59 ! [P: list_node > $o,Xs: list_node] :
% 2.65/1.59 ( ( P @ nil_node )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node] :
% 2.65/1.59 ( ( P @ Xs2 )
% 2.65/1.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) ) )
% 2.65/1.59 => ( P @ Xs ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_264_split__list,axiom,
% 2.65/1.59 ! [X: val,Xs: list_val] :
% 2.65/1.59 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.65/1.59 => ? [Ys3: list_val,Zs3: list_val] :
% 2.65/1.59 ( Xs
% 2.65/1.59 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs3 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_265_split__list,axiom,
% 2.65/1.59 ! [X: node,Xs: list_node] :
% 2.65/1.59 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.65/1.59 => ? [Ys3: list_node,Zs3: list_node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs3 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_266_split__list__last,axiom,
% 2.65/1.59 ! [X: val,Xs: list_val] :
% 2.65/1.59 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.65/1.59 => ? [Ys3: list_val,Zs3: list_val] :
% 2.65/1.59 ( ( Xs
% 2.65/1.59 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs3 ) ) )
% 2.65/1.59 & ~ ( member_val @ X @ ( set_val2 @ Zs3 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_267_split__list__last,axiom,
% 2.65/1.59 ! [X: node,Xs: list_node] :
% 2.65/1.59 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.65/1.59 => ? [Ys3: list_node,Zs3: list_node] :
% 2.65/1.59 ( ( Xs
% 2.65/1.59 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs3 ) ) )
% 2.65/1.59 & ~ ( member_node @ X @ ( set_node2 @ Zs3 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_268_split__list__prop,axiom,
% 2.65/1.59 ! [Xs: list_node,P: node > $o] :
% 2.65/1.59 ( ? [X4: node] :
% 2.65/1.59 ( ( member_node @ X4 @ ( set_node2 @ Xs ) )
% 2.65/1.59 & ( P @ X4 ) )
% 2.65/1.59 => ? [Ys3: list_node,X2: node] :
% 2.65/1.59 ( ? [Zs3: list_node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 = ( append_node @ Ys3 @ ( cons_node @ X2 @ Zs3 ) ) )
% 2.65/1.59 & ( P @ X2 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_269_xy__in__set__cases,axiom,
% 2.65/1.59 ! [X: val,L: list_val,Y3: val] :
% 2.65/1.59 ( ( member_val @ X @ ( set_val2 @ L ) )
% 2.65/1.59 => ( ( member_val @ Y3 @ ( set_val2 @ L ) )
% 2.65/1.59 => ( ( ( X = Y3 )
% 2.65/1.59 => ! [L12: list_val,L22: list_val] :
% 2.65/1.59 ( L
% 2.65/1.59 != ( append_val @ L12 @ ( cons_val @ Y3 @ L22 ) ) ) )
% 2.65/1.59 => ( ( ( X != Y3 )
% 2.65/1.59 => ! [L12: list_val,L22: list_val,L3: list_val] :
% 2.65/1.59 ( L
% 2.65/1.59 != ( append_val @ L12 @ ( cons_val @ X @ ( append_val @ L22 @ ( cons_val @ Y3 @ L3 ) ) ) ) ) )
% 2.65/1.59 => ~ ( ( X != Y3 )
% 2.65/1.59 => ! [L12: list_val,L22: list_val,L3: list_val] :
% 2.65/1.59 ( L
% 2.65/1.59 != ( append_val @ L12 @ ( cons_val @ Y3 @ ( append_val @ L22 @ ( cons_val @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_270_xy__in__set__cases,axiom,
% 2.65/1.59 ! [X: node,L: list_node,Y3: node] :
% 2.65/1.59 ( ( member_node @ X @ ( set_node2 @ L ) )
% 2.65/1.59 => ( ( member_node @ Y3 @ ( set_node2 @ L ) )
% 2.65/1.59 => ( ( ( X = Y3 )
% 2.65/1.59 => ! [L12: list_node,L22: list_node] :
% 2.65/1.59 ( L
% 2.65/1.59 != ( append_node @ L12 @ ( cons_node @ Y3 @ L22 ) ) ) )
% 2.65/1.59 => ( ( ( X != Y3 )
% 2.65/1.59 => ! [L12: list_node,L22: list_node,L3: list_node] :
% 2.65/1.59 ( L
% 2.65/1.59 != ( append_node @ L12 @ ( cons_node @ X @ ( append_node @ L22 @ ( cons_node @ Y3 @ L3 ) ) ) ) ) )
% 2.65/1.59 => ~ ( ( X != Y3 )
% 2.65/1.59 => ! [L12: list_node,L22: list_node,L3: list_node] :
% 2.65/1.59 ( L
% 2.65/1.59 != ( append_node @ L12 @ ( cons_node @ Y3 @ ( append_node @ L22 @ ( cons_node @ X @ L3 ) ) ) ) ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_271_split__list__first,axiom,
% 2.65/1.59 ! [X: val,Xs: list_val] :
% 2.65/1.59 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.65/1.59 => ? [Ys3: list_val,Zs3: list_val] :
% 2.65/1.59 ( ( Xs
% 2.65/1.59 = ( append_val @ Ys3 @ ( cons_val @ X @ Zs3 ) ) )
% 2.65/1.59 & ~ ( member_val @ X @ ( set_val2 @ Ys3 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_272_split__list__first,axiom,
% 2.65/1.59 ! [X: node,Xs: list_node] :
% 2.65/1.59 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.65/1.59 => ? [Ys3: list_node,Zs3: list_node] :
% 2.65/1.59 ( ( Xs
% 2.65/1.59 = ( append_node @ Ys3 @ ( cons_node @ X @ Zs3 ) ) )
% 2.65/1.59 & ~ ( member_node @ X @ ( set_node2 @ Ys3 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_273_split__list__propE,axiom,
% 2.65/1.59 ! [Xs: list_node,P: node > $o] :
% 2.65/1.59 ( ? [X4: node] :
% 2.65/1.59 ( ( member_node @ X4 @ ( set_node2 @ Xs ) )
% 2.65/1.59 & ( P @ X4 ) )
% 2.65/1.59 => ~ ! [Ys3: list_node,X2: node] :
% 2.65/1.59 ( ? [Zs3: list_node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 = ( append_node @ Ys3 @ ( cons_node @ X2 @ Zs3 ) ) )
% 2.65/1.59 => ~ ( P @ X2 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_274_append__Cons__eq__iff,axiom,
% 2.65/1.59 ! [X: val,Xs: list_val,Ys: list_val,Xs4: list_val,Ys6: list_val] :
% 2.65/1.59 ( ~ ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.65/1.59 => ( ~ ( member_val @ X @ ( set_val2 @ Ys ) )
% 2.65/1.59 => ( ( ( append_val @ Xs @ ( cons_val @ X @ Ys ) )
% 2.65/1.59 = ( append_val @ Xs4 @ ( cons_val @ X @ Ys6 ) ) )
% 2.65/1.59 = ( ( Xs = Xs4 )
% 2.65/1.59 & ( Ys = Ys6 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_275_append__Cons__eq__iff,axiom,
% 2.65/1.59 ! [X: node,Xs: list_node,Ys: list_node,Xs4: list_node,Ys6: list_node] :
% 2.65/1.59 ( ~ ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.65/1.59 => ( ~ ( member_node @ X @ ( set_node2 @ Ys ) )
% 2.65/1.59 => ( ( ( append_node @ Xs @ ( cons_node @ X @ Ys ) )
% 2.65/1.59 = ( append_node @ Xs4 @ ( cons_node @ X @ Ys6 ) ) )
% 2.65/1.59 = ( ( Xs = Xs4 )
% 2.65/1.59 & ( Ys = Ys6 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_276_in__set__conv__decomp,axiom,
% 2.65/1.59 ! [X: val,Xs: list_val] :
% 2.65/1.59 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.65/1.59 = ( ? [Ys2: list_val,Zs2: list_val] :
% 2.65/1.59 ( Xs
% 2.65/1.59 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs2 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_277_in__set__conv__decomp,axiom,
% 2.65/1.59 ! [X: node,Xs: list_node] :
% 2.65/1.59 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.65/1.59 = ( ? [Ys2: list_node,Zs2: list_node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs2 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_278_in__set__list__format,axiom,
% 2.65/1.59 ! [E: val,L: list_val] :
% 2.65/1.59 ( ( member_val @ E @ ( set_val2 @ L ) )
% 2.65/1.59 => ~ ! [L12: list_val,L22: list_val] :
% 2.65/1.59 ( L
% 2.65/1.59 != ( append_val @ L12 @ ( cons_val @ E @ L22 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_279_in__set__list__format,axiom,
% 2.65/1.59 ! [E: node,L: list_node] :
% 2.65/1.59 ( ( member_node @ E @ ( set_node2 @ L ) )
% 2.65/1.59 => ~ ! [L12: list_node,L22: list_node] :
% 2.65/1.59 ( L
% 2.65/1.59 != ( append_node @ L12 @ ( cons_node @ E @ L22 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_280_split__list__last__prop,axiom,
% 2.65/1.59 ! [Xs: list_node,P: node > $o] :
% 2.65/1.59 ( ? [X4: node] :
% 2.65/1.59 ( ( member_node @ X4 @ ( set_node2 @ Xs ) )
% 2.65/1.59 & ( P @ X4 ) )
% 2.65/1.59 => ? [Ys3: list_node,X2: node,Zs3: list_node] :
% 2.65/1.59 ( ( Xs
% 2.65/1.59 = ( append_node @ Ys3 @ ( cons_node @ X2 @ Zs3 ) ) )
% 2.65/1.59 & ( P @ X2 )
% 2.65/1.59 & ! [Xa: node] :
% 2.65/1.59 ( ( member_node @ Xa @ ( set_node2 @ Zs3 ) )
% 2.65/1.59 => ~ ( P @ Xa ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_281_split__list__first__prop,axiom,
% 2.65/1.59 ! [Xs: list_node,P: node > $o] :
% 2.65/1.59 ( ? [X4: node] :
% 2.65/1.59 ( ( member_node @ X4 @ ( set_node2 @ Xs ) )
% 2.65/1.59 & ( P @ X4 ) )
% 2.65/1.59 => ? [Ys3: list_node,X2: node] :
% 2.65/1.59 ( ? [Zs3: list_node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 = ( append_node @ Ys3 @ ( cons_node @ X2 @ Zs3 ) ) )
% 2.65/1.59 & ( P @ X2 )
% 2.65/1.59 & ! [Xa: node] :
% 2.65/1.59 ( ( member_node @ Xa @ ( set_node2 @ Ys3 ) )
% 2.65/1.59 => ~ ( P @ Xa ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_282_split__list__last__propE,axiom,
% 2.65/1.59 ! [Xs: list_node,P: node > $o] :
% 2.65/1.59 ( ? [X4: node] :
% 2.65/1.59 ( ( member_node @ X4 @ ( set_node2 @ Xs ) )
% 2.65/1.59 & ( P @ X4 ) )
% 2.65/1.59 => ~ ! [Ys3: list_node,X2: node,Zs3: list_node] :
% 2.65/1.59 ( ( Xs
% 2.65/1.59 = ( append_node @ Ys3 @ ( cons_node @ X2 @ Zs3 ) ) )
% 2.65/1.59 => ( ( P @ X2 )
% 2.65/1.59 => ~ ! [Xa: node] :
% 2.65/1.59 ( ( member_node @ Xa @ ( set_node2 @ Zs3 ) )
% 2.65/1.59 => ~ ( P @ Xa ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_283_split__list__first__propE,axiom,
% 2.65/1.59 ! [Xs: list_node,P: node > $o] :
% 2.65/1.59 ( ? [X4: node] :
% 2.65/1.59 ( ( member_node @ X4 @ ( set_node2 @ Xs ) )
% 2.65/1.59 & ( P @ X4 ) )
% 2.65/1.59 => ~ ! [Ys3: list_node,X2: node] :
% 2.65/1.59 ( ? [Zs3: list_node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 = ( append_node @ Ys3 @ ( cons_node @ X2 @ Zs3 ) ) )
% 2.65/1.59 => ( ( P @ X2 )
% 2.65/1.59 => ~ ! [Xa: node] :
% 2.65/1.59 ( ( member_node @ Xa @ ( set_node2 @ Ys3 ) )
% 2.65/1.59 => ~ ( P @ Xa ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_284_in__set__conv__decomp__last,axiom,
% 2.65/1.59 ! [X: val,Xs: list_val] :
% 2.65/1.59 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.65/1.59 = ( ? [Ys2: list_val,Zs2: list_val] :
% 2.65/1.59 ( ( Xs
% 2.65/1.59 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs2 ) ) )
% 2.65/1.59 & ~ ( member_val @ X @ ( set_val2 @ Zs2 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_285_in__set__conv__decomp__last,axiom,
% 2.65/1.59 ! [X: node,Xs: list_node] :
% 2.65/1.59 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.65/1.59 = ( ? [Ys2: list_node,Zs2: list_node] :
% 2.65/1.59 ( ( Xs
% 2.65/1.59 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs2 ) ) )
% 2.65/1.59 & ~ ( member_node @ X @ ( set_node2 @ Zs2 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_286_in__set__conv__decomp__first,axiom,
% 2.65/1.59 ! [X: val,Xs: list_val] :
% 2.65/1.59 ( ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.65/1.59 = ( ? [Ys2: list_val,Zs2: list_val] :
% 2.65/1.59 ( ( Xs
% 2.65/1.59 = ( append_val @ Ys2 @ ( cons_val @ X @ Zs2 ) ) )
% 2.65/1.59 & ~ ( member_val @ X @ ( set_val2 @ Ys2 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_287_in__set__conv__decomp__first,axiom,
% 2.65/1.59 ! [X: node,Xs: list_node] :
% 2.65/1.59 ( ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.65/1.59 = ( ? [Ys2: list_node,Zs2: list_node] :
% 2.65/1.59 ( ( Xs
% 2.65/1.59 = ( append_node @ Ys2 @ ( cons_node @ X @ Zs2 ) ) )
% 2.65/1.59 & ~ ( member_node @ X @ ( set_node2 @ Ys2 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_288_split__list__last__prop__iff,axiom,
% 2.65/1.59 ! [Xs: list_node,P: node > $o] :
% 2.65/1.59 ( ( ? [X3: node] :
% 2.65/1.59 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 2.65/1.59 & ( P @ X3 ) ) )
% 2.65/1.59 = ( ? [Ys2: list_node,X3: node,Zs2: list_node] :
% 2.65/1.59 ( ( Xs
% 2.65/1.59 = ( append_node @ Ys2 @ ( cons_node @ X3 @ Zs2 ) ) )
% 2.65/1.59 & ( P @ X3 )
% 2.65/1.59 & ! [Y2: node] :
% 2.65/1.59 ( ( member_node @ Y2 @ ( set_node2 @ Zs2 ) )
% 2.65/1.59 => ~ ( P @ Y2 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_289_split__list__first__prop__iff,axiom,
% 2.65/1.59 ! [Xs: list_node,P: node > $o] :
% 2.65/1.59 ( ( ? [X3: node] :
% 2.65/1.59 ( ( member_node @ X3 @ ( set_node2 @ Xs ) )
% 2.65/1.59 & ( P @ X3 ) ) )
% 2.65/1.59 = ( ? [Ys2: list_node,X3: node] :
% 2.65/1.59 ( ? [Zs2: list_node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 = ( append_node @ Ys2 @ ( cons_node @ X3 @ Zs2 ) ) )
% 2.65/1.59 & ( P @ X3 )
% 2.65/1.59 & ! [Y2: node] :
% 2.65/1.59 ( ( member_node @ Y2 @ ( set_node2 @ Ys2 ) )
% 2.65/1.59 => ~ ( P @ Y2 ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_290_distinct__singleton,axiom,
% 2.65/1.59 ! [X: produc1453890942D_node] : ( distin1098566007D_node @ ( cons_P1018517044D_node @ X @ nil_Pr1769730692D_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_291_distinct__singleton,axiom,
% 2.65/1.59 ! [X: node] : ( distinct_node @ ( cons_node @ X @ nil_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_292_distinct_Osimps_I2_J,axiom,
% 2.65/1.59 ! [X: val,Xs: list_val] :
% 2.65/1.59 ( ( distinct_val @ ( cons_val @ X @ Xs ) )
% 2.65/1.59 = ( ~ ( member_val @ X @ ( set_val2 @ Xs ) )
% 2.65/1.59 & ( distinct_val @ Xs ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_293_distinct_Osimps_I2_J,axiom,
% 2.65/1.59 ! [X: node,Xs: list_node] :
% 2.65/1.59 ( ( distinct_node @ ( cons_node @ X @ Xs ) )
% 2.65/1.59 = ( ~ ( member_node @ X @ ( set_node2 @ Xs ) )
% 2.65/1.59 & ( distinct_node @ Xs ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_294_distinct__match,axiom,
% 2.65/1.59 ! [Al: list_node,E: node,Bl: list_node,Al2: list_node,Bl2: list_node] :
% 2.65/1.59 ( ( distinct_node @ ( append_node @ Al @ ( cons_node @ E @ Bl ) ) )
% 2.65/1.59 => ( ( ( append_node @ Al @ ( cons_node @ E @ Bl ) )
% 2.65/1.59 = ( append_node @ Al2 @ ( cons_node @ E @ Bl2 ) ) )
% 2.65/1.59 = ( ( Al = Al2 )
% 2.65/1.59 & ( Bl = Bl2 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_295_Nil__tl,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node] :
% 2.65/1.59 ( ( nil_Pr1769730692D_node
% 2.65/1.59 = ( tl_Pro1633633005D_node @ Xs ) )
% 2.65/1.59 = ( ( Xs = nil_Pr1769730692D_node )
% 2.65/1.59 | ? [X3: produc1453890942D_node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 = ( cons_P1018517044D_node @ X3 @ nil_Pr1769730692D_node ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_296_Nil__tl,axiom,
% 2.65/1.59 ! [Xs: list_node] :
% 2.65/1.59 ( ( nil_node
% 2.65/1.59 = ( tl_node @ Xs ) )
% 2.65/1.59 = ( ( Xs = nil_node )
% 2.65/1.59 | ? [X3: node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 = ( cons_node @ X3 @ nil_node ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_297_tl__Nil,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node] :
% 2.65/1.59 ( ( ( tl_Pro1633633005D_node @ Xs )
% 2.65/1.59 = nil_Pr1769730692D_node )
% 2.65/1.59 = ( ( Xs = nil_Pr1769730692D_node )
% 2.65/1.59 | ? [X3: produc1453890942D_node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 = ( cons_P1018517044D_node @ X3 @ nil_Pr1769730692D_node ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_298_tl__Nil,axiom,
% 2.65/1.59 ! [Xs: list_node] :
% 2.65/1.59 ( ( ( tl_node @ Xs )
% 2.65/1.59 = nil_node )
% 2.65/1.59 = ( ( Xs = nil_node )
% 2.65/1.59 | ? [X3: node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 = ( cons_node @ X3 @ nil_node ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_299_tl__obtain__elem,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node] :
% 2.65/1.59 ( ( Xs != nil_Pr1769730692D_node )
% 2.65/1.59 => ( ( ( tl_Pro1633633005D_node @ Xs )
% 2.65/1.59 = nil_Pr1769730692D_node )
% 2.65/1.59 => ~ ! [E4: produc1453890942D_node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 != ( cons_P1018517044D_node @ E4 @ nil_Pr1769730692D_node ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_300_tl__obtain__elem,axiom,
% 2.65/1.59 ! [Xs: list_node] :
% 2.65/1.59 ( ( Xs != nil_node )
% 2.65/1.59 => ( ( ( tl_node @ Xs )
% 2.65/1.59 = nil_node )
% 2.65/1.59 => ~ ! [E4: node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 != ( cons_node @ E4 @ nil_node ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_301_not__distinct__decomp,axiom,
% 2.65/1.59 ! [Ws: list_P738500740D_node] :
% 2.65/1.59 ( ~ ( distin1098566007D_node @ Ws )
% 2.65/1.59 => ? [Xs2: list_P738500740D_node,Ys3: list_P738500740D_node,Zs3: list_P738500740D_node,Y4: produc1453890942D_node] :
% 2.65/1.59 ( Ws
% 2.65/1.59 = ( append2096883353D_node @ Xs2 @ ( append2096883353D_node @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) @ ( append2096883353D_node @ Ys3 @ ( append2096883353D_node @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) @ Zs3 ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_302_not__distinct__decomp,axiom,
% 2.65/1.59 ! [Ws: list_node] :
% 2.65/1.59 ( ~ ( distinct_node @ Ws )
% 2.65/1.59 => ? [Xs2: list_node,Ys3: list_node,Zs3: list_node,Y4: node] :
% 2.65/1.59 ( Ws
% 2.65/1.59 = ( append_node @ Xs2 @ ( append_node @ ( cons_node @ Y4 @ nil_node ) @ ( append_node @ Ys3 @ ( append_node @ ( cons_node @ Y4 @ nil_node ) @ Zs3 ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_303_not__distinct__conv__prefix,axiom,
% 2.65/1.59 ! [As2: list_val] :
% 2.65/1.59 ( ( ~ ( distinct_val @ As2 ) )
% 2.65/1.59 = ( ? [Xs3: list_val,Y2: val,Ys2: list_val] :
% 2.65/1.59 ( ( member_val @ Y2 @ ( set_val2 @ Xs3 ) )
% 2.65/1.59 & ( distinct_val @ Xs3 )
% 2.65/1.59 & ( As2
% 2.65/1.59 = ( append_val @ Xs3 @ ( cons_val @ Y2 @ Ys2 ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_304_not__distinct__conv__prefix,axiom,
% 2.65/1.59 ! [As2: list_node] :
% 2.65/1.59 ( ( ~ ( distinct_node @ As2 ) )
% 2.65/1.59 = ( ? [Xs3: list_node,Y2: node,Ys2: list_node] :
% 2.65/1.59 ( ( member_node @ Y2 @ ( set_node2 @ Xs3 ) )
% 2.65/1.59 & ( distinct_node @ Xs3 )
% 2.65/1.59 & ( As2
% 2.65/1.59 = ( append_node @ Xs3 @ ( cons_node @ Y2 @ Ys2 ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_305_not__suffix__induct,axiom,
% 2.65/1.59 ! [Ps: list_P738500740D_node,Ls: list_P738500740D_node,P: list_P738500740D_node > list_P738500740D_node > $o] :
% 2.65/1.59 ( ~ ( suffix1143830554D_node @ Ps @ Ls )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] : ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( X2 != Y4 )
% 2.65/1.59 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) )
% 2.65/1.59 => ( ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node,Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( X2 = Y4 )
% 2.65/1.59 => ( ~ ( suffix1143830554D_node @ Xs2 @ Ys3 )
% 2.65/1.59 => ( ( P @ Xs2 @ Ys3 )
% 2.65/1.59 => ( P @ ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) @ ( append2096883353D_node @ Ys3 @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) ) ) ) ) )
% 2.65/1.59 => ( P @ Ps @ Ls ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_306_not__suffix__induct,axiom,
% 2.65/1.59 ! [Ps: list_node,Ls: list_node,P: list_node > list_node > $o] :
% 2.65/1.59 ( ~ ( suffix_node @ Ps @ Ls )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node] : ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ nil_node )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ( X2 != Y4 )
% 2.65/1.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) )
% 2.65/1.59 => ( ! [X2: node,Xs2: list_node,Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ( X2 = Y4 )
% 2.65/1.59 => ( ~ ( suffix_node @ Xs2 @ Ys3 )
% 2.65/1.59 => ( ( P @ Xs2 @ Ys3 )
% 2.65/1.59 => ( P @ ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) @ ( append_node @ Ys3 @ ( cons_node @ Y4 @ nil_node ) ) ) ) ) )
% 2.65/1.59 => ( P @ Ps @ Ls ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_307_not__suffix__cases,axiom,
% 2.65/1.59 ! [Ps: list_P738500740D_node,Ls: list_P738500740D_node] :
% 2.65/1.59 ( ~ ( suffix1143830554D_node @ Ps @ Ls )
% 2.65/1.59 => ( ( ( Ps != nil_Pr1769730692D_node )
% 2.65/1.59 => ( Ls != nil_Pr1769730692D_node ) )
% 2.65/1.59 => ( ! [A3: produc1453890942D_node,As: list_P738500740D_node] :
% 2.65/1.59 ( ( Ps
% 2.65/1.59 = ( append2096883353D_node @ As @ ( cons_P1018517044D_node @ A3 @ nil_Pr1769730692D_node ) ) )
% 2.65/1.59 => ! [X2: produc1453890942D_node,Xs2: list_P738500740D_node] :
% 2.65/1.59 ( ( Ls
% 2.65/1.59 = ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) )
% 2.65/1.59 => ( ( X2 = A3 )
% 2.65/1.59 => ( suffix1143830554D_node @ As @ Xs2 ) ) ) )
% 2.65/1.59 => ~ ! [A3: produc1453890942D_node] :
% 2.65/1.59 ( ? [As: list_P738500740D_node] :
% 2.65/1.59 ( Ps
% 2.65/1.59 = ( append2096883353D_node @ As @ ( cons_P1018517044D_node @ A3 @ nil_Pr1769730692D_node ) ) )
% 2.65/1.59 => ! [X2: produc1453890942D_node] :
% 2.65/1.59 ( ? [Xs2: list_P738500740D_node] :
% 2.65/1.59 ( Ls
% 2.65/1.59 = ( append2096883353D_node @ Xs2 @ ( cons_P1018517044D_node @ X2 @ nil_Pr1769730692D_node ) ) )
% 2.65/1.59 => ( X2 = A3 ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_308_not__suffix__cases,axiom,
% 2.65/1.59 ! [Ps: list_node,Ls: list_node] :
% 2.65/1.59 ( ~ ( suffix_node @ Ps @ Ls )
% 2.65/1.59 => ( ( ( Ps != nil_node )
% 2.65/1.59 => ( Ls != nil_node ) )
% 2.65/1.59 => ( ! [A3: node,As: list_node] :
% 2.65/1.59 ( ( Ps
% 2.65/1.59 = ( append_node @ As @ ( cons_node @ A3 @ nil_node ) ) )
% 2.65/1.59 => ! [X2: node,Xs2: list_node] :
% 2.65/1.59 ( ( Ls
% 2.65/1.59 = ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) )
% 2.65/1.59 => ( ( X2 = A3 )
% 2.65/1.59 => ( suffix_node @ As @ Xs2 ) ) ) )
% 2.65/1.59 => ~ ! [A3: node] :
% 2.65/1.59 ( ? [As: list_node] :
% 2.65/1.59 ( Ps
% 2.65/1.59 = ( append_node @ As @ ( cons_node @ A3 @ nil_node ) ) )
% 2.65/1.59 => ! [X2: node] :
% 2.65/1.59 ( ? [Xs2: list_node] :
% 2.65/1.59 ( Ls
% 2.65/1.59 = ( append_node @ Xs2 @ ( cons_node @ X2 @ nil_node ) ) )
% 2.65/1.59 => ( X2 = A3 ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_309_list_Oexhaust__sel,axiom,
% 2.65/1.59 ! [List: list_P738500740D_node] :
% 2.65/1.59 ( ( List != nil_Pr1769730692D_node )
% 2.65/1.59 => ( List
% 2.65/1.59 = ( cons_P1018517044D_node @ ( hd_Pro1395892457D_node @ List ) @ ( tl_Pro1633633005D_node @ List ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_310_list_Oexhaust__sel,axiom,
% 2.65/1.59 ! [List: list_node] :
% 2.65/1.59 ( ( List != nil_node )
% 2.65/1.59 => ( List
% 2.65/1.59 = ( cons_node @ ( hd_node @ List ) @ ( tl_node @ List ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_311_not__distinct__split__distinct,axiom,
% 2.65/1.59 ! [Xs: list_val] :
% 2.65/1.59 ( ~ ( distinct_val @ Xs )
% 2.65/1.59 => ~ ! [Y4: val,Ys3: list_val] :
% 2.65/1.59 ( ( distinct_val @ Ys3 )
% 2.65/1.59 => ( ( member_val @ Y4 @ ( set_val2 @ Ys3 ) )
% 2.65/1.59 => ! [Zs3: list_val] :
% 2.65/1.59 ( Xs
% 2.65/1.59 != ( append_val @ Ys3 @ ( append_val @ ( cons_val @ Y4 @ nil_val ) @ Zs3 ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_312_not__distinct__split__distinct,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node] :
% 2.65/1.59 ( ~ ( distin1098566007D_node @ Xs )
% 2.65/1.59 => ~ ! [Y4: produc1453890942D_node,Ys3: list_P738500740D_node] :
% 2.65/1.59 ( ( distin1098566007D_node @ Ys3 )
% 2.65/1.59 => ( ( member1797643303D_node @ Y4 @ ( set_Pr1238794387D_node @ Ys3 ) )
% 2.65/1.59 => ! [Zs3: list_P738500740D_node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 != ( append2096883353D_node @ Ys3 @ ( append2096883353D_node @ ( cons_P1018517044D_node @ Y4 @ nil_Pr1769730692D_node ) @ Zs3 ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_313_not__distinct__split__distinct,axiom,
% 2.65/1.59 ! [Xs: list_node] :
% 2.65/1.59 ( ~ ( distinct_node @ Xs )
% 2.65/1.59 => ~ ! [Y4: node,Ys3: list_node] :
% 2.65/1.59 ( ( distinct_node @ Ys3 )
% 2.65/1.59 => ( ( member_node @ Y4 @ ( set_node2 @ Ys3 ) )
% 2.65/1.59 => ! [Zs3: list_node] :
% 2.65/1.59 ( Xs
% 2.65/1.59 != ( append_node @ Ys3 @ ( append_node @ ( cons_node @ Y4 @ nil_node ) @ Zs3 ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_314_append__eq__append__conv2,axiom,
% 2.65/1.59 ! [Xs: list_node,Ys: list_node,Zs: list_node,Ts: list_node] :
% 2.65/1.59 ( ( ( append_node @ Xs @ Ys )
% 2.65/1.59 = ( append_node @ Zs @ Ts ) )
% 2.65/1.59 = ( ? [Us: list_node] :
% 2.65/1.59 ( ( ( Xs
% 2.65/1.59 = ( append_node @ Zs @ Us ) )
% 2.65/1.59 & ( ( append_node @ Us @ Ys )
% 2.65/1.59 = Ts ) )
% 2.65/1.59 | ( ( ( append_node @ Xs @ Us )
% 2.65/1.59 = Zs )
% 2.65/1.59 & ( Ys
% 2.65/1.59 = ( append_node @ Us @ Ts ) ) ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_315_append__eq__appendI,axiom,
% 2.65/1.59 ! [Xs: list_node,Xs1: list_node,Zs: list_node,Ys: list_node,Us2: list_node] :
% 2.65/1.59 ( ( ( append_node @ Xs @ Xs1 )
% 2.65/1.59 = Zs )
% 2.65/1.59 => ( ( Ys
% 2.65/1.59 = ( append_node @ Xs1 @ Us2 ) )
% 2.65/1.59 => ( ( append_node @ Xs @ Ys )
% 2.65/1.59 = ( append_node @ Zs @ Us2 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_316_suffix__order_Odual__order_Oantisym,axiom,
% 2.65/1.59 ! [B: list_node,A: list_node] :
% 2.65/1.59 ( ( suffix_node @ B @ A )
% 2.65/1.59 => ( ( suffix_node @ A @ B )
% 2.65/1.59 => ( A = B ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_317_suffix__order_Odual__order_Oeq__iff,axiom,
% 2.65/1.59 ( ( ^ [Y5: list_node,Z: list_node] : ( Y5 = Z ) )
% 2.65/1.59 = ( ^ [A4: list_node,B3: list_node] :
% 2.65/1.59 ( ( suffix_node @ B3 @ A4 )
% 2.65/1.59 & ( suffix_node @ A4 @ B3 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_318_suffix__order_Odual__order_Otrans,axiom,
% 2.65/1.59 ! [B: list_node,A: list_node,C: list_node] :
% 2.65/1.59 ( ( suffix_node @ B @ A )
% 2.65/1.59 => ( ( suffix_node @ C @ B )
% 2.65/1.59 => ( suffix_node @ C @ A ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_319_suffix__order_Oord__le__eq__trans,axiom,
% 2.65/1.59 ! [A: list_node,B: list_node,C: list_node] :
% 2.65/1.59 ( ( suffix_node @ A @ B )
% 2.65/1.59 => ( ( B = C )
% 2.65/1.59 => ( suffix_node @ A @ C ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_320_suffix__order_Oord__eq__le__trans,axiom,
% 2.65/1.59 ! [A: list_node,B: list_node,C: list_node] :
% 2.65/1.59 ( ( A = B )
% 2.65/1.59 => ( ( suffix_node @ B @ C )
% 2.65/1.59 => ( suffix_node @ A @ C ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_321_suffix__order_Oorder_Oantisym,axiom,
% 2.65/1.59 ! [A: list_node,B: list_node] :
% 2.65/1.59 ( ( suffix_node @ A @ B )
% 2.65/1.59 => ( ( suffix_node @ B @ A )
% 2.65/1.59 => ( A = B ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_322_suffix__order_Oorder_Oeq__iff,axiom,
% 2.65/1.59 ( ( ^ [Y5: list_node,Z: list_node] : ( Y5 = Z ) )
% 2.65/1.59 = ( ^ [A4: list_node,B3: list_node] :
% 2.65/1.59 ( ( suffix_node @ A4 @ B3 )
% 2.65/1.59 & ( suffix_node @ B3 @ A4 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_323_suffix__order_Oantisym__conv,axiom,
% 2.65/1.59 ! [Y3: list_node,X: list_node] :
% 2.65/1.59 ( ( suffix_node @ Y3 @ X )
% 2.65/1.59 => ( ( suffix_node @ X @ Y3 )
% 2.65/1.59 = ( X = Y3 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_324_suffix__order_Oorder__trans,axiom,
% 2.65/1.59 ! [X: list_node,Y3: list_node,Z3: list_node] :
% 2.65/1.59 ( ( suffix_node @ X @ Y3 )
% 2.65/1.59 => ( ( suffix_node @ Y3 @ Z3 )
% 2.65/1.59 => ( suffix_node @ X @ Z3 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_325_suffix__order_Oorder_Otrans,axiom,
% 2.65/1.59 ! [A: list_node,B: list_node,C: list_node] :
% 2.65/1.59 ( ( suffix_node @ A @ B )
% 2.65/1.59 => ( ( suffix_node @ B @ C )
% 2.65/1.59 => ( suffix_node @ A @ C ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_326_suffix__order_Oeq__refl,axiom,
% 2.65/1.59 ! [X: list_node,Y3: list_node] :
% 2.65/1.59 ( ( X = Y3 )
% 2.65/1.59 => ( suffix_node @ X @ Y3 ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_327_suffix__order_Oantisym,axiom,
% 2.65/1.59 ! [X: list_node,Y3: list_node] :
% 2.65/1.59 ( ( suffix_node @ X @ Y3 )
% 2.65/1.59 => ( ( suffix_node @ Y3 @ X )
% 2.65/1.59 => ( X = Y3 ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_328_suffix__order_Oeq__iff,axiom,
% 2.65/1.59 ( ( ^ [Y5: list_node,Z: list_node] : ( Y5 = Z ) )
% 2.65/1.59 = ( ^ [X3: list_node,Y2: list_node] :
% 2.65/1.59 ( ( suffix_node @ X3 @ Y2 )
% 2.65/1.59 & ( suffix_node @ Y2 @ X3 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_329_suffix__same__cases,axiom,
% 2.65/1.59 ! [Xs_1: list_node,Ys: list_node,Xs_2: list_node] :
% 2.65/1.59 ( ( suffix_node @ Xs_1 @ Ys )
% 2.65/1.59 => ( ( suffix_node @ Xs_2 @ Ys )
% 2.65/1.59 => ( ( suffix_node @ Xs_1 @ Xs_2 )
% 2.65/1.59 | ( suffix_node @ Xs_2 @ Xs_1 ) ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_330_finite__list,axiom,
% 2.65/1.59 ! [A2: set_node] :
% 2.65/1.59 ( ( finite_finite_node @ A2 )
% 2.65/1.59 => ? [Xs2: list_node] :
% 2.65/1.59 ( ( set_node2 @ Xs2 )
% 2.65/1.59 = A2 ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_331_finite__list,axiom,
% 2.65/1.59 ! [A2: set_val] :
% 2.65/1.59 ( ( finite_finite_val @ A2 )
% 2.65/1.59 => ? [Xs2: list_val] :
% 2.65/1.59 ( ( set_val2 @ Xs2 )
% 2.65/1.59 = A2 ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_332_append_Oleft__neutral,axiom,
% 2.65/1.59 ! [A: list_node] :
% 2.65/1.59 ( ( append_node @ nil_node @ A )
% 2.65/1.59 = A ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_333_append_Oleft__neutral,axiom,
% 2.65/1.59 ! [A: list_P738500740D_node] :
% 2.65/1.59 ( ( append2096883353D_node @ nil_Pr1769730692D_node @ A )
% 2.65/1.59 = A ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_334_append__Nil,axiom,
% 2.65/1.59 ! [Ys: list_node] :
% 2.65/1.59 ( ( append_node @ nil_node @ Ys )
% 2.65/1.59 = Ys ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_335_append__Nil,axiom,
% 2.65/1.59 ! [Ys: list_P738500740D_node] :
% 2.65/1.59 ( ( append2096883353D_node @ nil_Pr1769730692D_node @ Ys )
% 2.65/1.59 = Ys ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_336_eq__Nil__appendI,axiom,
% 2.65/1.59 ! [Xs: list_node,Ys: list_node] :
% 2.65/1.59 ( ( Xs = Ys )
% 2.65/1.59 => ( Xs
% 2.65/1.59 = ( append_node @ nil_node @ Ys ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_337_eq__Nil__appendI,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node,Ys: list_P738500740D_node] :
% 2.65/1.59 ( ( Xs = Ys )
% 2.65/1.59 => ( Xs
% 2.65/1.59 = ( append2096883353D_node @ nil_Pr1769730692D_node @ Ys ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_338_distinct_Osimps_I1_J,axiom,
% 2.65/1.59 distinct_node @ nil_node ).
% 2.65/1.59
% 2.65/1.59 thf(fact_339_distinct_Osimps_I1_J,axiom,
% 2.65/1.59 distin1098566007D_node @ nil_Pr1769730692D_node ).
% 2.65/1.59
% 2.65/1.59 thf(fact_340_suffix__bot_Obot_Oextremum__uniqueI,axiom,
% 2.65/1.59 ! [A: list_P738500740D_node] :
% 2.65/1.59 ( ( suffix1143830554D_node @ A @ nil_Pr1769730692D_node )
% 2.65/1.59 => ( A = nil_Pr1769730692D_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_341_suffix__bot_Obot_Oextremum__uniqueI,axiom,
% 2.65/1.59 ! [A: list_node] :
% 2.65/1.59 ( ( suffix_node @ A @ nil_node )
% 2.65/1.59 => ( A = nil_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_342_suffix__bot_Obot_Oextremum,axiom,
% 2.65/1.59 ! [A: list_P738500740D_node] : ( suffix1143830554D_node @ nil_Pr1769730692D_node @ A ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_343_suffix__bot_Obot_Oextremum,axiom,
% 2.65/1.59 ! [A: list_node] : ( suffix_node @ nil_node @ A ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_344_Nil__suffix,axiom,
% 2.65/1.59 ! [Xs: list_P738500740D_node] : ( suffix1143830554D_node @ nil_Pr1769730692D_node @ Xs ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_345_Nil__suffix,axiom,
% 2.65/1.59 ! [Xs: list_node] : ( suffix_node @ nil_node @ Xs ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_346_list_Osel_I2_J,axiom,
% 2.65/1.59 ( ( tl_node @ nil_node )
% 2.65/1.59 = nil_node ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_347_list_Osel_I2_J,axiom,
% 2.65/1.59 ( ( tl_Pro1633633005D_node @ nil_Pr1769730692D_node )
% 2.65/1.59 = nil_Pr1769730692D_node ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_348_suffix__appendI,axiom,
% 2.65/1.59 ! [Xs: list_node,Ys: list_node,Zs: list_node] :
% 2.65/1.59 ( ( suffix_node @ Xs @ Ys )
% 2.65/1.59 => ( suffix_node @ Xs @ ( append_node @ Zs @ Ys ) ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_349_suffix__appendD,axiom,
% 2.65/1.59 ! [Zs: list_node,Xs: list_node,Ys: list_node] :
% 2.65/1.59 ( ( suffix_node @ ( append_node @ Zs @ Xs ) @ Ys )
% 2.65/1.59 => ( suffix_node @ Xs @ Ys ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(fact_350_old_OEntry__unreachable,axiom,
% 2.65/1.59 ! [G: g] :
% 2.65/1.59 ( ( invar @ G )
% 2.65/1.59 => ( ( graph_1947481694_edgeD @ inEdges @ G @ ( entry @ G ) )
% 2.65/1.59 = nil_Pr1769730692D_node ) ) ).
% 2.65/1.59
% 2.65/1.59 thf(conj_0,conjecture,
% 2.65/1.59 ~ ( member_node @ ( sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r ) @ ( set_node2 @ ( tl_node @ rs ) ) ) ).
% 2.65/1.59 ------------------------
% 2.84/1.64 % (2451)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2101 for (2999ds/183Mi)
% 2.84/1.64 % (2453)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_2101 for (2999ds/27Mi)
% 2.84/1.64 % (2454)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2101 for (2999ds/2Mi)
% 2.84/1.64 % (2458)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2101 for (2999ds/18Mi)
% 2.84/1.64 % (2454)Instruction limit reached!
% 2.84/1.64 % (2454)------------------------------
% 2.84/1.64 % (2454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.64 % (2454)Termination reason: Unknown
% 2.84/1.64 % (2454)Termination phase: shuffling
% 2.84/1.64
% 2.84/1.64 % (2454)Memory used [KB]: 1535
% 2.84/1.64 % (2454)Time elapsed: 0.002 s
% 2.84/1.64 % (2454)Instructions burned: 2 (million)
% 2.84/1.64 % (2454)------------------------------
% 2.84/1.64 % (2454)------------------------------
% 2.84/1.65 % (2458)Instruction limit reached!
% 2.84/1.65 % (2458)------------------------------
% 2.84/1.65 % (2458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.65 % (2458)Termination reason: Unknown
% 2.84/1.65 % (2458)Termination phase: shuffling
% 2.84/1.65
% 2.84/1.65 % (2458)Memory used [KB]: 1791
% 2.84/1.65 % (2458)Time elapsed: 0.007 s
% 2.84/1.65 % (2458)Instructions burned: 18 (million)
% 2.84/1.65 % (2458)------------------------------
% 2.84/1.65 % (2458)------------------------------
% 2.84/1.65 % (2452)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_2101 for (2999ds/4Mi)
% 2.84/1.65 % (2455)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_2101 for (2999ds/2Mi)
% 2.84/1.65 % (2457)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_2101 for (2999ds/275Mi)
% 2.84/1.65 % (2453)Instruction limit reached!
% 2.84/1.65 % (2453)------------------------------
% 2.84/1.65 % (2453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.65 % (2453)Termination reason: Unknown
% 2.84/1.65 % (2453)Termination phase: shuffling
% 2.84/1.65
% 2.84/1.65 % (2453)Memory used [KB]: 1918
% 2.84/1.65 % (2453)Time elapsed: 0.010 s
% 2.84/1.65 % (2453)Instructions burned: 27 (million)
% 2.84/1.65 % (2453)------------------------------
% 2.84/1.65 % (2453)------------------------------
% 2.84/1.65 % (2455)Instruction limit reached!
% 2.84/1.65 % (2455)------------------------------
% 2.84/1.65 % (2455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.65 % (2455)Termination reason: Unknown
% 2.84/1.65 % (2455)Termination phase: shuffling
% 2.84/1.65
% 2.84/1.65 % (2455)Memory used [KB]: 1535
% 2.84/1.65 % (2455)Time elapsed: 0.004 s
% 2.84/1.65 % (2455)Instructions burned: 2 (million)
% 2.84/1.65 % (2455)------------------------------
% 2.84/1.65 % (2455)------------------------------
% 2.84/1.65 % (2464)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_2101 for (2999ds/3Mi)
% 2.84/1.65 % (2452)Instruction limit reached!
% 2.84/1.65 % (2452)------------------------------
% 2.84/1.65 % (2452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.65 % (2452)Termination reason: Unknown
% 2.84/1.65 % (2452)Termination phase: shuffling
% 2.84/1.65
% 2.84/1.65 % (2452)Memory used [KB]: 1663
% 2.84/1.65 % (2452)Time elapsed: 0.005 s
% 2.84/1.65 % (2452)Instructions burned: 4 (million)
% 2.84/1.65 % (2452)------------------------------
% 2.84/1.65 % (2452)------------------------------
% 2.84/1.65 % (2464)Instruction limit reached!
% 2.84/1.65 % (2464)------------------------------
% 2.84/1.65 % (2464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.65 % (2464)Termination reason: Unknown
% 2.84/1.65 % (2464)Termination phase: shuffling
% 2.84/1.65
% 2.84/1.65 % (2464)Memory used [KB]: 1535
% 2.84/1.65 % (2464)Time elapsed: 0.003 s
% 2.84/1.65 % (2464)Instructions burned: 6 (million)
% 2.84/1.65 % (2464)------------------------------
% 2.84/1.65 % (2464)------------------------------
% 2.84/1.66 % (2465)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_2101 for (2999ds/37Mi)
% 2.84/1.66 % (2466)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_2101 for (2999ds/15Mi)
% 2.84/1.66 % (2469)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_2101 for (2999ds/7Mi)
% 2.84/1.66 % (2466)Instruction limit reached!
% 2.84/1.66 % (2466)------------------------------
% 2.84/1.66 % (2466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.66 % (2466)Termination reason: Unknown
% 2.84/1.66 % (2466)Termination phase: shuffling
% 2.84/1.66
% 2.84/1.66 % (2466)Memory used [KB]: 1791
% 2.84/1.66 % (2466)Time elapsed: 0.006 s
% 2.84/1.66 % (2466)Instructions burned: 15 (million)
% 2.84/1.66 % (2466)------------------------------
% 2.84/1.66 % (2466)------------------------------
% 2.84/1.66 % (2469)Instruction limit reached!
% 2.84/1.66 % (2469)------------------------------
% 2.84/1.66 % (2469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.66 % (2469)Termination reason: Unknown
% 2.84/1.66 % (2469)Termination phase: shuffling
% 2.84/1.66
% 2.84/1.66 % (2469)Memory used [KB]: 1663
% 2.84/1.66 % (2469)Time elapsed: 0.004 s
% 2.84/1.66 % (2469)Instructions burned: 8 (million)
% 2.84/1.66 % (2469)------------------------------
% 2.84/1.66 % (2469)------------------------------
% 2.84/1.67 % (2465)Instruction limit reached!
% 2.84/1.67 % (2465)------------------------------
% 2.84/1.67 % (2465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.67 % (2465)Termination reason: Unknown
% 2.84/1.67 % (2465)Termination phase: shuffling
% 2.84/1.67
% 2.84/1.67 % (2465)Memory used [KB]: 2302
% 2.84/1.67 % (2465)Time elapsed: 0.012 s
% 2.84/1.67 % (2465)Instructions burned: 39 (million)
% 2.84/1.67 % (2465)------------------------------
% 2.84/1.67 % (2465)------------------------------
% 2.84/1.67 % (2467)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_2101 for (2999ds/3Mi)
% 2.84/1.67 % (2468)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_2101 for (2999ds/1041Mi)
% 2.84/1.67 % (2467)Instruction limit reached!
% 2.84/1.67 % (2467)------------------------------
% 2.84/1.67 % (2467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.67 % (2467)Termination reason: Unknown
% 2.84/1.67 % (2467)Termination phase: shuffling
% 2.84/1.67
% 2.84/1.67 % (2467)Memory used [KB]: 1535
% 2.84/1.67 % (2467)Time elapsed: 0.004 s
% 2.84/1.67 % (2467)Instructions burned: 3 (million)
% 2.84/1.67 % (2467)------------------------------
% 2.84/1.67 % (2467)------------------------------
% 2.84/1.67 % (2470)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_2101 for (2999ds/16Mi)
% 2.84/1.67 % (2472)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_2101 for (2999ds/3Mi)
% 2.84/1.68 % (2472)Instruction limit reached!
% 2.84/1.68 % (2472)------------------------------
% 2.84/1.68 % (2472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.68 % (2472)Termination reason: Unknown
% 2.84/1.68 % (2472)Termination phase: shuffling
% 2.84/1.68
% 2.84/1.68 % (2472)Memory used [KB]: 1535
% 2.84/1.68 % (2472)Time elapsed: 0.003 s
% 2.84/1.68 % (2472)Instructions burned: 6 (million)
% 2.84/1.68 % (2472)------------------------------
% 2.84/1.68 % (2472)------------------------------
% 2.84/1.68 % (2474)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_2101 for (2999ds/3Mi)
% 2.84/1.68 % (2474)Instruction limit reached!
% 2.84/1.68 % (2474)------------------------------
% 2.84/1.68 % (2474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.68 % (2474)Termination reason: Unknown
% 2.84/1.68 % (2474)Termination phase: shuffling
% 2.84/1.68
% 2.84/1.68 % (2474)Memory used [KB]: 1535
% 2.84/1.68 % (2474)Time elapsed: 0.002 s
% 2.84/1.68 % (2474)Instructions burned: 3 (million)
% 2.84/1.68 % (2474)------------------------------
% 2.84/1.68 % (2474)------------------------------
% 2.84/1.68 % (2470)Instruction limit reached!
% 2.84/1.68 % (2470)------------------------------
% 2.84/1.68 % (2470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.68 % (2470)Termination reason: Unknown
% 2.84/1.68 % (2470)Termination phase: shuffling
% 2.84/1.68
% 2.84/1.68 % (2470)Memory used [KB]: 1791
% 2.84/1.68 % (2470)Time elapsed: 0.006 s
% 2.84/1.68 % (2470)Instructions burned: 16 (million)
% 2.84/1.68 % (2470)------------------------------
% 2.84/1.68 % (2470)------------------------------
% 2.84/1.68 % (2476)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_2101 for (2999ds/7Mi)
% 2.84/1.69 % (2479)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_2101 for (2999ds/3Mi)
% 2.84/1.69 % (2479)Instruction limit reached!
% 2.84/1.69 % (2479)------------------------------
% 2.84/1.69 % (2479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.69 % (2479)Termination reason: Unknown
% 2.84/1.69 % (2479)Termination phase: shuffling
% 2.84/1.69
% 2.84/1.69 % (2479)Memory used [KB]: 1535
% 2.84/1.69 % (2479)Time elapsed: 0.002 s
% 2.84/1.69 % (2479)Instructions burned: 3 (million)
% 2.84/1.69 % (2479)------------------------------
% 2.84/1.69 % (2479)------------------------------
% 2.84/1.69 % (2481)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_2101 for (2999ds/4Mi)
% 2.84/1.69 % (2482)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_2101 for (2999ds/18Mi)
% 2.84/1.69 % (2476)Instruction limit reached!
% 2.84/1.69 % (2476)------------------------------
% 2.84/1.69 % (2476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.69 % (2476)Termination reason: Unknown
% 2.84/1.69 % (2476)Termination phase: shuffling
% 2.84/1.69
% 2.84/1.69 % (2476)Memory used [KB]: 1663
% 2.84/1.69 % (2476)Time elapsed: 0.005 s
% 2.84/1.69 % (2476)Instructions burned: 8 (million)
% 2.84/1.69 % (2476)------------------------------
% 2.84/1.69 % (2476)------------------------------
% 2.84/1.69 % (2481)Instruction limit reached!
% 2.84/1.69 % (2481)------------------------------
% 2.84/1.69 % (2481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.69 % (2481)Termination reason: Unknown
% 2.84/1.69 % (2481)Termination phase: shuffling
% 2.84/1.69
% 2.84/1.69 % (2481)Memory used [KB]: 1535
% 2.84/1.69 % (2481)Time elapsed: 0.003 s
% 2.84/1.69 % (2481)Instructions burned: 6 (million)
% 2.84/1.69 % (2481)------------------------------
% 2.84/1.69 % (2481)------------------------------
% 2.84/1.69 % (2451)Instruction limit reached!
% 2.84/1.69 % (2451)------------------------------
% 2.84/1.69 % (2451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.69 % (2451)Termination reason: Unknown
% 2.84/1.69 % (2451)Termination phase: Property scanning
% 2.84/1.69
% 2.84/1.69 % (2451)Memory used [KB]: 3326
% 2.84/1.69 % (2451)Time elapsed: 0.053 s
% 2.84/1.69 % (2451)Instructions burned: 184 (million)
% 2.84/1.69 % (2451)------------------------------
% 2.84/1.69 % (2451)------------------------------
% 2.84/1.69 % (2482)Instruction limit reached!
% 2.84/1.69 % (2482)------------------------------
% 2.84/1.69 % (2482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.69 % (2482)Termination reason: Unknown
% 2.84/1.69 % (2482)Termination phase: shuffling
% 2.84/1.69
% 2.84/1.69 % (2482)Memory used [KB]: 1791
% 2.84/1.69 % (2482)Time elapsed: 0.007 s
% 2.84/1.69 % (2482)Instructions burned: 18 (million)
% 2.84/1.69 % (2482)------------------------------
% 2.84/1.69 % (2482)------------------------------
% 2.84/1.70 % (2483)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_2101 for (2999ds/710Mi)
% 2.84/1.70 % (2485)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_2101 for (2999ds/902Mi)
% 2.84/1.70 % (2488)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_2101 for (2999ds/21Mi)
% 2.84/1.70 % (2489)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_2101 for (2999ds/5Mi)
% 2.84/1.70 % (2489)Instruction limit reached!
% 2.84/1.70 % (2489)------------------------------
% 2.84/1.70 % (2489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.70 % (2489)Termination reason: Unknown
% 2.84/1.70 % (2489)Termination phase: shuffling
% 2.84/1.70
% 2.84/1.70 % (2489)Memory used [KB]: 1663
% 2.84/1.70 % (2489)Time elapsed: 0.003 s
% 2.84/1.70 % (2489)Instructions burned: 7 (million)
% 2.84/1.70 % (2489)------------------------------
% 2.84/1.70 % (2489)------------------------------
% 2.84/1.71 % (2484)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2101 for (2999ds/6Mi)
% 2.84/1.71 % (2488)Instruction limit reached!
% 2.84/1.71 % (2488)------------------------------
% 2.84/1.71 % (2488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.71 % (2488)Termination reason: Unknown
% 2.84/1.71 % (2488)Termination phase: shuffling
% 2.84/1.71
% 2.84/1.71 % (2488)Memory used [KB]: 1791
% 2.84/1.71 % (2488)Time elapsed: 0.008 s
% 2.84/1.71 % (2488)Instructions burned: 22 (million)
% 2.84/1.71 % (2488)------------------------------
% 2.84/1.71 % (2488)------------------------------
% 2.84/1.71 % (2484)Instruction limit reached!
% 2.84/1.71 % (2484)------------------------------
% 2.84/1.71 % (2484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.71 % (2484)Termination reason: Unknown
% 2.84/1.71 % (2484)Termination phase: shuffling
% 2.84/1.71
% 2.84/1.71 % (2484)Memory used [KB]: 1663
% 2.84/1.71 % (2484)Time elapsed: 0.006 s
% 2.84/1.71 % (2484)Instructions burned: 7 (million)
% 2.84/1.71 % (2484)------------------------------
% 2.84/1.71 % (2484)------------------------------
% 2.84/1.71 % (2491)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_2101 for (2999ds/6Mi)
% 2.84/1.72 % (2491)Instruction limit reached!
% 2.84/1.72 % (2491)------------------------------
% 2.84/1.72 % (2491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.72 % (2491)Termination reason: Unknown
% 2.84/1.72 % (2491)Termination phase: shuffling
% 2.84/1.72
% 2.84/1.72 % (2491)Memory used [KB]: 1663
% 2.84/1.72 % (2491)Time elapsed: 0.003 s
% 2.84/1.72 % (2491)Instructions burned: 6 (million)
% 2.84/1.72 % (2491)------------------------------
% 2.84/1.72 % (2491)------------------------------
% 2.84/1.72 % (2494)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_2101 for (2998ds/377Mi)
% 2.84/1.72 % (2500)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_2101 for (2998ds/19Mi)
% 2.84/1.73 % (2496)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_2101 for (2998ds/779Mi)
% 2.84/1.73 % (2500)Instruction limit reached!
% 2.84/1.73 % (2500)------------------------------
% 2.84/1.73 % (2500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.73 % (2500)Termination reason: Unknown
% 2.84/1.73 % (2500)Termination phase: shuffling
% 2.84/1.73
% 2.84/1.73 % (2500)Memory used [KB]: 2046
% 2.84/1.73 % (2500)Time elapsed: 0.007 s
% 2.84/1.73 % (2500)Instructions burned: 21 (million)
% 2.84/1.73 % (2500)------------------------------
% 2.84/1.73 % (2500)------------------------------
% 2.84/1.74 % (2509)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_2101 for (2998ds/879Mi)
% 2.84/1.75 % (2457)Refutation not found, incomplete strategy
% 2.84/1.75 % (2457)------------------------------
% 2.84/1.75 % (2457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.75 % (2457)Termination reason: Refutation not found, incomplete strategy
% 2.84/1.75
% 2.84/1.75
% 2.84/1.75 % (2457)Memory used [KB]: 7931
% 2.84/1.75 % (2457)Time elapsed: 0.100 s
% 2.84/1.75 % (2457)Instructions burned: 199 (million)
% 2.84/1.75 % (2457)------------------------------
% 2.84/1.75 % (2457)------------------------------
% 2.84/1.76 % (2520)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_2101 for (2998ds/17Mi)
% 2.84/1.76 % (2520)Instruction limit reached!
% 2.84/1.76 % (2520)------------------------------
% 2.84/1.76 % (2520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.76 % (2520)Termination reason: Unknown
% 2.84/1.76 % (2520)Termination phase: shuffling
% 2.84/1.76
% 2.84/1.76 % (2520)Memory used [KB]: 1791
% 2.84/1.76 % (2520)Time elapsed: 0.008 s
% 2.84/1.76 % (2520)Instructions burned: 18 (million)
% 2.84/1.76 % (2520)------------------------------
% 2.84/1.76 % (2520)------------------------------
% 2.84/1.77 % (2530)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_2101 for (2998ds/3Mi)
% 2.84/1.78 % (2530)Instruction limit reached!
% 2.84/1.78 % (2530)------------------------------
% 2.84/1.78 % (2530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.78 % (2530)Termination reason: Unknown
% 2.84/1.78 % (2530)Termination phase: shuffling
% 2.84/1.78
% 2.84/1.78 % (2530)Memory used [KB]: 1535
% 2.84/1.78 % (2530)Time elapsed: 0.003 s
% 2.84/1.78 % (2530)Instructions burned: 3 (million)
% 2.84/1.78 % (2530)------------------------------
% 2.84/1.78 % (2530)------------------------------
% 2.84/1.79 % (2533)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_2101 for (2998ds/30Mi)
% 2.84/1.80 % (2485)Refutation not found, incomplete strategy
% 2.84/1.80 % (2485)------------------------------
% 2.84/1.80 % (2485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.80 % (2485)Termination reason: Refutation not found, incomplete strategy
% 2.84/1.80
% 2.84/1.80
% 2.84/1.80 % (2485)Memory used [KB]: 9210
% 2.84/1.80 % (2485)Time elapsed: 0.098 s
% 2.84/1.80 % (2485)Instructions burned: 336 (million)
% 2.84/1.80 % (2485)------------------------------
% 2.84/1.80 % (2485)------------------------------
% 2.84/1.80 % (2533)Instruction limit reached!
% 2.84/1.80 % (2533)------------------------------
% 2.84/1.80 % (2533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.80 % (2533)Termination reason: Unknown
% 2.84/1.80 % (2533)Termination phase: shuffling
% 2.84/1.80
% 2.84/1.80 % (2533)Memory used [KB]: 2046
% 2.84/1.80 % (2533)Time elapsed: 0.013 s
% 2.84/1.80 % (2533)Instructions burned: 32 (million)
% 2.84/1.80 % (2533)------------------------------
% 2.84/1.80 % (2533)------------------------------
% 2.84/1.81 % (2538)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_2101 for (2998ds/127Mi)
% 2.84/1.81 % (2539)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_2101 for (2998ds/100Mi)
% 2.84/1.83 % (2494)Instruction limit reached!
% 2.84/1.83 % (2494)------------------------------
% 2.84/1.83 % (2494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.83 % (2494)Termination reason: Unknown
% 2.84/1.83 % (2494)Termination phase: Saturation
% 2.84/1.83
% 2.84/1.83 % (2494)Memory used [KB]: 9210
% 2.84/1.83 % (2494)Time elapsed: 0.109 s
% 2.84/1.83 % (2494)Instructions burned: 377 (million)
% 2.84/1.83 % (2494)------------------------------
% 2.84/1.83 % (2494)------------------------------
% 2.84/1.84 % (2540)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_2101 for (2997ds/3Mi)
% 2.84/1.84 % (2539)Instruction limit reached!
% 2.84/1.84 % (2539)------------------------------
% 2.84/1.84 % (2539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.84 % (2539)Termination reason: Unknown
% 2.84/1.84 % (2539)Termination phase: Property scanning
% 2.84/1.84
% 2.84/1.84 % (2539)Memory used [KB]: 3070
% 2.84/1.84 % (2539)Time elapsed: 0.031 s
% 2.84/1.84 % (2539)Instructions burned: 100 (million)
% 2.84/1.84 % (2539)------------------------------
% 2.84/1.84 % (2539)------------------------------
% 2.84/1.84 % (2540)Instruction limit reached!
% 2.84/1.84 % (2540)------------------------------
% 2.84/1.84 % (2540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.84 % (2540)Termination reason: Unknown
% 2.84/1.84 % (2540)Termination phase: shuffling
% 2.84/1.84
% 2.84/1.84 % (2540)Memory used [KB]: 1535
% 2.84/1.84 % (2540)Time elapsed: 0.002 s
% 2.84/1.84 % (2540)Instructions burned: 3 (million)
% 2.84/1.84 % (2540)------------------------------
% 2.84/1.84 % (2540)------------------------------
% 2.84/1.84 % (2538)Instruction limit reached!
% 2.84/1.84 % (2538)------------------------------
% 2.84/1.84 % (2538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.84 % (2538)Termination reason: Unknown
% 2.84/1.84 % (2538)Termination phase: Preprocessing 3
% 2.84/1.84
% 2.84/1.84 % (2538)Memory used [KB]: 3198
% 2.84/1.84 % (2538)Time elapsed: 0.039 s
% 2.84/1.84 % (2538)Instructions burned: 130 (million)
% 2.84/1.84 % (2538)------------------------------
% 2.84/1.84 % (2538)------------------------------
% 2.84/1.85 % (2541)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_2101 for (2997ds/20Mi)
% 2.84/1.85 % (2542)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_2101 for (2997ds/86Mi)
% 2.84/1.85 % (2541)Instruction limit reached!
% 2.84/1.85 % (2541)------------------------------
% 2.84/1.85 % (2541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.85 % (2541)Termination reason: Unknown
% 2.84/1.85 % (2541)Termination phase: shuffling
% 2.84/1.85
% 2.84/1.85 % (2541)Memory used [KB]: 1791
% 2.84/1.85 % (2541)Time elapsed: 0.008 s
% 2.84/1.85 % (2541)Instructions burned: 21 (million)
% 2.84/1.85 % (2541)------------------------------
% 2.84/1.85 % (2541)------------------------------
% 2.84/1.85 % (2543)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_2101 for (2997ds/107Mi)
% 2.84/1.86 % (2544)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_2101 for (2997ds/39Mi)
% 2.84/1.87 % (2544)Instruction limit reached!
% 2.84/1.87 % (2544)------------------------------
% 2.84/1.87 % (2544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.87 % (2544)Termination reason: Unknown
% 2.84/1.87 % (2544)Termination phase: shuffling
% 2.84/1.87
% 2.84/1.87 % (2544)Memory used [KB]: 2302
% 2.84/1.87 % (2544)Time elapsed: 0.012 s
% 2.84/1.87 % (2544)Instructions burned: 40 (million)
% 2.84/1.87 % (2544)------------------------------
% 2.84/1.87 % (2544)------------------------------
% 2.84/1.87 % (2542)Instruction limit reached!
% 2.84/1.87 % (2542)------------------------------
% 2.84/1.87 % (2542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.87 % (2542)Termination reason: Unknown
% 2.84/1.87 % (2542)Termination phase: Unused predicate definition removal
% 2.84/1.87
% 2.84/1.87 % (2542)Memory used [KB]: 2430
% 2.84/1.87 % (2542)Time elapsed: 0.030 s
% 2.84/1.87 % (2542)Instructions burned: 88 (million)
% 2.84/1.87 % (2542)------------------------------
% 2.84/1.87 % (2542)------------------------------
% 2.84/1.88 % (2545)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_2101 for (2997ds/448Mi)
% 2.84/1.88 % (2543)Instruction limit reached!
% 2.84/1.88 % (2543)------------------------------
% 2.84/1.88 % (2543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.88 % (2543)Termination reason: Unknown
% 2.84/1.88 % (2543)Termination phase: Naming
% 2.84/1.88
% 2.84/1.88 % (2543)Memory used [KB]: 2686
% 2.84/1.88 % (2543)Time elapsed: 0.033 s
% 2.84/1.88 % (2543)Instructions burned: 109 (million)
% 2.84/1.88 % (2543)------------------------------
% 2.84/1.88 % (2543)------------------------------
% 2.84/1.88 % (2546)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_2101 for (2997ds/46Mi)
% 2.84/1.89 % (2547)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_2101 for (2997ds/98Mi)
% 2.84/1.90 % (2546)Instruction limit reached!
% 2.84/1.90 % (2546)------------------------------
% 2.84/1.90 % (2546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.90 % (2546)Termination reason: Unknown
% 2.84/1.90 % (2546)Termination phase: shuffling
% 2.84/1.90
% 2.84/1.90 % (2546)Memory used [KB]: 2174
% 2.84/1.90 % (2546)Time elapsed: 0.018 s
% 2.84/1.90 % (2546)Instructions burned: 48 (million)
% 2.84/1.90 % (2546)------------------------------
% 2.84/1.90 % (2546)------------------------------
% 2.84/1.91 % (2483)Instruction limit reached!
% 2.84/1.91 % (2483)------------------------------
% 2.84/1.91 % (2483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.91 % (2483)Termination reason: Unknown
% 2.84/1.91 % (2483)Termination phase: Saturation
% 2.84/1.91
% 2.84/1.91 % (2483)Memory used [KB]: 9722
% 2.84/1.91 % (2483)Time elapsed: 0.216 s
% 2.84/1.91 % (2483)Instructions burned: 712 (million)
% 2.84/1.91 % (2483)------------------------------
% 2.84/1.91 % (2483)------------------------------
% 2.84/1.91 % (2548)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_2101 for (2996ds/507Mi)
% 2.84/1.92 % (2547)Instruction limit reached!
% 2.84/1.92 % (2547)------------------------------
% 2.84/1.92 % (2547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.92 % (2547)Termination reason: Unknown
% 2.84/1.92 % (2547)Termination phase: Property scanning
% 2.84/1.92
% 2.84/1.92 % (2547)Memory used [KB]: 3070
% 2.84/1.92 % (2547)Time elapsed: 0.028 s
% 2.84/1.92 % (2547)Instructions burned: 100 (million)
% 2.84/1.92 % (2547)------------------------------
% 2.84/1.92 % (2547)------------------------------
% 2.84/1.93 % (2549)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_2101 for (2996ds/149Mi)
% 2.84/1.93 % (2550)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_2101 for (2996ds/39Mi)
% 2.84/1.94 % (2550)Instruction limit reached!
% 2.84/1.94 % (2550)------------------------------
% 2.84/1.94 % (2550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.94 % (2550)Termination reason: Unknown
% 2.84/1.94 % (2550)Termination phase: shuffling
% 2.84/1.94
% 2.84/1.94 % (2550)Memory used [KB]: 2046
% 2.84/1.94 % (2550)Time elapsed: 0.014 s
% 2.84/1.94 % (2550)Instructions burned: 39 (million)
% 2.84/1.94 % (2550)------------------------------
% 2.84/1.94 % (2550)------------------------------
% 2.84/1.95 % (2551)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_2101 for (2996ds/6Mi)
% 2.84/1.96 % (2551)Instruction limit reached!
% 2.84/1.96 % (2551)------------------------------
% 2.84/1.96 % (2551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.96 % (2551)Termination reason: Unknown
% 2.84/1.96 % (2551)Termination phase: shuffling
% 2.84/1.96
% 2.84/1.96 % (2551)Memory used [KB]: 1663
% 2.84/1.96 % (2551)Time elapsed: 0.003 s
% 2.84/1.96 % (2551)Instructions burned: 7 (million)
% 2.84/1.96 % (2551)------------------------------
% 2.84/1.96 % (2551)------------------------------
% 2.84/1.96 % (2552)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_2101 for (2996ds/1087Mi)
% 2.84/1.97 % (2496)Instruction limit reached!
% 2.84/1.97 % (2496)------------------------------
% 2.84/1.97 % (2496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/1.97 % (2496)Termination reason: Unknown
% 2.84/1.97 % (2496)Termination phase: Saturation
% 2.84/1.97
% 2.84/1.97 % (2496)Memory used [KB]: 11641
% 2.84/1.97 % (2496)Time elapsed: 0.242 s
% 2.84/1.97 % (2496)Instructions burned: 780 (million)
% 2.84/1.97 % (2496)------------------------------
% 2.84/1.97 % (2496)------------------------------
% 2.84/1.98 % (2553)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_2101 for (2996ds/47Mi)
% 2.84/2.00 % (2553)Instruction limit reached!
% 2.84/2.00 % (2553)------------------------------
% 2.84/2.00 % (2553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/2.00 % (2553)Termination reason: Unknown
% 2.84/2.00 % (2553)Termination phase: shuffling
% 2.84/2.00
% 2.84/2.00 % (2553)Memory used [KB]: 2174
% 2.84/2.00 % (2553)Time elapsed: 0.017 s
% 2.84/2.00 % (2553)Instructions burned: 47 (million)
% 2.84/2.00 % (2553)------------------------------
% 2.84/2.00 % (2553)------------------------------
% 2.84/2.00 % (2468)Instruction limit reached!
% 2.84/2.00 % (2468)------------------------------
% 2.84/2.00 % (2468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/2.00 % (2468)Termination reason: Unknown
% 2.84/2.00 % (2468)Termination phase: Saturation
% 2.84/2.00
% 2.84/2.00 % (2468)Memory used [KB]: 10106
% 2.84/2.00 % (2468)Time elapsed: 0.332 s
% 2.84/2.00 % (2468)Instructions burned: 1043 (million)
% 2.84/2.00 % (2468)------------------------------
% 2.84/2.00 % (2468)------------------------------
% 2.84/2.00 % (2545)Instruction limit reached!
% 2.84/2.00 % (2545)------------------------------
% 2.84/2.00 % (2545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/2.00 % (2545)Termination reason: Unknown
% 2.84/2.00 % (2545)Termination phase: Saturation
% 2.84/2.00
% 2.84/2.00 % (2545)Memory used [KB]: 9210
% 2.84/2.00 % (2545)Time elapsed: 0.123 s
% 2.84/2.00 % (2545)Instructions burned: 451 (million)
% 2.84/2.00 % (2545)------------------------------
% 2.84/2.00 % (2545)------------------------------
% 2.84/2.01 % (2549)Instruction limit reached!
% 2.84/2.01 % (2549)------------------------------
% 2.84/2.01 % (2549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/2.01 % (2549)Termination reason: Unknown
% 2.84/2.01 % (2549)Termination phase: Property scanning
% 2.84/2.01
% 2.84/2.01 % (2549)Memory used [KB]: 3326
% 2.84/2.01 % (2549)Time elapsed: 0.081 s
% 2.84/2.01 % (2549)Instructions burned: 151 (million)
% 2.84/2.01 % (2549)------------------------------
% 2.84/2.01 % (2549)------------------------------
% 2.84/2.01 % (2555)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_2101 for (2995ds/432Mi)
% 2.84/2.01 % (2509)Instruction limit reached!
% 2.84/2.01 % (2509)------------------------------
% 2.84/2.01 % (2509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.84/2.01 % (2509)Termination reason: Unknown
% 2.84/2.01 % (2509)Termination phase: Saturation
% 2.84/2.01
% 2.84/2.01 % (2509)Memory used [KB]: 9210
% 2.84/2.01 % (2509)Time elapsed: 0.271 s
% 2.84/2.01 % (2509)Instructions burned: 879 (million)
% 2.84/2.01 % (2509)------------------------------
% 2.84/2.01 % (2509)------------------------------
% 5.46/2.01 % (2556)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_2101 for (2995ds/62Mi)
% 5.46/2.02 % (2554)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_2101 for (2996ds/44Mi)
% 5.46/2.02 % (2558)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_2101 for (2995ds/96Mi)
% 5.46/2.02 % (2557)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_2101 for (2995ds/31Mi)
% 5.46/2.03 % (2554)Instruction limit reached!
% 5.46/2.03 % (2554)------------------------------
% 5.46/2.03 % (2554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.03 % (2554)Termination reason: Unknown
% 5.46/2.03 % (2554)Termination phase: shuffling
% 5.46/2.03
% 5.46/2.03 % (2554)Memory used [KB]: 2430
% 5.46/2.03 % (2554)Time elapsed: 0.014 s
% 5.46/2.03 % (2554)Instructions burned: 45 (million)
% 5.46/2.03 % (2554)------------------------------
% 5.46/2.03 % (2554)------------------------------
% 5.46/2.03 % (2556)Instruction limit reached!
% 5.46/2.03 % (2556)------------------------------
% 5.46/2.03 % (2556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.03 % (2556)Termination reason: Unknown
% 5.46/2.03 % (2556)Termination phase: shuffling
% 5.46/2.03
% 5.46/2.03 % (2556)Memory used [KB]: 2814
% 5.46/2.03 % (2556)Time elapsed: 0.018 s
% 5.46/2.03 % (2556)Instructions burned: 62 (million)
% 5.46/2.03 % (2556)------------------------------
% 5.46/2.03 % (2556)------------------------------
% 5.46/2.03 % (2557)Instruction limit reached!
% 5.46/2.03 % (2557)------------------------------
% 5.46/2.03 % (2557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.03 % (2557)Termination reason: Unknown
% 5.46/2.03 % (2557)Termination phase: shuffling
% 5.46/2.03
% 5.46/2.03 % (2557)Memory used [KB]: 1918
% 5.46/2.03 % (2557)Time elapsed: 0.013 s
% 5.46/2.03 % (2557)Instructions burned: 32 (million)
% 5.46/2.03 % (2557)------------------------------
% 5.46/2.03 % (2557)------------------------------
% 5.46/2.04 % (2559)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_2101 for (2995ds/453Mi)
% 5.46/2.04 % (2560)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_2101 for (2995ds/71Mi)
% 5.46/2.04 % (2561)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_2101 for (2995ds/83Mi)
% 5.46/2.05 % (2558)Instruction limit reached!
% 5.46/2.05 % (2558)------------------------------
% 5.46/2.05 % (2558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.05 % (2558)Termination reason: Unknown
% 5.46/2.05 % (2558)Termination phase: Preprocessing 3
% 5.46/2.05
% 5.46/2.05 % (2558)Memory used [KB]: 2814
% 5.46/2.05 % (2558)Time elapsed: 0.031 s
% 5.46/2.05 % (2558)Instructions burned: 99 (million)
% 5.46/2.05 % (2558)------------------------------
% 5.46/2.05 % (2558)------------------------------
% 5.46/2.06 % (2562)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_2101 for (2995ds/11Mi)
% 5.46/2.06 % (2560)Instruction limit reached!
% 5.46/2.06 % (2560)------------------------------
% 5.46/2.06 % (2560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.06 % (2560)Termination reason: Unknown
% 5.46/2.06 % (2560)Termination phase: Property scanning
% 5.46/2.06
% 5.46/2.06 % (2560)Memory used [KB]: 2430
% 5.46/2.06 % (2560)Time elapsed: 0.024 s
% 5.46/2.06 % (2560)Instructions burned: 73 (million)
% 5.46/2.06 % (2560)------------------------------
% 5.46/2.06 % (2560)------------------------------
% 5.46/2.06 % (2562)Instruction limit reached!
% 5.46/2.06 % (2562)------------------------------
% 5.46/2.06 % (2562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.06 % (2562)Termination reason: Unknown
% 5.46/2.06 % (2562)Termination phase: shuffling
% 5.46/2.06
% 5.46/2.06 % (2562)Memory used [KB]: 1791
% 5.46/2.06 % (2562)Time elapsed: 0.005 s
% 5.46/2.06 % (2562)Instructions burned: 13 (million)
% 5.46/2.06 % (2562)------------------------------
% 5.46/2.06 % (2562)------------------------------
% 5.46/2.07 % (2561)Instruction limit reached!
% 5.46/2.07 % (2561)------------------------------
% 5.46/2.07 % (2561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.07 % (2561)Termination reason: Unknown
% 5.46/2.07 % (2561)Termination phase: SInE selection
% 5.46/2.07
% 5.46/2.07 % (2561)Memory used [KB]: 2302
% 5.46/2.07 % (2561)Time elapsed: 0.029 s
% 5.46/2.07 % (2561)Instructions burned: 85 (million)
% 5.46/2.07 % (2561)------------------------------
% 5.46/2.07 % (2561)------------------------------
% 5.46/2.07 % (2563)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_2101 for (2995ds/41Mi)
% 5.46/2.07 % (2564)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_2101 for (2995ds/6Mi)
% 5.46/2.07 % (2548)Instruction limit reached!
% 5.46/2.07 % (2548)------------------------------
% 5.46/2.07 % (2548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.07 % (2548)Termination reason: Unknown
% 5.46/2.07 % (2548)Termination phase: Saturation
% 5.46/2.07
% 5.46/2.07 % (2548)Memory used [KB]: 9850
% 5.46/2.07 % (2548)Time elapsed: 0.164 s
% 5.46/2.07 % (2548)Instructions burned: 508 (million)
% 5.46/2.07 % (2548)------------------------------
% 5.46/2.07 % (2548)------------------------------
% 5.46/2.07 % (2564)Instruction limit reached!
% 5.46/2.07 % (2564)------------------------------
% 5.46/2.07 % (2564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.07 % (2564)Termination reason: Unknown
% 5.46/2.07 % (2564)Termination phase: shuffling
% 5.46/2.07
% 5.46/2.07 % (2564)Memory used [KB]: 1535
% 5.46/2.07 % (2564)Time elapsed: 0.003 s
% 5.46/2.07 % (2564)Instructions burned: 6 (million)
% 5.46/2.07 % (2564)------------------------------
% 5.46/2.07 % (2564)------------------------------
% 5.46/2.08 % (2565)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_2101 for (2995ds/150Mi)
% 5.46/2.08 % (2566)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_2101 for (2995ds/343Mi)
% 5.46/2.08 % (2567)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_2101 for (2995ds/109Mi)
% 5.46/2.08 % (2563)Instruction limit reached!
% 5.46/2.08 % (2563)------------------------------
% 5.46/2.08 % (2563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.46/2.08 % (2563)Termination reason: Unknown
% 5.46/2.08 % (2563)Termination phase: shuffling
% 5.46/2.08
% 5.46/2.08 % (2563)Memory used [KB]: 2430
% 5.46/2.08 % (2563)Time elapsed: 0.013 s
% 5.46/2.08 % (2563)Instructions burned: 44 (million)
% 5.46/2.08 % (2563)------------------------------
% 5.46/2.08 % (2563)------------------------------
% 5.46/2.09 % (2568)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_2101 for (2995ds/253Mi)
% 5.88/2.12 % (2567)Instruction limit reached!
% 5.88/2.12 % (2567)------------------------------
% 5.88/2.12 % (2567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.12 % (2567)Termination reason: Unknown
% 5.88/2.12 % (2567)Termination phase: Naming
% 5.88/2.12
% 5.88/2.12 % (2567)Memory used [KB]: 2686
% 5.88/2.12 % (2567)Time elapsed: 0.033 s
% 5.88/2.12 % (2567)Instructions burned: 109 (million)
% 5.88/2.12 % (2567)------------------------------
% 5.88/2.12 % (2567)------------------------------
% 5.88/2.13 % (2569)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_2101 for (2994ds/140Mi)
% 5.88/2.13 % (2565)Instruction limit reached!
% 5.88/2.13 % (2565)------------------------------
% 5.88/2.13 % (2565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.13 % (2565)Termination reason: Unknown
% 5.88/2.13 % (2565)Termination phase: Property scanning
% 5.88/2.13
% 5.88/2.13 % (2565)Memory used [KB]: 3454
% 5.88/2.13 % (2565)Time elapsed: 0.049 s
% 5.88/2.13 % (2565)Instructions burned: 152 (million)
% 5.88/2.13 % (2565)------------------------------
% 5.88/2.13 % (2565)------------------------------
% 5.88/2.13 % (2555)Instruction limit reached!
% 5.88/2.13 % (2555)------------------------------
% 5.88/2.13 % (2555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.13 % (2555)Termination reason: Unknown
% 5.88/2.13 % (2555)Termination phase: Saturation
% 5.88/2.13
% 5.88/2.13 % (2555)Memory used [KB]: 4605
% 5.88/2.13 % (2555)Time elapsed: 0.122 s
% 5.88/2.13 % (2555)Instructions burned: 433 (million)
% 5.88/2.13 % (2555)------------------------------
% 5.88/2.13 % (2555)------------------------------
% 5.88/2.14 % (2570)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_2101 for (2994ds/614Mi)
% 5.88/2.14 % (2571)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_2101 for (2994ds/202Mi)
% 5.88/2.16 % (2559)Instruction limit reached!
% 5.88/2.16 % (2559)------------------------------
% 5.88/2.16 % (2559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.16 % (2559)Termination reason: Unknown
% 5.88/2.16 % (2559)Termination phase: Saturation
% 5.88/2.16
% 5.88/2.16 % (2559)Memory used [KB]: 8315
% 5.88/2.16 % (2559)Time elapsed: 0.124 s
% 5.88/2.16 % (2559)Instructions burned: 453 (million)
% 5.88/2.16 % (2559)------------------------------
% 5.88/2.16 % (2559)------------------------------
% 5.88/2.17 % (2569)Instruction limit reached!
% 5.88/2.17 % (2569)------------------------------
% 5.88/2.17 % (2569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.17 % (2569)Termination reason: Unknown
% 5.88/2.17 % (2569)Termination phase: Saturation
% 5.88/2.17
% 5.88/2.17 % (2569)Memory used [KB]: 7291
% 5.88/2.17 % (2569)Time elapsed: 0.045 s
% 5.88/2.17 % (2569)Instructions burned: 141 (million)
% 5.88/2.17 % (2569)------------------------------
% 5.88/2.17 % (2569)------------------------------
% 5.88/2.17 % (2568)Instruction limit reached!
% 5.88/2.17 % (2568)------------------------------
% 5.88/2.17 % (2568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.17 % (2568)Termination reason: Unknown
% 5.88/2.17 % (2568)Termination phase: Saturation
% 5.88/2.17
% 5.88/2.17 % (2568)Memory used [KB]: 8571
% 5.88/2.17 % (2568)Time elapsed: 0.077 s
% 5.88/2.17 % (2568)Instructions burned: 253 (million)
% 5.88/2.17 % (2568)------------------------------
% 5.88/2.17 % (2568)------------------------------
% 5.88/2.17 % (2572)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_2101 for (2994ds/339Mi)
% 5.88/2.18 % (2573)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_2101 for (2994ds/283Mi)
% 5.88/2.18 % (2574)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_2101 for (2994ds/134Mi)
% 5.88/2.18 % (2566)Instruction limit reached!
% 5.88/2.18 % (2566)------------------------------
% 5.88/2.18 % (2566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.18 % (2566)Termination reason: Unknown
% 5.88/2.18 % (2566)Termination phase: Saturation
% 5.88/2.18
% 5.88/2.18 % (2566)Memory used [KB]: 8699
% 5.88/2.18 % (2566)Time elapsed: 0.100 s
% 5.88/2.18 % (2566)Instructions burned: 343 (million)
% 5.88/2.18 % (2566)------------------------------
% 5.88/2.18 % (2566)------------------------------
% 5.88/2.19 % (2575)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_2101 for (2994ds/298Mi)
% 6.56/2.20 % (2571)Refutation not found, incomplete strategy
% 6.56/2.20 % (2571)------------------------------
% 6.56/2.20 % (2571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.20 % (2571)Termination reason: Refutation not found, incomplete strategy
% 6.56/2.20
% 6.56/2.20
% 6.56/2.20 % (2571)Memory used [KB]: 8059
% 6.56/2.20 % (2571)Time elapsed: 0.062 s
% 6.56/2.20 % (2571)Instructions burned: 201 (million)
% 6.56/2.20 % (2571)------------------------------
% 6.56/2.20 % (2571)------------------------------
% 6.56/2.21 % (2576)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_2101 for (2994ds/192Mi)
% 6.56/2.22 % (2574)Instruction limit reached!
% 6.56/2.22 % (2574)------------------------------
% 6.56/2.22 % (2574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.22 % (2574)Termination reason: Unknown
% 6.56/2.22 % (2574)Termination phase: Property scanning
% 6.56/2.22
% 6.56/2.22 % (2574)Memory used [KB]: 3326
% 6.56/2.22 % (2574)Time elapsed: 0.040 s
% 6.56/2.22 % (2574)Instructions burned: 134 (million)
% 6.56/2.22 % (2574)------------------------------
% 6.56/2.22 % (2574)------------------------------
% 6.56/2.23 % (2577)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_2101 for (2993ds/258Mi)
% 6.56/2.25 % (2573)Instruction limit reached!
% 6.56/2.25 % (2573)------------------------------
% 6.56/2.25 % (2573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.25 % (2573)Termination reason: Unknown
% 6.56/2.25 % (2573)Termination phase: Saturation
% 6.56/2.25
% 6.56/2.25 % (2573)Memory used [KB]: 7675
% 6.56/2.25 % (2573)Time elapsed: 0.073 s
% 6.56/2.25 % (2573)Instructions burned: 283 (million)
% 6.56/2.25 % (2573)------------------------------
% 6.56/2.25 % (2573)------------------------------
% 6.56/2.26 % (2578)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_2101 for (2993ds/90Mi)
% 6.56/2.26 % (2576)Instruction limit reached!
% 6.56/2.26 % (2576)------------------------------
% 6.56/2.26 % (2576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.26 % (2576)Termination reason: Unknown
% 6.56/2.26 % (2576)Termination phase: Property scanning
% 6.56/2.26
% 6.56/2.26 % (2576)Memory used [KB]: 3326
% 6.56/2.26 % (2576)Time elapsed: 0.054 s
% 6.56/2.26 % (2576)Instructions burned: 194 (million)
% 6.56/2.26 % (2576)------------------------------
% 6.56/2.26 % (2576)------------------------------
% 6.56/2.27 % (2572)Instruction limit reached!
% 6.56/2.27 % (2572)------------------------------
% 6.56/2.27 % (2572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.27 % (2572)Termination reason: Unknown
% 6.56/2.27 % (2572)Termination phase: Saturation
% 6.56/2.27
% 6.56/2.27 % (2572)Memory used [KB]: 8443
% 6.56/2.27 % (2572)Time elapsed: 0.097 s
% 6.56/2.27 % (2572)Instructions burned: 340 (million)
% 6.56/2.27 % (2572)------------------------------
% 6.56/2.27 % (2572)------------------------------
% 6.56/2.27 % (2575)Instruction limit reached!
% 6.56/2.27 % (2575)------------------------------
% 6.56/2.27 % (2575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.27 % (2575)Termination reason: Unknown
% 6.56/2.27 % (2575)Termination phase: Saturation
% 6.56/2.27
% 6.56/2.27 % (2575)Memory used [KB]: 7803
% 6.56/2.27 % (2575)Time elapsed: 0.078 s
% 6.56/2.27 % (2575)Instructions burned: 300 (million)
% 6.56/2.27 % (2575)------------------------------
% 6.56/2.27 % (2575)------------------------------
% 6.56/2.27 % (2579)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_2101 for (2993ds/231Mi)
% 6.56/2.28 % (2580)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_2101 for (2993ds/458Mi)
% 6.56/2.28 % (2581)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_2101 for (2993ds/31Mi)
% 6.56/2.29 % (2578)Instruction limit reached!
% 6.56/2.29 % (2578)------------------------------
% 6.56/2.29 % (2578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.29 % (2578)Termination reason: Unknown
% 6.56/2.29 % (2578)Termination phase: Naming
% 6.56/2.29
% 6.56/2.29 % (2578)Memory used [KB]: 2686
% 6.56/2.29 % (2578)Time elapsed: 0.029 s
% 6.56/2.29 % (2578)Instructions burned: 91 (million)
% 6.56/2.29 % (2578)------------------------------
% 6.56/2.29 % (2578)------------------------------
% 6.56/2.29 % (2581)Instruction limit reached!
% 6.56/2.29 % (2581)------------------------------
% 6.56/2.29 % (2581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.56/2.29 % (2581)Termination reason: Unknown
% 6.56/2.29 % (2581)Termination phase: shuffling
% 6.56/2.29
% 6.56/2.29 % (2581)Memory used [KB]: 2046
% 6.56/2.29 % (2581)Time elapsed: 0.012 s
% 6.56/2.29 % (2581)Instructions burned: 33 (million)
% 6.56/2.29 % (2581)------------------------------
% 6.56/2.29 % (2581)------------------------------
% 7.19/2.30 % (2582)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_2101 for (2993ds/297Mi)
% 7.19/2.30 % (2583)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_2101 for (2993ds/987Mi)
% 7.19/2.30 % (2577)Instruction limit reached!
% 7.19/2.30 % (2577)------------------------------
% 7.19/2.30 % (2577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.19/2.30 % (2577)Termination reason: Unknown
% 7.19/2.30 % (2577)Termination phase: Saturation
% 7.19/2.30
% 7.19/2.30 % (2577)Memory used [KB]: 3965
% 7.19/2.30 % (2577)Time elapsed: 0.075 s
% 7.19/2.30 % (2577)Instructions burned: 258 (million)
% 7.19/2.30 % (2577)------------------------------
% 7.19/2.30 % (2577)------------------------------
% 7.19/2.31 % (2552)Instruction limit reached!
% 7.19/2.31 % (2552)------------------------------
% 7.19/2.31 % (2552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.19/2.31 % (2552)Termination reason: Unknown
% 7.19/2.31 % (2552)Termination phase: Saturation
% 7.19/2.31
% 7.19/2.31 % (2552)Memory used [KB]: 9338
% 7.19/2.31 % (2552)Time elapsed: 0.344 s
% 7.19/2.31 % (2552)Instructions burned: 1088 (million)
% 7.19/2.31 % (2552)------------------------------
% 7.19/2.31 % (2552)------------------------------
% 7.19/2.31 % (2584)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_2101 for (2993ds/182Mi)
% 7.19/2.32 % (2585)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_2101 for (2993ds/182Mi)
% 7.19/2.33 % (2570)Instruction limit reached!
% 7.19/2.33 % (2570)------------------------------
% 7.19/2.33 % (2570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.19/2.33 % (2570)Termination reason: Unknown
% 7.19/2.33 % (2570)Termination phase: Saturation
% 7.19/2.33
% 7.19/2.33 % (2570)Memory used [KB]: 10362
% 7.19/2.33 % (2570)Time elapsed: 0.196 s
% 7.19/2.33 % (2570)Instructions burned: 617 (million)
% 7.19/2.33 % (2570)------------------------------
% 7.19/2.33 % (2570)------------------------------
% 7.19/2.33 % (2579)Instruction limit reached!
% 7.19/2.33 % (2579)------------------------------
% 7.19/2.33 % (2579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.19/2.33 % (2579)Termination reason: Unknown
% 7.19/2.33 % (2579)Termination phase: Property scanning
% 7.19/2.33
% 7.19/2.33 % (2579)Memory used [KB]: 3198
% 7.19/2.33 % (2579)Time elapsed: 0.061 s
% 7.19/2.33 % (2579)Instructions burned: 234 (million)
% 7.19/2.33 % (2579)------------------------------
% 7.19/2.33 % (2579)------------------------------
% 7.19/2.34 % (2586)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_2101 for (2992ds/154Mi)
% 7.19/2.34 % (2587)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_2101 for (2992ds/79Mi)
% 7.19/2.36 % (2584)Instruction limit reached!
% 7.19/2.36 % (2584)------------------------------
% 7.19/2.36 % (2584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.19/2.36 % (2584)Termination reason: Unknown
% 7.19/2.36 % (2584)Termination phase: Function definition elimination
% 7.19/2.36
% 7.19/2.36 % (2584)Memory used [KB]: 3326
% 7.19/2.36 % (2584)Time elapsed: 0.052 s
% 7.19/2.36 % (2584)Instructions burned: 182 (million)
% 7.19/2.36 % (2584)------------------------------
% 7.19/2.36 % (2584)------------------------------
% 7.19/2.37 % (2587)Instruction limit reached!
% 7.19/2.37 % (2587)------------------------------
% 7.19/2.37 % (2587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.19/2.37 % (2587)Termination reason: Unknown
% 7.19/2.37 % (2587)Termination phase: Property scanning
% 7.19/2.37
% 7.19/2.37 % (2587)Memory used [KB]: 2302
% 7.19/2.37 % (2587)Time elapsed: 0.028 s
% 7.19/2.37 % (2587)Instructions burned: 82 (million)
% 7.19/2.37 % (2587)------------------------------
% 7.19/2.37 % (2587)------------------------------
% 7.19/2.37 % (2585)Instruction limit reached!
% 7.19/2.37 % (2585)------------------------------
% 7.19/2.37 % (2585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.19/2.37 % (2585)Termination reason: Unknown
% 7.19/2.37 % (2585)Termination phase: Property scanning
% 7.19/2.37
% 7.19/2.37 % (2585)Memory used [KB]: 3454
% 7.19/2.37 % (2585)Time elapsed: 0.054 s
% 7.19/2.37 % (2585)Instructions burned: 185 (million)
% 7.19/2.37 % (2585)------------------------------
% 7.19/2.37 % (2585)------------------------------
% 7.19/2.37 % (2588)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_2101 for (2992ds/216Mi)
% 7.19/2.38 % (2589)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_2101 for (2992ds/114Mi)
% 7.19/2.38 % (2582)Instruction limit reached!
% 7.19/2.38 % (2582)------------------------------
% 7.19/2.38 % (2582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.19/2.38 % (2582)Termination reason: Unknown
% 7.19/2.38 % (2582)Termination phase: Saturation
% 7.19/2.38
% 7.19/2.38 % (2582)Memory used [KB]: 7931
% 7.19/2.38 % (2582)Time elapsed: 0.082 s
% 7.19/2.38 % (2582)Instructions burned: 297 (million)
% 7.19/2.38 % (2582)------------------------------
% 7.19/2.38 % (2582)------------------------------
% 7.19/2.38 % (2590)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_2101 for (2992ds/922Mi)
% 7.19/2.38 % (2586)Instruction limit reached!
% 7.19/2.38 % (2586)------------------------------
% 7.19/2.38 % (2586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.19/2.38 % (2586)Termination reason: Unknown
% 7.19/2.38 % (2586)Termination phase: Property scanning
% 7.19/2.38
% 7.19/2.38 % (2586)Memory used [KB]: 3198
% 7.19/2.38 % (2586)Time elapsed: 0.043 s
% 7.19/2.38 % (2586)Instructions burned: 155 (million)
% 7.19/2.38 % (2586)------------------------------
% 7.19/2.38 % (2586)------------------------------
% 7.19/2.39 % (2591)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_2101 for (2992ds/182Mi)
% 7.19/2.39 % (2592)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_2101 for (2992ds/164Mi)
% 7.87/2.41 % (2580)Instruction limit reached!
% 7.87/2.41 % (2580)------------------------------
% 7.87/2.41 % (2580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.41 % (2580)Termination reason: Unknown
% 7.87/2.41 % (2580)Termination phase: Saturation
% 7.87/2.41
% 7.87/2.41 % (2580)Memory used [KB]: 9338
% 7.87/2.41 % (2580)Time elapsed: 0.136 s
% 7.87/2.41 % (2580)Instructions burned: 459 (million)
% 7.87/2.41 % (2580)------------------------------
% 7.87/2.41 % (2580)------------------------------
% 7.87/2.41 % (2589)Instruction limit reached!
% 7.87/2.41 % (2589)------------------------------
% 7.87/2.41 % (2589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.41 % (2589)Termination reason: Unknown
% 7.87/2.41 % (2589)Termination phase: Preprocessing 3
% 7.87/2.41
% 7.87/2.41 % (2589)Memory used [KB]: 3198
% 7.87/2.41 % (2589)Time elapsed: 0.035 s
% 7.87/2.41 % (2589)Instructions burned: 115 (million)
% 7.87/2.41 % (2589)------------------------------
% 7.87/2.41 % (2589)------------------------------
% 7.87/2.42 % (2593)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_2101 for (2991ds/50Mi)
% 7.87/2.42 % (2594)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_2101 for (2991ds/368Mi)
% 7.87/2.43 % (2588)Instruction limit reached!
% 7.87/2.43 % (2588)------------------------------
% 7.87/2.43 % (2588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.43 % (2588)Termination reason: Unknown
% 7.87/2.43 % (2588)Termination phase: Property scanning
% 7.87/2.43
% 7.87/2.43 % (2588)Memory used [KB]: 3198
% 7.87/2.43 % (2588)Time elapsed: 0.058 s
% 7.87/2.43 % (2588)Instructions burned: 216 (million)
% 7.87/2.43 % (2588)------------------------------
% 7.87/2.43 % (2588)------------------------------
% 7.87/2.44 % (2591)Instruction limit reached!
% 7.87/2.44 % (2591)------------------------------
% 7.87/2.44 % (2591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.44 % (2591)Termination reason: Unknown
% 7.87/2.44 % (2591)Termination phase: Property scanning
% 7.87/2.44
% 7.87/2.44 % (2591)Memory used [KB]: 3198
% 7.87/2.44 % (2591)Time elapsed: 0.049 s
% 7.87/2.44 % (2591)Instructions burned: 185 (million)
% 7.87/2.44 % (2591)------------------------------
% 7.87/2.44 % (2591)------------------------------
% 7.87/2.44 % (2593)Instruction limit reached!
% 7.87/2.44 % (2593)------------------------------
% 7.87/2.44 % (2593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.44 % (2593)Termination reason: Unknown
% 7.87/2.44 % (2593)Termination phase: shuffling
% 7.87/2.44
% 7.87/2.44 % (2593)Memory used [KB]: 2558
% 7.87/2.44 % (2593)Time elapsed: 0.016 s
% 7.87/2.44 % (2593)Instructions burned: 53 (million)
% 7.87/2.44 % (2593)------------------------------
% 7.87/2.44 % (2593)------------------------------
% 7.87/2.44 % (2592)Instruction limit reached!
% 7.87/2.44 % (2592)------------------------------
% 7.87/2.44 % (2592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.44 % (2592)Termination reason: Unknown
% 7.87/2.44 % (2592)Termination phase: SInE selection
% 7.87/2.44
% 7.87/2.44 % (2592)Memory used [KB]: 3070
% 7.87/2.44 % (2592)Time elapsed: 0.045 s
% 7.87/2.44 % (2592)Instructions burned: 164 (million)
% 7.87/2.44 % (2592)------------------------------
% 7.87/2.44 % (2592)------------------------------
% 7.87/2.44 % (2595)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_2101 for (2991ds/1021Mi)
% 7.87/2.45 % (2596)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_2101 for (2991ds/267Mi)
% 7.87/2.45 % (2597)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_2101 for (2991ds/204Mi)
% 7.87/2.45 % (2598)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_2101 for (2991ds/26Mi)
% 7.87/2.46 % (2598)Instruction limit reached!
% 7.87/2.46 % (2598)------------------------------
% 7.87/2.46 % (2598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.46 % (2598)Termination reason: Unknown
% 7.87/2.46 % (2598)Termination phase: shuffling
% 7.87/2.46
% 7.87/2.46 % (2598)Memory used [KB]: 2174
% 7.87/2.46 % (2598)Time elapsed: 0.009 s
% 7.87/2.46 % (2598)Instructions burned: 29 (million)
% 7.87/2.46 % (2598)------------------------------
% 7.87/2.46 % (2598)------------------------------
% 7.87/2.47 % (2599)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_2101 for (2991ds/53Mi)
% 7.87/2.48 % (2599)Instruction limit reached!
% 7.87/2.48 % (2599)------------------------------
% 7.87/2.48 % (2599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.87/2.48 % (2599)Termination reason: Unknown
% 7.87/2.48 % (2599)Termination phase: shuffling
% 7.87/2.48
% 7.87/2.48 % (2599)Memory used [KB]: 2558
% 7.87/2.48 % (2599)Time elapsed: 0.016 s
% 7.87/2.48 % (2599)Instructions burned: 53 (million)
% 7.87/2.48 % (2599)------------------------------
% 7.87/2.48 % (2599)------------------------------
% 7.87/2.49 % (2600)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_2101 for (2991ds/4436Mi)
% 8.30/2.50 % (2597)Instruction limit reached!
% 8.30/2.50 % (2597)------------------------------
% 8.30/2.50 % (2597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.30/2.50 % (2597)Termination reason: Unknown
% 8.30/2.50 % (2597)Termination phase: Property scanning
% 8.30/2.50
% 8.30/2.50 % (2597)Memory used [KB]: 3326
% 8.30/2.50 % (2597)Time elapsed: 0.059 s
% 8.30/2.50 % (2597)Instructions burned: 207 (million)
% 8.30/2.50 % (2597)------------------------------
% 8.30/2.50 % (2597)------------------------------
% 8.30/2.51 % (2601)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_2101 for (2990ds/1539Mi)
% 8.30/2.51 % (2596)Instruction limit reached!
% 8.30/2.51 % (2596)------------------------------
% 8.30/2.51 % (2596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.30/2.51 % (2596)Termination reason: Unknown
% 8.30/2.51 % (2596)Termination phase: Saturation
% 8.30/2.51
% 8.30/2.51 % (2596)Memory used [KB]: 7675
% 8.30/2.51 % (2596)Time elapsed: 0.069 s
% 8.30/2.51 % (2596)Instructions burned: 267 (million)
% 8.30/2.51 % (2596)------------------------------
% 8.30/2.51 % (2596)------------------------------
% 8.30/2.52 % (2602)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_2101 for (2990ds/408Mi)
% 8.30/2.53 % (2594)Instruction limit reached!
% 8.30/2.53 % (2594)------------------------------
% 8.30/2.53 % (2594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.30/2.53 % (2594)Termination reason: Unknown
% 8.30/2.53 % (2594)Termination phase: Saturation
% 8.30/2.53
% 8.30/2.53 % (2594)Memory used [KB]: 9210
% 8.30/2.53 % (2594)Time elapsed: 0.108 s
% 8.30/2.53 % (2594)Instructions burned: 370 (million)
% 8.30/2.53 % (2594)------------------------------
% 8.30/2.53 % (2594)------------------------------
% 8.30/2.54 % (2603)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_2101 for (2990ds/5205Mi)
% 8.30/2.60 % (2583)Instruction limit reached!
% 8.30/2.60 % (2583)------------------------------
% 8.30/2.60 % (2583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.30/2.60 % (2583)Termination reason: Unknown
% 8.30/2.60 % (2583)Termination phase: Saturation
% 8.30/2.60
% 8.30/2.60 % (2583)Memory used [KB]: 10490
% 8.30/2.60 % (2583)Time elapsed: 0.298 s
% 8.30/2.60 % (2583)Instructions burned: 988 (million)
% 8.30/2.60 % (2583)------------------------------
% 8.30/2.60 % (2583)------------------------------
% 8.57/2.61 % (2604)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_2101 for (2990ds/1913Mi)
% 8.57/2.64 % (2602)Instruction limit reached!
% 8.57/2.64 % (2602)------------------------------
% 8.57/2.64 % (2602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.64 % (2602)Termination reason: Unknown
% 8.57/2.64 % (2602)Termination phase: Saturation
% 8.57/2.64
% 8.57/2.64 % (2602)Memory used [KB]: 9850
% 8.57/2.64 % (2602)Time elapsed: 0.116 s
% 8.57/2.64 % (2602)Instructions burned: 409 (million)
% 8.57/2.64 % (2602)------------------------------
% 8.57/2.64 % (2602)------------------------------
% 8.57/2.65 % (2605)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_2101 for (2989ds/4350Mi)
% 8.57/2.67 % (2590)Instruction limit reached!
% 8.57/2.67 % (2590)------------------------------
% 8.57/2.67 % (2590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.57/2.67 % (2590)Termination reason: Unknown
% 8.57/2.67 % (2590)Termination phase: Saturation
% 8.57/2.67
% 8.57/2.67 % (2590)Memory used [KB]: 9083
% 8.57/2.67 % (2590)Time elapsed: 0.290 s
% 8.57/2.67 % (2590)Instructions burned: 924 (million)
% 8.57/2.67 % (2590)------------------------------
% 8.57/2.67 % (2590)------------------------------
% 8.57/2.68 % (2606)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_2101 for (2989ds/68Mi)
% 9.31/2.70 % (2606)Instruction limit reached!
% 9.31/2.70 % (2606)------------------------------
% 9.31/2.70 % (2606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.31/2.70 % (2606)Termination reason: Unknown
% 9.31/2.70 % (2606)Termination phase: Property scanning
% 9.31/2.70
% 9.31/2.70 % (2606)Memory used [KB]: 2302
% 9.31/2.70 % (2606)Time elapsed: 0.023 s
% 9.31/2.70 % (2606)Instructions burned: 69 (million)
% 9.31/2.70 % (2606)------------------------------
% 9.31/2.70 % (2606)------------------------------
% 9.31/2.71 % (2607)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_2101 for (2989ds/358Mi)
% 9.31/2.75 % (2595)Instruction limit reached!
% 9.31/2.75 % (2595)------------------------------
% 9.31/2.75 % (2595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.31/2.75 % (2595)Termination reason: Unknown
% 9.31/2.75 % (2595)Termination phase: Saturation
% 9.31/2.75
% 9.31/2.75 % (2595)Memory used [KB]: 9594
% 9.31/2.75 % (2595)Time elapsed: 0.313 s
% 9.31/2.75 % (2595)Instructions burned: 1022 (million)
% 9.31/2.75 % (2595)------------------------------
% 9.31/2.75 % (2595)------------------------------
% 9.31/2.76 % (2608)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_2101 for (2988ds/31Mi)
% 9.31/2.77 % (2608)Instruction limit reached!
% 9.31/2.77 % (2608)------------------------------
% 9.31/2.77 % (2608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.31/2.77 % (2608)Termination reason: Unknown
% 9.31/2.77 % (2608)Termination phase: shuffling
% 9.31/2.77
% 9.31/2.77 % (2608)Memory used [KB]: 1918
% 9.31/2.77 % (2608)Time elapsed: 0.011 s
% 9.31/2.77 % (2608)Instructions burned: 32 (million)
% 9.31/2.77 % (2608)------------------------------
% 9.31/2.77 % (2608)------------------------------
% 9.31/2.78 % (2609)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_2101 for (2988ds/279Mi)
% 9.67/2.81 % (2607)Instruction limit reached!
% 9.67/2.81 % (2607)------------------------------
% 9.67/2.81 % (2607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.81 % (2607)Termination reason: Unknown
% 9.67/2.81 % (2607)Termination phase: Saturation
% 9.67/2.81
% 9.67/2.81 % (2607)Memory used [KB]: 8571
% 9.67/2.81 % (2607)Time elapsed: 0.103 s
% 9.67/2.81 % (2607)Instructions burned: 359 (million)
% 9.67/2.81 % (2607)------------------------------
% 9.67/2.81 % (2607)------------------------------
% 9.67/2.82 % (2610)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_2101 for (2987ds/258Mi)
% 9.67/2.86 % (2609)Refutation not found, incomplete strategy
% 9.67/2.86 % (2609)------------------------------
% 9.67/2.86 % (2609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.86 % (2609)Termination reason: Refutation not found, incomplete strategy
% 9.67/2.86
% 9.67/2.86
% 9.67/2.86 % (2609)Memory used [KB]: 8059
% 9.67/2.86 % (2609)Time elapsed: 0.075 s
% 9.67/2.86 % (2609)Instructions burned: 278 (million)
% 9.67/2.86 % (2609)------------------------------
% 9.67/2.86 % (2609)------------------------------
% 9.67/2.87 % (2611)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_2101 for (2987ds/26Mi)
% 9.67/2.87 % (2611)Instruction limit reached!
% 9.67/2.87 % (2611)------------------------------
% 9.67/2.87 % (2611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.87 % (2611)Termination reason: Unknown
% 9.67/2.87 % (2611)Termination phase: shuffling
% 9.67/2.87
% 9.67/2.87 % (2611)Memory used [KB]: 2174
% 9.67/2.87 % (2611)Time elapsed: 0.009 s
% 9.67/2.87 % (2611)Instructions burned: 29 (million)
% 9.67/2.87 % (2611)------------------------------
% 9.67/2.87 % (2611)------------------------------
% 9.67/2.88 % (2612)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_2101 for (2987ds/995Mi)
% 9.67/2.89 % (2610)Instruction limit reached!
% 9.67/2.89 % (2610)------------------------------
% 9.67/2.89 % (2610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.89 % (2610)Termination reason: Unknown
% 9.67/2.89 % (2610)Termination phase: Saturation
% 9.67/2.89
% 9.67/2.89 % (2610)Memory used [KB]: 8187
% 9.67/2.89 % (2610)Time elapsed: 0.074 s
% 9.67/2.89 % (2610)Instructions burned: 259 (million)
% 9.67/2.89 % (2610)------------------------------
% 9.67/2.89 % (2610)------------------------------
% 9.97/2.90 % (2613)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_2101 for (2987ds/373Mi)
% 9.97/2.97 % (2601)Instruction limit reached!
% 9.97/2.97 % (2601)------------------------------
% 9.97/2.97 % (2601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.97/2.97 % (2601)Termination reason: Unknown
% 9.97/2.97 % (2601)Termination phase: Saturation
% 9.97/2.97
% 9.97/2.97 % (2601)Memory used [KB]: 11641
% 9.97/2.97 % (2601)Time elapsed: 0.452 s
% 9.97/2.97 % (2601)Instructions burned: 1541 (million)
% 9.97/2.97 % (2601)------------------------------
% 9.97/2.97 % (2601)------------------------------
% 9.97/2.98 % (2614)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_2101 for (2986ds/253Mi)
% 9.97/3.01 % (2613)Instruction limit reached!
% 9.97/3.01 % (2613)------------------------------
% 9.97/3.01 % (2613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.97/3.01 % (2613)Termination reason: Unknown
% 9.97/3.01 % (2613)Termination phase: Saturation
% 9.97/3.01
% 9.97/3.01 % (2613)Memory used [KB]: 9210
% 9.97/3.01 % (2613)Time elapsed: 0.111 s
% 9.97/3.01 % (2613)Instructions burned: 373 (million)
% 9.97/3.01 % (2613)------------------------------
% 9.97/3.01 % (2613)------------------------------
% 12.54/3.02 % (2615)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_2101 for (2985ds/832Mi)
% 12.54/3.04 % (2614)Instruction limit reached!
% 12.54/3.04 % (2614)------------------------------
% 12.54/3.04 % (2614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.54/3.04 % (2614)Termination reason: Unknown
% 12.54/3.04 % (2614)Termination phase: Saturation
% 12.54/3.04
% 12.54/3.04 % (2614)Memory used [KB]: 7547
% 12.54/3.04 % (2614)Time elapsed: 0.067 s
% 12.54/3.04 % (2614)Instructions burned: 256 (million)
% 12.54/3.04 % (2614)------------------------------
% 12.54/3.04 % (2614)------------------------------
% 12.54/3.05 % (2616)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_2101 for (2985ds/668Mi)
% 13.09/3.13 % (2615)Refutation not found, incomplete strategy
% 13.09/3.13 % (2615)------------------------------
% 13.09/3.13 % (2615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.09/3.13 % (2615)Termination reason: Refutation not found, incomplete strategy
% 13.09/3.13
% 13.09/3.13
% 13.09/3.13 % (2615)Memory used [KB]: 9850
% 13.09/3.13 % (2615)Time elapsed: 0.107 s
% 13.09/3.13 % (2615)Instructions burned: 366 (million)
% 13.09/3.13 % (2615)------------------------------
% 13.09/3.13 % (2615)------------------------------
% 13.09/3.14 % (2617)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_2101 for (2984ds/40Mi)
% 13.09/3.15 % (2617)Instruction limit reached!
% 13.09/3.15 % (2617)------------------------------
% 13.09/3.15 % (2617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.09/3.15 % (2617)Termination reason: Unknown
% 13.09/3.15 % (2617)Termination phase: shuffling
% 13.09/3.15
% 13.09/3.15 % (2617)Memory used [KB]: 2302
% 13.09/3.15 % (2617)Time elapsed: 0.013 s
% 13.09/3.15 % (2617)Instructions burned: 41 (million)
% 13.09/3.15 % (2617)------------------------------
% 13.09/3.15 % (2617)------------------------------
% 13.09/3.16 % (2618)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_2101 for (2984ds/294Mi)
% 13.09/3.17 % (2612)Instruction limit reached!
% 13.09/3.17 % (2612)------------------------------
% 13.09/3.17 % (2612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.09/3.17 % (2612)Termination reason: Unknown
% 13.09/3.17 % (2612)Termination phase: Saturation
% 13.09/3.17
% 13.09/3.17 % (2612)Memory used [KB]: 10106
% 13.09/3.17 % (2612)Time elapsed: 0.288 s
% 13.09/3.17 % (2612)Instructions burned: 997 (million)
% 13.09/3.17 % (2612)------------------------------
% 13.09/3.17 % (2612)------------------------------
% 13.09/3.18 % (2619)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_2101 for (2984ds/187Mi)
% 13.09/3.18 % (2604)Instruction limit reached!
% 13.09/3.18 % (2604)------------------------------
% 13.09/3.18 % (2604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.09/3.18 % (2604)Termination reason: Unknown
% 13.09/3.18 % (2604)Termination phase: Saturation
% 13.09/3.18
% 13.09/3.18 % (2604)Memory used [KB]: 6268
% 13.09/3.18 % (2604)Time elapsed: 0.578 s
% 13.09/3.18 % (2604)Instructions burned: 1914 (million)
% 13.09/3.18 % (2604)------------------------------
% 13.09/3.18 % (2604)------------------------------
% 13.09/3.19 % (2620)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_2101 for (2984ds/371Mi)
% 13.57/3.21 % (2618)Refutation not found, incomplete strategy
% 13.57/3.21 % (2618)------------------------------
% 13.57/3.21 % (2618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.57/3.21 % (2618)Termination reason: Refutation not found, incomplete strategy
% 13.57/3.21
% 13.57/3.21
% 13.57/3.21 % (2618)Memory used [KB]: 7675
% 13.57/3.21 % (2618)Time elapsed: 0.048 s
% 13.57/3.21 % (2618)Instructions burned: 175 (million)
% 13.57/3.21 % (2618)------------------------------
% 13.57/3.21 % (2618)------------------------------
% 13.57/3.22 % (2621)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_2101 for (2983ds/1827Mi)
% 13.57/3.23 % (2619)Instruction limit reached!
% 13.57/3.23 % (2619)------------------------------
% 13.57/3.23 % (2619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.57/3.23 % (2619)Termination reason: Unknown
% 13.57/3.23 % (2619)Termination phase: Property scanning
% 13.57/3.23
% 13.57/3.23 % (2619)Memory used [KB]: 3326
% 13.57/3.23 % (2619)Time elapsed: 0.055 s
% 13.57/3.23 % (2619)Instructions burned: 189 (million)
% 13.57/3.23 % (2619)------------------------------
% 13.57/3.23 % (2619)------------------------------
% 13.57/3.24 % (2616)Instruction limit reached!
% 13.57/3.24 % (2616)------------------------------
% 13.57/3.24 % (2616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.57/3.24 % (2616)Termination reason: Unknown
% 13.57/3.24 % (2616)Termination phase: Saturation
% 13.57/3.24
% 13.57/3.24 % (2616)Memory used [KB]: 14200
% 13.57/3.24 % (2616)Time elapsed: 0.191 s
% 13.57/3.24 % (2616)Instructions burned: 668 (million)
% 13.57/3.24 % (2616)------------------------------
% 13.57/3.24 % (2616)------------------------------
% 13.57/3.24 % (2622)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_2101 for (2983ds/70Mi)
% 13.57/3.25 % (2623)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_2101 for (2983ds/316Mi)
% 13.57/3.26 % (2622)Instruction limit reached!
% 13.57/3.26 % (2622)------------------------------
% 13.57/3.26 % (2622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.57/3.26 % (2622)Termination reason: Unknown
% 13.57/3.26 % (2622)Termination phase: shuffling
% 13.57/3.26
% 13.57/3.26 % (2622)Memory used [KB]: 2942
% 13.57/3.26 % (2622)Time elapsed: 0.021 s
% 13.57/3.26 % (2622)Instructions burned: 71 (million)
% 13.57/3.26 % (2622)------------------------------
% 13.57/3.26 % (2622)------------------------------
% 13.57/3.27 % (2624)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_2101 for (2983ds/932Mi)
% 14.22/3.30 % (2620)Instruction limit reached!
% 14.22/3.30 % (2620)------------------------------
% 14.22/3.30 % (2620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.22/3.30 % (2620)Termination reason: Unknown
% 14.22/3.30 % (2620)Termination phase: Saturation
% 14.22/3.30
% 14.22/3.30 % (2620)Memory used [KB]: 9210
% 14.22/3.30 % (2620)Time elapsed: 0.111 s
% 14.22/3.30 % (2620)Instructions burned: 372 (million)
% 14.22/3.30 % (2620)------------------------------
% 14.22/3.30 % (2620)------------------------------
% 14.22/3.31 % (2625)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_2101 for (2982ds/4714Mi)
% 14.22/3.33 % (2623)Refutation not found, incomplete strategy
% 14.22/3.33 % (2623)------------------------------
% 14.22/3.33 % (2623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.22/3.33 % (2623)Termination reason: Refutation not found, incomplete strategy
% 14.22/3.33
% 14.22/3.33
% 14.22/3.33 % (2623)Memory used [KB]: 7931
% 14.22/3.33 % (2623)Time elapsed: 0.081 s
% 14.22/3.33 % (2623)Instructions burned: 303 (million)
% 14.22/3.33 % (2623)------------------------------
% 14.22/3.33 % (2623)------------------------------
% 14.22/3.34 % (2626)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_2101 for (2982ds/8250Mi)
% 14.22/3.39 % (2625)Refutation not found, incomplete strategy
% 14.22/3.39 % (2625)------------------------------
% 14.22/3.39 % (2625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.22/3.39 % (2625)Termination reason: Refutation not found, incomplete strategy
% 14.22/3.39
% 14.22/3.39
% 14.22/3.39 % (2625)Memory used [KB]: 8187
% 14.22/3.39 % (2625)Time elapsed: 0.083 s
% 14.22/3.40 % (2625)Instructions burned: 310 (million)
% 14.22/3.40 % (2625)------------------------------
% 14.22/3.40 % (2625)------------------------------
% 14.83/3.41 % (2627)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_2101 for (2982ds/770Mi)
% 14.83/3.44 % (2627)Refutation not found, incomplete strategy
% 14.83/3.44 % (2627)------------------------------
% 14.83/3.44 % (2627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.83/3.44 % (2627)Termination reason: Refutation not found, incomplete strategy
% 14.83/3.44
% 14.83/3.44
% 14.83/3.44 % (2627)Memory used [KB]: 7291
% 14.83/3.44 % (2627)Time elapsed: 0.038 s
% 14.83/3.44 % (2627)Instructions burned: 122 (million)
% 14.83/3.44 % (2627)------------------------------
% 14.83/3.44 % (2627)------------------------------
% 14.83/3.45 % (2628)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_2101 for (2981ds/794Mi)
% 15.17/3.54 % (2624)Instruction limit reached!
% 15.17/3.54 % (2624)------------------------------
% 15.17/3.54 % (2624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.17/3.54 % (2624)Termination reason: Unknown
% 15.17/3.54 % (2624)Termination phase: Saturation
% 15.17/3.54
% 15.17/3.54 % (2624)Memory used [KB]: 10106
% 15.17/3.54 % (2624)Time elapsed: 0.270 s
% 15.17/3.54 % (2624)Instructions burned: 933 (million)
% 15.17/3.54 % (2624)------------------------------
% 15.17/3.54 % (2624)------------------------------
% 15.17/3.55 % (2629)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_2101 for (2980ds/464Mi)
% 15.76/3.69 % (2629)Instruction limit reached!
% 15.76/3.69 % (2629)------------------------------
% 15.76/3.69 % (2629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.76/3.69 % (2629)Termination reason: Unknown
% 15.76/3.69 % (2629)Termination phase: Saturation
% 15.76/3.69
% 15.76/3.69 % (2629)Memory used [KB]: 8827
% 15.76/3.69 % (2629)Time elapsed: 0.135 s
% 15.76/3.69 % (2629)Instructions burned: 465 (million)
% 15.76/3.69 % (2629)------------------------------
% 15.76/3.69 % (2629)------------------------------
% 15.76/3.69 % (2628)Instruction limit reached!
% 15.76/3.69 % (2628)------------------------------
% 15.76/3.69 % (2628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.76/3.69 % (2628)Termination reason: Unknown
% 15.76/3.69 % (2628)Termination phase: Saturation
% 15.76/3.69
% 15.76/3.69 % (2628)Memory used [KB]: 7803
% 15.76/3.69 % (2628)Time elapsed: 0.238 s
% 15.76/3.69 % (2628)Instructions burned: 794 (million)
% 15.76/3.69 % (2628)------------------------------
% 15.76/3.69 % (2628)------------------------------
% 15.76/3.70 % (2630)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_2101 for (2979ds/1376Mi)
% 16.45/3.70 % (2631)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_2101 for (2979ds/906Mi)
% 16.45/3.79 % (2621)Instruction limit reached!
% 16.45/3.79 % (2621)------------------------------
% 16.45/3.79 % (2621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.45/3.79 % (2621)Termination reason: Unknown
% 16.45/3.79 % (2621)Termination phase: Saturation
% 16.45/3.79
% 16.45/3.79 % (2621)Memory used [KB]: 11385
% 16.45/3.79 % (2621)Time elapsed: 0.567 s
% 16.45/3.79 % (2621)Instructions burned: 1828 (million)
% 16.45/3.79 % (2621)------------------------------
% 16.45/3.79 % (2621)------------------------------
% 16.45/3.80 % (2632)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_2101 for (2978ds/434Mi)
% 17.33/3.80 % (2605)Refutation not found, non-redundant clauses discarded% (2605)------------------------------
% 17.33/3.80 % (2605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.33/3.80 % (2605)Termination reason: Refutation not found, non-redundant clauses discarded
% 17.33/3.80
% 17.33/3.80 % (2605)Memory used [KB]: 12665
% 17.33/3.80 % (2605)Time elapsed: 1.154 s
% 17.33/3.80 % (2605)Instructions burned: 3997 (million)
% 17.33/3.80 % (2605)------------------------------
% 17.33/3.80 % (2605)------------------------------
% 17.33/3.81 % (2633)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_2101 for (2978ds/865Mi)
% 17.33/3.86 % (2600)Instruction limit reached!
% 17.33/3.86 % (2600)------------------------------
% 17.33/3.86 % (2600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.33/3.86 % (2600)Termination reason: Unknown
% 17.33/3.86 % (2600)Termination phase: Saturation
% 17.33/3.86
% 17.33/3.86 % (2600)Memory used [KB]: 13432
% 17.33/3.86 % (2600)Time elapsed: 1.373 s
% 17.33/3.86 % (2600)Instructions burned: 4439 (million)
% 17.33/3.86 % (2600)------------------------------
% 17.33/3.86 % (2600)------------------------------
% 17.33/3.87 % (2634)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_2101 for (2977ds/593Mi)
% 17.51/3.92 % (2632)Instruction limit reached!
% 17.51/3.92 % (2632)------------------------------
% 17.51/3.92 % (2632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.51/3.92 % (2632)Termination reason: Unknown
% 17.51/3.92 % (2632)Termination phase: Saturation
% 17.51/3.92
% 17.51/3.92 % (2632)Memory used [KB]: 8443
% 17.51/3.92 % (2632)Time elapsed: 0.122 s
% 17.51/3.92 % (2632)Instructions burned: 435 (million)
% 17.51/3.92 % (2632)------------------------------
% 17.51/3.92 % (2632)------------------------------
% 17.51/3.93 % (2635)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_2101 for (2976ds/443Mi)
% 17.51/4.02 % (2631)Instruction limit reached!
% 17.51/4.02 % (2631)------------------------------
% 17.51/4.02 % (2631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.51/4.02 % (2631)Termination reason: Unknown
% 17.51/4.02 % (2631)Termination phase: Saturation
% 17.51/4.02
% 17.51/4.02 % (2631)Memory used [KB]: 13944
% 17.51/4.02 % (2631)Time elapsed: 0.319 s
% 17.51/4.02 % (2631)Instructions burned: 906 (million)
% 17.51/4.02 % (2631)------------------------------
% 17.51/4.02 % (2631)------------------------------
% 19.55/4.03 % (2636)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_2101 for (2975ds/594Mi)
% 19.55/4.03 % (2634)Instruction limit reached!
% 19.55/4.03 % (2634)------------------------------
% 19.55/4.03 % (2634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.55/4.03 % (2634)Termination reason: Unknown
% 19.55/4.03 % (2634)Termination phase: Saturation
% 19.55/4.03
% 19.55/4.03 % (2634)Memory used [KB]: 9722
% 19.55/4.03 % (2634)Time elapsed: 0.160 s
% 19.55/4.03 % (2634)Instructions burned: 595 (million)
% 19.55/4.03 % (2634)------------------------------
% 19.55/4.03 % (2634)------------------------------
% 19.55/4.04 % (2637)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_2101 for (2975ds/327Mi)
% 19.55/4.05 % (2635)Instruction limit reached!
% 19.55/4.05 % (2635)------------------------------
% 19.55/4.05 % (2635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.55/4.05 % (2635)Termination reason: Unknown
% 19.55/4.05 % (2635)Termination phase: Saturation
% 19.55/4.05
% 19.55/4.05 % (2635)Memory used [KB]: 8827
% 19.55/4.05 % (2635)Time elapsed: 0.129 s
% 19.55/4.05 % (2635)Instructions burned: 444 (million)
% 19.55/4.05 % (2635)------------------------------
% 19.55/4.05 % (2635)------------------------------
% 19.55/4.06 % (2633)Instruction limit reached!
% 19.55/4.06 % (2633)------------------------------
% 19.55/4.06 % (2633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.55/4.06 % (2633)Termination reason: Unknown
% 19.55/4.06 % (2633)Termination phase: Saturation
% 19.55/4.06
% 19.55/4.06 % (2633)Memory used [KB]: 9850
% 19.55/4.06 % (2633)Time elapsed: 0.251 s
% 19.55/4.06 % (2633)Instructions burned: 866 (million)
% 19.55/4.06 % (2633)------------------------------
% 19.55/4.06 % (2633)------------------------------
% 19.55/4.06 % (2638)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_2101 for (2975ds/5411Mi)
% 19.55/4.07 % (2639)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_2101 for (2975ds/1762Mi)
% 19.55/4.09 % (2630)Instruction limit reached!
% 19.55/4.09 % (2630)------------------------------
% 19.55/4.09 % (2630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.55/4.09 % (2630)Termination reason: Unknown
% 19.55/4.09 % (2630)Termination phase: Saturation
% 19.55/4.09
% 19.55/4.09 % (2630)Memory used [KB]: 14839
% 19.55/4.09 % (2630)Time elapsed: 0.397 s
% 19.55/4.09 % (2630)Instructions burned: 1376 (million)
% 19.55/4.09 % (2630)------------------------------
% 19.55/4.09 % (2630)------------------------------
% 19.55/4.10 % (2640)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_2101 for (2975ds/96Mi)
% 19.55/4.11 % (2603)Instruction limit reached!
% 19.55/4.11 % (2603)------------------------------
% 19.55/4.11 % (2603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.55/4.11 % (2603)Termination reason: Unknown
% 19.55/4.11 % (2603)Termination phase: Saturation
% 19.55/4.11
% 19.55/4.11 % (2603)Memory used [KB]: 14967
% 19.55/4.11 % (2603)Time elapsed: 1.568 s
% 19.55/4.11 % (2603)Instructions burned: 5206 (million)
% 19.55/4.11 % (2603)------------------------------
% 19.55/4.11 % (2603)------------------------------
% 19.55/4.12 % (2641)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_2101 for (2974ds/503Mi)
% 19.55/4.12 % (2638)Refutation not found, incomplete strategy
% 19.55/4.12 % (2638)------------------------------
% 19.55/4.12 % (2638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.55/4.12 % (2638)Termination reason: Refutation not found, incomplete strategy
% 19.55/4.12
% 19.55/4.12
% 19.55/4.12 % (2638)Memory used [KB]: 7931
% 19.55/4.12 % (2638)Time elapsed: 0.059 s
% 19.55/4.12 % (2638)Instructions burned: 199 (million)
% 19.55/4.12 % (2638)------------------------------
% 19.55/4.12 % (2638)------------------------------
% 20.03/4.13 % (2640)Instruction limit reached!
% 20.03/4.13 % (2640)------------------------------
% 20.03/4.13 % (2640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.03/4.13 % (2640)Termination reason: Unknown
% 20.03/4.13 % (2640)Termination phase: Property scanning
% 20.03/4.13
% 20.03/4.13 % (2640)Memory used [KB]: 3070
% 20.03/4.13 % (2640)Time elapsed: 0.028 s
% 20.03/4.13 % (2640)Instructions burned: 98 (million)
% 20.03/4.13 % (2640)------------------------------
% 20.03/4.13 % (2640)------------------------------
% 20.03/4.13 % (2642)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_2101 for (2974ds/90Mi)
% 20.03/4.13 % (2637)Instruction limit reached!
% 20.03/4.13 % (2637)------------------------------
% 20.03/4.13 % (2637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.03/4.13 % (2637)Termination reason: Unknown
% 20.03/4.13 % (2637)Termination phase: Saturation
% 20.03/4.13
% 20.03/4.13 % (2637)Memory used [KB]: 8955
% 20.03/4.13 % (2637)Time elapsed: 0.095 s
% 20.03/4.13 % (2637)Instructions burned: 327 (million)
% 20.03/4.13 % (2637)------------------------------
% 20.03/4.13 % (2637)------------------------------
% 20.03/4.14 % (2643)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_2101 for (2974ds/593Mi)
% 20.03/4.14 % (2644)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_2101 for (2974ds/1512Mi)
% 20.03/4.16 % (2642)Instruction limit reached!
% 20.03/4.16 % (2642)------------------------------
% 20.03/4.16 % (2642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.03/4.16 % (2642)Termination reason: Unknown
% 20.03/4.16 % (2642)Termination phase: shuffling
% 20.03/4.16
% 20.03/4.16 % (2642)Memory used [KB]: 2686
% 20.03/4.16 % (2642)Time elapsed: 0.028 s
% 20.03/4.16 % (2642)Instructions burned: 90 (million)
% 20.03/4.16 % (2642)------------------------------
% 20.03/4.16 % (2642)------------------------------
% 20.03/4.17 % (2645)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_2101 for (2974ds/569Mi)
% 20.29/4.21 % (2636)Instruction limit reached!
% 20.29/4.21 % (2636)------------------------------
% 20.29/4.21 % (2636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.29/4.21 % (2636)Termination reason: Unknown
% 20.29/4.21 % (2636)Termination phase: Saturation
% 20.29/4.21
% 20.29/4.21 % (2636)Memory used [KB]: 9083
% 20.29/4.21 % (2636)Time elapsed: 0.180 s
% 20.29/4.21 % (2636)Instructions burned: 596 (million)
% 20.29/4.21 % (2636)------------------------------
% 20.29/4.21 % (2636)------------------------------
% 20.29/4.22 % (2646)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_2101 for (2973ds/501Mi)
% 20.29/4.25 % (2644)Refutation not found, incomplete strategy
% 20.29/4.25 % (2644)------------------------------
% 20.29/4.25 % (2644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.29/4.25 % (2644)Termination reason: Refutation not found, incomplete strategy
% 20.29/4.25
% 20.29/4.25
% 20.29/4.25 % (2644)Memory used [KB]: 9722
% 20.29/4.25 % (2644)Time elapsed: 0.104 s
% 20.29/4.25 % (2644)Instructions burned: 359 (million)
% 20.29/4.25 % (2644)------------------------------
% 20.29/4.25 % (2644)------------------------------
% 20.29/4.26 % (2647)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_2101 for (2973ds/562Mi)
% 20.29/4.26 % (2641)Instruction limit reached!
% 20.29/4.26 % (2641)------------------------------
% 20.29/4.26 % (2641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.29/4.26 % (2641)Termination reason: Unknown
% 20.29/4.26 % (2641)Termination phase: Saturation
% 20.29/4.26
% 20.29/4.26 % (2641)Memory used [KB]: 10746
% 20.29/4.26 % (2641)Time elapsed: 0.145 s
% 20.29/4.26 % (2641)Instructions burned: 503 (million)
% 20.29/4.26 % (2641)------------------------------
% 20.29/4.26 % (2641)------------------------------
% 20.29/4.27 % (2648)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_2101 for (2973ds/406Mi)
% 20.85/4.31 % (2643)Instruction limit reached!
% 20.85/4.31 % (2643)------------------------------
% 20.85/4.31 % (2643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.85/4.31 % (2643)Termination reason: Unknown
% 20.85/4.31 % (2643)Termination phase: Saturation
% 20.85/4.31
% 20.85/4.31 % (2643)Memory used [KB]: 9850
% 20.85/4.31 % (2643)Time elapsed: 0.178 s
% 20.85/4.31 % (2643)Instructions burned: 596 (million)
% 20.85/4.31 % (2643)------------------------------
% 20.85/4.31 % (2643)------------------------------
% 20.85/4.33 % (2649)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_2101 for (2972ds/582Mi)
% 20.85/4.33 % (2645)Instruction limit reached!
% 20.85/4.33 % (2645)------------------------------
% 20.85/4.33 % (2645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.85/4.33 % (2645)Termination reason: Unknown
% 20.85/4.33 % (2645)Termination phase: Saturation
% 20.85/4.33
% 20.85/4.33 % (2645)Memory used [KB]: 9210
% 20.85/4.33 % (2645)Time elapsed: 0.159 s
% 20.85/4.33 % (2645)Instructions burned: 571 (million)
% 20.85/4.33 % (2645)------------------------------
% 20.85/4.33 % (2645)------------------------------
% 20.85/4.34 % (2650)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_2101 for (2972ds/456Mi)
% 20.85/4.36 % (2646)Instruction limit reached!
% 20.85/4.36 % (2646)------------------------------
% 20.85/4.36 % (2646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.85/4.36 % (2646)Termination reason: Unknown
% 20.85/4.36 % (2646)Termination phase: Saturation
% 20.85/4.36
% 20.85/4.36 % (2646)Memory used [KB]: 10874
% 20.85/4.36 % (2646)Time elapsed: 0.143 s
% 20.85/4.36 % (2646)Instructions burned: 503 (million)
% 20.85/4.36 % (2646)------------------------------
% 20.85/4.36 % (2646)------------------------------
% 20.85/4.37 % (2651)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_2101 for (2972ds/393Mi)
% 20.85/4.39 % (2648)Instruction limit reached!
% 20.85/4.39 % (2648)------------------------------
% 20.85/4.39 % (2648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.85/4.39 % (2648)Termination reason: Unknown
% 20.85/4.39 % (2648)Termination phase: Saturation
% 20.85/4.39
% 20.85/4.39 % (2648)Memory used [KB]: 9210
% 20.85/4.39 % (2648)Time elapsed: 0.120 s
% 20.85/4.39 % (2648)Instructions burned: 406 (million)
% 20.85/4.39 % (2648)------------------------------
% 20.85/4.39 % (2648)------------------------------
% 21.58/4.40 % (2652)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_2101 for (2972ds/1335Mi)
% 21.58/4.42 % (2647)Instruction limit reached!
% 21.58/4.42 % (2647)------------------------------
% 21.58/4.42 % (2647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.58/4.42 % (2647)Termination reason: Unknown
% 21.58/4.42 % (2647)Termination phase: Saturation
% 21.58/4.42
% 21.58/4.42 % (2647)Memory used [KB]: 9338
% 21.58/4.42 % (2647)Time elapsed: 0.159 s
% 21.58/4.42 % (2647)Instructions burned: 564 (million)
% 21.58/4.42 % (2647)------------------------------
% 21.58/4.42 % (2647)------------------------------
% 21.58/4.43 % (2653)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_2101 for (2971ds/3373Mi)
% 21.58/4.47 % (2650)Instruction limit reached!
% 21.58/4.47 % (2650)------------------------------
% 21.58/4.47 % (2650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.58/4.47 % (2650)Termination reason: Unknown
% 21.58/4.47 % (2650)Termination phase: Saturation
% 21.58/4.47
% 21.58/4.47 % (2650)Memory used [KB]: 9210
% 21.58/4.47 % (2650)Time elapsed: 0.134 s
% 21.58/4.47 % (2650)Instructions burned: 457 (million)
% 21.58/4.47 % (2650)------------------------------
% 21.58/4.47 % (2650)------------------------------
% 21.58/4.47 % (2651)Instruction limit reached!
% 21.58/4.47 % (2651)------------------------------
% 21.58/4.47 % (2651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.58/4.47 % (2651)Termination reason: Unknown
% 21.58/4.47 % (2651)Termination phase: Saturation
% 21.58/4.47
% 21.58/4.47 % (2651)Memory used [KB]: 7931
% 21.58/4.47 % (2651)Time elapsed: 0.105 s
% 21.58/4.47 % (2651)Instructions burned: 393 (million)
% 21.58/4.47 % (2651)------------------------------
% 21.58/4.47 % (2651)------------------------------
% 21.58/4.48 % (2654)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_2101 for (2971ds/474Mi)
% 21.58/4.48 % (2655)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_2101 for (2971ds/157Mi)
% 22.10/4.50 % (2649)Instruction limit reached!
% 22.10/4.50 % (2649)------------------------------
% 22.10/4.50 % (2649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.10/4.50 % (2649)Termination reason: Unknown
% 22.10/4.50 % (2649)Termination phase: Saturation
% 22.10/4.50
% 22.10/4.50 % (2649)Memory used [KB]: 8955
% 22.10/4.50 % (2649)Time elapsed: 0.177 s
% 22.10/4.50 % (2649)Instructions burned: 584 (million)
% 22.10/4.50 % (2649)------------------------------
% 22.10/4.50 % (2649)------------------------------
% 22.10/4.51 % (2656)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_2101 for (2971ds/590Mi)
% 22.10/4.52 % (2655)Instruction limit reached!
% 22.10/4.52 % (2655)------------------------------
% 22.10/4.52 % (2655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.10/4.52 % (2655)Termination reason: Unknown
% 22.10/4.52 % (2655)Termination phase: Property scanning
% 22.10/4.52
% 22.10/4.52 % (2655)Memory used [KB]: 3198
% 22.10/4.52 % (2655)Time elapsed: 0.044 s
% 22.10/4.52 % (2655)Instructions burned: 159 (million)
% 22.10/4.52 % (2655)------------------------------
% 22.10/4.52 % (2655)------------------------------
% 22.10/4.53 % (2657)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_2101 for (2970ds/104Mi)
% 22.10/4.57 % (2657)Instruction limit reached!
% 22.10/4.57 % (2657)------------------------------
% 22.10/4.57 % (2657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.10/4.57 % (2657)Termination reason: Unknown
% 22.10/4.57 % (2657)Termination phase: Preprocessing 3
% 22.10/4.57
% 22.10/4.57 % (2657)Memory used [KB]: 2942
% 22.10/4.57 % (2657)Time elapsed: 0.032 s
% 22.10/4.57 % (2657)Instructions burned: 106 (million)
% 22.10/4.57 % (2657)------------------------------
% 22.10/4.57 % (2657)------------------------------
% 22.10/4.57 % (2658)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_2101 for (2970ds/414Mi)
% 22.10/4.60 % (2639)Instruction limit reached!
% 22.10/4.60 % (2639)------------------------------
% 22.10/4.60 % (2639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.10/4.60 % (2639)Termination reason: Unknown
% 22.10/4.60 % (2639)Termination phase: Saturation
% 22.10/4.60
% 22.10/4.60 % (2639)Memory used [KB]: 10618
% 22.10/4.60 % (2639)Time elapsed: 0.523 s
% 22.10/4.60 % (2639)Instructions burned: 1763 (million)
% 22.10/4.60 % (2639)------------------------------
% 22.10/4.60 % (2639)------------------------------
% 23.02/4.61 % (2659)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_2101 for (2970ds/715Mi)
% 23.02/4.61 % (2654)Instruction limit reached!
% 23.02/4.61 % (2654)------------------------------
% 23.02/4.61 % (2654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.02/4.61 % (2654)Termination reason: Unknown
% 23.02/4.61 % (2654)Termination phase: Saturation
% 23.02/4.61
% 23.02/4.61 % (2654)Memory used [KB]: 8315
% 23.02/4.61 % (2654)Time elapsed: 0.136 s
% 23.02/4.61 % (2654)Instructions burned: 475 (million)
% 23.02/4.61 % (2654)------------------------------
% 23.02/4.61 % (2654)------------------------------
% 23.02/4.62 % (2660)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_2101 for (2969ds/961Mi)
% 23.02/4.68 % (2656)Instruction limit reached!
% 23.02/4.68 % (2656)------------------------------
% 23.02/4.68 % (2656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.02/4.68 % (2656)Termination reason: Unknown
% 23.02/4.68 % (2656)Termination phase: Saturation
% 23.02/4.68
% 23.02/4.68 % (2656)Memory used [KB]: 9594
% 23.02/4.68 % (2656)Time elapsed: 0.166 s
% 23.02/4.68 % (2656)Instructions burned: 591 (million)
% 23.02/4.68 % (2656)------------------------------
% 23.02/4.68 % (2656)------------------------------
% 23.02/4.69 % (2661)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_2101 for (2969ds/1213Mi)
% 23.02/4.69 % (2658)Instruction limit reached!
% 23.02/4.69 % (2658)------------------------------
% 23.02/4.69 % (2658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.02/4.69 % (2658)Termination reason: Unknown
% 23.02/4.69 % (2658)Termination phase: Saturation
% 23.02/4.69
% 23.02/4.69 % (2658)Memory used [KB]: 8187
% 23.02/4.69 % (2658)Time elapsed: 0.112 s
% 23.02/4.69 % (2658)Instructions burned: 416 (million)
% 23.02/4.69 % (2658)------------------------------
% 23.02/4.69 % (2658)------------------------------
% 23.02/4.70 % (2662)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_2101 for (2969ds/1979Mi)
% 23.56/4.79 % (2652)Instruction limit reached!
% 23.56/4.79 % (2652)------------------------------
% 23.56/4.79 % (2652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.56/4.79 % (2652)Termination reason: Unknown
% 23.56/4.79 % (2652)Termination phase: Saturation
% 23.56/4.79
% 23.56/4.79 % (2652)Memory used [KB]: 10618
% 23.56/4.79 % (2652)Time elapsed: 0.391 s
% 23.56/4.79 % (2652)Instructions burned: 1336 (million)
% 23.56/4.79 % (2652)------------------------------
% 23.56/4.79 % (2652)------------------------------
% 24.06/4.80 % (2663)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_2101 for (2968ds/481Mi)
% 24.06/4.82 % (2659)Instruction limit reached!
% 24.06/4.82 % (2659)------------------------------
% 24.06/4.82 % (2659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.06/4.82 % (2659)Termination reason: Unknown
% 24.06/4.82 % (2659)Termination phase: Saturation
% 24.06/4.82
% 24.06/4.82 % (2659)Memory used [KB]: 5884
% 24.06/4.82 % (2659)Time elapsed: 0.216 s
% 24.06/4.82 % (2659)Instructions burned: 715 (million)
% 24.06/4.82 % (2659)------------------------------
% 24.06/4.82 % (2659)------------------------------
% 24.06/4.83 % (2664)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_2101 for (2967ds/783Mi)
% 24.37/4.91 % (2660)Instruction limit reached!
% 24.37/4.91 % (2660)------------------------------
% 24.37/4.91 % (2660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.37/4.91 % (2660)Termination reason: Unknown
% 24.37/4.91 % (2660)Termination phase: Saturation
% 24.37/4.91
% 24.37/4.91 % (2660)Memory used [KB]: 9210
% 24.37/4.91 % (2660)Time elapsed: 0.285 s
% 24.37/4.91 % (2660)Instructions burned: 964 (million)
% 24.37/4.91 % (2660)------------------------------
% 24.37/4.91 % (2660)------------------------------
% 24.37/4.92 % (2665)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_2101 for (2967ds/432Mi)
% 24.37/4.94 % (2663)Instruction limit reached!
% 24.37/4.94 % (2663)------------------------------
% 24.37/4.94 % (2663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.37/4.94 % (2663)Termination reason: Unknown
% 24.37/4.94 % (2663)Termination phase: Saturation
% 24.37/4.94
% 24.37/4.94 % (2663)Memory used [KB]: 8315
% 24.37/4.94 % (2663)Time elapsed: 0.161 s
% 24.37/4.94 % (2663)Instructions burned: 482 (million)
% 24.37/4.94 % (2663)------------------------------
% 24.37/4.94 % (2663)------------------------------
% 24.37/4.95 % (2666)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_2101 for (2966ds/1670Mi)
% 26.58/5.05 % (2665)Instruction limit reached!
% 26.58/5.05 % (2665)------------------------------
% 26.58/5.05 % (2665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.58/5.05 % (2665)Termination reason: Unknown
% 26.58/5.05 % (2665)Termination phase: Saturation
% 26.58/5.05
% 26.58/5.05 % (2665)Memory used [KB]: 8187
% 26.58/5.05 % (2665)Time elapsed: 0.150 s
% 26.58/5.05 % (2665)Instructions burned: 434 (million)
% 26.58/5.05 % (2665)------------------------------
% 26.58/5.05 % (2665)------------------------------
% 26.58/5.06 % (2667)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_2101 for (2965ds/90Mi)
% 26.58/5.06 % (2661)Instruction limit reached!
% 26.58/5.06 % (2661)------------------------------
% 26.58/5.06 % (2661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.58/5.06 % (2661)Termination reason: Unknown
% 26.58/5.06 % (2661)Termination phase: Saturation
% 26.58/5.06
% 26.58/5.06 % (2661)Memory used [KB]: 11513
% 26.58/5.06 % (2661)Time elapsed: 0.395 s
% 26.58/5.06 % (2661)Instructions burned: 1213 (million)
% 26.58/5.06 % (2661)------------------------------
% 26.58/5.06 % (2661)------------------------------
% 26.58/5.06 % (2664)Instruction limit reached!
% 26.58/5.06 % (2664)------------------------------
% 26.58/5.06 % (2664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.58/5.06 % (2664)Termination reason: Unknown
% 26.58/5.06 % (2664)Termination phase: Saturation
% 26.58/5.06
% 26.58/5.06 % (2664)Memory used [KB]: 9594
% 26.58/5.06 % (2664)Time elapsed: 0.256 s
% 26.58/5.06 % (2664)Instructions burned: 783 (million)
% 26.58/5.06 % (2664)------------------------------
% 26.58/5.06 % (2664)------------------------------
% 26.58/5.07 % (2668)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_2101 for (2965ds/346Mi)
% 26.58/5.07 % (2669)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_2101 for (2965ds/401Mi)
% 26.58/5.08 % (2667)Instruction limit reached!
% 26.58/5.08 % (2667)------------------------------
% 26.58/5.08 % (2667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.58/5.08 % (2667)Termination reason: Unknown
% 26.58/5.08 % (2667)Termination phase: shuffling
% 26.58/5.08
% 26.58/5.08 % (2667)Memory used [KB]: 2558
% 26.58/5.08 % (2667)Time elapsed: 0.029 s
% 26.58/5.08 % (2667)Instructions burned: 90 (million)
% 26.58/5.08 % (2667)------------------------------
% 26.58/5.08 % (2667)------------------------------
% 26.58/5.09 % (2670)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_2101 for (2965ds/6454Mi)
% 27.17/5.16 % (2668)Instruction limit reached!
% 27.17/5.16 % (2668)------------------------------
% 27.17/5.16 % (2668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.17/5.16 % (2668)Termination reason: Unknown
% 27.17/5.16 % (2668)Termination phase: Saturation
% 27.17/5.16
% 27.17/5.16 % (2668)Memory used [KB]: 7931
% 27.17/5.16 % (2668)Time elapsed: 0.095 s
% 27.17/5.16 % (2668)Instructions burned: 348 (million)
% 27.17/5.16 % (2668)------------------------------
% 27.17/5.16 % (2668)------------------------------
% 27.17/5.17 % (2671)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_2101 for (2964ds/283Mi)
% 27.17/5.18 % (2669)Instruction limit reached!
% 27.17/5.18 % (2669)------------------------------
% 27.17/5.18 % (2669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.17/5.18 % (2669)Termination reason: Unknown
% 27.17/5.18 % (2669)Termination phase: Saturation
% 27.17/5.18
% 27.17/5.18 % (2669)Memory used [KB]: 8699
% 27.17/5.18 % (2669)Time elapsed: 0.106 s
% 27.17/5.18 % (2669)Instructions burned: 402 (million)
% 27.17/5.18 % (2669)------------------------------
% 27.17/5.18 % (2669)------------------------------
% 27.17/5.19 % (2672)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_2101 for (2964ds/865Mi)
% 27.66/5.25 % (2671)Instruction limit reached!
% 27.66/5.25 % (2671)------------------------------
% 27.66/5.25 % (2671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.66/5.25 % (2671)Termination reason: Unknown
% 27.66/5.25 % (2671)Termination phase: Saturation
% 27.66/5.25
% 27.66/5.25 % (2671)Memory used [KB]: 8315
% 27.66/5.25 % (2671)Time elapsed: 0.080 s
% 27.66/5.25 % (2671)Instructions burned: 286 (million)
% 27.66/5.25 % (2671)------------------------------
% 27.66/5.25 % (2671)------------------------------
% 27.66/5.26 % (2673)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_2101 for (2963ds/4528Mi)
% 27.66/5.30 % (2662)Instruction limit reached!
% 27.66/5.30 % (2662)------------------------------
% 27.66/5.30 % (2662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.66/5.30 % (2662)Termination reason: Unknown
% 27.66/5.30 % (2662)Termination phase: Saturation
% 27.66/5.30
% 27.66/5.30 % (2662)Memory used [KB]: 10362
% 27.66/5.30 % (2662)Time elapsed: 0.622 s
% 27.66/5.30 % (2662)Instructions burned: 1982 (million)
% 27.66/5.30 % (2662)------------------------------
% 27.66/5.30 % (2662)------------------------------
% 28.17/5.30 % (2673)Refutation not found, incomplete strategy
% 28.17/5.30 % (2673)------------------------------
% 28.17/5.30 % (2673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.17/5.30 % (2673)Termination reason: Refutation not found, incomplete strategy
% 28.17/5.30
% 28.17/5.30
% 28.17/5.30 % (2673)Memory used [KB]: 2814
% 28.17/5.30 % (2673)Time elapsed: 0.039 s
% 28.17/5.30 % (2673)Instructions burned: 123 (million)
% 28.17/5.30 % (2673)------------------------------
% 28.17/5.30 % (2673)------------------------------
% 28.17/5.31 % (2674)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_2101 for (2963ds/1001Mi)
% 28.17/5.31 % (2675)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_2101 for (2963ds/102Mi)
% 28.17/5.34 % (2675)Instruction limit reached!
% 28.17/5.34 % (2675)------------------------------
% 28.17/5.34 % (2675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.17/5.34 % (2675)Termination reason: Unknown
% 28.17/5.34 % (2675)Termination phase: Property scanning
% 28.17/5.34
% 28.17/5.34 % (2675)Memory used [KB]: 3070
% 28.17/5.34 % (2675)Time elapsed: 0.028 s
% 28.17/5.34 % (2675)Instructions burned: 102 (million)
% 28.17/5.34 % (2675)------------------------------
% 28.17/5.34 % (2675)------------------------------
% 28.17/5.35 % (2676)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_2101 for (2962ds/952Mi)
% 28.56/5.44 % (2666)Instruction limit reached!
% 28.56/5.44 % (2666)------------------------------
% 28.56/5.44 % (2666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.56/5.44 % (2666)Termination reason: Unknown
% 28.56/5.44 % (2666)Termination phase: Saturation
% 28.56/5.44
% 28.56/5.44 % (2666)Memory used [KB]: 12409
% 28.56/5.44 % (2666)Time elapsed: 0.494 s
% 28.56/5.44 % (2666)Instructions burned: 1670 (million)
% 28.56/5.44 % (2666)------------------------------
% 28.56/5.44 % (2666)------------------------------
% 28.56/5.45 % (2653)Instruction limit reached!
% 28.56/5.45 % (2653)------------------------------
% 28.56/5.45 % (2653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.56/5.45 % (2653)Termination reason: Unknown
% 28.56/5.45 % (2653)Termination phase: Saturation
% 28.56/5.45
% 28.56/5.45 % (2653)Memory used [KB]: 14200
% 28.56/5.45 % (2653)Time elapsed: 1.025 s
% 28.56/5.45 % (2653)Instructions burned: 3374 (million)
% 28.56/5.45 % (2653)------------------------------
% 28.56/5.45 % (2653)------------------------------
% 28.56/5.45 % (2677)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_2101 for (2961ds/578Mi)
% 28.56/5.45 % (2672)Instruction limit reached!
% 28.56/5.45 % (2672)------------------------------
% 28.56/5.45 % (2672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.56/5.45 % (2672)Termination reason: Unknown
% 28.56/5.45 % (2672)Termination phase: Saturation
% 28.56/5.45
% 28.56/5.45 % (2672)Memory used [KB]: 12025
% 28.56/5.45 % (2672)Time elapsed: 0.268 s
% 28.56/5.45 % (2672)Instructions burned: 867 (million)
% 28.56/5.45 % (2672)------------------------------
% 28.56/5.45 % (2672)------------------------------
% 28.56/5.46 % (2678)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_2101 for (2961ds/643Mi)
% 28.56/5.47 % (2679)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_2101 for (2961ds/865Mi)
% 29.16/5.60 % (2674)Instruction limit reached!
% 29.16/5.60 % (2674)------------------------------
% 29.16/5.60 % (2674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.16/5.60 % (2674)Termination reason: Unknown
% 29.16/5.60 % (2674)Termination phase: Saturation
% 29.16/5.60
% 29.16/5.60 % (2674)Memory used [KB]: 13176
% 29.16/5.60 % (2674)Time elapsed: 0.297 s
% 29.16/5.60 % (2674)Instructions burned: 1002 (million)
% 29.16/5.60 % (2674)------------------------------
% 29.16/5.60 % (2674)------------------------------
% 29.16/5.61 % (2680)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_2101 for (2960ds/1174Mi)
% 29.16/5.62 % (2677)Instruction limit reached!
% 29.16/5.62 % (2677)------------------------------
% 29.16/5.62 % (2677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.16/5.62 % (2677)Termination reason: Unknown
% 29.16/5.62 % (2677)Termination phase: Saturation
% 29.16/5.62
% 29.16/5.62 % (2677)Memory used [KB]: 8443
% 29.16/5.62 % (2677)Time elapsed: 0.166 s
% 29.16/5.62 % (2677)Instructions burned: 581 (million)
% 29.16/5.62 % (2677)------------------------------
% 29.16/5.62 % (2677)------------------------------
% 29.16/5.63 % (2681)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_2101 for (2959ds/644Mi)
% 29.16/5.63 % (2678)Instruction limit reached!
% 29.16/5.63 % (2678)------------------------------
% 29.16/5.63 % (2678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.16/5.63 % (2678)Termination reason: Unknown
% 29.16/5.63 % (2678)Termination phase: Saturation
% 29.16/5.63
% 29.16/5.63 % (2678)Memory used [KB]: 11257
% 29.16/5.63 % (2678)Time elapsed: 0.174 s
% 29.16/5.63 % (2678)Instructions burned: 643 (million)
% 29.16/5.63 % (2678)------------------------------
% 29.16/5.63 % (2678)------------------------------
% 29.16/5.64 % (2676)Instruction limit reached!
% 29.16/5.64 % (2676)------------------------------
% 29.16/5.64 % (2676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.16/5.64 % (2676)Termination reason: Unknown
% 29.16/5.64 % (2676)Termination phase: Saturation
% 29.16/5.64
% 29.16/5.64 % (2676)Memory used [KB]: 11001
% 29.16/5.64 % (2676)Time elapsed: 0.292 s
% 29.16/5.64 % (2676)Instructions burned: 954 (million)
% 29.16/5.64 % (2676)------------------------------
% 29.16/5.64 % (2676)------------------------------
% 29.16/5.64 % (2682)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_2101 for (2959ds/1201Mi)
% 29.16/5.65 % (2683)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_2101 for (2959ds/1046Mi)
% 30.22/5.77 % (2626)Instruction limit reached!
% 30.22/5.77 % (2626)------------------------------
% 30.22/5.77 % (2626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.22/5.77 % (2626)Termination reason: Unknown
% 30.22/5.77 % (2626)Termination phase: Saturation
% 30.22/5.77
% 30.22/5.77 % (2626)Memory used [KB]: 15863
% 30.22/5.77 % (2626)Time elapsed: 2.434 s
% 30.22/5.77 % (2626)Instructions burned: 8253 (million)
% 30.22/5.77 % (2626)------------------------------
% 30.22/5.77 % (2626)------------------------------
% 30.22/5.78 % (2684)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_2101 for (2958ds/222Mi)
% 30.32/5.80 % (2679)Instruction limit reached!
% 30.32/5.80 % (2679)------------------------------
% 30.32/5.80 % (2679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.32/5.80 % (2679)Termination reason: Unknown
% 30.32/5.80 % (2679)Termination phase: Saturation
% 30.32/5.80
% 30.32/5.80 % (2679)Memory used [KB]: 11385
% 30.32/5.80 % (2679)Time elapsed: 0.332 s
% 30.32/5.80 % (2679)Instructions burned: 866 (million)
% 30.32/5.80 % (2679)------------------------------
% 30.32/5.80 % (2679)------------------------------
% 30.32/5.81 % (2685)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_2101 for (2958ds/68Mi)
% 30.32/5.81 % (2681)Instruction limit reached!
% 30.32/5.81 % (2681)------------------------------
% 30.32/5.81 % (2681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.32/5.81 % (2681)Termination reason: Unknown
% 30.32/5.81 % (2681)Termination phase: Saturation
% 30.32/5.81
% 30.32/5.81 % (2681)Memory used [KB]: 11641
% 30.32/5.81 % (2681)Time elapsed: 0.191 s
% 30.32/5.81 % (2681)Instructions burned: 646 (million)
% 30.32/5.81 % (2681)------------------------------
% 30.32/5.81 % (2681)------------------------------
% 30.32/5.82 % (2686)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_2101 for (2957ds/454Mi)
% 30.32/5.84 % (2685)Instruction limit reached!
% 30.32/5.84 % (2685)------------------------------
% 30.32/5.84 % (2685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.32/5.84 % (2685)Termination reason: Unknown
% 30.32/5.84 % (2685)Termination phase: Property scanning
% 30.32/5.84
% 30.32/5.84 % (2685)Memory used [KB]: 2430
% 30.32/5.84 % (2685)Time elapsed: 0.024 s
% 30.32/5.84 % (2685)Instructions burned: 70 (million)
% 30.32/5.84 % (2685)------------------------------
% 30.32/5.84 % (2685)------------------------------
% 30.32/5.84 % (2684)Instruction limit reached!
% 30.32/5.84 % (2684)------------------------------
% 30.32/5.84 % (2684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.32/5.84 % (2684)Termination reason: Unknown
% 30.32/5.84 % (2684)Termination phase: Property scanning
% 30.32/5.84
% 30.32/5.84 % (2684)Memory used [KB]: 3198
% 30.32/5.84 % (2684)Time elapsed: 0.059 s
% 30.32/5.84 % (2684)Instructions burned: 223 (million)
% 30.32/5.84 % (2684)------------------------------
% 30.32/5.84 % (2684)------------------------------
% 30.32/5.85 % (2687)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_2101 for (2957ds/360Mi)
% 30.32/5.85 % (2688)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_2101 for (2957ds/157Mi)
% 30.32/5.89 % (2688)Instruction limit reached!
% 30.32/5.89 % (2688)------------------------------
% 30.32/5.89 % (2688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.32/5.89 % (2688)Termination reason: Unknown
% 30.32/5.89 % (2688)Termination phase: Property scanning
% 30.32/5.89
% 30.32/5.89 % (2688)Memory used [KB]: 3198
% 30.32/5.89 % (2688)Time elapsed: 0.043 s
% 30.32/5.89 % (2688)Instructions burned: 159 (million)
% 30.32/5.89 % (2688)------------------------------
% 30.32/5.89 % (2688)------------------------------
% 31.02/5.90 % (2689)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_2101 for (2957ds/5061Mi)
% 31.02/5.95 % (2687)Instruction limit reached!
% 31.02/5.95 % (2687)------------------------------
% 31.02/5.95 % (2687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.02/5.95 % (2687)Termination reason: Unknown
% 31.02/5.95 % (2687)Termination phase: Saturation
% 31.02/5.95
% 31.02/5.95 % (2687)Memory used [KB]: 8571
% 31.02/5.95 % (2687)Time elapsed: 0.102 s
% 31.02/5.95 % (2687)Instructions burned: 361 (million)
% 31.02/5.95 % (2687)------------------------------
% 31.02/5.95 % (2687)------------------------------
% 31.02/5.95 % (2683)Instruction limit reached!
% 31.02/5.95 % (2683)------------------------------
% 31.02/5.95 % (2683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.02/5.95 % (2683)Termination reason: Unknown
% 31.02/5.95 % (2683)Termination phase: Saturation
% 31.02/5.95
% 31.02/5.95 % (2683)Memory used [KB]: 10106
% 31.02/5.95 % (2683)Time elapsed: 0.304 s
% 31.02/5.95 % (2683)Instructions burned: 1048 (million)
% 31.02/5.95 % (2683)------------------------------
% 31.02/5.95 % (2683)------------------------------
% 31.02/5.95 % (2686)Instruction limit reached!
% 31.02/5.95 % (2686)------------------------------
% 31.02/5.95 % (2686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.02/5.95 % (2686)Termination reason: Unknown
% 31.02/5.95 % (2686)Termination phase: Saturation
% 31.02/5.95
% 31.02/5.95 % (2686)Memory used [KB]: 13432
% 31.02/5.95 % (2686)Time elapsed: 0.127 s
% 31.02/5.95 % (2686)Instructions burned: 456 (million)
% 31.02/5.95 % (2686)------------------------------
% 31.02/5.95 % (2686)------------------------------
% 31.02/5.96 % (2690)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_2101 for (2956ds/2401Mi)
% 31.02/5.96 % (2691)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_2101 for (2956ds/5798Mi)
% 31.02/5.96 % (2692)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_2101 for (2956ds/346Mi)
% 31.02/5.96 % (2680)Instruction limit reached!
% 31.02/5.96 % (2680)------------------------------
% 31.02/5.96 % (2680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.02/5.96 % (2680)Termination reason: Unknown
% 31.02/5.96 % (2680)Termination phase: Saturation
% 31.02/5.96
% 31.02/5.96 % (2680)Memory used [KB]: 12665
% 31.02/5.96 % (2680)Time elapsed: 0.350 s
% 31.02/5.96 % (2680)Instructions burned: 1177 (million)
% 31.02/5.96 % (2680)------------------------------
% 31.02/5.96 % (2680)------------------------------
% 31.02/5.97 % (2682)Instruction limit reached!
% 31.02/5.97 % (2682)------------------------------
% 31.02/5.97 % (2682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.02/5.97 % (2682)Termination reason: Unknown
% 31.02/5.97 % (2682)Termination phase: Saturation
% 31.02/5.97
% 31.02/5.97 % (2682)Memory used [KB]: 10362
% 31.02/5.97 % (2682)Time elapsed: 0.327 s
% 31.02/5.97 % (2682)Instructions burned: 1204 (million)
% 31.02/5.97 % (2682)------------------------------
% 31.02/5.97 % (2682)------------------------------
% 31.02/5.97 % (2693)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_2101 for (2956ds/1321Mi)
% 31.02/5.98 % (2694)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_2101 for (2956ds/1312Mi)
% 33.53/6.05 % (2692)Instruction limit reached!
% 33.53/6.05 % (2692)------------------------------
% 33.53/6.05 % (2692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.53/6.05 % (2692)Termination reason: Unknown
% 33.53/6.05 % (2692)Termination phase: Saturation
% 33.53/6.05
% 33.53/6.05 % (2692)Memory used [KB]: 7931
% 33.53/6.05 % (2692)Time elapsed: 0.094 s
% 33.53/6.05 % (2692)Instructions burned: 348 (million)
% 33.53/6.05 % (2692)------------------------------
% 33.53/6.05 % (2692)------------------------------
% 33.53/6.06 % (2695)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_2101 for (2955ds/672Mi)
% 33.53/6.11 % (2693)Refutation not found, incomplete strategy
% 33.53/6.11 % (2693)------------------------------
% 33.53/6.11 % (2693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.53/6.11 % (2693)Termination reason: Refutation not found, incomplete strategy
% 33.53/6.11
% 33.53/6.11
% 33.53/6.11 % (2693)Memory used [KB]: 6140
% 33.53/6.11 % (2693)Time elapsed: 0.137 s
% 33.53/6.11 % (2693)Instructions burned: 480 (million)
% 33.53/6.11 % (2693)------------------------------
% 33.53/6.11 % (2693)------------------------------
% 34.19/6.12 % (2696)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_2101 for (2954ds/1897Mi)
% 34.61/6.27 % (2695)Instruction limit reached!
% 34.61/6.27 % (2695)------------------------------
% 34.61/6.27 % (2695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.61/6.27 % (2695)Termination reason: Unknown
% 34.61/6.27 % (2695)Termination phase: Saturation
% 34.61/6.27
% 34.61/6.27 % (2695)Memory used [KB]: 10234
% 34.61/6.27 % (2695)Time elapsed: 0.209 s
% 34.61/6.27 % (2695)Instructions burned: 674 (million)
% 34.61/6.27 % (2695)------------------------------
% 34.61/6.27 % (2695)------------------------------
% 34.61/6.28 % (2697)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_2101 for (2953ds/1202Mi)
% 35.34/6.36 % (2694)Instruction limit reached!
% 35.34/6.36 % (2694)------------------------------
% 35.34/6.36 % (2694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.34/6.36 % (2694)Termination reason: Unknown
% 35.34/6.36 % (2694)Termination phase: Saturation
% 35.34/6.36
% 35.34/6.36 % (2694)Memory used [KB]: 10618
% 35.34/6.36 % (2694)Time elapsed: 0.385 s
% 35.34/6.36 % (2694)Instructions burned: 1313 (million)
% 35.34/6.36 % (2694)------------------------------
% 35.34/6.36 % (2694)------------------------------
% 35.34/6.37 % (2698)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_2101 for (2952ds/1493Mi)
% 35.82/6.43 % (2698)Refutation not found, incomplete strategy
% 35.82/6.43 % (2698)------------------------------
% 35.82/6.43 % (2698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.82/6.43 % (2698)Termination reason: Refutation not found, incomplete strategy
% 35.82/6.43
% 35.82/6.43
% 35.82/6.43 % (2698)Memory used [KB]: 7931
% 35.82/6.43 % (2698)Time elapsed: 0.061 s
% 35.82/6.43 % (2698)Instructions burned: 228 (million)
% 35.82/6.43 % (2698)------------------------------
% 35.82/6.43 % (2698)------------------------------
% 35.82/6.44 % (2699)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_2101 for (2951ds/7679Mi)
% 36.70/6.65 % (2697)Instruction limit reached!
% 36.70/6.65 % (2697)------------------------------
% 36.70/6.65 % (2697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.70/6.65 % (2697)Termination reason: Unknown
% 36.70/6.65 % (2697)Termination phase: Saturation
% 36.70/6.65
% 36.70/6.65 % (2697)Memory used [KB]: 7291
% 36.70/6.65 % (2697)Time elapsed: 0.368 s
% 36.70/6.65 % (2697)Instructions burned: 1204 (million)
% 36.70/6.65 % (2697)------------------------------
% 36.70/6.65 % (2697)------------------------------
% 36.70/6.66 % (2700)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_2101 for (2949ds/340Mi)
% 36.70/6.67 % (2696)Instruction limit reached!
% 36.70/6.67 % (2696)------------------------------
% 36.70/6.67 % (2696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.70/6.67 % (2696)Termination reason: Unknown
% 36.70/6.67 % (2696)Termination phase: Saturation
% 36.70/6.67
% 36.70/6.67 % (2696)Memory used [KB]: 10874
% 36.70/6.67 % (2696)Time elapsed: 0.552 s
% 36.70/6.67 % (2696)Instructions burned: 1899 (million)
% 36.70/6.67 % (2696)------------------------------
% 36.70/6.67 % (2696)------------------------------
% 36.70/6.68 % (2701)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_2101 for (2949ds/3672Mi)
% 38.04/6.73 % (2690)Instruction limit reached!
% 38.04/6.73 % (2690)------------------------------
% 38.04/6.73 % (2690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.04/6.73 % (2690)Termination reason: Unknown
% 38.04/6.73 % (2690)Termination phase: Saturation
% 38.04/6.73
% 38.04/6.73 % (2690)Memory used [KB]: 9210
% 38.04/6.73 % (2690)Time elapsed: 0.772 s
% 38.04/6.73 % (2690)Instructions burned: 2401 (million)
% 38.04/6.73 % (2690)------------------------------
% 38.04/6.73 % (2690)------------------------------
% 38.04/6.74 % (2702)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_2101 for (2948ds/1535Mi)
% 38.04/6.76 % (2700)Instruction limit reached!
% 38.04/6.76 % (2700)------------------------------
% 38.04/6.76 % (2700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.04/6.76 % (2700)Termination reason: Unknown
% 38.04/6.76 % (2700)Termination phase: Saturation
% 38.04/6.76
% 38.04/6.76 % (2700)Memory used [KB]: 9210
% 38.04/6.76 % (2700)Time elapsed: 0.098 s
% 38.04/6.76 % (2700)Instructions burned: 341 (million)
% 38.04/6.76 % (2700)------------------------------
% 38.04/6.76 % (2700)------------------------------
% 38.04/6.77 % (2703)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_2101 for (2948ds/4637Mi)
% 40.61/7.09 % (2670)Instruction limit reached!
% 40.61/7.09 % (2670)------------------------------
% 40.61/7.09 % (2670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.61/7.09 % (2670)Termination reason: Unknown
% 40.61/7.09 % (2670)Termination phase: Saturation
% 40.61/7.09
% 40.61/7.09 % (2670)Memory used [KB]: 15479
% 40.61/7.09 % (2670)Time elapsed: 1.994 s
% 40.61/7.09 % (2670)Instructions burned: 6456 (million)
% 40.61/7.09 % (2670)------------------------------
% 40.61/7.09 % (2670)------------------------------
% 40.61/7.10 % (2704)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_2101 for (2945ds/3174Mi)
% 41.33/7.19 % (2702)Instruction limit reached!
% 41.33/7.19 % (2702)------------------------------
% 41.33/7.19 % (2702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.33/7.19 % (2702)Termination reason: Unknown
% 41.33/7.19 % (2702)Termination phase: Saturation
% 41.33/7.19
% 41.33/7.19 % (2702)Memory used [KB]: 13816
% 41.33/7.19 % (2702)Time elapsed: 0.450 s
% 41.33/7.19 % (2702)Instructions burned: 1536 (million)
% 41.33/7.19 % (2702)------------------------------
% 41.33/7.19 % (2702)------------------------------
% 41.33/7.20 % (2705)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_2101 for (2944ds/307Mi)
% 41.75/7.28 % (2705)Instruction limit reached!
% 41.75/7.28 % (2705)------------------------------
% 41.75/7.28 % (2705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.75/7.28 % (2705)Termination reason: Unknown
% 41.75/7.28 % (2705)Termination phase: Saturation
% 41.75/7.28
% 41.75/7.28 % (2705)Memory used [KB]: 7803
% 41.75/7.28 % (2705)Time elapsed: 0.080 s
% 41.75/7.28 % (2705)Instructions burned: 308 (million)
% 41.75/7.28 % (2705)------------------------------
% 41.75/7.28 % (2705)------------------------------
% 41.75/7.29 % (2706)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_2101 for (2943ds/3619Mi)
% 42.34/7.38 % (2706)Refutation not found, incomplete strategy
% 42.34/7.38 % (2706)------------------------------
% 42.34/7.38 % (2706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.34/7.38 % (2706)Termination reason: Refutation not found, incomplete strategy
% 42.34/7.38
% 42.34/7.38
% 42.34/7.38 % (2706)Memory used [KB]: 9210
% 42.34/7.38 % (2706)Time elapsed: 0.097 s
% 42.34/7.38 % (2706)Instructions burned: 327 (million)
% 42.34/7.38 % (2706)------------------------------
% 42.34/7.38 % (2706)------------------------------
% 42.34/7.39 % (2707)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_2101 for (2942ds/2325Mi)
% 42.95/7.45 % (2689)Instruction limit reached!
% 42.95/7.45 % (2689)------------------------------
% 42.95/7.45 % (2689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.95/7.45 % (2689)Termination reason: Unknown
% 42.95/7.45 % (2689)Termination phase: Saturation
% 42.95/7.45
% 42.95/7.45 % (2689)Memory used [KB]: 15479
% 42.95/7.45 % (2689)Time elapsed: 1.543 s
% 42.95/7.45 % (2689)Instructions burned: 5062 (million)
% 42.95/7.45 % (2689)------------------------------
% 42.95/7.45 % (2689)------------------------------
% 42.95/7.46 % (2708)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_2101 for (2941ds/2341Mi)
% 44.21/7.70 % (2691)Instruction limit reached!
% 44.21/7.70 % (2691)------------------------------
% 44.21/7.70 % (2691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.21/7.70 % (2691)Termination reason: Unknown
% 44.21/7.70 % (2691)Termination phase: Saturation
% 44.21/7.70
% 44.21/7.70 % (2691)Memory used [KB]: 15095
% 44.21/7.70 % (2691)Time elapsed: 1.743 s
% 44.21/7.70 % (2691)Instructions burned: 5799 (million)
% 44.21/7.70 % (2691)------------------------------
% 44.21/7.70 % (2691)------------------------------
% 44.21/7.71 % (2709)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_2101 for (2938ds/7257Mi)
% 44.53/7.80 % (2701)Instruction limit reached!
% 44.53/7.80 % (2701)------------------------------
% 44.53/7.80 % (2701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.53/7.80 % (2701)Termination reason: Unknown
% 44.53/7.80 % (2701)Termination phase: Saturation
% 44.53/7.80
% 44.53/7.80 % (2701)Memory used [KB]: 12153
% 44.53/7.80 % (2701)Time elapsed: 1.121 s
% 44.53/7.80 % (2701)Instructions burned: 3672 (million)
% 44.53/7.80 % (2701)------------------------------
% 44.53/7.80 % (2701)------------------------------
% 44.53/7.81 % (2710)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_2101 for (2937ds/3710Mi)
% 44.75/7.92 % (2704)First to succeed.
% 44.75/7.93 % (2704)Refutation found. Thanks to Tanya!
% 44.75/7.93 % SZS status Theorem for DTF2THF_2101
% 44.75/7.93 % SZS output start Proof for DTF2THF_2101
% 44.75/7.93 thf(type_def_5, type, set_node: $tType).
% 44.75/7.93 thf(type_def_7, type, set_val: $tType).
% 44.75/7.93 thf(type_def_8, type, g: $tType).
% 44.75/7.93 thf(type_def_9, type, list_node: $tType).
% 44.75/7.93 thf(type_def_10, type, node: $tType).
% 44.75/7.93 thf(type_def_11, type, list_P561207620_edgeD: $tType).
% 44.75/7.93 thf(type_def_12, type, list_P738500740D_node: $tType).
% 44.75/7.93 thf(type_def_13, type, list_val: $tType).
% 44.75/7.93 thf(type_def_14, type, list_l1129649930D_node: $tType).
% 44.75/7.93 thf(type_def_15, type, list_list_node: $tType).
% 44.75/7.93 thf(type_def_16, type, produc1453890942D_node: $tType).
% 44.75/7.93 thf(type_def_17, type, val: $tType).
% 44.75/7.93 thf(type_def_18, type, set_Pr1040144478D_node: $tType).
% 44.75/7.93 thf(type_def_19, type, produc1432036078de_val: $tType).
% 44.75/7.93 thf(type_def_20, type, option_list_val: $tType).
% 44.75/7.93 thf(func_def_0, type, list_l1129649930D_node: $tType).
% 44.75/7.93 thf(func_def_1, type, list_P738500740D_node: $tType).
% 44.75/7.93 thf(func_def_2, type, set_Pr1040144478D_node: $tType).
% 44.75/7.93 thf(func_def_3, type, produc1453890942D_node: $tType).
% 44.75/7.93 thf(func_def_4, type, list_P561207620_edgeD: $tType).
% 44.75/7.93 thf(func_def_5, type, option_list_val: $tType).
% 44.75/7.93 thf(func_def_6, type, produc1432036078de_val: $tType).
% 44.75/7.93 thf(func_def_7, type, list_list_node: $tType).
% 44.75/7.93 thf(func_def_8, type, list_node: $tType).
% 44.75/7.93 thf(func_def_9, type, list_val: $tType).
% 44.75/7.93 thf(func_def_10, type, set_node: $tType).
% 44.75/7.93 thf(func_def_11, type, set_val: $tType).
% 44.75/7.93 thf(func_def_12, type, node: $tType).
% 44.75/7.93 thf(func_def_13, type, val: $tType).
% 44.75/7.93 thf(func_def_14, type, g: $tType).
% 44.75/7.93 thf(func_def_15, type, finite_finite_node: set_node > $o).
% 44.75/7.93 thf(func_def_16, type, finite_finite_val: set_val > $o).
% 44.75/7.93 thf(func_def_17, type, graph_1994935542_edgeD: (g > list_node) > (g > $o) > (g > node > list_P561207620_edgeD) > (g > node) > g > list_node > $o).
% 44.75/7.93 thf(func_def_18, type, graph_1670286392_edgeD: (g > list_node) > (g > $o) > (g > node > list_P561207620_edgeD) > (g > node) > g > node > node > $o).
% 44.75/7.93 thf(func_def_19, type, graph_436675702_edgeD: (g > list_node) > (g > $o) > (g > node > list_P561207620_edgeD) > (g > node) > g > node > node > $o).
% 44.75/7.93 thf(func_def_20, type, graph_1947481694_edgeD: (g > node > list_P561207620_edgeD) > g > node > list_P738500740D_node).
% 44.75/7.93 thf(func_def_21, type, graph_1012773594_edgeD: (g > list_node) > (g > $o) > (g > node > list_P561207620_edgeD) > g > node > list_node > node > $o).
% 44.75/7.93 thf(func_def_22, type, graph_272749361_edgeD: (g > node > list_P561207620_edgeD) > g > node > list_node).
% 44.75/7.93 thf(func_def_23, type, append2096883353D_node: list_P738500740D_node > list_P738500740D_node > list_P738500740D_node).
% 44.75/7.93 thf(func_def_24, type, append_node: list_node > list_node > list_node).
% 44.75/7.93 thf(func_def_25, type, append_val: list_val > list_val > list_val).
% 44.75/7.93 thf(func_def_26, type, distin1098566007D_node: list_P738500740D_node > $o).
% 44.75/7.93 thf(func_def_27, type, distinct_node: list_node > $o).
% 44.75/7.93 thf(func_def_28, type, distinct_val: list_val > $o).
% 44.75/7.93 thf(func_def_29, type, cons_l1288865338D_node: list_P738500740D_node > list_l1129649930D_node > list_l1129649930D_node).
% 44.75/7.93 thf(func_def_30, type, cons_list_node: list_node > list_list_node > list_list_node).
% 44.75/7.93 thf(func_def_31, type, cons_P1018517044D_node: produc1453890942D_node > list_P738500740D_node > list_P738500740D_node).
% 44.75/7.93 thf(func_def_32, type, cons_node: node > list_node > list_node).
% 44.75/7.93 thf(func_def_33, type, cons_val: val > list_val > list_val).
% 44.75/7.93 thf(func_def_34, type, nil_li1626782346D_node: list_l1129649930D_node).
% 44.75/7.93 thf(func_def_35, type, nil_list_node: list_list_node).
% 44.75/7.93 thf(func_def_36, type, nil_Pr1769730692D_node: list_P738500740D_node).
% 44.75/7.93 thf(func_def_37, type, nil_node: list_node).
% 44.75/7.93 thf(func_def_38, type, nil_val: list_val).
% 44.75/7.93 thf(func_def_39, type, hd_Pro1395892457D_node: list_P738500740D_node > produc1453890942D_node).
% 44.75/7.93 thf(func_def_40, type, hd_node: list_node > node).
% 44.75/7.93 thf(func_def_41, type, hd_val: list_val > val).
% 44.75/7.93 thf(func_def_42, type, set_Pr1238794387D_node: list_P738500740D_node > set_Pr1040144478D_node).
% 44.75/7.93 thf(func_def_43, type, set_node2: list_node > set_node).
% 44.75/7.93 thf(func_def_44, type, set_val2: list_val > set_val).
% 44.75/7.93 thf(func_def_45, type, tl_Pro1633633005D_node: list_P738500740D_node > list_P738500740D_node).
% 44.75/7.93 thf(func_def_46, type, tl_node: list_node > list_node).
% 44.75/7.93 thf(func_def_47, type, tl_val: list_val > list_val).
% 44.75/7.93 thf(func_def_48, type, graph_589078910_edgeD: (g > list_node) > (g > $o) > (g > node > list_P561207620_edgeD) > (g > node) > g > $o).
% 44.75/7.93 thf(func_def_49, type, sSA_CF139593942de_val: (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > node > set_val).
% 44.75/7.93 thf(func_def_50, type, sSA_CF1156973626eD_val: (g > list_node) > (g > $o) > (g > node > list_P561207620_edgeD) > (g > node) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > node > val > $o).
% 44.75/7.93 thf(func_def_51, type, sSA_CF370335846de_val: (g > produc1432036078de_val > option_list_val) > g > node > set_val).
% 44.75/7.93 thf(func_def_52, type, sSA_CF848637139eD_val: (g > list_node) > (g > node > list_P561207620_edgeD) > (g > produc1432036078de_val > option_list_val) > g > node > set_val).
% 44.75/7.93 thf(func_def_53, type, sSA_CF551432799de_val: (g > list_node) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > val > node).
% 44.75/7.93 thf(func_def_54, type, sSA_CF1252180629de_val: (g > list_node) > (g > node > set_val) > (g > produc1432036078de_val > option_list_val) > g > val > val > $o).
% 44.75/7.93 thf(func_def_55, type, sSA_CF1558836456eD_val: (g > list_node) > (g > $o) > (g > node > list_P561207620_edgeD) > (g > node) > (g > node > set_val) > g > node > val > $o).
% 44.75/7.93 thf(func_def_56, type, collect_node: (node > $o) > set_node).
% 44.75/7.93 thf(func_def_57, type, collect_val: (val > $o) > set_val).
% 44.75/7.93 thf(func_def_58, type, suffix1143830554D_node: list_P738500740D_node > list_P738500740D_node > $o).
% 44.75/7.93 thf(func_def_59, type, suffix_node: list_node > list_node > $o).
% 44.75/7.93 thf(func_def_60, type, member1797643303D_node: produc1453890942D_node > set_Pr1040144478D_node > $o).
% 44.75/7.93 thf(func_def_61, type, member_node: node > set_node > $o).
% 44.75/7.93 thf(func_def_62, type, member_val: val > set_val > $o).
% 44.75/7.93 thf(func_def_63, type, entry: g > node).
% 44.75/7.93 thf(func_def_64, type, alpha_n: g > list_node).
% 44.75/7.93 thf(func_def_65, type, phi_r: val).
% 44.75/7.93 thf(func_def_66, type, defs: g > node > set_val).
% 44.75/7.93 thf(func_def_67, type, g2: g).
% 44.75/7.93 thf(func_def_68, type, inEdges: g > node > list_P561207620_edgeD).
% 44.75/7.93 thf(func_def_69, type, invar: g > $o).
% 44.75/7.93 thf(func_def_70, type, m: node).
% 44.75/7.93 thf(func_def_71, type, ms: list_node).
% 44.75/7.93 thf(func_def_72, type, n: node).
% 44.75/7.93 thf(func_def_73, type, ns: list_node).
% 44.75/7.93 thf(func_def_74, type, phis: g > produc1432036078de_val > option_list_val).
% 44.75/7.93 thf(func_def_75, type, pred_phi_r: node).
% 44.75/7.93 thf(func_def_76, type, r: val).
% 44.75/7.93 thf(func_def_77, type, rs: list_node).
% 44.75/7.93 thf(func_def_78, type, rs2: list_node).
% 44.75/7.93 thf(func_def_79, type, s: val).
% 44.75/7.93 thf(func_def_95, type, sP0: list_node > list_node > list_node > list_node > node > node > $o).
% 44.75/7.93 thf(func_def_96, type, sP1: (list_node > list_node > $o) > $o).
% 44.75/7.93 thf(func_def_97, type, sP2: (list_node > list_node > $o) > (node > node > $o) > $o).
% 44.75/7.93 thf(func_def_98, type, sP3: list_node > list_node > $o).
% 44.75/7.93 thf(func_def_99, type, sK4: list_node > node).
% 44.75/7.93 thf(func_def_100, type, sK5: list_node > list_node).
% 44.75/7.93 thf(func_def_101, type, sK6: list_node > node).
% 44.75/7.93 thf(func_def_102, type, sK7: list_node > node).
% 44.75/7.93 thf(func_def_103, type, sK8: node > list_node > node > list_node > list_node > list_node > list_node).
% 44.75/7.93 thf(func_def_104, type, sK9: node > list_node > node > list_node > list_node > list_node > list_node).
% 44.75/7.93 thf(func_def_105, type, sK10: (node > list_node > node > $o) > node > g > node).
% 44.75/7.93 thf(func_def_106, type, sK11: (node > list_node > node > $o) > node > g > list_node).
% 44.75/7.93 thf(func_def_107, type, sK12: (node > list_node > node > $o) > node > g > node).
% 44.75/7.93 thf(func_def_108, type, sK13: list_node > node > node).
% 44.75/7.93 thf(func_def_109, type, sK14: list_node > node > list_node).
% 44.75/7.93 thf(func_def_110, type, sK15: list_node > node > list_node).
% 44.75/7.93 thf(func_def_111, type, sK16: g > node > node).
% 44.75/7.93 thf(func_def_112, type, sK17: list_node > list_node).
% 44.75/7.93 thf(func_def_113, type, sK18: list_node > node).
% 44.75/7.93 thf(func_def_114, type, sK19: ((node > node > $o) > list_node > $o) > node > node > $o).
% 44.75/7.93 thf(func_def_115, type, sK20: ((node > node > $o) > list_node > $o) > node > node > $o).
% 44.75/7.93 thf(func_def_116, type, sK21: ((node > node > $o) > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_117, type, sK22: ((node > node > $o) > list_node > $o) > node).
% 44.75/7.93 thf(func_def_118, type, sK23: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_119, type, sK24: (list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_120, type, sK25: list_node > list_node > node > list_node > list_node).
% 44.75/7.93 thf(func_def_121, type, sK26: (list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_122, type, sK27: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_123, type, sK28: node > list_node > list_node).
% 44.75/7.93 thf(func_def_124, type, sK29: node > list_node > list_node).
% 44.75/7.93 thf(func_def_125, type, sK30: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_126, type, sK31: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_127, type, sK32: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_128, type, sK33: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_129, type, sK34: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_130, type, sK35: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_131, type, sK36: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_132, type, sK37: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_133, type, sK38: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_134, type, sK39: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_135, type, sK40: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_136, type, sK41: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_137, type, sK42: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_138, type, sK43: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_139, type, sK44: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_140, type, sK45: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_141, type, sK46: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_142, type, sK47: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_143, type, sK48: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_144, type, sK49: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_145, type, sK50: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_146, type, sK51: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_147, type, sK52: (node > list_node > node > $o) > g > node > list_node).
% 44.75/7.93 thf(func_def_148, type, sK53: (node > list_node > node > $o) > g > node > node).
% 44.75/7.93 thf(func_def_149, type, sK54: (node > list_node > node > $o) > g > node > node).
% 44.75/7.93 thf(func_def_150, type, sK55: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_151, type, sK56: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_152, type, sK57: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_153, type, sK58: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_154, type, sK59: list_node > node).
% 44.75/7.93 thf(func_def_155, type, sK60: list_node > list_node).
% 44.75/7.93 thf(func_def_156, type, sK61: ((node > node > $o) > list_node > $o) > node > node > $o).
% 44.75/7.93 thf(func_def_157, type, sK62: ((node > node > $o) > list_node > $o) > node > node > $o).
% 44.75/7.93 thf(func_def_158, type, sK63: ((node > node > $o) > list_node > $o) > node).
% 44.75/7.93 thf(func_def_159, type, sK64: ((node > node > $o) > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_160, type, sK65: ((node > node > $o) > list_node > $o) > node).
% 44.75/7.93 thf(func_def_161, type, sK66: ((node > node > $o) > list_node > $o) > node > node > $o).
% 44.75/7.93 thf(func_def_162, type, sK67: ((node > node > $o) > list_node > $o) > node).
% 44.75/7.93 thf(func_def_163, type, sK68: set_val > list_val).
% 44.75/7.93 thf(func_def_164, type, sK69: list_node > node).
% 44.75/7.93 thf(func_def_165, type, sK70: list_node > list_node).
% 44.75/7.93 thf(func_def_166, type, sK71: list_node > node).
% 44.75/7.93 thf(func_def_167, type, sK72: val > list_node > g > node).
% 44.75/7.93 thf(func_def_168, type, sK73: list_node > list_node).
% 44.75/7.93 thf(func_def_169, type, sK74: list_node > node).
% 44.75/7.93 thf(func_def_170, type, sK75: (node > $o) > list_node > node).
% 44.75/7.93 thf(func_def_171, type, sK76: (node > $o) > list_node > list_node).
% 44.75/7.93 thf(func_def_172, type, sK77: (node > $o) > list_node > list_node).
% 44.75/7.93 thf(func_def_173, type, sK78: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_174, type, sK79: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_175, type, sK80: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_176, type, sK81: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_177, type, sK82: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_178, type, sK83: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_179, type, sK84: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_180, type, sK85: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_181, type, sK86: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_182, type, sK87: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_183, type, sK88: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_184, type, sK89: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_185, type, sK90: (list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_186, type, sK91: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_187, type, sK92: list_node > node > list_node).
% 44.75/7.93 thf(func_def_188, type, sK93: list_node > node > list_node).
% 44.75/7.93 thf(func_def_189, type, sK94: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_190, type, sK95: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_191, type, sK96: (list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_192, type, sK97: node > g > node > list_node).
% 44.75/7.93 thf(func_def_193, type, sK98: list_node > list_node).
% 44.75/7.93 thf(func_def_194, type, sK99: list_node > node).
% 44.75/7.93 thf(func_def_195, type, sK100: list_node > list_node).
% 44.75/7.93 thf(func_def_196, type, sK101: list_node > list_node).
% 44.75/7.93 thf(func_def_197, type, sK102: list_node > node).
% 44.75/7.93 thf(func_def_198, type, sK103: list_node > list_node).
% 44.75/7.93 thf(func_def_199, type, sK104: list_node > val > g > node).
% 44.75/7.93 thf(func_def_200, type, sK105: node > g > val > list_node).
% 44.75/7.93 thf(func_def_201, type, sK106: ((node > node) > list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_202, type, sK107: ((node > node) > list_node > list_node > $o) > node > node).
% 44.75/7.93 thf(func_def_203, type, sK108: ((node > node) > list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_204, type, sK109: ((node > node) > list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_205, type, sK110: ((node > node) > list_node > list_node > $o) > node > node).
% 44.75/7.93 thf(func_def_206, type, sK111: ((node > node) > list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_207, type, sK112: list_node > list_node > list_node > node > list_node).
% 44.75/7.93 thf(func_def_208, type, sK113: ((node > node > $o) > list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_209, type, sK114: ((node > node > $o) > list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_210, type, sK115: ((node > node > $o) > list_node > list_node > $o) > node > node > $o).
% 44.75/7.93 thf(func_def_211, type, sK116: ((node > node > $o) > list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_212, type, sK117: ((node > node > $o) > list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_213, type, sK118: ((node > node > $o) > list_node > list_node > $o) > node > node > $o).
% 44.75/7.93 thf(func_def_214, type, sK119: ((node > node > $o) > list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_215, type, sK120: ((node > node > $o) > list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_216, type, sK121: ((node > node > $o) > list_node > list_node > $o) > node > node > $o).
% 44.75/7.93 thf(func_def_217, type, sK122: ((node > node > $o) > list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_218, type, sK123: g > node > val > list_node).
% 44.75/7.93 thf(func_def_219, type, sK124: (list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_220, type, sK125: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_221, type, sK126: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_222, type, sK127: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_223, type, sK128: node > list_node > list_node).
% 44.75/7.93 thf(func_def_224, type, sK129: node > list_node > list_node).
% 44.75/7.93 thf(func_def_225, type, sK130: (node > $o) > list_node > node).
% 44.75/7.93 thf(func_def_226, type, sK131: (node > $o) > list_node > list_node).
% 44.75/7.93 thf(func_def_227, type, sK132: (node > $o) > list_node > list_node).
% 44.75/7.93 thf(func_def_228, type, sK133: (list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_229, type, sK134: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_230, type, sK135: (node > $o) > list_node > node).
% 44.75/7.93 thf(func_def_231, type, sK136: (node > $o) > list_node > list_node).
% 44.75/7.93 thf(func_def_232, type, sK137: (node > $o) > list_node > list_node).
% 44.75/7.93 thf(func_def_233, type, sK138: list_node > node > list_node).
% 44.75/7.93 thf(func_def_234, type, sK139: list_node > node > list_node).
% 44.75/7.93 thf(func_def_235, type, sK140: list_node > g > val > node).
% 44.75/7.93 thf(func_def_236, type, sK141: val > g > list_node > node).
% 44.75/7.93 thf(func_def_237, type, sK142: list_node > list_node).
% 44.75/7.93 thf(func_def_238, type, sK143: list_node > node).
% 44.75/7.93 thf(func_def_239, type, sK144: list_node > list_node).
% 44.75/7.93 thf(func_def_240, type, sK145: (list_node > list_node > $o) > (node > node > $o) > node).
% 44.75/7.93 thf(func_def_241, type, sK146: (list_node > list_node > $o) > (node > node > $o) > list_node).
% 44.75/7.93 thf(func_def_242, type, sK147: (list_node > list_node > $o) > (node > node > $o) > list_node).
% 44.75/7.93 thf(func_def_243, type, sK148: (list_node > list_node > $o) > (node > node > $o) > node).
% 44.75/7.93 thf(func_def_244, type, sK149: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_245, type, sK150: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_246, type, sK151: (list_node > list_node > $o) > (node > node > $o) > list_node).
% 44.75/7.93 thf(func_def_247, type, sK152: (list_node > list_node > $o) > (node > node > $o) > node).
% 44.75/7.93 thf(func_def_248, type, sK153: (list_node > list_node > $o) > (node > node > $o) > list_node).
% 44.75/7.93 thf(func_def_249, type, sK154: (list_node > list_node > $o) > (node > node > $o) > node).
% 44.75/7.93 thf(func_def_250, type, sK155: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_251, type, sK156: (list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_252, type, sK157: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_253, type, sK158: (list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_254, type, sK159: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_255, type, sK160: list_node > (node > $o) > node > g > list_node).
% 44.75/7.93 thf(func_def_256, type, sK161: list_node > (node > $o) > node > g > node).
% 44.75/7.93 thf(func_def_257, type, sK162: (node > $o) > list_node > list_node).
% 44.75/7.93 thf(func_def_258, type, sK163: (node > $o) > list_node > node).
% 44.75/7.93 thf(func_def_259, type, sK164: (node > $o) > list_node > list_node).
% 44.75/7.93 thf(func_def_260, type, sK165: list_node > (node > $o) > list_node).
% 44.75/7.93 thf(func_def_261, type, sK166: list_node > (node > $o) > list_node).
% 44.75/7.93 thf(func_def_262, type, sK167: list_node > (node > $o) > node).
% 44.75/7.93 thf(func_def_263, type, sK168: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_264, type, sK169: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_265, type, sK170: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_266, type, sK171: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_267, type, sK172: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_268, type, sK173: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_269, type, sK174: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_270, type, sK175: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_271, type, sK176: (node > $o) > list_node > list_node).
% 44.75/7.93 thf(func_def_272, type, sK177: (node > $o) > list_node > node).
% 44.75/7.93 thf(func_def_273, type, sK178: (node > $o) > list_node > list_node).
% 44.75/7.93 thf(func_def_274, type, sK179: node > g > list_node).
% 44.75/7.93 thf(func_def_275, type, sK180: node > list_node > node).
% 44.75/7.93 thf(func_def_276, type, sK181: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_277, type, sK182: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_278, type, sK183: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_279, type, sK184: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_280, type, sK185: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_281, type, sK186: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_282, type, sK187: ((node > node > $o) > list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_283, type, sK188: ((node > node > $o) > list_node > list_node > $o) > node > node > $o).
% 44.75/7.93 thf(func_def_284, type, sK189: ((node > node > $o) > list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_285, type, sK190: ((node > node > $o) > list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_286, type, sK191: ((node > node > $o) > list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_287, type, sK192: ((node > node > $o) > list_node > list_node > $o) > node > node > $o).
% 44.75/7.93 thf(func_def_288, type, sK193: ((node > node > $o) > list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_289, type, sK194: ((node > node > $o) > list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_290, type, sK195: ((node > node > $o) > list_node > list_node > $o) > node > node > $o).
% 44.75/7.93 thf(func_def_291, type, sK196: ((node > node > $o) > list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_292, type, sK197: ((node > node > $o) > list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_293, type, sK198: ((node > node > $o) > list_node > list_node > $o) > node > node > $o).
% 44.75/7.93 thf(func_def_294, type, sK199: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_295, type, sK200: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_296, type, sK201: (list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_297, type, sK202: (list_node > $o) > node).
% 44.75/7.93 thf(func_def_298, type, sK203: node > g > node > list_node).
% 44.75/7.93 thf(func_def_299, type, sK204: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_300, type, sK205: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_301, type, sK206: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_302, type, sK207: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_303, type, sK208: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_304, type, sK209: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_305, type, sK210: list_node).
% 44.75/7.93 thf(func_def_306, type, sK211: node).
% 44.75/7.93 thf(func_def_307, type, sK212: list_node > list_node > list_node).
% 44.75/7.93 thf(func_def_308, type, sK213: list_node > list_node > node).
% 44.75/7.93 thf(func_def_309, type, sK214: list_node > list_node > list_node).
% 44.75/7.93 thf(func_def_310, type, sK215: list_node > list_node > node).
% 44.75/7.93 thf(func_def_311, type, sK216: list_node > list_node > node).
% 44.75/7.93 thf(func_def_312, type, sK217: list_node > list_node > node).
% 44.75/7.93 thf(func_def_313, type, sK218: list_node > list_node > list_node).
% 44.75/7.93 thf(func_def_314, type, sK219: list_node > list_node > list_node).
% 44.75/7.93 thf(func_def_315, type, sK220: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_316, type, sK221: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_317, type, sK222: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_318, type, sK223: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_319, type, sK224: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_320, type, sK225: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_321, type, sK226: (list_node > list_node > $o) > list_node).
% 44.75/7.93 thf(func_def_322, type, sK227: (list_node > list_node > $o) > node).
% 44.75/7.93 thf(func_def_323, type, sK228: list_node > node > list_node).
% 44.75/7.93 thf(func_def_324, type, sK229: list_node > node > list_node).
% 44.75/7.93 thf(func_def_325, type, sK230: node > list_node > node > list_node).
% 44.75/7.93 thf(func_def_326, type, sK231: node > list_node > node > list_node).
% 44.75/7.93 thf(func_def_327, type, sK232: node > list_node > node > list_node).
% 44.75/7.93 thf(func_def_328, type, sK233: node > list_node > node > list_node).
% 44.75/7.93 thf(func_def_329, type, sK234: node > list_node > node > list_node).
% 44.75/7.93 thf(func_def_330, type, sK235: node > list_node > node > list_node).
% 44.75/7.93 thf(func_def_331, type, sK236: node > g > list_node).
% 44.75/7.93 thf(func_def_333, type, sK238: list_node > (node > $o) > list_node).
% 44.75/7.93 thf(func_def_334, type, sK239: list_node > (node > $o) > node).
% 44.75/7.93 thf(func_def_335, type, sK240: list_node > (node > $o) > list_node).
% 44.75/7.93 thf(func_def_336, type, sK241: list_node > (node > $o) > node).
% 44.75/7.93 thf(func_def_337, type, sK242: (node > $o) > list_node > node).
% 44.75/7.93 thf(func_def_338, type, sK243: (node > $o) > list_node > node).
% 44.75/7.93 thf(func_def_339, type, sK244: list_node > node > list_node).
% 44.75/7.93 thf(func_def_340, type, sK245: list_node > node > list_node).
% 44.75/7.93 thf(func_def_341, type, sK246: list_P738500740D_node > produc1453890942D_node).
% 44.75/7.93 thf(func_def_342, type, sK247: g > list_node > node).
% 44.75/7.93 thf(func_def_343, type, sK248: g > node).
% 44.75/7.93 thf(func_def_344, type, sK249: g > list_node).
% 44.75/7.93 thf(func_def_345, type, sK250: node > g > node).
% 44.75/7.93 thf(func_def_346, type, sK251: node > list_node > list_node).
% 44.75/7.93 thf(func_def_347, type, sK252: node > list_node > list_node).
% 44.75/7.93 thf(func_def_348, type, sK253: list_P738500740D_node > produc1453890942D_node).
% 44.75/7.93 thf(func_def_349, type, sK254: list_P738500740D_node > list_P738500740D_node).
% 44.75/7.93 thf(func_def_350, type, sK255: val > list_val > list_val).
% 44.75/7.93 thf(func_def_351, type, sK256: val > list_val > list_val).
% 44.75/7.93 thf(func_def_352, type, sK257: list_P738500740D_node > produc1453890942D_node).
% 44.75/7.93 thf(func_def_353, type, sK258: node > list_node > list_node > list_node > list_node).
% 44.75/7.93 thf(func_def_354, type, sK259: node > list_node > list_node > list_node > list_node).
% 44.75/7.93 thf(func_def_355, type, sK260: list_node > list_node > list_node > list_node > list_node).
% 44.75/7.93 thf(func_def_356, type, sK261: val > list_val > list_val).
% 44.75/7.93 thf(func_def_357, type, sK262: val > list_val > list_val).
% 44.75/7.93 thf(func_def_358, type, sK263: g > node > node > node).
% 44.75/7.93 thf(func_def_359, type, sK264: list_node > node).
% 44.75/7.93 thf(func_def_360, type, sK265: list_node > list_node).
% 44.75/7.93 thf(func_def_361, type, sK266: list_node > list_node).
% 44.75/7.93 thf(func_def_362, type, sK267: val > list_val > list_val).
% 44.75/7.93 thf(func_def_363, type, sK268: val > list_val > list_val).
% 44.75/7.93 thf(func_def_364, type, sK269: produc1453890942D_node > list_P738500740D_node > list_P738500740D_node > list_P738500740D_node > list_P738500740D_node).
% 44.75/7.93 thf(func_def_365, type, sK270: list_node > node > list_node > list_node > list_node).
% 44.75/7.93 thf(func_def_366, type, sK271: list_node > node > list_node).
% 44.75/7.93 thf(func_def_367, type, sK272: list_node > node > list_node).
% 44.75/7.93 thf(func_def_368, type, sK273: val > list_node > g > node).
% 44.75/7.93 thf(func_def_369, type, sK274: node > g > val > list_node).
% 44.75/7.93 thf(func_def_370, type, sK275: node > node > g > list_node).
% 44.75/7.93 thf(func_def_371, type, sK276: list_P738500740D_node > produc1453890942D_node > list_P738500740D_node > list_P738500740D_node > list_P738500740D_node).
% 44.75/7.93 thf(func_def_372, type, sK277: list_node > list_node > node > list_node).
% 44.75/7.93 thf(func_def_373, type, sK278: list_P738500740D_node > produc1453890942D_node).
% 44.75/7.93 thf(func_def_374, type, sK279: list_P738500740D_node > list_P738500740D_node).
% 44.75/7.93 thf(func_def_375, type, sK280: g > node > val > node).
% 44.75/7.93 thf(func_def_376, type, sK281: list_val > list_val).
% 44.75/7.93 thf(func_def_377, type, sK282: list_val > val).
% 44.75/7.93 thf(func_def_378, type, sK283: list_val > list_val).
% 44.75/7.93 thf(func_def_379, type, sK284: list_node > list_node).
% 44.75/7.93 thf(func_def_380, type, sK285: list_node > node).
% 44.75/7.93 thf(func_def_381, type, sK286: list_node > node).
% 44.75/7.93 thf(func_def_382, type, sK287: list_node > node).
% 44.75/7.93 thf(func_def_383, type, sK288: (node > $o) > list_node > list_node).
% 44.75/7.93 thf(func_def_384, type, sK289: (node > $o) > list_node > node).
% 44.75/7.93 thf(func_def_385, type, sK290: (node > $o) > list_node > list_node).
% 44.75/7.93 thf(func_def_386, type, sK291: (node > $o) > list_node > node).
% 44.75/7.93 thf(func_def_387, type, sK292: (node > $o) > list_node > node).
% 44.75/7.93 thf(func_def_388, type, sK293: (node > $o) > list_node > node).
% 44.75/7.93 thf(func_def_389, type, sK294: list_P738500740D_node > produc1453890942D_node > list_P738500740D_node > list_P738500740D_node).
% 44.75/7.93 thf(func_def_390, type, sK295: list_node > node).
% 44.75/7.93 thf(func_def_391, type, sK296: list_node > list_node).
% 44.75/7.93 thf(func_def_392, type, sK297: val > list_node > g > node).
% 44.75/7.93 thf(func_def_393, type, sK298: val > node > g > list_node).
% 44.75/7.93 thf(func_def_394, type, ph299: !>[X0: $tType]:(X0)).
% 44.75/7.93 thf(f7344,plain,(
% 44.75/7.93 $false),
% 44.75/7.93 inference(subsumption_resolution,[status(thm)],[f7332,f6897])).
% 44.75/7.93 thf(f6897,plain,(
% 44.75/7.93 ($true = (distinct_node @ rs))),
% 44.75/7.93 inference(trivial_inequality_removal,[status(thm)],[f6895])).
% 44.75/7.93 thf(f6895,plain,(
% 44.75/7.93 ($true != $true) | ($true = (distinct_node @ rs))),
% 44.75/7.93 inference(superposition,[status(thm)],[f1729,f1645])).
% 44.75/7.93 thf(f1645,plain,(
% 44.75/7.93 ((graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs) = $true)),
% 44.75/7.93 inference(cnf_transformation,[status(thm)],[f894])).
% 44.75/7.93 thf(f894,plain,(
% 44.75/7.93 ((graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs) = $true)),
% 44.75/7.93 inference(fool_elimination,[status(thm)],[f893])).
% 44.75/7.93 thf(f893,plain,(
% 44.75/7.93 (graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs)),
% 44.75/7.93 inference(rectify,[status(thm)],[f4])).
% 44.75/7.93 thf(f4,axiom,(
% 44.75/7.93 (graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ g2 @ rs)),
% 44.75/7.93 file('/export/starexec/sandbox/tmp/tmp.zlt6T4WObL/DTF2THF_2101.p',fact_3_rs_H__props_I2_J)).
% 44.75/7.93 thf(f1729,plain,(
% 44.75/7.93 ( ! [X0 : g,X1 : list_node] : (($true != (graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ X0 @ X1)) | ((distinct_node @ X1) = $true)) )),
% 44.75/7.93 inference(cnf_transformation,[status(thm)],[f1089])).
% 44.75/7.93 thf(f1089,plain,(
% 44.75/7.93 ! [X0 : g,X1 : list_node] : (($true != (graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ X0 @ X1)) | ((distinct_node @ X1) = $true))),
% 44.75/7.93 inference(ennf_transformation,[status(thm)],[f360])).
% 44.75/7.93 thf(f360,plain,(
% 44.75/7.93 ! [X0 : g,X1 : list_node] : (($true = (graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ X0 @ X1)) => ((distinct_node @ X1) = $true))),
% 44.75/7.93 inference(fool_elimination,[status(thm)],[f359])).
% 44.75/7.93 thf(f359,plain,(
% 44.75/7.93 ! [X0 : g,X1 : list_node] : ((graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ X0 @ X1) => (distinct_node @ X1))),
% 44.75/7.93 inference(rectify,[status(thm)],[f6])).
% 44.75/7.93 thf(f6,axiom,(
% 44.75/7.93 ! [X0 : g,X2 : list_node] : ((graph_1994935542_edgeD @ alpha_n @ invar @ inEdges @ entry @ X0 @ X2) => (distinct_node @ X2))),
% 44.75/7.93 file('/export/starexec/sandbox/tmp/tmp.zlt6T4WObL/DTF2THF_2101.p',fact_5_old_OEntryPath__distinct)).
% 44.75/7.93 thf(f7332,plain,(
% 44.75/7.93 ($true != (distinct_node @ rs))),
% 44.75/7.93 inference(trivial_inequality_removal,[status(thm)],[f7302])).
% 44.75/7.93 thf(f7302,plain,(
% 44.75/7.93 ($true != (distinct_node @ rs)) | ($true != $true)),
% 44.75/7.93 inference(superposition,[status(thm)],[f1667,f7286])).
% 44.75/7.93 thf(f7286,plain,(
% 44.75/7.93 ((member_node @ (hd_node @ rs) @ (set_node2 @ (tl_node @ rs))) = $true)),
% 44.75/7.93 inference(backward_demodulation,[status(thm)],[f1575,f7282])).
% 44.75/7.93 thf(f7282,plain,(
% 44.75/7.93 ((sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) = (hd_node @ rs))),
% 44.75/7.93 inference(trivial_inequality_removal,[status(thm)],[f7279])).
% 44.75/7.93 thf(f7279,plain,(
% 44.75/7.93 ($true != $true) | ((sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) = (hd_node @ rs))),
% 44.75/7.93 inference(superposition,[status(thm)],[f1587,f1766])).
% 44.75/7.93 thf(f1766,plain,(
% 44.75/7.93 ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ rs @ pred_phi_r) = $true)),
% 44.75/7.93 inference(cnf_transformation,[status(thm)],[f604])).
% 44.75/7.93 thf(f604,plain,(
% 44.75/7.93 ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ rs @ pred_phi_r) = $true)),
% 44.75/7.93 inference(fool_elimination,[status(thm)],[f603])).
% 44.75/7.93 thf(f603,plain,(
% 44.75/7.93 (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ rs @ pred_phi_r)),
% 44.75/7.93 inference(rectify,[status(thm)],[f5])).
% 44.75/7.93 thf(f5,axiom,(
% 44.75/7.93 (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ g2 @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ rs @ pred_phi_r)),
% 44.75/7.93 file('/export/starexec/sandbox/tmp/tmp.zlt6T4WObL/DTF2THF_2101.p',fact_4_rs_H__props_I1_J)).
% 44.75/7.93 thf(f1587,plain,(
% 44.75/7.93 ( ! [X2 : node,X3 : g,X0 : node,X1 : list_node] : (($true != (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X3 @ X0 @ X1 @ X2)) | ((hd_node @ X1) = X0)) )),
% 44.75/7.93 inference(cnf_transformation,[status(thm)],[f1233])).
% 44.75/7.93 thf(f1233,plain,(
% 44.75/7.93 ! [X0 : node,X1 : list_node,X2 : node,X3 : g] : (($true != (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X3 @ X0 @ X1 @ X2)) | ((hd_node @ X1) = X0))),
% 44.75/7.93 inference(ennf_transformation,[status(thm)],[f586])).
% 44.75/7.93 thf(f586,plain,(
% 44.75/7.93 ! [X0 : node,X1 : list_node,X2 : node,X3 : g] : (($true = (graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X3 @ X0 @ X1 @ X2)) => ((hd_node @ X1) = X0))),
% 44.75/7.93 inference(fool_elimination,[status(thm)],[f585])).
% 44.75/7.93 thf(f585,plain,(
% 44.75/7.93 ! [X0 : node,X1 : list_node,X2 : node,X3 : g] : ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X3 @ X0 @ X1 @ X2) => ((hd_node @ X1) = X0))),
% 44.75/7.93 inference(rectify,[status(thm)],[f1])).
% 44.75/7.93 thf(f1,axiom,(
% 44.75/7.93 ! [X1 : node,X2 : list_node,X3 : node,X0 : g] : ((graph_1012773594_edgeD @ alpha_n @ invar @ inEdges @ X0 @ X1 @ X2 @ X3) => ((hd_node @ X2) = X1))),
% 44.75/7.93 file('/export/starexec/sandbox/tmp/tmp.zlt6T4WObL/DTF2THF_2101.p',fact_0_old_Opath2__hd)).
% 44.75/7.93 thf(f1575,plain,(
% 44.75/7.93 ((member_node @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ (set_node2 @ (tl_node @ rs))) = $true)),
% 44.75/7.93 inference(cnf_transformation,[status(thm)],[f937])).
% 44.75/7.93 thf(f937,plain,(
% 44.75/7.93 ((member_node @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ (set_node2 @ (tl_node @ rs))) = $true)),
% 44.75/7.93 inference(flattening,[status(thm)],[f644])).
% 44.75/7.93 thf(f644,plain,(
% 44.75/7.93 ~~((member_node @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ (set_node2 @ (tl_node @ rs))) = $true)),
% 44.75/7.93 inference(fool_elimination,[status(thm)],[f643])).
% 44.75/7.93 thf(f643,plain,(
% 44.75/7.93 ~~(member_node @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ (set_node2 @ (tl_node @ rs)))),
% 44.75/7.93 inference(rectify,[status(thm)],[f353])).
% 44.75/7.93 thf(f353,negated_conjecture,(
% 44.75/7.93 ~~(member_node @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ (set_node2 @ (tl_node @ rs)))),
% 44.75/7.93 inference(negated_conjecture,[status(cth)],[f352])).
% 44.75/7.93 thf(f352,conjecture,(
% 44.75/7.93 ~(member_node @ (sSA_CF551432799de_val @ alpha_n @ defs @ phis @ g2 @ r) @ (set_node2 @ (tl_node @ rs)))),
% 44.75/7.93 file('/export/starexec/sandbox/tmp/tmp.zlt6T4WObL/DTF2THF_2101.p',conj_0)).
% 44.75/7.93 thf(f1667,plain,(
% 44.75/7.93 ( ! [X0 : list_node] : (($true != (member_node @ (hd_node @ X0) @ (set_node2 @ (tl_node @ X0)))) | ((distinct_node @ X0) != $true)) )),
% 44.75/7.93 inference(cnf_transformation,[status(thm)],[f1209])).
% 44.75/7.93 thf(f1209,plain,(
% 44.75/7.93 ! [X0 : list_node] : (($true != (member_node @ (hd_node @ X0) @ (set_node2 @ (tl_node @ X0)))) | ((distinct_node @ X0) != $true))),
% 44.75/7.93 inference(ennf_transformation,[status(thm)],[f955])).
% 44.75/7.93 thf(f955,plain,(
% 44.75/7.93 ! [X0 : list_node] : (((distinct_node @ X0) = $true) => ($true != (member_node @ (hd_node @ X0) @ (set_node2 @ (tl_node @ X0)))))),
% 44.75/7.93 inference(flattening,[status(thm)],[f756])).
% 44.75/7.93 thf(f756,plain,(
% 44.75/7.93 ! [X0 : list_node] : (((distinct_node @ X0) = $true) => ~($true = (member_node @ (hd_node @ X0) @ (set_node2 @ (tl_node @ X0)))))),
% 44.75/7.93 inference(fool_elimination,[status(thm)],[f755])).
% 44.75/7.93 thf(f755,plain,(
% 44.75/7.93 ! [X0 : list_node] : ((distinct_node @ X0) => ~(member_node @ (hd_node @ X0) @ (set_node2 @ (tl_node @ X0))))),
% 44.75/7.93 inference(rectify,[status(thm)],[f31])).
% 44.75/7.93 thf(f31,axiom,(
% 44.75/7.93 ! [X6 : list_node] : ((distinct_node @ X6) => ~(member_node @ (hd_node @ X6) @ (set_node2 @ (tl_node @ X6))))),
% 44.75/7.93 file('/export/starexec/sandbox/tmp/tmp.zlt6T4WObL/DTF2THF_2101.p',fact_30_FormalSSA__Misc_Odistinct__hd__tl)).
% 44.75/7.93 % SZS output end Proof for DTF2THF_2101
% 44.75/7.93 % (2704)------------------------------
% 44.75/7.93 % (2704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.75/7.93 % (2704)Termination reason: Refutation
% 44.75/7.93
% 44.75/7.93 % (2704)Memory used [KB]: 13176
% 44.75/7.93 % (2704)Time elapsed: 0.852 s
% 44.75/7.93 % (2704)Instructions burned: 2659 (million)
% 44.75/7.93 % (2704)------------------------------
% 44.75/7.93 % (2704)------------------------------
% 44.75/7.93 % (2444)Success in time 6.333 s
%------------------------------------------------------------------------------