%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP030^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 08:54:59 AM UTC 2026
% Result : ContradictoryAxioms 3.10s 1.71s
% Output : Refutation 3.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 1
% Syntax : Number of formulae : 3 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 3 ( 2 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 2 ~; 0 |; 0 &; 4 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Number of types : 10 ( 9 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 195 ( 193 usr; 12 con; 0-4 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
binary1176601351tion_a: $tType ).
thf(type_def_6,type,
option_a: $tType ).
thf(type_def_8,type,
binary1439146945Tree_a: $tType ).
thf(type_def_9,type,
a: $tType ).
thf(type_def_10,type,
set_a: $tType ).
thf(type_def_11,type,
int: $tType ).
thf(type_def_12,type,
set_option_a: $tType ).
thf(type_def_13,type,
option_option_a: $tType ).
thf(type_def_14,type,
set_option_option_a: $tType ).
thf(func_def_0,type,
binary1176601351tion_a: $tType ).
thf(func_def_1,type,
set_option_option_a: $tType ).
thf(func_def_2,type,
binary1439146945Tree_a: $tType ).
thf(func_def_3,type,
option_option_a: $tType ).
thf(func_def_4,type,
set_option_a: $tType ).
thf(func_def_5,type,
option_a: $tType ).
thf(func_def_6,type,
set_a: $tType ).
thf(func_def_7,type,
int: $tType ).
thf(func_def_8,type,
a: $tType ).
thf(func_def_9,type,
binary1007279693tion_a: binary1176601351tion_a > option_a > binary1176601351tion_a > binary1176601351tion_a ).
thf(func_def_10,type,
binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_11,type,
binary471442758tion_a: binary1176601351tion_a ).
thf(func_def_12,type,
binary476621312_Tip_a: binary1439146945Tree_a ).
thf(func_def_13,type,
binary256242811Tree_a: binary1439146945Tree_a > set_a ).
thf(func_def_14,type,
binary301690796tion_a: ( option_a > int ) > option_a > set_option_a ).
thf(func_def_15,type,
binary504661350_eqs_a: ( a > int ) > a > set_a ).
thf(func_def_16,type,
binary2053421120memb_a: ( a > int ) > a > binary1439146945Tree_a > $o ).
thf(func_def_17,type,
binary1117200954tion_a: binary1176601351tion_a > set_option_a ).
thf(func_def_18,type,
binary945792244etOf_a: binary1439146945Tree_a > set_a ).
thf(func_def_19,type,
binary995005080tion_a: ( option_a > int ) > binary1176601351tion_a > $o ).
thf(func_def_20,type,
binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
thf(func_def_21,type,
binary1691793817tion_a: ( option_a > int ) > option_a > option_a > binary1176601351tion_a > $o ).
thf(func_def_22,type,
binary670562003pred_a: ( a > int ) > a > a > binary1439146945Tree_a > $o ).
thf(func_def_23,type,
binary1040190117tion_a: ( option_a > int ) > int > binary1176601351tion_a > option_option_a ).
thf(func_def_24,type,
binary779405791okup_a: ( a > int ) > int > binary1439146945Tree_a > option_a ).
thf(func_def_25,type,
the_option_a: ( option_a > $o ) > option_a ).
thf(func_def_26,type,
the_a: ( a > $o ) > a ).
thf(func_def_27,type,
undefined_a: a ).
thf(func_def_28,type,
sup_sup_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
thf(func_def_29,type,
sup_sup_set_option_a: set_option_a > set_option_a > set_option_a ).
thf(func_def_30,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(func_def_31,type,
none_option_a: option_option_a ).
thf(func_def_32,type,
none_a: option_a ).
thf(func_def_33,type,
some_option_a: option_a > option_option_a ).
thf(func_def_34,type,
some_a: a > option_a ).
thf(func_def_35,type,
case_option_o_a: $o > ( a > $o ) > option_a > $o ).
thf(func_def_36,type,
case_option_a_a: a > ( a > a ) > option_a > a ).
thf(func_def_37,type,
set_option_option_a2: option_option_a > set_option_a ).
thf(func_def_38,type,
set_option_a2: option_a > set_a ).
thf(func_def_39,type,
the_option_a2: option_option_a > option_a ).
thf(func_def_40,type,
the_a2: option_a > a ).
thf(func_def_41,type,
these_option_a: set_option_option_a > set_option_a ).
thf(func_def_42,type,
these_a: set_option_a > set_a ).
thf(func_def_43,type,
bot_bot_option_a_o: option_a > $o ).
thf(func_def_44,type,
bot_bot_a_o: a > $o ).
thf(func_def_46,type,
bot_bo1607647958tion_a: set_option_option_a ).
thf(func_def_47,type,
bot_bot_set_option_a: set_option_a ).
thf(func_def_48,type,
bot_bot_set_a: set_a ).
thf(func_def_49,type,
ord_less_option_a_o: ( option_a > $o ) > ( option_a > $o ) > $o ).
thf(func_def_50,type,
ord_less_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_51,type,
ord_less_int: int > int > $o ).
thf(func_def_52,type,
ord_le1280890064tion_a: set_option_a > set_option_a > $o ).
thf(func_def_53,type,
ord_less_set_a: set_a > set_a > $o ).
thf(func_def_54,type,
top_top_set_a: set_a ).
thf(func_def_55,type,
collect_option_a: ( option_a > $o ) > set_option_a ).
thf(func_def_56,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_57,type,
image_139503237tion_a: ( option_a > option_a ) > set_option_a > set_option_a ).
thf(func_def_58,type,
image_option_a_a: ( option_a > a ) > set_option_a > set_a ).
thf(func_def_59,type,
image_a_option_a: ( a > option_a ) > set_a > set_option_a ).
thf(func_def_60,type,
image_a_a: ( a > a ) > set_a > set_a ).
thf(func_def_61,type,
insert1662731738tion_a: option_option_a > set_option_option_a > set_option_option_a ).
thf(func_def_62,type,
insert_option_a: option_a > set_option_a > set_option_a ).
thf(func_def_63,type,
insert_a: a > set_a > set_a ).
thf(func_def_64,type,
is_empty_option_a: set_option_a > $o ).
thf(func_def_65,type,
is_empty_a: set_a > $o ).
thf(func_def_66,type,
is_sin1624444472tion_a: set_option_a > $o ).
thf(func_def_67,type,
is_singleton_a: set_a > $o ).
thf(func_def_68,type,
the_elem_option_a: set_option_a > option_a ).
thf(func_def_69,type,
the_elem_a: set_a > a ).
thf(func_def_70,type,
member553679923tion_a: option_option_a > set_option_option_a > $o ).
thf(func_def_71,type,
member_option_a: option_a > set_option_a > $o ).
thf(func_def_72,type,
member_a: a > set_a > $o ).
thf(func_def_73,type,
h: a > int ).
thf(func_def_74,type,
t: binary1439146945Tree_a ).
thf(func_def_75,type,
x: a ).
thf(func_def_91,type,
sP0: ( option_a > option_a > $o ) > option_a > option_a > $o ).
thf(func_def_92,type,
sK1: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_93,type,
sK2: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_94,type,
sK3: ( set_a > set_a ) > set_a ).
thf(func_def_95,type,
sK4: ( set_a > set_a ) > set_a ).
thf(func_def_96,type,
sK5: ( set_a > int ) > set_a ).
thf(func_def_97,type,
sK6: ( set_a > int ) > set_a ).
thf(func_def_98,type,
sK7: ( ( a > $o ) > set_a ) > a > $o ).
thf(func_def_99,type,
sK8: ( ( a > $o ) > set_a ) > a > $o ).
thf(func_def_100,type,
sK9: ( option_a > $o ) > ( option_a > $o ) > option_a ).
thf(func_def_101,type,
sK10: int > int ).
thf(func_def_102,type,
sK11: ( set_a > int ) > set_a ).
thf(func_def_103,type,
sK12: ( set_a > int ) > set_a ).
thf(func_def_104,type,
sK13: option_a > ( a > $o ) > a ).
thf(func_def_105,type,
sK14: set_a > ( a > a ) > a > a ).
thf(func_def_106,type,
sK15: ( set_a > int ) > set_a ).
thf(func_def_107,type,
sK16: ( set_a > int ) > set_a ).
thf(func_def_108,type,
sK17: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_109,type,
sK18: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_110,type,
sK19: ( set_a > set_a ) > set_a ).
thf(func_def_111,type,
sK20: ( set_a > set_a ) > set_a ).
thf(func_def_112,type,
sK21: ( set_a > int ) > set_a ).
thf(func_def_113,type,
sK22: ( set_a > int ) > set_a ).
thf(func_def_114,type,
sK23: set_option_a > option_a ).
thf(func_def_115,type,
sK24: set_option_a > option_a ).
thf(func_def_116,type,
sK25: ( int > set_a ) > int ).
thf(func_def_117,type,
sK26: ( int > set_a ) > int ).
thf(func_def_118,type,
sK27: option_a > ( a > $o ) > a ).
thf(func_def_119,type,
sK28: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_120,type,
sK29: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_121,type,
sK30: a > set_a > set_a ).
thf(func_def_122,type,
sK31: ( int > int ) > int ).
thf(func_def_123,type,
sK32: ( int > int ) > int ).
thf(func_def_124,type,
sK33: ( int > set_a ) > int ).
thf(func_def_125,type,
sK34: ( int > set_a ) > int ).
thf(func_def_126,type,
sK35: ( int > int ) > int ).
thf(func_def_127,type,
sK36: ( int > int ) > int ).
thf(func_def_128,type,
sK37: ( int > a > $o ) > int ).
thf(func_def_129,type,
sK38: ( int > a > $o ) > int ).
thf(func_def_130,type,
sK39: ( int > set_a ) > int ).
thf(func_def_131,type,
sK40: ( int > set_a ) > int ).
thf(func_def_132,type,
sK41: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_133,type,
sK42: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_134,type,
sK43: ( int > int ) > int ).
thf(func_def_135,type,
sK44: ( int > int ) > int ).
thf(func_def_136,type,
sK45: set_a > a ).
thf(func_def_137,type,
sK46: a > set_a > set_a ).
thf(func_def_138,type,
sK47: ( binary1439146945Tree_a > $o ) > binary1439146945Tree_a ).
thf(func_def_139,type,
sK48: ( binary1439146945Tree_a > $o ) > binary1439146945Tree_a ).
thf(func_def_140,type,
sK49: ( binary1439146945Tree_a > $o ) > a ).
thf(func_def_141,type,
sK50: ( int > int ) > int ).
thf(func_def_142,type,
sK51: ( int > int ) > int ).
thf(func_def_143,type,
sK52: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_144,type,
sK53: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_145,type,
sK54: ( option_a > $o ) > a ).
thf(func_def_146,type,
sK55: ( set_a > a > $o ) > set_a ).
thf(func_def_147,type,
sK56: ( set_a > a > $o ) > set_a ).
thf(func_def_148,type,
sK57: ( set_a > set_a ) > set_a ).
thf(func_def_149,type,
sK58: ( set_a > set_a ) > set_a ).
thf(func_def_150,type,
sK59: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_151,type,
sK60: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_152,type,
sK61: ( option_a > option_a > $o ) > option_a > option_a > a ).
thf(func_def_153,type,
sK62: ( option_a > option_a > $o ) > option_a > option_a > a ).
thf(func_def_154,type,
sK63: ( int > a > $o ) > int ).
thf(func_def_155,type,
sK64: ( int > a > $o ) > int ).
thf(func_def_156,type,
sK65: option_a > a ).
thf(func_def_157,type,
sK66: ( int > set_a ) > int ).
thf(func_def_158,type,
sK67: ( int > set_a ) > int ).
thf(func_def_159,type,
sK68: ( ( a > $o ) > set_a ) > a > $o ).
thf(func_def_160,type,
sK69: ( ( a > $o ) > set_a ) > a > $o ).
thf(func_def_161,type,
sK70: ( set_a > set_a ) > set_a ).
thf(func_def_162,type,
sK71: ( set_a > set_a ) > set_a ).
thf(func_def_163,type,
sK72: option_a > set_option_a > set_option_a ).
thf(func_def_164,type,
sK73: binary1439146945Tree_a > a ).
thf(func_def_165,type,
sK74: binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_166,type,
sK75: binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_167,type,
sK76: ( set_a > a > $o ) > set_a ).
thf(func_def_168,type,
sK77: ( set_a > a > $o ) > set_a ).
thf(func_def_169,type,
sK78: ( set_a > a > $o ) > set_a ).
thf(func_def_170,type,
sK79: ( set_a > a > $o ) > set_a ).
thf(func_def_171,type,
sK80: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_172,type,
sK81: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_173,type,
sK82: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_174,type,
sK83: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_175,type,
sK84: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_176,type,
sK85: set_a > a ).
thf(func_def_177,type,
sK86: set_a > a ).
thf(func_def_178,type,
sK87: ( int > a > $o ) > int ).
thf(func_def_179,type,
sK88: ( int > a > $o ) > int ).
thf(func_def_180,type,
sK89: ( ( a > $o ) > set_a ) > a > $o ).
thf(func_def_181,type,
sK90: ( ( a > $o ) > set_a ) > a > $o ).
thf(func_def_182,type,
sK91: ( int > a > $o ) > int ).
thf(func_def_183,type,
sK92: ( int > a > $o ) > int ).
thf(func_def_184,type,
sK93: a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_185,type,
sK94: a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_186,type,
sK95: a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_187,type,
sK96: a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_188,type,
sK97: a > binary1439146945Tree_a > a ).
thf(func_def_189,type,
sK98: a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_190,type,
sK99: a > binary1439146945Tree_a > a ).
thf(func_def_191,type,
sK100: a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_192,type,
sK101: int > int ).
thf(func_def_193,type,
sK102: set_option_a > option_a ).
thf(func_def_194,type,
sK103: set_a > a ).
thf(func_def_195,type,
sK104: ( ( a > $o ) > set_a ) > a > $o ).
thf(func_def_196,type,
sK105: ( ( a > $o ) > set_a ) > a > $o ).
thf(func_def_197,type,
sK106: ( set_a > a > $o ) > set_a ).
thf(func_def_198,type,
sK107: ( set_a > a > $o ) > set_a ).
thf(func_def_199,type,
sK108: ( $o > $o ) > ( a > $o ) > ( a > $o ) > a ).
thf(func_def_200,type,
sK109: ( int > int > $o ) > int ).
thf(func_def_201,type,
sK110: ( int > int > $o ) > int ).
thf(func_def_202,type,
sK111: ( int > int > $o ) > int ).
thf(func_def_203,type,
sK112: ( int > int > $o ) > int ).
thf(func_def_204,type,
sK113: ( int > int > $o ) > int ).
thf(func_def_205,type,
sK114: option_a > set_option_a > set_option_a ).
thf(func_def_206,type,
sK115: set_option_a > option_a ).
thf(func_def_208,type,
sK117: set_a > a ).
thf(func_def_209,type,
sK118: set_a > set_a > a > a > set_a ).
thf(func_def_210,type,
sK119: option_a > a ).
thf(func_def_211,type,
sK120: set_a > a ).
thf(func_def_212,type,
sK121: option_a > a ).
thf(func_def_213,type,
sK122: ( a > $o ) > a ).
thf(func_def_214,type,
sK123: ( option_a > $o ) > option_a ).
thf(func_def_215,type,
sK124: set_a > a ).
thf(func_def_216,type,
sK125: ( a > $o ) > a ).
thf(func_def_217,type,
sK126: a > a ).
thf(func_def_218,type,
sK127: option_a > option_a ).
thf(f2701,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f1486]) ).
thf(f1486,plain,
( ( h @ x )
!= ( h @ x ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( h @ x )
!= ( h @ x ) ),
file('/export/starexec/sandbox2/tmp/tmp.A9HM2VC1Um/DTF2THF_27294.p',fact_4__092_060open_062h_Ax_A_092_060noteq_062_Ah_Ax_092_060close_062) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP030^1 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n016.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 08:24:21 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : ITP030^1 : TPTP v9.2.1. Released v7.5.0.
% 0.18/0.45 % Domain : Interactive Theorem Proving
% 0.18/0.45 % Problem : Sledgehammer BinaryTree problem prob_220__3252356_1
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.18/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Des21]
% 0.18/0.45 % Names : BinaryTree/prob_220__3252356_1 [Des21]
% 0.18/0.45
% 0.18/0.45 % Status : ContradictoryAxioms
% 0.18/0.45 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.23 v8.1.0, 0.36 v7.5.0
% 0.18/0.45 % Syntax : Number of formulae : 431 ( 180 unt; 76 typ; 0 def)
% 0.18/0.45 % Number of atoms : 964 ( 427 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 7 ( 2 avg)
% 0.18/0.45 % Number of connectives : 2559 ( 158 ~; 17 |; 59 &;1941 @)
% 0.18/0.45 % ( 0 <=>; 384 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 14 ( 6 avg)
% 0.18/0.45 % Number of types : 10 ( 9 usr)
% 0.18/0.45 % Number of type conns : 375 ( 375 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 70 ( 67 usr; 14 con; 0-4 aty)
% 0.18/0.45 % Number of variables : 963 ( 98 ^; 850 !; 15 ?; 963 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 15:30:19.933
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % Could-be-implicit typings (9)
% 0.18/0.45 thf(ty_n_t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_It__Option__Ooption_Itf__a_J_J,type,
% 0.18/0.45 binary1176601351tion_a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_J,type,
% 0.18/0.45 set_option_option_a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_Itf__a_J,type,
% 0.18/0.45 binary1439146945Tree_a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
% 0.18/0.45 option_option_a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
% 0.18/0.45 set_option_a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 option_a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.18/0.45 set_a: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_t__Int__Oint,type,
% 0.18/0.45 int: $tType ).
% 0.18/0.45
% 0.18/0.45 thf(ty_n_tf__a,type,
% 0.18/0.45 a: $tType ).
% 0.18/0.45
% 0.18/0.45 % Explicit typings (67)
% 0.18/0.45 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OT_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 binary1007279693tion_a: binary1176601351tion_a > option_a > binary1176601351tion_a > binary1176601351tion_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OT_001tf__a,type,
% 0.18/0.45 binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OTip_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 binary471442758tion_a: binary1176601351tion_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OTip_001tf__a,type,
% 0.18/0.45 binary476621312_Tip_a: binary1439146945Tree_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_Oset__Tree_001tf__a,type,
% 0.18/0.45 binary256242811Tree_a: binary1439146945Tree_a > set_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Oeqs_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 binary301690796tion_a: ( option_a > int ) > option_a > set_option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Oeqs_001tf__a,type,
% 0.18/0.45 binary504661350_eqs_a: ( a > int ) > a > set_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Omemb_001tf__a,type,
% 0.18/0.45 binary2053421120memb_a: ( a > int ) > a > binary1439146945Tree_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsetOf_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 binary1117200954tion_a: binary1176601351tion_a > set_option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsetOf_001tf__a,type,
% 0.18/0.45 binary945792244etOf_a: binary1439146945Tree_a > set_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsortedTree_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 binary995005080tion_a: ( option_a > int ) > binary1176601351tion_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsortedTree_001tf__a,type,
% 0.18/0.45 binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Osorted__distinct__pred_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 binary1691793817tion_a: ( option_a > int ) > option_a > option_a > binary1176601351tion_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Osorted__distinct__pred_001tf__a,type,
% 0.18/0.45 binary670562003pred_a: ( a > int ) > a > a > binary1439146945Tree_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Otlookup_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 binary1040190117tion_a: ( option_a > int ) > int > binary1176601351tion_a > option_option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Otlookup_001tf__a,type,
% 0.18/0.45 binary779405791okup_a: ( a > int ) > int > binary1439146945Tree_a > option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_HOL_OThe_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 the_option_a: ( option_a > $o ) > option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_HOL_OThe_001tf__a,type,
% 0.18/0.45 the_a: ( a > $o ) > a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_HOL_Oundefined_001tf__a,type,
% 0.18/0.45 undefined_a: a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Lattices_Osup__class_Osup_001_062_Itf__a_M_Eo_J,type,
% 0.18/0.45 sup_sup_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
% 0.18/0.45 sup_sup_set_option_a: set_option_a > set_option_a > set_option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__a_J,type,
% 0.18/0.45 sup_sup_set_a: set_a > set_a > set_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Option_Ooption_ONone_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 none_option_a: option_option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Option_Ooption_ONone_001tf__a,type,
% 0.18/0.45 none_a: option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Option_Ooption_OSome_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 some_option_a: option_a > option_option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Option_Ooption_OSome_001tf__a,type,
% 0.18/0.45 some_a: a > option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001tf__a,type,
% 0.18/0.45 case_option_o_a: $o > ( a > $o ) > option_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Option_Ooption_Ocase__option_001tf__a_001tf__a,type,
% 0.18/0.45 case_option_a_a: a > ( a > a ) > option_a > a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Option_Ooption_Oset__option_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 set_option_option_a2: option_option_a > set_option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Option_Ooption_Oset__option_001tf__a,type,
% 0.18/0.45 set_option_a2: option_a > set_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Option_Ooption_Othe_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 the_option_a2: option_option_a > option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Option_Ooption_Othe_001tf__a,type,
% 0.18/0.45 the_a2: option_a > a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Option_Othese_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 these_option_a: set_option_option_a > set_option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Option_Othese_001tf__a,type,
% 0.18/0.45 these_a: set_option_a > set_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J,type,
% 0.18/0.45 bot_bot_option_a_o: option_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__a_M_Eo_J,type,
% 0.18/0.45 bot_bot_a_o: a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
% 0.18/0.45 bot_bot_o: $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_J,type,
% 0.18/0.45 bot_bo1607647958tion_a: set_option_option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
% 0.18/0.45 bot_bot_set_option_a: set_option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 0.18/0.45 bot_bot_set_a: set_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Oord__class_Oless_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J,type,
% 0.18/0.45 ord_less_option_a_o: ( option_a > $o ) > ( option_a > $o ) > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Oord__class_Oless_001_062_Itf__a_M_Eo_J,type,
% 0.18/0.45 ord_less_a_o: ( a > $o ) > ( a > $o ) > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 0.18/0.45 ord_less_int: int > int > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
% 0.18/0.45 ord_le1280890064tion_a: set_option_a > set_option_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__a_J,type,
% 0.18/0.45 ord_less_set_a: set_a > set_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__a_J,type,
% 0.18/0.45 top_top_set_a: set_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_OCollect_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 collect_option_a: ( option_a > $o ) > set_option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.18/0.45 collect_a: ( a > $o ) > set_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Oimage_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 image_139503237tion_a: ( option_a > option_a ) > set_option_a > set_option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Oimage_001t__Option__Ooption_Itf__a_J_001tf__a,type,
% 0.18/0.45 image_option_a_a: ( option_a > a ) > set_option_a > set_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Oimage_001tf__a_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 image_a_option_a: ( a > option_a ) > set_a > set_option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Oimage_001tf__a_001tf__a,type,
% 0.18/0.45 image_a_a: ( a > a ) > set_a > set_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
% 0.18/0.45 insert1662731738tion_a: option_option_a > set_option_option_a > set_option_option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Oinsert_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 insert_option_a: option_a > set_option_a > set_option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Oinsert_001tf__a,type,
% 0.18/0.45 insert_a: a > set_a > set_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Ois__empty_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 is_empty_option_a: set_option_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Ois__empty_001tf__a,type,
% 0.18/0.45 is_empty_a: set_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Ois__singleton_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 is_sin1624444472tion_a: set_option_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Ois__singleton_001tf__a,type,
% 0.18/0.45 is_singleton_a: set_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Othe__elem_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 the_elem_option_a: set_option_a > option_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Set_Othe__elem_001tf__a,type,
% 0.18/0.45 the_elem_a: set_a > a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_member_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
% 0.18/0.45 member553679923tion_a: option_option_a > set_option_option_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_member_001t__Option__Ooption_Itf__a_J,type,
% 0.18/0.45 member_option_a: option_a > set_option_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_member_001tf__a,type,
% 0.18/0.45 member_a: a > set_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_h,type,
% 0.18/0.45 h: a > int ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_t,type,
% 0.18/0.45 t: binary1439146945Tree_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_x,type,
% 0.18/0.45 x: a ).
% 0.18/0.45
% 0.18/0.45 % Relevant facts (354)
% 0.18/0.45 thf(fact_0_h,axiom,
% 0.18/0.45 member_a @ x @ ( binary945792244etOf_a @ t ) ).
% 0.18/0.45
% 0.18/0.45 % h
% 0.18/0.45 thf(fact_1_sorted__distinct,axiom,
% 0.18/0.45 ! [H: a > int,A: a,B: a,T: binary1439146945Tree_a] : ( binary670562003pred_a @ H @ A @ B @ T ) ).
% 0.18/0.45
% 0.18/0.45 % sorted_distinct
% 0.18/0.45 thf(fact_2_s,axiom,
% 0.18/0.45 binary1721989714Tree_a @ h @ t ).
% 0.18/0.45
% 0.18/0.45 % s
% 0.18/0.45 thf(fact_3_res,axiom,
% 0.18/0.45 ~ ( binary2053421120memb_a @ h @ x @ t ) ).
% 0.18/0.45
% 0.18/0.45 % res
% 0.18/0.45 thf(fact_4__092_060open_062h_Ax_A_092_060noteq_062_Ah_Ax_092_060close_062,axiom,
% 0.18/0.45 ( ( h @ x )
% 0.18/0.45 != ( h @ x ) ) ).
% 0.18/0.45
% 0.18/0.45 % \<open>h x \<noteq> h x\<close>
% 0.18/0.45 thf(fact_5_o1,axiom,
% 0.18/0.45 ! [X: a] :
% 0.18/0.45 ( ( member_a @ X @ ( binary945792244etOf_a @ t ) )
% 0.18/0.45 => ( ( h @ X )
% 0.18/0.45 != ( h @ x ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % o1
% 0.18/0.45 thf(fact_6_sorted__distinct__pred__def,axiom,
% 0.18/0.45 ( binary1691793817tion_a
% 0.18/0.45 = ( ^ [H2: option_a > int,A2: option_a,B2: option_a,T2: binary1176601351tion_a] :
% 0.18/0.45 ( ( ( binary995005080tion_a @ H2 @ T2 )
% 0.18/0.45 & ( member_option_a @ A2 @ ( binary1117200954tion_a @ T2 ) )
% 0.18/0.45 & ( member_option_a @ B2 @ ( binary1117200954tion_a @ T2 ) )
% 0.18/0.45 & ( ( H2 @ A2 )
% 0.18/0.45 = ( H2 @ B2 ) ) )
% 0.18/0.45 => ( A2 = B2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sorted_distinct_pred_def
% 0.18/0.45 thf(fact_7_sorted__distinct__pred__def,axiom,
% 0.18/0.45 ( binary670562003pred_a
% 0.18/0.45 = ( ^ [H2: a > int,A2: a,B2: a,T2: binary1439146945Tree_a] :
% 0.18/0.45 ( ( ( binary1721989714Tree_a @ H2 @ T2 )
% 0.18/0.45 & ( member_a @ A2 @ ( binary945792244etOf_a @ T2 ) )
% 0.18/0.45 & ( member_a @ B2 @ ( binary945792244etOf_a @ T2 ) )
% 0.18/0.45 & ( ( H2 @ A2 )
% 0.18/0.45 = ( H2 @ B2 ) ) )
% 0.18/0.45 => ( A2 = B2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sorted_distinct_pred_def
% 0.18/0.45 thf(fact_8_tNone,axiom,
% 0.18/0.45 ( ( binary779405791okup_a @ h @ ( h @ x ) @ t )
% 0.18/0.45 = none_a ) ).
% 0.18/0.45
% 0.18/0.45 % tNone
% 0.18/0.45 thf(fact_9_sortedTree_Osimps_I1_J,axiom,
% 0.18/0.45 ! [H: a > int] : ( binary1721989714Tree_a @ H @ binary476621312_Tip_a ) ).
% 0.18/0.45
% 0.18/0.45 % sortedTree.simps(1)
% 0.18/0.45 thf(fact_10_sortLemmaL,axiom,
% 0.18/0.45 ! [H: a > int,T1: binary1439146945Tree_a,X2: a,T22: binary1439146945Tree_a] :
% 0.18/0.45 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X2 @ T22 ) )
% 0.18/0.45 => ( binary1721989714Tree_a @ H @ T1 ) ) ).
% 0.18/0.45
% 0.18/0.45 % sortLemmaL
% 0.18/0.45 thf(fact_11_sortLemmaR,axiom,
% 0.18/0.45 ! [H: a > int,T1: binary1439146945Tree_a,X2: a,T22: binary1439146945Tree_a] :
% 0.18/0.45 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X2 @ T22 ) )
% 0.18/0.45 => ( binary1721989714Tree_a @ H @ T22 ) ) ).
% 0.18/0.45
% 0.18/0.45 % sortLemmaR
% 0.18/0.45 thf(fact_12_tlookup__none,axiom,
% 0.18/0.45 ! [H: a > int,T: binary1439146945Tree_a,K: int] :
% 0.18/0.45 ( ( ( binary1721989714Tree_a @ H @ T )
% 0.18/0.45 & ( ( binary779405791okup_a @ H @ K @ T )
% 0.18/0.45 = none_a ) )
% 0.18/0.45 => ! [X: a] :
% 0.18/0.45 ( ( member_a @ X @ ( binary945792244etOf_a @ T ) )
% 0.18/0.45 => ( ( H @ X )
% 0.18/0.45 != K ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % tlookup_none
% 0.18/0.45 thf(fact_13_tlookup__some,axiom,
% 0.18/0.45 ! [H: option_a > int,T: binary1176601351tion_a,K: int,X2: option_a] :
% 0.18/0.45 ( ( ( binary995005080tion_a @ H @ T )
% 0.18/0.45 & ( ( binary1040190117tion_a @ H @ K @ T )
% 0.18/0.45 = ( some_option_a @ X2 ) ) )
% 0.18/0.45 => ( ( member_option_a @ X2 @ ( binary1117200954tion_a @ T ) )
% 0.18/0.45 & ( ( H @ X2 )
% 0.18/0.45 = K ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % tlookup_some
% 0.18/0.45 thf(fact_14_tlookup__some,axiom,
% 0.18/0.45 ! [H: a > int,T: binary1439146945Tree_a,K: int,X2: a] :
% 0.18/0.45 ( ( ( binary1721989714Tree_a @ H @ T )
% 0.18/0.45 & ( ( binary779405791okup_a @ H @ K @ T )
% 0.18/0.45 = ( some_a @ X2 ) ) )
% 0.18/0.45 => ( ( member_a @ X2 @ ( binary945792244etOf_a @ T ) )
% 0.18/0.45 & ( ( H @ X2 )
% 0.18/0.45 = K ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % tlookup_some
% 0.18/0.45 thf(fact_15_tlookup__finds,axiom,
% 0.18/0.45 ! [H: option_a > int,T: binary1176601351tion_a,Y: option_a] :
% 0.18/0.45 ( ( ( binary995005080tion_a @ H @ T )
% 0.18/0.45 & ( member_option_a @ Y @ ( binary1117200954tion_a @ T ) ) )
% 0.18/0.45 => ( ( binary1040190117tion_a @ H @ ( H @ Y ) @ T )
% 0.18/0.45 = ( some_option_a @ Y ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % tlookup_finds
% 0.18/0.45 thf(fact_16_tlookup__finds,axiom,
% 0.18/0.45 ! [H: a > int,T: binary1439146945Tree_a,Y: a] :
% 0.18/0.45 ( ( ( binary1721989714Tree_a @ H @ T )
% 0.18/0.45 & ( member_a @ Y @ ( binary945792244etOf_a @ T ) ) )
% 0.18/0.45 => ( ( binary779405791okup_a @ H @ ( H @ Y ) @ T )
% 0.18/0.45 = ( some_a @ Y ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % tlookup_finds
% 0.18/0.45 thf(fact_17_sortedTree_Osimps_I2_J,axiom,
% 0.18/0.45 ! [H: a > int,T1: binary1439146945Tree_a,X2: a,T22: binary1439146945Tree_a] :
% 0.18/0.45 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X2 @ T22 ) )
% 0.18/0.45 = ( ( binary1721989714Tree_a @ H @ T1 )
% 0.18/0.45 & ! [X3: a] :
% 0.18/0.45 ( ( member_a @ X3 @ ( binary945792244etOf_a @ T1 ) )
% 0.18/0.45 => ( ord_less_int @ ( H @ X3 ) @ ( H @ X2 ) ) )
% 0.18/0.45 & ! [X3: a] :
% 0.18/0.45 ( ( member_a @ X3 @ ( binary945792244etOf_a @ T22 ) )
% 0.18/0.45 => ( ord_less_int @ ( H @ X2 ) @ ( H @ X3 ) ) )
% 0.18/0.45 & ( binary1721989714Tree_a @ H @ T22 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sortedTree.simps(2)
% 0.18/0.45 thf(fact_18_setOf_Osimps_I1_J,axiom,
% 0.18/0.45 ( ( binary1117200954tion_a @ binary471442758tion_a )
% 0.18/0.45 = bot_bot_set_option_a ) ).
% 0.18/0.45
% 0.18/0.45 % setOf.simps(1)
% 0.18/0.45 thf(fact_19_setOf_Osimps_I1_J,axiom,
% 0.18/0.45 ( ( binary945792244etOf_a @ binary476621312_Tip_a )
% 0.18/0.45 = bot_bot_set_a ) ).
% 0.18/0.45
% 0.18/0.45 % setOf.simps(1)
% 0.18/0.45 thf(fact_20_memb__def,axiom,
% 0.18/0.45 ( binary2053421120memb_a
% 0.18/0.45 = ( ^ [H2: a > int,X3: a,T2: binary1439146945Tree_a] :
% 0.18/0.45 ( case_option_o_a @ $false
% 0.18/0.45 @ ( ^ [Y2: a,Z: a] : ( Y2 = Z )
% 0.18/0.45 @ X3 )
% 0.18/0.45 @ ( binary779405791okup_a @ H2 @ ( H2 @ X3 ) @ T2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % memb_def
% 0.18/0.45 thf(fact_21_Tree_Oinject,axiom,
% 0.18/0.45 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a,Y21: binary1439146945Tree_a,Y22: a,Y23: binary1439146945Tree_a] :
% 0.18/0.45 ( ( ( binary717961607le_T_a @ X21 @ X22 @ X23 )
% 0.18/0.45 = ( binary717961607le_T_a @ Y21 @ Y22 @ Y23 ) )
% 0.18/0.45 = ( ( X21 = Y21 )
% 0.18/0.45 & ( X22 = Y22 )
% 0.18/0.45 & ( X23 = Y23 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Tree.inject
% 0.18/0.45 thf(fact_22_Tree_Oexhaust,axiom,
% 0.18/0.45 ! [Y: binary1439146945Tree_a] :
% 0.18/0.45 ( ( Y != binary476621312_Tip_a )
% 0.18/0.45 => ~ ! [X212: binary1439146945Tree_a,X222: a,X232: binary1439146945Tree_a] :
% 0.18/0.45 ( Y
% 0.18/0.45 != ( binary717961607le_T_a @ X212 @ X222 @ X232 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Tree.exhaust
% 0.18/0.45 thf(fact_23_Tree_Oinduct,axiom,
% 0.18/0.45 ! [P: binary1439146945Tree_a > $o,Tree: binary1439146945Tree_a] :
% 0.18/0.45 ( ( P @ binary476621312_Tip_a )
% 0.18/0.45 => ( ! [X1: binary1439146945Tree_a,X24: a,X32: binary1439146945Tree_a] :
% 0.18/0.45 ( ( P @ X1 )
% 0.18/0.45 => ( ( P @ X32 )
% 0.18/0.45 => ( P @ ( binary717961607le_T_a @ X1 @ X24 @ X32 ) ) ) )
% 0.18/0.45 => ( P @ Tree ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Tree.induct
% 0.18/0.45 thf(fact_24_tlookup_Osimps_I1_J,axiom,
% 0.18/0.45 ! [H: a > int,K: int] :
% 0.18/0.45 ( ( binary779405791okup_a @ H @ K @ binary476621312_Tip_a )
% 0.18/0.45 = none_a ) ).
% 0.18/0.45
% 0.18/0.45 % tlookup.simps(1)
% 0.18/0.45 thf(fact_25_tlookup_Osimps_I2_J,axiom,
% 0.18/0.45 ! [K: int,H: a > int,X2: a,T1: binary1439146945Tree_a,T22: binary1439146945Tree_a] :
% 0.18/0.45 ( ( ( ord_less_int @ K @ ( H @ X2 ) )
% 0.18/0.45 => ( ( binary779405791okup_a @ H @ K @ ( binary717961607le_T_a @ T1 @ X2 @ T22 ) )
% 0.18/0.45 = ( binary779405791okup_a @ H @ K @ T1 ) ) )
% 0.18/0.45 & ( ~ ( ord_less_int @ K @ ( H @ X2 ) )
% 0.18/0.45 => ( ( ( ord_less_int @ ( H @ X2 ) @ K )
% 0.18/0.45 => ( ( binary779405791okup_a @ H @ K @ ( binary717961607le_T_a @ T1 @ X2 @ T22 ) )
% 0.18/0.45 = ( binary779405791okup_a @ H @ K @ T22 ) ) )
% 0.18/0.45 & ( ~ ( ord_less_int @ ( H @ X2 ) @ K )
% 0.18/0.45 => ( ( binary779405791okup_a @ H @ K @ ( binary717961607le_T_a @ T1 @ X2 @ T22 ) )
% 0.18/0.45 = ( some_a @ X2 ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % tlookup.simps(2)
% 0.18/0.45 thf(fact_26_Tree_Odistinct_I1_J,axiom,
% 0.18/0.45 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 0.18/0.45 ( binary476621312_Tip_a
% 0.18/0.45 != ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ).
% 0.18/0.45
% 0.18/0.45 % Tree.distinct(1)
% 0.18/0.45 thf(fact_27_not__Some__eq,axiom,
% 0.18/0.45 ! [X2: option_a] :
% 0.18/0.45 ( ( ! [Y3: a] :
% 0.18/0.45 ( X2
% 0.18/0.45 != ( some_a @ Y3 ) ) )
% 0.18/0.45 = ( X2 = none_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % not_Some_eq
% 0.18/0.45 thf(fact_28_not__None__eq,axiom,
% 0.18/0.45 ! [X2: option_a] :
% 0.18/0.45 ( ( X2 != none_a )
% 0.18/0.45 = ( ? [Y3: a] :
% 0.18/0.45 ( X2
% 0.18/0.45 = ( some_a @ Y3 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % not_None_eq
% 0.18/0.45 thf(fact_29_case__optionE,axiom,
% 0.18/0.45 ! [P: $o,Q: a > $o,X2: option_a] :
% 0.18/0.45 ( ( case_option_o_a @ P @ Q @ X2 )
% 0.18/0.45 => ( ( ( X2 = none_a )
% 0.18/0.45 => ~ P )
% 0.18/0.45 => ~ ! [Y4: a] :
% 0.18/0.45 ( ( X2
% 0.18/0.45 = ( some_a @ Y4 ) )
% 0.18/0.45 => ~ ( Q @ Y4 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % case_optionE
% 0.18/0.45 thf(fact_30_disjE__realizer2,axiom,
% 0.18/0.45 ! [P: $o,Q: a > $o,X2: option_a,R: $o > $o,F: $o,G: a > $o] :
% 0.18/0.45 ( ( case_option_o_a @ P @ Q @ X2 )
% 0.18/0.45 => ( ( P
% 0.18/0.45 => ( R @ F ) )
% 0.18/0.45 => ( ! [Q2: a] :
% 0.18/0.45 ( ( Q @ Q2 )
% 0.18/0.45 => ( R @ ( G @ Q2 ) ) )
% 0.18/0.45 => ( R @ ( case_option_o_a @ F @ G @ X2 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % disjE_realizer2
% 0.18/0.45 thf(fact_31_option_Odisc__eq__case_I1_J,axiom,
% 0.18/0.45 ! [Option: option_a] :
% 0.18/0.45 ( ( Option = none_a )
% 0.18/0.45 = ( case_option_o_a @ $true
% 0.18/0.45 @ ^ [Uu: a] : $false
% 0.18/0.45 @ Option ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.disc_eq_case(1)
% 0.18/0.45 thf(fact_32_option_Odisc__eq__case_I2_J,axiom,
% 0.18/0.45 ! [Option: option_a] :
% 0.18/0.45 ( ( Option != none_a )
% 0.18/0.45 = ( case_option_o_a @ $false
% 0.18/0.45 @ ^ [Uu: a] : $true
% 0.18/0.45 @ Option ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.disc_eq_case(2)
% 0.18/0.45 thf(fact_33_option_Oinject,axiom,
% 0.18/0.45 ! [X25: a,Y24: a] :
% 0.18/0.45 ( ( ( some_a @ X25 )
% 0.18/0.45 = ( some_a @ Y24 ) )
% 0.18/0.45 = ( X25 = Y24 ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.inject
% 0.18/0.45 thf(fact_34_empty__Collect__eq,axiom,
% 0.18/0.45 ! [P: a > $o] :
% 0.18/0.45 ( ( bot_bot_set_a
% 0.18/0.45 = ( collect_a @ P ) )
% 0.18/0.45 = ( ! [X3: a] :
% 0.18/0.45 ~ ( P @ X3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % empty_Collect_eq
% 0.18/0.45 thf(fact_35_empty__Collect__eq,axiom,
% 0.18/0.45 ! [P: option_a > $o] :
% 0.18/0.45 ( ( bot_bot_set_option_a
% 0.18/0.45 = ( collect_option_a @ P ) )
% 0.18/0.45 = ( ! [X3: option_a] :
% 0.18/0.45 ~ ( P @ X3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % empty_Collect_eq
% 0.18/0.45 thf(fact_36_Collect__empty__eq,axiom,
% 0.18/0.45 ! [P: a > $o] :
% 0.18/0.45 ( ( ( collect_a @ P )
% 0.18/0.45 = bot_bot_set_a )
% 0.18/0.45 = ( ! [X3: a] :
% 0.18/0.45 ~ ( P @ X3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Collect_empty_eq
% 0.18/0.45 thf(fact_37_Collect__empty__eq,axiom,
% 0.18/0.45 ! [P: option_a > $o] :
% 0.18/0.45 ( ( ( collect_option_a @ P )
% 0.18/0.45 = bot_bot_set_option_a )
% 0.18/0.45 = ( ! [X3: option_a] :
% 0.18/0.45 ~ ( P @ X3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Collect_empty_eq
% 0.18/0.45 thf(fact_38_all__not__in__conv,axiom,
% 0.18/0.45 ! [A3: set_option_a] :
% 0.18/0.45 ( ( ! [X3: option_a] :
% 0.18/0.45 ~ ( member_option_a @ X3 @ A3 ) )
% 0.18/0.45 = ( A3 = bot_bot_set_option_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % all_not_in_conv
% 0.18/0.45 thf(fact_39_all__not__in__conv,axiom,
% 0.18/0.45 ! [A3: set_a] :
% 0.18/0.45 ( ( ! [X3: a] :
% 0.18/0.45 ~ ( member_a @ X3 @ A3 ) )
% 0.18/0.45 = ( A3 = bot_bot_set_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % all_not_in_conv
% 0.18/0.45 thf(fact_40_empty__iff,axiom,
% 0.18/0.45 ! [C: option_a] :
% 0.18/0.45 ~ ( member_option_a @ C @ bot_bot_set_option_a ) ).
% 0.18/0.45
% 0.18/0.45 % empty_iff
% 0.18/0.45 thf(fact_41_empty__iff,axiom,
% 0.18/0.45 ! [C: a] :
% 0.18/0.45 ~ ( member_a @ C @ bot_bot_set_a ) ).
% 0.18/0.45
% 0.18/0.45 % empty_iff
% 0.18/0.45 thf(fact_42_emptyE,axiom,
% 0.18/0.45 ! [A: option_a] :
% 0.18/0.45 ~ ( member_option_a @ A @ bot_bot_set_option_a ) ).
% 0.18/0.45
% 0.18/0.45 % emptyE
% 0.18/0.45 thf(fact_43_emptyE,axiom,
% 0.18/0.45 ! [A: a] :
% 0.18/0.45 ~ ( member_a @ A @ bot_bot_set_a ) ).
% 0.18/0.45
% 0.18/0.45 % emptyE
% 0.18/0.45 thf(fact_44_equals0D,axiom,
% 0.18/0.45 ! [A3: set_option_a,A: option_a] :
% 0.18/0.45 ( ( A3 = bot_bot_set_option_a )
% 0.18/0.45 => ~ ( member_option_a @ A @ A3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % equals0D
% 0.18/0.45 thf(fact_45_equals0D,axiom,
% 0.18/0.45 ! [A3: set_a,A: a] :
% 0.18/0.45 ( ( A3 = bot_bot_set_a )
% 0.18/0.45 => ~ ( member_a @ A @ A3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % equals0D
% 0.18/0.45 thf(fact_46_equals0I,axiom,
% 0.18/0.45 ! [A3: set_option_a] :
% 0.18/0.45 ( ! [Y4: option_a] :
% 0.18/0.45 ~ ( member_option_a @ Y4 @ A3 )
% 0.18/0.45 => ( A3 = bot_bot_set_option_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % equals0I
% 0.18/0.45 thf(fact_47_equals0I,axiom,
% 0.18/0.45 ! [A3: set_a] :
% 0.18/0.45 ( ! [Y4: a] :
% 0.18/0.45 ~ ( member_a @ Y4 @ A3 )
% 0.18/0.45 => ( A3 = bot_bot_set_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % equals0I
% 0.18/0.45 thf(fact_48_ex__in__conv,axiom,
% 0.18/0.45 ! [A3: set_option_a] :
% 0.18/0.45 ( ( ? [X3: option_a] : ( member_option_a @ X3 @ A3 ) )
% 0.18/0.45 = ( A3 != bot_bot_set_option_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % ex_in_conv
% 0.18/0.45 thf(fact_49_ex__in__conv,axiom,
% 0.18/0.45 ! [A3: set_a] :
% 0.18/0.45 ( ( ? [X3: a] : ( member_a @ X3 @ A3 ) )
% 0.18/0.45 = ( A3 != bot_bot_set_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % ex_in_conv
% 0.18/0.45 thf(fact_50_empty__def,axiom,
% 0.18/0.45 ( bot_bot_set_a
% 0.18/0.45 = ( collect_a
% 0.18/0.45 @ ^ [X3: a] : $false ) ) ).
% 0.18/0.45
% 0.18/0.45 % empty_def
% 0.18/0.45 thf(fact_51_empty__def,axiom,
% 0.18/0.45 ( bot_bot_set_option_a
% 0.18/0.45 = ( collect_option_a
% 0.18/0.45 @ ^ [X3: option_a] : $false ) ) ).
% 0.18/0.45
% 0.18/0.45 % empty_def
% 0.18/0.45 thf(fact_52_option_Ocase__distrib,axiom,
% 0.18/0.45 ! [H: $o > $o,F1: $o,F2: a > $o,Option: option_a] :
% 0.18/0.45 ( ( H @ ( case_option_o_a @ F1 @ F2 @ Option ) )
% 0.18/0.45 = ( case_option_o_a @ ( H @ F1 )
% 0.18/0.45 @ ^ [X3: a] : ( H @ ( F2 @ X3 ) )
% 0.18/0.45 @ Option ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.case_distrib
% 0.18/0.45 thf(fact_53_option_Odistinct_I1_J,axiom,
% 0.18/0.45 ! [X25: a] :
% 0.18/0.45 ( none_a
% 0.18/0.45 != ( some_a @ X25 ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.distinct(1)
% 0.18/0.45 thf(fact_54_option_OdiscI,axiom,
% 0.18/0.45 ! [Option: option_a,X25: a] :
% 0.18/0.45 ( ( Option
% 0.18/0.45 = ( some_a @ X25 ) )
% 0.18/0.45 => ( Option != none_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.discI
% 0.18/0.45 thf(fact_55_option_Oexhaust,axiom,
% 0.18/0.45 ! [Y: option_a] :
% 0.18/0.45 ( ( Y != none_a )
% 0.18/0.45 => ~ ! [X24: a] :
% 0.18/0.45 ( Y
% 0.18/0.45 != ( some_a @ X24 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.exhaust
% 0.18/0.45 thf(fact_56_option_Oinducts,axiom,
% 0.18/0.45 ! [P: option_a > $o,Option: option_a] :
% 0.18/0.45 ( ( P @ none_a )
% 0.18/0.45 => ( ! [X4: a] : ( P @ ( some_a @ X4 ) )
% 0.18/0.45 => ( P @ Option ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.inducts
% 0.18/0.45 thf(fact_57_mem__Collect__eq,axiom,
% 0.18/0.45 ! [A: option_a,P: option_a > $o] :
% 0.18/0.45 ( ( member_option_a @ A @ ( collect_option_a @ P ) )
% 0.18/0.45 = ( P @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % mem_Collect_eq
% 0.18/0.45 thf(fact_58_mem__Collect__eq,axiom,
% 0.18/0.45 ! [A: a,P: a > $o] :
% 0.18/0.45 ( ( member_a @ A @ ( collect_a @ P ) )
% 0.18/0.45 = ( P @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % mem_Collect_eq
% 0.18/0.45 thf(fact_59_Collect__mem__eq,axiom,
% 0.18/0.45 ! [A3: set_option_a] :
% 0.18/0.45 ( ( collect_option_a
% 0.18/0.45 @ ^ [X3: option_a] : ( member_option_a @ X3 @ A3 ) )
% 0.18/0.45 = A3 ) ).
% 0.18/0.45
% 0.18/0.45 % Collect_mem_eq
% 0.18/0.45 thf(fact_60_Collect__mem__eq,axiom,
% 0.18/0.45 ! [A3: set_a] :
% 0.18/0.45 ( ( collect_a
% 0.18/0.45 @ ^ [X3: a] : ( member_a @ X3 @ A3 ) )
% 0.18/0.45 = A3 ) ).
% 0.18/0.45
% 0.18/0.45 % Collect_mem_eq
% 0.18/0.45 thf(fact_61_Collect__cong,axiom,
% 0.18/0.45 ! [P: a > $o,Q: a > $o] :
% 0.18/0.45 ( ! [X4: a] :
% 0.18/0.45 ( ( P @ X4 )
% 0.18/0.45 = ( Q @ X4 ) )
% 0.18/0.45 => ( ( collect_a @ P )
% 0.18/0.45 = ( collect_a @ Q ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Collect_cong
% 0.18/0.45 thf(fact_62_Collect__cong,axiom,
% 0.18/0.45 ! [P: option_a > $o,Q: option_a > $o] :
% 0.18/0.45 ( ! [X4: option_a] :
% 0.18/0.45 ( ( P @ X4 )
% 0.18/0.45 = ( Q @ X4 ) )
% 0.18/0.45 => ( ( collect_option_a @ P )
% 0.18/0.45 = ( collect_option_a @ Q ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Collect_cong
% 0.18/0.45 thf(fact_63_split__option__ex,axiom,
% 0.18/0.45 ( ( ^ [P2: option_a > $o] :
% 0.18/0.45 ? [X5: option_a] : ( P2 @ X5 ) )
% 0.18/0.45 = ( ^ [P3: option_a > $o] :
% 0.18/0.45 ( ( P3 @ none_a )
% 0.18/0.45 | ? [X3: a] : ( P3 @ ( some_a @ X3 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % split_option_ex
% 0.18/0.45 thf(fact_64_split__option__all,axiom,
% 0.18/0.45 ( ( ^ [P2: option_a > $o] :
% 0.18/0.45 ! [X5: option_a] : ( P2 @ X5 ) )
% 0.18/0.45 = ( ^ [P3: option_a > $o] :
% 0.18/0.45 ( ( P3 @ none_a )
% 0.18/0.45 & ! [X3: a] : ( P3 @ ( some_a @ X3 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % split_option_all
% 0.18/0.45 thf(fact_65_combine__options__cases,axiom,
% 0.18/0.45 ! [X2: option_a,P: option_a > option_a > $o,Y: option_a] :
% 0.18/0.45 ( ( ( X2 = none_a )
% 0.18/0.45 => ( P @ X2 @ Y ) )
% 0.18/0.45 => ( ( ( Y = none_a )
% 0.18/0.45 => ( P @ X2 @ Y ) )
% 0.18/0.45 => ( ! [A4: a,B3: a] :
% 0.18/0.45 ( ( X2
% 0.18/0.45 = ( some_a @ A4 ) )
% 0.18/0.45 => ( ( Y
% 0.18/0.45 = ( some_a @ B3 ) )
% 0.18/0.45 => ( P @ X2 @ Y ) ) )
% 0.18/0.45 => ( P @ X2 @ Y ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % combine_options_cases
% 0.18/0.45 thf(fact_66_option_Osimps_I4_J,axiom,
% 0.18/0.45 ! [F1: $o,F2: a > $o] :
% 0.18/0.45 ( ( case_option_o_a @ F1 @ F2 @ none_a )
% 0.18/0.45 = F1 ) ).
% 0.18/0.45
% 0.18/0.45 % option.simps(4)
% 0.18/0.45 thf(fact_67_option_Osimps_I5_J,axiom,
% 0.18/0.45 ! [F1: $o,F2: a > $o,X25: a] :
% 0.18/0.45 ( ( case_option_o_a @ F1 @ F2 @ ( some_a @ X25 ) )
% 0.18/0.45 = ( F2 @ X25 ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.simps(5)
% 0.18/0.45 thf(fact_68_bot__apply,axiom,
% 0.18/0.45 ( bot_bot_a_o
% 0.18/0.45 = ( ^ [X3: a] : bot_bot_o ) ) ).
% 0.18/0.45
% 0.18/0.45 % bot_apply
% 0.18/0.45 thf(fact_69_bot_Oextremum__strict,axiom,
% 0.18/0.45 ! [A: set_option_a] :
% 0.18/0.45 ~ ( ord_le1280890064tion_a @ A @ bot_bot_set_option_a ) ).
% 0.18/0.45
% 0.18/0.45 % bot.extremum_strict
% 0.18/0.45 thf(fact_70_bot_Oextremum__strict,axiom,
% 0.18/0.45 ! [A: set_a] :
% 0.18/0.45 ~ ( ord_less_set_a @ A @ bot_bot_set_a ) ).
% 0.18/0.45
% 0.18/0.45 % bot.extremum_strict
% 0.18/0.45 thf(fact_71_bot_Oextremum__strict,axiom,
% 0.18/0.45 ! [A: a > $o] :
% 0.18/0.45 ~ ( ord_less_a_o @ A @ bot_bot_a_o ) ).
% 0.18/0.45
% 0.18/0.45 % bot.extremum_strict
% 0.18/0.45 thf(fact_72_bot_Onot__eq__extremum,axiom,
% 0.18/0.45 ! [A: set_option_a] :
% 0.18/0.45 ( ( A != bot_bot_set_option_a )
% 0.18/0.45 = ( ord_le1280890064tion_a @ bot_bot_set_option_a @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % bot.not_eq_extremum
% 0.18/0.45 thf(fact_73_bot_Onot__eq__extremum,axiom,
% 0.18/0.45 ! [A: set_a] :
% 0.18/0.45 ( ( A != bot_bot_set_a )
% 0.18/0.45 = ( ord_less_set_a @ bot_bot_set_a @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % bot.not_eq_extremum
% 0.18/0.45 thf(fact_74_bot_Onot__eq__extremum,axiom,
% 0.18/0.45 ! [A: a > $o] :
% 0.18/0.45 ( ( A != bot_bot_a_o )
% 0.18/0.45 = ( ord_less_a_o @ bot_bot_a_o @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % bot.not_eq_extremum
% 0.18/0.45 thf(fact_75_Set_Ois__empty__def,axiom,
% 0.18/0.45 ( is_empty_a
% 0.18/0.45 = ( ^ [A5: set_a] : ( A5 = bot_bot_set_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Set.is_empty_def
% 0.18/0.45 thf(fact_76_Set_Ois__empty__def,axiom,
% 0.18/0.45 ( is_empty_option_a
% 0.18/0.45 = ( ^ [A5: set_option_a] : ( A5 = bot_bot_set_option_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Set.is_empty_def
% 0.18/0.45 thf(fact_77_eqs__def,axiom,
% 0.18/0.45 ( binary504661350_eqs_a
% 0.18/0.45 = ( ^ [H2: a > int,X3: a] :
% 0.18/0.45 ( collect_a
% 0.18/0.45 @ ^ [Y3: a] :
% 0.18/0.45 ( ( H2 @ Y3 )
% 0.18/0.45 = ( H2 @ X3 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % eqs_def
% 0.18/0.45 thf(fact_78_eqs__def,axiom,
% 0.18/0.45 ( binary301690796tion_a
% 0.18/0.45 = ( ^ [H2: option_a > int,X3: option_a] :
% 0.18/0.45 ( collect_option_a
% 0.18/0.45 @ ^ [Y3: option_a] :
% 0.18/0.45 ( ( H2 @ Y3 )
% 0.18/0.45 = ( H2 @ X3 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % eqs_def
% 0.18/0.45 thf(fact_79_option_Osplit__sel,axiom,
% 0.18/0.45 ! [P: $o > $o,F1: $o,F2: a > $o,Option: option_a] :
% 0.18/0.45 ( ( P @ ( case_option_o_a @ F1 @ F2 @ Option ) )
% 0.18/0.45 = ( ( ( Option = none_a )
% 0.18/0.45 => ( P @ F1 ) )
% 0.18/0.45 & ( ( Option
% 0.18/0.45 = ( some_a @ ( the_a2 @ Option ) ) )
% 0.18/0.45 => ( P @ ( F2 @ ( the_a2 @ Option ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.split_sel
% 0.18/0.45 thf(fact_80_option_Osplit__sel__asm,axiom,
% 0.18/0.45 ! [P: $o > $o,F1: $o,F2: a > $o,Option: option_a] :
% 0.18/0.45 ( ( P @ ( case_option_o_a @ F1 @ F2 @ Option ) )
% 0.18/0.45 = ( ~ ( ( ( Option = none_a )
% 0.18/0.45 & ~ ( P @ F1 ) )
% 0.18/0.45 | ( ( Option
% 0.18/0.45 = ( some_a @ ( the_a2 @ Option ) ) )
% 0.18/0.45 & ~ ( P @ ( F2 @ ( the_a2 @ Option ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.split_sel_asm
% 0.18/0.45 thf(fact_81_set__empty__eq,axiom,
% 0.18/0.45 ! [Xo: option_option_a] :
% 0.18/0.45 ( ( ( set_option_option_a2 @ Xo )
% 0.18/0.45 = bot_bot_set_option_a )
% 0.18/0.45 = ( Xo = none_option_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % set_empty_eq
% 0.18/0.45 thf(fact_82_set__empty__eq,axiom,
% 0.18/0.45 ! [Xo: option_a] :
% 0.18/0.45 ( ( ( set_option_a2 @ Xo )
% 0.18/0.45 = bot_bot_set_a )
% 0.18/0.45 = ( Xo = none_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % set_empty_eq
% 0.18/0.45 thf(fact_83_bot__fun__def,axiom,
% 0.18/0.45 ( bot_bot_a_o
% 0.18/0.45 = ( ^ [X3: a] : bot_bot_o ) ) ).
% 0.18/0.45
% 0.18/0.45 % bot_fun_def
% 0.18/0.45 thf(fact_84_elem__set,axiom,
% 0.18/0.45 ! [X2: option_a,Xo: option_option_a] :
% 0.18/0.45 ( ( member_option_a @ X2 @ ( set_option_option_a2 @ Xo ) )
% 0.18/0.45 = ( Xo
% 0.18/0.45 = ( some_option_a @ X2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % elem_set
% 0.18/0.45 thf(fact_85_elem__set,axiom,
% 0.18/0.45 ! [X2: a,Xo: option_a] :
% 0.18/0.45 ( ( member_a @ X2 @ ( set_option_a2 @ Xo ) )
% 0.18/0.45 = ( Xo
% 0.18/0.45 = ( some_a @ X2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % elem_set
% 0.18/0.45 thf(fact_86_option_Ocollapse,axiom,
% 0.18/0.45 ! [Option: option_a] :
% 0.18/0.45 ( ( Option != none_a )
% 0.18/0.45 => ( ( some_a @ ( the_a2 @ Option ) )
% 0.18/0.45 = Option ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.collapse
% 0.18/0.45 thf(fact_87_option_Oset__sel,axiom,
% 0.18/0.45 ! [A: option_option_a] :
% 0.18/0.45 ( ( A != none_option_a )
% 0.18/0.45 => ( member_option_a @ ( the_option_a2 @ A ) @ ( set_option_option_a2 @ A ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.set_sel
% 0.18/0.45 thf(fact_88_option_Oset__sel,axiom,
% 0.18/0.45 ! [A: option_a] :
% 0.18/0.45 ( ( A != none_a )
% 0.18/0.45 => ( member_a @ ( the_a2 @ A ) @ ( set_option_a2 @ A ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.set_sel
% 0.18/0.45 thf(fact_89_bot__set__def,axiom,
% 0.18/0.45 ( bot_bot_set_a
% 0.18/0.45 = ( collect_a @ bot_bot_a_o ) ) ).
% 0.18/0.45
% 0.18/0.45 % bot_set_def
% 0.18/0.45 thf(fact_90_bot__set__def,axiom,
% 0.18/0.45 ( bot_bot_set_option_a
% 0.18/0.45 = ( collect_option_a @ bot_bot_option_a_o ) ) ).
% 0.18/0.45
% 0.18/0.45 % bot_set_def
% 0.18/0.45 thf(fact_91_not__psubset__empty,axiom,
% 0.18/0.45 ! [A3: set_option_a] :
% 0.18/0.45 ~ ( ord_le1280890064tion_a @ A3 @ bot_bot_set_option_a ) ).
% 0.18/0.45
% 0.18/0.45 % not_psubset_empty
% 0.18/0.45 thf(fact_92_not__psubset__empty,axiom,
% 0.18/0.45 ! [A3: set_a] :
% 0.18/0.45 ~ ( ord_less_set_a @ A3 @ bot_bot_set_a ) ).
% 0.18/0.45
% 0.18/0.45 % not_psubset_empty
% 0.18/0.45 thf(fact_93_option_Oexpand,axiom,
% 0.18/0.45 ! [Option: option_a,Option2: option_a] :
% 0.18/0.45 ( ( ( Option = none_a )
% 0.18/0.45 = ( Option2 = none_a ) )
% 0.18/0.45 => ( ( ( Option != none_a )
% 0.18/0.45 => ( ( Option2 != none_a )
% 0.18/0.45 => ( ( the_a2 @ Option )
% 0.18/0.45 = ( the_a2 @ Option2 ) ) ) )
% 0.18/0.45 => ( Option = Option2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.expand
% 0.18/0.45 thf(fact_94_option_Osel,axiom,
% 0.18/0.45 ! [X25: a] :
% 0.18/0.45 ( ( the_a2 @ ( some_a @ X25 ) )
% 0.18/0.45 = X25 ) ).
% 0.18/0.45
% 0.18/0.45 % option.sel
% 0.18/0.45 thf(fact_95_option_Oset__intros,axiom,
% 0.18/0.45 ! [X25: option_a] : ( member_option_a @ X25 @ ( set_option_option_a2 @ ( some_option_a @ X25 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.set_intros
% 0.18/0.45 thf(fact_96_option_Oset__intros,axiom,
% 0.18/0.45 ! [X25: a] : ( member_a @ X25 @ ( set_option_a2 @ ( some_a @ X25 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.set_intros
% 0.18/0.45 thf(fact_97_option_Oset__cases,axiom,
% 0.18/0.45 ! [E: option_a,A: option_option_a] :
% 0.18/0.45 ( ( member_option_a @ E @ ( set_option_option_a2 @ A ) )
% 0.18/0.45 => ( A
% 0.18/0.45 = ( some_option_a @ E ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.set_cases
% 0.18/0.45 thf(fact_98_option_Oset__cases,axiom,
% 0.18/0.45 ! [E: a,A: option_a] :
% 0.18/0.45 ( ( member_a @ E @ ( set_option_a2 @ A ) )
% 0.18/0.45 => ( A
% 0.18/0.45 = ( some_a @ E ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.set_cases
% 0.18/0.45 thf(fact_99_ospec,axiom,
% 0.18/0.45 ! [A3: option_a,P: a > $o,X2: a] :
% 0.18/0.45 ( ! [X4: a] :
% 0.18/0.45 ( ( member_a @ X4 @ ( set_option_a2 @ A3 ) )
% 0.18/0.45 => ( P @ X4 ) )
% 0.18/0.45 => ( ( A3
% 0.18/0.45 = ( some_a @ X2 ) )
% 0.18/0.45 => ( P @ X2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ospec
% 0.18/0.45 thf(fact_100_option_Oexhaust__sel,axiom,
% 0.18/0.45 ! [Option: option_a] :
% 0.18/0.45 ( ( Option != none_a )
% 0.18/0.45 => ( Option
% 0.18/0.45 = ( some_a @ ( the_a2 @ Option ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.exhaust_sel
% 0.18/0.45 thf(fact_101_option_Osimps_I14_J,axiom,
% 0.18/0.45 ( ( set_option_option_a2 @ none_option_a )
% 0.18/0.45 = bot_bot_set_option_a ) ).
% 0.18/0.45
% 0.18/0.45 % option.simps(14)
% 0.18/0.45 thf(fact_102_option_Osimps_I14_J,axiom,
% 0.18/0.45 ( ( set_option_a2 @ none_a )
% 0.18/0.45 = bot_bot_set_a ) ).
% 0.18/0.45
% 0.18/0.45 % option.simps(14)
% 0.18/0.45 thf(fact_103_option_Ocase__eq__if,axiom,
% 0.18/0.45 ( case_option_o_a
% 0.18/0.45 = ( ^ [F12: $o,F22: a > $o,Option3: option_a] :
% 0.18/0.45 ( ( ( Option3 = none_a )
% 0.18/0.45 => F12 )
% 0.18/0.45 & ( ( Option3 != none_a )
% 0.18/0.45 => ( F22 @ ( the_a2 @ Option3 ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.case_eq_if
% 0.18/0.45 thf(fact_104_dual__order_Ostrict__implies__not__eq,axiom,
% 0.18/0.45 ! [B: int,A: int] :
% 0.18/0.45 ( ( ord_less_int @ B @ A )
% 0.18/0.45 => ( A != B ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.strict_implies_not_eq
% 0.18/0.45 thf(fact_105_dual__order_Ostrict__implies__not__eq,axiom,
% 0.18/0.45 ! [B: set_a,A: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ B @ A )
% 0.18/0.45 => ( A != B ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.strict_implies_not_eq
% 0.18/0.45 thf(fact_106_dual__order_Ostrict__implies__not__eq,axiom,
% 0.18/0.45 ! [B: a > $o,A: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ B @ A )
% 0.18/0.45 => ( A != B ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.strict_implies_not_eq
% 0.18/0.45 thf(fact_107_order_Ostrict__implies__not__eq,axiom,
% 0.18/0.45 ! [A: int,B: int] :
% 0.18/0.45 ( ( ord_less_int @ A @ B )
% 0.18/0.45 => ( A != B ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.strict_implies_not_eq
% 0.18/0.45 thf(fact_108_order_Ostrict__implies__not__eq,axiom,
% 0.18/0.45 ! [A: set_a,B: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A @ B )
% 0.18/0.45 => ( A != B ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.strict_implies_not_eq
% 0.18/0.45 thf(fact_109_order_Ostrict__implies__not__eq,axiom,
% 0.18/0.45 ! [A: a > $o,B: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ A @ B )
% 0.18/0.45 => ( A != B ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.strict_implies_not_eq
% 0.18/0.45 thf(fact_110_not__less__iff__gr__or__eq,axiom,
% 0.18/0.45 ! [X2: int,Y: int] :
% 0.18/0.45 ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 0.18/0.45 = ( ( ord_less_int @ Y @ X2 )
% 0.18/0.45 | ( X2 = Y ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % not_less_iff_gr_or_eq
% 0.18/0.45 thf(fact_111_dual__order_Ostrict__trans,axiom,
% 0.18/0.45 ! [B: int,A: int,C: int] :
% 0.18/0.45 ( ( ord_less_int @ B @ A )
% 0.18/0.45 => ( ( ord_less_int @ C @ B )
% 0.18/0.45 => ( ord_less_int @ C @ A ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.strict_trans
% 0.18/0.45 thf(fact_112_dual__order_Ostrict__trans,axiom,
% 0.18/0.45 ! [B: set_a,A: set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ B @ A )
% 0.18/0.45 => ( ( ord_less_set_a @ C @ B )
% 0.18/0.45 => ( ord_less_set_a @ C @ A ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.strict_trans
% 0.18/0.45 thf(fact_113_dual__order_Ostrict__trans,axiom,
% 0.18/0.45 ! [B: a > $o,A: a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ B @ A )
% 0.18/0.45 => ( ( ord_less_a_o @ C @ B )
% 0.18/0.45 => ( ord_less_a_o @ C @ A ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.strict_trans
% 0.18/0.45 thf(fact_114_linorder__less__wlog,axiom,
% 0.18/0.45 ! [P: int > int > $o,A: int,B: int] :
% 0.18/0.45 ( ! [A4: int,B3: int] :
% 0.18/0.45 ( ( ord_less_int @ A4 @ B3 )
% 0.18/0.45 => ( P @ A4 @ B3 ) )
% 0.18/0.45 => ( ! [A4: int] : ( P @ A4 @ A4 )
% 0.18/0.45 => ( ! [A4: int,B3: int] :
% 0.18/0.45 ( ( P @ B3 @ A4 )
% 0.18/0.45 => ( P @ A4 @ B3 ) )
% 0.18/0.45 => ( P @ A @ B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % linorder_less_wlog
% 0.18/0.45 thf(fact_115_less__imp__not__less,axiom,
% 0.18/0.45 ! [X2: int,Y: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y )
% 0.18/0.45 => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_less
% 0.18/0.45 thf(fact_116_less__imp__not__less,axiom,
% 0.18/0.45 ! [X2: set_a,Y: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y )
% 0.18/0.45 => ~ ( ord_less_set_a @ Y @ X2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_less
% 0.18/0.45 thf(fact_117_less__imp__not__less,axiom,
% 0.18/0.45 ! [X2: a > $o,Y: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y )
% 0.18/0.45 => ~ ( ord_less_a_o @ Y @ X2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_less
% 0.18/0.45 thf(fact_118_order_Ostrict__trans,axiom,
% 0.18/0.45 ! [A: int,B: int,C: int] :
% 0.18/0.45 ( ( ord_less_int @ A @ B )
% 0.18/0.45 => ( ( ord_less_int @ B @ C )
% 0.18/0.45 => ( ord_less_int @ A @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.strict_trans
% 0.18/0.45 thf(fact_119_order_Ostrict__trans,axiom,
% 0.18/0.45 ! [A: set_a,B: set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A @ B )
% 0.18/0.45 => ( ( ord_less_set_a @ B @ C )
% 0.18/0.45 => ( ord_less_set_a @ A @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.strict_trans
% 0.18/0.45 thf(fact_120_order_Ostrict__trans,axiom,
% 0.18/0.45 ! [A: a > $o,B: a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ A @ B )
% 0.18/0.45 => ( ( ord_less_a_o @ B @ C )
% 0.18/0.45 => ( ord_less_a_o @ A @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.strict_trans
% 0.18/0.45 thf(fact_121_dual__order_Oirrefl,axiom,
% 0.18/0.45 ! [A: int] :
% 0.18/0.45 ~ ( ord_less_int @ A @ A ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.irrefl
% 0.18/0.45 thf(fact_122_dual__order_Oirrefl,axiom,
% 0.18/0.45 ! [A: set_a] :
% 0.18/0.45 ~ ( ord_less_set_a @ A @ A ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.irrefl
% 0.18/0.45 thf(fact_123_dual__order_Oirrefl,axiom,
% 0.18/0.45 ! [A: a > $o] :
% 0.18/0.45 ~ ( ord_less_a_o @ A @ A ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.irrefl
% 0.18/0.45 thf(fact_124_linorder__cases,axiom,
% 0.18/0.45 ! [X2: int,Y: int] :
% 0.18/0.45 ( ~ ( ord_less_int @ X2 @ Y )
% 0.18/0.45 => ( ( X2 != Y )
% 0.18/0.45 => ( ord_less_int @ Y @ X2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % linorder_cases
% 0.18/0.45 thf(fact_125_less__imp__triv,axiom,
% 0.18/0.45 ! [X2: int,Y: int,P: $o] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y )
% 0.18/0.45 => ( ( ord_less_int @ Y @ X2 )
% 0.18/0.45 => P ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_triv
% 0.18/0.45 thf(fact_126_less__imp__triv,axiom,
% 0.18/0.45 ! [X2: set_a,Y: set_a,P: $o] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y )
% 0.18/0.45 => ( ( ord_less_set_a @ Y @ X2 )
% 0.18/0.45 => P ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_triv
% 0.18/0.45 thf(fact_127_less__imp__triv,axiom,
% 0.18/0.45 ! [X2: a > $o,Y: a > $o,P: $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y )
% 0.18/0.45 => ( ( ord_less_a_o @ Y @ X2 )
% 0.18/0.45 => P ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_triv
% 0.18/0.45 thf(fact_128_less__imp__not__eq2,axiom,
% 0.18/0.45 ! [X2: int,Y: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y )
% 0.18/0.45 => ( Y != X2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_eq2
% 0.18/0.45 thf(fact_129_less__imp__not__eq2,axiom,
% 0.18/0.45 ! [X2: set_a,Y: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y )
% 0.18/0.45 => ( Y != X2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_eq2
% 0.18/0.45 thf(fact_130_less__imp__not__eq2,axiom,
% 0.18/0.45 ! [X2: a > $o,Y: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y )
% 0.18/0.45 => ( Y != X2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_eq2
% 0.18/0.45 thf(fact_131_antisym__conv3,axiom,
% 0.18/0.45 ! [Y: int,X2: int] :
% 0.18/0.45 ( ~ ( ord_less_int @ Y @ X2 )
% 0.18/0.45 => ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 0.18/0.45 = ( X2 = Y ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % antisym_conv3
% 0.18/0.45 thf(fact_132_less__not__sym,axiom,
% 0.18/0.45 ! [X2: int,Y: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y )
% 0.18/0.45 => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_not_sym
% 0.18/0.45 thf(fact_133_less__not__sym,axiom,
% 0.18/0.45 ! [X2: set_a,Y: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y )
% 0.18/0.45 => ~ ( ord_less_set_a @ Y @ X2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_not_sym
% 0.18/0.45 thf(fact_134_less__not__sym,axiom,
% 0.18/0.45 ! [X2: a > $o,Y: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y )
% 0.18/0.45 => ~ ( ord_less_a_o @ Y @ X2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_not_sym
% 0.18/0.45 thf(fact_135_less__imp__not__eq,axiom,
% 0.18/0.45 ! [X2: int,Y: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y )
% 0.18/0.45 => ( X2 != Y ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_eq
% 0.18/0.45 thf(fact_136_less__imp__not__eq,axiom,
% 0.18/0.45 ! [X2: set_a,Y: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y )
% 0.18/0.45 => ( X2 != Y ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_eq
% 0.18/0.45 thf(fact_137_less__imp__not__eq,axiom,
% 0.18/0.45 ! [X2: a > $o,Y: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y )
% 0.18/0.45 => ( X2 != Y ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_eq
% 0.18/0.45 thf(fact_138_dual__order_Oasym,axiom,
% 0.18/0.45 ! [B: int,A: int] :
% 0.18/0.45 ( ( ord_less_int @ B @ A )
% 0.18/0.45 => ~ ( ord_less_int @ A @ B ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.asym
% 0.18/0.45 thf(fact_139_dual__order_Oasym,axiom,
% 0.18/0.45 ! [B: set_a,A: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ B @ A )
% 0.18/0.45 => ~ ( ord_less_set_a @ A @ B ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.asym
% 0.18/0.45 thf(fact_140_dual__order_Oasym,axiom,
% 0.18/0.45 ! [B: a > $o,A: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ B @ A )
% 0.18/0.45 => ~ ( ord_less_a_o @ A @ B ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.asym
% 0.18/0.45 thf(fact_141_ord__less__eq__trans,axiom,
% 0.18/0.45 ! [A: int,B: int,C: int] :
% 0.18/0.45 ( ( ord_less_int @ A @ B )
% 0.18/0.45 => ( ( B = C )
% 0.18/0.45 => ( ord_less_int @ A @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_trans
% 0.18/0.45 thf(fact_142_ord__less__eq__trans,axiom,
% 0.18/0.45 ! [A: set_a,B: set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A @ B )
% 0.18/0.45 => ( ( B = C )
% 0.18/0.45 => ( ord_less_set_a @ A @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_trans
% 0.18/0.45 thf(fact_143_ord__less__eq__trans,axiom,
% 0.18/0.45 ! [A: a > $o,B: a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ A @ B )
% 0.18/0.45 => ( ( B = C )
% 0.18/0.45 => ( ord_less_a_o @ A @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_trans
% 0.18/0.45 thf(fact_144_ord__eq__less__trans,axiom,
% 0.18/0.45 ! [A: int,B: int,C: int] :
% 0.18/0.45 ( ( A = B )
% 0.18/0.45 => ( ( ord_less_int @ B @ C )
% 0.18/0.45 => ( ord_less_int @ A @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_trans
% 0.18/0.45 thf(fact_145_ord__eq__less__trans,axiom,
% 0.18/0.45 ! [A: set_a,B: set_a,C: set_a] :
% 0.18/0.45 ( ( A = B )
% 0.18/0.45 => ( ( ord_less_set_a @ B @ C )
% 0.18/0.45 => ( ord_less_set_a @ A @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_trans
% 0.18/0.45 thf(fact_146_ord__eq__less__trans,axiom,
% 0.18/0.45 ! [A: a > $o,B: a > $o,C: a > $o] :
% 0.18/0.45 ( ( A = B )
% 0.18/0.45 => ( ( ord_less_a_o @ B @ C )
% 0.18/0.45 => ( ord_less_a_o @ A @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_trans
% 0.18/0.45 thf(fact_147_less__irrefl,axiom,
% 0.18/0.45 ! [X2: int] :
% 0.18/0.45 ~ ( ord_less_int @ X2 @ X2 ) ).
% 0.18/0.45
% 0.18/0.45 % less_irrefl
% 0.18/0.45 thf(fact_148_less__irrefl,axiom,
% 0.18/0.45 ! [X2: set_a] :
% 0.18/0.45 ~ ( ord_less_set_a @ X2 @ X2 ) ).
% 0.18/0.45
% 0.18/0.45 % less_irrefl
% 0.18/0.45 thf(fact_149_less__irrefl,axiom,
% 0.18/0.45 ! [X2: a > $o] :
% 0.18/0.45 ~ ( ord_less_a_o @ X2 @ X2 ) ).
% 0.18/0.45
% 0.18/0.45 % less_irrefl
% 0.18/0.45 thf(fact_150_less__linear,axiom,
% 0.18/0.45 ! [X2: int,Y: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y )
% 0.18/0.45 | ( X2 = Y )
% 0.18/0.45 | ( ord_less_int @ Y @ X2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_linear
% 0.18/0.45 thf(fact_151_less__trans,axiom,
% 0.18/0.45 ! [X2: int,Y: int,Z2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y )
% 0.18/0.45 => ( ( ord_less_int @ Y @ Z2 )
% 0.18/0.45 => ( ord_less_int @ X2 @ Z2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_trans
% 0.18/0.45 thf(fact_152_less__trans,axiom,
% 0.18/0.45 ! [X2: set_a,Y: set_a,Z2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y )
% 0.18/0.45 => ( ( ord_less_set_a @ Y @ Z2 )
% 0.18/0.45 => ( ord_less_set_a @ X2 @ Z2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_trans
% 0.18/0.45 thf(fact_153_less__trans,axiom,
% 0.18/0.45 ! [X2: a > $o,Y: a > $o,Z2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y )
% 0.18/0.45 => ( ( ord_less_a_o @ Y @ Z2 )
% 0.18/0.45 => ( ord_less_a_o @ X2 @ Z2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_trans
% 0.18/0.45 thf(fact_154_less__asym_H,axiom,
% 0.18/0.45 ! [A: int,B: int] :
% 0.18/0.45 ( ( ord_less_int @ A @ B )
% 0.18/0.45 => ~ ( ord_less_int @ B @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_asym'
% 0.18/0.45 thf(fact_155_less__asym_H,axiom,
% 0.18/0.45 ! [A: set_a,B: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A @ B )
% 0.18/0.45 => ~ ( ord_less_set_a @ B @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_asym'
% 0.18/0.45 thf(fact_156_less__asym_H,axiom,
% 0.18/0.45 ! [A: a > $o,B: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ A @ B )
% 0.18/0.45 => ~ ( ord_less_a_o @ B @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_asym'
% 0.18/0.45 thf(fact_157_less__asym,axiom,
% 0.18/0.45 ! [X2: int,Y: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y )
% 0.18/0.45 => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_asym
% 0.18/0.45 thf(fact_158_less__asym,axiom,
% 0.18/0.45 ! [X2: set_a,Y: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y )
% 0.18/0.45 => ~ ( ord_less_set_a @ Y @ X2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_asym
% 0.18/0.45 thf(fact_159_less__asym,axiom,
% 0.18/0.45 ! [X2: a > $o,Y: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y )
% 0.18/0.45 => ~ ( ord_less_a_o @ Y @ X2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_asym
% 0.18/0.45 thf(fact_160_less__imp__neq,axiom,
% 0.18/0.45 ! [X2: int,Y: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y )
% 0.18/0.45 => ( X2 != Y ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_neq
% 0.18/0.45 thf(fact_161_less__imp__neq,axiom,
% 0.18/0.45 ! [X2: set_a,Y: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y )
% 0.18/0.45 => ( X2 != Y ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_neq
% 0.18/0.45 thf(fact_162_less__imp__neq,axiom,
% 0.18/0.45 ! [X2: a > $o,Y: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y )
% 0.18/0.45 => ( X2 != Y ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_neq
% 0.18/0.45 thf(fact_163_order_Oasym,axiom,
% 0.18/0.45 ! [A: int,B: int] :
% 0.18/0.45 ( ( ord_less_int @ A @ B )
% 0.18/0.45 => ~ ( ord_less_int @ B @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.asym
% 0.18/0.45 thf(fact_164_order_Oasym,axiom,
% 0.18/0.45 ! [A: set_a,B: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A @ B )
% 0.18/0.45 => ~ ( ord_less_set_a @ B @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.asym
% 0.18/0.45 thf(fact_165_order_Oasym,axiom,
% 0.18/0.45 ! [A: a > $o,B: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ A @ B )
% 0.18/0.45 => ~ ( ord_less_a_o @ B @ A ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.asym
% 0.18/0.45 thf(fact_166_neq__iff,axiom,
% 0.18/0.45 ! [X2: int,Y: int] :
% 0.18/0.45 ( ( X2 != Y )
% 0.18/0.45 = ( ( ord_less_int @ X2 @ Y )
% 0.18/0.45 | ( ord_less_int @ Y @ X2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % neq_iff
% 0.18/0.45 thf(fact_167_neqE,axiom,
% 0.18/0.45 ! [X2: int,Y: int] :
% 0.18/0.45 ( ( X2 != Y )
% 0.18/0.45 => ( ~ ( ord_less_int @ X2 @ Y )
% 0.18/0.45 => ( ord_less_int @ Y @ X2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % neqE
% 0.18/0.45 thf(fact_168_gt__ex,axiom,
% 0.18/0.45 ! [X2: int] :
% 0.18/0.45 ? [X_1: int] : ( ord_less_int @ X2 @ X_1 ) ).
% 0.18/0.45
% 0.18/0.45 % gt_ex
% 0.18/0.45 thf(fact_169_lt__ex,axiom,
% 0.18/0.45 ! [X2: int] :
% 0.18/0.45 ? [Y4: int] : ( ord_less_int @ Y4 @ X2 ) ).
% 0.18/0.45
% 0.18/0.45 % lt_ex
% 0.18/0.45 thf(fact_170_order__less__subst2,axiom,
% 0.18/0.45 ! [A: int,B: int,F: int > int,C: int] :
% 0.18/0.45 ( ( ord_less_int @ A @ B )
% 0.18/0.45 => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.18/0.45 => ( ! [X4: int,Y4: int] :
% 0.18/0.45 ( ( ord_less_int @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_171_order__less__subst2,axiom,
% 0.18/0.45 ! [A: int,B: int,F: int > set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_int @ A @ B )
% 0.18/0.45 => ( ( ord_less_set_a @ ( F @ B ) @ C )
% 0.18/0.45 => ( ! [X4: int,Y4: int] :
% 0.18/0.45 ( ( ord_less_int @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_172_order__less__subst2,axiom,
% 0.18/0.45 ! [A: int,B: int,F: int > a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_int @ A @ B )
% 0.18/0.45 => ( ( ord_less_a_o @ ( F @ B ) @ C )
% 0.18/0.45 => ( ! [X4: int,Y4: int] :
% 0.18/0.45 ( ( ord_less_int @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_173_order__less__subst2,axiom,
% 0.18/0.45 ! [A: set_a,B: set_a,F: set_a > int,C: int] :
% 0.18/0.45 ( ( ord_less_set_a @ A @ B )
% 0.18/0.45 => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.18/0.45 => ( ! [X4: set_a,Y4: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_174_order__less__subst2,axiom,
% 0.18/0.45 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A @ B )
% 0.18/0.45 => ( ( ord_less_set_a @ ( F @ B ) @ C )
% 0.18/0.45 => ( ! [X4: set_a,Y4: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_175_order__less__subst2,axiom,
% 0.18/0.45 ! [A: set_a,B: set_a,F: set_a > a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_set_a @ A @ B )
% 0.18/0.45 => ( ( ord_less_a_o @ ( F @ B ) @ C )
% 0.18/0.45 => ( ! [X4: set_a,Y4: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_176_order__less__subst2,axiom,
% 0.18/0.45 ! [A: a > $o,B: a > $o,F: ( a > $o ) > int,C: int] :
% 0.18/0.45 ( ( ord_less_a_o @ A @ B )
% 0.18/0.45 => ( ( ord_less_int @ ( F @ B ) @ C )
% 0.18/0.45 => ( ! [X4: a > $o,Y4: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_177_order__less__subst2,axiom,
% 0.18/0.45 ! [A: a > $o,B: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_a_o @ A @ B )
% 0.18/0.45 => ( ( ord_less_set_a @ ( F @ B ) @ C )
% 0.18/0.45 => ( ! [X4: a > $o,Y4: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_178_order__less__subst2,axiom,
% 0.18/0.45 ! [A: a > $o,B: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ A @ B )
% 0.18/0.45 => ( ( ord_less_a_o @ ( F @ B ) @ C )
% 0.18/0.45 => ( ! [X4: a > $o,Y4: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_179_order__less__subst1,axiom,
% 0.18/0.45 ! [A: int,F: int > int,B: int,C: int] :
% 0.18/0.45 ( ( ord_less_int @ A @ ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_int @ B @ C )
% 0.18/0.45 => ( ! [X4: int,Y4: int] :
% 0.18/0.45 ( ( ord_less_int @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_180_order__less__subst1,axiom,
% 0.18/0.45 ! [A: int,F: set_a > int,B: set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_int @ A @ ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_set_a @ B @ C )
% 0.18/0.45 => ( ! [X4: set_a,Y4: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_181_order__less__subst1,axiom,
% 0.18/0.45 ! [A: int,F: ( a > $o ) > int,B: a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_int @ A @ ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_a_o @ B @ C )
% 0.18/0.45 => ( ! [X4: a > $o,Y4: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_182_order__less__subst1,axiom,
% 0.18/0.45 ! [A: set_a,F: int > set_a,B: int,C: int] :
% 0.18/0.45 ( ( ord_less_set_a @ A @ ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_int @ B @ C )
% 0.18/0.45 => ( ! [X4: int,Y4: int] :
% 0.18/0.45 ( ( ord_less_int @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_183_order__less__subst1,axiom,
% 0.18/0.45 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A @ ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_set_a @ B @ C )
% 0.18/0.45 => ( ! [X4: set_a,Y4: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_184_order__less__subst1,axiom,
% 0.18/0.45 ! [A: set_a,F: ( a > $o ) > set_a,B: a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_set_a @ A @ ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_a_o @ B @ C )
% 0.18/0.45 => ( ! [X4: a > $o,Y4: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_185_order__less__subst1,axiom,
% 0.18/0.45 ! [A: a > $o,F: int > a > $o,B: int,C: int] :
% 0.18/0.45 ( ( ord_less_a_o @ A @ ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_int @ B @ C )
% 0.18/0.45 => ( ! [X4: int,Y4: int] :
% 0.18/0.45 ( ( ord_less_int @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_186_order__less__subst1,axiom,
% 0.18/0.45 ! [A: a > $o,F: set_a > a > $o,B: set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_a_o @ A @ ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_set_a @ B @ C )
% 0.18/0.45 => ( ! [X4: set_a,Y4: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_187_order__less__subst1,axiom,
% 0.18/0.45 ! [A: a > $o,F: ( a > $o ) > a > $o,B: a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ A @ ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_a_o @ B @ C )
% 0.18/0.45 => ( ! [X4: a > $o,Y4: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_188_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A: int,B: int,F: int > int,C: int] :
% 0.18/0.45 ( ( ord_less_int @ A @ B )
% 0.18/0.45 => ( ( ( F @ B )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X4: int,Y4: int] :
% 0.18/0.45 ( ( ord_less_int @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_189_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A: int,B: int,F: int > set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_int @ A @ B )
% 0.18/0.45 => ( ( ( F @ B )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X4: int,Y4: int] :
% 0.18/0.45 ( ( ord_less_int @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_190_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A: int,B: int,F: int > a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_int @ A @ B )
% 0.18/0.45 => ( ( ( F @ B )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X4: int,Y4: int] :
% 0.18/0.45 ( ( ord_less_int @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_191_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A: set_a,B: set_a,F: set_a > int,C: int] :
% 0.18/0.45 ( ( ord_less_set_a @ A @ B )
% 0.18/0.45 => ( ( ( F @ B )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X4: set_a,Y4: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_192_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A @ B )
% 0.18/0.45 => ( ( ( F @ B )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X4: set_a,Y4: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_193_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A: set_a,B: set_a,F: set_a > a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_set_a @ A @ B )
% 0.18/0.45 => ( ( ( F @ B )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X4: set_a,Y4: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_194_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A: a > $o,B: a > $o,F: ( a > $o ) > int,C: int] :
% 0.18/0.45 ( ( ord_less_a_o @ A @ B )
% 0.18/0.45 => ( ( ( F @ B )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X4: a > $o,Y4: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_195_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A: a > $o,B: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_a_o @ A @ B )
% 0.18/0.45 => ( ( ( F @ B )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X4: a > $o,Y4: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_196_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A: a > $o,B: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ A @ B )
% 0.18/0.45 => ( ( ( F @ B )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X4: a > $o,Y4: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_197_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A: int,F: int > int,B: int,C: int] :
% 0.18/0.45 ( ( A
% 0.18/0.45 = ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_int @ B @ C )
% 0.18/0.45 => ( ! [X4: int,Y4: int] :
% 0.18/0.45 ( ( ord_less_int @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_198_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A: set_a,F: int > set_a,B: int,C: int] :
% 0.18/0.45 ( ( A
% 0.18/0.45 = ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_int @ B @ C )
% 0.18/0.45 => ( ! [X4: int,Y4: int] :
% 0.18/0.45 ( ( ord_less_int @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_199_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A: a > $o,F: int > a > $o,B: int,C: int] :
% 0.18/0.45 ( ( A
% 0.18/0.45 = ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_int @ B @ C )
% 0.18/0.45 => ( ! [X4: int,Y4: int] :
% 0.18/0.45 ( ( ord_less_int @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_200_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A: int,F: set_a > int,B: set_a,C: set_a] :
% 0.18/0.45 ( ( A
% 0.18/0.45 = ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_set_a @ B @ C )
% 0.18/0.45 => ( ! [X4: set_a,Y4: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_201_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 0.18/0.45 ( ( A
% 0.18/0.45 = ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_set_a @ B @ C )
% 0.18/0.45 => ( ! [X4: set_a,Y4: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_202_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A: a > $o,F: set_a > a > $o,B: set_a,C: set_a] :
% 0.18/0.45 ( ( A
% 0.18/0.45 = ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_set_a @ B @ C )
% 0.18/0.45 => ( ! [X4: set_a,Y4: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_203_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A: int,F: ( a > $o ) > int,B: a > $o,C: a > $o] :
% 0.18/0.45 ( ( A
% 0.18/0.45 = ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_a_o @ B @ C )
% 0.18/0.45 => ( ! [X4: a > $o,Y4: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_204_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A: set_a,F: ( a > $o ) > set_a,B: a > $o,C: a > $o] :
% 0.18/0.45 ( ( A
% 0.18/0.45 = ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_a_o @ B @ C )
% 0.18/0.45 => ( ! [X4: a > $o,Y4: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_205_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A: a > $o,F: ( a > $o ) > a > $o,B: a > $o,C: a > $o] :
% 0.18/0.45 ( ( A
% 0.18/0.45 = ( F @ B ) )
% 0.18/0.45 => ( ( ord_less_a_o @ B @ C )
% 0.18/0.45 => ( ! [X4: a > $o,Y4: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X4 @ Y4 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_206_option_Osimps_I15_J,axiom,
% 0.18/0.45 ! [X25: option_a] :
% 0.18/0.45 ( ( set_option_option_a2 @ ( some_option_a @ X25 ) )
% 0.18/0.45 = ( insert_option_a @ X25 @ bot_bot_set_option_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.simps(15)
% 0.18/0.45 thf(fact_207_option_Osimps_I15_J,axiom,
% 0.18/0.45 ! [X25: a] :
% 0.18/0.45 ( ( set_option_a2 @ ( some_a @ X25 ) )
% 0.18/0.45 = ( insert_a @ X25 @ bot_bot_set_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.simps(15)
% 0.18/0.45 thf(fact_208_option_Othe__def,axiom,
% 0.18/0.45 ( the_a2
% 0.18/0.45 = ( case_option_a_a @ undefined_a
% 0.18/0.45 @ ^ [X26: a] : X26 ) ) ).
% 0.18/0.45
% 0.18/0.45 % option.the_def
% 0.18/0.45 thf(fact_209_bot__empty__eq,axiom,
% 0.18/0.46 ( bot_bot_option_a_o
% 0.18/0.46 = ( ^ [X3: option_a] : ( member_option_a @ X3 @ bot_bot_set_option_a ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % bot_empty_eq
% 0.18/0.46 thf(fact_210_bot__empty__eq,axiom,
% 0.18/0.46 ( bot_bot_a_o
% 0.18/0.46 = ( ^ [X3: a] : ( member_a @ X3 @ bot_bot_set_a ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % bot_empty_eq
% 0.18/0.46 thf(fact_211_Collect__empty__eq__bot,axiom,
% 0.18/0.46 ! [P: a > $o] :
% 0.18/0.46 ( ( ( collect_a @ P )
% 0.18/0.46 = bot_bot_set_a )
% 0.18/0.46 = ( P = bot_bot_a_o ) ) ).
% 0.18/0.46
% 0.18/0.46 % Collect_empty_eq_bot
% 0.18/0.46 thf(fact_212_Collect__empty__eq__bot,axiom,
% 0.18/0.46 ! [P: option_a > $o] :
% 0.18/0.46 ( ( ( collect_option_a @ P )
% 0.18/0.46 = bot_bot_set_option_a )
% 0.18/0.46 = ( P = bot_bot_option_a_o ) ) ).
% 0.18/0.46
% 0.18/0.46 % Collect_empty_eq_bot
% 0.18/0.46 thf(fact_213_linorder__neqE__linordered__idom,axiom,
% 0.18/0.46 ! [X2: int,Y: int] :
% 0.18/0.46 ( ( X2 != Y )
% 0.18/0.46 => ( ~ ( ord_less_int @ X2 @ Y )
% 0.18/0.46 => ( ord_less_int @ Y @ X2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % linorder_neqE_linordered_idom
% 0.18/0.46 thf(fact_214_insert__absorb2,axiom,
% 0.18/0.46 ! [X2: a,A3: set_a] :
% 0.18/0.46 ( ( insert_a @ X2 @ ( insert_a @ X2 @ A3 ) )
% 0.18/0.46 = ( insert_a @ X2 @ A3 ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_absorb2
% 0.18/0.46 thf(fact_215_insert__absorb2,axiom,
% 0.18/0.46 ! [X2: option_a,A3: set_option_a] :
% 0.18/0.46 ( ( insert_option_a @ X2 @ ( insert_option_a @ X2 @ A3 ) )
% 0.18/0.46 = ( insert_option_a @ X2 @ A3 ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_absorb2
% 0.18/0.46 thf(fact_216_insert__iff,axiom,
% 0.18/0.46 ! [A: option_a,B: option_a,A3: set_option_a] :
% 0.18/0.46 ( ( member_option_a @ A @ ( insert_option_a @ B @ A3 ) )
% 0.18/0.46 = ( ( A = B )
% 0.18/0.46 | ( member_option_a @ A @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_iff
% 0.18/0.46 thf(fact_217_insert__iff,axiom,
% 0.18/0.46 ! [A: a,B: a,A3: set_a] :
% 0.18/0.46 ( ( member_a @ A @ ( insert_a @ B @ A3 ) )
% 0.18/0.46 = ( ( A = B )
% 0.18/0.46 | ( member_a @ A @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_iff
% 0.18/0.46 thf(fact_218_insertCI,axiom,
% 0.18/0.46 ! [A: option_a,B4: set_option_a,B: option_a] :
% 0.18/0.46 ( ( ~ ( member_option_a @ A @ B4 )
% 0.18/0.46 => ( A = B ) )
% 0.18/0.46 => ( member_option_a @ A @ ( insert_option_a @ B @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insertCI
% 0.18/0.46 thf(fact_219_insertCI,axiom,
% 0.18/0.46 ! [A: a,B4: set_a,B: a] :
% 0.18/0.46 ( ( ~ ( member_a @ A @ B4 )
% 0.18/0.46 => ( A = B ) )
% 0.18/0.46 => ( member_a @ A @ ( insert_a @ B @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insertCI
% 0.18/0.46 thf(fact_220_singletonI,axiom,
% 0.18/0.46 ! [A: option_a] : ( member_option_a @ A @ ( insert_option_a @ A @ bot_bot_set_option_a ) ) ).
% 0.18/0.46
% 0.18/0.46 % singletonI
% 0.18/0.46 thf(fact_221_singletonI,axiom,
% 0.18/0.46 ! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ) ).
% 0.18/0.46
% 0.18/0.46 % singletonI
% 0.18/0.46 thf(fact_222_singleton__conv,axiom,
% 0.18/0.46 ! [A: a] :
% 0.18/0.46 ( ( collect_a
% 0.18/0.46 @ ^ [X3: a] : ( X3 = A ) )
% 0.18/0.46 = ( insert_a @ A @ bot_bot_set_a ) ) ).
% 0.18/0.46
% 0.18/0.46 % singleton_conv
% 0.18/0.46 thf(fact_223_singleton__conv,axiom,
% 0.18/0.46 ! [A: option_a] :
% 0.18/0.46 ( ( collect_option_a
% 0.18/0.46 @ ^ [X3: option_a] : ( X3 = A ) )
% 0.18/0.46 = ( insert_option_a @ A @ bot_bot_set_option_a ) ) ).
% 0.18/0.46
% 0.18/0.46 % singleton_conv
% 0.18/0.46 thf(fact_224_singleton__conv2,axiom,
% 0.18/0.46 ! [A: a] :
% 0.18/0.46 ( ( collect_a
% 0.18/0.46 @ ( ^ [Y2: a,Z: a] : ( Y2 = Z )
% 0.18/0.46 @ A ) )
% 0.18/0.46 = ( insert_a @ A @ bot_bot_set_a ) ) ).
% 0.18/0.46
% 0.18/0.46 % singleton_conv2
% 0.18/0.46 thf(fact_225_singleton__conv2,axiom,
% 0.18/0.46 ! [A: option_a] :
% 0.18/0.46 ( ( collect_option_a
% 0.18/0.46 @ ( ^ [Y2: option_a,Z: option_a] : ( Y2 = Z )
% 0.18/0.46 @ A ) )
% 0.18/0.46 = ( insert_option_a @ A @ bot_bot_set_option_a ) ) ).
% 0.18/0.46
% 0.18/0.46 % singleton_conv2
% 0.18/0.46 thf(fact_226_psubset__trans,axiom,
% 0.18/0.46 ! [A3: set_a,B4: set_a,C2: set_a] :
% 0.18/0.46 ( ( ord_less_set_a @ A3 @ B4 )
% 0.18/0.46 => ( ( ord_less_set_a @ B4 @ C2 )
% 0.18/0.46 => ( ord_less_set_a @ A3 @ C2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % psubset_trans
% 0.18/0.46 thf(fact_227_less__set__def,axiom,
% 0.18/0.46 ( ord_le1280890064tion_a
% 0.18/0.46 = ( ^ [A5: set_option_a,B5: set_option_a] :
% 0.18/0.46 ( ord_less_option_a_o
% 0.18/0.46 @ ^ [X3: option_a] : ( member_option_a @ X3 @ A5 )
% 0.18/0.46 @ ^ [X3: option_a] : ( member_option_a @ X3 @ B5 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_set_def
% 0.18/0.46 thf(fact_228_less__set__def,axiom,
% 0.18/0.46 ( ord_less_set_a
% 0.18/0.46 = ( ^ [A5: set_a,B5: set_a] :
% 0.18/0.46 ( ord_less_a_o
% 0.18/0.46 @ ^ [X3: a] : ( member_a @ X3 @ A5 )
% 0.18/0.46 @ ^ [X3: a] : ( member_a @ X3 @ B5 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % less_set_def
% 0.18/0.46 thf(fact_229_psubsetD,axiom,
% 0.18/0.46 ! [A3: set_option_a,B4: set_option_a,C: option_a] :
% 0.18/0.46 ( ( ord_le1280890064tion_a @ A3 @ B4 )
% 0.18/0.46 => ( ( member_option_a @ C @ A3 )
% 0.18/0.46 => ( member_option_a @ C @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % psubsetD
% 0.18/0.46 thf(fact_230_psubsetD,axiom,
% 0.18/0.46 ! [A3: set_a,B4: set_a,C: a] :
% 0.18/0.46 ( ( ord_less_set_a @ A3 @ B4 )
% 0.18/0.46 => ( ( member_a @ C @ A3 )
% 0.18/0.46 => ( member_a @ C @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % psubsetD
% 0.18/0.46 thf(fact_231_mk__disjoint__insert,axiom,
% 0.18/0.46 ! [A: option_a,A3: set_option_a] :
% 0.18/0.46 ( ( member_option_a @ A @ A3 )
% 0.18/0.46 => ? [B6: set_option_a] :
% 0.18/0.46 ( ( A3
% 0.18/0.46 = ( insert_option_a @ A @ B6 ) )
% 0.18/0.46 & ~ ( member_option_a @ A @ B6 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % mk_disjoint_insert
% 0.18/0.46 thf(fact_232_mk__disjoint__insert,axiom,
% 0.18/0.46 ! [A: a,A3: set_a] :
% 0.18/0.46 ( ( member_a @ A @ A3 )
% 0.18/0.46 => ? [B6: set_a] :
% 0.18/0.46 ( ( A3
% 0.18/0.46 = ( insert_a @ A @ B6 ) )
% 0.18/0.46 & ~ ( member_a @ A @ B6 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % mk_disjoint_insert
% 0.18/0.46 thf(fact_233_insert__commute,axiom,
% 0.18/0.46 ! [X2: a,Y: a,A3: set_a] :
% 0.18/0.46 ( ( insert_a @ X2 @ ( insert_a @ Y @ A3 ) )
% 0.18/0.46 = ( insert_a @ Y @ ( insert_a @ X2 @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_commute
% 0.18/0.46 thf(fact_234_insert__commute,axiom,
% 0.18/0.46 ! [X2: option_a,Y: option_a,A3: set_option_a] :
% 0.18/0.46 ( ( insert_option_a @ X2 @ ( insert_option_a @ Y @ A3 ) )
% 0.18/0.46 = ( insert_option_a @ Y @ ( insert_option_a @ X2 @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_commute
% 0.18/0.46 thf(fact_235_insert__eq__iff,axiom,
% 0.18/0.46 ! [A: option_a,A3: set_option_a,B: option_a,B4: set_option_a] :
% 0.18/0.46 ( ~ ( member_option_a @ A @ A3 )
% 0.18/0.46 => ( ~ ( member_option_a @ B @ B4 )
% 0.18/0.46 => ( ( ( insert_option_a @ A @ A3 )
% 0.18/0.46 = ( insert_option_a @ B @ B4 ) )
% 0.18/0.46 = ( ( ( A = B )
% 0.18/0.46 => ( A3 = B4 ) )
% 0.18/0.46 & ( ( A != B )
% 0.18/0.46 => ? [C3: set_option_a] :
% 0.18/0.46 ( ( A3
% 0.18/0.46 = ( insert_option_a @ B @ C3 ) )
% 0.18/0.46 & ~ ( member_option_a @ B @ C3 )
% 0.18/0.46 & ( B4
% 0.18/0.46 = ( insert_option_a @ A @ C3 ) )
% 0.18/0.46 & ~ ( member_option_a @ A @ C3 ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_eq_iff
% 0.18/0.46 thf(fact_236_insert__eq__iff,axiom,
% 0.18/0.46 ! [A: a,A3: set_a,B: a,B4: set_a] :
% 0.18/0.46 ( ~ ( member_a @ A @ A3 )
% 0.18/0.46 => ( ~ ( member_a @ B @ B4 )
% 0.18/0.46 => ( ( ( insert_a @ A @ A3 )
% 0.18/0.46 = ( insert_a @ B @ B4 ) )
% 0.18/0.46 = ( ( ( A = B )
% 0.18/0.46 => ( A3 = B4 ) )
% 0.18/0.46 & ( ( A != B )
% 0.18/0.46 => ? [C3: set_a] :
% 0.18/0.46 ( ( A3
% 0.18/0.46 = ( insert_a @ B @ C3 ) )
% 0.18/0.46 & ~ ( member_a @ B @ C3 )
% 0.18/0.46 & ( B4
% 0.18/0.46 = ( insert_a @ A @ C3 ) )
% 0.18/0.46 & ~ ( member_a @ A @ C3 ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_eq_iff
% 0.18/0.46 thf(fact_237_insert__absorb,axiom,
% 0.18/0.46 ! [A: option_a,A3: set_option_a] :
% 0.18/0.46 ( ( member_option_a @ A @ A3 )
% 0.18/0.46 => ( ( insert_option_a @ A @ A3 )
% 0.18/0.46 = A3 ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_absorb
% 0.18/0.46 thf(fact_238_insert__absorb,axiom,
% 0.18/0.46 ! [A: a,A3: set_a] :
% 0.18/0.46 ( ( member_a @ A @ A3 )
% 0.18/0.46 => ( ( insert_a @ A @ A3 )
% 0.18/0.46 = A3 ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_absorb
% 0.18/0.46 thf(fact_239_insert__ident,axiom,
% 0.18/0.46 ! [X2: option_a,A3: set_option_a,B4: set_option_a] :
% 0.18/0.46 ( ~ ( member_option_a @ X2 @ A3 )
% 0.18/0.46 => ( ~ ( member_option_a @ X2 @ B4 )
% 0.18/0.46 => ( ( ( insert_option_a @ X2 @ A3 )
% 0.18/0.46 = ( insert_option_a @ X2 @ B4 ) )
% 0.18/0.46 = ( A3 = B4 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_ident
% 0.18/0.46 thf(fact_240_insert__ident,axiom,
% 0.18/0.46 ! [X2: a,A3: set_a,B4: set_a] :
% 0.18/0.46 ( ~ ( member_a @ X2 @ A3 )
% 0.18/0.46 => ( ~ ( member_a @ X2 @ B4 )
% 0.18/0.46 => ( ( ( insert_a @ X2 @ A3 )
% 0.18/0.46 = ( insert_a @ X2 @ B4 ) )
% 0.18/0.46 = ( A3 = B4 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_ident
% 0.18/0.46 thf(fact_241_Set_Oset__insert,axiom,
% 0.18/0.46 ! [X2: option_a,A3: set_option_a] :
% 0.18/0.46 ( ( member_option_a @ X2 @ A3 )
% 0.18/0.46 => ~ ! [B6: set_option_a] :
% 0.18/0.46 ( ( A3
% 0.18/0.46 = ( insert_option_a @ X2 @ B6 ) )
% 0.18/0.46 => ( member_option_a @ X2 @ B6 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Set.set_insert
% 0.18/0.46 thf(fact_242_Set_Oset__insert,axiom,
% 0.18/0.46 ! [X2: a,A3: set_a] :
% 0.18/0.46 ( ( member_a @ X2 @ A3 )
% 0.18/0.46 => ~ ! [B6: set_a] :
% 0.18/0.46 ( ( A3
% 0.18/0.46 = ( insert_a @ X2 @ B6 ) )
% 0.18/0.46 => ( member_a @ X2 @ B6 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Set.set_insert
% 0.18/0.46 thf(fact_243_insertI2,axiom,
% 0.18/0.46 ! [A: option_a,B4: set_option_a,B: option_a] :
% 0.18/0.46 ( ( member_option_a @ A @ B4 )
% 0.18/0.46 => ( member_option_a @ A @ ( insert_option_a @ B @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insertI2
% 0.18/0.46 thf(fact_244_insertI2,axiom,
% 0.18/0.46 ! [A: a,B4: set_a,B: a] :
% 0.18/0.46 ( ( member_a @ A @ B4 )
% 0.18/0.46 => ( member_a @ A @ ( insert_a @ B @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insertI2
% 0.18/0.46 thf(fact_245_insertI1,axiom,
% 0.18/0.46 ! [A: option_a,B4: set_option_a] : ( member_option_a @ A @ ( insert_option_a @ A @ B4 ) ) ).
% 0.18/0.46
% 0.18/0.46 % insertI1
% 0.18/0.46 thf(fact_246_insertI1,axiom,
% 0.18/0.46 ! [A: a,B4: set_a] : ( member_a @ A @ ( insert_a @ A @ B4 ) ) ).
% 0.18/0.46
% 0.18/0.46 % insertI1
% 0.18/0.46 thf(fact_247_insertE,axiom,
% 0.18/0.46 ! [A: option_a,B: option_a,A3: set_option_a] :
% 0.18/0.46 ( ( member_option_a @ A @ ( insert_option_a @ B @ A3 ) )
% 0.18/0.46 => ( ( A != B )
% 0.18/0.46 => ( member_option_a @ A @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insertE
% 0.18/0.46 thf(fact_248_insertE,axiom,
% 0.18/0.46 ! [A: a,B: a,A3: set_a] :
% 0.18/0.46 ( ( member_a @ A @ ( insert_a @ B @ A3 ) )
% 0.18/0.46 => ( ( A != B )
% 0.18/0.46 => ( member_a @ A @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insertE
% 0.18/0.46 thf(fact_249_insert__compr,axiom,
% 0.18/0.46 ( insert_option_a
% 0.18/0.46 = ( ^ [A2: option_a,B5: set_option_a] :
% 0.18/0.46 ( collect_option_a
% 0.18/0.46 @ ^ [X3: option_a] :
% 0.18/0.46 ( ( X3 = A2 )
% 0.18/0.46 | ( member_option_a @ X3 @ B5 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_compr
% 0.18/0.46 thf(fact_250_insert__compr,axiom,
% 0.18/0.46 ( insert_a
% 0.18/0.46 = ( ^ [A2: a,B5: set_a] :
% 0.18/0.46 ( collect_a
% 0.18/0.46 @ ^ [X3: a] :
% 0.18/0.46 ( ( X3 = A2 )
% 0.18/0.46 | ( member_a @ X3 @ B5 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_compr
% 0.18/0.46 thf(fact_251_insert__Collect,axiom,
% 0.18/0.46 ! [A: a,P: a > $o] :
% 0.18/0.46 ( ( insert_a @ A @ ( collect_a @ P ) )
% 0.18/0.46 = ( collect_a
% 0.18/0.46 @ ^ [U: a] :
% 0.18/0.46 ( ( U != A )
% 0.18/0.46 => ( P @ U ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_Collect
% 0.18/0.46 thf(fact_252_insert__Collect,axiom,
% 0.18/0.46 ! [A: option_a,P: option_a > $o] :
% 0.18/0.46 ( ( insert_option_a @ A @ ( collect_option_a @ P ) )
% 0.18/0.46 = ( collect_option_a
% 0.18/0.46 @ ^ [U: option_a] :
% 0.18/0.46 ( ( U != A )
% 0.18/0.46 => ( P @ U ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_Collect
% 0.18/0.46 thf(fact_253_singletonD,axiom,
% 0.18/0.46 ! [B: option_a,A: option_a] :
% 0.18/0.46 ( ( member_option_a @ B @ ( insert_option_a @ A @ bot_bot_set_option_a ) )
% 0.18/0.46 => ( B = A ) ) ).
% 0.18/0.46
% 0.18/0.46 % singletonD
% 0.18/0.46 thf(fact_254_singletonD,axiom,
% 0.18/0.46 ! [B: a,A: a] :
% 0.18/0.46 ( ( member_a @ B @ ( insert_a @ A @ bot_bot_set_a ) )
% 0.18/0.46 => ( B = A ) ) ).
% 0.18/0.46
% 0.18/0.46 % singletonD
% 0.18/0.46 thf(fact_255_singleton__iff,axiom,
% 0.18/0.46 ! [B: option_a,A: option_a] :
% 0.18/0.46 ( ( member_option_a @ B @ ( insert_option_a @ A @ bot_bot_set_option_a ) )
% 0.18/0.46 = ( B = A ) ) ).
% 0.18/0.46
% 0.18/0.46 % singleton_iff
% 0.18/0.46 thf(fact_256_singleton__iff,axiom,
% 0.18/0.46 ! [B: a,A: a] :
% 0.18/0.46 ( ( member_a @ B @ ( insert_a @ A @ bot_bot_set_a ) )
% 0.18/0.46 = ( B = A ) ) ).
% 0.18/0.46
% 0.18/0.46 % singleton_iff
% 0.18/0.46 thf(fact_257_doubleton__eq__iff,axiom,
% 0.18/0.46 ! [A: a,B: a,C: a,D: a] :
% 0.18/0.46 ( ( ( insert_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
% 0.18/0.46 = ( insert_a @ C @ ( insert_a @ D @ bot_bot_set_a ) ) )
% 0.18/0.46 = ( ( ( A = C )
% 0.18/0.46 & ( B = D ) )
% 0.18/0.46 | ( ( A = D )
% 0.18/0.46 & ( B = C ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % doubleton_eq_iff
% 0.18/0.46 thf(fact_258_doubleton__eq__iff,axiom,
% 0.18/0.46 ! [A: option_a,B: option_a,C: option_a,D: option_a] :
% 0.18/0.46 ( ( ( insert_option_a @ A @ ( insert_option_a @ B @ bot_bot_set_option_a ) )
% 0.18/0.46 = ( insert_option_a @ C @ ( insert_option_a @ D @ bot_bot_set_option_a ) ) )
% 0.18/0.46 = ( ( ( A = C )
% 0.18/0.46 & ( B = D ) )
% 0.18/0.46 | ( ( A = D )
% 0.18/0.46 & ( B = C ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % doubleton_eq_iff
% 0.18/0.46 thf(fact_259_insert__not__empty,axiom,
% 0.18/0.46 ! [A: a,A3: set_a] :
% 0.18/0.46 ( ( insert_a @ A @ A3 )
% 0.18/0.46 != bot_bot_set_a ) ).
% 0.18/0.46
% 0.18/0.46 % insert_not_empty
% 0.18/0.46 thf(fact_260_insert__not__empty,axiom,
% 0.18/0.46 ! [A: option_a,A3: set_option_a] :
% 0.18/0.46 ( ( insert_option_a @ A @ A3 )
% 0.18/0.46 != bot_bot_set_option_a ) ).
% 0.18/0.46
% 0.18/0.46 % insert_not_empty
% 0.18/0.46 thf(fact_261_singleton__inject,axiom,
% 0.18/0.46 ! [A: a,B: a] :
% 0.18/0.46 ( ( ( insert_a @ A @ bot_bot_set_a )
% 0.18/0.46 = ( insert_a @ B @ bot_bot_set_a ) )
% 0.18/0.46 => ( A = B ) ) ).
% 0.18/0.46
% 0.18/0.46 % singleton_inject
% 0.18/0.46 thf(fact_262_singleton__inject,axiom,
% 0.18/0.46 ! [A: option_a,B: option_a] :
% 0.18/0.46 ( ( ( insert_option_a @ A @ bot_bot_set_option_a )
% 0.18/0.46 = ( insert_option_a @ B @ bot_bot_set_option_a ) )
% 0.18/0.46 => ( A = B ) ) ).
% 0.18/0.46
% 0.18/0.46 % singleton_inject
% 0.18/0.46 thf(fact_263_Collect__conv__if,axiom,
% 0.18/0.46 ! [P: a > $o,A: a] :
% 0.18/0.46 ( ( ( P @ A )
% 0.18/0.46 => ( ( collect_a
% 0.18/0.46 @ ^ [X3: a] :
% 0.18/0.46 ( ( X3 = A )
% 0.18/0.46 & ( P @ X3 ) ) )
% 0.18/0.46 = ( insert_a @ A @ bot_bot_set_a ) ) )
% 0.18/0.46 & ( ~ ( P @ A )
% 0.18/0.46 => ( ( collect_a
% 0.18/0.46 @ ^ [X3: a] :
% 0.18/0.46 ( ( X3 = A )
% 0.18/0.46 & ( P @ X3 ) ) )
% 0.18/0.46 = bot_bot_set_a ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Collect_conv_if
% 0.18/0.46 thf(fact_264_Collect__conv__if,axiom,
% 0.18/0.46 ! [P: option_a > $o,A: option_a] :
% 0.18/0.46 ( ( ( P @ A )
% 0.18/0.46 => ( ( collect_option_a
% 0.18/0.46 @ ^ [X3: option_a] :
% 0.18/0.46 ( ( X3 = A )
% 0.18/0.46 & ( P @ X3 ) ) )
% 0.18/0.46 = ( insert_option_a @ A @ bot_bot_set_option_a ) ) )
% 0.18/0.46 & ( ~ ( P @ A )
% 0.18/0.46 => ( ( collect_option_a
% 0.18/0.46 @ ^ [X3: option_a] :
% 0.18/0.46 ( ( X3 = A )
% 0.18/0.46 & ( P @ X3 ) ) )
% 0.18/0.46 = bot_bot_set_option_a ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Collect_conv_if
% 0.18/0.46 thf(fact_265_Collect__conv__if2,axiom,
% 0.18/0.46 ! [P: a > $o,A: a] :
% 0.18/0.46 ( ( ( P @ A )
% 0.18/0.46 => ( ( collect_a
% 0.18/0.46 @ ^ [X3: a] :
% 0.18/0.46 ( ( A = X3 )
% 0.18/0.46 & ( P @ X3 ) ) )
% 0.18/0.46 = ( insert_a @ A @ bot_bot_set_a ) ) )
% 0.18/0.46 & ( ~ ( P @ A )
% 0.18/0.46 => ( ( collect_a
% 0.18/0.46 @ ^ [X3: a] :
% 0.18/0.46 ( ( A = X3 )
% 0.18/0.46 & ( P @ X3 ) ) )
% 0.18/0.46 = bot_bot_set_a ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Collect_conv_if2
% 0.18/0.46 thf(fact_266_Collect__conv__if2,axiom,
% 0.18/0.46 ! [P: option_a > $o,A: option_a] :
% 0.18/0.46 ( ( ( P @ A )
% 0.18/0.46 => ( ( collect_option_a
% 0.18/0.46 @ ^ [X3: option_a] :
% 0.18/0.46 ( ( A = X3 )
% 0.18/0.46 & ( P @ X3 ) ) )
% 0.18/0.46 = ( insert_option_a @ A @ bot_bot_set_option_a ) ) )
% 0.18/0.46 & ( ~ ( P @ A )
% 0.18/0.46 => ( ( collect_option_a
% 0.18/0.46 @ ^ [X3: option_a] :
% 0.18/0.46 ( ( A = X3 )
% 0.18/0.46 & ( P @ X3 ) ) )
% 0.18/0.46 = bot_bot_set_option_a ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Collect_conv_if2
% 0.18/0.46 thf(fact_267_the__elem__eq,axiom,
% 0.18/0.46 ! [X2: a] :
% 0.18/0.46 ( ( the_elem_a @ ( insert_a @ X2 @ bot_bot_set_a ) )
% 0.18/0.46 = X2 ) ).
% 0.18/0.46
% 0.18/0.46 % the_elem_eq
% 0.18/0.46 thf(fact_268_the__elem__eq,axiom,
% 0.18/0.46 ! [X2: option_a] :
% 0.18/0.46 ( ( the_elem_option_a @ ( insert_option_a @ X2 @ bot_bot_set_option_a ) )
% 0.18/0.46 = X2 ) ).
% 0.18/0.46
% 0.18/0.46 % the_elem_eq
% 0.18/0.46 thf(fact_269_is__singletonI,axiom,
% 0.18/0.46 ! [X2: a] : ( is_singleton_a @ ( insert_a @ X2 @ bot_bot_set_a ) ) ).
% 0.18/0.46
% 0.18/0.46 % is_singletonI
% 0.18/0.46 thf(fact_270_is__singletonI,axiom,
% 0.18/0.46 ! [X2: option_a] : ( is_sin1624444472tion_a @ ( insert_option_a @ X2 @ bot_bot_set_option_a ) ) ).
% 0.18/0.46
% 0.18/0.46 % is_singletonI
% 0.18/0.46 thf(fact_271_these__insert__Some,axiom,
% 0.18/0.46 ! [X2: option_a,A3: set_option_option_a] :
% 0.18/0.46 ( ( these_option_a @ ( insert1662731738tion_a @ ( some_option_a @ X2 ) @ A3 ) )
% 0.18/0.46 = ( insert_option_a @ X2 @ ( these_option_a @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % these_insert_Some
% 0.18/0.46 thf(fact_272_these__insert__Some,axiom,
% 0.18/0.46 ! [X2: a,A3: set_option_a] :
% 0.18/0.46 ( ( these_a @ ( insert_option_a @ ( some_a @ X2 ) @ A3 ) )
% 0.18/0.46 = ( insert_a @ X2 @ ( these_a @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % these_insert_Some
% 0.18/0.46 thf(fact_273_is__singletonE,axiom,
% 0.18/0.46 ! [A3: set_a] :
% 0.18/0.46 ( ( is_singleton_a @ A3 )
% 0.18/0.46 => ~ ! [X4: a] :
% 0.18/0.46 ( A3
% 0.18/0.46 != ( insert_a @ X4 @ bot_bot_set_a ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % is_singletonE
% 0.18/0.46 thf(fact_274_is__singletonE,axiom,
% 0.18/0.46 ! [A3: set_option_a] :
% 0.18/0.46 ( ( is_sin1624444472tion_a @ A3 )
% 0.18/0.46 => ~ ! [X4: option_a] :
% 0.18/0.46 ( A3
% 0.18/0.46 != ( insert_option_a @ X4 @ bot_bot_set_option_a ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % is_singletonE
% 0.18/0.46 thf(fact_275_these__empty,axiom,
% 0.18/0.46 ( ( these_option_a @ bot_bo1607647958tion_a )
% 0.18/0.46 = bot_bot_set_option_a ) ).
% 0.18/0.46
% 0.18/0.46 % these_empty
% 0.18/0.46 thf(fact_276_these__empty,axiom,
% 0.18/0.46 ( ( these_a @ bot_bot_set_option_a )
% 0.18/0.46 = bot_bot_set_a ) ).
% 0.18/0.46
% 0.18/0.46 % these_empty
% 0.18/0.46 thf(fact_277_these__insert__None,axiom,
% 0.18/0.46 ! [A3: set_option_a] :
% 0.18/0.46 ( ( these_a @ ( insert_option_a @ none_a @ A3 ) )
% 0.18/0.46 = ( these_a @ A3 ) ) ).
% 0.18/0.46
% 0.18/0.46 % these_insert_None
% 0.18/0.46 thf(fact_278_in__these__eq,axiom,
% 0.18/0.46 ! [X2: option_a,A3: set_option_option_a] :
% 0.18/0.46 ( ( member_option_a @ X2 @ ( these_option_a @ A3 ) )
% 0.18/0.46 = ( member553679923tion_a @ ( some_option_a @ X2 ) @ A3 ) ) ).
% 0.18/0.46
% 0.18/0.46 % in_these_eq
% 0.18/0.46 thf(fact_279_in__these__eq,axiom,
% 0.18/0.46 ! [X2: a,A3: set_option_a] :
% 0.18/0.46 ( ( member_a @ X2 @ ( these_a @ A3 ) )
% 0.18/0.46 = ( member_option_a @ ( some_a @ X2 ) @ A3 ) ) ).
% 0.18/0.46
% 0.18/0.46 % in_these_eq
% 0.18/0.46 thf(fact_280_is__singleton__the__elem,axiom,
% 0.18/0.46 ( is_singleton_a
% 0.18/0.46 = ( ^ [A5: set_a] :
% 0.18/0.46 ( A5
% 0.18/0.46 = ( insert_a @ ( the_elem_a @ A5 ) @ bot_bot_set_a ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % is_singleton_the_elem
% 0.18/0.46 thf(fact_281_is__singleton__the__elem,axiom,
% 0.18/0.46 ( is_sin1624444472tion_a
% 0.18/0.46 = ( ^ [A5: set_option_a] :
% 0.18/0.46 ( A5
% 0.18/0.46 = ( insert_option_a @ ( the_elem_option_a @ A5 ) @ bot_bot_set_option_a ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % is_singleton_the_elem
% 0.18/0.46 thf(fact_282_is__singletonI_H,axiom,
% 0.18/0.46 ! [A3: set_option_a] :
% 0.18/0.46 ( ( A3 != bot_bot_set_option_a )
% 0.18/0.46 => ( ! [X4: option_a,Y4: option_a] :
% 0.18/0.46 ( ( member_option_a @ X4 @ A3 )
% 0.18/0.46 => ( ( member_option_a @ Y4 @ A3 )
% 0.18/0.46 => ( X4 = Y4 ) ) )
% 0.18/0.46 => ( is_sin1624444472tion_a @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % is_singletonI'
% 0.18/0.46 thf(fact_283_is__singletonI_H,axiom,
% 0.18/0.46 ! [A3: set_a] :
% 0.18/0.46 ( ( A3 != bot_bot_set_a )
% 0.18/0.46 => ( ! [X4: a,Y4: a] :
% 0.18/0.46 ( ( member_a @ X4 @ A3 )
% 0.18/0.46 => ( ( member_a @ Y4 @ A3 )
% 0.18/0.46 => ( X4 = Y4 ) ) )
% 0.18/0.46 => ( is_singleton_a @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % is_singletonI'
% 0.18/0.46 thf(fact_284_these__not__empty__eq,axiom,
% 0.18/0.46 ! [B4: set_option_option_a] :
% 0.18/0.46 ( ( ( these_option_a @ B4 )
% 0.18/0.46 != bot_bot_set_option_a )
% 0.18/0.46 = ( ( B4 != bot_bo1607647958tion_a )
% 0.18/0.46 & ( B4
% 0.18/0.46 != ( insert1662731738tion_a @ none_option_a @ bot_bo1607647958tion_a ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % these_not_empty_eq
% 0.18/0.46 thf(fact_285_these__not__empty__eq,axiom,
% 0.18/0.46 ! [B4: set_option_a] :
% 0.18/0.46 ( ( ( these_a @ B4 )
% 0.18/0.46 != bot_bot_set_a )
% 0.18/0.46 = ( ( B4 != bot_bot_set_option_a )
% 0.18/0.46 & ( B4
% 0.18/0.46 != ( insert_option_a @ none_a @ bot_bot_set_option_a ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % these_not_empty_eq
% 0.18/0.46 thf(fact_286_these__empty__eq,axiom,
% 0.18/0.46 ! [B4: set_option_option_a] :
% 0.18/0.46 ( ( ( these_option_a @ B4 )
% 0.18/0.46 = bot_bot_set_option_a )
% 0.18/0.46 = ( ( B4 = bot_bo1607647958tion_a )
% 0.18/0.46 | ( B4
% 0.18/0.46 = ( insert1662731738tion_a @ none_option_a @ bot_bo1607647958tion_a ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % these_empty_eq
% 0.18/0.46 thf(fact_287_these__empty__eq,axiom,
% 0.18/0.46 ! [B4: set_option_a] :
% 0.18/0.46 ( ( ( these_a @ B4 )
% 0.18/0.46 = bot_bot_set_a )
% 0.18/0.46 = ( ( B4 = bot_bot_set_option_a )
% 0.18/0.46 | ( B4
% 0.18/0.46 = ( insert_option_a @ none_a @ bot_bot_set_option_a ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % these_empty_eq
% 0.18/0.46 thf(fact_288_is__singleton__def,axiom,
% 0.18/0.46 ( is_singleton_a
% 0.18/0.46 = ( ^ [A5: set_a] :
% 0.18/0.46 ? [X3: a] :
% 0.18/0.46 ( A5
% 0.18/0.46 = ( insert_a @ X3 @ bot_bot_set_a ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % is_singleton_def
% 0.18/0.46 thf(fact_289_is__singleton__def,axiom,
% 0.18/0.46 ( is_sin1624444472tion_a
% 0.18/0.46 = ( ^ [A5: set_option_a] :
% 0.18/0.46 ? [X3: option_a] :
% 0.18/0.46 ( A5
% 0.18/0.46 = ( insert_option_a @ X3 @ bot_bot_set_option_a ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % is_singleton_def
% 0.18/0.46 thf(fact_290_the__elem__def,axiom,
% 0.18/0.46 ( the_elem_a
% 0.18/0.46 = ( ^ [X6: set_a] :
% 0.18/0.46 ( the_a
% 0.18/0.46 @ ^ [X3: a] :
% 0.18/0.46 ( X6
% 0.18/0.46 = ( insert_a @ X3 @ bot_bot_set_a ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % the_elem_def
% 0.18/0.46 thf(fact_291_the__elem__def,axiom,
% 0.18/0.46 ( the_elem_option_a
% 0.18/0.46 = ( ^ [X6: set_option_a] :
% 0.18/0.46 ( the_option_a
% 0.18/0.46 @ ^ [X3: option_a] :
% 0.18/0.46 ( X6
% 0.18/0.46 = ( insert_option_a @ X3 @ bot_bot_set_option_a ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % the_elem_def
% 0.18/0.46 thf(fact_292_setOf_Osimps_I2_J,axiom,
% 0.18/0.46 ! [T1: binary1176601351tion_a,X2: option_a,T22: binary1176601351tion_a] :
% 0.18/0.46 ( ( binary1117200954tion_a @ ( binary1007279693tion_a @ T1 @ X2 @ T22 ) )
% 0.18/0.46 = ( sup_sup_set_option_a @ ( sup_sup_set_option_a @ ( binary1117200954tion_a @ T1 ) @ ( binary1117200954tion_a @ T22 ) ) @ ( insert_option_a @ X2 @ bot_bot_set_option_a ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % setOf.simps(2)
% 0.18/0.46 thf(fact_293_setOf_Osimps_I2_J,axiom,
% 0.18/0.46 ! [T1: binary1439146945Tree_a,X2: a,T22: binary1439146945Tree_a] :
% 0.18/0.46 ( ( binary945792244etOf_a @ ( binary717961607le_T_a @ T1 @ X2 @ T22 ) )
% 0.18/0.46 = ( sup_sup_set_a @ ( sup_sup_set_a @ ( binary945792244etOf_a @ T1 ) @ ( binary945792244etOf_a @ T22 ) ) @ ( insert_a @ X2 @ bot_bot_set_a ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % setOf.simps(2)
% 0.18/0.46 thf(fact_294_Option_Othese__def,axiom,
% 0.18/0.46 ( these_a
% 0.18/0.46 = ( ^ [A5: set_option_a] :
% 0.18/0.46 ( image_option_a_a @ the_a2
% 0.18/0.46 @ ( collect_option_a
% 0.18/0.46 @ ^ [X3: option_a] :
% 0.18/0.46 ( ( member_option_a @ X3 @ A5 )
% 0.18/0.46 & ( X3 != none_a ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Option.these_def
% 0.18/0.46 thf(fact_295_image__eqI,axiom,
% 0.18/0.46 ! [B: option_a,F: a > option_a,X2: a,A3: set_a] :
% 0.18/0.46 ( ( B
% 0.18/0.46 = ( F @ X2 ) )
% 0.18/0.46 => ( ( member_a @ X2 @ A3 )
% 0.18/0.46 => ( member_option_a @ B @ ( image_a_option_a @ F @ A3 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % image_eqI
% 0.18/0.46 thf(fact_296_image__eqI,axiom,
% 0.18/0.46 ! [B: a,F: option_a > a,X2: option_a,A3: set_option_a] :
% 0.18/0.46 ( ( B
% 0.18/0.46 = ( F @ X2 ) )
% 0.18/0.46 => ( ( member_option_a @ X2 @ A3 )
% 0.18/0.46 => ( member_a @ B @ ( image_option_a_a @ F @ A3 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % image_eqI
% 0.18/0.46 thf(fact_297_image__eqI,axiom,
% 0.18/0.46 ! [B: option_a,F: option_a > option_a,X2: option_a,A3: set_option_a] :
% 0.18/0.46 ( ( B
% 0.18/0.46 = ( F @ X2 ) )
% 0.18/0.46 => ( ( member_option_a @ X2 @ A3 )
% 0.18/0.46 => ( member_option_a @ B @ ( image_139503237tion_a @ F @ A3 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % image_eqI
% 0.18/0.46 thf(fact_298_image__eqI,axiom,
% 0.18/0.46 ! [B: a,F: a > a,X2: a,A3: set_a] :
% 0.18/0.46 ( ( B
% 0.18/0.46 = ( F @ X2 ) )
% 0.18/0.46 => ( ( member_a @ X2 @ A3 )
% 0.18/0.46 => ( member_a @ B @ ( image_a_a @ F @ A3 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % image_eqI
% 0.18/0.46 thf(fact_299_Un__iff,axiom,
% 0.18/0.46 ! [C: option_a,A3: set_option_a,B4: set_option_a] :
% 0.18/0.46 ( ( member_option_a @ C @ ( sup_sup_set_option_a @ A3 @ B4 ) )
% 0.18/0.46 = ( ( member_option_a @ C @ A3 )
% 0.18/0.46 | ( member_option_a @ C @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Un_iff
% 0.18/0.46 thf(fact_300_Un__iff,axiom,
% 0.18/0.46 ! [C: a,A3: set_a,B4: set_a] :
% 0.18/0.46 ( ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) )
% 0.18/0.46 = ( ( member_a @ C @ A3 )
% 0.18/0.46 | ( member_a @ C @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Un_iff
% 0.18/0.46 thf(fact_301_UnCI,axiom,
% 0.18/0.46 ! [C: option_a,B4: set_option_a,A3: set_option_a] :
% 0.18/0.46 ( ( ~ ( member_option_a @ C @ B4 )
% 0.18/0.46 => ( member_option_a @ C @ A3 ) )
% 0.18/0.46 => ( member_option_a @ C @ ( sup_sup_set_option_a @ A3 @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % UnCI
% 0.18/0.46 thf(fact_302_UnCI,axiom,
% 0.18/0.46 ! [C: a,B4: set_a,A3: set_a] :
% 0.18/0.46 ( ( ~ ( member_a @ C @ B4 )
% 0.18/0.46 => ( member_a @ C @ A3 ) )
% 0.18/0.46 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % UnCI
% 0.18/0.46 thf(fact_303_image__ident,axiom,
% 0.18/0.46 ! [Y5: set_a] :
% 0.18/0.46 ( ( image_a_a
% 0.18/0.46 @ ^ [X3: a] : X3
% 0.18/0.46 @ Y5 )
% 0.18/0.46 = Y5 ) ).
% 0.18/0.46
% 0.18/0.46 % image_ident
% 0.18/0.46 thf(fact_304_image__is__empty,axiom,
% 0.18/0.46 ! [F: a > a,A3: set_a] :
% 0.18/0.46 ( ( ( image_a_a @ F @ A3 )
% 0.18/0.46 = bot_bot_set_a )
% 0.18/0.46 = ( A3 = bot_bot_set_a ) ) ).
% 0.18/0.46
% 0.18/0.46 % image_is_empty
% 0.18/0.46 thf(fact_305_image__is__empty,axiom,
% 0.18/0.46 ! [F: option_a > a,A3: set_option_a] :
% 0.18/0.46 ( ( ( image_option_a_a @ F @ A3 )
% 0.18/0.46 = bot_bot_set_a )
% 0.18/0.46 = ( A3 = bot_bot_set_option_a ) ) ).
% 0.18/0.46
% 0.18/0.46 % image_is_empty
% 0.18/0.46 thf(fact_306_image__is__empty,axiom,
% 0.18/0.46 ! [F: a > option_a,A3: set_a] :
% 0.18/0.46 ( ( ( image_a_option_a @ F @ A3 )
% 0.18/0.46 = bot_bot_set_option_a )
% 0.18/0.46 = ( A3 = bot_bot_set_a ) ) ).
% 0.18/0.46
% 0.18/0.46 % image_is_empty
% 0.18/0.46 thf(fact_307_image__is__empty,axiom,
% 0.18/0.46 ! [F: option_a > option_a,A3: set_option_a] :
% 0.18/0.46 ( ( ( image_139503237tion_a @ F @ A3 )
% 0.18/0.46 = bot_bot_set_option_a )
% 0.18/0.46 = ( A3 = bot_bot_set_option_a ) ) ).
% 0.18/0.46
% 0.18/0.46 % image_is_empty
% 0.18/0.46 thf(fact_308_empty__is__image,axiom,
% 0.18/0.46 ! [F: a > a,A3: set_a] :
% 0.18/0.46 ( ( bot_bot_set_a
% 0.18/0.46 = ( image_a_a @ F @ A3 ) )
% 0.18/0.46 = ( A3 = bot_bot_set_a ) ) ).
% 0.18/0.46
% 0.18/0.46 % empty_is_image
% 0.18/0.46 thf(fact_309_empty__is__image,axiom,
% 0.18/0.46 ! [F: option_a > a,A3: set_option_a] :
% 0.18/0.46 ( ( bot_bot_set_a
% 0.18/0.46 = ( image_option_a_a @ F @ A3 ) )
% 0.18/0.46 = ( A3 = bot_bot_set_option_a ) ) ).
% 0.18/0.46
% 0.18/0.46 % empty_is_image
% 0.18/0.46 thf(fact_310_empty__is__image,axiom,
% 0.18/0.46 ! [F: a > option_a,A3: set_a] :
% 0.18/0.46 ( ( bot_bot_set_option_a
% 0.18/0.46 = ( image_a_option_a @ F @ A3 ) )
% 0.18/0.46 = ( A3 = bot_bot_set_a ) ) ).
% 0.18/0.46
% 0.18/0.46 % empty_is_image
% 0.18/0.46 thf(fact_311_empty__is__image,axiom,
% 0.18/0.46 ! [F: option_a > option_a,A3: set_option_a] :
% 0.18/0.46 ( ( bot_bot_set_option_a
% 0.18/0.46 = ( image_139503237tion_a @ F @ A3 ) )
% 0.18/0.46 = ( A3 = bot_bot_set_option_a ) ) ).
% 0.18/0.46
% 0.18/0.46 % empty_is_image
% 0.18/0.46 thf(fact_312_image__empty,axiom,
% 0.18/0.46 ! [F: a > a] :
% 0.18/0.46 ( ( image_a_a @ F @ bot_bot_set_a )
% 0.18/0.46 = bot_bot_set_a ) ).
% 0.18/0.46
% 0.18/0.46 % image_empty
% 0.18/0.46 thf(fact_313_image__empty,axiom,
% 0.18/0.46 ! [F: a > option_a] :
% 0.18/0.46 ( ( image_a_option_a @ F @ bot_bot_set_a )
% 0.18/0.46 = bot_bot_set_option_a ) ).
% 0.18/0.46
% 0.18/0.46 % image_empty
% 0.18/0.46 thf(fact_314_image__empty,axiom,
% 0.18/0.46 ! [F: option_a > a] :
% 0.18/0.46 ( ( image_option_a_a @ F @ bot_bot_set_option_a )
% 0.18/0.46 = bot_bot_set_a ) ).
% 0.18/0.46
% 0.18/0.46 % image_empty
% 0.18/0.46 thf(fact_315_image__empty,axiom,
% 0.18/0.46 ! [F: option_a > option_a] :
% 0.18/0.46 ( ( image_139503237tion_a @ F @ bot_bot_set_option_a )
% 0.18/0.46 = bot_bot_set_option_a ) ).
% 0.18/0.46
% 0.18/0.46 % image_empty
% 0.18/0.46 thf(fact_316_image__insert,axiom,
% 0.18/0.46 ! [F: a > a,A: a,B4: set_a] :
% 0.18/0.46 ( ( image_a_a @ F @ ( insert_a @ A @ B4 ) )
% 0.18/0.46 = ( insert_a @ ( F @ A ) @ ( image_a_a @ F @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % image_insert
% 0.18/0.46 thf(fact_317_image__insert,axiom,
% 0.18/0.46 ! [F: a > option_a,A: a,B4: set_a] :
% 0.18/0.46 ( ( image_a_option_a @ F @ ( insert_a @ A @ B4 ) )
% 0.18/0.46 = ( insert_option_a @ ( F @ A ) @ ( image_a_option_a @ F @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % image_insert
% 0.18/0.46 thf(fact_318_image__insert,axiom,
% 0.18/0.46 ! [F: option_a > a,A: option_a,B4: set_option_a] :
% 0.18/0.46 ( ( image_option_a_a @ F @ ( insert_option_a @ A @ B4 ) )
% 0.18/0.46 = ( insert_a @ ( F @ A ) @ ( image_option_a_a @ F @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % image_insert
% 0.18/0.46 thf(fact_319_image__insert,axiom,
% 0.18/0.46 ! [F: option_a > option_a,A: option_a,B4: set_option_a] :
% 0.18/0.46 ( ( image_139503237tion_a @ F @ ( insert_option_a @ A @ B4 ) )
% 0.18/0.46 = ( insert_option_a @ ( F @ A ) @ ( image_139503237tion_a @ F @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % image_insert
% 0.18/0.46 thf(fact_320_insert__image,axiom,
% 0.18/0.46 ! [X2: a,A3: set_a,F: a > a] :
% 0.18/0.46 ( ( member_a @ X2 @ A3 )
% 0.18/0.46 => ( ( insert_a @ ( F @ X2 ) @ ( image_a_a @ F @ A3 ) )
% 0.18/0.46 = ( image_a_a @ F @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_image
% 0.18/0.46 thf(fact_321_insert__image,axiom,
% 0.18/0.46 ! [X2: a,A3: set_a,F: a > option_a] :
% 0.18/0.46 ( ( member_a @ X2 @ A3 )
% 0.18/0.46 => ( ( insert_option_a @ ( F @ X2 ) @ ( image_a_option_a @ F @ A3 ) )
% 0.18/0.46 = ( image_a_option_a @ F @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_image
% 0.18/0.46 thf(fact_322_insert__image,axiom,
% 0.18/0.46 ! [X2: option_a,A3: set_option_a,F: option_a > a] :
% 0.18/0.46 ( ( member_option_a @ X2 @ A3 )
% 0.18/0.46 => ( ( insert_a @ ( F @ X2 ) @ ( image_option_a_a @ F @ A3 ) )
% 0.18/0.46 = ( image_option_a_a @ F @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_image
% 0.18/0.46 thf(fact_323_insert__image,axiom,
% 0.18/0.46 ! [X2: option_a,A3: set_option_a,F: option_a > option_a] :
% 0.18/0.46 ( ( member_option_a @ X2 @ A3 )
% 0.18/0.46 => ( ( insert_option_a @ ( F @ X2 ) @ ( image_139503237tion_a @ F @ A3 ) )
% 0.18/0.46 = ( image_139503237tion_a @ F @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_image
% 0.18/0.46 thf(fact_324_Un__empty,axiom,
% 0.18/0.46 ! [A3: set_a,B4: set_a] :
% 0.18/0.46 ( ( ( sup_sup_set_a @ A3 @ B4 )
% 0.18/0.46 = bot_bot_set_a )
% 0.18/0.46 = ( ( A3 = bot_bot_set_a )
% 0.18/0.46 & ( B4 = bot_bot_set_a ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Un_empty
% 0.18/0.46 thf(fact_325_Un__empty,axiom,
% 0.18/0.46 ! [A3: set_option_a,B4: set_option_a] :
% 0.18/0.46 ( ( ( sup_sup_set_option_a @ A3 @ B4 )
% 0.18/0.46 = bot_bot_set_option_a )
% 0.18/0.46 = ( ( A3 = bot_bot_set_option_a )
% 0.18/0.46 & ( B4 = bot_bot_set_option_a ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Un_empty
% 0.18/0.46 thf(fact_326_Un__insert__left,axiom,
% 0.18/0.46 ! [A: option_a,B4: set_option_a,C2: set_option_a] :
% 0.18/0.46 ( ( sup_sup_set_option_a @ ( insert_option_a @ A @ B4 ) @ C2 )
% 0.18/0.46 = ( insert_option_a @ A @ ( sup_sup_set_option_a @ B4 @ C2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Un_insert_left
% 0.18/0.46 thf(fact_327_Un__insert__left,axiom,
% 0.18/0.46 ! [A: a,B4: set_a,C2: set_a] :
% 0.18/0.46 ( ( sup_sup_set_a @ ( insert_a @ A @ B4 ) @ C2 )
% 0.18/0.46 = ( insert_a @ A @ ( sup_sup_set_a @ B4 @ C2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Un_insert_left
% 0.18/0.46 thf(fact_328_Un__insert__right,axiom,
% 0.18/0.46 ! [A3: set_option_a,A: option_a,B4: set_option_a] :
% 0.18/0.46 ( ( sup_sup_set_option_a @ A3 @ ( insert_option_a @ A @ B4 ) )
% 0.18/0.46 = ( insert_option_a @ A @ ( sup_sup_set_option_a @ A3 @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Un_insert_right
% 0.18/0.46 thf(fact_329_Un__insert__right,axiom,
% 0.18/0.46 ! [A3: set_a,A: a,B4: set_a] :
% 0.18/0.46 ( ( sup_sup_set_a @ A3 @ ( insert_a @ A @ B4 ) )
% 0.18/0.46 = ( insert_a @ A @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Un_insert_right
% 0.18/0.46 thf(fact_330_insert__def,axiom,
% 0.18/0.46 ( insert_option_a
% 0.18/0.46 = ( ^ [A2: option_a] :
% 0.18/0.46 ( sup_sup_set_option_a
% 0.18/0.46 @ ( collect_option_a
% 0.18/0.46 @ ^ [X3: option_a] : ( X3 = A2 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_def
% 0.18/0.46 thf(fact_331_insert__def,axiom,
% 0.18/0.46 ( insert_a
% 0.18/0.46 = ( ^ [A2: a] :
% 0.18/0.46 ( sup_sup_set_a
% 0.18/0.46 @ ( collect_a
% 0.18/0.46 @ ^ [X3: a] : ( X3 = A2 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % insert_def
% 0.18/0.46 thf(fact_332_Un__left__commute,axiom,
% 0.18/0.46 ! [A3: set_a,B4: set_a,C2: set_a] :
% 0.18/0.46 ( ( sup_sup_set_a @ A3 @ ( sup_sup_set_a @ B4 @ C2 ) )
% 0.18/0.46 = ( sup_sup_set_a @ B4 @ ( sup_sup_set_a @ A3 @ C2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Un_left_commute
% 0.18/0.46 thf(fact_333_Un__left__absorb,axiom,
% 0.18/0.46 ! [A3: set_a,B4: set_a] :
% 0.18/0.46 ( ( sup_sup_set_a @ A3 @ ( sup_sup_set_a @ A3 @ B4 ) )
% 0.18/0.46 = ( sup_sup_set_a @ A3 @ B4 ) ) ).
% 0.18/0.46
% 0.18/0.46 % Un_left_absorb
% 0.18/0.46 thf(fact_334_rev__image__eqI,axiom,
% 0.18/0.46 ! [X2: option_a,A3: set_option_a,B: option_a,F: option_a > option_a] :
% 0.18/0.46 ( ( member_option_a @ X2 @ A3 )
% 0.18/0.46 => ( ( B
% 0.18/0.46 = ( F @ X2 ) )
% 0.18/0.46 => ( member_option_a @ B @ ( image_139503237tion_a @ F @ A3 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % rev_image_eqI
% 0.18/0.46 thf(fact_335_rev__image__eqI,axiom,
% 0.18/0.46 ! [X2: a,A3: set_a,B: a,F: a > a] :
% 0.18/0.46 ( ( member_a @ X2 @ A3 )
% 0.18/0.46 => ( ( B
% 0.18/0.46 = ( F @ X2 ) )
% 0.18/0.46 => ( member_a @ B @ ( image_a_a @ F @ A3 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % rev_image_eqI
% 0.18/0.46 thf(fact_336_imageI,axiom,
% 0.18/0.46 ! [X2: a,A3: set_a,F: a > a] :
% 0.18/0.46 ( ( member_a @ X2 @ A3 )
% 0.18/0.46 => ( member_a @ ( F @ X2 ) @ ( image_a_a @ F @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % imageI
% 0.18/0.46 thf(fact_337_UnI2,axiom,
% 0.18/0.46 ! [C: a,B4: set_a,A3: set_a] :
% 0.18/0.46 ( ( member_a @ C @ B4 )
% 0.18/0.46 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % UnI2
% 0.18/0.46 thf(fact_338_UnI1,axiom,
% 0.18/0.46 ! [C: a,A3: set_a,B4: set_a] :
% 0.18/0.46 ( ( member_a @ C @ A3 )
% 0.18/0.46 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % UnI1
% 0.18/0.46 thf(fact_339_UnE,axiom,
% 0.18/0.46 ! [C: a,A3: set_a,B4: set_a] :
% 0.18/0.46 ( ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) )
% 0.18/0.46 => ( ~ ( member_a @ C @ A3 )
% 0.18/0.46 => ( member_a @ C @ B4 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % UnE
% 0.18/0.46 thf(fact_340_Un__def,axiom,
% 0.18/0.46 ( sup_sup_set_a
% 0.18/0.46 = ( ^ [A5: set_a,B5: set_a] :
% 0.18/0.46 ( collect_a
% 0.18/0.46 @ ^ [X3: a] :
% 0.18/0.46 ( ( member_a @ X3 @ A5 )
% 0.18/0.46 | ( member_a @ X3 @ B5 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Un_def
% 0.18/0.46 thf(fact_341_imageE,axiom,
% 0.18/0.46 ! [B: a,F: a > a,A3: set_a] :
% 0.18/0.46 ( ( member_a @ B @ ( image_a_a @ F @ A3 ) )
% 0.18/0.46 => ~ ! [X4: a] :
% 0.18/0.46 ( ( B
% 0.18/0.46 = ( F @ X4 ) )
% 0.18/0.46 => ~ ( member_a @ X4 @ A3 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % imageE
% 0.18/0.46 thf(fact_342_Compr__image__eq,axiom,
% 0.18/0.46 ! [F: a > a,A3: set_a,P: a > $o] :
% 0.18/0.46 ( ( collect_a
% 0.18/0.46 @ ^ [X3: a] :
% 0.18/0.46 ( ( member_a @ X3 @ ( image_a_a @ F @ A3 ) )
% 0.18/0.46 & ( P @ X3 ) ) )
% 0.18/0.46 = ( image_a_a @ F
% 0.18/0.46 @ ( collect_a
% 0.18/0.46 @ ^ [X3: a] :
% 0.18/0.46 ( ( member_a @ X3 @ A3 )
% 0.18/0.46 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Compr_image_eq
% 0.18/0.46 thf(fact_343_sup__set__def,axiom,
% 0.18/0.46 ( sup_sup_set_a
% 0.18/0.46 = ( ^ [A5: set_a,B5: set_a] :
% 0.18/0.46 ( collect_a
% 0.18/0.46 @ ( sup_sup_a_o
% 0.18/0.46 @ ^ [X3: a] : ( member_a @ X3 @ A5 )
% 0.18/0.46 @ ^ [X3: a] : ( member_a @ X3 @ B5 ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % sup_set_def
% 0.18/0.46 thf(fact_344_sup__Un__eq,axiom,
% 0.18/0.46 ! [R: set_a,S: set_a] :
% 0.18/0.46 ( ( sup_sup_a_o
% 0.18/0.46 @ ^ [X3: a] : ( member_a @ X3 @ R )
% 0.18/0.46 @ ^ [X3: a] : ( member_a @ X3 @ S ) )
% 0.18/0.46 = ( ^ [X3: a] : ( member_a @ X3 @ ( sup_sup_set_a @ R @ S ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % sup_Un_eq
% 0.18/0.46 thf(fact_345_None__notin__image__Some,axiom,
% 0.18/0.46 ! [A3: set_a] :
% 0.18/0.46 ~ ( member_option_a @ none_a @ ( image_a_option_a @ some_a @ A3 ) ) ).
% 0.18/0.46
% 0.18/0.46 % None_notin_image_Some
% 0.18/0.46 thf(fact_346_Some__image__these__eq,axiom,
% 0.18/0.46 ! [A3: set_option_a] :
% 0.18/0.46 ( ( image_a_option_a @ some_a @ ( these_a @ A3 ) )
% 0.18/0.46 = ( collect_option_a
% 0.18/0.46 @ ^ [X3: option_a] :
% 0.18/0.46 ( ( member_option_a @ X3 @ A3 )
% 0.18/0.46 & ( X3 != none_a ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Some_image_these_eq
% 0.18/0.46 thf(fact_347_Tree_Osimps_I15_J,axiom,
% 0.18/0.46 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 0.18/0.46 ( ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) )
% 0.18/0.46 = ( sup_sup_set_a @ ( sup_sup_set_a @ ( binary256242811Tree_a @ X21 ) @ ( insert_a @ X22 @ bot_bot_set_a ) ) @ ( binary256242811Tree_a @ X23 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Tree.simps(15)
% 0.18/0.46 thf(fact_348_Tree_Oset__intros_I3_J,axiom,
% 0.18/0.46 ! [Ya: a,X23: binary1439146945Tree_a,X21: binary1439146945Tree_a,X22: a] :
% 0.18/0.46 ( ( member_a @ Ya @ ( binary256242811Tree_a @ X23 ) )
% 0.18/0.46 => ( member_a @ Ya @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Tree.set_intros(3)
% 0.18/0.46 thf(fact_349_Tree_Oset__intros_I2_J,axiom,
% 0.18/0.46 ! [X22: a,X21: binary1439146945Tree_a,X23: binary1439146945Tree_a] : ( member_a @ X22 @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Tree.set_intros(2)
% 0.18/0.46 thf(fact_350_Tree_Oset__intros_I1_J,axiom,
% 0.18/0.46 ! [Y: a,X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 0.18/0.46 ( ( member_a @ Y @ ( binary256242811Tree_a @ X21 ) )
% 0.18/0.46 => ( member_a @ Y @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Tree.set_intros(1)
% 0.18/0.46 thf(fact_351_Tree_Oset__cases,axiom,
% 0.18/0.46 ! [E: a,A: binary1439146945Tree_a] :
% 0.18/0.46 ( ( member_a @ E @ ( binary256242811Tree_a @ A ) )
% 0.18/0.46 => ( ! [Z1: binary1439146945Tree_a] :
% 0.18/0.46 ( ? [Z22: a,Z3: binary1439146945Tree_a] :
% 0.18/0.46 ( A
% 0.18/0.46 = ( binary717961607le_T_a @ Z1 @ Z22 @ Z3 ) )
% 0.18/0.46 => ~ ( member_a @ E @ ( binary256242811Tree_a @ Z1 ) ) )
% 0.18/0.46 => ( ! [Z1: binary1439146945Tree_a,Z3: binary1439146945Tree_a] :
% 0.18/0.46 ( A
% 0.18/0.46 != ( binary717961607le_T_a @ Z1 @ E @ Z3 ) )
% 0.18/0.46 => ~ ! [Z1: binary1439146945Tree_a,Z22: a,Z3: binary1439146945Tree_a] :
% 0.18/0.46 ( ( A
% 0.18/0.46 = ( binary717961607le_T_a @ Z1 @ Z22 @ Z3 ) )
% 0.18/0.46 => ~ ( member_a @ E @ ( binary256242811Tree_a @ Z3 ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 % Tree.set_cases
% 0.18/0.46 thf(fact_352_Tree_Osimps_I14_J,axiom,
% 0.18/0.46 ( ( binary256242811Tree_a @ binary476621312_Tip_a )
% 0.18/0.46 = bot_bot_set_a ) ).
% 0.18/0.46
% 0.18/0.46 % Tree.simps(14)
% 0.18/0.46 thf(fact_353_UNIV__I,axiom,
% 0.18/0.46 ! [X2: a] : ( member_a @ X2 @ top_top_set_a ) ).
% 0.18/0.46
% 0.18/0.46 % UNIV_I
% 0.18/0.46
% 0.18/0.46 % Conjectures (1)
% 0.18/0.46 thf(conj_0,conjecture,
% 0.18/0.46 $false ).
% 0.18/0.46
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 ------------------------
% 2.81/1.56 ---- Embedded in THF ---
% 2.81/1.57 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.81/1.57 %%% Generated on Tue Feb 24 08:24:22 EST 2026
% 2.81/1.57 %%% using '$$dhol' embedding, version 1.3.0.
% 2.81/1.57 %%% Logic specification used:
% 2.81/1.57 %%% thf(spec, logic, $$dhol).
% 2.81/1.57
% 2.81/1.57 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.A9HM2VC1Um/DTF2DTF27294.p
% See solution above
% 2.81/1.57 ------------------------
% 3.05/1.62 ---- Cleaned THF ---
% 3.05/1.62 thf(ty_n_t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_It__Option__Ooption_Itf__a_J_J,type,
% 3.05/1.62 binary1176601351tion_a: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Set__Oset_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_J,type,
% 3.05/1.62 set_option_option_a: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_Itf__a_J,type,
% 3.05/1.62 binary1439146945Tree_a: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
% 3.05/1.62 option_option_a: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
% 3.05/1.62 set_option_a: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 option_a: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 3.05/1.62 set_a: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_t__Int__Oint,type,
% 3.05/1.62 int: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(ty_n_tf__a,type,
% 3.05/1.62 a: $tType ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OT_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 binary1007279693tion_a: binary1176601351tion_a > option_a > binary1176601351tion_a > binary1176601351tion_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OT_001tf__a,type,
% 3.05/1.62 binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OTip_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 binary471442758tion_a: binary1176601351tion_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OTip_001tf__a,type,
% 3.05/1.62 binary476621312_Tip_a: binary1439146945Tree_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_Oset__Tree_001tf__a,type,
% 3.05/1.62 binary256242811Tree_a: binary1439146945Tree_a > set_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Oeqs_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 binary301690796tion_a: ( option_a > int ) > option_a > set_option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Oeqs_001tf__a,type,
% 3.05/1.62 binary504661350_eqs_a: ( a > int ) > a > set_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Omemb_001tf__a,type,
% 3.05/1.62 binary2053421120memb_a: ( a > int ) > a > binary1439146945Tree_a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsetOf_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 binary1117200954tion_a: binary1176601351tion_a > set_option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsetOf_001tf__a,type,
% 3.05/1.62 binary945792244etOf_a: binary1439146945Tree_a > set_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsortedTree_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 binary995005080tion_a: ( option_a > int ) > binary1176601351tion_a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsortedTree_001tf__a,type,
% 3.05/1.62 binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Osorted__distinct__pred_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 binary1691793817tion_a: ( option_a > int ) > option_a > option_a > binary1176601351tion_a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Osorted__distinct__pred_001tf__a,type,
% 3.05/1.62 binary670562003pred_a: ( a > int ) > a > a > binary1439146945Tree_a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Otlookup_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 binary1040190117tion_a: ( option_a > int ) > int > binary1176601351tion_a > option_option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Otlookup_001tf__a,type,
% 3.05/1.62 binary779405791okup_a: ( a > int ) > int > binary1439146945Tree_a > option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_HOL_OThe_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 the_option_a: ( option_a > $o ) > option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_HOL_OThe_001tf__a,type,
% 3.05/1.62 the_a: ( a > $o ) > a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_HOL_Oundefined_001tf__a,type,
% 3.05/1.62 undefined_a: a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_Itf__a_M_Eo_J,type,
% 3.05/1.62 sup_sup_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
% 3.05/1.62 sup_sup_set_option_a: set_option_a > set_option_a > set_option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__a_J,type,
% 3.05/1.62 sup_sup_set_a: set_a > set_a > set_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_ONone_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 none_option_a: option_option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_ONone_001tf__a,type,
% 3.05/1.62 none_a: option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_OSome_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 some_option_a: option_a > option_option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_OSome_001tf__a,type,
% 3.05/1.62 some_a: a > option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001tf__a,type,
% 3.05/1.62 case_option_o_a: $o > ( a > $o ) > option_a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_Ocase__option_001tf__a_001tf__a,type,
% 3.05/1.62 case_option_a_a: a > ( a > a ) > option_a > a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_Oset__option_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 set_option_option_a2: option_option_a > set_option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_Oset__option_001tf__a,type,
% 3.05/1.62 set_option_a2: option_a > set_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_Othe_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 the_option_a2: option_option_a > option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Ooption_Othe_001tf__a,type,
% 3.05/1.62 the_a2: option_a > a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Othese_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 these_option_a: set_option_option_a > set_option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Option_Othese_001tf__a,type,
% 3.05/1.62 these_a: set_option_a > set_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J,type,
% 3.05/1.62 bot_bot_option_a_o: option_a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__a_M_Eo_J,type,
% 3.05/1.62 bot_bot_a_o: a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
% 3.05/1.62 bot_bot_o: $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_It__Option__Ooption_Itf__a_J_J_J,type,
% 3.05/1.62 bot_bo1607647958tion_a: set_option_option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
% 3.05/1.62 bot_bot_set_option_a: set_option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 3.05/1.62 bot_bot_set_a: set_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Oord__class_Oless_001_062_It__Option__Ooption_Itf__a_J_M_Eo_J,type,
% 3.05/1.62 ord_less_option_a_o: ( option_a > $o ) > ( option_a > $o ) > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Oord__class_Oless_001_062_Itf__a_M_Eo_J,type,
% 3.05/1.62 ord_less_a_o: ( a > $o ) > ( a > $o ) > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 3.05/1.62 ord_less_int: int > int > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Option__Ooption_Itf__a_J_J,type,
% 3.05/1.62 ord_le1280890064tion_a: set_option_a > set_option_a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__a_J,type,
% 3.05/1.62 ord_less_set_a: set_a > set_a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_Itf__a_J,type,
% 3.05/1.62 top_top_set_a: set_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_OCollect_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 collect_option_a: ( option_a > $o ) > set_option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_OCollect_001tf__a,type,
% 3.05/1.62 collect_a: ( a > $o ) > set_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_Oimage_001t__Option__Ooption_Itf__a_J_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 image_139503237tion_a: ( option_a > option_a ) > set_option_a > set_option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_Oimage_001t__Option__Ooption_Itf__a_J_001tf__a,type,
% 3.05/1.62 image_option_a_a: ( option_a > a ) > set_option_a > set_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_Oimage_001tf__a_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 image_a_option_a: ( a > option_a ) > set_a > set_option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_Oimage_001tf__a_001tf__a,type,
% 3.05/1.62 image_a_a: ( a > a ) > set_a > set_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_Oinsert_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
% 3.05/1.62 insert1662731738tion_a: option_option_a > set_option_option_a > set_option_option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_Oinsert_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 insert_option_a: option_a > set_option_a > set_option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_Oinsert_001tf__a,type,
% 3.05/1.62 insert_a: a > set_a > set_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_Ois__empty_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 is_empty_option_a: set_option_a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_Ois__empty_001tf__a,type,
% 3.05/1.62 is_empty_a: set_a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_Ois__singleton_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 is_sin1624444472tion_a: set_option_a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_Ois__singleton_001tf__a,type,
% 3.05/1.62 is_singleton_a: set_a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_Othe__elem_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 the_elem_option_a: set_option_a > option_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_Set_Othe__elem_001tf__a,type,
% 3.05/1.62 the_elem_a: set_a > a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_member_001t__Option__Ooption_It__Option__Ooption_Itf__a_J_J,type,
% 3.05/1.62 member553679923tion_a: option_option_a > set_option_option_a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_member_001t__Option__Ooption_Itf__a_J,type,
% 3.05/1.62 member_option_a: option_a > set_option_a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_c_member_001tf__a,type,
% 3.05/1.62 member_a: a > set_a > $o ).
% 3.05/1.62
% 3.05/1.62 thf(sy_v_h,type,
% 3.05/1.62 h: a > int ).
% 3.05/1.62
% 3.05/1.62 thf(sy_v_t,type,
% 3.05/1.62 t: binary1439146945Tree_a ).
% 3.05/1.62
% 3.05/1.62 thf(sy_v_x,type,
% 3.05/1.62 x: a ).
% 3.05/1.62
% 3.05/1.62 thf(fact_0_h,axiom,
% 3.05/1.62 member_a @ x @ ( binary945792244etOf_a @ t ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_1_sorted__distinct,axiom,
% 3.05/1.62 ! [H: a > int,A: a,B: a,T: binary1439146945Tree_a] : ( binary670562003pred_a @ H @ A @ B @ T ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_2_s,axiom,
% 3.05/1.62 binary1721989714Tree_a @ h @ t ).
% 3.05/1.62
% 3.05/1.62 thf(fact_3_res,axiom,
% 3.05/1.62 ~ ( binary2053421120memb_a @ h @ x @ t ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_4__092_060open_062h_Ax_A_092_060noteq_062_Ah_Ax_092_060close_062,axiom,
% 3.05/1.62 ( ( h @ x )
% 3.05/1.62 != ( h @ x ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_5_o1,axiom,
% 3.05/1.62 ! [X: a] :
% 3.05/1.62 ( ( member_a @ X @ ( binary945792244etOf_a @ t ) )
% 3.05/1.62 => ( ( h @ X )
% 3.05/1.62 != ( h @ x ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_6_sorted__distinct__pred__def,axiom,
% 3.05/1.62 ( binary1691793817tion_a
% 3.05/1.62 = ( ^ [H2: option_a > int,A2: option_a,B2: option_a,T2: binary1176601351tion_a] :
% 3.05/1.62 ( ( ( binary995005080tion_a @ H2 @ T2 )
% 3.05/1.62 & ( member_option_a @ A2 @ ( binary1117200954tion_a @ T2 ) )
% 3.05/1.62 & ( member_option_a @ B2 @ ( binary1117200954tion_a @ T2 ) )
% 3.05/1.62 & ( ( H2 @ A2 )
% 3.05/1.62 = ( H2 @ B2 ) ) )
% 3.05/1.62 => ( A2 = B2 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_7_sorted__distinct__pred__def,axiom,
% 3.05/1.62 ( binary670562003pred_a
% 3.05/1.62 = ( ^ [H2: a > int,A2: a,B2: a,T2: binary1439146945Tree_a] :
% 3.05/1.62 ( ( ( binary1721989714Tree_a @ H2 @ T2 )
% 3.05/1.62 & ( member_a @ A2 @ ( binary945792244etOf_a @ T2 ) )
% 3.05/1.62 & ( member_a @ B2 @ ( binary945792244etOf_a @ T2 ) )
% 3.05/1.62 & ( ( H2 @ A2 )
% 3.05/1.62 = ( H2 @ B2 ) ) )
% 3.05/1.62 => ( A2 = B2 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_8_tNone,axiom,
% 3.05/1.62 ( ( binary779405791okup_a @ h @ ( h @ x ) @ t )
% 3.05/1.62 = none_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_9_sortedTree_Osimps_I1_J,axiom,
% 3.05/1.62 ! [H: a > int] : ( binary1721989714Tree_a @ H @ binary476621312_Tip_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_10_sortLemmaL,axiom,
% 3.05/1.62 ! [H: a > int,T1: binary1439146945Tree_a,X2: a,T22: binary1439146945Tree_a] :
% 3.05/1.62 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X2 @ T22 ) )
% 3.05/1.62 => ( binary1721989714Tree_a @ H @ T1 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_11_sortLemmaR,axiom,
% 3.05/1.62 ! [H: a > int,T1: binary1439146945Tree_a,X2: a,T22: binary1439146945Tree_a] :
% 3.05/1.62 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X2 @ T22 ) )
% 3.05/1.62 => ( binary1721989714Tree_a @ H @ T22 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_12_tlookup__none,axiom,
% 3.05/1.62 ! [H: a > int,T: binary1439146945Tree_a,K: int] :
% 3.05/1.62 ( ( ( binary1721989714Tree_a @ H @ T )
% 3.05/1.62 & ( ( binary779405791okup_a @ H @ K @ T )
% 3.05/1.62 = none_a ) )
% 3.05/1.62 => ! [X: a] :
% 3.05/1.62 ( ( member_a @ X @ ( binary945792244etOf_a @ T ) )
% 3.05/1.62 => ( ( H @ X )
% 3.05/1.62 != K ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_13_tlookup__some,axiom,
% 3.05/1.62 ! [H: option_a > int,T: binary1176601351tion_a,K: int,X2: option_a] :
% 3.05/1.62 ( ( ( binary995005080tion_a @ H @ T )
% 3.05/1.62 & ( ( binary1040190117tion_a @ H @ K @ T )
% 3.05/1.62 = ( some_option_a @ X2 ) ) )
% 3.05/1.62 => ( ( member_option_a @ X2 @ ( binary1117200954tion_a @ T ) )
% 3.05/1.62 & ( ( H @ X2 )
% 3.05/1.62 = K ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_14_tlookup__some,axiom,
% 3.05/1.62 ! [H: a > int,T: binary1439146945Tree_a,K: int,X2: a] :
% 3.05/1.62 ( ( ( binary1721989714Tree_a @ H @ T )
% 3.05/1.62 & ( ( binary779405791okup_a @ H @ K @ T )
% 3.05/1.62 = ( some_a @ X2 ) ) )
% 3.05/1.62 => ( ( member_a @ X2 @ ( binary945792244etOf_a @ T ) )
% 3.05/1.62 & ( ( H @ X2 )
% 3.05/1.62 = K ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_15_tlookup__finds,axiom,
% 3.05/1.62 ! [H: option_a > int,T: binary1176601351tion_a,Y: option_a] :
% 3.05/1.62 ( ( ( binary995005080tion_a @ H @ T )
% 3.05/1.62 & ( member_option_a @ Y @ ( binary1117200954tion_a @ T ) ) )
% 3.05/1.62 => ( ( binary1040190117tion_a @ H @ ( H @ Y ) @ T )
% 3.05/1.62 = ( some_option_a @ Y ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_16_tlookup__finds,axiom,
% 3.05/1.62 ! [H: a > int,T: binary1439146945Tree_a,Y: a] :
% 3.05/1.62 ( ( ( binary1721989714Tree_a @ H @ T )
% 3.05/1.62 & ( member_a @ Y @ ( binary945792244etOf_a @ T ) ) )
% 3.05/1.62 => ( ( binary779405791okup_a @ H @ ( H @ Y ) @ T )
% 3.05/1.62 = ( some_a @ Y ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_17_sortedTree_Osimps_I2_J,axiom,
% 3.05/1.62 ! [H: a > int,T1: binary1439146945Tree_a,X2: a,T22: binary1439146945Tree_a] :
% 3.05/1.62 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X2 @ T22 ) )
% 3.05/1.62 = ( ( binary1721989714Tree_a @ H @ T1 )
% 3.05/1.62 & ! [X3: a] :
% 3.05/1.62 ( ( member_a @ X3 @ ( binary945792244etOf_a @ T1 ) )
% 3.05/1.62 => ( ord_less_int @ ( H @ X3 ) @ ( H @ X2 ) ) )
% 3.05/1.62 & ! [X3: a] :
% 3.05/1.62 ( ( member_a @ X3 @ ( binary945792244etOf_a @ T22 ) )
% 3.05/1.62 => ( ord_less_int @ ( H @ X2 ) @ ( H @ X3 ) ) )
% 3.05/1.62 & ( binary1721989714Tree_a @ H @ T22 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_18_setOf_Osimps_I1_J,axiom,
% 3.05/1.62 ( ( binary1117200954tion_a @ binary471442758tion_a )
% 3.05/1.62 = bot_bot_set_option_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_19_setOf_Osimps_I1_J,axiom,
% 3.05/1.62 ( ( binary945792244etOf_a @ binary476621312_Tip_a )
% 3.05/1.62 = bot_bot_set_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_20_memb__def,axiom,
% 3.05/1.62 ( binary2053421120memb_a
% 3.05/1.62 = ( ^ [H2: a > int,X3: a,T2: binary1439146945Tree_a] :
% 3.05/1.62 ( case_option_o_a @ $false
% 3.05/1.62 @ ( ^ [Y2: a,Z: a] : ( Y2 = Z )
% 3.05/1.62 @ X3 )
% 3.05/1.62 @ ( binary779405791okup_a @ H2 @ ( H2 @ X3 ) @ T2 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_21_Tree_Oinject,axiom,
% 3.05/1.62 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a,Y21: binary1439146945Tree_a,Y22: a,Y23: binary1439146945Tree_a] :
% 3.05/1.62 ( ( ( binary717961607le_T_a @ X21 @ X22 @ X23 )
% 3.05/1.62 = ( binary717961607le_T_a @ Y21 @ Y22 @ Y23 ) )
% 3.05/1.62 = ( ( X21 = Y21 )
% 3.05/1.62 & ( X22 = Y22 )
% 3.05/1.62 & ( X23 = Y23 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_22_Tree_Oexhaust,axiom,
% 3.05/1.62 ! [Y: binary1439146945Tree_a] :
% 3.05/1.62 ( ( Y != binary476621312_Tip_a )
% 3.05/1.62 => ~ ! [X212: binary1439146945Tree_a,X222: a,X232: binary1439146945Tree_a] :
% 3.05/1.62 ( Y
% 3.05/1.62 != ( binary717961607le_T_a @ X212 @ X222 @ X232 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_23_Tree_Oinduct,axiom,
% 3.05/1.62 ! [P: binary1439146945Tree_a > $o,Tree: binary1439146945Tree_a] :
% 3.05/1.62 ( ( P @ binary476621312_Tip_a )
% 3.05/1.62 => ( ! [X1: binary1439146945Tree_a,X24: a,X32: binary1439146945Tree_a] :
% 3.05/1.62 ( ( P @ X1 )
% 3.05/1.62 => ( ( P @ X32 )
% 3.05/1.62 => ( P @ ( binary717961607le_T_a @ X1 @ X24 @ X32 ) ) ) )
% 3.05/1.62 => ( P @ Tree ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_24_tlookup_Osimps_I1_J,axiom,
% 3.05/1.62 ! [H: a > int,K: int] :
% 3.05/1.62 ( ( binary779405791okup_a @ H @ K @ binary476621312_Tip_a )
% 3.05/1.62 = none_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_25_tlookup_Osimps_I2_J,axiom,
% 3.05/1.62 ! [K: int,H: a > int,X2: a,T1: binary1439146945Tree_a,T22: binary1439146945Tree_a] :
% 3.05/1.62 ( ( ( ord_less_int @ K @ ( H @ X2 ) )
% 3.05/1.62 => ( ( binary779405791okup_a @ H @ K @ ( binary717961607le_T_a @ T1 @ X2 @ T22 ) )
% 3.05/1.62 = ( binary779405791okup_a @ H @ K @ T1 ) ) )
% 3.05/1.62 & ( ~ ( ord_less_int @ K @ ( H @ X2 ) )
% 3.05/1.62 => ( ( ( ord_less_int @ ( H @ X2 ) @ K )
% 3.05/1.62 => ( ( binary779405791okup_a @ H @ K @ ( binary717961607le_T_a @ T1 @ X2 @ T22 ) )
% 3.05/1.62 = ( binary779405791okup_a @ H @ K @ T22 ) ) )
% 3.05/1.62 & ( ~ ( ord_less_int @ ( H @ X2 ) @ K )
% 3.05/1.62 => ( ( binary779405791okup_a @ H @ K @ ( binary717961607le_T_a @ T1 @ X2 @ T22 ) )
% 3.05/1.62 = ( some_a @ X2 ) ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_26_Tree_Odistinct_I1_J,axiom,
% 3.05/1.62 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 3.05/1.62 ( binary476621312_Tip_a
% 3.05/1.62 != ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_27_not__Some__eq,axiom,
% 3.05/1.62 ! [X2: option_a] :
% 3.05/1.62 ( ( ! [Y3: a] :
% 3.05/1.62 ( X2
% 3.05/1.62 != ( some_a @ Y3 ) ) )
% 3.05/1.62 = ( X2 = none_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_28_not__None__eq,axiom,
% 3.05/1.62 ! [X2: option_a] :
% 3.05/1.62 ( ( X2 != none_a )
% 3.05/1.62 = ( ? [Y3: a] :
% 3.05/1.62 ( X2
% 3.05/1.62 = ( some_a @ Y3 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_29_case__optionE,axiom,
% 3.05/1.62 ! [P: $o,Q: a > $o,X2: option_a] :
% 3.05/1.62 ( ( case_option_o_a @ P @ Q @ X2 )
% 3.05/1.62 => ( ( ( X2 = none_a )
% 3.05/1.62 => ~ P )
% 3.05/1.62 => ~ ! [Y4: a] :
% 3.05/1.62 ( ( X2
% 3.05/1.62 = ( some_a @ Y4 ) )
% 3.05/1.62 => ~ ( Q @ Y4 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_30_disjE__realizer2,axiom,
% 3.05/1.62 ! [P: $o,Q: a > $o,X2: option_a,R: $o > $o,F: $o,G: a > $o] :
% 3.05/1.62 ( ( case_option_o_a @ P @ Q @ X2 )
% 3.05/1.62 => ( ( P
% 3.05/1.62 => ( R @ F ) )
% 3.05/1.62 => ( ! [Q2: a] :
% 3.05/1.62 ( ( Q @ Q2 )
% 3.05/1.62 => ( R @ ( G @ Q2 ) ) )
% 3.05/1.62 => ( R @ ( case_option_o_a @ F @ G @ X2 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_31_option_Odisc__eq__case_I1_J,axiom,
% 3.05/1.62 ! [Option: option_a] :
% 3.05/1.62 ( ( Option = none_a )
% 3.05/1.62 = ( case_option_o_a @ $true
% 3.05/1.62 @ ^ [Uu: a] : $false
% 3.05/1.62 @ Option ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_32_option_Odisc__eq__case_I2_J,axiom,
% 3.05/1.62 ! [Option: option_a] :
% 3.05/1.62 ( ( Option != none_a )
% 3.05/1.62 = ( case_option_o_a @ $false
% 3.05/1.62 @ ^ [Uu: a] : $true
% 3.05/1.62 @ Option ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_33_option_Oinject,axiom,
% 3.05/1.62 ! [X25: a,Y24: a] :
% 3.05/1.62 ( ( ( some_a @ X25 )
% 3.05/1.62 = ( some_a @ Y24 ) )
% 3.05/1.62 = ( X25 = Y24 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_34_empty__Collect__eq,axiom,
% 3.05/1.62 ! [P: a > $o] :
% 3.05/1.62 ( ( bot_bot_set_a
% 3.05/1.62 = ( collect_a @ P ) )
% 3.05/1.62 = ( ! [X3: a] :
% 3.05/1.62 ~ ( P @ X3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_35_empty__Collect__eq,axiom,
% 3.05/1.62 ! [P: option_a > $o] :
% 3.05/1.62 ( ( bot_bot_set_option_a
% 3.05/1.62 = ( collect_option_a @ P ) )
% 3.05/1.62 = ( ! [X3: option_a] :
% 3.05/1.62 ~ ( P @ X3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_36_Collect__empty__eq,axiom,
% 3.05/1.62 ! [P: a > $o] :
% 3.05/1.62 ( ( ( collect_a @ P )
% 3.05/1.62 = bot_bot_set_a )
% 3.05/1.62 = ( ! [X3: a] :
% 3.05/1.62 ~ ( P @ X3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_37_Collect__empty__eq,axiom,
% 3.05/1.62 ! [P: option_a > $o] :
% 3.05/1.62 ( ( ( collect_option_a @ P )
% 3.05/1.62 = bot_bot_set_option_a )
% 3.05/1.62 = ( ! [X3: option_a] :
% 3.05/1.62 ~ ( P @ X3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_38_all__not__in__conv,axiom,
% 3.05/1.62 ! [A3: set_option_a] :
% 3.05/1.62 ( ( ! [X3: option_a] :
% 3.05/1.62 ~ ( member_option_a @ X3 @ A3 ) )
% 3.05/1.62 = ( A3 = bot_bot_set_option_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_39_all__not__in__conv,axiom,
% 3.05/1.62 ! [A3: set_a] :
% 3.05/1.62 ( ( ! [X3: a] :
% 3.05/1.62 ~ ( member_a @ X3 @ A3 ) )
% 3.05/1.62 = ( A3 = bot_bot_set_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_40_empty__iff,axiom,
% 3.05/1.62 ! [C: option_a] :
% 3.05/1.62 ~ ( member_option_a @ C @ bot_bot_set_option_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_41_empty__iff,axiom,
% 3.05/1.62 ! [C: a] :
% 3.05/1.62 ~ ( member_a @ C @ bot_bot_set_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_42_emptyE,axiom,
% 3.05/1.62 ! [A: option_a] :
% 3.05/1.62 ~ ( member_option_a @ A @ bot_bot_set_option_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_43_emptyE,axiom,
% 3.05/1.62 ! [A: a] :
% 3.05/1.62 ~ ( member_a @ A @ bot_bot_set_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_44_equals0D,axiom,
% 3.05/1.62 ! [A3: set_option_a,A: option_a] :
% 3.05/1.62 ( ( A3 = bot_bot_set_option_a )
% 3.05/1.62 => ~ ( member_option_a @ A @ A3 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_45_equals0D,axiom,
% 3.05/1.62 ! [A3: set_a,A: a] :
% 3.05/1.62 ( ( A3 = bot_bot_set_a )
% 3.05/1.62 => ~ ( member_a @ A @ A3 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_46_equals0I,axiom,
% 3.05/1.62 ! [A3: set_option_a] :
% 3.05/1.62 ( ! [Y4: option_a] :
% 3.05/1.62 ~ ( member_option_a @ Y4 @ A3 )
% 3.05/1.62 => ( A3 = bot_bot_set_option_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_47_equals0I,axiom,
% 3.05/1.62 ! [A3: set_a] :
% 3.05/1.62 ( ! [Y4: a] :
% 3.05/1.62 ~ ( member_a @ Y4 @ A3 )
% 3.05/1.62 => ( A3 = bot_bot_set_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_48_ex__in__conv,axiom,
% 3.05/1.62 ! [A3: set_option_a] :
% 3.05/1.62 ( ( ? [X3: option_a] : ( member_option_a @ X3 @ A3 ) )
% 3.05/1.62 = ( A3 != bot_bot_set_option_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_49_ex__in__conv,axiom,
% 3.05/1.62 ! [A3: set_a] :
% 3.05/1.62 ( ( ? [X3: a] : ( member_a @ X3 @ A3 ) )
% 3.05/1.62 = ( A3 != bot_bot_set_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_50_empty__def,axiom,
% 3.05/1.62 ( bot_bot_set_a
% 3.05/1.62 = ( collect_a
% 3.05/1.62 @ ^ [X3: a] : $false ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_51_empty__def,axiom,
% 3.05/1.62 ( bot_bot_set_option_a
% 3.05/1.62 = ( collect_option_a
% 3.05/1.62 @ ^ [X3: option_a] : $false ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_52_option_Ocase__distrib,axiom,
% 3.05/1.62 ! [H: $o > $o,F1: $o,F2: a > $o,Option: option_a] :
% 3.05/1.62 ( ( H @ ( case_option_o_a @ F1 @ F2 @ Option ) )
% 3.05/1.62 = ( case_option_o_a @ ( H @ F1 )
% 3.05/1.62 @ ^ [X3: a] : ( H @ ( F2 @ X3 ) )
% 3.05/1.62 @ Option ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_53_option_Odistinct_I1_J,axiom,
% 3.05/1.62 ! [X25: a] :
% 3.05/1.62 ( none_a
% 3.05/1.62 != ( some_a @ X25 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_54_option_OdiscI,axiom,
% 3.05/1.62 ! [Option: option_a,X25: a] :
% 3.05/1.62 ( ( Option
% 3.05/1.62 = ( some_a @ X25 ) )
% 3.05/1.62 => ( Option != none_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_55_option_Oexhaust,axiom,
% 3.05/1.62 ! [Y: option_a] :
% 3.05/1.62 ( ( Y != none_a )
% 3.05/1.62 => ~ ! [X24: a] :
% 3.05/1.62 ( Y
% 3.05/1.62 != ( some_a @ X24 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_56_option_Oinducts,axiom,
% 3.05/1.62 ! [P: option_a > $o,Option: option_a] :
% 3.05/1.62 ( ( P @ none_a )
% 3.05/1.62 => ( ! [X4: a] : ( P @ ( some_a @ X4 ) )
% 3.05/1.62 => ( P @ Option ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_57_mem__Collect__eq,axiom,
% 3.05/1.62 ! [A: option_a,P: option_a > $o] :
% 3.05/1.62 ( ( member_option_a @ A @ ( collect_option_a @ P ) )
% 3.05/1.62 = ( P @ A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_58_mem__Collect__eq,axiom,
% 3.05/1.62 ! [A: a,P: a > $o] :
% 3.05/1.62 ( ( member_a @ A @ ( collect_a @ P ) )
% 3.05/1.62 = ( P @ A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_59_Collect__mem__eq,axiom,
% 3.05/1.62 ! [A3: set_option_a] :
% 3.05/1.62 ( ( collect_option_a
% 3.05/1.62 @ ^ [X3: option_a] : ( member_option_a @ X3 @ A3 ) )
% 3.05/1.62 = A3 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_60_Collect__mem__eq,axiom,
% 3.05/1.62 ! [A3: set_a] :
% 3.05/1.62 ( ( collect_a
% 3.05/1.62 @ ^ [X3: a] : ( member_a @ X3 @ A3 ) )
% 3.05/1.62 = A3 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_61_Collect__cong,axiom,
% 3.05/1.62 ! [P: a > $o,Q: a > $o] :
% 3.05/1.62 ( ! [X4: a] :
% 3.05/1.62 ( ( P @ X4 )
% 3.05/1.62 = ( Q @ X4 ) )
% 3.05/1.62 => ( ( collect_a @ P )
% 3.05/1.62 = ( collect_a @ Q ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_62_Collect__cong,axiom,
% 3.05/1.62 ! [P: option_a > $o,Q: option_a > $o] :
% 3.05/1.62 ( ! [X4: option_a] :
% 3.05/1.62 ( ( P @ X4 )
% 3.05/1.62 = ( Q @ X4 ) )
% 3.05/1.62 => ( ( collect_option_a @ P )
% 3.05/1.62 = ( collect_option_a @ Q ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_63_split__option__ex,axiom,
% 3.05/1.62 ( ( ^ [P2: option_a > $o] :
% 3.05/1.62 ? [X5: option_a] : ( P2 @ X5 ) )
% 3.05/1.62 = ( ^ [P3: option_a > $o] :
% 3.05/1.62 ( ( P3 @ none_a )
% 3.05/1.62 | ? [X3: a] : ( P3 @ ( some_a @ X3 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_64_split__option__all,axiom,
% 3.05/1.62 ( ( ^ [P2: option_a > $o] :
% 3.05/1.62 ! [X5: option_a] : ( P2 @ X5 ) )
% 3.05/1.62 = ( ^ [P3: option_a > $o] :
% 3.05/1.62 ( ( P3 @ none_a )
% 3.05/1.62 & ! [X3: a] : ( P3 @ ( some_a @ X3 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_65_combine__options__cases,axiom,
% 3.05/1.62 ! [X2: option_a,P: option_a > option_a > $o,Y: option_a] :
% 3.05/1.62 ( ( ( X2 = none_a )
% 3.05/1.62 => ( P @ X2 @ Y ) )
% 3.05/1.62 => ( ( ( Y = none_a )
% 3.05/1.62 => ( P @ X2 @ Y ) )
% 3.05/1.62 => ( ! [A4: a,B3: a] :
% 3.05/1.62 ( ( X2
% 3.05/1.62 = ( some_a @ A4 ) )
% 3.05/1.62 => ( ( Y
% 3.05/1.62 = ( some_a @ B3 ) )
% 3.05/1.62 => ( P @ X2 @ Y ) ) )
% 3.05/1.62 => ( P @ X2 @ Y ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_66_option_Osimps_I4_J,axiom,
% 3.05/1.62 ! [F1: $o,F2: a > $o] :
% 3.05/1.62 ( ( case_option_o_a @ F1 @ F2 @ none_a )
% 3.05/1.62 = F1 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_67_option_Osimps_I5_J,axiom,
% 3.05/1.62 ! [F1: $o,F2: a > $o,X25: a] :
% 3.05/1.62 ( ( case_option_o_a @ F1 @ F2 @ ( some_a @ X25 ) )
% 3.05/1.62 = ( F2 @ X25 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_68_bot__apply,axiom,
% 3.05/1.62 ( bot_bot_a_o
% 3.05/1.62 = ( ^ [X3: a] : bot_bot_o ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_69_bot_Oextremum__strict,axiom,
% 3.05/1.62 ! [A: set_option_a] :
% 3.05/1.62 ~ ( ord_le1280890064tion_a @ A @ bot_bot_set_option_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_70_bot_Oextremum__strict,axiom,
% 3.05/1.62 ! [A: set_a] :
% 3.05/1.62 ~ ( ord_less_set_a @ A @ bot_bot_set_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_71_bot_Oextremum__strict,axiom,
% 3.05/1.62 ! [A: a > $o] :
% 3.05/1.62 ~ ( ord_less_a_o @ A @ bot_bot_a_o ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_72_bot_Onot__eq__extremum,axiom,
% 3.05/1.62 ! [A: set_option_a] :
% 3.05/1.62 ( ( A != bot_bot_set_option_a )
% 3.05/1.62 = ( ord_le1280890064tion_a @ bot_bot_set_option_a @ A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_73_bot_Onot__eq__extremum,axiom,
% 3.05/1.62 ! [A: set_a] :
% 3.05/1.62 ( ( A != bot_bot_set_a )
% 3.05/1.62 = ( ord_less_set_a @ bot_bot_set_a @ A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_74_bot_Onot__eq__extremum,axiom,
% 3.05/1.62 ! [A: a > $o] :
% 3.05/1.62 ( ( A != bot_bot_a_o )
% 3.05/1.62 = ( ord_less_a_o @ bot_bot_a_o @ A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_75_Set_Ois__empty__def,axiom,
% 3.05/1.62 ( is_empty_a
% 3.05/1.62 = ( ^ [A5: set_a] : ( A5 = bot_bot_set_a ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_76_Set_Ois__empty__def,axiom,
% 3.05/1.62 ( is_empty_option_a
% 3.05/1.62 = ( ^ [A5: set_option_a] : ( A5 = bot_bot_set_option_a ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_77_eqs__def,axiom,
% 3.05/1.62 ( binary504661350_eqs_a
% 3.05/1.62 = ( ^ [H2: a > int,X3: a] :
% 3.05/1.62 ( collect_a
% 3.05/1.62 @ ^ [Y3: a] :
% 3.05/1.62 ( ( H2 @ Y3 )
% 3.05/1.62 = ( H2 @ X3 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_78_eqs__def,axiom,
% 3.05/1.62 ( binary301690796tion_a
% 3.05/1.62 = ( ^ [H2: option_a > int,X3: option_a] :
% 3.05/1.62 ( collect_option_a
% 3.05/1.62 @ ^ [Y3: option_a] :
% 3.05/1.62 ( ( H2 @ Y3 )
% 3.05/1.62 = ( H2 @ X3 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_79_option_Osplit__sel,axiom,
% 3.05/1.62 ! [P: $o > $o,F1: $o,F2: a > $o,Option: option_a] :
% 3.05/1.62 ( ( P @ ( case_option_o_a @ F1 @ F2 @ Option ) )
% 3.05/1.62 = ( ( ( Option = none_a )
% 3.05/1.62 => ( P @ F1 ) )
% 3.05/1.62 & ( ( Option
% 3.05/1.62 = ( some_a @ ( the_a2 @ Option ) ) )
% 3.05/1.62 => ( P @ ( F2 @ ( the_a2 @ Option ) ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_80_option_Osplit__sel__asm,axiom,
% 3.05/1.62 ! [P: $o > $o,F1: $o,F2: a > $o,Option: option_a] :
% 3.05/1.62 ( ( P @ ( case_option_o_a @ F1 @ F2 @ Option ) )
% 3.05/1.62 = ( ~ ( ( ( Option = none_a )
% 3.05/1.62 & ~ ( P @ F1 ) )
% 3.05/1.62 | ( ( Option
% 3.05/1.62 = ( some_a @ ( the_a2 @ Option ) ) )
% 3.05/1.62 & ~ ( P @ ( F2 @ ( the_a2 @ Option ) ) ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_81_set__empty__eq,axiom,
% 3.05/1.62 ! [Xo: option_option_a] :
% 3.05/1.62 ( ( ( set_option_option_a2 @ Xo )
% 3.05/1.62 = bot_bot_set_option_a )
% 3.05/1.62 = ( Xo = none_option_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_82_set__empty__eq,axiom,
% 3.05/1.62 ! [Xo: option_a] :
% 3.05/1.62 ( ( ( set_option_a2 @ Xo )
% 3.05/1.62 = bot_bot_set_a )
% 3.05/1.62 = ( Xo = none_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_83_bot__fun__def,axiom,
% 3.05/1.62 ( bot_bot_a_o
% 3.05/1.62 = ( ^ [X3: a] : bot_bot_o ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_84_elem__set,axiom,
% 3.05/1.62 ! [X2: option_a,Xo: option_option_a] :
% 3.05/1.62 ( ( member_option_a @ X2 @ ( set_option_option_a2 @ Xo ) )
% 3.05/1.62 = ( Xo
% 3.05/1.62 = ( some_option_a @ X2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_85_elem__set,axiom,
% 3.05/1.62 ! [X2: a,Xo: option_a] :
% 3.05/1.62 ( ( member_a @ X2 @ ( set_option_a2 @ Xo ) )
% 3.05/1.62 = ( Xo
% 3.05/1.62 = ( some_a @ X2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_86_option_Ocollapse,axiom,
% 3.05/1.62 ! [Option: option_a] :
% 3.05/1.62 ( ( Option != none_a )
% 3.05/1.62 => ( ( some_a @ ( the_a2 @ Option ) )
% 3.05/1.62 = Option ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_87_option_Oset__sel,axiom,
% 3.05/1.62 ! [A: option_option_a] :
% 3.05/1.62 ( ( A != none_option_a )
% 3.05/1.62 => ( member_option_a @ ( the_option_a2 @ A ) @ ( set_option_option_a2 @ A ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_88_option_Oset__sel,axiom,
% 3.05/1.62 ! [A: option_a] :
% 3.05/1.62 ( ( A != none_a )
% 3.05/1.62 => ( member_a @ ( the_a2 @ A ) @ ( set_option_a2 @ A ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_89_bot__set__def,axiom,
% 3.05/1.62 ( bot_bot_set_a
% 3.05/1.62 = ( collect_a @ bot_bot_a_o ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_90_bot__set__def,axiom,
% 3.05/1.62 ( bot_bot_set_option_a
% 3.05/1.62 = ( collect_option_a @ bot_bot_option_a_o ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_91_not__psubset__empty,axiom,
% 3.05/1.62 ! [A3: set_option_a] :
% 3.05/1.62 ~ ( ord_le1280890064tion_a @ A3 @ bot_bot_set_option_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_92_not__psubset__empty,axiom,
% 3.05/1.62 ! [A3: set_a] :
% 3.05/1.62 ~ ( ord_less_set_a @ A3 @ bot_bot_set_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_93_option_Oexpand,axiom,
% 3.05/1.62 ! [Option: option_a,Option2: option_a] :
% 3.05/1.62 ( ( ( Option = none_a )
% 3.05/1.62 = ( Option2 = none_a ) )
% 3.05/1.62 => ( ( ( Option != none_a )
% 3.05/1.62 => ( ( Option2 != none_a )
% 3.05/1.62 => ( ( the_a2 @ Option )
% 3.05/1.62 = ( the_a2 @ Option2 ) ) ) )
% 3.05/1.62 => ( Option = Option2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_94_option_Osel,axiom,
% 3.05/1.62 ! [X25: a] :
% 3.05/1.62 ( ( the_a2 @ ( some_a @ X25 ) )
% 3.05/1.62 = X25 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_95_option_Oset__intros,axiom,
% 3.05/1.62 ! [X25: option_a] : ( member_option_a @ X25 @ ( set_option_option_a2 @ ( some_option_a @ X25 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_96_option_Oset__intros,axiom,
% 3.05/1.62 ! [X25: a] : ( member_a @ X25 @ ( set_option_a2 @ ( some_a @ X25 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_97_option_Oset__cases,axiom,
% 3.05/1.62 ! [E: option_a,A: option_option_a] :
% 3.05/1.62 ( ( member_option_a @ E @ ( set_option_option_a2 @ A ) )
% 3.05/1.62 => ( A
% 3.05/1.62 = ( some_option_a @ E ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_98_option_Oset__cases,axiom,
% 3.05/1.62 ! [E: a,A: option_a] :
% 3.05/1.62 ( ( member_a @ E @ ( set_option_a2 @ A ) )
% 3.05/1.62 => ( A
% 3.05/1.62 = ( some_a @ E ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_99_ospec,axiom,
% 3.05/1.62 ! [A3: option_a,P: a > $o,X2: a] :
% 3.05/1.62 ( ! [X4: a] :
% 3.05/1.62 ( ( member_a @ X4 @ ( set_option_a2 @ A3 ) )
% 3.05/1.62 => ( P @ X4 ) )
% 3.05/1.62 => ( ( A3
% 3.05/1.62 = ( some_a @ X2 ) )
% 3.05/1.62 => ( P @ X2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_100_option_Oexhaust__sel,axiom,
% 3.05/1.62 ! [Option: option_a] :
% 3.05/1.62 ( ( Option != none_a )
% 3.05/1.62 => ( Option
% 3.05/1.62 = ( some_a @ ( the_a2 @ Option ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_101_option_Osimps_I14_J,axiom,
% 3.05/1.62 ( ( set_option_option_a2 @ none_option_a )
% 3.05/1.62 = bot_bot_set_option_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_102_option_Osimps_I14_J,axiom,
% 3.05/1.62 ( ( set_option_a2 @ none_a )
% 3.05/1.62 = bot_bot_set_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_103_option_Ocase__eq__if,axiom,
% 3.05/1.62 ( case_option_o_a
% 3.05/1.62 = ( ^ [F12: $o,F22: a > $o,Option3: option_a] :
% 3.05/1.62 ( ( ( Option3 = none_a )
% 3.05/1.62 => F12 )
% 3.05/1.62 & ( ( Option3 != none_a )
% 3.05/1.62 => ( F22 @ ( the_a2 @ Option3 ) ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_104_dual__order_Ostrict__implies__not__eq,axiom,
% 3.05/1.62 ! [B: int,A: int] :
% 3.05/1.62 ( ( ord_less_int @ B @ A )
% 3.05/1.62 => ( A != B ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_105_dual__order_Ostrict__implies__not__eq,axiom,
% 3.05/1.62 ! [B: set_a,A: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ B @ A )
% 3.05/1.62 => ( A != B ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_106_dual__order_Ostrict__implies__not__eq,axiom,
% 3.05/1.62 ! [B: a > $o,A: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ B @ A )
% 3.05/1.62 => ( A != B ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_107_order_Ostrict__implies__not__eq,axiom,
% 3.05/1.62 ! [A: int,B: int] :
% 3.05/1.62 ( ( ord_less_int @ A @ B )
% 3.05/1.62 => ( A != B ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_108_order_Ostrict__implies__not__eq,axiom,
% 3.05/1.62 ! [A: set_a,B: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ A @ B )
% 3.05/1.62 => ( A != B ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_109_order_Ostrict__implies__not__eq,axiom,
% 3.05/1.62 ! [A: a > $o,B: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ A @ B )
% 3.05/1.62 => ( A != B ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_110_not__less__iff__gr__or__eq,axiom,
% 3.05/1.62 ! [X2: int,Y: int] :
% 3.05/1.62 ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 3.05/1.62 = ( ( ord_less_int @ Y @ X2 )
% 3.05/1.62 | ( X2 = Y ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_111_dual__order_Ostrict__trans,axiom,
% 3.05/1.62 ! [B: int,A: int,C: int] :
% 3.05/1.62 ( ( ord_less_int @ B @ A )
% 3.05/1.62 => ( ( ord_less_int @ C @ B )
% 3.05/1.62 => ( ord_less_int @ C @ A ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_112_dual__order_Ostrict__trans,axiom,
% 3.05/1.62 ! [B: set_a,A: set_a,C: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ B @ A )
% 3.05/1.62 => ( ( ord_less_set_a @ C @ B )
% 3.05/1.62 => ( ord_less_set_a @ C @ A ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_113_dual__order_Ostrict__trans,axiom,
% 3.05/1.62 ! [B: a > $o,A: a > $o,C: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ B @ A )
% 3.05/1.62 => ( ( ord_less_a_o @ C @ B )
% 3.05/1.62 => ( ord_less_a_o @ C @ A ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_114_linorder__less__wlog,axiom,
% 3.05/1.62 ! [P: int > int > $o,A: int,B: int] :
% 3.05/1.62 ( ! [A4: int,B3: int] :
% 3.05/1.62 ( ( ord_less_int @ A4 @ B3 )
% 3.05/1.62 => ( P @ A4 @ B3 ) )
% 3.05/1.62 => ( ! [A4: int] : ( P @ A4 @ A4 )
% 3.05/1.62 => ( ! [A4: int,B3: int] :
% 3.05/1.62 ( ( P @ B3 @ A4 )
% 3.05/1.62 => ( P @ A4 @ B3 ) )
% 3.05/1.62 => ( P @ A @ B ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_115_less__imp__not__less,axiom,
% 3.05/1.62 ! [X2: int,Y: int] :
% 3.05/1.62 ( ( ord_less_int @ X2 @ Y )
% 3.05/1.62 => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_116_less__imp__not__less,axiom,
% 3.05/1.62 ! [X2: set_a,Y: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X2 @ Y )
% 3.05/1.62 => ~ ( ord_less_set_a @ Y @ X2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_117_less__imp__not__less,axiom,
% 3.05/1.62 ! [X2: a > $o,Y: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X2 @ Y )
% 3.05/1.62 => ~ ( ord_less_a_o @ Y @ X2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_118_order_Ostrict__trans,axiom,
% 3.05/1.62 ! [A: int,B: int,C: int] :
% 3.05/1.62 ( ( ord_less_int @ A @ B )
% 3.05/1.62 => ( ( ord_less_int @ B @ C )
% 3.05/1.62 => ( ord_less_int @ A @ C ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_119_order_Ostrict__trans,axiom,
% 3.05/1.62 ! [A: set_a,B: set_a,C: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ A @ B )
% 3.05/1.62 => ( ( ord_less_set_a @ B @ C )
% 3.05/1.62 => ( ord_less_set_a @ A @ C ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_120_order_Ostrict__trans,axiom,
% 3.05/1.62 ! [A: a > $o,B: a > $o,C: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ A @ B )
% 3.05/1.62 => ( ( ord_less_a_o @ B @ C )
% 3.05/1.62 => ( ord_less_a_o @ A @ C ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_121_dual__order_Oirrefl,axiom,
% 3.05/1.62 ! [A: int] :
% 3.05/1.62 ~ ( ord_less_int @ A @ A ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_122_dual__order_Oirrefl,axiom,
% 3.05/1.62 ! [A: set_a] :
% 3.05/1.62 ~ ( ord_less_set_a @ A @ A ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_123_dual__order_Oirrefl,axiom,
% 3.05/1.62 ! [A: a > $o] :
% 3.05/1.62 ~ ( ord_less_a_o @ A @ A ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_124_linorder__cases,axiom,
% 3.05/1.62 ! [X2: int,Y: int] :
% 3.05/1.62 ( ~ ( ord_less_int @ X2 @ Y )
% 3.05/1.62 => ( ( X2 != Y )
% 3.05/1.62 => ( ord_less_int @ Y @ X2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_125_less__imp__triv,axiom,
% 3.05/1.62 ! [X2: int,Y: int,P: $o] :
% 3.05/1.62 ( ( ord_less_int @ X2 @ Y )
% 3.05/1.62 => ( ( ord_less_int @ Y @ X2 )
% 3.05/1.62 => P ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_126_less__imp__triv,axiom,
% 3.05/1.62 ! [X2: set_a,Y: set_a,P: $o] :
% 3.05/1.62 ( ( ord_less_set_a @ X2 @ Y )
% 3.05/1.62 => ( ( ord_less_set_a @ Y @ X2 )
% 3.05/1.62 => P ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_127_less__imp__triv,axiom,
% 3.05/1.62 ! [X2: a > $o,Y: a > $o,P: $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X2 @ Y )
% 3.05/1.62 => ( ( ord_less_a_o @ Y @ X2 )
% 3.05/1.62 => P ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_128_less__imp__not__eq2,axiom,
% 3.05/1.62 ! [X2: int,Y: int] :
% 3.05/1.62 ( ( ord_less_int @ X2 @ Y )
% 3.05/1.62 => ( Y != X2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_129_less__imp__not__eq2,axiom,
% 3.05/1.62 ! [X2: set_a,Y: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X2 @ Y )
% 3.05/1.62 => ( Y != X2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_130_less__imp__not__eq2,axiom,
% 3.05/1.62 ! [X2: a > $o,Y: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X2 @ Y )
% 3.05/1.62 => ( Y != X2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_131_antisym__conv3,axiom,
% 3.05/1.62 ! [Y: int,X2: int] :
% 3.05/1.62 ( ~ ( ord_less_int @ Y @ X2 )
% 3.05/1.62 => ( ( ~ ( ord_less_int @ X2 @ Y ) )
% 3.05/1.62 = ( X2 = Y ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_132_less__not__sym,axiom,
% 3.05/1.62 ! [X2: int,Y: int] :
% 3.05/1.62 ( ( ord_less_int @ X2 @ Y )
% 3.05/1.62 => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_133_less__not__sym,axiom,
% 3.05/1.62 ! [X2: set_a,Y: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X2 @ Y )
% 3.05/1.62 => ~ ( ord_less_set_a @ Y @ X2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_134_less__not__sym,axiom,
% 3.05/1.62 ! [X2: a > $o,Y: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X2 @ Y )
% 3.05/1.62 => ~ ( ord_less_a_o @ Y @ X2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_135_less__imp__not__eq,axiom,
% 3.05/1.62 ! [X2: int,Y: int] :
% 3.05/1.62 ( ( ord_less_int @ X2 @ Y )
% 3.05/1.62 => ( X2 != Y ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_136_less__imp__not__eq,axiom,
% 3.05/1.62 ! [X2: set_a,Y: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X2 @ Y )
% 3.05/1.62 => ( X2 != Y ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_137_less__imp__not__eq,axiom,
% 3.05/1.62 ! [X2: a > $o,Y: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X2 @ Y )
% 3.05/1.62 => ( X2 != Y ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_138_dual__order_Oasym,axiom,
% 3.05/1.62 ! [B: int,A: int] :
% 3.05/1.62 ( ( ord_less_int @ B @ A )
% 3.05/1.62 => ~ ( ord_less_int @ A @ B ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_139_dual__order_Oasym,axiom,
% 3.05/1.62 ! [B: set_a,A: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ B @ A )
% 3.05/1.62 => ~ ( ord_less_set_a @ A @ B ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_140_dual__order_Oasym,axiom,
% 3.05/1.62 ! [B: a > $o,A: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ B @ A )
% 3.05/1.62 => ~ ( ord_less_a_o @ A @ B ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_141_ord__less__eq__trans,axiom,
% 3.05/1.62 ! [A: int,B: int,C: int] :
% 3.05/1.62 ( ( ord_less_int @ A @ B )
% 3.05/1.62 => ( ( B = C )
% 3.05/1.62 => ( ord_less_int @ A @ C ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_142_ord__less__eq__trans,axiom,
% 3.05/1.62 ! [A: set_a,B: set_a,C: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ A @ B )
% 3.05/1.62 => ( ( B = C )
% 3.05/1.62 => ( ord_less_set_a @ A @ C ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_143_ord__less__eq__trans,axiom,
% 3.05/1.62 ! [A: a > $o,B: a > $o,C: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ A @ B )
% 3.05/1.62 => ( ( B = C )
% 3.05/1.62 => ( ord_less_a_o @ A @ C ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_144_ord__eq__less__trans,axiom,
% 3.05/1.62 ! [A: int,B: int,C: int] :
% 3.05/1.62 ( ( A = B )
% 3.05/1.62 => ( ( ord_less_int @ B @ C )
% 3.05/1.62 => ( ord_less_int @ A @ C ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_145_ord__eq__less__trans,axiom,
% 3.05/1.62 ! [A: set_a,B: set_a,C: set_a] :
% 3.05/1.62 ( ( A = B )
% 3.05/1.62 => ( ( ord_less_set_a @ B @ C )
% 3.05/1.62 => ( ord_less_set_a @ A @ C ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_146_ord__eq__less__trans,axiom,
% 3.05/1.62 ! [A: a > $o,B: a > $o,C: a > $o] :
% 3.05/1.62 ( ( A = B )
% 3.05/1.62 => ( ( ord_less_a_o @ B @ C )
% 3.05/1.62 => ( ord_less_a_o @ A @ C ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_147_less__irrefl,axiom,
% 3.05/1.62 ! [X2: int] :
% 3.05/1.62 ~ ( ord_less_int @ X2 @ X2 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_148_less__irrefl,axiom,
% 3.05/1.62 ! [X2: set_a] :
% 3.05/1.62 ~ ( ord_less_set_a @ X2 @ X2 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_149_less__irrefl,axiom,
% 3.05/1.62 ! [X2: a > $o] :
% 3.05/1.62 ~ ( ord_less_a_o @ X2 @ X2 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_150_less__linear,axiom,
% 3.05/1.62 ! [X2: int,Y: int] :
% 3.05/1.62 ( ( ord_less_int @ X2 @ Y )
% 3.05/1.62 | ( X2 = Y )
% 3.05/1.62 | ( ord_less_int @ Y @ X2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_151_less__trans,axiom,
% 3.05/1.62 ! [X2: int,Y: int,Z2: int] :
% 3.05/1.62 ( ( ord_less_int @ X2 @ Y )
% 3.05/1.62 => ( ( ord_less_int @ Y @ Z2 )
% 3.05/1.62 => ( ord_less_int @ X2 @ Z2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_152_less__trans,axiom,
% 3.05/1.62 ! [X2: set_a,Y: set_a,Z2: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X2 @ Y )
% 3.05/1.62 => ( ( ord_less_set_a @ Y @ Z2 )
% 3.05/1.62 => ( ord_less_set_a @ X2 @ Z2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_153_less__trans,axiom,
% 3.05/1.62 ! [X2: a > $o,Y: a > $o,Z2: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X2 @ Y )
% 3.05/1.62 => ( ( ord_less_a_o @ Y @ Z2 )
% 3.05/1.62 => ( ord_less_a_o @ X2 @ Z2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_154_less__asym_H,axiom,
% 3.05/1.62 ! [A: int,B: int] :
% 3.05/1.62 ( ( ord_less_int @ A @ B )
% 3.05/1.62 => ~ ( ord_less_int @ B @ A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_155_less__asym_H,axiom,
% 3.05/1.62 ! [A: set_a,B: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ A @ B )
% 3.05/1.62 => ~ ( ord_less_set_a @ B @ A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_156_less__asym_H,axiom,
% 3.05/1.62 ! [A: a > $o,B: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ A @ B )
% 3.05/1.62 => ~ ( ord_less_a_o @ B @ A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_157_less__asym,axiom,
% 3.05/1.62 ! [X2: int,Y: int] :
% 3.05/1.62 ( ( ord_less_int @ X2 @ Y )
% 3.05/1.62 => ~ ( ord_less_int @ Y @ X2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_158_less__asym,axiom,
% 3.05/1.62 ! [X2: set_a,Y: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X2 @ Y )
% 3.05/1.62 => ~ ( ord_less_set_a @ Y @ X2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_159_less__asym,axiom,
% 3.05/1.62 ! [X2: a > $o,Y: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X2 @ Y )
% 3.05/1.62 => ~ ( ord_less_a_o @ Y @ X2 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_160_less__imp__neq,axiom,
% 3.05/1.62 ! [X2: int,Y: int] :
% 3.05/1.62 ( ( ord_less_int @ X2 @ Y )
% 3.05/1.62 => ( X2 != Y ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_161_less__imp__neq,axiom,
% 3.05/1.62 ! [X2: set_a,Y: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X2 @ Y )
% 3.05/1.62 => ( X2 != Y ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_162_less__imp__neq,axiom,
% 3.05/1.62 ! [X2: a > $o,Y: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X2 @ Y )
% 3.05/1.62 => ( X2 != Y ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_163_order_Oasym,axiom,
% 3.05/1.62 ! [A: int,B: int] :
% 3.05/1.62 ( ( ord_less_int @ A @ B )
% 3.05/1.62 => ~ ( ord_less_int @ B @ A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_164_order_Oasym,axiom,
% 3.05/1.62 ! [A: set_a,B: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ A @ B )
% 3.05/1.62 => ~ ( ord_less_set_a @ B @ A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_165_order_Oasym,axiom,
% 3.05/1.62 ! [A: a > $o,B: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ A @ B )
% 3.05/1.62 => ~ ( ord_less_a_o @ B @ A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_166_neq__iff,axiom,
% 3.05/1.62 ! [X2: int,Y: int] :
% 3.05/1.62 ( ( X2 != Y )
% 3.05/1.62 = ( ( ord_less_int @ X2 @ Y )
% 3.05/1.62 | ( ord_less_int @ Y @ X2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_167_neqE,axiom,
% 3.05/1.62 ! [X2: int,Y: int] :
% 3.05/1.62 ( ( X2 != Y )
% 3.05/1.62 => ( ~ ( ord_less_int @ X2 @ Y )
% 3.05/1.62 => ( ord_less_int @ Y @ X2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_168_gt__ex,axiom,
% 3.05/1.62 ! [X2: int] :
% 3.05/1.62 ? [X_1: int] : ( ord_less_int @ X2 @ X_1 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_169_lt__ex,axiom,
% 3.05/1.62 ! [X2: int] :
% 3.05/1.62 ? [Y4: int] : ( ord_less_int @ Y4 @ X2 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_170_order__less__subst2,axiom,
% 3.05/1.62 ! [A: int,B: int,F: int > int,C: int] :
% 3.05/1.62 ( ( ord_less_int @ A @ B )
% 3.05/1.62 => ( ( ord_less_int @ ( F @ B ) @ C )
% 3.05/1.62 => ( ! [X4: int,Y4: int] :
% 3.05/1.62 ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_171_order__less__subst2,axiom,
% 3.05/1.62 ! [A: int,B: int,F: int > set_a,C: set_a] :
% 3.05/1.62 ( ( ord_less_int @ A @ B )
% 3.05/1.62 => ( ( ord_less_set_a @ ( F @ B ) @ C )
% 3.05/1.62 => ( ! [X4: int,Y4: int] :
% 3.05/1.62 ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_172_order__less__subst2,axiom,
% 3.05/1.62 ! [A: int,B: int,F: int > a > $o,C: a > $o] :
% 3.05/1.62 ( ( ord_less_int @ A @ B )
% 3.05/1.62 => ( ( ord_less_a_o @ ( F @ B ) @ C )
% 3.05/1.62 => ( ! [X4: int,Y4: int] :
% 3.05/1.62 ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_173_order__less__subst2,axiom,
% 3.05/1.62 ! [A: set_a,B: set_a,F: set_a > int,C: int] :
% 3.05/1.62 ( ( ord_less_set_a @ A @ B )
% 3.05/1.62 => ( ( ord_less_int @ ( F @ B ) @ C )
% 3.05/1.62 => ( ! [X4: set_a,Y4: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_174_order__less__subst2,axiom,
% 3.05/1.62 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ A @ B )
% 3.05/1.62 => ( ( ord_less_set_a @ ( F @ B ) @ C )
% 3.05/1.62 => ( ! [X4: set_a,Y4: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_175_order__less__subst2,axiom,
% 3.05/1.62 ! [A: set_a,B: set_a,F: set_a > a > $o,C: a > $o] :
% 3.05/1.62 ( ( ord_less_set_a @ A @ B )
% 3.05/1.62 => ( ( ord_less_a_o @ ( F @ B ) @ C )
% 3.05/1.62 => ( ! [X4: set_a,Y4: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_176_order__less__subst2,axiom,
% 3.05/1.62 ! [A: a > $o,B: a > $o,F: ( a > $o ) > int,C: int] :
% 3.05/1.62 ( ( ord_less_a_o @ A @ B )
% 3.05/1.62 => ( ( ord_less_int @ ( F @ B ) @ C )
% 3.05/1.62 => ( ! [X4: a > $o,Y4: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_177_order__less__subst2,axiom,
% 3.05/1.62 ! [A: a > $o,B: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 3.05/1.62 ( ( ord_less_a_o @ A @ B )
% 3.05/1.62 => ( ( ord_less_set_a @ ( F @ B ) @ C )
% 3.05/1.62 => ( ! [X4: a > $o,Y4: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_178_order__less__subst2,axiom,
% 3.05/1.62 ! [A: a > $o,B: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ A @ B )
% 3.05/1.62 => ( ( ord_less_a_o @ ( F @ B ) @ C )
% 3.05/1.62 => ( ! [X4: a > $o,Y4: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_179_order__less__subst1,axiom,
% 3.05/1.62 ! [A: int,F: int > int,B: int,C: int] :
% 3.05/1.62 ( ( ord_less_int @ A @ ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_int @ B @ C )
% 3.05/1.62 => ( ! [X4: int,Y4: int] :
% 3.05/1.62 ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_180_order__less__subst1,axiom,
% 3.05/1.62 ! [A: int,F: set_a > int,B: set_a,C: set_a] :
% 3.05/1.62 ( ( ord_less_int @ A @ ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_set_a @ B @ C )
% 3.05/1.62 => ( ! [X4: set_a,Y4: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_181_order__less__subst1,axiom,
% 3.05/1.62 ! [A: int,F: ( a > $o ) > int,B: a > $o,C: a > $o] :
% 3.05/1.62 ( ( ord_less_int @ A @ ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_a_o @ B @ C )
% 3.05/1.62 => ( ! [X4: a > $o,Y4: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_182_order__less__subst1,axiom,
% 3.05/1.62 ! [A: set_a,F: int > set_a,B: int,C: int] :
% 3.05/1.62 ( ( ord_less_set_a @ A @ ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_int @ B @ C )
% 3.05/1.62 => ( ! [X4: int,Y4: int] :
% 3.05/1.62 ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_183_order__less__subst1,axiom,
% 3.05/1.62 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ A @ ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_set_a @ B @ C )
% 3.05/1.62 => ( ! [X4: set_a,Y4: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_184_order__less__subst1,axiom,
% 3.05/1.62 ! [A: set_a,F: ( a > $o ) > set_a,B: a > $o,C: a > $o] :
% 3.05/1.62 ( ( ord_less_set_a @ A @ ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_a_o @ B @ C )
% 3.05/1.62 => ( ! [X4: a > $o,Y4: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_185_order__less__subst1,axiom,
% 3.05/1.62 ! [A: a > $o,F: int > a > $o,B: int,C: int] :
% 3.05/1.62 ( ( ord_less_a_o @ A @ ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_int @ B @ C )
% 3.05/1.62 => ( ! [X4: int,Y4: int] :
% 3.05/1.62 ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_186_order__less__subst1,axiom,
% 3.05/1.62 ! [A: a > $o,F: set_a > a > $o,B: set_a,C: set_a] :
% 3.05/1.62 ( ( ord_less_a_o @ A @ ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_set_a @ B @ C )
% 3.05/1.62 => ( ! [X4: set_a,Y4: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_187_order__less__subst1,axiom,
% 3.05/1.62 ! [A: a > $o,F: ( a > $o ) > a > $o,B: a > $o,C: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ A @ ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_a_o @ B @ C )
% 3.05/1.62 => ( ! [X4: a > $o,Y4: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_188_ord__less__eq__subst,axiom,
% 3.05/1.62 ! [A: int,B: int,F: int > int,C: int] :
% 3.05/1.62 ( ( ord_less_int @ A @ B )
% 3.05/1.62 => ( ( ( F @ B )
% 3.05/1.62 = C )
% 3.05/1.62 => ( ! [X4: int,Y4: int] :
% 3.05/1.62 ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_189_ord__less__eq__subst,axiom,
% 3.05/1.62 ! [A: int,B: int,F: int > set_a,C: set_a] :
% 3.05/1.62 ( ( ord_less_int @ A @ B )
% 3.05/1.62 => ( ( ( F @ B )
% 3.05/1.62 = C )
% 3.05/1.62 => ( ! [X4: int,Y4: int] :
% 3.05/1.62 ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_190_ord__less__eq__subst,axiom,
% 3.05/1.62 ! [A: int,B: int,F: int > a > $o,C: a > $o] :
% 3.05/1.62 ( ( ord_less_int @ A @ B )
% 3.05/1.62 => ( ( ( F @ B )
% 3.05/1.62 = C )
% 3.05/1.62 => ( ! [X4: int,Y4: int] :
% 3.05/1.62 ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_191_ord__less__eq__subst,axiom,
% 3.05/1.62 ! [A: set_a,B: set_a,F: set_a > int,C: int] :
% 3.05/1.62 ( ( ord_less_set_a @ A @ B )
% 3.05/1.62 => ( ( ( F @ B )
% 3.05/1.62 = C )
% 3.05/1.62 => ( ! [X4: set_a,Y4: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_192_ord__less__eq__subst,axiom,
% 3.05/1.62 ! [A: set_a,B: set_a,F: set_a > set_a,C: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ A @ B )
% 3.05/1.62 => ( ( ( F @ B )
% 3.05/1.62 = C )
% 3.05/1.62 => ( ! [X4: set_a,Y4: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_193_ord__less__eq__subst,axiom,
% 3.05/1.62 ! [A: set_a,B: set_a,F: set_a > a > $o,C: a > $o] :
% 3.05/1.62 ( ( ord_less_set_a @ A @ B )
% 3.05/1.62 => ( ( ( F @ B )
% 3.05/1.62 = C )
% 3.05/1.62 => ( ! [X4: set_a,Y4: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_194_ord__less__eq__subst,axiom,
% 3.05/1.62 ! [A: a > $o,B: a > $o,F: ( a > $o ) > int,C: int] :
% 3.05/1.62 ( ( ord_less_a_o @ A @ B )
% 3.05/1.62 => ( ( ( F @ B )
% 3.05/1.62 = C )
% 3.05/1.62 => ( ! [X4: a > $o,Y4: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_195_ord__less__eq__subst,axiom,
% 3.05/1.62 ! [A: a > $o,B: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 3.05/1.62 ( ( ord_less_a_o @ A @ B )
% 3.05/1.62 => ( ( ( F @ B )
% 3.05/1.62 = C )
% 3.05/1.62 => ( ! [X4: a > $o,Y4: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_196_ord__less__eq__subst,axiom,
% 3.05/1.62 ! [A: a > $o,B: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ A @ B )
% 3.05/1.62 => ( ( ( F @ B )
% 3.05/1.62 = C )
% 3.05/1.62 => ( ! [X4: a > $o,Y4: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ A ) @ C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_197_ord__eq__less__subst,axiom,
% 3.05/1.62 ! [A: int,F: int > int,B: int,C: int] :
% 3.05/1.62 ( ( A
% 3.05/1.62 = ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_int @ B @ C )
% 3.05/1.62 => ( ! [X4: int,Y4: int] :
% 3.05/1.62 ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_198_ord__eq__less__subst,axiom,
% 3.05/1.62 ! [A: set_a,F: int > set_a,B: int,C: int] :
% 3.05/1.62 ( ( A
% 3.05/1.62 = ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_int @ B @ C )
% 3.05/1.62 => ( ! [X4: int,Y4: int] :
% 3.05/1.62 ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_199_ord__eq__less__subst,axiom,
% 3.05/1.62 ! [A: a > $o,F: int > a > $o,B: int,C: int] :
% 3.05/1.62 ( ( A
% 3.05/1.62 = ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_int @ B @ C )
% 3.05/1.62 => ( ! [X4: int,Y4: int] :
% 3.05/1.62 ( ( ord_less_int @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_200_ord__eq__less__subst,axiom,
% 3.05/1.62 ! [A: int,F: set_a > int,B: set_a,C: set_a] :
% 3.05/1.62 ( ( A
% 3.05/1.62 = ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_set_a @ B @ C )
% 3.05/1.62 => ( ! [X4: set_a,Y4: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_201_ord__eq__less__subst,axiom,
% 3.05/1.62 ! [A: set_a,F: set_a > set_a,B: set_a,C: set_a] :
% 3.05/1.62 ( ( A
% 3.05/1.62 = ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_set_a @ B @ C )
% 3.05/1.62 => ( ! [X4: set_a,Y4: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_202_ord__eq__less__subst,axiom,
% 3.05/1.62 ! [A: a > $o,F: set_a > a > $o,B: set_a,C: set_a] :
% 3.05/1.62 ( ( A
% 3.05/1.62 = ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_set_a @ B @ C )
% 3.05/1.62 => ( ! [X4: set_a,Y4: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_203_ord__eq__less__subst,axiom,
% 3.05/1.62 ! [A: int,F: ( a > $o ) > int,B: a > $o,C: a > $o] :
% 3.05/1.62 ( ( A
% 3.05/1.62 = ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_a_o @ B @ C )
% 3.05/1.62 => ( ! [X4: a > $o,Y4: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_int @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_204_ord__eq__less__subst,axiom,
% 3.05/1.62 ! [A: set_a,F: ( a > $o ) > set_a,B: a > $o,C: a > $o] :
% 3.05/1.62 ( ( A
% 3.05/1.62 = ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_a_o @ B @ C )
% 3.05/1.62 => ( ! [X4: a > $o,Y4: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_set_a @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_set_a @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_205_ord__eq__less__subst,axiom,
% 3.05/1.62 ! [A: a > $o,F: ( a > $o ) > a > $o,B: a > $o,C: a > $o] :
% 3.05/1.62 ( ( A
% 3.05/1.62 = ( F @ B ) )
% 3.05/1.62 => ( ( ord_less_a_o @ B @ C )
% 3.05/1.62 => ( ! [X4: a > $o,Y4: a > $o] :
% 3.05/1.62 ( ( ord_less_a_o @ X4 @ Y4 )
% 3.05/1.62 => ( ord_less_a_o @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.05/1.62 => ( ord_less_a_o @ A @ ( F @ C ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_206_option_Osimps_I15_J,axiom,
% 3.05/1.62 ! [X25: option_a] :
% 3.05/1.62 ( ( set_option_option_a2 @ ( some_option_a @ X25 ) )
% 3.05/1.62 = ( insert_option_a @ X25 @ bot_bot_set_option_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_207_option_Osimps_I15_J,axiom,
% 3.05/1.62 ! [X25: a] :
% 3.05/1.62 ( ( set_option_a2 @ ( some_a @ X25 ) )
% 3.05/1.62 = ( insert_a @ X25 @ bot_bot_set_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_208_option_Othe__def,axiom,
% 3.05/1.62 ( the_a2
% 3.05/1.62 = ( case_option_a_a @ undefined_a
% 3.05/1.62 @ ^ [X26: a] : X26 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_209_bot__empty__eq,axiom,
% 3.05/1.62 ( bot_bot_option_a_o
% 3.05/1.62 = ( ^ [X3: option_a] : ( member_option_a @ X3 @ bot_bot_set_option_a ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_210_bot__empty__eq,axiom,
% 3.05/1.62 ( bot_bot_a_o
% 3.05/1.62 = ( ^ [X3: a] : ( member_a @ X3 @ bot_bot_set_a ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_211_Collect__empty__eq__bot,axiom,
% 3.05/1.62 ! [P: a > $o] :
% 3.05/1.62 ( ( ( collect_a @ P )
% 3.05/1.62 = bot_bot_set_a )
% 3.05/1.62 = ( P = bot_bot_a_o ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_212_Collect__empty__eq__bot,axiom,
% 3.05/1.62 ! [P: option_a > $o] :
% 3.05/1.62 ( ( ( collect_option_a @ P )
% 3.05/1.62 = bot_bot_set_option_a )
% 3.05/1.62 = ( P = bot_bot_option_a_o ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_213_linorder__neqE__linordered__idom,axiom,
% 3.05/1.62 ! [X2: int,Y: int] :
% 3.05/1.62 ( ( X2 != Y )
% 3.05/1.62 => ( ~ ( ord_less_int @ X2 @ Y )
% 3.05/1.62 => ( ord_less_int @ Y @ X2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_214_insert__absorb2,axiom,
% 3.05/1.62 ! [X2: a,A3: set_a] :
% 3.05/1.62 ( ( insert_a @ X2 @ ( insert_a @ X2 @ A3 ) )
% 3.05/1.62 = ( insert_a @ X2 @ A3 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_215_insert__absorb2,axiom,
% 3.05/1.62 ! [X2: option_a,A3: set_option_a] :
% 3.05/1.62 ( ( insert_option_a @ X2 @ ( insert_option_a @ X2 @ A3 ) )
% 3.05/1.62 = ( insert_option_a @ X2 @ A3 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_216_insert__iff,axiom,
% 3.05/1.62 ! [A: option_a,B: option_a,A3: set_option_a] :
% 3.05/1.62 ( ( member_option_a @ A @ ( insert_option_a @ B @ A3 ) )
% 3.05/1.62 = ( ( A = B )
% 3.05/1.62 | ( member_option_a @ A @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_217_insert__iff,axiom,
% 3.05/1.62 ! [A: a,B: a,A3: set_a] :
% 3.05/1.62 ( ( member_a @ A @ ( insert_a @ B @ A3 ) )
% 3.05/1.62 = ( ( A = B )
% 3.05/1.62 | ( member_a @ A @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_218_insertCI,axiom,
% 3.05/1.62 ! [A: option_a,B4: set_option_a,B: option_a] :
% 3.05/1.62 ( ( ~ ( member_option_a @ A @ B4 )
% 3.05/1.62 => ( A = B ) )
% 3.05/1.62 => ( member_option_a @ A @ ( insert_option_a @ B @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_219_insertCI,axiom,
% 3.05/1.62 ! [A: a,B4: set_a,B: a] :
% 3.05/1.62 ( ( ~ ( member_a @ A @ B4 )
% 3.05/1.62 => ( A = B ) )
% 3.05/1.62 => ( member_a @ A @ ( insert_a @ B @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_220_singletonI,axiom,
% 3.05/1.62 ! [A: option_a] : ( member_option_a @ A @ ( insert_option_a @ A @ bot_bot_set_option_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_221_singletonI,axiom,
% 3.05/1.62 ! [A: a] : ( member_a @ A @ ( insert_a @ A @ bot_bot_set_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_222_singleton__conv,axiom,
% 3.05/1.62 ! [A: a] :
% 3.05/1.62 ( ( collect_a
% 3.05/1.62 @ ^ [X3: a] : ( X3 = A ) )
% 3.05/1.62 = ( insert_a @ A @ bot_bot_set_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_223_singleton__conv,axiom,
% 3.05/1.62 ! [A: option_a] :
% 3.05/1.62 ( ( collect_option_a
% 3.05/1.62 @ ^ [X3: option_a] : ( X3 = A ) )
% 3.05/1.62 = ( insert_option_a @ A @ bot_bot_set_option_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_224_singleton__conv2,axiom,
% 3.05/1.62 ! [A: a] :
% 3.05/1.62 ( ( collect_a
% 3.05/1.62 @ ( ^ [Y2: a,Z: a] : ( Y2 = Z )
% 3.05/1.62 @ A ) )
% 3.05/1.62 = ( insert_a @ A @ bot_bot_set_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_225_singleton__conv2,axiom,
% 3.05/1.62 ! [A: option_a] :
% 3.05/1.62 ( ( collect_option_a
% 3.05/1.62 @ ( ^ [Y2: option_a,Z: option_a] : ( Y2 = Z )
% 3.05/1.62 @ A ) )
% 3.05/1.62 = ( insert_option_a @ A @ bot_bot_set_option_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_226_psubset__trans,axiom,
% 3.05/1.62 ! [A3: set_a,B4: set_a,C2: set_a] :
% 3.05/1.62 ( ( ord_less_set_a @ A3 @ B4 )
% 3.05/1.62 => ( ( ord_less_set_a @ B4 @ C2 )
% 3.05/1.62 => ( ord_less_set_a @ A3 @ C2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_227_less__set__def,axiom,
% 3.05/1.62 ( ord_le1280890064tion_a
% 3.05/1.62 = ( ^ [A5: set_option_a,B5: set_option_a] :
% 3.05/1.62 ( ord_less_option_a_o
% 3.05/1.62 @ ^ [X3: option_a] : ( member_option_a @ X3 @ A5 )
% 3.05/1.62 @ ^ [X3: option_a] : ( member_option_a @ X3 @ B5 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_228_less__set__def,axiom,
% 3.05/1.62 ( ord_less_set_a
% 3.05/1.62 = ( ^ [A5: set_a,B5: set_a] :
% 3.05/1.62 ( ord_less_a_o
% 3.05/1.62 @ ^ [X3: a] : ( member_a @ X3 @ A5 )
% 3.05/1.62 @ ^ [X3: a] : ( member_a @ X3 @ B5 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_229_psubsetD,axiom,
% 3.05/1.62 ! [A3: set_option_a,B4: set_option_a,C: option_a] :
% 3.05/1.62 ( ( ord_le1280890064tion_a @ A3 @ B4 )
% 3.05/1.62 => ( ( member_option_a @ C @ A3 )
% 3.05/1.62 => ( member_option_a @ C @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_230_psubsetD,axiom,
% 3.05/1.62 ! [A3: set_a,B4: set_a,C: a] :
% 3.05/1.62 ( ( ord_less_set_a @ A3 @ B4 )
% 3.05/1.62 => ( ( member_a @ C @ A3 )
% 3.05/1.62 => ( member_a @ C @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_231_mk__disjoint__insert,axiom,
% 3.05/1.62 ! [A: option_a,A3: set_option_a] :
% 3.05/1.62 ( ( member_option_a @ A @ A3 )
% 3.05/1.62 => ? [B6: set_option_a] :
% 3.05/1.62 ( ( A3
% 3.05/1.62 = ( insert_option_a @ A @ B6 ) )
% 3.05/1.62 & ~ ( member_option_a @ A @ B6 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_232_mk__disjoint__insert,axiom,
% 3.05/1.62 ! [A: a,A3: set_a] :
% 3.05/1.62 ( ( member_a @ A @ A3 )
% 3.05/1.62 => ? [B6: set_a] :
% 3.05/1.62 ( ( A3
% 3.05/1.62 = ( insert_a @ A @ B6 ) )
% 3.05/1.62 & ~ ( member_a @ A @ B6 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_233_insert__commute,axiom,
% 3.05/1.62 ! [X2: a,Y: a,A3: set_a] :
% 3.05/1.62 ( ( insert_a @ X2 @ ( insert_a @ Y @ A3 ) )
% 3.05/1.62 = ( insert_a @ Y @ ( insert_a @ X2 @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_234_insert__commute,axiom,
% 3.05/1.62 ! [X2: option_a,Y: option_a,A3: set_option_a] :
% 3.05/1.62 ( ( insert_option_a @ X2 @ ( insert_option_a @ Y @ A3 ) )
% 3.05/1.62 = ( insert_option_a @ Y @ ( insert_option_a @ X2 @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_235_insert__eq__iff,axiom,
% 3.05/1.62 ! [A: option_a,A3: set_option_a,B: option_a,B4: set_option_a] :
% 3.05/1.62 ( ~ ( member_option_a @ A @ A3 )
% 3.05/1.62 => ( ~ ( member_option_a @ B @ B4 )
% 3.05/1.62 => ( ( ( insert_option_a @ A @ A3 )
% 3.05/1.62 = ( insert_option_a @ B @ B4 ) )
% 3.05/1.62 = ( ( ( A = B )
% 3.05/1.62 => ( A3 = B4 ) )
% 3.05/1.62 & ( ( A != B )
% 3.05/1.62 => ? [C3: set_option_a] :
% 3.05/1.62 ( ( A3
% 3.05/1.62 = ( insert_option_a @ B @ C3 ) )
% 3.05/1.62 & ~ ( member_option_a @ B @ C3 )
% 3.05/1.62 & ( B4
% 3.05/1.62 = ( insert_option_a @ A @ C3 ) )
% 3.05/1.62 & ~ ( member_option_a @ A @ C3 ) ) ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_236_insert__eq__iff,axiom,
% 3.05/1.62 ! [A: a,A3: set_a,B: a,B4: set_a] :
% 3.05/1.62 ( ~ ( member_a @ A @ A3 )
% 3.05/1.62 => ( ~ ( member_a @ B @ B4 )
% 3.05/1.62 => ( ( ( insert_a @ A @ A3 )
% 3.05/1.62 = ( insert_a @ B @ B4 ) )
% 3.05/1.62 = ( ( ( A = B )
% 3.05/1.62 => ( A3 = B4 ) )
% 3.05/1.62 & ( ( A != B )
% 3.05/1.62 => ? [C3: set_a] :
% 3.05/1.62 ( ( A3
% 3.05/1.62 = ( insert_a @ B @ C3 ) )
% 3.05/1.62 & ~ ( member_a @ B @ C3 )
% 3.05/1.62 & ( B4
% 3.05/1.62 = ( insert_a @ A @ C3 ) )
% 3.05/1.62 & ~ ( member_a @ A @ C3 ) ) ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_237_insert__absorb,axiom,
% 3.05/1.62 ! [A: option_a,A3: set_option_a] :
% 3.05/1.62 ( ( member_option_a @ A @ A3 )
% 3.05/1.62 => ( ( insert_option_a @ A @ A3 )
% 3.05/1.62 = A3 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_238_insert__absorb,axiom,
% 3.05/1.62 ! [A: a,A3: set_a] :
% 3.05/1.62 ( ( member_a @ A @ A3 )
% 3.05/1.62 => ( ( insert_a @ A @ A3 )
% 3.05/1.62 = A3 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_239_insert__ident,axiom,
% 3.05/1.62 ! [X2: option_a,A3: set_option_a,B4: set_option_a] :
% 3.05/1.62 ( ~ ( member_option_a @ X2 @ A3 )
% 3.05/1.62 => ( ~ ( member_option_a @ X2 @ B4 )
% 3.05/1.62 => ( ( ( insert_option_a @ X2 @ A3 )
% 3.05/1.62 = ( insert_option_a @ X2 @ B4 ) )
% 3.05/1.62 = ( A3 = B4 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_240_insert__ident,axiom,
% 3.05/1.62 ! [X2: a,A3: set_a,B4: set_a] :
% 3.05/1.62 ( ~ ( member_a @ X2 @ A3 )
% 3.05/1.62 => ( ~ ( member_a @ X2 @ B4 )
% 3.05/1.62 => ( ( ( insert_a @ X2 @ A3 )
% 3.05/1.62 = ( insert_a @ X2 @ B4 ) )
% 3.05/1.62 = ( A3 = B4 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_241_Set_Oset__insert,axiom,
% 3.05/1.62 ! [X2: option_a,A3: set_option_a] :
% 3.05/1.62 ( ( member_option_a @ X2 @ A3 )
% 3.05/1.62 => ~ ! [B6: set_option_a] :
% 3.05/1.62 ( ( A3
% 3.05/1.62 = ( insert_option_a @ X2 @ B6 ) )
% 3.05/1.62 => ( member_option_a @ X2 @ B6 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_242_Set_Oset__insert,axiom,
% 3.05/1.62 ! [X2: a,A3: set_a] :
% 3.05/1.62 ( ( member_a @ X2 @ A3 )
% 3.05/1.62 => ~ ! [B6: set_a] :
% 3.05/1.62 ( ( A3
% 3.05/1.62 = ( insert_a @ X2 @ B6 ) )
% 3.05/1.62 => ( member_a @ X2 @ B6 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_243_insertI2,axiom,
% 3.05/1.62 ! [A: option_a,B4: set_option_a,B: option_a] :
% 3.05/1.62 ( ( member_option_a @ A @ B4 )
% 3.05/1.62 => ( member_option_a @ A @ ( insert_option_a @ B @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_244_insertI2,axiom,
% 3.05/1.62 ! [A: a,B4: set_a,B: a] :
% 3.05/1.62 ( ( member_a @ A @ B4 )
% 3.05/1.62 => ( member_a @ A @ ( insert_a @ B @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_245_insertI1,axiom,
% 3.05/1.62 ! [A: option_a,B4: set_option_a] : ( member_option_a @ A @ ( insert_option_a @ A @ B4 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_246_insertI1,axiom,
% 3.05/1.62 ! [A: a,B4: set_a] : ( member_a @ A @ ( insert_a @ A @ B4 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_247_insertE,axiom,
% 3.05/1.62 ! [A: option_a,B: option_a,A3: set_option_a] :
% 3.05/1.62 ( ( member_option_a @ A @ ( insert_option_a @ B @ A3 ) )
% 3.05/1.62 => ( ( A != B )
% 3.05/1.62 => ( member_option_a @ A @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_248_insertE,axiom,
% 3.05/1.62 ! [A: a,B: a,A3: set_a] :
% 3.05/1.62 ( ( member_a @ A @ ( insert_a @ B @ A3 ) )
% 3.05/1.62 => ( ( A != B )
% 3.05/1.62 => ( member_a @ A @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_249_insert__compr,axiom,
% 3.05/1.62 ( insert_option_a
% 3.05/1.62 = ( ^ [A2: option_a,B5: set_option_a] :
% 3.05/1.62 ( collect_option_a
% 3.05/1.62 @ ^ [X3: option_a] :
% 3.05/1.62 ( ( X3 = A2 )
% 3.05/1.62 | ( member_option_a @ X3 @ B5 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_250_insert__compr,axiom,
% 3.05/1.62 ( insert_a
% 3.05/1.62 = ( ^ [A2: a,B5: set_a] :
% 3.05/1.62 ( collect_a
% 3.05/1.62 @ ^ [X3: a] :
% 3.05/1.62 ( ( X3 = A2 )
% 3.05/1.62 | ( member_a @ X3 @ B5 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_251_insert__Collect,axiom,
% 3.05/1.62 ! [A: a,P: a > $o] :
% 3.05/1.62 ( ( insert_a @ A @ ( collect_a @ P ) )
% 3.05/1.62 = ( collect_a
% 3.05/1.62 @ ^ [U: a] :
% 3.05/1.62 ( ( U != A )
% 3.05/1.62 => ( P @ U ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_252_insert__Collect,axiom,
% 3.05/1.62 ! [A: option_a,P: option_a > $o] :
% 3.05/1.62 ( ( insert_option_a @ A @ ( collect_option_a @ P ) )
% 3.05/1.62 = ( collect_option_a
% 3.05/1.62 @ ^ [U: option_a] :
% 3.05/1.62 ( ( U != A )
% 3.05/1.62 => ( P @ U ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_253_singletonD,axiom,
% 3.05/1.62 ! [B: option_a,A: option_a] :
% 3.05/1.62 ( ( member_option_a @ B @ ( insert_option_a @ A @ bot_bot_set_option_a ) )
% 3.05/1.62 => ( B = A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_254_singletonD,axiom,
% 3.05/1.62 ! [B: a,A: a] :
% 3.05/1.62 ( ( member_a @ B @ ( insert_a @ A @ bot_bot_set_a ) )
% 3.05/1.62 => ( B = A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_255_singleton__iff,axiom,
% 3.05/1.62 ! [B: option_a,A: option_a] :
% 3.05/1.62 ( ( member_option_a @ B @ ( insert_option_a @ A @ bot_bot_set_option_a ) )
% 3.05/1.62 = ( B = A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_256_singleton__iff,axiom,
% 3.05/1.62 ! [B: a,A: a] :
% 3.05/1.62 ( ( member_a @ B @ ( insert_a @ A @ bot_bot_set_a ) )
% 3.05/1.62 = ( B = A ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_257_doubleton__eq__iff,axiom,
% 3.05/1.62 ! [A: a,B: a,C: a,D: a] :
% 3.05/1.62 ( ( ( insert_a @ A @ ( insert_a @ B @ bot_bot_set_a ) )
% 3.05/1.62 = ( insert_a @ C @ ( insert_a @ D @ bot_bot_set_a ) ) )
% 3.05/1.62 = ( ( ( A = C )
% 3.05/1.62 & ( B = D ) )
% 3.05/1.62 | ( ( A = D )
% 3.05/1.62 & ( B = C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_258_doubleton__eq__iff,axiom,
% 3.05/1.62 ! [A: option_a,B: option_a,C: option_a,D: option_a] :
% 3.05/1.62 ( ( ( insert_option_a @ A @ ( insert_option_a @ B @ bot_bot_set_option_a ) )
% 3.05/1.62 = ( insert_option_a @ C @ ( insert_option_a @ D @ bot_bot_set_option_a ) ) )
% 3.05/1.62 = ( ( ( A = C )
% 3.05/1.62 & ( B = D ) )
% 3.05/1.62 | ( ( A = D )
% 3.05/1.62 & ( B = C ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_259_insert__not__empty,axiom,
% 3.05/1.62 ! [A: a,A3: set_a] :
% 3.05/1.62 ( ( insert_a @ A @ A3 )
% 3.05/1.62 != bot_bot_set_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_260_insert__not__empty,axiom,
% 3.05/1.62 ! [A: option_a,A3: set_option_a] :
% 3.05/1.62 ( ( insert_option_a @ A @ A3 )
% 3.05/1.62 != bot_bot_set_option_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_261_singleton__inject,axiom,
% 3.05/1.62 ! [A: a,B: a] :
% 3.05/1.62 ( ( ( insert_a @ A @ bot_bot_set_a )
% 3.05/1.62 = ( insert_a @ B @ bot_bot_set_a ) )
% 3.05/1.62 => ( A = B ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_262_singleton__inject,axiom,
% 3.05/1.62 ! [A: option_a,B: option_a] :
% 3.05/1.62 ( ( ( insert_option_a @ A @ bot_bot_set_option_a )
% 3.05/1.62 = ( insert_option_a @ B @ bot_bot_set_option_a ) )
% 3.05/1.62 => ( A = B ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_263_Collect__conv__if,axiom,
% 3.05/1.62 ! [P: a > $o,A: a] :
% 3.05/1.62 ( ( ( P @ A )
% 3.05/1.62 => ( ( collect_a
% 3.05/1.62 @ ^ [X3: a] :
% 3.05/1.62 ( ( X3 = A )
% 3.05/1.62 & ( P @ X3 ) ) )
% 3.05/1.62 = ( insert_a @ A @ bot_bot_set_a ) ) )
% 3.05/1.62 & ( ~ ( P @ A )
% 3.05/1.62 => ( ( collect_a
% 3.05/1.62 @ ^ [X3: a] :
% 3.05/1.62 ( ( X3 = A )
% 3.05/1.62 & ( P @ X3 ) ) )
% 3.05/1.62 = bot_bot_set_a ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_264_Collect__conv__if,axiom,
% 3.05/1.62 ! [P: option_a > $o,A: option_a] :
% 3.05/1.62 ( ( ( P @ A )
% 3.05/1.62 => ( ( collect_option_a
% 3.05/1.62 @ ^ [X3: option_a] :
% 3.05/1.62 ( ( X3 = A )
% 3.05/1.62 & ( P @ X3 ) ) )
% 3.05/1.62 = ( insert_option_a @ A @ bot_bot_set_option_a ) ) )
% 3.05/1.62 & ( ~ ( P @ A )
% 3.05/1.62 => ( ( collect_option_a
% 3.05/1.62 @ ^ [X3: option_a] :
% 3.05/1.62 ( ( X3 = A )
% 3.05/1.62 & ( P @ X3 ) ) )
% 3.05/1.62 = bot_bot_set_option_a ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_265_Collect__conv__if2,axiom,
% 3.05/1.62 ! [P: a > $o,A: a] :
% 3.05/1.62 ( ( ( P @ A )
% 3.05/1.62 => ( ( collect_a
% 3.05/1.62 @ ^ [X3: a] :
% 3.05/1.62 ( ( A = X3 )
% 3.05/1.62 & ( P @ X3 ) ) )
% 3.05/1.62 = ( insert_a @ A @ bot_bot_set_a ) ) )
% 3.05/1.62 & ( ~ ( P @ A )
% 3.05/1.62 => ( ( collect_a
% 3.05/1.62 @ ^ [X3: a] :
% 3.05/1.62 ( ( A = X3 )
% 3.05/1.62 & ( P @ X3 ) ) )
% 3.05/1.62 = bot_bot_set_a ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_266_Collect__conv__if2,axiom,
% 3.05/1.62 ! [P: option_a > $o,A: option_a] :
% 3.05/1.62 ( ( ( P @ A )
% 3.05/1.62 => ( ( collect_option_a
% 3.05/1.62 @ ^ [X3: option_a] :
% 3.05/1.62 ( ( A = X3 )
% 3.05/1.62 & ( P @ X3 ) ) )
% 3.05/1.62 = ( insert_option_a @ A @ bot_bot_set_option_a ) ) )
% 3.05/1.62 & ( ~ ( P @ A )
% 3.05/1.62 => ( ( collect_option_a
% 3.05/1.62 @ ^ [X3: option_a] :
% 3.05/1.62 ( ( A = X3 )
% 3.05/1.62 & ( P @ X3 ) ) )
% 3.05/1.62 = bot_bot_set_option_a ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_267_the__elem__eq,axiom,
% 3.05/1.62 ! [X2: a] :
% 3.05/1.62 ( ( the_elem_a @ ( insert_a @ X2 @ bot_bot_set_a ) )
% 3.05/1.62 = X2 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_268_the__elem__eq,axiom,
% 3.05/1.62 ! [X2: option_a] :
% 3.05/1.62 ( ( the_elem_option_a @ ( insert_option_a @ X2 @ bot_bot_set_option_a ) )
% 3.05/1.62 = X2 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_269_is__singletonI,axiom,
% 3.05/1.62 ! [X2: a] : ( is_singleton_a @ ( insert_a @ X2 @ bot_bot_set_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_270_is__singletonI,axiom,
% 3.05/1.62 ! [X2: option_a] : ( is_sin1624444472tion_a @ ( insert_option_a @ X2 @ bot_bot_set_option_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_271_these__insert__Some,axiom,
% 3.05/1.62 ! [X2: option_a,A3: set_option_option_a] :
% 3.05/1.62 ( ( these_option_a @ ( insert1662731738tion_a @ ( some_option_a @ X2 ) @ A3 ) )
% 3.05/1.62 = ( insert_option_a @ X2 @ ( these_option_a @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_272_these__insert__Some,axiom,
% 3.05/1.62 ! [X2: a,A3: set_option_a] :
% 3.05/1.62 ( ( these_a @ ( insert_option_a @ ( some_a @ X2 ) @ A3 ) )
% 3.05/1.62 = ( insert_a @ X2 @ ( these_a @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_273_is__singletonE,axiom,
% 3.05/1.62 ! [A3: set_a] :
% 3.05/1.62 ( ( is_singleton_a @ A3 )
% 3.05/1.62 => ~ ! [X4: a] :
% 3.05/1.62 ( A3
% 3.05/1.62 != ( insert_a @ X4 @ bot_bot_set_a ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_274_is__singletonE,axiom,
% 3.05/1.62 ! [A3: set_option_a] :
% 3.05/1.62 ( ( is_sin1624444472tion_a @ A3 )
% 3.05/1.62 => ~ ! [X4: option_a] :
% 3.05/1.62 ( A3
% 3.05/1.62 != ( insert_option_a @ X4 @ bot_bot_set_option_a ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_275_these__empty,axiom,
% 3.05/1.62 ( ( these_option_a @ bot_bo1607647958tion_a )
% 3.05/1.62 = bot_bot_set_option_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_276_these__empty,axiom,
% 3.05/1.62 ( ( these_a @ bot_bot_set_option_a )
% 3.05/1.62 = bot_bot_set_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_277_these__insert__None,axiom,
% 3.05/1.62 ! [A3: set_option_a] :
% 3.05/1.62 ( ( these_a @ ( insert_option_a @ none_a @ A3 ) )
% 3.05/1.62 = ( these_a @ A3 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_278_in__these__eq,axiom,
% 3.05/1.62 ! [X2: option_a,A3: set_option_option_a] :
% 3.05/1.62 ( ( member_option_a @ X2 @ ( these_option_a @ A3 ) )
% 3.05/1.62 = ( member553679923tion_a @ ( some_option_a @ X2 ) @ A3 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_279_in__these__eq,axiom,
% 3.05/1.62 ! [X2: a,A3: set_option_a] :
% 3.05/1.62 ( ( member_a @ X2 @ ( these_a @ A3 ) )
% 3.05/1.62 = ( member_option_a @ ( some_a @ X2 ) @ A3 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_280_is__singleton__the__elem,axiom,
% 3.05/1.62 ( is_singleton_a
% 3.05/1.62 = ( ^ [A5: set_a] :
% 3.05/1.62 ( A5
% 3.05/1.62 = ( insert_a @ ( the_elem_a @ A5 ) @ bot_bot_set_a ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_281_is__singleton__the__elem,axiom,
% 3.05/1.62 ( is_sin1624444472tion_a
% 3.05/1.62 = ( ^ [A5: set_option_a] :
% 3.05/1.62 ( A5
% 3.05/1.62 = ( insert_option_a @ ( the_elem_option_a @ A5 ) @ bot_bot_set_option_a ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_282_is__singletonI_H,axiom,
% 3.05/1.62 ! [A3: set_option_a] :
% 3.05/1.62 ( ( A3 != bot_bot_set_option_a )
% 3.05/1.62 => ( ! [X4: option_a,Y4: option_a] :
% 3.05/1.62 ( ( member_option_a @ X4 @ A3 )
% 3.05/1.62 => ( ( member_option_a @ Y4 @ A3 )
% 3.05/1.62 => ( X4 = Y4 ) ) )
% 3.05/1.62 => ( is_sin1624444472tion_a @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_283_is__singletonI_H,axiom,
% 3.05/1.62 ! [A3: set_a] :
% 3.05/1.62 ( ( A3 != bot_bot_set_a )
% 3.05/1.62 => ( ! [X4: a,Y4: a] :
% 3.05/1.62 ( ( member_a @ X4 @ A3 )
% 3.05/1.62 => ( ( member_a @ Y4 @ A3 )
% 3.05/1.62 => ( X4 = Y4 ) ) )
% 3.05/1.62 => ( is_singleton_a @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_284_these__not__empty__eq,axiom,
% 3.05/1.62 ! [B4: set_option_option_a] :
% 3.05/1.62 ( ( ( these_option_a @ B4 )
% 3.05/1.62 != bot_bot_set_option_a )
% 3.05/1.62 = ( ( B4 != bot_bo1607647958tion_a )
% 3.05/1.62 & ( B4
% 3.05/1.62 != ( insert1662731738tion_a @ none_option_a @ bot_bo1607647958tion_a ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_285_these__not__empty__eq,axiom,
% 3.05/1.62 ! [B4: set_option_a] :
% 3.05/1.62 ( ( ( these_a @ B4 )
% 3.05/1.62 != bot_bot_set_a )
% 3.05/1.62 = ( ( B4 != bot_bot_set_option_a )
% 3.05/1.62 & ( B4
% 3.05/1.62 != ( insert_option_a @ none_a @ bot_bot_set_option_a ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_286_these__empty__eq,axiom,
% 3.05/1.62 ! [B4: set_option_option_a] :
% 3.05/1.62 ( ( ( these_option_a @ B4 )
% 3.05/1.62 = bot_bot_set_option_a )
% 3.05/1.62 = ( ( B4 = bot_bo1607647958tion_a )
% 3.05/1.62 | ( B4
% 3.05/1.62 = ( insert1662731738tion_a @ none_option_a @ bot_bo1607647958tion_a ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_287_these__empty__eq,axiom,
% 3.05/1.62 ! [B4: set_option_a] :
% 3.05/1.62 ( ( ( these_a @ B4 )
% 3.05/1.62 = bot_bot_set_a )
% 3.05/1.62 = ( ( B4 = bot_bot_set_option_a )
% 3.05/1.62 | ( B4
% 3.05/1.62 = ( insert_option_a @ none_a @ bot_bot_set_option_a ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_288_is__singleton__def,axiom,
% 3.05/1.62 ( is_singleton_a
% 3.05/1.62 = ( ^ [A5: set_a] :
% 3.05/1.62 ? [X3: a] :
% 3.05/1.62 ( A5
% 3.05/1.62 = ( insert_a @ X3 @ bot_bot_set_a ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_289_is__singleton__def,axiom,
% 3.05/1.62 ( is_sin1624444472tion_a
% 3.05/1.62 = ( ^ [A5: set_option_a] :
% 3.05/1.62 ? [X3: option_a] :
% 3.05/1.62 ( A5
% 3.05/1.62 = ( insert_option_a @ X3 @ bot_bot_set_option_a ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_290_the__elem__def,axiom,
% 3.05/1.62 ( the_elem_a
% 3.05/1.62 = ( ^ [X6: set_a] :
% 3.05/1.62 ( the_a
% 3.05/1.62 @ ^ [X3: a] :
% 3.05/1.62 ( X6
% 3.05/1.62 = ( insert_a @ X3 @ bot_bot_set_a ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_291_the__elem__def,axiom,
% 3.05/1.62 ( the_elem_option_a
% 3.05/1.62 = ( ^ [X6: set_option_a] :
% 3.05/1.62 ( the_option_a
% 3.05/1.62 @ ^ [X3: option_a] :
% 3.05/1.62 ( X6
% 3.05/1.62 = ( insert_option_a @ X3 @ bot_bot_set_option_a ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_292_setOf_Osimps_I2_J,axiom,
% 3.05/1.62 ! [T1: binary1176601351tion_a,X2: option_a,T22: binary1176601351tion_a] :
% 3.05/1.62 ( ( binary1117200954tion_a @ ( binary1007279693tion_a @ T1 @ X2 @ T22 ) )
% 3.05/1.62 = ( sup_sup_set_option_a @ ( sup_sup_set_option_a @ ( binary1117200954tion_a @ T1 ) @ ( binary1117200954tion_a @ T22 ) ) @ ( insert_option_a @ X2 @ bot_bot_set_option_a ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_293_setOf_Osimps_I2_J,axiom,
% 3.05/1.62 ! [T1: binary1439146945Tree_a,X2: a,T22: binary1439146945Tree_a] :
% 3.05/1.62 ( ( binary945792244etOf_a @ ( binary717961607le_T_a @ T1 @ X2 @ T22 ) )
% 3.05/1.62 = ( sup_sup_set_a @ ( sup_sup_set_a @ ( binary945792244etOf_a @ T1 ) @ ( binary945792244etOf_a @ T22 ) ) @ ( insert_a @ X2 @ bot_bot_set_a ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_294_Option_Othese__def,axiom,
% 3.05/1.62 ( these_a
% 3.05/1.62 = ( ^ [A5: set_option_a] :
% 3.05/1.62 ( image_option_a_a @ the_a2
% 3.05/1.62 @ ( collect_option_a
% 3.05/1.62 @ ^ [X3: option_a] :
% 3.05/1.62 ( ( member_option_a @ X3 @ A5 )
% 3.05/1.62 & ( X3 != none_a ) ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_295_image__eqI,axiom,
% 3.05/1.62 ! [B: option_a,F: a > option_a,X2: a,A3: set_a] :
% 3.05/1.62 ( ( B
% 3.05/1.62 = ( F @ X2 ) )
% 3.05/1.62 => ( ( member_a @ X2 @ A3 )
% 3.05/1.62 => ( member_option_a @ B @ ( image_a_option_a @ F @ A3 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_296_image__eqI,axiom,
% 3.05/1.62 ! [B: a,F: option_a > a,X2: option_a,A3: set_option_a] :
% 3.05/1.62 ( ( B
% 3.05/1.62 = ( F @ X2 ) )
% 3.05/1.62 => ( ( member_option_a @ X2 @ A3 )
% 3.05/1.62 => ( member_a @ B @ ( image_option_a_a @ F @ A3 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_297_image__eqI,axiom,
% 3.05/1.62 ! [B: option_a,F: option_a > option_a,X2: option_a,A3: set_option_a] :
% 3.05/1.62 ( ( B
% 3.05/1.62 = ( F @ X2 ) )
% 3.05/1.62 => ( ( member_option_a @ X2 @ A3 )
% 3.05/1.62 => ( member_option_a @ B @ ( image_139503237tion_a @ F @ A3 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_298_image__eqI,axiom,
% 3.05/1.62 ! [B: a,F: a > a,X2: a,A3: set_a] :
% 3.05/1.62 ( ( B
% 3.05/1.62 = ( F @ X2 ) )
% 3.05/1.62 => ( ( member_a @ X2 @ A3 )
% 3.05/1.62 => ( member_a @ B @ ( image_a_a @ F @ A3 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_299_Un__iff,axiom,
% 3.05/1.62 ! [C: option_a,A3: set_option_a,B4: set_option_a] :
% 3.05/1.62 ( ( member_option_a @ C @ ( sup_sup_set_option_a @ A3 @ B4 ) )
% 3.05/1.62 = ( ( member_option_a @ C @ A3 )
% 3.05/1.62 | ( member_option_a @ C @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_300_Un__iff,axiom,
% 3.05/1.62 ! [C: a,A3: set_a,B4: set_a] :
% 3.05/1.62 ( ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) )
% 3.05/1.62 = ( ( member_a @ C @ A3 )
% 3.05/1.62 | ( member_a @ C @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_301_UnCI,axiom,
% 3.05/1.62 ! [C: option_a,B4: set_option_a,A3: set_option_a] :
% 3.05/1.62 ( ( ~ ( member_option_a @ C @ B4 )
% 3.05/1.62 => ( member_option_a @ C @ A3 ) )
% 3.05/1.62 => ( member_option_a @ C @ ( sup_sup_set_option_a @ A3 @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_302_UnCI,axiom,
% 3.05/1.62 ! [C: a,B4: set_a,A3: set_a] :
% 3.05/1.62 ( ( ~ ( member_a @ C @ B4 )
% 3.05/1.62 => ( member_a @ C @ A3 ) )
% 3.05/1.62 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_303_image__ident,axiom,
% 3.05/1.62 ! [Y5: set_a] :
% 3.05/1.62 ( ( image_a_a
% 3.05/1.62 @ ^ [X3: a] : X3
% 3.05/1.62 @ Y5 )
% 3.05/1.62 = Y5 ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_304_image__is__empty,axiom,
% 3.05/1.62 ! [F: a > a,A3: set_a] :
% 3.05/1.62 ( ( ( image_a_a @ F @ A3 )
% 3.05/1.62 = bot_bot_set_a )
% 3.05/1.62 = ( A3 = bot_bot_set_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_305_image__is__empty,axiom,
% 3.05/1.62 ! [F: option_a > a,A3: set_option_a] :
% 3.05/1.62 ( ( ( image_option_a_a @ F @ A3 )
% 3.05/1.62 = bot_bot_set_a )
% 3.05/1.62 = ( A3 = bot_bot_set_option_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_306_image__is__empty,axiom,
% 3.05/1.62 ! [F: a > option_a,A3: set_a] :
% 3.05/1.62 ( ( ( image_a_option_a @ F @ A3 )
% 3.05/1.62 = bot_bot_set_option_a )
% 3.05/1.62 = ( A3 = bot_bot_set_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_307_image__is__empty,axiom,
% 3.05/1.62 ! [F: option_a > option_a,A3: set_option_a] :
% 3.05/1.62 ( ( ( image_139503237tion_a @ F @ A3 )
% 3.05/1.62 = bot_bot_set_option_a )
% 3.05/1.62 = ( A3 = bot_bot_set_option_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_308_empty__is__image,axiom,
% 3.05/1.62 ! [F: a > a,A3: set_a] :
% 3.05/1.62 ( ( bot_bot_set_a
% 3.05/1.62 = ( image_a_a @ F @ A3 ) )
% 3.05/1.62 = ( A3 = bot_bot_set_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_309_empty__is__image,axiom,
% 3.05/1.62 ! [F: option_a > a,A3: set_option_a] :
% 3.05/1.62 ( ( bot_bot_set_a
% 3.05/1.62 = ( image_option_a_a @ F @ A3 ) )
% 3.05/1.62 = ( A3 = bot_bot_set_option_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_310_empty__is__image,axiom,
% 3.05/1.62 ! [F: a > option_a,A3: set_a] :
% 3.05/1.62 ( ( bot_bot_set_option_a
% 3.05/1.62 = ( image_a_option_a @ F @ A3 ) )
% 3.05/1.62 = ( A3 = bot_bot_set_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_311_empty__is__image,axiom,
% 3.05/1.62 ! [F: option_a > option_a,A3: set_option_a] :
% 3.05/1.62 ( ( bot_bot_set_option_a
% 3.05/1.62 = ( image_139503237tion_a @ F @ A3 ) )
% 3.05/1.62 = ( A3 = bot_bot_set_option_a ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_312_image__empty,axiom,
% 3.05/1.62 ! [F: a > a] :
% 3.05/1.62 ( ( image_a_a @ F @ bot_bot_set_a )
% 3.05/1.62 = bot_bot_set_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_313_image__empty,axiom,
% 3.05/1.62 ! [F: a > option_a] :
% 3.05/1.62 ( ( image_a_option_a @ F @ bot_bot_set_a )
% 3.05/1.62 = bot_bot_set_option_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_314_image__empty,axiom,
% 3.05/1.62 ! [F: option_a > a] :
% 3.05/1.62 ( ( image_option_a_a @ F @ bot_bot_set_option_a )
% 3.05/1.62 = bot_bot_set_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_315_image__empty,axiom,
% 3.05/1.62 ! [F: option_a > option_a] :
% 3.05/1.62 ( ( image_139503237tion_a @ F @ bot_bot_set_option_a )
% 3.05/1.62 = bot_bot_set_option_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_316_image__insert,axiom,
% 3.05/1.62 ! [F: a > a,A: a,B4: set_a] :
% 3.05/1.62 ( ( image_a_a @ F @ ( insert_a @ A @ B4 ) )
% 3.05/1.62 = ( insert_a @ ( F @ A ) @ ( image_a_a @ F @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_317_image__insert,axiom,
% 3.05/1.62 ! [F: a > option_a,A: a,B4: set_a] :
% 3.05/1.62 ( ( image_a_option_a @ F @ ( insert_a @ A @ B4 ) )
% 3.05/1.62 = ( insert_option_a @ ( F @ A ) @ ( image_a_option_a @ F @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_318_image__insert,axiom,
% 3.05/1.62 ! [F: option_a > a,A: option_a,B4: set_option_a] :
% 3.05/1.62 ( ( image_option_a_a @ F @ ( insert_option_a @ A @ B4 ) )
% 3.05/1.62 = ( insert_a @ ( F @ A ) @ ( image_option_a_a @ F @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_319_image__insert,axiom,
% 3.05/1.62 ! [F: option_a > option_a,A: option_a,B4: set_option_a] :
% 3.05/1.62 ( ( image_139503237tion_a @ F @ ( insert_option_a @ A @ B4 ) )
% 3.05/1.62 = ( insert_option_a @ ( F @ A ) @ ( image_139503237tion_a @ F @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_320_insert__image,axiom,
% 3.05/1.62 ! [X2: a,A3: set_a,F: a > a] :
% 3.05/1.62 ( ( member_a @ X2 @ A3 )
% 3.05/1.62 => ( ( insert_a @ ( F @ X2 ) @ ( image_a_a @ F @ A3 ) )
% 3.05/1.62 = ( image_a_a @ F @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_321_insert__image,axiom,
% 3.05/1.62 ! [X2: a,A3: set_a,F: a > option_a] :
% 3.05/1.62 ( ( member_a @ X2 @ A3 )
% 3.05/1.62 => ( ( insert_option_a @ ( F @ X2 ) @ ( image_a_option_a @ F @ A3 ) )
% 3.05/1.62 = ( image_a_option_a @ F @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_322_insert__image,axiom,
% 3.05/1.62 ! [X2: option_a,A3: set_option_a,F: option_a > a] :
% 3.05/1.62 ( ( member_option_a @ X2 @ A3 )
% 3.05/1.62 => ( ( insert_a @ ( F @ X2 ) @ ( image_option_a_a @ F @ A3 ) )
% 3.05/1.62 = ( image_option_a_a @ F @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_323_insert__image,axiom,
% 3.05/1.62 ! [X2: option_a,A3: set_option_a,F: option_a > option_a] :
% 3.05/1.62 ( ( member_option_a @ X2 @ A3 )
% 3.05/1.62 => ( ( insert_option_a @ ( F @ X2 ) @ ( image_139503237tion_a @ F @ A3 ) )
% 3.05/1.62 = ( image_139503237tion_a @ F @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_324_Un__empty,axiom,
% 3.05/1.62 ! [A3: set_a,B4: set_a] :
% 3.05/1.62 ( ( ( sup_sup_set_a @ A3 @ B4 )
% 3.05/1.62 = bot_bot_set_a )
% 3.05/1.62 = ( ( A3 = bot_bot_set_a )
% 3.05/1.62 & ( B4 = bot_bot_set_a ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_325_Un__empty,axiom,
% 3.05/1.62 ! [A3: set_option_a,B4: set_option_a] :
% 3.05/1.62 ( ( ( sup_sup_set_option_a @ A3 @ B4 )
% 3.05/1.62 = bot_bot_set_option_a )
% 3.05/1.62 = ( ( A3 = bot_bot_set_option_a )
% 3.05/1.62 & ( B4 = bot_bot_set_option_a ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_326_Un__insert__left,axiom,
% 3.05/1.62 ! [A: option_a,B4: set_option_a,C2: set_option_a] :
% 3.05/1.62 ( ( sup_sup_set_option_a @ ( insert_option_a @ A @ B4 ) @ C2 )
% 3.05/1.62 = ( insert_option_a @ A @ ( sup_sup_set_option_a @ B4 @ C2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_327_Un__insert__left,axiom,
% 3.05/1.62 ! [A: a,B4: set_a,C2: set_a] :
% 3.05/1.62 ( ( sup_sup_set_a @ ( insert_a @ A @ B4 ) @ C2 )
% 3.05/1.62 = ( insert_a @ A @ ( sup_sup_set_a @ B4 @ C2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_328_Un__insert__right,axiom,
% 3.05/1.62 ! [A3: set_option_a,A: option_a,B4: set_option_a] :
% 3.05/1.62 ( ( sup_sup_set_option_a @ A3 @ ( insert_option_a @ A @ B4 ) )
% 3.05/1.62 = ( insert_option_a @ A @ ( sup_sup_set_option_a @ A3 @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_329_Un__insert__right,axiom,
% 3.05/1.62 ! [A3: set_a,A: a,B4: set_a] :
% 3.05/1.62 ( ( sup_sup_set_a @ A3 @ ( insert_a @ A @ B4 ) )
% 3.05/1.62 = ( insert_a @ A @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_330_insert__def,axiom,
% 3.05/1.62 ( insert_option_a
% 3.05/1.62 = ( ^ [A2: option_a] :
% 3.05/1.62 ( sup_sup_set_option_a
% 3.05/1.62 @ ( collect_option_a
% 3.05/1.62 @ ^ [X3: option_a] : ( X3 = A2 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_331_insert__def,axiom,
% 3.05/1.62 ( insert_a
% 3.05/1.62 = ( ^ [A2: a] :
% 3.05/1.62 ( sup_sup_set_a
% 3.05/1.62 @ ( collect_a
% 3.05/1.62 @ ^ [X3: a] : ( X3 = A2 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_332_Un__left__commute,axiom,
% 3.05/1.62 ! [A3: set_a,B4: set_a,C2: set_a] :
% 3.05/1.62 ( ( sup_sup_set_a @ A3 @ ( sup_sup_set_a @ B4 @ C2 ) )
% 3.05/1.62 = ( sup_sup_set_a @ B4 @ ( sup_sup_set_a @ A3 @ C2 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_333_Un__left__absorb,axiom,
% 3.05/1.62 ! [A3: set_a,B4: set_a] :
% 3.05/1.62 ( ( sup_sup_set_a @ A3 @ ( sup_sup_set_a @ A3 @ B4 ) )
% 3.05/1.62 = ( sup_sup_set_a @ A3 @ B4 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_334_rev__image__eqI,axiom,
% 3.05/1.62 ! [X2: option_a,A3: set_option_a,B: option_a,F: option_a > option_a] :
% 3.05/1.62 ( ( member_option_a @ X2 @ A3 )
% 3.05/1.62 => ( ( B
% 3.05/1.62 = ( F @ X2 ) )
% 3.05/1.62 => ( member_option_a @ B @ ( image_139503237tion_a @ F @ A3 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_335_rev__image__eqI,axiom,
% 3.05/1.62 ! [X2: a,A3: set_a,B: a,F: a > a] :
% 3.05/1.62 ( ( member_a @ X2 @ A3 )
% 3.05/1.62 => ( ( B
% 3.05/1.62 = ( F @ X2 ) )
% 3.05/1.62 => ( member_a @ B @ ( image_a_a @ F @ A3 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_336_imageI,axiom,
% 3.05/1.62 ! [X2: a,A3: set_a,F: a > a] :
% 3.05/1.62 ( ( member_a @ X2 @ A3 )
% 3.05/1.62 => ( member_a @ ( F @ X2 ) @ ( image_a_a @ F @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_337_UnI2,axiom,
% 3.05/1.62 ! [C: a,B4: set_a,A3: set_a] :
% 3.05/1.62 ( ( member_a @ C @ B4 )
% 3.05/1.62 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_338_UnI1,axiom,
% 3.05/1.62 ! [C: a,A3: set_a,B4: set_a] :
% 3.05/1.62 ( ( member_a @ C @ A3 )
% 3.05/1.62 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_339_UnE,axiom,
% 3.05/1.62 ! [C: a,A3: set_a,B4: set_a] :
% 3.05/1.62 ( ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) )
% 3.05/1.62 => ( ~ ( member_a @ C @ A3 )
% 3.05/1.62 => ( member_a @ C @ B4 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_340_Un__def,axiom,
% 3.05/1.62 ( sup_sup_set_a
% 3.05/1.62 = ( ^ [A5: set_a,B5: set_a] :
% 3.05/1.62 ( collect_a
% 3.05/1.62 @ ^ [X3: a] :
% 3.05/1.62 ( ( member_a @ X3 @ A5 )
% 3.05/1.62 | ( member_a @ X3 @ B5 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_341_imageE,axiom,
% 3.05/1.62 ! [B: a,F: a > a,A3: set_a] :
% 3.05/1.62 ( ( member_a @ B @ ( image_a_a @ F @ A3 ) )
% 3.05/1.62 => ~ ! [X4: a] :
% 3.05/1.62 ( ( B
% 3.05/1.62 = ( F @ X4 ) )
% 3.05/1.62 => ~ ( member_a @ X4 @ A3 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_342_Compr__image__eq,axiom,
% 3.05/1.62 ! [F: a > a,A3: set_a,P: a > $o] :
% 3.05/1.62 ( ( collect_a
% 3.05/1.62 @ ^ [X3: a] :
% 3.05/1.62 ( ( member_a @ X3 @ ( image_a_a @ F @ A3 ) )
% 3.05/1.62 & ( P @ X3 ) ) )
% 3.05/1.62 = ( image_a_a @ F
% 3.05/1.62 @ ( collect_a
% 3.05/1.62 @ ^ [X3: a] :
% 3.05/1.62 ( ( member_a @ X3 @ A3 )
% 3.05/1.62 & ( P @ ( F @ X3 ) ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_343_sup__set__def,axiom,
% 3.05/1.62 ( sup_sup_set_a
% 3.05/1.62 = ( ^ [A5: set_a,B5: set_a] :
% 3.05/1.62 ( collect_a
% 3.05/1.62 @ ( sup_sup_a_o
% 3.05/1.62 @ ^ [X3: a] : ( member_a @ X3 @ A5 )
% 3.05/1.62 @ ^ [X3: a] : ( member_a @ X3 @ B5 ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_344_sup__Un__eq,axiom,
% 3.05/1.62 ! [R: set_a,S: set_a] :
% 3.05/1.62 ( ( sup_sup_a_o
% 3.05/1.62 @ ^ [X3: a] : ( member_a @ X3 @ R )
% 3.05/1.62 @ ^ [X3: a] : ( member_a @ X3 @ S ) )
% 3.05/1.62 = ( ^ [X3: a] : ( member_a @ X3 @ ( sup_sup_set_a @ R @ S ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_345_None__notin__image__Some,axiom,
% 3.05/1.62 ! [A3: set_a] :
% 3.05/1.62 ~ ( member_option_a @ none_a @ ( image_a_option_a @ some_a @ A3 ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_346_Some__image__these__eq,axiom,
% 3.05/1.62 ! [A3: set_option_a] :
% 3.05/1.62 ( ( image_a_option_a @ some_a @ ( these_a @ A3 ) )
% 3.05/1.62 = ( collect_option_a
% 3.05/1.62 @ ^ [X3: option_a] :
% 3.05/1.62 ( ( member_option_a @ X3 @ A3 )
% 3.05/1.62 & ( X3 != none_a ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_347_Tree_Osimps_I15_J,axiom,
% 3.05/1.62 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 3.05/1.62 ( ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) )
% 3.05/1.62 = ( sup_sup_set_a @ ( sup_sup_set_a @ ( binary256242811Tree_a @ X21 ) @ ( insert_a @ X22 @ bot_bot_set_a ) ) @ ( binary256242811Tree_a @ X23 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_348_Tree_Oset__intros_I3_J,axiom,
% 3.05/1.62 ! [Ya: a,X23: binary1439146945Tree_a,X21: binary1439146945Tree_a,X22: a] :
% 3.05/1.62 ( ( member_a @ Ya @ ( binary256242811Tree_a @ X23 ) )
% 3.05/1.62 => ( member_a @ Ya @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_349_Tree_Oset__intros_I2_J,axiom,
% 3.05/1.62 ! [X22: a,X21: binary1439146945Tree_a,X23: binary1439146945Tree_a] : ( member_a @ X22 @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_350_Tree_Oset__intros_I1_J,axiom,
% 3.05/1.62 ! [Y: a,X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 3.05/1.62 ( ( member_a @ Y @ ( binary256242811Tree_a @ X21 ) )
% 3.05/1.62 => ( member_a @ Y @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_351_Tree_Oset__cases,axiom,
% 3.05/1.62 ! [E: a,A: binary1439146945Tree_a] :
% 3.05/1.62 ( ( member_a @ E @ ( binary256242811Tree_a @ A ) )
% 3.05/1.62 => ( ! [Z1: binary1439146945Tree_a] :
% 3.05/1.62 ( ? [Z22: a,Z3: binary1439146945Tree_a] :
% 3.05/1.62 ( A
% 3.05/1.62 = ( binary717961607le_T_a @ Z1 @ Z22 @ Z3 ) )
% 3.05/1.62 => ~ ( member_a @ E @ ( binary256242811Tree_a @ Z1 ) ) )
% 3.05/1.62 => ( ! [Z1: binary1439146945Tree_a,Z3: binary1439146945Tree_a] :
% 3.05/1.62 ( A
% 3.05/1.62 != ( binary717961607le_T_a @ Z1 @ E @ Z3 ) )
% 3.05/1.62 => ~ ! [Z1: binary1439146945Tree_a,Z22: a,Z3: binary1439146945Tree_a] :
% 3.05/1.62 ( ( A
% 3.05/1.62 = ( binary717961607le_T_a @ Z1 @ Z22 @ Z3 ) )
% 3.05/1.62 => ~ ( member_a @ E @ ( binary256242811Tree_a @ Z3 ) ) ) ) ) ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_352_Tree_Osimps_I14_J,axiom,
% 3.05/1.62 ( ( binary256242811Tree_a @ binary476621312_Tip_a )
% 3.05/1.62 = bot_bot_set_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(fact_353_UNIV__I,axiom,
% 3.05/1.62 ! [X2: a] : ( member_a @ X2 @ top_top_set_a ) ).
% 3.05/1.62
% 3.05/1.62 thf(conj_0,conjecture,
% 3.05/1.62 $false ).
% 3.05/1.62 ------------------------
% 3.05/1.64 % (27454)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/183Mi)
% 3.05/1.65 % (27457)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/2Mi)
% 3.05/1.65 % (27458)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_27294 for (2999ds/2Mi)
% 3.05/1.65 % (27455)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_27294 for (2999ds/4Mi)
% 3.05/1.65 % (27459)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_27294 for (2999ds/275Mi)
% 3.05/1.65 % (27457)Instruction limit reached!
% 3.05/1.65 % (27457)------------------------------
% 3.05/1.65 % (27457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.65 % (27457)Termination reason: Unknown
% 3.05/1.65 % (27457)Termination phase: shuffling
% 3.05/1.65
% 3.05/1.65 % (27458)Instruction limit reached!
% 3.05/1.65 % (27458)------------------------------
% 3.05/1.65 % (27458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.65 % (27458)Termination reason: Unknown
% 3.05/1.65 % (27458)Termination phase: shuffling
% 3.05/1.65
% 3.05/1.65 % (27458)Memory used [KB]: 1407
% 3.05/1.65 % (27458)Time elapsed: 0.003 s
% 3.05/1.65 % (27458)Instructions burned: 3 (million)
% 3.05/1.65 % (27458)------------------------------
% 3.05/1.65 % (27458)------------------------------
% 3.05/1.65 % (27457)Memory used [KB]: 1407
% 3.05/1.65 % (27457)Time elapsed: 0.003 s
% 3.05/1.65 % (27457)Instructions burned: 3 (million)
% 3.05/1.65 % (27457)------------------------------
% 3.05/1.65 % (27457)------------------------------
% 3.05/1.65 % (27456)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_27294 for (2999ds/27Mi)
% 3.05/1.65 % (27460)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/18Mi)
% 3.05/1.65 % (27455)Instruction limit reached!
% 3.05/1.65 % (27455)------------------------------
% 3.05/1.65 % (27455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.65 % (27455)Termination reason: Unknown
% 3.05/1.65 % (27455)Termination phase: shuffling
% 3.05/1.65
% 3.05/1.65 % (27455)Memory used [KB]: 1407
% 3.05/1.65 % (27455)Time elapsed: 0.004 s
% 3.05/1.65 % (27455)Instructions burned: 4 (million)
% 3.05/1.65 % (27455)------------------------------
% 3.05/1.65 % (27455)------------------------------
% 3.05/1.66 % (27460)Instruction limit reached!
% 3.05/1.66 % (27460)------------------------------
% 3.05/1.66 % (27460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.66 % (27460)Termination reason: Unknown
% 3.05/1.66 % (27460)Termination phase: shuffling
% 3.05/1.66
% 3.05/1.66 % (27460)Memory used [KB]: 1663
% 3.05/1.66 % (27460)Time elapsed: 0.011 s
% 3.05/1.66 % (27460)Instructions burned: 18 (million)
% 3.05/1.66 % (27460)------------------------------
% 3.05/1.66 % (27460)------------------------------
% 3.05/1.66 % (27459)Refutation not found, incomplete strategy
% 3.05/1.66 % (27459)------------------------------
% 3.05/1.66 % (27459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.66 % (27459)Termination reason: Refutation not found, incomplete strategy
% 3.05/1.66
% 3.05/1.66
% 3.05/1.66 % (27459)Memory used [KB]: 6396
% 3.05/1.66 % (27459)Time elapsed: 0.016 s
% 3.05/1.66 % (27459)Instructions burned: 41 (million)
% 3.05/1.66 % (27459)------------------------------
% 3.05/1.66 % (27459)------------------------------
% 3.05/1.66 % (27456)Instruction limit reached!
% 3.05/1.66 % (27456)------------------------------
% 3.05/1.66 % (27456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.66 % (27456)Termination reason: Unknown
% 3.05/1.66 % (27456)Termination phase: Property scanning
% 3.05/1.66
% 3.05/1.66 % (27456)Memory used [KB]: 1918
% 3.05/1.66 % (27456)Time elapsed: 0.017 s
% 3.05/1.66 % (27456)Instructions burned: 27 (million)
% 3.05/1.66 % (27456)------------------------------
% 3.05/1.66 % (27456)------------------------------
% 3.05/1.67 % (27464)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_27294 for (2999ds/37Mi)
% 3.05/1.67 % (27463)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/3Mi)
% 3.05/1.67 % (27463)Instruction limit reached!
% 3.05/1.67 % (27463)------------------------------
% 3.05/1.67 % (27463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.67 % (27463)Termination reason: Unknown
% 3.05/1.67 % (27463)Termination phase: shuffling
% 3.05/1.67
% 3.05/1.67 % (27463)Memory used [KB]: 1407
% 3.05/1.67 % (27463)Time elapsed: 0.004 s
% 3.05/1.67 % (27463)Instructions burned: 4 (million)
% 3.05/1.67 % (27463)------------------------------
% 3.05/1.67 % (27463)------------------------------
% 3.05/1.67 % (27465)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_27294 for (2999ds/15Mi)
% 3.05/1.67 % (27469)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_27294 for (2999ds/1041Mi)
% 3.05/1.68 % (27468)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_27294 for (2999ds/3Mi)
% 3.05/1.68 % (27465)Instruction limit reached!
% 3.05/1.68 % (27465)------------------------------
% 3.05/1.68 % (27465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.68 % (27465)Termination reason: Unknown
% 3.05/1.68 % (27465)Termination phase: shuffling
% 3.05/1.68
% 3.05/1.68 % (27465)Memory used [KB]: 1663
% 3.05/1.68 % (27465)Time elapsed: 0.009 s
% 3.05/1.68 % (27465)Instructions burned: 15 (million)
% 3.05/1.68 % (27465)------------------------------
% 3.05/1.68 % (27465)------------------------------
% 3.05/1.68 % (27468)Instruction limit reached!
% 3.05/1.68 % (27468)------------------------------
% 3.05/1.68 % (27468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.68 % (27468)Termination reason: Unknown
% 3.05/1.68 % (27468)Termination phase: shuffling
% 3.05/1.68
% 3.05/1.68 % (27468)Memory used [KB]: 1407
% 3.05/1.68 % (27468)Time elapsed: 0.003 s
% 3.05/1.68 % (27468)Instructions burned: 3 (million)
% 3.05/1.68 % (27468)------------------------------
% 3.05/1.68 % (27468)------------------------------
% 3.05/1.68 % (27464)Instruction limit reached!
% 3.05/1.68 % (27464)------------------------------
% 3.05/1.68 % (27464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.68 % (27464)Termination reason: Unknown
% 3.05/1.68 % (27464)Termination phase: shuffling
% 3.05/1.68
% 3.05/1.68 % (27464)Memory used [KB]: 2174
% 3.05/1.68 % (27464)Time elapsed: 0.019 s
% 3.05/1.68 % (27464)Instructions burned: 38 (million)
% 3.05/1.68 % (27464)------------------------------
% 3.05/1.68 % (27464)------------------------------
% 3.05/1.69 % (27471)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/16Mi)
% 3.05/1.69 % (27470)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/7Mi)
% 3.05/1.69 % (27471)Instruction limit reached!
% 3.05/1.69 % (27471)------------------------------
% 3.05/1.69 % (27471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.05/1.69 % (27471)Termination reason: Unknown
% 3.05/1.69 % (27471)Termination phase: shuffling
% 3.05/1.69
% 3.05/1.69 % (27471)Memory used [KB]: 1791
% 3.05/1.69 % (27471)Time elapsed: 0.010 s
% 3.05/1.69 % (27471)Instructions burned: 17 (million)
% 3.05/1.69 % (27471)------------------------------
% 3.05/1.69 % (27471)------------------------------
% 3.05/1.69 % (27474)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_27294 for (2999ds/3Mi)
% 3.10/1.70 % (27474)Instruction limit reached!
% 3.10/1.70 % (27474)------------------------------
% 3.10/1.70 % (27474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.70 % (27474)Termination reason: Unknown
% 3.10/1.70 % (27474)Termination phase: shuffling
% 3.10/1.70
% 3.10/1.70 % (27474)Memory used [KB]: 1407
% 3.10/1.70 % (27474)Time elapsed: 0.003 s
% 3.10/1.70 % (27474)Instructions burned: 3 (million)
% 3.10/1.70 % (27474)------------------------------
% 3.10/1.70 % (27474)------------------------------
% 3.10/1.70 % (27470)Instruction limit reached!
% 3.10/1.70 % (27470)------------------------------
% 3.10/1.70 % (27470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.70 % (27470)Termination reason: Unknown
% 3.10/1.70 % (27470)Termination phase: shuffling
% 3.10/1.70
% 3.10/1.70 % (27470)Memory used [KB]: 1535
% 3.10/1.70 % (27470)Time elapsed: 0.006 s
% 3.10/1.70 % (27470)Instructions burned: 7 (million)
% 3.10/1.70 % (27470)------------------------------
% 3.10/1.70 % (27470)------------------------------
% 3.10/1.70 % (27475)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27294 for (2999ds/7Mi)
% 3.10/1.70 % (27473)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_27294 for (2999ds/3Mi)
% 3.10/1.70 % (27473)Instruction limit reached!
% 3.10/1.70 % (27473)------------------------------
% 3.10/1.70 % (27473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.70 % (27473)Termination reason: Unknown
% 3.10/1.70 % (27473)Termination phase: shuffling
% 3.10/1.70
% 3.10/1.70 % (27473)Memory used [KB]: 1407
% 3.10/1.70 % (27473)Time elapsed: 0.003 s
% 3.10/1.70 % (27473)Instructions burned: 3 (million)
% 3.10/1.70 % (27473)------------------------------
% 3.10/1.70 % (27473)------------------------------
% 3.10/1.70 % (27475)Instruction limit reached!
% 3.10/1.70 % (27475)------------------------------
% 3.10/1.70 % (27475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.70 % (27475)Termination reason: Unknown
% 3.10/1.70 % (27475)Termination phase: shuffling
% 3.10/1.70
% 3.10/1.70 % (27475)Memory used [KB]: 1535
% 3.10/1.70 % (27475)Time elapsed: 0.005 s
% 3.10/1.70 % (27475)Instructions burned: 7 (million)
% 3.10/1.70 % (27475)------------------------------
% 3.10/1.70 % (27475)------------------------------
% 3.10/1.71 % (27454)First to succeed.
% 3.10/1.71 % (27454)Refutation found. Thanks to Tanya!
% 3.10/1.71 % SZS status ContradictoryAxioms for DTF2THF_27294
% 3.10/1.71 % SZS output start Proof for DTF2THF_27294
% 3.10/1.71 thf(type_def_5, type, binary1176601351tion_a: $tType).
% 3.10/1.71 thf(type_def_6, type, option_a: $tType).
% 3.10/1.71 thf(type_def_8, type, binary1439146945Tree_a: $tType).
% 3.10/1.71 thf(type_def_9, type, a: $tType).
% 3.10/1.71 thf(type_def_10, type, set_a: $tType).
% 3.10/1.71 thf(type_def_11, type, int: $tType).
% 3.10/1.71 thf(type_def_12, type, set_option_a: $tType).
% 3.10/1.71 thf(type_def_13, type, option_option_a: $tType).
% 3.10/1.71 thf(type_def_14, type, set_option_option_a: $tType).
% 3.10/1.71 thf(func_def_0, type, binary1176601351tion_a: $tType).
% 3.10/1.71 thf(func_def_1, type, set_option_option_a: $tType).
% 3.10/1.71 thf(func_def_2, type, binary1439146945Tree_a: $tType).
% 3.10/1.71 thf(func_def_3, type, option_option_a: $tType).
% 3.10/1.71 thf(func_def_4, type, set_option_a: $tType).
% 3.10/1.71 thf(func_def_5, type, option_a: $tType).
% 3.10/1.71 thf(func_def_6, type, set_a: $tType).
% 3.10/1.71 thf(func_def_7, type, int: $tType).
% 3.10/1.71 thf(func_def_8, type, a: $tType).
% 3.10/1.71 thf(func_def_9, type, binary1007279693tion_a: binary1176601351tion_a > option_a > binary1176601351tion_a > binary1176601351tion_a).
% 3.10/1.71 thf(func_def_10, type, binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a).
% 3.10/1.71 thf(func_def_11, type, binary471442758tion_a: binary1176601351tion_a).
% 3.10/1.71 thf(func_def_12, type, binary476621312_Tip_a: binary1439146945Tree_a).
% 3.10/1.71 thf(func_def_13, type, binary256242811Tree_a: binary1439146945Tree_a > set_a).
% 3.10/1.71 thf(func_def_14, type, binary301690796tion_a: (option_a > int) > option_a > set_option_a).
% 3.10/1.71 thf(func_def_15, type, binary504661350_eqs_a: (a > int) > a > set_a).
% 3.10/1.71 thf(func_def_16, type, binary2053421120memb_a: (a > int) > a > binary1439146945Tree_a > $o).
% 3.10/1.71 thf(func_def_17, type, binary1117200954tion_a: binary1176601351tion_a > set_option_a).
% 3.10/1.71 thf(func_def_18, type, binary945792244etOf_a: binary1439146945Tree_a > set_a).
% 3.10/1.71 thf(func_def_19, type, binary995005080tion_a: (option_a > int) > binary1176601351tion_a > $o).
% 3.10/1.71 thf(func_def_20, type, binary1721989714Tree_a: (a > int) > binary1439146945Tree_a > $o).
% 3.10/1.71 thf(func_def_21, type, binary1691793817tion_a: (option_a > int) > option_a > option_a > binary1176601351tion_a > $o).
% 3.10/1.71 thf(func_def_22, type, binary670562003pred_a: (a > int) > a > a > binary1439146945Tree_a > $o).
% 3.10/1.71 thf(func_def_23, type, binary1040190117tion_a: (option_a > int) > int > binary1176601351tion_a > option_option_a).
% 3.10/1.71 thf(func_def_24, type, binary779405791okup_a: (a > int) > int > binary1439146945Tree_a > option_a).
% 3.10/1.71 thf(func_def_25, type, the_option_a: (option_a > $o) > option_a).
% 3.10/1.71 thf(func_def_26, type, the_a: (a > $o) > a).
% 3.10/1.71 thf(func_def_27, type, undefined_a: a).
% 3.10/1.71 thf(func_def_28, type, sup_sup_a_o: (a > $o) > (a > $o) > a > $o).
% 3.10/1.71 thf(func_def_29, type, sup_sup_set_option_a: set_option_a > set_option_a > set_option_a).
% 3.10/1.71 thf(func_def_30, type, sup_sup_set_a: set_a > set_a > set_a).
% 3.10/1.71 thf(func_def_31, type, none_option_a: option_option_a).
% 3.10/1.71 thf(func_def_32, type, none_a: option_a).
% 3.10/1.71 thf(func_def_33, type, some_option_a: option_a > option_option_a).
% 3.10/1.71 thf(func_def_34, type, some_a: a > option_a).
% 3.10/1.71 thf(func_def_35, type, case_option_o_a: $o > (a > $o) > option_a > $o).
% 3.10/1.71 thf(func_def_36, type, case_option_a_a: a > (a > a) > option_a > a).
% 3.10/1.71 thf(func_def_37, type, set_option_option_a2: option_option_a > set_option_a).
% 3.10/1.71 thf(func_def_38, type, set_option_a2: option_a > set_a).
% 3.10/1.71 thf(func_def_39, type, the_option_a2: option_option_a > option_a).
% 3.10/1.71 thf(func_def_40, type, the_a2: option_a > a).
% 3.10/1.71 thf(func_def_41, type, these_option_a: set_option_option_a > set_option_a).
% 3.10/1.71 thf(func_def_42, type, these_a: set_option_a > set_a).
% 3.10/1.71 thf(func_def_43, type, bot_bot_option_a_o: option_a > $o).
% 3.10/1.71 thf(func_def_44, type, bot_bot_a_o: a > $o).
% 3.10/1.71 thf(func_def_46, type, bot_bo1607647958tion_a: set_option_option_a).
% 3.10/1.71 thf(func_def_47, type, bot_bot_set_option_a: set_option_a).
% 3.10/1.71 thf(func_def_48, type, bot_bot_set_a: set_a).
% 3.10/1.71 thf(func_def_49, type, ord_less_option_a_o: (option_a > $o) > (option_a > $o) > $o).
% 3.10/1.71 thf(func_def_50, type, ord_less_a_o: (a > $o) > (a > $o) > $o).
% 3.10/1.71 thf(func_def_51, type, ord_less_int: int > int > $o).
% 3.10/1.71 thf(func_def_52, type, ord_le1280890064tion_a: set_option_a > set_option_a > $o).
% 3.10/1.71 thf(func_def_53, type, ord_less_set_a: set_a > set_a > $o).
% 3.10/1.71 thf(func_def_54, type, top_top_set_a: set_a).
% 3.10/1.71 thf(func_def_55, type, collect_option_a: (option_a > $o) > set_option_a).
% 3.10/1.71 thf(func_def_56, type, collect_a: (a > $o) > set_a).
% 3.10/1.71 thf(func_def_57, type, image_139503237tion_a: (option_a > option_a) > set_option_a > set_option_a).
% 3.10/1.71 thf(func_def_58, type, image_option_a_a: (option_a > a) > set_option_a > set_a).
% 3.10/1.71 thf(func_def_59, type, image_a_option_a: (a > option_a) > set_a > set_option_a).
% 3.10/1.71 thf(func_def_60, type, image_a_a: (a > a) > set_a > set_a).
% 3.10/1.71 thf(func_def_61, type, insert1662731738tion_a: option_option_a > set_option_option_a > set_option_option_a).
% 3.10/1.71 thf(func_def_62, type, insert_option_a: option_a > set_option_a > set_option_a).
% 3.10/1.71 thf(func_def_63, type, insert_a: a > set_a > set_a).
% 3.10/1.71 thf(func_def_64, type, is_empty_option_a: set_option_a > $o).
% 3.10/1.71 thf(func_def_65, type, is_empty_a: set_a > $o).
% 3.10/1.71 thf(func_def_66, type, is_sin1624444472tion_a: set_option_a > $o).
% 3.10/1.71 thf(func_def_67, type, is_singleton_a: set_a > $o).
% 3.10/1.71 thf(func_def_68, type, the_elem_option_a: set_option_a > option_a).
% 3.10/1.71 thf(func_def_69, type, the_elem_a: set_a > a).
% 3.10/1.71 thf(func_def_70, type, member553679923tion_a: option_option_a > set_option_option_a > $o).
% 3.10/1.71 thf(func_def_71, type, member_option_a: option_a > set_option_a > $o).
% 3.10/1.71 thf(func_def_72, type, member_a: a > set_a > $o).
% 3.10/1.71 thf(func_def_73, type, h: a > int).
% 3.10/1.71 thf(func_def_74, type, t: binary1439146945Tree_a).
% 3.10/1.71 thf(func_def_75, type, x: a).
% 3.10/1.71 thf(func_def_91, type, sP0: (option_a > option_a > $o) > option_a > option_a > $o).
% 3.10/1.71 thf(func_def_92, type, sK1: ((a > $o) > int) > a > $o).
% 3.10/1.71 thf(func_def_93, type, sK2: ((a > $o) > int) > a > $o).
% 3.10/1.71 thf(func_def_94, type, sK3: (set_a > set_a) > set_a).
% 3.10/1.71 thf(func_def_95, type, sK4: (set_a > set_a) > set_a).
% 3.10/1.71 thf(func_def_96, type, sK5: (set_a > int) > set_a).
% 3.10/1.71 thf(func_def_97, type, sK6: (set_a > int) > set_a).
% 3.10/1.71 thf(func_def_98, type, sK7: ((a > $o) > set_a) > a > $o).
% 3.10/1.71 thf(func_def_99, type, sK8: ((a > $o) > set_a) > a > $o).
% 3.10/1.71 thf(func_def_100, type, sK9: (option_a > $o) > (option_a > $o) > option_a).
% 3.10/1.71 thf(func_def_101, type, sK10: int > int).
% 3.10/1.71 thf(func_def_102, type, sK11: (set_a > int) > set_a).
% 3.10/1.71 thf(func_def_103, type, sK12: (set_a > int) > set_a).
% 3.10/1.71 thf(func_def_104, type, sK13: option_a > (a > $o) > a).
% 3.10/1.71 thf(func_def_105, type, sK14: set_a > (a > a) > a > a).
% 3.10/1.71 thf(func_def_106, type, sK15: (set_a > int) > set_a).
% 3.10/1.71 thf(func_def_107, type, sK16: (set_a > int) > set_a).
% 3.10/1.71 thf(func_def_108, type, sK17: ((a > $o) > int) > a > $o).
% 3.10/1.71 thf(func_def_109, type, sK18: ((a > $o) > int) > a > $o).
% 3.10/1.71 thf(func_def_110, type, sK19: (set_a > set_a) > set_a).
% 3.10/1.71 thf(func_def_111, type, sK20: (set_a > set_a) > set_a).
% 3.10/1.71 thf(func_def_112, type, sK21: (set_a > int) > set_a).
% 3.10/1.71 thf(func_def_113, type, sK22: (set_a > int) > set_a).
% 3.10/1.71 thf(func_def_114, type, sK23: set_option_a > option_a).
% 3.10/1.71 thf(func_def_115, type, sK24: set_option_a > option_a).
% 3.10/1.71 thf(func_def_116, type, sK25: (int > set_a) > int).
% 3.10/1.71 thf(func_def_117, type, sK26: (int > set_a) > int).
% 3.10/1.71 thf(func_def_118, type, sK27: option_a > (a > $o) > a).
% 3.10/1.71 thf(func_def_119, type, sK28: ((a > $o) > int) > a > $o).
% 3.10/1.71 thf(func_def_120, type, sK29: ((a > $o) > int) > a > $o).
% 3.10/1.71 thf(func_def_121, type, sK30: a > set_a > set_a).
% 3.10/1.71 thf(func_def_122, type, sK31: (int > int) > int).
% 3.10/1.71 thf(func_def_123, type, sK32: (int > int) > int).
% 3.10/1.71 thf(func_def_124, type, sK33: (int > set_a) > int).
% 3.10/1.71 thf(func_def_125, type, sK34: (int > set_a) > int).
% 3.10/1.71 thf(func_def_126, type, sK35: (int > int) > int).
% 3.10/1.71 thf(func_def_127, type, sK36: (int > int) > int).
% 3.10/1.71 thf(func_def_128, type, sK37: (int > a > $o) > int).
% 3.10/1.71 thf(func_def_129, type, sK38: (int > a > $o) > int).
% 3.10/1.71 thf(func_def_130, type, sK39: (int > set_a) > int).
% 3.10/1.71 thf(func_def_131, type, sK40: (int > set_a) > int).
% 3.10/1.71 thf(func_def_132, type, sK41: ((a > $o) > a > $o) > a > $o).
% 3.10/1.71 thf(func_def_133, type, sK42: ((a > $o) > a > $o) > a > $o).
% 3.10/1.71 thf(func_def_134, type, sK43: (int > int) > int).
% 3.10/1.71 thf(func_def_135, type, sK44: (int > int) > int).
% 3.10/1.71 thf(func_def_136, type, sK45: set_a > a).
% 3.10/1.71 thf(func_def_137, type, sK46: a > set_a > set_a).
% 3.10/1.71 thf(func_def_138, type, sK47: (binary1439146945Tree_a > $o) > binary1439146945Tree_a).
% 3.10/1.71 thf(func_def_139, type, sK48: (binary1439146945Tree_a > $o) > binary1439146945Tree_a).
% 3.10/1.71 thf(func_def_140, type, sK49: (binary1439146945Tree_a > $o) > a).
% 3.10/1.71 thf(func_def_141, type, sK50: (int > int) > int).
% 3.10/1.71 thf(func_def_142, type, sK51: (int > int) > int).
% 3.10/1.71 thf(func_def_143, type, sK52: ((a > $o) > a > $o) > a > $o).
% 3.10/1.71 thf(func_def_144, type, sK53: ((a > $o) > a > $o) > a > $o).
% 3.10/1.71 thf(func_def_145, type, sK54: (option_a > $o) > a).
% 3.10/1.71 thf(func_def_146, type, sK55: (set_a > a > $o) > set_a).
% 3.10/1.71 thf(func_def_147, type, sK56: (set_a > a > $o) > set_a).
% 3.10/1.71 thf(func_def_148, type, sK57: (set_a > set_a) > set_a).
% 3.10/1.71 thf(func_def_149, type, sK58: (set_a > set_a) > set_a).
% 3.10/1.71 thf(func_def_150, type, sK59: ((a > $o) > a > $o) > a > $o).
% 3.10/1.71 thf(func_def_151, type, sK60: ((a > $o) > a > $o) > a > $o).
% 3.10/1.71 thf(func_def_152, type, sK61: (option_a > option_a > $o) > option_a > option_a > a).
% 3.10/1.71 thf(func_def_153, type, sK62: (option_a > option_a > $o) > option_a > option_a > a).
% 3.10/1.71 thf(func_def_154, type, sK63: (int > a > $o) > int).
% 3.10/1.71 thf(func_def_155, type, sK64: (int > a > $o) > int).
% 3.10/1.71 thf(func_def_156, type, sK65: option_a > a).
% 3.10/1.71 thf(func_def_157, type, sK66: (int > set_a) > int).
% 3.10/1.71 thf(func_def_158, type, sK67: (int > set_a) > int).
% 3.10/1.71 thf(func_def_159, type, sK68: ((a > $o) > set_a) > a > $o).
% 3.10/1.71 thf(func_def_160, type, sK69: ((a > $o) > set_a) > a > $o).
% 3.10/1.71 thf(func_def_161, type, sK70: (set_a > set_a) > set_a).
% 3.10/1.71 thf(func_def_162, type, sK71: (set_a > set_a) > set_a).
% 3.10/1.71 thf(func_def_163, type, sK72: option_a > set_option_a > set_option_a).
% 3.10/1.71 thf(func_def_164, type, sK73: binary1439146945Tree_a > a).
% 3.10/1.71 thf(func_def_165, type, sK74: binary1439146945Tree_a > binary1439146945Tree_a).
% 3.10/1.71 thf(func_def_166, type, sK75: binary1439146945Tree_a > binary1439146945Tree_a).
% 3.10/1.71 thf(func_def_167, type, sK76: (set_a > a > $o) > set_a).
% 3.10/1.71 thf(func_def_168, type, sK77: (set_a > a > $o) > set_a).
% 3.10/1.71 thf(func_def_169, type, sK78: (set_a > a > $o) > set_a).
% 3.10/1.71 thf(func_def_170, type, sK79: (set_a > a > $o) > set_a).
% 3.10/1.71 thf(func_def_171, type, sK80: ((a > $o) > a > $o) > a > $o).
% 3.10/1.71 thf(func_def_172, type, sK81: ((a > $o) > a > $o) > a > $o).
% 3.10/1.71 thf(func_def_173, type, sK82: (a > $o) > (a > $o) > a).
% 3.10/1.71 thf(func_def_174, type, sK83: ((a > $o) > int) > a > $o).
% 3.10/1.71 thf(func_def_175, type, sK84: ((a > $o) > int) > a > $o).
% 3.10/1.71 thf(func_def_176, type, sK85: set_a > a).
% 3.10/1.71 thf(func_def_177, type, sK86: set_a > a).
% 3.10/1.71 thf(func_def_178, type, sK87: (int > a > $o) > int).
% 3.10/1.71 thf(func_def_179, type, sK88: (int > a > $o) > int).
% 3.10/1.71 thf(func_def_180, type, sK89: ((a > $o) > set_a) > a > $o).
% 3.10/1.71 thf(func_def_181, type, sK90: ((a > $o) > set_a) > a > $o).
% 3.10/1.71 thf(func_def_182, type, sK91: (int > a > $o) > int).
% 3.10/1.71 thf(func_def_183, type, sK92: (int > a > $o) > int).
% 3.10/1.71 thf(func_def_184, type, sK93: a > binary1439146945Tree_a > binary1439146945Tree_a).
% 3.10/1.71 thf(func_def_185, type, sK94: a > binary1439146945Tree_a > binary1439146945Tree_a).
% 3.10/1.71 thf(func_def_186, type, sK95: a > binary1439146945Tree_a > binary1439146945Tree_a).
% 3.10/1.71 thf(func_def_187, type, sK96: a > binary1439146945Tree_a > binary1439146945Tree_a).
% 3.10/1.71 thf(func_def_188, type, sK97: a > binary1439146945Tree_a > a).
% 3.10/1.71 thf(func_def_189, type, sK98: a > binary1439146945Tree_a > binary1439146945Tree_a).
% 3.10/1.71 thf(func_def_190, type, sK99: a > binary1439146945Tree_a > a).
% 3.10/1.71 thf(func_def_191, type, sK100: a > binary1439146945Tree_a > binary1439146945Tree_a).
% 3.10/1.71 thf(func_def_192, type, sK101: int > int).
% 3.10/1.71 thf(func_def_193, type, sK102: set_option_a > option_a).
% 3.10/1.71 thf(func_def_194, type, sK103: set_a > a).
% 3.10/1.71 thf(func_def_195, type, sK104: ((a > $o) > set_a) > a > $o).
% 3.10/1.71 thf(func_def_196, type, sK105: ((a > $o) > set_a) > a > $o).
% 3.10/1.71 thf(func_def_197, type, sK106: (set_a > a > $o) > set_a).
% 3.10/1.71 thf(func_def_198, type, sK107: (set_a > a > $o) > set_a).
% 3.10/1.71 thf(func_def_199, type, sK108: ($o > $o) > (a > $o) > (a > $o) > a).
% 3.10/1.71 thf(func_def_200, type, sK109: (int > int > $o) > int).
% 3.10/1.71 thf(func_def_201, type, sK110: (int > int > $o) > int).
% 3.10/1.71 thf(func_def_202, type, sK111: (int > int > $o) > int).
% 3.10/1.71 thf(func_def_203, type, sK112: (int > int > $o) > int).
% 3.10/1.71 thf(func_def_204, type, sK113: (int > int > $o) > int).
% 3.10/1.71 thf(func_def_205, type, sK114: option_a > set_option_a > set_option_a).
% 3.10/1.71 thf(func_def_206, type, sK115: set_option_a > option_a).
% 3.10/1.71 thf(func_def_208, type, sK117: set_a > a).
% 3.10/1.71 thf(func_def_209, type, sK118: set_a > set_a > a > a > set_a).
% 3.10/1.71 thf(func_def_210, type, sK119: option_a > a).
% 3.10/1.71 thf(func_def_211, type, sK120: set_a > a).
% 3.10/1.71 thf(func_def_212, type, sK121: option_a > a).
% 3.10/1.71 thf(func_def_213, type, sK122: (a > $o) > a).
% 3.10/1.71 thf(func_def_214, type, sK123: (option_a > $o) > option_a).
% 3.10/1.71 thf(func_def_215, type, sK124: set_a > a).
% 3.10/1.71 thf(func_def_216, type, sK125: (a > $o) > a).
% 3.10/1.71 thf(func_def_217, type, sK126: a > a).
% 3.10/1.71 thf(func_def_218, type, sK127: option_a > option_a).
% 3.10/1.71 thf(f2701,plain,(
% 3.10/1.71 $false),
% 3.10/1.71 inference(trivial_inequality_removal,[status(thm)],[f1486])).
% 3.10/1.71 thf(f1486,plain,(
% 3.10/1.71 ((h @ x) != (h @ x))),
% 3.10/1.71 inference(cnf_transformation,[status(thm)],[f5])).
% 3.10/1.71 thf(f5,axiom,(
% 3.10/1.71 ((h @ x) != (h @ x))),
% 3.10/1.71 file('/export/starexec/sandbox2/tmp/tmp.A9HM2VC1Um/DTF2THF_27294.p',fact_4__092_060open_062h_Ax_A_092_060noteq_062_Ah_Ax_092_060close_062)).
% 3.10/1.71 % SZS output end Proof for DTF2THF_27294
% 3.10/1.71 % (27454)------------------------------
% 3.10/1.71 % (27454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.10/1.71 % (27454)Termination reason: Refutation
% 3.10/1.71
% 3.10/1.71 % (27454)Memory used [KB]: 7164
% 3.10/1.71 % (27454)Time elapsed: 0.067 s
% 3.10/1.71 % (27454)Instructions burned: 153 (million)
% 3.10/1.71 % (27454)------------------------------
% 3.10/1.71 % (27454)------------------------------
% 3.10/1.71 % (27449)Success in time 0.081 s
%------------------------------------------------------------------------------