%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP032^1 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:00 AM UTC 2026
% Result : Theorem 20.73s 4.42s
% Output : Refutation 20.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 362 ( 128 equ; 0 cnn)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 644 ( 65 ~; 41 |; 48 &; 480 @)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 188 ( 185 usr; 9 con; 0-4 aty)
% Number of variables : 99 ( 16 ^; 75 !; 8 ?; 99 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
binary1439146945Tree_a: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_8,type,
set_a: $tType ).
thf(type_def_9,type,
int: $tType ).
thf(func_def_0,type,
binary1439146945Tree_a: $tType ).
thf(func_def_1,type,
set_a: $tType ).
thf(func_def_2,type,
int: $tType ).
thf(func_def_3,type,
a: $tType ).
thf(func_def_4,type,
binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_5,type,
binary476621312_Tip_a: binary1439146945Tree_a ).
thf(func_def_6,type,
binary1452917696Tree_a: ( a > $o ) > binary1439146945Tree_a > $o ).
thf(func_def_7,type,
binary256242811Tree_a: binary1439146945Tree_a > set_a ).
thf(func_def_8,type,
binary1226383794sert_a: ( a > int ) > a > binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_9,type,
binary504661350_eqs_a: ( a > int ) > a > set_a ).
thf(func_def_10,type,
binary2053421120memb_a: ( a > int ) > a > binary1439146945Tree_a > $o ).
thf(func_def_11,type,
binary945792244etOf_a: binary1439146945Tree_a > set_a ).
thf(func_def_12,type,
binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
thf(func_def_13,type,
binary670562003pred_a: ( a > int ) > a > a > binary1439146945Tree_a > $o ).
thf(func_def_14,type,
minus_minus_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
thf(func_def_15,type,
minus_minus_o: $o > $o > $o ).
thf(func_def_16,type,
minus_minus_int: int > int > int ).
thf(func_def_17,type,
minus_minus_set_a: set_a > set_a > set_a ).
thf(func_def_18,type,
the_a: ( a > $o ) > a ).
thf(func_def_19,type,
sup_sup_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
thf(func_def_20,type,
sup_sup_o: $o > $o > $o ).
thf(func_def_21,type,
sup_sup_int: int > int > int ).
thf(func_def_22,type,
sup_sup_set_a: set_a > set_a > set_a ).
thf(func_def_23,type,
bot_bot_a_o: a > $o ).
thf(func_def_25,type,
bot_bot_set_a: set_a ).
thf(func_def_26,type,
ord_less_a_o: ( a > $o ) > ( a > $o ) > $o ).
thf(func_def_27,type,
ord_less_int: int > int > $o ).
thf(func_def_28,type,
ord_less_set_a: set_a > set_a > $o ).
thf(func_def_29,type,
ord_less_eq_set_a: set_a > set_a > $o ).
thf(func_def_30,type,
collect_a: ( a > $o ) > set_a ).
thf(func_def_31,type,
insert_a: a > set_a > set_a ).
thf(func_def_32,type,
is_empty_a: set_a > $o ).
thf(func_def_33,type,
is_singleton_a: set_a > $o ).
thf(func_def_34,type,
remove_a: a > set_a > set_a ).
thf(func_def_35,type,
the_elem_a: set_a > a ).
thf(func_def_36,type,
member_a: a > set_a > $o ).
thf(func_def_37,type,
e: a ).
thf(func_def_38,type,
h: a > int ).
thf(func_def_39,type,
t1: binary1439146945Tree_a ).
thf(func_def_40,type,
t2: binary1439146945Tree_a ).
thf(func_def_41,type,
w: a ).
thf(func_def_42,type,
x: a ).
thf(func_def_57,type,
diff:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > ( X0 > X1 ) > X0 ) ).
thf(func_def_58,type,
sP0: set_a > a > set_a > $o ).
thf(func_def_59,type,
sP1: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > $o ).
thf(func_def_60,type,
sP2: a > a > set_a > set_a > $o ).
thf(func_def_61,type,
sP3: a > a > set_a > set_a > $o ).
thf(func_def_62,type,
sP4: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > $o ).
thf(func_def_63,type,
sP5: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > $o ).
thf(func_def_64,type,
sP6: set_a > a > set_a > $o ).
thf(func_def_65,type,
sP7: set_a > a > set_a > $o ).
thf(func_def_66,type,
sP8: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > $o ).
thf(func_def_67,type,
sK9: int > int ).
thf(func_def_68,type,
sK10: ( int > set_a ) > int ).
thf(func_def_69,type,
sK11: ( int > set_a ) > int ).
thf(func_def_70,type,
sK12: ( a > $o ) > binary1439146945Tree_a > ( a > $o ) > a ).
thf(func_def_71,type,
sK13: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_72,type,
sK14: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_73,type,
sK15: set_a > a ).
thf(func_def_74,type,
sK16: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_75,type,
sK17: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_76,type,
sK18: ( ( a > $o ) > set_a ) > a > $o ).
thf(func_def_77,type,
sK19: ( ( a > $o ) > set_a ) > a > $o ).
thf(func_def_78,type,
sK20: ( int > int ) > int ).
thf(func_def_79,type,
sK21: ( int > int ) > int ).
thf(func_def_80,type,
sK22: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_81,type,
sK23: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_82,type,
sK24: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_83,type,
sK25: int > int ).
thf(func_def_84,type,
sK26: ( int > int > $o ) > int ).
thf(func_def_85,type,
sK27: ( int > int > $o ) > int ).
thf(func_def_86,type,
sK28: ( int > int > $o ) > int ).
thf(func_def_87,type,
sK29: ( int > int > $o ) > int ).
thf(func_def_88,type,
sK30: ( int > int > $o ) > int ).
thf(func_def_89,type,
sK31: ( int > a > $o ) > int ).
thf(func_def_90,type,
sK32: ( int > a > $o ) > int ).
thf(func_def_91,type,
sK33: int > int ).
thf(func_def_92,type,
sK34: ( a > $o ) > ( a > $o ) > binary1439146945Tree_a > a ).
thf(func_def_93,type,
sK35: a > a > set_a > set_a > set_a ).
thf(func_def_94,type,
sK36: ( binary1439146945Tree_a > $o ) > binary1439146945Tree_a ).
thf(func_def_95,type,
sK37: ( binary1439146945Tree_a > $o ) > a ).
thf(func_def_96,type,
sK38: ( binary1439146945Tree_a > $o ) > binary1439146945Tree_a ).
thf(func_def_97,type,
sK39: set_a > a ).
thf(func_def_98,type,
sK40: int > int ).
thf(func_def_99,type,
sK41: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_100,type,
sK42: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_101,type,
sK43: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_102,type,
sK44: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_103,type,
sK45: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_104,type,
sK46: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_105,type,
sK47: int > int ).
thf(func_def_106,type,
sK48: ( set_a > a > $o ) > set_a ).
thf(func_def_107,type,
sK49: ( set_a > a > $o ) > set_a ).
thf(func_def_108,type,
sK50: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_109,type,
sK51: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_110,type,
sK52: ( int > set_a ) > int ).
thf(func_def_111,type,
sK53: ( int > set_a ) > int ).
thf(func_def_112,type,
sK54: set_a > a ).
thf(func_def_113,type,
sK55: ( set_a > int ) > set_a ).
thf(func_def_114,type,
sK56: ( set_a > int ) > set_a ).
thf(func_def_115,type,
sK57: ( set_a > int ) > set_a ).
thf(func_def_116,type,
sK58: ( set_a > int ) > set_a ).
thf(func_def_117,type,
sK59: ( set_a > a > $o ) > set_a ).
thf(func_def_118,type,
sK60: ( set_a > a > $o ) > set_a ).
thf(func_def_119,type,
sK61: ( int > int ) > int ).
thf(func_def_120,type,
sK62: ( int > int ) > int ).
thf(func_def_121,type,
sK63: ( int > a > $o ) > int ).
thf(func_def_122,type,
sK64: ( int > a > $o ) > int ).
thf(func_def_123,type,
sK65: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_124,type,
sK66: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_125,type,
sK67: int > int ).
thf(func_def_126,type,
sK68: set_a > ( a > $o ) > set_a > a ).
thf(func_def_127,type,
sK69: ( a > $o ) > set_a > a ).
thf(func_def_128,type,
sK70: set_a > ( a > $o ) > a ).
thf(func_def_129,type,
sK71: a > set_a > set_a ).
thf(func_def_130,type,
sK72: ( set_a > set_a ) > set_a ).
thf(func_def_131,type,
sK73: ( set_a > set_a ) > set_a ).
thf(func_def_132,type,
sK74: ( ( a > $o ) > set_a ) > a > $o ).
thf(func_def_133,type,
sK75: ( ( a > $o ) > set_a ) > a > $o ).
thf(func_def_134,type,
sK76: set_a > set_a > a ).
thf(func_def_135,type,
sK77: ( set_a > set_a ) > set_a ).
thf(func_def_136,type,
sK78: ( set_a > set_a ) > set_a ).
thf(func_def_137,type,
sK79: ( set_a > a > $o ) > set_a ).
thf(func_def_138,type,
sK80: ( set_a > a > $o ) > set_a ).
thf(func_def_139,type,
sK81: ( int > set_a ) > int ).
thf(func_def_140,type,
sK82: ( int > set_a ) > int ).
thf(func_def_141,type,
sK83: set_a > a > set_a ).
thf(func_def_142,type,
sK84: binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_143,type,
sK85: binary1439146945Tree_a > binary1439146945Tree_a ).
thf(func_def_144,type,
sK86: binary1439146945Tree_a > a ).
thf(func_def_145,type,
sK87: ( int > int ) > int ).
thf(func_def_146,type,
sK88: ( int > int ) > int ).
thf(func_def_147,type,
sK89: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_148,type,
sK90: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_149,type,
sK91: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_150,type,
sK92: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_151,type,
sK93: ( a > $o ) > ( a > $o ) > a ).
thf(func_def_152,type,
sK94: set_a > a ).
thf(func_def_153,type,
sK95: ( int > a > $o ) > int ).
thf(func_def_154,type,
sK96: ( int > a > $o ) > int ).
thf(func_def_155,type,
sK97: ( a > $o ) > a ).
thf(func_def_156,type,
sK98: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_157,type,
sK99: ( ( a > $o ) > a > $o ) > a > $o ).
thf(func_def_158,type,
sK100: ( ( a > $o ) > set_a ) > a > $o ).
thf(func_def_159,type,
sK101: ( ( a > $o ) > set_a ) > a > $o ).
thf(func_def_160,type,
sK102: ( a > $o ) > a ).
thf(func_def_161,type,
sK103: int > int ).
thf(func_def_162,type,
sK104: binary1439146945Tree_a > a > a ).
thf(func_def_163,type,
sK105: binary1439146945Tree_a > a > binary1439146945Tree_a ).
thf(func_def_164,type,
sK106: binary1439146945Tree_a > a > binary1439146945Tree_a ).
thf(func_def_165,type,
sK107: binary1439146945Tree_a > a > binary1439146945Tree_a ).
thf(func_def_166,type,
sK108: binary1439146945Tree_a > a > binary1439146945Tree_a ).
thf(func_def_167,type,
sK109: binary1439146945Tree_a > a > binary1439146945Tree_a ).
thf(func_def_168,type,
sK110: binary1439146945Tree_a > a > a ).
thf(func_def_169,type,
sK111: binary1439146945Tree_a > a > binary1439146945Tree_a ).
thf(func_def_170,type,
sK112: ( int > set_a ) > int ).
thf(func_def_171,type,
sK113: ( int > set_a ) > int ).
thf(func_def_172,type,
sK114: ( int > a > $o ) > int ).
thf(func_def_173,type,
sK115: ( int > a > $o ) > int ).
thf(func_def_174,type,
sK116: ( set_a > a > $o ) > set_a ).
thf(func_def_175,type,
sK117: ( set_a > a > $o ) > set_a ).
thf(func_def_176,type,
sK118: ( ( a > $o ) > set_a ) > a > $o ).
thf(func_def_177,type,
sK119: ( ( a > $o ) > set_a ) > a > $o ).
thf(func_def_178,type,
sK120: ( set_a > int ) > set_a ).
thf(func_def_179,type,
sK121: ( set_a > int ) > set_a ).
thf(func_def_180,type,
sK122: a > ( a > int ) > binary1439146945Tree_a > a ).
thf(func_def_181,type,
sK123: a > ( a > int ) > binary1439146945Tree_a > a ).
thf(func_def_182,type,
sK124: int > int ).
thf(func_def_183,type,
sK125: ( set_a > int ) > set_a ).
thf(func_def_184,type,
sK126: ( set_a > int ) > set_a ).
thf(func_def_185,type,
sK127: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_186,type,
sK128: ( ( a > $o ) > int ) > a > $o ).
thf(func_def_187,type,
sK129: set_a > a ).
thf(func_def_188,type,
sK130: set_a > a ).
thf(func_def_189,type,
sK131: ( int > int ) > int ).
thf(func_def_190,type,
sK132: ( int > int ) > int ).
thf(func_def_191,type,
sK133: set_a > ( a > $o ) > set_a > a ).
thf(func_def_192,type,
sK134: set_a > ( a > $o ) > a ).
thf(func_def_193,type,
sK135: ( a > $o ) > set_a > a ).
thf(func_def_194,type,
sK136: int > int ).
thf(func_def_195,type,
sK137: int > int ).
thf(func_def_196,type,
sK138: ( int > $o ) > ( int > $o ) > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_197,type,
sK139: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_198,type,
sK140: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_199,type,
sK141: ( set_a > set_a ) > set_a ).
thf(func_def_200,type,
sK142: ( set_a > set_a ) > set_a ).
thf(func_def_201,type,
sK143: ( set_a > set_a ) > set_a ).
thf(func_def_202,type,
sK144: ( set_a > set_a ) > set_a ).
thf(func_def_204,type,
ph146:
!>[X0: $tType] : X0 ).
thf(f3340,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f3326,f2027]) ).
thf(f2027,plain,
( ( member_a @ w @ ( binary945792244etOf_a @ t1 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f533]) ).
thf(f533,plain,
( ( member_a @ w @ ( binary945792244etOf_a @ t1 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f532]) ).
thf(f532,plain,
member_a @ w @ ( binary945792244etOf_a @ t1 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
member_a @ w @ ( binary945792244etOf_a @ t1 ),
file('/export/starexec/sandbox/tmp/tmp.xPc2I3SSGn/DTF2THF_929.p',fact_0_whSet) ).
thf(f3326,plain,
( ( member_a @ w @ ( binary945792244etOf_a @ t1 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f3319]) ).
thf(f3319,plain,
( ( ( member_a @ w @ ( binary945792244etOf_a @ t1 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f3266,f2000]) ).
thf(f2000,plain,
( ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f761]) ).
thf(f761,plain,
( ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
= $true ),
inference(fool_elimination,[status(thm)],[f760]) ).
thf(f760,plain,
binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ),
file('/export/starexec/sandbox/tmp/tmp.xPc2I3SSGn/DTF2THF_929.p',fact_1_s) ).
thf(f3266,plain,
! [X0: binary1439146945Tree_a,X1: binary1439146945Tree_a] :
( ( $true
!= ( binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ X0 @ x @ X1 ) ) )
| ( $true
!= ( member_a @ w @ ( binary945792244etOf_a @ X0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3265]) ).
thf(f3265,plain,
! [X0: binary1439146945Tree_a,X1: binary1439146945Tree_a] :
( ( ( binary1721989714Tree_a
@ ^ [Y0: a] :
( h
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( binary717961607le_T_a @ X0 @ x @ X1 ) )
!= $true )
| ( $true
!= ( member_a @ w @ ( binary945792244etOf_a @ X0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3248]) ).
thf(f3248,plain,
! [X0: binary1439146945Tree_a,X1: binary1439146945Tree_a] :
( ( ( binary1721989714Tree_a
@ ^ [Y0: a] :
( h
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( binary717961607le_T_a @ X0 @ x @ X1 ) )
!= $true )
| ( $true
!= ( member_a @ w @ ( binary945792244etOf_a @ X0 ) ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f3239,f2956]) ).
thf(f2956,plain,
! [X2: a > int,X3: a,X0: binary1439146945Tree_a,X1: binary1439146945Tree_a,X7: a] :
( ( $true
= ( ( ( sup_sup_int @ ( X2 @ X3 ) @ ( X2 @ X7 ) )
= ( X2 @ X3 ) )
& ( ( X2 @ X7 )
!= ( X2 @ X3 ) ) ) )
| ( ( member_a @ X7 @ ( binary945792244etOf_a @ X0 ) )
!= $true )
| ( ( binary1721989714Tree_a @ X2 @ ( binary717961607le_T_a @ X0 @ X3 @ X1 ) )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f2562]) ).
thf(f2562,plain,
! [X2: a > int,X3: a,X0: binary1439146945Tree_a,X1: binary1439146945Tree_a,X7: a] :
( ( ( ^ [Y0: int,Y1: int] :
( ( ( sup_sup_int @ Y1 @ Y0 )
= Y1 )
& ( Y0 != Y1 ) )
@ ( X2 @ X7 )
@ ( X2 @ X3 ) )
= $true )
| ( ( member_a @ X7 @ ( binary945792244etOf_a @ X0 ) )
!= $true )
| ( ( binary1721989714Tree_a @ X2 @ ( binary717961607le_T_a @ X0 @ X3 @ X1 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f2107,f1702]) ).
thf(f1702,plain,
( ord_less_int
= ( ^ [Y0: int,Y1: int] :
( ( ( sup_sup_int @ Y1 @ Y0 )
= Y1 )
& ( Y0 != Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f670]) ).
thf(f670,plain,
( ord_less_int
= ( ^ [Y0: int,Y1: int] :
( ( ( sup_sup_int @ Y1 @ Y0 )
= Y1 )
& ( Y0 != Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f669]) ).
thf(f669,plain,
( ord_less_int
= ( ^ [X0: int,X1: int] :
( ( X0 != X1 )
& ( ( sup_sup_int @ X1 @ X0 )
= X1 ) ) ) ),
inference(rectify,[status(thm)],[f302]) ).
thf(f302,axiom,
( ord_less_int
= ( ^ [X22: int,X21: int] :
( ( X21 != X22 )
& ( ( sup_sup_int @ X21 @ X22 )
= X21 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xPc2I3SSGn/DTF2THF_929.p',fact_301_sup_Ostrict__order__iff) ).
thf(f2107,plain,
! [X2: a > int,X3: a,X0: binary1439146945Tree_a,X1: binary1439146945Tree_a,X7: a] :
( ( $true
= ( ord_less_int @ ( X2 @ X7 ) @ ( X2 @ X3 ) ) )
| ( ( member_a @ X7 @ ( binary945792244etOf_a @ X0 ) )
!= $true )
| ( ( binary1721989714Tree_a @ X2 @ ( binary717961607le_T_a @ X0 @ X3 @ X1 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1599]) ).
thf(f1599,plain,
! [X0: binary1439146945Tree_a,X1: binary1439146945Tree_a,X2: a > int,X3: a] :
( ( ( ( binary1721989714Tree_a @ X2 @ ( binary717961607le_T_a @ X0 @ X3 @ X1 ) )
= $true )
| ( ( $true
!= ( ord_less_int @ ( X2 @ X3 ) @ ( X2 @ ( sK122 @ X3 @ X2 @ X1 ) ) ) )
& ( $true
= ( member_a @ ( sK122 @ X3 @ X2 @ X1 ) @ ( binary945792244etOf_a @ X1 ) ) ) )
| ( ( binary1721989714Tree_a @ X2 @ X0 )
!= $true )
| ( ( binary1721989714Tree_a @ X2 @ X1 )
!= $true )
| ( ( ( ord_less_int @ ( X2 @ ( sK123 @ X3 @ X2 @ X0 ) ) @ ( X2 @ X3 ) )
!= $true )
& ( $true
= ( member_a @ ( sK123 @ X3 @ X2 @ X0 ) @ ( binary945792244etOf_a @ X0 ) ) ) ) )
& ( ( ! [X6: a] :
( ( ( ord_less_int @ ( X2 @ X3 ) @ ( X2 @ X6 ) )
= $true )
| ( $true
!= ( member_a @ X6 @ ( binary945792244etOf_a @ X1 ) ) ) )
& ( ( binary1721989714Tree_a @ X2 @ X0 )
= $true )
& ( ( binary1721989714Tree_a @ X2 @ X1 )
= $true )
& ! [X7: a] :
( ( $true
= ( ord_less_int @ ( X2 @ X7 ) @ ( X2 @ X3 ) ) )
| ( ( member_a @ X7 @ ( binary945792244etOf_a @ X0 ) )
!= $true ) ) )
| ( ( binary1721989714Tree_a @ X2 @ ( binary717961607le_T_a @ X0 @ X3 @ X1 ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK122,sK123])],[f1596,f1598,f1597]) ).
thf(f1597,plain,
! [X1: binary1439146945Tree_a,X2: a > int,X3: a] :
( ? [X4: a] :
( ( $true
!= ( ord_less_int @ ( X2 @ X3 ) @ ( X2 @ X4 ) ) )
& ( ( member_a @ X4 @ ( binary945792244etOf_a @ X1 ) )
= $true ) )
=> ( ( $true
!= ( ord_less_int @ ( X2 @ X3 ) @ ( X2 @ ( sK122 @ X3 @ X2 @ X1 ) ) ) )
& ( $true
= ( member_a @ ( sK122 @ X3 @ X2 @ X1 ) @ ( binary945792244etOf_a @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1598,plain,
! [X0: binary1439146945Tree_a,X2: a > int,X3: a] :
( ? [X5: a] :
( ( $true
!= ( ord_less_int @ ( X2 @ X5 ) @ ( X2 @ X3 ) ) )
& ( $true
= ( member_a @ X5 @ ( binary945792244etOf_a @ X0 ) ) ) )
=> ( ( ( ord_less_int @ ( X2 @ ( sK123 @ X3 @ X2 @ X0 ) ) @ ( X2 @ X3 ) )
!= $true )
& ( $true
= ( member_a @ ( sK123 @ X3 @ X2 @ X0 ) @ ( binary945792244etOf_a @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1596,plain,
! [X0: binary1439146945Tree_a,X1: binary1439146945Tree_a,X2: a > int,X3: a] :
( ( ( ( binary1721989714Tree_a @ X2 @ ( binary717961607le_T_a @ X0 @ X3 @ X1 ) )
= $true )
| ? [X4: a] :
( ( $true
!= ( ord_less_int @ ( X2 @ X3 ) @ ( X2 @ X4 ) ) )
& ( ( member_a @ X4 @ ( binary945792244etOf_a @ X1 ) )
= $true ) )
| ( ( binary1721989714Tree_a @ X2 @ X0 )
!= $true )
| ( ( binary1721989714Tree_a @ X2 @ X1 )
!= $true )
| ? [X5: a] :
( ( $true
!= ( ord_less_int @ ( X2 @ X5 ) @ ( X2 @ X3 ) ) )
& ( $true
= ( member_a @ X5 @ ( binary945792244etOf_a @ X0 ) ) ) ) )
& ( ( ! [X6: a] :
( ( ( ord_less_int @ ( X2 @ X3 ) @ ( X2 @ X6 ) )
= $true )
| ( $true
!= ( member_a @ X6 @ ( binary945792244etOf_a @ X1 ) ) ) )
& ( ( binary1721989714Tree_a @ X2 @ X0 )
= $true )
& ( ( binary1721989714Tree_a @ X2 @ X1 )
= $true )
& ! [X7: a] :
( ( $true
= ( ord_less_int @ ( X2 @ X7 ) @ ( X2 @ X3 ) ) )
| ( ( member_a @ X7 @ ( binary945792244etOf_a @ X0 ) )
!= $true ) ) )
| ( ( binary1721989714Tree_a @ X2 @ ( binary717961607le_T_a @ X0 @ X3 @ X1 ) )
!= $true ) ) ),
inference(rectify,[status(thm)],[f1595]) ).
thf(f1595,plain,
! [X0: binary1439146945Tree_a,X1: binary1439146945Tree_a,X2: a > int,X3: a] :
( ( ( ( binary1721989714Tree_a @ X2 @ ( binary717961607le_T_a @ X0 @ X3 @ X1 ) )
= $true )
| ? [X5: a] :
( ( ( ord_less_int @ ( X2 @ X3 ) @ ( X2 @ X5 ) )
!= $true )
& ( ( member_a @ X5 @ ( binary945792244etOf_a @ X1 ) )
= $true ) )
| ( ( binary1721989714Tree_a @ X2 @ X0 )
!= $true )
| ( ( binary1721989714Tree_a @ X2 @ X1 )
!= $true )
| ? [X4: a] :
( ( $true
!= ( ord_less_int @ ( X2 @ X4 ) @ ( X2 @ X3 ) ) )
& ( $true
= ( member_a @ X4 @ ( binary945792244etOf_a @ X0 ) ) ) ) )
& ( ( ! [X5: a] :
( ( ( ord_less_int @ ( X2 @ X3 ) @ ( X2 @ X5 ) )
= $true )
| ( ( member_a @ X5 @ ( binary945792244etOf_a @ X1 ) )
!= $true ) )
& ( ( binary1721989714Tree_a @ X2 @ X0 )
= $true )
& ( ( binary1721989714Tree_a @ X2 @ X1 )
= $true )
& ! [X4: a] :
( ( $true
= ( ord_less_int @ ( X2 @ X4 ) @ ( X2 @ X3 ) ) )
| ( $true
!= ( member_a @ X4 @ ( binary945792244etOf_a @ X0 ) ) ) ) )
| ( ( binary1721989714Tree_a @ X2 @ ( binary717961607le_T_a @ X0 @ X3 @ X1 ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f1594]) ).
thf(f1594,plain,
! [X0: binary1439146945Tree_a,X1: binary1439146945Tree_a,X2: a > int,X3: a] :
( ( ( ( binary1721989714Tree_a @ X2 @ ( binary717961607le_T_a @ X0 @ X3 @ X1 ) )
= $true )
| ? [X5: a] :
( ( ( ord_less_int @ ( X2 @ X3 ) @ ( X2 @ X5 ) )
!= $true )
& ( ( member_a @ X5 @ ( binary945792244etOf_a @ X1 ) )
= $true ) )
| ( ( binary1721989714Tree_a @ X2 @ X0 )
!= $true )
| ( ( binary1721989714Tree_a @ X2 @ X1 )
!= $true )
| ? [X4: a] :
( ( $true
!= ( ord_less_int @ ( X2 @ X4 ) @ ( X2 @ X3 ) ) )
& ( $true
= ( member_a @ X4 @ ( binary945792244etOf_a @ X0 ) ) ) ) )
& ( ( ! [X5: a] :
( ( ( ord_less_int @ ( X2 @ X3 ) @ ( X2 @ X5 ) )
= $true )
| ( ( member_a @ X5 @ ( binary945792244etOf_a @ X1 ) )
!= $true ) )
& ( ( binary1721989714Tree_a @ X2 @ X0 )
= $true )
& ( ( binary1721989714Tree_a @ X2 @ X1 )
= $true )
& ! [X4: a] :
( ( $true
= ( ord_less_int @ ( X2 @ X4 ) @ ( X2 @ X3 ) ) )
| ( $true
!= ( member_a @ X4 @ ( binary945792244etOf_a @ X0 ) ) ) ) )
| ( ( binary1721989714Tree_a @ X2 @ ( binary717961607le_T_a @ X0 @ X3 @ X1 ) )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1179]) ).
thf(f1179,plain,
! [X0: binary1439146945Tree_a,X1: binary1439146945Tree_a,X2: a > int,X3: a] :
( ( ( binary1721989714Tree_a @ X2 @ ( binary717961607le_T_a @ X0 @ X3 @ X1 ) )
= $true )
<=> ( ! [X5: a] :
( ( ( ord_less_int @ ( X2 @ X3 ) @ ( X2 @ X5 ) )
= $true )
| ( ( member_a @ X5 @ ( binary945792244etOf_a @ X1 ) )
!= $true ) )
& ( ( binary1721989714Tree_a @ X2 @ X0 )
= $true )
& ( ( binary1721989714Tree_a @ X2 @ X1 )
= $true )
& ! [X4: a] :
( ( $true
= ( ord_less_int @ ( X2 @ X4 ) @ ( X2 @ X3 ) ) )
| ( $true
!= ( member_a @ X4 @ ( binary945792244etOf_a @ X0 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f858]) ).
thf(f858,plain,
! [X0: binary1439146945Tree_a,X1: binary1439146945Tree_a,X2: a > int,X3: a] :
( ( ! [X4: a] :
( ( $true
= ( member_a @ X4 @ ( binary945792244etOf_a @ X0 ) ) )
=> ( $true
= ( ord_less_int @ ( X2 @ X4 ) @ ( X2 @ X3 ) ) ) )
& ( ( binary1721989714Tree_a @ X2 @ X1 )
= $true )
& ! [X5: a] :
( ( ( member_a @ X5 @ ( binary945792244etOf_a @ X1 ) )
= $true )
=> ( ( ord_less_int @ ( X2 @ X3 ) @ ( X2 @ X5 ) )
= $true ) )
& ( ( binary1721989714Tree_a @ X2 @ X0 )
= $true ) )
<=> ( ( binary1721989714Tree_a @ X2 @ ( binary717961607le_T_a @ X0 @ X3 @ X1 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f857]) ).
thf(f857,plain,
! [X0: binary1439146945Tree_a,X1: binary1439146945Tree_a,X2: a > int,X3: a] :
( ( ( binary1721989714Tree_a @ X2 @ ( binary717961607le_T_a @ X0 @ X3 @ X1 ) )
= ( ! [X4: a] :
( ( member_a @ X4 @ ( binary945792244etOf_a @ X0 ) )
=> ( ord_less_int @ ( X2 @ X4 ) @ ( X2 @ X3 ) ) ) ) )
& ( binary1721989714Tree_a @ X2 @ X1 )
& ! [X5: a] :
( ( member_a @ X5 @ ( binary945792244etOf_a @ X1 ) )
=> ( ord_less_int @ ( X2 @ X3 ) @ ( X2 @ X5 ) ) )
& ( binary1721989714Tree_a @ X2 @ X0 ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,axiom,
! [X16: binary1439146945Tree_a,X18: binary1439146945Tree_a,X15: a > int,X17: a] :
( ( ( binary1721989714Tree_a @ X15 @ ( binary717961607le_T_a @ X16 @ X17 @ X18 ) )
= ( ! [X19: a] :
( ( member_a @ X19 @ ( binary945792244etOf_a @ X16 ) )
=> ( ord_less_int @ ( X15 @ X19 ) @ ( X15 @ X17 ) ) ) ) )
& ( binary1721989714Tree_a @ X15 @ X18 )
& ! [X19: a] :
( ( member_a @ X19 @ ( binary945792244etOf_a @ X18 ) )
=> ( ord_less_int @ ( X15 @ X17 ) @ ( X15 @ X19 ) ) )
& ( binary1721989714Tree_a @ X15 @ X16 ) ),
file('/export/starexec/sandbox/tmp/tmp.xPc2I3SSGn/DTF2THF_929.p',fact_19_sortedTree_Osimps_I2_J) ).
thf(f3239,plain,
( ( ( ( sup_sup_int @ ( h @ x ) @ ( h @ w ) )
= ( h @ x ) )
& ( ( h @ w )
!= ( h @ x ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f2382]) ).
thf(f2382,plain,
( ( ^ [Y0: int,Y1: int] :
( ( ( sup_sup_int @ Y1 @ Y0 )
= Y1 )
& ( Y0 != Y1 ) )
@ ( h @ w )
@ ( h @ x ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f1876,f1702]) ).
thf(f1876,plain,
( ( ord_less_int @ ( h @ w ) @ ( h @ x ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f1067]) ).
thf(f1067,plain,
( ( ord_less_int @ ( h @ w ) @ ( h @ x ) )
!= $true ),
inference(flattening,[status(thm)],[f529]) ).
thf(f529,plain,
( ( ord_less_int @ ( h @ w ) @ ( h @ x ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f528]) ).
thf(f528,plain,
~ ( ord_less_int @ ( h @ w ) @ ( h @ x ) ),
inference(rectify,[status(thm)],[f352]) ).
thf(f352,negated_conjecture,
~ ( ord_less_int @ ( h @ w ) @ ( h @ x ) ),
inference(negated_conjecture,[status(cth)],[f351]) ).
thf(f351,conjecture,
ord_less_int @ ( h @ w ) @ ( h @ x ),
file('/export/starexec/sandbox/tmp/tmp.xPc2I3SSGn/DTF2THF_929.p',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP032^1 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.32 % Computer : n025.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue Feb 24 08:24:12 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.44 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : ITP032^1 : 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_359__3253628_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_359__3253628_1 [Des21]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.50 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0
% 0.18/0.45 % Syntax : Number of formulae : 394 ( 179 unt; 43 typ; 0 def)
% 0.18/0.45 % Number of atoms : 957 ( 355 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 7 ( 2 avg)
% 0.18/0.45 % Number of connectives : 2711 ( 120 ~; 19 |; 56 &;2148 @)
% 0.18/0.45 % ( 0 <=>; 368 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 14 ( 6 avg)
% 0.18/0.45 % Number of types : 5 ( 4 usr)
% 0.18/0.45 % Number of type conns : 342 ( 342 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 41 ( 39 usr; 9 con; 0-4 aty)
% 0.18/0.45 % Number of variables : 987 ( 91 ^; 864 !; 32 ?; 987 :)
% 0.18/0.45 % SPC : TH0_CAX_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 15:30:56.100
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % Could-be-implicit typings (4)
% 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__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 (39)
% 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_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_Opred__Tree_001tf__a,type,
% 0.18/0.45 binary1452917696Tree_a: ( a > $o ) > binary1439146945Tree_a > $o ).
% 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_Obinsert_001tf__a,type,
% 0.18/0.45 binary1226383794sert_a: ( a > int ) > a > binary1439146945Tree_a > binary1439146945Tree_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_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_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_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_Groups_Ominus__class_Ominus_001_062_Itf__a_M_Eo_J,type,
% 0.18/0.45 minus_minus_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Ominus__class_Ominus_001_Eo,type,
% 0.18/0.45 minus_minus_o: $o > $o > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
% 0.18/0.45 minus_minus_int: int > int > int ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__a_J,type,
% 0.18/0.45 minus_minus_set_a: set_a > set_a > set_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_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_001_Eo,type,
% 0.18/0.45 sup_sup_o: $o > $o > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 0.18/0.45 sup_sup_int: int > int > int ).
% 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_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_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_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_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_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.18/0.45 ord_less_eq_set_a: set_a > set_a > $o ).
% 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_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_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_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_Oremove_001tf__a,type,
% 0.18/0.45 remove_a: a > set_a > set_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_001tf__a,type,
% 0.18/0.45 member_a: a > set_a > $o ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_e,type,
% 0.18/0.45 e: a ).
% 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_t1____,type,
% 0.18/0.45 t1: binary1439146945Tree_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_t2____,type,
% 0.18/0.45 t2: binary1439146945Tree_a ).
% 0.18/0.45
% 0.18/0.45 thf(sy_v_w____,type,
% 0.18/0.45 w: 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 (350)
% 0.18/0.45 thf(fact_0_whSet,axiom,
% 0.18/0.45 member_a @ w @ ( binary945792244etOf_a @ t1 ) ).
% 0.18/0.45
% 0.18/0.45 % whSet
% 0.18/0.45 thf(fact_1_s,axiom,
% 0.18/0.45 binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ).
% 0.18/0.45
% 0.18/0.45 % s
% 0.18/0.45 thf(fact_2_s2,axiom,
% 0.18/0.45 binary1721989714Tree_a @ h @ t2 ).
% 0.18/0.45
% 0.18/0.45 % s2
% 0.18/0.45 thf(fact_3_s1,axiom,
% 0.18/0.45 binary1721989714Tree_a @ h @ t1 ).
% 0.18/0.45
% 0.18/0.45 % s1
% 0.18/0.45 thf(fact_4_eNotLess,axiom,
% 0.18/0.45 ~ ( ord_less_int @ ( h @ e ) @ ( h @ x ) ) ).
% 0.18/0.45
% 0.18/0.45 % eNotLess
% 0.18/0.45 thf(fact_5_xNotLess,axiom,
% 0.18/0.45 ~ ( ord_less_int @ ( h @ x ) @ ( h @ e ) ) ).
% 0.18/0.45
% 0.18/0.45 % xNotLess
% 0.18/0.45 thf(fact_6_whEq,axiom,
% 0.18/0.45 member_a @ w @ ( binary504661350_eqs_a @ h @ e ) ).
% 0.18/0.45
% 0.18/0.45 % whEq
% 0.18/0.45 thf(fact_7_xeqe,axiom,
% 0.18/0.45 ( ( h @ x )
% 0.18/0.45 = ( h @ e ) ) ).
% 0.18/0.45
% 0.18/0.45 % xeqe
% 0.18/0.45 thf(fact_8_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_9_calculation,axiom,
% 0.18/0.45 member_a @ x @ ( binary504661350_eqs_a @ h @ e ) ).
% 0.18/0.45
% 0.18/0.45 % calculation
% 0.18/0.45 thf(fact_10_minf_I7_J,axiom,
% 0.18/0.45 ! [T: int] :
% 0.18/0.45 ? [Z: int] :
% 0.18/0.45 ! [X: int] :
% 0.18/0.45 ( ( ord_less_int @ X @ Z )
% 0.18/0.45 => ~ ( ord_less_int @ T @ X ) ) ).
% 0.18/0.45
% 0.18/0.45 % minf(7)
% 0.18/0.45 thf(fact_11_minf_I5_J,axiom,
% 0.18/0.45 ! [T: int] :
% 0.18/0.45 ? [Z: int] :
% 0.18/0.45 ! [X: int] :
% 0.18/0.45 ( ( ord_less_int @ X @ Z )
% 0.18/0.45 => ( ord_less_int @ X @ T ) ) ).
% 0.18/0.45
% 0.18/0.45 % minf(5)
% 0.18/0.45 thf(fact_12_minf_I4_J,axiom,
% 0.18/0.45 ! [T: int] :
% 0.18/0.45 ? [Z: int] :
% 0.18/0.45 ! [X: int] :
% 0.18/0.45 ( ( ord_less_int @ X @ Z )
% 0.18/0.45 => ( X != T ) ) ).
% 0.18/0.45
% 0.18/0.45 % minf(4)
% 0.18/0.45 thf(fact_13_minf_I3_J,axiom,
% 0.18/0.45 ! [T: int] :
% 0.18/0.45 ? [Z: int] :
% 0.18/0.45 ! [X: int] :
% 0.18/0.45 ( ( ord_less_int @ X @ Z )
% 0.18/0.45 => ( X != T ) ) ).
% 0.18/0.45
% 0.18/0.45 % minf(3)
% 0.18/0.45 thf(fact_14_minf_I2_J,axiom,
% 0.18/0.45 ! [P: int > $o,P2: int > $o,Q: int > $o,Q2: int > $o] :
% 0.18/0.45 ( ? [Z2: int] :
% 0.18/0.45 ! [X2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Z2 )
% 0.18/0.45 => ( ( P @ X2 )
% 0.18/0.45 = ( P2 @ X2 ) ) )
% 0.18/0.45 => ( ? [Z2: int] :
% 0.18/0.45 ! [X2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Z2 )
% 0.18/0.45 => ( ( Q @ X2 )
% 0.18/0.45 = ( Q2 @ X2 ) ) )
% 0.18/0.45 => ? [Z: int] :
% 0.18/0.45 ! [X: int] :
% 0.18/0.45 ( ( ord_less_int @ X @ Z )
% 0.18/0.45 => ( ( ( P @ X )
% 0.18/0.45 | ( Q @ X ) )
% 0.18/0.45 = ( ( P2 @ X )
% 0.18/0.45 | ( Q2 @ X ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % minf(2)
% 0.18/0.45 thf(fact_15_minf_I1_J,axiom,
% 0.18/0.45 ! [P: int > $o,P2: int > $o,Q: int > $o,Q2: int > $o] :
% 0.18/0.45 ( ? [Z2: int] :
% 0.18/0.45 ! [X2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Z2 )
% 0.18/0.45 => ( ( P @ X2 )
% 0.18/0.45 = ( P2 @ X2 ) ) )
% 0.18/0.45 => ( ? [Z2: int] :
% 0.18/0.45 ! [X2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Z2 )
% 0.18/0.45 => ( ( Q @ X2 )
% 0.18/0.45 = ( Q2 @ X2 ) ) )
% 0.18/0.45 => ? [Z: int] :
% 0.18/0.45 ! [X: int] :
% 0.18/0.45 ( ( ord_less_int @ X @ Z )
% 0.18/0.45 => ( ( ( P @ X )
% 0.18/0.45 & ( Q @ X ) )
% 0.18/0.45 = ( ( P2 @ X )
% 0.18/0.45 & ( Q2 @ X ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % minf(1)
% 0.18/0.45 thf(fact_16_res,axiom,
% 0.18/0.45 ( ( binary1226383794sert_a @ h @ e @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
% 0.18/0.45 = ( binary717961607le_T_a @ t1 @ e @ t2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % res
% 0.18/0.45 thf(fact_17_sortLemmaR,axiom,
% 0.18/0.45 ! [H: a > int,T1: binary1439146945Tree_a,X3: a,T2: binary1439146945Tree_a] :
% 0.18/0.45 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X3 @ T2 ) )
% 0.18/0.45 => ( binary1721989714Tree_a @ H @ T2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % sortLemmaR
% 0.18/0.45 thf(fact_18_sortLemmaL,axiom,
% 0.18/0.45 ! [H: a > int,T1: binary1439146945Tree_a,X3: a,T2: binary1439146945Tree_a] :
% 0.18/0.45 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X3 @ T2 ) )
% 0.18/0.45 => ( binary1721989714Tree_a @ H @ T1 ) ) ).
% 0.18/0.45
% 0.18/0.45 % sortLemmaL
% 0.18/0.45 thf(fact_19_sortedTree_Osimps_I2_J,axiom,
% 0.18/0.45 ! [H: a > int,T1: binary1439146945Tree_a,X3: a,T2: binary1439146945Tree_a] :
% 0.18/0.45 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X3 @ T2 ) )
% 0.18/0.45 = ( ( binary1721989714Tree_a @ H @ T1 )
% 0.18/0.45 & ! [X4: a] :
% 0.18/0.45 ( ( member_a @ X4 @ ( binary945792244etOf_a @ T1 ) )
% 0.18/0.45 => ( ord_less_int @ ( H @ X4 ) @ ( H @ X3 ) ) )
% 0.18/0.45 & ! [X4: a] :
% 0.18/0.45 ( ( member_a @ X4 @ ( binary945792244etOf_a @ T2 ) )
% 0.18/0.45 => ( ord_less_int @ ( H @ X3 ) @ ( H @ X4 ) ) )
% 0.18/0.45 & ( binary1721989714Tree_a @ H @ T2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sortedTree.simps(2)
% 0.18/0.45 thf(fact_20_pinf_I1_J,axiom,
% 0.18/0.45 ! [P: int > $o,P2: int > $o,Q: int > $o,Q2: int > $o] :
% 0.18/0.45 ( ? [Z2: int] :
% 0.18/0.45 ! [X2: int] :
% 0.18/0.45 ( ( ord_less_int @ Z2 @ X2 )
% 0.18/0.45 => ( ( P @ X2 )
% 0.18/0.45 = ( P2 @ X2 ) ) )
% 0.18/0.45 => ( ? [Z2: int] :
% 0.18/0.45 ! [X2: int] :
% 0.18/0.45 ( ( ord_less_int @ Z2 @ X2 )
% 0.18/0.45 => ( ( Q @ X2 )
% 0.18/0.45 = ( Q2 @ X2 ) ) )
% 0.18/0.45 => ? [Z: int] :
% 0.18/0.45 ! [X: int] :
% 0.18/0.45 ( ( ord_less_int @ Z @ X )
% 0.18/0.45 => ( ( ( P @ X )
% 0.18/0.45 & ( Q @ X ) )
% 0.18/0.45 = ( ( P2 @ X )
% 0.18/0.45 & ( Q2 @ X ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % pinf(1)
% 0.18/0.45 thf(fact_21_pinf_I2_J,axiom,
% 0.18/0.45 ! [P: int > $o,P2: int > $o,Q: int > $o,Q2: int > $o] :
% 0.18/0.45 ( ? [Z2: int] :
% 0.18/0.45 ! [X2: int] :
% 0.18/0.45 ( ( ord_less_int @ Z2 @ X2 )
% 0.18/0.45 => ( ( P @ X2 )
% 0.18/0.45 = ( P2 @ X2 ) ) )
% 0.18/0.45 => ( ? [Z2: int] :
% 0.18/0.45 ! [X2: int] :
% 0.18/0.45 ( ( ord_less_int @ Z2 @ X2 )
% 0.18/0.45 => ( ( Q @ X2 )
% 0.18/0.45 = ( Q2 @ X2 ) ) )
% 0.18/0.45 => ? [Z: int] :
% 0.18/0.45 ! [X: int] :
% 0.18/0.45 ( ( ord_less_int @ Z @ X )
% 0.18/0.45 => ( ( ( P @ X )
% 0.18/0.45 | ( Q @ X ) )
% 0.18/0.45 = ( ( P2 @ X )
% 0.18/0.45 | ( Q2 @ X ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % pinf(2)
% 0.18/0.45 thf(fact_22_pinf_I3_J,axiom,
% 0.18/0.45 ! [T: int] :
% 0.18/0.45 ? [Z: int] :
% 0.18/0.45 ! [X: int] :
% 0.18/0.45 ( ( ord_less_int @ Z @ X )
% 0.18/0.45 => ( X != T ) ) ).
% 0.18/0.45
% 0.18/0.45 % pinf(3)
% 0.18/0.45 thf(fact_23_pinf_I4_J,axiom,
% 0.18/0.45 ! [T: int] :
% 0.18/0.45 ? [Z: int] :
% 0.18/0.45 ! [X: int] :
% 0.18/0.45 ( ( ord_less_int @ Z @ X )
% 0.18/0.45 => ( X != T ) ) ).
% 0.18/0.45
% 0.18/0.45 % pinf(4)
% 0.18/0.45 thf(fact_24_pinf_I5_J,axiom,
% 0.18/0.45 ! [T: int] :
% 0.18/0.45 ? [Z: int] :
% 0.18/0.45 ! [X: int] :
% 0.18/0.45 ( ( ord_less_int @ Z @ X )
% 0.18/0.45 => ~ ( ord_less_int @ X @ T ) ) ).
% 0.18/0.45
% 0.18/0.45 % pinf(5)
% 0.18/0.45 thf(fact_25_pinf_I7_J,axiom,
% 0.18/0.45 ! [T: int] :
% 0.18/0.45 ? [Z: int] :
% 0.18/0.45 ! [X: int] :
% 0.18/0.45 ( ( ord_less_int @ Z @ X )
% 0.18/0.45 => ( ord_less_int @ T @ X ) ) ).
% 0.18/0.45
% 0.18/0.45 % pinf(7)
% 0.18/0.45 thf(fact_26_sorted__distinct__pred__def,axiom,
% 0.18/0.45 ( binary670562003pred_a
% 0.18/0.45 = ( ^ [H2: a > int,A: a,B: a,T3: binary1439146945Tree_a] :
% 0.18/0.45 ( ( ( binary1721989714Tree_a @ H2 @ T3 )
% 0.18/0.45 & ( member_a @ A @ ( binary945792244etOf_a @ T3 ) )
% 0.18/0.45 & ( member_a @ B @ ( binary945792244etOf_a @ T3 ) )
% 0.18/0.45 & ( ( H2 @ A )
% 0.18/0.45 = ( H2 @ B ) ) )
% 0.18/0.45 => ( A = B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sorted_distinct_pred_def
% 0.18/0.45 thf(fact_27_memb__spec,axiom,
% 0.18/0.45 ! [H: a > int,T: binary1439146945Tree_a,X3: a] :
% 0.18/0.45 ( ( binary1721989714Tree_a @ H @ T )
% 0.18/0.45 => ( ( binary2053421120memb_a @ H @ X3 @ T )
% 0.18/0.45 = ( member_a @ X3 @ ( binary945792244etOf_a @ T ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % memb_spec
% 0.18/0.45 thf(fact_28_binsert_Osimps_I2_J,axiom,
% 0.18/0.45 ! [H: a > int,E: a,X3: a,T1: binary1439146945Tree_a,T2: binary1439146945Tree_a] :
% 0.18/0.45 ( ( ( ord_less_int @ ( H @ E ) @ ( H @ X3 ) )
% 0.18/0.45 => ( ( binary1226383794sert_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X3 @ T2 ) )
% 0.18/0.45 = ( binary717961607le_T_a @ ( binary1226383794sert_a @ H @ E @ T1 ) @ X3 @ T2 ) ) )
% 0.18/0.45 & ( ~ ( ord_less_int @ ( H @ E ) @ ( H @ X3 ) )
% 0.18/0.45 => ( ( ( ord_less_int @ ( H @ X3 ) @ ( H @ E ) )
% 0.18/0.45 => ( ( binary1226383794sert_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X3 @ T2 ) )
% 0.18/0.45 = ( binary717961607le_T_a @ T1 @ X3 @ ( binary1226383794sert_a @ H @ E @ T2 ) ) ) )
% 0.18/0.45 & ( ~ ( ord_less_int @ ( H @ X3 ) @ ( H @ E ) )
% 0.18/0.45 => ( ( binary1226383794sert_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X3 @ T2 ) )
% 0.18/0.45 = ( binary717961607le_T_a @ T1 @ E @ T2 ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % binsert.simps(2)
% 0.18/0.45 thf(fact_29_linorder__neqE__linordered__idom,axiom,
% 0.18/0.45 ! [X3: int,Y: int] :
% 0.18/0.45 ( ( X3 != Y )
% 0.18/0.45 => ( ~ ( ord_less_int @ X3 @ Y )
% 0.18/0.45 => ( ord_less_int @ Y @ X3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % linorder_neqE_linordered_idom
% 0.18/0.45 thf(fact_30_dual__order_Ostrict__implies__not__eq,axiom,
% 0.18/0.45 ! [B2: set_a,A2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ B2 @ A2 )
% 0.18/0.45 => ( A2 != B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.strict_implies_not_eq
% 0.18/0.45 thf(fact_31_dual__order_Ostrict__implies__not__eq,axiom,
% 0.18/0.45 ! [B2: a > $o,A2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ B2 @ A2 )
% 0.18/0.45 => ( A2 != B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.strict_implies_not_eq
% 0.18/0.45 thf(fact_32_dual__order_Ostrict__implies__not__eq,axiom,
% 0.18/0.45 ! [B2: int,A2: int] :
% 0.18/0.45 ( ( ord_less_int @ B2 @ A2 )
% 0.18/0.45 => ( A2 != B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.strict_implies_not_eq
% 0.18/0.45 thf(fact_33_order_Ostrict__implies__not__eq,axiom,
% 0.18/0.45 ! [A2: set_a,B2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A2 @ B2 )
% 0.18/0.45 => ( A2 != B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.strict_implies_not_eq
% 0.18/0.45 thf(fact_34_order_Ostrict__implies__not__eq,axiom,
% 0.18/0.45 ! [A2: a > $o,B2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ A2 @ B2 )
% 0.18/0.45 => ( A2 != B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.strict_implies_not_eq
% 0.18/0.45 thf(fact_35_order_Ostrict__implies__not__eq,axiom,
% 0.18/0.45 ! [A2: int,B2: int] :
% 0.18/0.45 ( ( ord_less_int @ A2 @ B2 )
% 0.18/0.45 => ( A2 != B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.strict_implies_not_eq
% 0.18/0.45 thf(fact_36_sorted__distinct,axiom,
% 0.18/0.45 ! [H: a > int,A2: a,B2: a,T: binary1439146945Tree_a] : ( binary670562003pred_a @ H @ A2 @ B2 @ T ) ).
% 0.18/0.45
% 0.18/0.45 % sorted_distinct
% 0.18/0.45 thf(fact_37_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A2: set_a,F: int > set_a,B2: int,C: int] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_int @ B2 @ C )
% 0.18/0.45 => ( ! [X2: int,Y2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_38_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A2: a > $o,F: int > a > $o,B2: int,C: int] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_int @ B2 @ C )
% 0.18/0.45 => ( ! [X2: int,Y2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_39_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A2: int,F: set_a > int,B2: set_a,C: set_a] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_set_a @ B2 @ C )
% 0.18/0.45 => ( ! [X2: set_a,Y2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_40_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_set_a @ B2 @ C )
% 0.18/0.45 => ( ! [X2: set_a,Y2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_41_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_set_a @ B2 @ C )
% 0.18/0.45 => ( ! [X2: set_a,Y2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_42_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A2: int,F: ( a > $o ) > int,B2: a > $o,C: a > $o] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_a_o @ B2 @ C )
% 0.18/0.45 => ( ! [X2: a > $o,Y2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_43_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_a_o @ B2 @ C )
% 0.18/0.45 => ( ! [X2: a > $o,Y2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_44_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_a_o @ B2 @ C )
% 0.18/0.45 => ( ! [X2: a > $o,Y2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_45_ord__eq__less__subst,axiom,
% 0.18/0.45 ! [A2: int,F: int > int,B2: int,C: int] :
% 0.18/0.45 ( ( A2
% 0.18/0.45 = ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_int @ B2 @ C )
% 0.18/0.45 => ( ! [X2: int,Y2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_subst
% 0.18/0.45 thf(fact_46_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A2: int,B2: int,F: int > set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_int @ A2 @ B2 )
% 0.18/0.45 => ( ( ( F @ B2 )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X2: int,Y2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_47_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A2: int,B2: int,F: int > a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_int @ A2 @ B2 )
% 0.18/0.45 => ( ( ( F @ B2 )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X2: int,Y2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_48_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A2: set_a,B2: set_a,F: set_a > int,C: int] :
% 0.18/0.45 ( ( ord_less_set_a @ A2 @ B2 )
% 0.18/0.45 => ( ( ( F @ B2 )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X2: set_a,Y2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_49_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A2 @ B2 )
% 0.18/0.45 => ( ( ( F @ B2 )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X2: set_a,Y2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_50_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_set_a @ A2 @ B2 )
% 0.18/0.45 => ( ( ( F @ B2 )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X2: set_a,Y2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_51_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > int,C: int] :
% 0.18/0.45 ( ( ord_less_a_o @ A2 @ B2 )
% 0.18/0.45 => ( ( ( F @ B2 )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X2: a > $o,Y2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_52_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_a_o @ A2 @ B2 )
% 0.18/0.45 => ( ( ( F @ B2 )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X2: a > $o,Y2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_53_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ A2 @ B2 )
% 0.18/0.45 => ( ( ( F @ B2 )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X2: a > $o,Y2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_54_ord__less__eq__subst,axiom,
% 0.18/0.45 ! [A2: int,B2: int,F: int > int,C: int] :
% 0.18/0.45 ( ( ord_less_int @ A2 @ B2 )
% 0.18/0.45 => ( ( ( F @ B2 )
% 0.18/0.45 = C )
% 0.18/0.45 => ( ! [X2: int,Y2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_subst
% 0.18/0.45 thf(fact_55_order__less__subst1,axiom,
% 0.18/0.45 ! [A2: int,F: set_a > int,B2: set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_set_a @ B2 @ C )
% 0.18/0.45 => ( ! [X2: set_a,Y2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_56_order__less__subst1,axiom,
% 0.18/0.45 ! [A2: int,F: ( a > $o ) > int,B2: a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_a_o @ B2 @ C )
% 0.18/0.45 => ( ! [X2: a > $o,Y2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_57_order__less__subst1,axiom,
% 0.18/0.45 ! [A2: set_a,F: int > set_a,B2: int,C: int] :
% 0.18/0.45 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_int @ B2 @ C )
% 0.18/0.45 => ( ! [X2: int,Y2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_58_order__less__subst1,axiom,
% 0.18/0.45 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_set_a @ B2 @ C )
% 0.18/0.45 => ( ! [X2: set_a,Y2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_59_order__less__subst1,axiom,
% 0.18/0.45 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_a_o @ B2 @ C )
% 0.18/0.45 => ( ! [X2: a > $o,Y2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_60_order__less__subst1,axiom,
% 0.18/0.45 ! [A2: a > $o,F: int > a > $o,B2: int,C: int] :
% 0.18/0.45 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_int @ B2 @ C )
% 0.18/0.45 => ( ! [X2: int,Y2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_61_order__less__subst1,axiom,
% 0.18/0.45 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_set_a @ B2 @ C )
% 0.18/0.45 => ( ! [X2: set_a,Y2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_62_order__less__subst1,axiom,
% 0.18/0.45 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_a_o @ B2 @ C )
% 0.18/0.45 => ( ! [X2: a > $o,Y2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_63_order__less__subst1,axiom,
% 0.18/0.45 ! [A2: int,F: int > int,B2: int,C: int] :
% 0.18/0.45 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 0.18/0.45 => ( ( ord_less_int @ B2 @ C )
% 0.18/0.45 => ( ! [X2: int,Y2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst1
% 0.18/0.45 thf(fact_64_order__less__subst2,axiom,
% 0.18/0.45 ! [A2: int,B2: int,F: int > set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_int @ A2 @ B2 )
% 0.18/0.45 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 0.18/0.45 => ( ! [X2: int,Y2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_65_order__less__subst2,axiom,
% 0.18/0.45 ! [A2: int,B2: int,F: int > a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_int @ A2 @ B2 )
% 0.18/0.45 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 0.18/0.45 => ( ! [X2: int,Y2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_66_order__less__subst2,axiom,
% 0.18/0.45 ! [A2: set_a,B2: set_a,F: set_a > int,C: int] :
% 0.18/0.45 ( ( ord_less_set_a @ A2 @ B2 )
% 0.18/0.45 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 0.18/0.45 => ( ! [X2: set_a,Y2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_67_order__less__subst2,axiom,
% 0.18/0.45 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A2 @ B2 )
% 0.18/0.45 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 0.18/0.45 => ( ! [X2: set_a,Y2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_68_order__less__subst2,axiom,
% 0.18/0.45 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_set_a @ A2 @ B2 )
% 0.18/0.45 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 0.18/0.45 => ( ! [X2: set_a,Y2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_69_order__less__subst2,axiom,
% 0.18/0.45 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > int,C: int] :
% 0.18/0.45 ( ( ord_less_a_o @ A2 @ B2 )
% 0.18/0.45 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 0.18/0.45 => ( ! [X2: a > $o,Y2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_70_order__less__subst2,axiom,
% 0.18/0.45 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_a_o @ A2 @ B2 )
% 0.18/0.45 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 0.18/0.45 => ( ! [X2: a > $o,Y2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_71_order__less__subst2,axiom,
% 0.18/0.45 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ A2 @ B2 )
% 0.18/0.45 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 0.18/0.45 => ( ! [X2: a > $o,Y2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_72_order__less__subst2,axiom,
% 0.18/0.45 ! [A2: int,B2: int,F: int > int,C: int] :
% 0.18/0.45 ( ( ord_less_int @ A2 @ B2 )
% 0.18/0.45 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 0.18/0.45 => ( ! [X2: int,Y2: int] :
% 0.18/0.45 ( ( ord_less_int @ X2 @ Y2 )
% 0.18/0.45 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 0.18/0.45 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order_less_subst2
% 0.18/0.45 thf(fact_73_lt__ex,axiom,
% 0.18/0.45 ! [X3: int] :
% 0.18/0.45 ? [Y2: int] : ( ord_less_int @ Y2 @ X3 ) ).
% 0.18/0.45
% 0.18/0.45 % lt_ex
% 0.18/0.45 thf(fact_74_gt__ex,axiom,
% 0.18/0.45 ! [X3: int] :
% 0.18/0.45 ? [X_1: int] : ( ord_less_int @ X3 @ X_1 ) ).
% 0.18/0.45
% 0.18/0.45 % gt_ex
% 0.18/0.45 thf(fact_75_mem__Collect__eq,axiom,
% 0.18/0.45 ! [A2: a,P: a > $o] :
% 0.18/0.45 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 0.18/0.45 = ( P @ A2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % mem_Collect_eq
% 0.18/0.45 thf(fact_76_Collect__mem__eq,axiom,
% 0.18/0.45 ! [A3: set_a] :
% 0.18/0.45 ( ( collect_a
% 0.18/0.45 @ ^ [X4: a] : ( member_a @ X4 @ A3 ) )
% 0.18/0.45 = A3 ) ).
% 0.18/0.45
% 0.18/0.45 % Collect_mem_eq
% 0.18/0.45 thf(fact_77_Collect__cong,axiom,
% 0.18/0.45 ! [P: a > $o,Q: a > $o] :
% 0.18/0.45 ( ! [X2: a] :
% 0.18/0.45 ( ( P @ X2 )
% 0.18/0.45 = ( Q @ X2 ) )
% 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_78_neqE,axiom,
% 0.18/0.45 ! [X3: int,Y: int] :
% 0.18/0.45 ( ( X3 != Y )
% 0.18/0.45 => ( ~ ( ord_less_int @ X3 @ Y )
% 0.18/0.45 => ( ord_less_int @ Y @ X3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % neqE
% 0.18/0.45 thf(fact_79_neq__iff,axiom,
% 0.18/0.45 ! [X3: int,Y: int] :
% 0.18/0.45 ( ( X3 != Y )
% 0.18/0.45 = ( ( ord_less_int @ X3 @ Y )
% 0.18/0.45 | ( ord_less_int @ Y @ X3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % neq_iff
% 0.18/0.45 thf(fact_80_order_Oasym,axiom,
% 0.18/0.45 ! [A2: set_a,B2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A2 @ B2 )
% 0.18/0.45 => ~ ( ord_less_set_a @ B2 @ A2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.asym
% 0.18/0.45 thf(fact_81_order_Oasym,axiom,
% 0.18/0.45 ! [A2: a > $o,B2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ A2 @ B2 )
% 0.18/0.45 => ~ ( ord_less_a_o @ B2 @ A2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.asym
% 0.18/0.45 thf(fact_82_order_Oasym,axiom,
% 0.18/0.45 ! [A2: int,B2: int] :
% 0.18/0.45 ( ( ord_less_int @ A2 @ B2 )
% 0.18/0.45 => ~ ( ord_less_int @ B2 @ A2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.asym
% 0.18/0.45 thf(fact_83_less__imp__neq,axiom,
% 0.18/0.45 ! [X3: set_a,Y: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X3 @ Y )
% 0.18/0.45 => ( X3 != Y ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_neq
% 0.18/0.45 thf(fact_84_less__imp__neq,axiom,
% 0.18/0.45 ! [X3: a > $o,Y: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X3 @ Y )
% 0.18/0.45 => ( X3 != Y ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_neq
% 0.18/0.45 thf(fact_85_less__imp__neq,axiom,
% 0.18/0.45 ! [X3: int,Y: int] :
% 0.18/0.45 ( ( ord_less_int @ X3 @ Y )
% 0.18/0.45 => ( X3 != Y ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_neq
% 0.18/0.45 thf(fact_86_less__asym,axiom,
% 0.18/0.45 ! [X3: set_a,Y: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X3 @ Y )
% 0.18/0.45 => ~ ( ord_less_set_a @ Y @ X3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_asym
% 0.18/0.45 thf(fact_87_less__asym,axiom,
% 0.18/0.45 ! [X3: a > $o,Y: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X3 @ Y )
% 0.18/0.45 => ~ ( ord_less_a_o @ Y @ X3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_asym
% 0.18/0.45 thf(fact_88_less__asym,axiom,
% 0.18/0.45 ! [X3: int,Y: int] :
% 0.18/0.45 ( ( ord_less_int @ X3 @ Y )
% 0.18/0.45 => ~ ( ord_less_int @ Y @ X3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_asym
% 0.18/0.45 thf(fact_89_less__asym_H,axiom,
% 0.18/0.45 ! [A2: set_a,B2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A2 @ B2 )
% 0.18/0.45 => ~ ( ord_less_set_a @ B2 @ A2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_asym'
% 0.18/0.45 thf(fact_90_less__asym_H,axiom,
% 0.18/0.45 ! [A2: a > $o,B2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ A2 @ B2 )
% 0.18/0.45 => ~ ( ord_less_a_o @ B2 @ A2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_asym'
% 0.18/0.45 thf(fact_91_less__asym_H,axiom,
% 0.18/0.45 ! [A2: int,B2: int] :
% 0.18/0.45 ( ( ord_less_int @ A2 @ B2 )
% 0.18/0.45 => ~ ( ord_less_int @ B2 @ A2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_asym'
% 0.18/0.45 thf(fact_92_less__trans,axiom,
% 0.18/0.45 ! [X3: set_a,Y: set_a,Z3: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X3 @ Y )
% 0.18/0.45 => ( ( ord_less_set_a @ Y @ Z3 )
% 0.18/0.45 => ( ord_less_set_a @ X3 @ Z3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_trans
% 0.18/0.45 thf(fact_93_less__trans,axiom,
% 0.18/0.45 ! [X3: a > $o,Y: a > $o,Z3: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X3 @ Y )
% 0.18/0.45 => ( ( ord_less_a_o @ Y @ Z3 )
% 0.18/0.45 => ( ord_less_a_o @ X3 @ Z3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_trans
% 0.18/0.45 thf(fact_94_less__trans,axiom,
% 0.18/0.45 ! [X3: int,Y: int,Z3: int] :
% 0.18/0.45 ( ( ord_less_int @ X3 @ Y )
% 0.18/0.45 => ( ( ord_less_int @ Y @ Z3 )
% 0.18/0.45 => ( ord_less_int @ X3 @ Z3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_trans
% 0.18/0.45 thf(fact_95_less__linear,axiom,
% 0.18/0.45 ! [X3: int,Y: int] :
% 0.18/0.45 ( ( ord_less_int @ X3 @ Y )
% 0.18/0.45 | ( X3 = Y )
% 0.18/0.45 | ( ord_less_int @ Y @ X3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_linear
% 0.18/0.45 thf(fact_96_less__irrefl,axiom,
% 0.18/0.45 ! [X3: set_a] :
% 0.18/0.45 ~ ( ord_less_set_a @ X3 @ X3 ) ).
% 0.18/0.45
% 0.18/0.45 % less_irrefl
% 0.18/0.45 thf(fact_97_less__irrefl,axiom,
% 0.18/0.45 ! [X3: a > $o] :
% 0.18/0.45 ~ ( ord_less_a_o @ X3 @ X3 ) ).
% 0.18/0.45
% 0.18/0.45 % less_irrefl
% 0.18/0.45 thf(fact_98_less__irrefl,axiom,
% 0.18/0.45 ! [X3: int] :
% 0.18/0.45 ~ ( ord_less_int @ X3 @ X3 ) ).
% 0.18/0.45
% 0.18/0.45 % less_irrefl
% 0.18/0.45 thf(fact_99_ord__eq__less__trans,axiom,
% 0.18/0.45 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.18/0.45 ( ( A2 = B2 )
% 0.18/0.45 => ( ( ord_less_set_a @ B2 @ C )
% 0.18/0.45 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_trans
% 0.18/0.45 thf(fact_100_ord__eq__less__trans,axiom,
% 0.18/0.45 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 0.18/0.45 ( ( A2 = B2 )
% 0.18/0.45 => ( ( ord_less_a_o @ B2 @ C )
% 0.18/0.45 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_trans
% 0.18/0.45 thf(fact_101_ord__eq__less__trans,axiom,
% 0.18/0.45 ! [A2: int,B2: int,C: int] :
% 0.18/0.45 ( ( A2 = B2 )
% 0.18/0.45 => ( ( ord_less_int @ B2 @ C )
% 0.18/0.45 => ( ord_less_int @ A2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_eq_less_trans
% 0.18/0.45 thf(fact_102_ord__less__eq__trans,axiom,
% 0.18/0.45 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A2 @ B2 )
% 0.18/0.45 => ( ( B2 = C )
% 0.18/0.45 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_trans
% 0.18/0.45 thf(fact_103_ord__less__eq__trans,axiom,
% 0.18/0.45 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ A2 @ B2 )
% 0.18/0.45 => ( ( B2 = C )
% 0.18/0.45 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_trans
% 0.18/0.45 thf(fact_104_ord__less__eq__trans,axiom,
% 0.18/0.45 ! [A2: int,B2: int,C: int] :
% 0.18/0.45 ( ( ord_less_int @ A2 @ B2 )
% 0.18/0.45 => ( ( B2 = C )
% 0.18/0.45 => ( ord_less_int @ A2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ord_less_eq_trans
% 0.18/0.45 thf(fact_105_dual__order_Oasym,axiom,
% 0.18/0.45 ! [B2: set_a,A2: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ B2 @ A2 )
% 0.18/0.45 => ~ ( ord_less_set_a @ A2 @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.asym
% 0.18/0.45 thf(fact_106_dual__order_Oasym,axiom,
% 0.18/0.45 ! [B2: a > $o,A2: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ B2 @ A2 )
% 0.18/0.45 => ~ ( ord_less_a_o @ A2 @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.asym
% 0.18/0.45 thf(fact_107_dual__order_Oasym,axiom,
% 0.18/0.45 ! [B2: int,A2: int] :
% 0.18/0.45 ( ( ord_less_int @ B2 @ A2 )
% 0.18/0.45 => ~ ( ord_less_int @ A2 @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.asym
% 0.18/0.45 thf(fact_108_less__imp__not__eq,axiom,
% 0.18/0.45 ! [X3: set_a,Y: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X3 @ Y )
% 0.18/0.45 => ( X3 != Y ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_eq
% 0.18/0.45 thf(fact_109_less__imp__not__eq,axiom,
% 0.18/0.45 ! [X3: a > $o,Y: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X3 @ Y )
% 0.18/0.45 => ( X3 != Y ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_eq
% 0.18/0.45 thf(fact_110_less__imp__not__eq,axiom,
% 0.18/0.45 ! [X3: int,Y: int] :
% 0.18/0.45 ( ( ord_less_int @ X3 @ Y )
% 0.18/0.45 => ( X3 != Y ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_eq
% 0.18/0.45 thf(fact_111_less__not__sym,axiom,
% 0.18/0.45 ! [X3: set_a,Y: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X3 @ Y )
% 0.18/0.45 => ~ ( ord_less_set_a @ Y @ X3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_not_sym
% 0.18/0.45 thf(fact_112_less__not__sym,axiom,
% 0.18/0.45 ! [X3: a > $o,Y: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X3 @ Y )
% 0.18/0.45 => ~ ( ord_less_a_o @ Y @ X3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_not_sym
% 0.18/0.45 thf(fact_113_less__not__sym,axiom,
% 0.18/0.45 ! [X3: int,Y: int] :
% 0.18/0.45 ( ( ord_less_int @ X3 @ Y )
% 0.18/0.45 => ~ ( ord_less_int @ Y @ X3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_not_sym
% 0.18/0.45 thf(fact_114_antisym__conv3,axiom,
% 0.18/0.45 ! [Y: int,X3: int] :
% 0.18/0.45 ( ~ ( ord_less_int @ Y @ X3 )
% 0.18/0.45 => ( ( ~ ( ord_less_int @ X3 @ Y ) )
% 0.18/0.45 = ( X3 = Y ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % antisym_conv3
% 0.18/0.45 thf(fact_115_less__imp__not__eq2,axiom,
% 0.18/0.45 ! [X3: set_a,Y: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X3 @ Y )
% 0.18/0.45 => ( Y != X3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_eq2
% 0.18/0.45 thf(fact_116_less__imp__not__eq2,axiom,
% 0.18/0.45 ! [X3: a > $o,Y: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X3 @ Y )
% 0.18/0.45 => ( Y != X3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_eq2
% 0.18/0.45 thf(fact_117_less__imp__not__eq2,axiom,
% 0.18/0.45 ! [X3: int,Y: int] :
% 0.18/0.45 ( ( ord_less_int @ X3 @ Y )
% 0.18/0.45 => ( Y != X3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_eq2
% 0.18/0.45 thf(fact_118_less__imp__triv,axiom,
% 0.18/0.45 ! [X3: set_a,Y: set_a,P: $o] :
% 0.18/0.45 ( ( ord_less_set_a @ X3 @ Y )
% 0.18/0.45 => ( ( ord_less_set_a @ Y @ X3 )
% 0.18/0.45 => P ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_triv
% 0.18/0.45 thf(fact_119_less__imp__triv,axiom,
% 0.18/0.45 ! [X3: a > $o,Y: a > $o,P: $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X3 @ Y )
% 0.18/0.45 => ( ( ord_less_a_o @ Y @ X3 )
% 0.18/0.45 => P ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_triv
% 0.18/0.45 thf(fact_120_less__imp__triv,axiom,
% 0.18/0.45 ! [X3: int,Y: int,P: $o] :
% 0.18/0.45 ( ( ord_less_int @ X3 @ Y )
% 0.18/0.45 => ( ( ord_less_int @ Y @ X3 )
% 0.18/0.45 => P ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_triv
% 0.18/0.45 thf(fact_121_linorder__cases,axiom,
% 0.18/0.45 ! [X3: int,Y: int] :
% 0.18/0.45 ( ~ ( ord_less_int @ X3 @ Y )
% 0.18/0.45 => ( ( X3 != Y )
% 0.18/0.45 => ( ord_less_int @ Y @ X3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % linorder_cases
% 0.18/0.45 thf(fact_122_dual__order_Oirrefl,axiom,
% 0.18/0.45 ! [A2: set_a] :
% 0.18/0.45 ~ ( ord_less_set_a @ A2 @ A2 ) ).
% 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 ! [A2: a > $o] :
% 0.18/0.45 ~ ( ord_less_a_o @ A2 @ A2 ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.irrefl
% 0.18/0.45 thf(fact_124_dual__order_Oirrefl,axiom,
% 0.18/0.45 ! [A2: int] :
% 0.18/0.45 ~ ( ord_less_int @ A2 @ A2 ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.irrefl
% 0.18/0.45 thf(fact_125_order_Ostrict__trans,axiom,
% 0.18/0.45 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A2 @ B2 )
% 0.18/0.45 => ( ( ord_less_set_a @ B2 @ C )
% 0.18/0.45 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.strict_trans
% 0.18/0.45 thf(fact_126_order_Ostrict__trans,axiom,
% 0.18/0.45 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ A2 @ B2 )
% 0.18/0.45 => ( ( ord_less_a_o @ B2 @ C )
% 0.18/0.45 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.strict_trans
% 0.18/0.45 thf(fact_127_order_Ostrict__trans,axiom,
% 0.18/0.45 ! [A2: int,B2: int,C: int] :
% 0.18/0.45 ( ( ord_less_int @ A2 @ B2 )
% 0.18/0.45 => ( ( ord_less_int @ B2 @ C )
% 0.18/0.45 => ( ord_less_int @ A2 @ C ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % order.strict_trans
% 0.18/0.45 thf(fact_128_less__imp__not__less,axiom,
% 0.18/0.45 ! [X3: set_a,Y: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ X3 @ Y )
% 0.18/0.45 => ~ ( ord_less_set_a @ Y @ X3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_less
% 0.18/0.45 thf(fact_129_less__imp__not__less,axiom,
% 0.18/0.45 ! [X3: a > $o,Y: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ X3 @ Y )
% 0.18/0.45 => ~ ( ord_less_a_o @ Y @ X3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_less
% 0.18/0.45 thf(fact_130_less__imp__not__less,axiom,
% 0.18/0.45 ! [X3: int,Y: int] :
% 0.18/0.45 ( ( ord_less_int @ X3 @ Y )
% 0.18/0.45 => ~ ( ord_less_int @ Y @ X3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % less_imp_not_less
% 0.18/0.45 thf(fact_131_linorder__less__wlog,axiom,
% 0.18/0.45 ! [P: int > int > $o,A2: int,B2: 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 @ A2 @ B2 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % linorder_less_wlog
% 0.18/0.45 thf(fact_132_dual__order_Ostrict__trans,axiom,
% 0.18/0.45 ! [B2: set_a,A2: set_a,C: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ B2 @ A2 )
% 0.18/0.45 => ( ( ord_less_set_a @ C @ B2 )
% 0.18/0.45 => ( ord_less_set_a @ C @ A2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.strict_trans
% 0.18/0.45 thf(fact_133_dual__order_Ostrict__trans,axiom,
% 0.18/0.45 ! [B2: a > $o,A2: a > $o,C: a > $o] :
% 0.18/0.45 ( ( ord_less_a_o @ B2 @ A2 )
% 0.18/0.45 => ( ( ord_less_a_o @ C @ B2 )
% 0.18/0.45 => ( ord_less_a_o @ C @ A2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.strict_trans
% 0.18/0.45 thf(fact_134_dual__order_Ostrict__trans,axiom,
% 0.18/0.45 ! [B2: int,A2: int,C: int] :
% 0.18/0.45 ( ( ord_less_int @ B2 @ A2 )
% 0.18/0.45 => ( ( ord_less_int @ C @ B2 )
% 0.18/0.45 => ( ord_less_int @ C @ A2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % dual_order.strict_trans
% 0.18/0.45 thf(fact_135_not__less__iff__gr__or__eq,axiom,
% 0.18/0.45 ! [X3: int,Y: int] :
% 0.18/0.45 ( ( ~ ( ord_less_int @ X3 @ Y ) )
% 0.18/0.45 = ( ( ord_less_int @ Y @ X3 )
% 0.18/0.45 | ( X3 = Y ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % not_less_iff_gr_or_eq
% 0.18/0.45 thf(fact_136_binsert_Osimps_I1_J,axiom,
% 0.18/0.45 ! [H: a > int,E: a] :
% 0.18/0.45 ( ( binary1226383794sert_a @ H @ E @ binary476621312_Tip_a )
% 0.18/0.45 = ( binary717961607le_T_a @ binary476621312_Tip_a @ E @ binary476621312_Tip_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % binsert.simps(1)
% 0.18/0.45 thf(fact_137_verit__comp__simplify1_I1_J,axiom,
% 0.18/0.45 ! [A2: set_a] :
% 0.18/0.45 ~ ( ord_less_set_a @ A2 @ A2 ) ).
% 0.18/0.45
% 0.18/0.45 % verit_comp_simplify1(1)
% 0.18/0.45 thf(fact_138_verit__comp__simplify1_I1_J,axiom,
% 0.18/0.45 ! [A2: a > $o] :
% 0.18/0.45 ~ ( ord_less_a_o @ A2 @ A2 ) ).
% 0.18/0.45
% 0.18/0.45 % verit_comp_simplify1(1)
% 0.18/0.45 thf(fact_139_verit__comp__simplify1_I1_J,axiom,
% 0.18/0.45 ! [A2: int] :
% 0.18/0.45 ~ ( ord_less_int @ A2 @ A2 ) ).
% 0.18/0.45
% 0.18/0.45 % verit_comp_simplify1(1)
% 0.18/0.45 thf(fact_140_c2,axiom,
% 0.18/0.45 ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t2 ) )
% 0.18/0.45 = ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t2 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % c2
% 0.18/0.45 thf(fact_141_c1,axiom,
% 0.18/0.45 ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t1 ) )
% 0.18/0.45 = ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t1 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % c1
% 0.18/0.45 thf(fact_142_Tree_Opred__inject_I2_J,axiom,
% 0.18/0.45 ! [P: a > $o,A2: binary1439146945Tree_a,Aa: a,Ab: binary1439146945Tree_a] :
% 0.18/0.45 ( ( binary1452917696Tree_a @ P @ ( binary717961607le_T_a @ A2 @ Aa @ Ab ) )
% 0.18/0.45 = ( ( binary1452917696Tree_a @ P @ A2 )
% 0.18/0.45 & ( P @ Aa )
% 0.18/0.45 & ( binary1452917696Tree_a @ P @ Ab ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Tree.pred_inject(2)
% 0.18/0.45 thf(fact_143_bot__apply,axiom,
% 0.18/0.45 ( bot_bot_a_o
% 0.18/0.45 = ( ^ [X4: a] : bot_bot_o ) ) ).
% 0.18/0.45
% 0.18/0.45 % bot_apply
% 0.18/0.45 thf(fact_144_bot__fun__def,axiom,
% 0.18/0.45 ( bot_bot_a_o
% 0.18/0.45 = ( ^ [X4: a] : bot_bot_o ) ) ).
% 0.18/0.45
% 0.18/0.45 % bot_fun_def
% 0.18/0.45 thf(fact_145_Tree_Opred__inject_I1_J,axiom,
% 0.18/0.45 ! [P: a > $o] : ( binary1452917696Tree_a @ P @ binary476621312_Tip_a ) ).
% 0.18/0.45
% 0.18/0.45 % Tree.pred_inject(1)
% 0.18/0.45 thf(fact_146_setOf_Osimps_I2_J,axiom,
% 0.18/0.45 ! [T1: binary1439146945Tree_a,X3: a,T2: binary1439146945Tree_a] :
% 0.18/0.45 ( ( binary945792244etOf_a @ ( binary717961607le_T_a @ T1 @ X3 @ T2 ) )
% 0.18/0.45 = ( sup_sup_set_a @ ( sup_sup_set_a @ ( binary945792244etOf_a @ T1 ) @ ( binary945792244etOf_a @ T2 ) ) @ ( insert_a @ X3 @ bot_bot_set_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % setOf.simps(2)
% 0.18/0.45 thf(fact_147_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_148_bot_Onot__eq__extremum,axiom,
% 0.18/0.45 ! [A2: a > $o] :
% 0.18/0.45 ( ( A2 != bot_bot_a_o )
% 0.18/0.45 = ( ord_less_a_o @ bot_bot_a_o @ A2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % bot.not_eq_extremum
% 0.18/0.45 thf(fact_149_bot_Onot__eq__extremum,axiom,
% 0.18/0.45 ! [A2: set_a] :
% 0.18/0.45 ( ( A2 != bot_bot_set_a )
% 0.18/0.45 = ( ord_less_set_a @ bot_bot_set_a @ A2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % bot.not_eq_extremum
% 0.18/0.45 thf(fact_150_bot_Oextremum__strict,axiom,
% 0.18/0.45 ! [A2: a > $o] :
% 0.18/0.45 ~ ( ord_less_a_o @ A2 @ bot_bot_a_o ) ).
% 0.18/0.45
% 0.18/0.45 % bot.extremum_strict
% 0.18/0.45 thf(fact_151_bot_Oextremum__strict,axiom,
% 0.18/0.45 ! [A2: set_a] :
% 0.18/0.45 ~ ( ord_less_set_a @ A2 @ bot_bot_set_a ) ).
% 0.18/0.45
% 0.18/0.45 % bot.extremum_strict
% 0.18/0.45 thf(fact_152_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_153_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_154_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_155_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_156_insert__Diff__single,axiom,
% 0.18/0.45 ! [A2: a,A3: set_a] :
% 0.18/0.45 ( ( insert_a @ A2 @ ( minus_minus_set_a @ A3 @ ( insert_a @ A2 @ bot_bot_set_a ) ) )
% 0.18/0.45 = ( insert_a @ A2 @ A3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % insert_Diff_single
% 0.18/0.45 thf(fact_157_Un__Diff__cancel,axiom,
% 0.18/0.45 ! [A3: set_a,B4: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ A3 @ ( minus_minus_set_a @ B4 @ A3 ) )
% 0.18/0.45 = ( sup_sup_set_a @ A3 @ B4 ) ) ).
% 0.18/0.45
% 0.18/0.45 % Un_Diff_cancel
% 0.18/0.45 thf(fact_158_Un__Diff__cancel2,axiom,
% 0.18/0.45 ! [B4: set_a,A3: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ ( minus_minus_set_a @ B4 @ A3 ) @ A3 )
% 0.18/0.45 = ( sup_sup_set_a @ B4 @ A3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % Un_Diff_cancel2
% 0.18/0.45 thf(fact_159_Diff__insert0,axiom,
% 0.18/0.45 ! [X3: a,A3: set_a,B4: set_a] :
% 0.18/0.45 ( ~ ( member_a @ X3 @ A3 )
% 0.18/0.45 => ( ( minus_minus_set_a @ A3 @ ( insert_a @ X3 @ B4 ) )
% 0.18/0.45 = ( minus_minus_set_a @ A3 @ B4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Diff_insert0
% 0.18/0.45 thf(fact_160_insert__Diff1,axiom,
% 0.18/0.45 ! [X3: a,B4: set_a,A3: set_a] :
% 0.18/0.45 ( ( member_a @ X3 @ B4 )
% 0.18/0.45 => ( ( minus_minus_set_a @ ( insert_a @ X3 @ A3 ) @ B4 )
% 0.18/0.45 = ( minus_minus_set_a @ A3 @ B4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % insert_Diff1
% 0.18/0.45 thf(fact_161_Un__insert__left,axiom,
% 0.18/0.45 ! [A2: a,B4: set_a,C2: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ ( insert_a @ A2 @ B4 ) @ C2 )
% 0.18/0.45 = ( insert_a @ A2 @ ( sup_sup_set_a @ B4 @ C2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Un_insert_left
% 0.18/0.45 thf(fact_162_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 = ( ! [X4: a] :
% 0.18/0.45 ~ ( P @ X4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % empty_Collect_eq
% 0.18/0.45 thf(fact_163_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 = ( ! [X4: a] :
% 0.18/0.45 ~ ( P @ X4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Collect_empty_eq
% 0.18/0.45 thf(fact_164_all__not__in__conv,axiom,
% 0.18/0.45 ! [A3: set_a] :
% 0.18/0.45 ( ( ! [X4: a] :
% 0.18/0.45 ~ ( member_a @ X4 @ 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_165_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_166_insert__absorb2,axiom,
% 0.18/0.45 ! [X3: a,A3: set_a] :
% 0.18/0.45 ( ( insert_a @ X3 @ ( insert_a @ X3 @ A3 ) )
% 0.18/0.45 = ( insert_a @ X3 @ A3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % insert_absorb2
% 0.18/0.45 thf(fact_167_insert__iff,axiom,
% 0.18/0.45 ! [A2: a,B2: a,A3: set_a] :
% 0.18/0.45 ( ( member_a @ A2 @ ( insert_a @ B2 @ A3 ) )
% 0.18/0.45 = ( ( A2 = B2 )
% 0.18/0.45 | ( member_a @ A2 @ A3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % insert_iff
% 0.18/0.45 thf(fact_168_insertCI,axiom,
% 0.18/0.45 ! [A2: a,B4: set_a,B2: a] :
% 0.18/0.45 ( ( ~ ( member_a @ A2 @ B4 )
% 0.18/0.45 => ( A2 = B2 ) )
% 0.18/0.45 => ( member_a @ A2 @ ( insert_a @ B2 @ B4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % insertCI
% 0.18/0.45 thf(fact_169_Un__iff,axiom,
% 0.18/0.45 ! [C: a,A3: set_a,B4: set_a] :
% 0.18/0.45 ( ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) )
% 0.18/0.45 = ( ( member_a @ C @ A3 )
% 0.18/0.45 | ( member_a @ C @ B4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Un_iff
% 0.18/0.45 thf(fact_170_UnCI,axiom,
% 0.18/0.45 ! [C: a,B4: set_a,A3: set_a] :
% 0.18/0.45 ( ( ~ ( member_a @ C @ B4 )
% 0.18/0.45 => ( member_a @ C @ A3 ) )
% 0.18/0.45 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % UnCI
% 0.18/0.45 thf(fact_171_Diff__idemp,axiom,
% 0.18/0.45 ! [A3: set_a,B4: set_a] :
% 0.18/0.45 ( ( minus_minus_set_a @ ( minus_minus_set_a @ A3 @ B4 ) @ B4 )
% 0.18/0.45 = ( minus_minus_set_a @ A3 @ B4 ) ) ).
% 0.18/0.45
% 0.18/0.45 % Diff_idemp
% 0.18/0.45 thf(fact_172_Diff__iff,axiom,
% 0.18/0.45 ! [C: a,A3: set_a,B4: set_a] :
% 0.18/0.45 ( ( member_a @ C @ ( minus_minus_set_a @ A3 @ B4 ) )
% 0.18/0.45 = ( ( member_a @ C @ A3 )
% 0.18/0.45 & ~ ( member_a @ C @ B4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Diff_iff
% 0.18/0.45 thf(fact_173_DiffI,axiom,
% 0.18/0.45 ! [C: a,A3: set_a,B4: set_a] :
% 0.18/0.45 ( ( member_a @ C @ A3 )
% 0.18/0.45 => ( ~ ( member_a @ C @ B4 )
% 0.18/0.45 => ( member_a @ C @ ( minus_minus_set_a @ A3 @ B4 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % DiffI
% 0.18/0.45 thf(fact_174_singletonI,axiom,
% 0.18/0.45 ! [A2: a] : ( member_a @ A2 @ ( insert_a @ A2 @ bot_bot_set_a ) ) ).
% 0.18/0.45
% 0.18/0.45 % singletonI
% 0.18/0.45 thf(fact_175_Un__empty,axiom,
% 0.18/0.45 ! [A3: set_a,B4: set_a] :
% 0.18/0.45 ( ( ( sup_sup_set_a @ A3 @ B4 )
% 0.18/0.45 = bot_bot_set_a )
% 0.18/0.45 = ( ( A3 = bot_bot_set_a )
% 0.18/0.45 & ( B4 = bot_bot_set_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Un_empty
% 0.18/0.45 thf(fact_176_Diff__cancel,axiom,
% 0.18/0.45 ! [A3: set_a] :
% 0.18/0.45 ( ( minus_minus_set_a @ A3 @ A3 )
% 0.18/0.45 = bot_bot_set_a ) ).
% 0.18/0.45
% 0.18/0.45 % Diff_cancel
% 0.18/0.45 thf(fact_177_empty__Diff,axiom,
% 0.18/0.45 ! [A3: set_a] :
% 0.18/0.45 ( ( minus_minus_set_a @ bot_bot_set_a @ A3 )
% 0.18/0.45 = bot_bot_set_a ) ).
% 0.18/0.45
% 0.18/0.45 % empty_Diff
% 0.18/0.45 thf(fact_178_Diff__empty,axiom,
% 0.18/0.45 ! [A3: set_a] :
% 0.18/0.45 ( ( minus_minus_set_a @ A3 @ bot_bot_set_a )
% 0.18/0.45 = A3 ) ).
% 0.18/0.45
% 0.18/0.45 % Diff_empty
% 0.18/0.45 thf(fact_179_Un__insert__right,axiom,
% 0.18/0.45 ! [A3: set_a,A2: a,B4: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ A3 @ ( insert_a @ A2 @ B4 ) )
% 0.18/0.45 = ( insert_a @ A2 @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Un_insert_right
% 0.18/0.45 thf(fact_180_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_181_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_182_ex__in__conv,axiom,
% 0.18/0.45 ! [A3: set_a] :
% 0.18/0.45 ( ( ? [X4: a] : ( member_a @ X4 @ 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_183_equals0I,axiom,
% 0.18/0.45 ! [A3: set_a] :
% 0.18/0.45 ( ! [Y2: a] :
% 0.18/0.45 ~ ( member_a @ Y2 @ 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_184_equals0D,axiom,
% 0.18/0.45 ! [A3: set_a,A2: a] :
% 0.18/0.45 ( ( A3 = bot_bot_set_a )
% 0.18/0.45 => ~ ( member_a @ A2 @ A3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % equals0D
% 0.18/0.45 thf(fact_185_emptyE,axiom,
% 0.18/0.45 ! [A2: a] :
% 0.18/0.45 ~ ( member_a @ A2 @ bot_bot_set_a ) ).
% 0.18/0.45
% 0.18/0.45 % emptyE
% 0.18/0.45 thf(fact_186_mk__disjoint__insert,axiom,
% 0.18/0.45 ! [A2: a,A3: set_a] :
% 0.18/0.45 ( ( member_a @ A2 @ A3 )
% 0.18/0.45 => ? [B5: set_a] :
% 0.18/0.45 ( ( A3
% 0.18/0.45 = ( insert_a @ A2 @ B5 ) )
% 0.18/0.45 & ~ ( member_a @ A2 @ B5 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % mk_disjoint_insert
% 0.18/0.45 thf(fact_187_insert__commute,axiom,
% 0.18/0.45 ! [X3: a,Y: a,A3: set_a] :
% 0.18/0.45 ( ( insert_a @ X3 @ ( insert_a @ Y @ A3 ) )
% 0.18/0.45 = ( insert_a @ Y @ ( insert_a @ X3 @ A3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % insert_commute
% 0.18/0.45 thf(fact_188_insert__eq__iff,axiom,
% 0.18/0.45 ! [A2: a,A3: set_a,B2: a,B4: set_a] :
% 0.18/0.45 ( ~ ( member_a @ A2 @ A3 )
% 0.18/0.45 => ( ~ ( member_a @ B2 @ B4 )
% 0.18/0.45 => ( ( ( insert_a @ A2 @ A3 )
% 0.18/0.45 = ( insert_a @ B2 @ B4 ) )
% 0.18/0.45 = ( ( ( A2 = B2 )
% 0.18/0.45 => ( A3 = B4 ) )
% 0.18/0.45 & ( ( A2 != B2 )
% 0.18/0.45 => ? [C3: set_a] :
% 0.18/0.45 ( ( A3
% 0.18/0.45 = ( insert_a @ B2 @ C3 ) )
% 0.18/0.45 & ~ ( member_a @ B2 @ C3 )
% 0.18/0.45 & ( B4
% 0.18/0.45 = ( insert_a @ A2 @ C3 ) )
% 0.18/0.45 & ~ ( member_a @ A2 @ C3 ) ) ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % insert_eq_iff
% 0.18/0.45 thf(fact_189_insert__absorb,axiom,
% 0.18/0.45 ! [A2: a,A3: set_a] :
% 0.18/0.45 ( ( member_a @ A2 @ A3 )
% 0.18/0.45 => ( ( insert_a @ A2 @ A3 )
% 0.18/0.45 = A3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % insert_absorb
% 0.18/0.45 thf(fact_190_insert__ident,axiom,
% 0.18/0.45 ! [X3: a,A3: set_a,B4: set_a] :
% 0.18/0.45 ( ~ ( member_a @ X3 @ A3 )
% 0.18/0.45 => ( ~ ( member_a @ X3 @ B4 )
% 0.18/0.45 => ( ( ( insert_a @ X3 @ A3 )
% 0.18/0.45 = ( insert_a @ X3 @ B4 ) )
% 0.18/0.45 = ( A3 = B4 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % insert_ident
% 0.18/0.45 thf(fact_191_Set_Oset__insert,axiom,
% 0.18/0.45 ! [X3: a,A3: set_a] :
% 0.18/0.45 ( ( member_a @ X3 @ A3 )
% 0.18/0.45 => ~ ! [B5: set_a] :
% 0.18/0.45 ( ( A3
% 0.18/0.45 = ( insert_a @ X3 @ B5 ) )
% 0.18/0.45 => ( member_a @ X3 @ B5 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Set.set_insert
% 0.18/0.45 thf(fact_192_insertI2,axiom,
% 0.18/0.45 ! [A2: a,B4: set_a,B2: a] :
% 0.18/0.45 ( ( member_a @ A2 @ B4 )
% 0.18/0.45 => ( member_a @ A2 @ ( insert_a @ B2 @ B4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % insertI2
% 0.18/0.45 thf(fact_193_insertI1,axiom,
% 0.18/0.45 ! [A2: a,B4: set_a] : ( member_a @ A2 @ ( insert_a @ A2 @ B4 ) ) ).
% 0.18/0.45
% 0.18/0.45 % insertI1
% 0.18/0.45 thf(fact_194_insertE,axiom,
% 0.18/0.45 ! [A2: a,B2: a,A3: set_a] :
% 0.18/0.45 ( ( member_a @ A2 @ ( insert_a @ B2 @ A3 ) )
% 0.18/0.45 => ( ( A2 != B2 )
% 0.18/0.45 => ( member_a @ A2 @ A3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % insertE
% 0.18/0.45 thf(fact_195_Un__left__commute,axiom,
% 0.18/0.45 ! [A3: set_a,B4: set_a,C2: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ A3 @ ( sup_sup_set_a @ B4 @ C2 ) )
% 0.18/0.45 = ( sup_sup_set_a @ B4 @ ( sup_sup_set_a @ A3 @ C2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Un_left_commute
% 0.18/0.45 thf(fact_196_Un__left__absorb,axiom,
% 0.18/0.45 ! [A3: set_a,B4: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ A3 @ ( sup_sup_set_a @ A3 @ B4 ) )
% 0.18/0.45 = ( sup_sup_set_a @ A3 @ B4 ) ) ).
% 0.18/0.45
% 0.18/0.45 % Un_left_absorb
% 0.18/0.45 thf(fact_197_Un__commute,axiom,
% 0.18/0.45 ( sup_sup_set_a
% 0.18/0.45 = ( ^ [A5: set_a,B6: set_a] : ( sup_sup_set_a @ B6 @ A5 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Un_commute
% 0.18/0.45 thf(fact_198_Un__absorb,axiom,
% 0.18/0.45 ! [A3: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ A3 @ A3 )
% 0.18/0.45 = A3 ) ).
% 0.18/0.45
% 0.18/0.45 % Un_absorb
% 0.18/0.45 thf(fact_199_Un__assoc,axiom,
% 0.18/0.45 ! [A3: set_a,B4: set_a,C2: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ ( sup_sup_set_a @ A3 @ B4 ) @ C2 )
% 0.18/0.45 = ( sup_sup_set_a @ A3 @ ( sup_sup_set_a @ B4 @ C2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Un_assoc
% 0.18/0.45 thf(fact_200_ball__Un,axiom,
% 0.18/0.45 ! [A3: set_a,B4: set_a,P: a > $o] :
% 0.18/0.45 ( ( ! [X4: a] :
% 0.18/0.45 ( ( member_a @ X4 @ ( sup_sup_set_a @ A3 @ B4 ) )
% 0.18/0.45 => ( P @ X4 ) ) )
% 0.18/0.45 = ( ! [X4: a] :
% 0.18/0.45 ( ( member_a @ X4 @ A3 )
% 0.18/0.45 => ( P @ X4 ) )
% 0.18/0.45 & ! [X4: a] :
% 0.18/0.45 ( ( member_a @ X4 @ B4 )
% 0.18/0.45 => ( P @ X4 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % ball_Un
% 0.18/0.45 thf(fact_201_bex__Un,axiom,
% 0.18/0.45 ! [A3: set_a,B4: set_a,P: a > $o] :
% 0.18/0.45 ( ( ? [X4: a] :
% 0.18/0.45 ( ( member_a @ X4 @ ( sup_sup_set_a @ A3 @ B4 ) )
% 0.18/0.45 & ( P @ X4 ) ) )
% 0.18/0.45 = ( ? [X4: a] :
% 0.18/0.45 ( ( member_a @ X4 @ A3 )
% 0.18/0.45 & ( P @ X4 ) )
% 0.18/0.45 | ? [X4: a] :
% 0.18/0.45 ( ( member_a @ X4 @ B4 )
% 0.18/0.45 & ( P @ X4 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % bex_Un
% 0.18/0.45 thf(fact_202_UnI2,axiom,
% 0.18/0.45 ! [C: a,B4: set_a,A3: set_a] :
% 0.18/0.45 ( ( member_a @ C @ B4 )
% 0.18/0.45 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % UnI2
% 0.18/0.45 thf(fact_203_UnI1,axiom,
% 0.18/0.45 ! [C: a,A3: set_a,B4: set_a] :
% 0.18/0.45 ( ( member_a @ C @ A3 )
% 0.18/0.45 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % UnI1
% 0.18/0.45 thf(fact_204_UnE,axiom,
% 0.18/0.45 ! [C: a,A3: set_a,B4: set_a] :
% 0.18/0.45 ( ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) )
% 0.18/0.45 => ( ~ ( member_a @ C @ A3 )
% 0.18/0.45 => ( member_a @ C @ B4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % UnE
% 0.18/0.45 thf(fact_205_psubset__imp__ex__mem,axiom,
% 0.18/0.45 ! [A3: set_a,B4: set_a] :
% 0.18/0.45 ( ( ord_less_set_a @ A3 @ B4 )
% 0.18/0.45 => ? [B3: a] : ( member_a @ B3 @ ( minus_minus_set_a @ B4 @ A3 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % psubset_imp_ex_mem
% 0.18/0.45 thf(fact_206_DiffD2,axiom,
% 0.18/0.45 ! [C: a,A3: set_a,B4: set_a] :
% 0.18/0.45 ( ( member_a @ C @ ( minus_minus_set_a @ A3 @ B4 ) )
% 0.18/0.45 => ~ ( member_a @ C @ B4 ) ) ).
% 0.18/0.45
% 0.18/0.45 % DiffD2
% 0.18/0.45 thf(fact_207_DiffD1,axiom,
% 0.18/0.45 ! [C: a,A3: set_a,B4: set_a] :
% 0.18/0.45 ( ( member_a @ C @ ( minus_minus_set_a @ A3 @ B4 ) )
% 0.18/0.45 => ( member_a @ C @ A3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % DiffD1
% 0.18/0.45 thf(fact_208_DiffE,axiom,
% 0.18/0.45 ! [C: a,A3: set_a,B4: set_a] :
% 0.18/0.45 ( ( member_a @ C @ ( minus_minus_set_a @ A3 @ B4 ) )
% 0.18/0.45 => ~ ( ( member_a @ C @ A3 )
% 0.18/0.45 => ( member_a @ C @ B4 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % DiffE
% 0.18/0.45 thf(fact_209_singleton__inject,axiom,
% 0.18/0.45 ! [A2: a,B2: a] :
% 0.18/0.45 ( ( ( insert_a @ A2 @ bot_bot_set_a )
% 0.18/0.45 = ( insert_a @ B2 @ bot_bot_set_a ) )
% 0.18/0.45 => ( A2 = B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % singleton_inject
% 0.18/0.45 thf(fact_210_insert__not__empty,axiom,
% 0.18/0.45 ! [A2: a,A3: set_a] :
% 0.18/0.45 ( ( insert_a @ A2 @ A3 )
% 0.18/0.45 != bot_bot_set_a ) ).
% 0.18/0.45
% 0.18/0.45 % insert_not_empty
% 0.18/0.45 thf(fact_211_doubleton__eq__iff,axiom,
% 0.18/0.45 ! [A2: a,B2: a,C: a,D: a] :
% 0.18/0.45 ( ( ( insert_a @ A2 @ ( insert_a @ B2 @ bot_bot_set_a ) )
% 0.18/0.45 = ( insert_a @ C @ ( insert_a @ D @ bot_bot_set_a ) ) )
% 0.18/0.45 = ( ( ( A2 = C )
% 0.18/0.45 & ( B2 = D ) )
% 0.18/0.45 | ( ( A2 = D )
% 0.18/0.45 & ( B2 = C ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % doubleton_eq_iff
% 0.18/0.45 thf(fact_212_singleton__iff,axiom,
% 0.18/0.45 ! [B2: a,A2: a] :
% 0.18/0.45 ( ( member_a @ B2 @ ( insert_a @ A2 @ bot_bot_set_a ) )
% 0.18/0.45 = ( B2 = A2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % singleton_iff
% 0.18/0.45 thf(fact_213_singletonD,axiom,
% 0.18/0.45 ! [B2: a,A2: a] :
% 0.18/0.45 ( ( member_a @ B2 @ ( insert_a @ A2 @ bot_bot_set_a ) )
% 0.18/0.45 => ( B2 = A2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % singletonD
% 0.18/0.45 thf(fact_214_Un__empty__right,axiom,
% 0.18/0.45 ! [A3: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ A3 @ bot_bot_set_a )
% 0.18/0.45 = A3 ) ).
% 0.18/0.45
% 0.18/0.45 % Un_empty_right
% 0.18/0.45 thf(fact_215_Un__empty__left,axiom,
% 0.18/0.45 ! [B4: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ bot_bot_set_a @ B4 )
% 0.18/0.45 = B4 ) ).
% 0.18/0.45
% 0.18/0.45 % Un_empty_left
% 0.18/0.45 thf(fact_216_insert__Diff__if,axiom,
% 0.18/0.45 ! [X3: a,B4: set_a,A3: set_a] :
% 0.18/0.45 ( ( ( member_a @ X3 @ B4 )
% 0.18/0.45 => ( ( minus_minus_set_a @ ( insert_a @ X3 @ A3 ) @ B4 )
% 0.18/0.45 = ( minus_minus_set_a @ A3 @ B4 ) ) )
% 0.18/0.45 & ( ~ ( member_a @ X3 @ B4 )
% 0.18/0.45 => ( ( minus_minus_set_a @ ( insert_a @ X3 @ A3 ) @ B4 )
% 0.18/0.45 = ( insert_a @ X3 @ ( minus_minus_set_a @ A3 @ B4 ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % insert_Diff_if
% 0.18/0.45 thf(fact_217_Un__Diff,axiom,
% 0.18/0.45 ! [A3: set_a,B4: set_a,C2: set_a] :
% 0.18/0.45 ( ( minus_minus_set_a @ ( sup_sup_set_a @ A3 @ B4 ) @ C2 )
% 0.18/0.45 = ( sup_sup_set_a @ ( minus_minus_set_a @ A3 @ C2 ) @ ( minus_minus_set_a @ B4 @ C2 ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Un_Diff
% 0.18/0.45 thf(fact_218_singleton__Un__iff,axiom,
% 0.18/0.45 ! [X3: a,A3: set_a,B4: set_a] :
% 0.18/0.45 ( ( ( insert_a @ X3 @ bot_bot_set_a )
% 0.18/0.45 = ( sup_sup_set_a @ A3 @ B4 ) )
% 0.18/0.45 = ( ( ( A3 = bot_bot_set_a )
% 0.18/0.45 & ( B4
% 0.18/0.45 = ( insert_a @ X3 @ bot_bot_set_a ) ) )
% 0.18/0.45 | ( ( A3
% 0.18/0.45 = ( insert_a @ X3 @ bot_bot_set_a ) )
% 0.18/0.45 & ( B4 = bot_bot_set_a ) )
% 0.18/0.45 | ( ( A3
% 0.18/0.45 = ( insert_a @ X3 @ bot_bot_set_a ) )
% 0.18/0.45 & ( B4
% 0.18/0.45 = ( insert_a @ X3 @ bot_bot_set_a ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % singleton_Un_iff
% 0.18/0.45 thf(fact_219_Un__singleton__iff,axiom,
% 0.18/0.45 ! [A3: set_a,B4: set_a,X3: a] :
% 0.18/0.45 ( ( ( sup_sup_set_a @ A3 @ B4 )
% 0.18/0.45 = ( insert_a @ X3 @ bot_bot_set_a ) )
% 0.18/0.45 = ( ( ( A3 = bot_bot_set_a )
% 0.18/0.45 & ( B4
% 0.18/0.45 = ( insert_a @ X3 @ bot_bot_set_a ) ) )
% 0.18/0.45 | ( ( A3
% 0.18/0.45 = ( insert_a @ X3 @ bot_bot_set_a ) )
% 0.18/0.45 & ( B4 = bot_bot_set_a ) )
% 0.18/0.45 | ( ( A3
% 0.18/0.45 = ( insert_a @ X3 @ bot_bot_set_a ) )
% 0.18/0.45 & ( B4
% 0.18/0.45 = ( insert_a @ X3 @ bot_bot_set_a ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Un_singleton_iff
% 0.18/0.45 thf(fact_220_insert__is__Un,axiom,
% 0.18/0.45 ( insert_a
% 0.18/0.45 = ( ^ [A: a] : ( sup_sup_set_a @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % insert_is_Un
% 0.18/0.45 thf(fact_221_Diff__insert__absorb,axiom,
% 0.18/0.45 ! [X3: a,A3: set_a] :
% 0.18/0.45 ( ~ ( member_a @ X3 @ A3 )
% 0.18/0.45 => ( ( minus_minus_set_a @ ( insert_a @ X3 @ A3 ) @ ( insert_a @ X3 @ bot_bot_set_a ) )
% 0.18/0.45 = A3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % Diff_insert_absorb
% 0.18/0.45 thf(fact_222_Diff__insert2,axiom,
% 0.18/0.45 ! [A3: set_a,A2: a,B4: set_a] :
% 0.18/0.45 ( ( minus_minus_set_a @ A3 @ ( insert_a @ A2 @ B4 ) )
% 0.18/0.45 = ( minus_minus_set_a @ ( minus_minus_set_a @ A3 @ ( insert_a @ A2 @ bot_bot_set_a ) ) @ B4 ) ) ).
% 0.18/0.45
% 0.18/0.45 % Diff_insert2
% 0.18/0.45 thf(fact_223_insert__Diff,axiom,
% 0.18/0.45 ! [A2: a,A3: set_a] :
% 0.18/0.45 ( ( member_a @ A2 @ A3 )
% 0.18/0.45 => ( ( insert_a @ A2 @ ( minus_minus_set_a @ A3 @ ( insert_a @ A2 @ bot_bot_set_a ) ) )
% 0.18/0.45 = A3 ) ) ).
% 0.18/0.45
% 0.18/0.45 % insert_Diff
% 0.18/0.45 thf(fact_224_Diff__insert,axiom,
% 0.18/0.45 ! [A3: set_a,A2: a,B4: set_a] :
% 0.18/0.45 ( ( minus_minus_set_a @ A3 @ ( insert_a @ A2 @ B4 ) )
% 0.18/0.45 = ( minus_minus_set_a @ ( minus_minus_set_a @ A3 @ B4 ) @ ( insert_a @ A2 @ bot_bot_set_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % Diff_insert
% 0.18/0.45 thf(fact_225_sup__bot_Oright__neutral,axiom,
% 0.18/0.45 ! [A2: a > $o] :
% 0.18/0.45 ( ( sup_sup_a_o @ A2 @ bot_bot_a_o )
% 0.18/0.45 = A2 ) ).
% 0.18/0.45
% 0.18/0.45 % sup_bot.right_neutral
% 0.18/0.45 thf(fact_226_sup__bot_Oright__neutral,axiom,
% 0.18/0.45 ! [A2: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ A2 @ bot_bot_set_a )
% 0.18/0.45 = A2 ) ).
% 0.18/0.45
% 0.18/0.45 % sup_bot.right_neutral
% 0.18/0.45 thf(fact_227_sup__bot_Oneutr__eq__iff,axiom,
% 0.18/0.45 ! [A2: a > $o,B2: a > $o] :
% 0.18/0.45 ( ( bot_bot_a_o
% 0.18/0.45 = ( sup_sup_a_o @ A2 @ B2 ) )
% 0.18/0.45 = ( ( A2 = bot_bot_a_o )
% 0.18/0.45 & ( B2 = bot_bot_a_o ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sup_bot.neutr_eq_iff
% 0.18/0.45 thf(fact_228_sup__bot_Oneutr__eq__iff,axiom,
% 0.18/0.45 ! [A2: set_a,B2: set_a] :
% 0.18/0.45 ( ( bot_bot_set_a
% 0.18/0.45 = ( sup_sup_set_a @ A2 @ B2 ) )
% 0.18/0.45 = ( ( A2 = bot_bot_set_a )
% 0.18/0.45 & ( B2 = bot_bot_set_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sup_bot.neutr_eq_iff
% 0.18/0.45 thf(fact_229_sup__bot_Oleft__neutral,axiom,
% 0.18/0.45 ! [A2: a > $o] :
% 0.18/0.45 ( ( sup_sup_a_o @ bot_bot_a_o @ A2 )
% 0.18/0.45 = A2 ) ).
% 0.18/0.45
% 0.18/0.45 % sup_bot.left_neutral
% 0.18/0.45 thf(fact_230_sup__bot_Oleft__neutral,axiom,
% 0.18/0.45 ! [A2: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ bot_bot_set_a @ A2 )
% 0.18/0.45 = A2 ) ).
% 0.18/0.45
% 0.18/0.45 % sup_bot.left_neutral
% 0.18/0.45 thf(fact_231_sup__bot_Oeq__neutr__iff,axiom,
% 0.18/0.45 ! [A2: a > $o,B2: a > $o] :
% 0.18/0.45 ( ( ( sup_sup_a_o @ A2 @ B2 )
% 0.18/0.45 = bot_bot_a_o )
% 0.18/0.45 = ( ( A2 = bot_bot_a_o )
% 0.18/0.45 & ( B2 = bot_bot_a_o ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sup_bot.eq_neutr_iff
% 0.18/0.45 thf(fact_232_sup__bot_Oeq__neutr__iff,axiom,
% 0.18/0.45 ! [A2: set_a,B2: set_a] :
% 0.18/0.45 ( ( ( sup_sup_set_a @ A2 @ B2 )
% 0.18/0.45 = bot_bot_set_a )
% 0.18/0.45 = ( ( A2 = bot_bot_set_a )
% 0.18/0.45 & ( B2 = bot_bot_set_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sup_bot.eq_neutr_iff
% 0.18/0.45 thf(fact_233_sup__eq__bot__iff,axiom,
% 0.18/0.45 ! [X3: a > $o,Y: a > $o] :
% 0.18/0.45 ( ( ( sup_sup_a_o @ X3 @ Y )
% 0.18/0.45 = bot_bot_a_o )
% 0.18/0.45 = ( ( X3 = bot_bot_a_o )
% 0.18/0.45 & ( Y = bot_bot_a_o ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sup_eq_bot_iff
% 0.18/0.45 thf(fact_234_sup__eq__bot__iff,axiom,
% 0.18/0.45 ! [X3: set_a,Y: set_a] :
% 0.18/0.45 ( ( ( sup_sup_set_a @ X3 @ Y )
% 0.18/0.45 = bot_bot_set_a )
% 0.18/0.45 = ( ( X3 = bot_bot_set_a )
% 0.18/0.45 & ( Y = bot_bot_set_a ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sup_eq_bot_iff
% 0.18/0.45 thf(fact_235_minus__apply,axiom,
% 0.18/0.45 ( minus_minus_a_o
% 0.18/0.45 = ( ^ [A5: a > $o,B6: a > $o,X4: a] : ( minus_minus_o @ ( A5 @ X4 ) @ ( B6 @ X4 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % minus_apply
% 0.18/0.45 thf(fact_236_sup__apply,axiom,
% 0.18/0.45 ( sup_sup_a_o
% 0.18/0.45 = ( ^ [F2: a > $o,G: a > $o,X4: a] : ( sup_sup_o @ ( F2 @ X4 ) @ ( G @ X4 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 % sup_apply
% 0.18/0.45 thf(fact_237_sup_Oidem,axiom,
% 0.18/0.45 ! [A2: int] :
% 0.18/0.45 ( ( sup_sup_int @ A2 @ A2 )
% 0.18/0.45 = A2 ) ).
% 0.18/0.45
% 0.18/0.45 % sup.idem
% 0.18/0.45 thf(fact_238_sup_Oidem,axiom,
% 0.18/0.45 ! [A2: a > $o] :
% 0.18/0.45 ( ( sup_sup_a_o @ A2 @ A2 )
% 0.18/0.45 = A2 ) ).
% 0.18/0.45
% 0.18/0.45 % sup.idem
% 0.18/0.45 thf(fact_239_sup_Oidem,axiom,
% 0.18/0.45 ! [A2: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ A2 @ A2 )
% 0.18/0.45 = A2 ) ).
% 0.18/0.45
% 0.18/0.45 % sup.idem
% 0.18/0.45 thf(fact_240_sup__idem,axiom,
% 0.18/0.45 ! [X3: int] :
% 0.18/0.45 ( ( sup_sup_int @ X3 @ X3 )
% 0.18/0.45 = X3 ) ).
% 0.18/0.45
% 0.18/0.45 % sup_idem
% 0.18/0.45 thf(fact_241_sup__idem,axiom,
% 0.18/0.45 ! [X3: a > $o] :
% 0.18/0.45 ( ( sup_sup_a_o @ X3 @ X3 )
% 0.18/0.45 = X3 ) ).
% 0.18/0.45
% 0.18/0.45 % sup_idem
% 0.18/0.45 thf(fact_242_sup__idem,axiom,
% 0.18/0.45 ! [X3: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ X3 @ X3 )
% 0.18/0.45 = X3 ) ).
% 0.18/0.45
% 0.18/0.45 % sup_idem
% 0.18/0.45 thf(fact_243_sup_Oleft__idem,axiom,
% 0.18/0.45 ! [A2: int,B2: int] :
% 0.18/0.45 ( ( sup_sup_int @ A2 @ ( sup_sup_int @ A2 @ B2 ) )
% 0.18/0.45 = ( sup_sup_int @ A2 @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % sup.left_idem
% 0.18/0.45 thf(fact_244_sup_Oleft__idem,axiom,
% 0.18/0.45 ! [A2: a > $o,B2: a > $o] :
% 0.18/0.45 ( ( sup_sup_a_o @ A2 @ ( sup_sup_a_o @ A2 @ B2 ) )
% 0.18/0.45 = ( sup_sup_a_o @ A2 @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % sup.left_idem
% 0.18/0.45 thf(fact_245_sup_Oleft__idem,axiom,
% 0.18/0.45 ! [A2: set_a,B2: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ A2 @ ( sup_sup_set_a @ A2 @ B2 ) )
% 0.18/0.45 = ( sup_sup_set_a @ A2 @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % sup.left_idem
% 0.18/0.45 thf(fact_246_sup__left__idem,axiom,
% 0.18/0.45 ! [X3: int,Y: int] :
% 0.18/0.45 ( ( sup_sup_int @ X3 @ ( sup_sup_int @ X3 @ Y ) )
% 0.18/0.45 = ( sup_sup_int @ X3 @ Y ) ) ).
% 0.18/0.45
% 0.18/0.45 % sup_left_idem
% 0.18/0.45 thf(fact_247_sup__left__idem,axiom,
% 0.18/0.45 ! [X3: a > $o,Y: a > $o] :
% 0.18/0.45 ( ( sup_sup_a_o @ X3 @ ( sup_sup_a_o @ X3 @ Y ) )
% 0.18/0.45 = ( sup_sup_a_o @ X3 @ Y ) ) ).
% 0.18/0.45
% 0.18/0.45 % sup_left_idem
% 0.18/0.45 thf(fact_248_sup__left__idem,axiom,
% 0.18/0.45 ! [X3: set_a,Y: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ X3 @ Y ) )
% 0.18/0.45 = ( sup_sup_set_a @ X3 @ Y ) ) ).
% 0.18/0.45
% 0.18/0.45 % sup_left_idem
% 0.18/0.45 thf(fact_249_sup_Oright__idem,axiom,
% 0.18/0.45 ! [A2: int,B2: int] :
% 0.18/0.45 ( ( sup_sup_int @ ( sup_sup_int @ A2 @ B2 ) @ B2 )
% 0.18/0.45 = ( sup_sup_int @ A2 @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % sup.right_idem
% 0.18/0.45 thf(fact_250_sup_Oright__idem,axiom,
% 0.18/0.45 ! [A2: a > $o,B2: a > $o] :
% 0.18/0.45 ( ( sup_sup_a_o @ ( sup_sup_a_o @ A2 @ B2 ) @ B2 )
% 0.18/0.45 = ( sup_sup_a_o @ A2 @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % sup.right_idem
% 0.18/0.45 thf(fact_251_sup_Oright__idem,axiom,
% 0.18/0.45 ! [A2: set_a,B2: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ ( sup_sup_set_a @ A2 @ B2 ) @ B2 )
% 0.18/0.45 = ( sup_sup_set_a @ A2 @ B2 ) ) ).
% 0.18/0.45
% 0.18/0.45 % sup.right_idem
% 0.18/0.45 thf(fact_252_sup__bot__left,axiom,
% 0.18/0.45 ! [X3: a > $o] :
% 0.18/0.45 ( ( sup_sup_a_o @ bot_bot_a_o @ X3 )
% 0.18/0.45 = X3 ) ).
% 0.18/0.45
% 0.18/0.45 % sup_bot_left
% 0.18/0.45 thf(fact_253_sup__bot__left,axiom,
% 0.18/0.45 ! [X3: set_a] :
% 0.18/0.45 ( ( sup_sup_set_a @ bot_bot_set_a @ X3 )
% 0.28/0.45 = X3 ) ).
% 0.28/0.45
% 0.28/0.45 % sup_bot_left
% 0.28/0.45 thf(fact_254_sup__bot__right,axiom,
% 0.28/0.45 ! [X3: a > $o] :
% 0.28/0.45 ( ( sup_sup_a_o @ X3 @ bot_bot_a_o )
% 0.28/0.45 = X3 ) ).
% 0.28/0.45
% 0.28/0.45 % sup_bot_right
% 0.28/0.45 thf(fact_255_sup__bot__right,axiom,
% 0.28/0.45 ! [X3: set_a] :
% 0.28/0.45 ( ( sup_sup_set_a @ X3 @ bot_bot_set_a )
% 0.28/0.45 = X3 ) ).
% 0.28/0.45
% 0.28/0.45 % sup_bot_right
% 0.28/0.45 thf(fact_256_bot__eq__sup__iff,axiom,
% 0.28/0.45 ! [X3: a > $o,Y: a > $o] :
% 0.28/0.45 ( ( bot_bot_a_o
% 0.28/0.45 = ( sup_sup_a_o @ X3 @ Y ) )
% 0.28/0.45 = ( ( X3 = bot_bot_a_o )
% 0.28/0.45 & ( Y = bot_bot_a_o ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % bot_eq_sup_iff
% 0.28/0.45 thf(fact_257_bot__eq__sup__iff,axiom,
% 0.28/0.45 ! [X3: set_a,Y: set_a] :
% 0.28/0.45 ( ( bot_bot_set_a
% 0.28/0.45 = ( sup_sup_set_a @ X3 @ Y ) )
% 0.28/0.45 = ( ( X3 = bot_bot_set_a )
% 0.28/0.45 & ( Y = bot_bot_set_a ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % bot_eq_sup_iff
% 0.28/0.45 thf(fact_258_psubsetD,axiom,
% 0.28/0.45 ! [A3: set_a,B4: set_a,C: a] :
% 0.28/0.45 ( ( ord_less_set_a @ A3 @ B4 )
% 0.28/0.45 => ( ( member_a @ C @ A3 )
% 0.28/0.45 => ( member_a @ C @ B4 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % psubsetD
% 0.28/0.45 thf(fact_259_psubset__trans,axiom,
% 0.28/0.45 ! [A3: set_a,B4: set_a,C2: set_a] :
% 0.28/0.45 ( ( ord_less_set_a @ A3 @ B4 )
% 0.28/0.45 => ( ( ord_less_set_a @ B4 @ C2 )
% 0.28/0.45 => ( ord_less_set_a @ A3 @ C2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % psubset_trans
% 0.28/0.45 thf(fact_260_fun__diff__def,axiom,
% 0.28/0.45 ( minus_minus_a_o
% 0.28/0.45 = ( ^ [A5: a > $o,B6: a > $o,X4: a] : ( minus_minus_o @ ( A5 @ X4 ) @ ( B6 @ X4 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % fun_diff_def
% 0.28/0.45 thf(fact_261_inf__sup__aci_I8_J,axiom,
% 0.28/0.45 ! [X3: int,Y: int] :
% 0.28/0.45 ( ( sup_sup_int @ X3 @ ( sup_sup_int @ X3 @ Y ) )
% 0.28/0.45 = ( sup_sup_int @ X3 @ Y ) ) ).
% 0.28/0.45
% 0.28/0.45 % inf_sup_aci(8)
% 0.28/0.45 thf(fact_262_inf__sup__aci_I8_J,axiom,
% 0.28/0.45 ! [X3: a > $o,Y: a > $o] :
% 0.28/0.45 ( ( sup_sup_a_o @ X3 @ ( sup_sup_a_o @ X3 @ Y ) )
% 0.28/0.45 = ( sup_sup_a_o @ X3 @ Y ) ) ).
% 0.28/0.45
% 0.28/0.45 % inf_sup_aci(8)
% 0.28/0.45 thf(fact_263_inf__sup__aci_I8_J,axiom,
% 0.28/0.45 ! [X3: set_a,Y: set_a] :
% 0.28/0.45 ( ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ X3 @ Y ) )
% 0.28/0.45 = ( sup_sup_set_a @ X3 @ Y ) ) ).
% 0.28/0.45
% 0.28/0.45 % inf_sup_aci(8)
% 0.28/0.45 thf(fact_264_inf__sup__aci_I7_J,axiom,
% 0.28/0.45 ! [X3: int,Y: int,Z3: int] :
% 0.28/0.45 ( ( sup_sup_int @ X3 @ ( sup_sup_int @ Y @ Z3 ) )
% 0.28/0.45 = ( sup_sup_int @ Y @ ( sup_sup_int @ X3 @ Z3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inf_sup_aci(7)
% 0.28/0.45 thf(fact_265_inf__sup__aci_I7_J,axiom,
% 0.28/0.45 ! [X3: a > $o,Y: a > $o,Z3: a > $o] :
% 0.28/0.45 ( ( sup_sup_a_o @ X3 @ ( sup_sup_a_o @ Y @ Z3 ) )
% 0.28/0.45 = ( sup_sup_a_o @ Y @ ( sup_sup_a_o @ X3 @ Z3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inf_sup_aci(7)
% 0.28/0.45 thf(fact_266_inf__sup__aci_I7_J,axiom,
% 0.28/0.45 ! [X3: set_a,Y: set_a,Z3: set_a] :
% 0.28/0.45 ( ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ Y @ Z3 ) )
% 0.28/0.45 = ( sup_sup_set_a @ Y @ ( sup_sup_set_a @ X3 @ Z3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inf_sup_aci(7)
% 0.28/0.45 thf(fact_267_inf__sup__aci_I6_J,axiom,
% 0.28/0.45 ! [X3: int,Y: int,Z3: int] :
% 0.28/0.45 ( ( sup_sup_int @ ( sup_sup_int @ X3 @ Y ) @ Z3 )
% 0.28/0.45 = ( sup_sup_int @ X3 @ ( sup_sup_int @ Y @ Z3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inf_sup_aci(6)
% 0.28/0.45 thf(fact_268_inf__sup__aci_I6_J,axiom,
% 0.28/0.45 ! [X3: a > $o,Y: a > $o,Z3: a > $o] :
% 0.28/0.45 ( ( sup_sup_a_o @ ( sup_sup_a_o @ X3 @ Y ) @ Z3 )
% 0.28/0.45 = ( sup_sup_a_o @ X3 @ ( sup_sup_a_o @ Y @ Z3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inf_sup_aci(6)
% 0.28/0.45 thf(fact_269_inf__sup__aci_I6_J,axiom,
% 0.28/0.45 ! [X3: set_a,Y: set_a,Z3: set_a] :
% 0.28/0.45 ( ( sup_sup_set_a @ ( sup_sup_set_a @ X3 @ Y ) @ Z3 )
% 0.28/0.45 = ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ Y @ Z3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inf_sup_aci(6)
% 0.28/0.45 thf(fact_270_inf__sup__aci_I5_J,axiom,
% 0.28/0.45 ( sup_sup_int
% 0.28/0.45 = ( ^ [X4: int,Y3: int] : ( sup_sup_int @ Y3 @ X4 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inf_sup_aci(5)
% 0.28/0.45 thf(fact_271_inf__sup__aci_I5_J,axiom,
% 0.28/0.45 ( sup_sup_a_o
% 0.28/0.45 = ( ^ [X4: a > $o,Y3: a > $o] : ( sup_sup_a_o @ Y3 @ X4 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inf_sup_aci(5)
% 0.28/0.45 thf(fact_272_inf__sup__aci_I5_J,axiom,
% 0.28/0.45 ( sup_sup_set_a
% 0.28/0.45 = ( ^ [X4: set_a,Y3: set_a] : ( sup_sup_set_a @ Y3 @ X4 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % inf_sup_aci(5)
% 0.28/0.45 thf(fact_273_sup__fun__def,axiom,
% 0.28/0.45 ( sup_sup_a_o
% 0.28/0.45 = ( ^ [F2: a > $o,G: a > $o,X4: a] : ( sup_sup_o @ ( F2 @ X4 ) @ ( G @ X4 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_fun_def
% 0.28/0.45 thf(fact_274_boolean__algebra__cancel_Osup1,axiom,
% 0.28/0.45 ! [A3: int,K: int,A2: int,B2: int] :
% 0.28/0.45 ( ( A3
% 0.28/0.45 = ( sup_sup_int @ K @ A2 ) )
% 0.28/0.45 => ( ( sup_sup_int @ A3 @ B2 )
% 0.28/0.45 = ( sup_sup_int @ K @ ( sup_sup_int @ A2 @ B2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % boolean_algebra_cancel.sup1
% 0.28/0.45 thf(fact_275_boolean__algebra__cancel_Osup1,axiom,
% 0.28/0.45 ! [A3: a > $o,K: a > $o,A2: a > $o,B2: a > $o] :
% 0.28/0.45 ( ( A3
% 0.28/0.45 = ( sup_sup_a_o @ K @ A2 ) )
% 0.28/0.45 => ( ( sup_sup_a_o @ A3 @ B2 )
% 0.28/0.45 = ( sup_sup_a_o @ K @ ( sup_sup_a_o @ A2 @ B2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % boolean_algebra_cancel.sup1
% 0.28/0.45 thf(fact_276_boolean__algebra__cancel_Osup1,axiom,
% 0.28/0.45 ! [A3: set_a,K: set_a,A2: set_a,B2: set_a] :
% 0.28/0.45 ( ( A3
% 0.28/0.45 = ( sup_sup_set_a @ K @ A2 ) )
% 0.28/0.45 => ( ( sup_sup_set_a @ A3 @ B2 )
% 0.28/0.45 = ( sup_sup_set_a @ K @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % boolean_algebra_cancel.sup1
% 0.28/0.45 thf(fact_277_boolean__algebra__cancel_Osup2,axiom,
% 0.28/0.45 ! [B4: int,K: int,B2: int,A2: int] :
% 0.28/0.45 ( ( B4
% 0.28/0.45 = ( sup_sup_int @ K @ B2 ) )
% 0.28/0.45 => ( ( sup_sup_int @ A2 @ B4 )
% 0.28/0.45 = ( sup_sup_int @ K @ ( sup_sup_int @ A2 @ B2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % boolean_algebra_cancel.sup2
% 0.28/0.45 thf(fact_278_boolean__algebra__cancel_Osup2,axiom,
% 0.28/0.45 ! [B4: a > $o,K: a > $o,B2: a > $o,A2: a > $o] :
% 0.28/0.45 ( ( B4
% 0.28/0.45 = ( sup_sup_a_o @ K @ B2 ) )
% 0.28/0.45 => ( ( sup_sup_a_o @ A2 @ B4 )
% 0.28/0.45 = ( sup_sup_a_o @ K @ ( sup_sup_a_o @ A2 @ B2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % boolean_algebra_cancel.sup2
% 0.28/0.45 thf(fact_279_boolean__algebra__cancel_Osup2,axiom,
% 0.28/0.45 ! [B4: set_a,K: set_a,B2: set_a,A2: set_a] :
% 0.28/0.45 ( ( B4
% 0.28/0.45 = ( sup_sup_set_a @ K @ B2 ) )
% 0.28/0.45 => ( ( sup_sup_set_a @ A2 @ B4 )
% 0.28/0.45 = ( sup_sup_set_a @ K @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % boolean_algebra_cancel.sup2
% 0.28/0.45 thf(fact_280_sup_Oassoc,axiom,
% 0.28/0.45 ! [A2: int,B2: int,C: int] :
% 0.28/0.45 ( ( sup_sup_int @ ( sup_sup_int @ A2 @ B2 ) @ C )
% 0.28/0.45 = ( sup_sup_int @ A2 @ ( sup_sup_int @ B2 @ C ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.assoc
% 0.28/0.45 thf(fact_281_sup_Oassoc,axiom,
% 0.28/0.45 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 0.28/0.45 ( ( sup_sup_a_o @ ( sup_sup_a_o @ A2 @ B2 ) @ C )
% 0.28/0.45 = ( sup_sup_a_o @ A2 @ ( sup_sup_a_o @ B2 @ C ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.assoc
% 0.28/0.45 thf(fact_282_sup_Oassoc,axiom,
% 0.28/0.45 ! [A2: set_a,B2: set_a,C: set_a] :
% 0.28/0.45 ( ( sup_sup_set_a @ ( sup_sup_set_a @ A2 @ B2 ) @ C )
% 0.28/0.45 = ( sup_sup_set_a @ A2 @ ( sup_sup_set_a @ B2 @ C ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.assoc
% 0.28/0.45 thf(fact_283_sup__assoc,axiom,
% 0.28/0.45 ! [X3: int,Y: int,Z3: int] :
% 0.28/0.45 ( ( sup_sup_int @ ( sup_sup_int @ X3 @ Y ) @ Z3 )
% 0.28/0.45 = ( sup_sup_int @ X3 @ ( sup_sup_int @ Y @ Z3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_assoc
% 0.28/0.45 thf(fact_284_sup__assoc,axiom,
% 0.28/0.45 ! [X3: a > $o,Y: a > $o,Z3: a > $o] :
% 0.28/0.45 ( ( sup_sup_a_o @ ( sup_sup_a_o @ X3 @ Y ) @ Z3 )
% 0.28/0.45 = ( sup_sup_a_o @ X3 @ ( sup_sup_a_o @ Y @ Z3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_assoc
% 0.28/0.45 thf(fact_285_sup__assoc,axiom,
% 0.28/0.45 ! [X3: set_a,Y: set_a,Z3: set_a] :
% 0.28/0.45 ( ( sup_sup_set_a @ ( sup_sup_set_a @ X3 @ Y ) @ Z3 )
% 0.28/0.45 = ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ Y @ Z3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_assoc
% 0.28/0.45 thf(fact_286_sup_Ocommute,axiom,
% 0.28/0.45 ( sup_sup_int
% 0.28/0.45 = ( ^ [A: int,B: int] : ( sup_sup_int @ B @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.commute
% 0.28/0.45 thf(fact_287_sup_Ocommute,axiom,
% 0.28/0.45 ( sup_sup_a_o
% 0.28/0.45 = ( ^ [A: a > $o,B: a > $o] : ( sup_sup_a_o @ B @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.commute
% 0.28/0.45 thf(fact_288_sup_Ocommute,axiom,
% 0.28/0.45 ( sup_sup_set_a
% 0.28/0.45 = ( ^ [A: set_a,B: set_a] : ( sup_sup_set_a @ B @ A ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.commute
% 0.28/0.45 thf(fact_289_sup__commute,axiom,
% 0.28/0.45 ( sup_sup_int
% 0.28/0.45 = ( ^ [X4: int,Y3: int] : ( sup_sup_int @ Y3 @ X4 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_commute
% 0.28/0.45 thf(fact_290_sup__commute,axiom,
% 0.28/0.45 ( sup_sup_a_o
% 0.28/0.45 = ( ^ [X4: a > $o,Y3: a > $o] : ( sup_sup_a_o @ Y3 @ X4 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_commute
% 0.28/0.45 thf(fact_291_sup__commute,axiom,
% 0.28/0.45 ( sup_sup_set_a
% 0.28/0.45 = ( ^ [X4: set_a,Y3: set_a] : ( sup_sup_set_a @ Y3 @ X4 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_commute
% 0.28/0.45 thf(fact_292_sup_Oleft__commute,axiom,
% 0.28/0.45 ! [B2: set_a,A2: set_a,C: set_a] :
% 0.28/0.45 ( ( sup_sup_set_a @ B2 @ ( sup_sup_set_a @ A2 @ C ) )
% 0.28/0.45 = ( sup_sup_set_a @ A2 @ ( sup_sup_set_a @ B2 @ C ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.left_commute
% 0.28/0.45 thf(fact_293_sup__left__commute,axiom,
% 0.28/0.45 ! [X3: set_a,Y: set_a,Z3: set_a] :
% 0.28/0.45 ( ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ Y @ Z3 ) )
% 0.28/0.45 = ( sup_sup_set_a @ Y @ ( sup_sup_set_a @ X3 @ Z3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_left_commute
% 0.28/0.45 thf(fact_294_less__supI1,axiom,
% 0.28/0.45 ! [X3: set_a,A2: set_a,B2: set_a] :
% 0.28/0.45 ( ( ord_less_set_a @ X3 @ A2 )
% 0.28/0.45 => ( ord_less_set_a @ X3 @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_supI1
% 0.28/0.45 thf(fact_295_less__supI1,axiom,
% 0.28/0.45 ! [X3: int,A2: int,B2: int] :
% 0.28/0.45 ( ( ord_less_int @ X3 @ A2 )
% 0.28/0.45 => ( ord_less_int @ X3 @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_supI1
% 0.28/0.45 thf(fact_296_less__supI2,axiom,
% 0.28/0.45 ! [X3: set_a,B2: set_a,A2: set_a] :
% 0.28/0.45 ( ( ord_less_set_a @ X3 @ B2 )
% 0.28/0.45 => ( ord_less_set_a @ X3 @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_supI2
% 0.28/0.45 thf(fact_297_less__supI2,axiom,
% 0.28/0.45 ! [X3: int,B2: int,A2: int] :
% 0.28/0.45 ( ( ord_less_int @ X3 @ B2 )
% 0.28/0.45 => ( ord_less_int @ X3 @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_supI2
% 0.28/0.45 thf(fact_298_sup_Ostrict__boundedE,axiom,
% 0.28/0.45 ! [B2: set_a,C: set_a,A2: set_a] :
% 0.28/0.45 ( ( ord_less_set_a @ ( sup_sup_set_a @ B2 @ C ) @ A2 )
% 0.28/0.45 => ~ ( ( ord_less_set_a @ B2 @ A2 )
% 0.28/0.45 => ~ ( ord_less_set_a @ C @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.strict_boundedE
% 0.28/0.45 thf(fact_299_sup_Ostrict__boundedE,axiom,
% 0.28/0.45 ! [B2: int,C: int,A2: int] :
% 0.28/0.45 ( ( ord_less_int @ ( sup_sup_int @ B2 @ C ) @ A2 )
% 0.28/0.45 => ~ ( ( ord_less_int @ B2 @ A2 )
% 0.28/0.45 => ~ ( ord_less_int @ C @ A2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.strict_boundedE
% 0.28/0.45 thf(fact_300_sup_Ostrict__order__iff,axiom,
% 0.28/0.45 ( ord_less_set_a
% 0.28/0.45 = ( ^ [B: set_a,A: set_a] :
% 0.28/0.45 ( ( A
% 0.28/0.45 = ( sup_sup_set_a @ A @ B ) )
% 0.28/0.45 & ( A != B ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.strict_order_iff
% 0.28/0.45 thf(fact_301_sup_Ostrict__order__iff,axiom,
% 0.28/0.45 ( ord_less_int
% 0.28/0.45 = ( ^ [B: int,A: int] :
% 0.28/0.45 ( ( A
% 0.28/0.45 = ( sup_sup_int @ A @ B ) )
% 0.28/0.45 & ( A != B ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.strict_order_iff
% 0.28/0.45 thf(fact_302_sup_Ostrict__coboundedI1,axiom,
% 0.28/0.45 ! [C: set_a,A2: set_a,B2: set_a] :
% 0.28/0.45 ( ( ord_less_set_a @ C @ A2 )
% 0.28/0.45 => ( ord_less_set_a @ C @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.strict_coboundedI1
% 0.28/0.45 thf(fact_303_sup_Ostrict__coboundedI1,axiom,
% 0.28/0.45 ! [C: int,A2: int,B2: int] :
% 0.28/0.45 ( ( ord_less_int @ C @ A2 )
% 0.28/0.45 => ( ord_less_int @ C @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.strict_coboundedI1
% 0.28/0.45 thf(fact_304_sup_Ostrict__coboundedI2,axiom,
% 0.28/0.45 ! [C: set_a,B2: set_a,A2: set_a] :
% 0.28/0.45 ( ( ord_less_set_a @ C @ B2 )
% 0.28/0.45 => ( ord_less_set_a @ C @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.strict_coboundedI2
% 0.28/0.45 thf(fact_305_sup_Ostrict__coboundedI2,axiom,
% 0.28/0.45 ! [C: int,B2: int,A2: int] :
% 0.28/0.45 ( ( ord_less_int @ C @ B2 )
% 0.28/0.45 => ( ord_less_int @ C @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup.strict_coboundedI2
% 0.28/0.45 thf(fact_306_h2,axiom,
% 0.28/0.45 ( ( binary1721989714Tree_a @ h @ t2 )
% 0.28/0.45 => ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t2 ) )
% 0.28/0.45 = ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t2 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % h2
% 0.28/0.45 thf(fact_307_h1,axiom,
% 0.28/0.45 ( ( binary1721989714Tree_a @ h @ t1 )
% 0.28/0.45 => ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t1 ) )
% 0.28/0.45 = ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t1 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % h1
% 0.28/0.45 thf(fact_308__092_060open_062sortedTree_Ah_ATip_A_092_060longrightarrow_062_AsetOf_A_Ibinsert_Ah_Ae_ATip_J_A_061_AsetOf_ATip_A_N_Aeqs_Ah_Ae_A_092_060union_062_A_123e_125_092_060close_062,axiom,
% 0.28/0.45 ( ( binary1721989714Tree_a @ h @ binary476621312_Tip_a )
% 0.28/0.45 => ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ binary476621312_Tip_a ) )
% 0.28/0.45 = ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ binary476621312_Tip_a ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % \<open>sortedTree h Tip \<longrightarrow> setOf (binsert h e Tip) = setOf Tip - eqs h e \<union> {e}\<close>
% 0.28/0.45 thf(fact_309_singleton__conv,axiom,
% 0.28/0.45 ! [A2: a] :
% 0.28/0.45 ( ( collect_a
% 0.28/0.45 @ ^ [X4: a] : ( X4 = A2 ) )
% 0.28/0.45 = ( insert_a @ A2 @ bot_bot_set_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % singleton_conv
% 0.28/0.45 thf(fact_310_singleton__conv2,axiom,
% 0.28/0.45 ! [A2: a] :
% 0.28/0.45 ( ( collect_a
% 0.28/0.45 @ ( ^ [Y4: a,Z4: a] : ( Y4 = Z4 )
% 0.28/0.45 @ A2 ) )
% 0.28/0.45 = ( insert_a @ A2 @ bot_bot_set_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % singleton_conv2
% 0.28/0.45 thf(fact_311_Un__def,axiom,
% 0.28/0.45 ( sup_sup_set_a
% 0.28/0.45 = ( ^ [A5: set_a,B6: set_a] :
% 0.28/0.45 ( collect_a
% 0.28/0.45 @ ^ [X4: a] :
% 0.28/0.45 ( ( member_a @ X4 @ A5 )
% 0.28/0.45 | ( member_a @ X4 @ B6 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Un_def
% 0.28/0.45 thf(fact_312_empty__def,axiom,
% 0.28/0.45 ( bot_bot_set_a
% 0.28/0.45 = ( collect_a
% 0.28/0.45 @ ^ [X4: a] : $false ) ) ).
% 0.28/0.45
% 0.28/0.45 % empty_def
% 0.28/0.45 thf(fact_313_insert__def,axiom,
% 0.28/0.45 ( insert_a
% 0.28/0.45 = ( ^ [A: a] :
% 0.28/0.45 ( sup_sup_set_a
% 0.28/0.45 @ ( collect_a
% 0.28/0.45 @ ^ [X4: a] : ( X4 = A ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insert_def
% 0.28/0.45 thf(fact_314_sup__set__def,axiom,
% 0.28/0.45 ( sup_sup_set_a
% 0.28/0.45 = ( ^ [A5: set_a,B6: set_a] :
% 0.28/0.45 ( collect_a
% 0.28/0.45 @ ( sup_sup_a_o
% 0.28/0.45 @ ^ [X4: a] : ( member_a @ X4 @ A5 )
% 0.28/0.45 @ ^ [X4: a] : ( member_a @ X4 @ B6 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_set_def
% 0.28/0.45 thf(fact_315_Collect__conv__if,axiom,
% 0.28/0.45 ! [P: a > $o,A2: a] :
% 0.28/0.45 ( ( ( P @ A2 )
% 0.28/0.45 => ( ( collect_a
% 0.28/0.45 @ ^ [X4: a] :
% 0.28/0.45 ( ( X4 = A2 )
% 0.28/0.45 & ( P @ X4 ) ) )
% 0.28/0.45 = ( insert_a @ A2 @ bot_bot_set_a ) ) )
% 0.28/0.45 & ( ~ ( P @ A2 )
% 0.28/0.45 => ( ( collect_a
% 0.28/0.45 @ ^ [X4: a] :
% 0.28/0.45 ( ( X4 = A2 )
% 0.28/0.45 & ( P @ X4 ) ) )
% 0.28/0.45 = bot_bot_set_a ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Collect_conv_if
% 0.28/0.45 thf(fact_316_Collect__disj__eq,axiom,
% 0.28/0.45 ! [P: a > $o,Q: a > $o] :
% 0.28/0.45 ( ( collect_a
% 0.28/0.45 @ ^ [X4: a] :
% 0.28/0.45 ( ( P @ X4 )
% 0.28/0.45 | ( Q @ X4 ) ) )
% 0.28/0.45 = ( sup_sup_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Collect_disj_eq
% 0.28/0.45 thf(fact_317_Collect__conv__if2,axiom,
% 0.28/0.45 ! [P: a > $o,A2: a] :
% 0.28/0.45 ( ( ( P @ A2 )
% 0.28/0.45 => ( ( collect_a
% 0.28/0.45 @ ^ [X4: a] :
% 0.28/0.45 ( ( A2 = X4 )
% 0.28/0.45 & ( P @ X4 ) ) )
% 0.28/0.45 = ( insert_a @ A2 @ bot_bot_set_a ) ) )
% 0.28/0.45 & ( ~ ( P @ A2 )
% 0.28/0.45 => ( ( collect_a
% 0.28/0.45 @ ^ [X4: a] :
% 0.28/0.45 ( ( A2 = X4 )
% 0.28/0.45 & ( P @ X4 ) ) )
% 0.28/0.45 = bot_bot_set_a ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Collect_conv_if2
% 0.28/0.45 thf(fact_318_less__set__def,axiom,
% 0.28/0.45 ( ord_less_set_a
% 0.28/0.45 = ( ^ [A5: set_a,B6: set_a] :
% 0.28/0.45 ( ord_less_a_o
% 0.28/0.45 @ ^ [X4: a] : ( member_a @ X4 @ A5 )
% 0.28/0.45 @ ^ [X4: a] : ( member_a @ X4 @ B6 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % less_set_def
% 0.28/0.45 thf(fact_319_eqs__def,axiom,
% 0.28/0.45 ( binary504661350_eqs_a
% 0.28/0.45 = ( ^ [H2: a > int,X4: a] :
% 0.28/0.45 ( collect_a
% 0.28/0.45 @ ^ [Y3: a] :
% 0.28/0.45 ( ( H2 @ Y3 )
% 0.28/0.45 = ( H2 @ X4 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % eqs_def
% 0.28/0.45 thf(fact_320_insert__Collect,axiom,
% 0.28/0.45 ! [A2: a,P: a > $o] :
% 0.28/0.45 ( ( insert_a @ A2 @ ( collect_a @ P ) )
% 0.28/0.45 = ( collect_a
% 0.28/0.45 @ ^ [U: a] :
% 0.28/0.45 ( ( U != A2 )
% 0.28/0.45 => ( P @ U ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insert_Collect
% 0.28/0.45 thf(fact_321_minus__set__def,axiom,
% 0.28/0.45 ( minus_minus_set_a
% 0.28/0.45 = ( ^ [A5: set_a,B6: set_a] :
% 0.28/0.45 ( collect_a
% 0.28/0.45 @ ( minus_minus_a_o
% 0.28/0.45 @ ^ [X4: a] : ( member_a @ X4 @ A5 )
% 0.28/0.45 @ ^ [X4: a] : ( member_a @ X4 @ B6 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % minus_set_def
% 0.28/0.45 thf(fact_322_insert__compr,axiom,
% 0.28/0.45 ( insert_a
% 0.28/0.45 = ( ^ [A: a,B6: set_a] :
% 0.28/0.45 ( collect_a
% 0.28/0.45 @ ^ [X4: a] :
% 0.28/0.45 ( ( X4 = A )
% 0.28/0.45 | ( member_a @ X4 @ B6 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % insert_compr
% 0.28/0.45 thf(fact_323_set__diff__eq,axiom,
% 0.28/0.45 ( minus_minus_set_a
% 0.28/0.45 = ( ^ [A5: set_a,B6: set_a] :
% 0.28/0.45 ( collect_a
% 0.28/0.45 @ ^ [X4: a] :
% 0.28/0.45 ( ( member_a @ X4 @ A5 )
% 0.28/0.45 & ~ ( member_a @ X4 @ B6 ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % set_diff_eq
% 0.28/0.45 thf(fact_324_the__elem__eq,axiom,
% 0.28/0.45 ! [X3: a] :
% 0.28/0.45 ( ( the_elem_a @ ( insert_a @ X3 @ bot_bot_set_a ) )
% 0.28/0.45 = X3 ) ).
% 0.28/0.45
% 0.28/0.45 % the_elem_eq
% 0.28/0.45 thf(fact_325_bot__empty__eq,axiom,
% 0.28/0.45 ( bot_bot_a_o
% 0.28/0.45 = ( ^ [X4: a] : ( member_a @ X4 @ bot_bot_set_a ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % bot_empty_eq
% 0.28/0.45 thf(fact_326_sup__Un__eq,axiom,
% 0.28/0.45 ! [R: set_a,S: set_a] :
% 0.28/0.45 ( ( sup_sup_a_o
% 0.28/0.45 @ ^ [X4: a] : ( member_a @ X4 @ R )
% 0.28/0.45 @ ^ [X4: a] : ( member_a @ X4 @ S ) )
% 0.28/0.45 = ( ^ [X4: a] : ( member_a @ X4 @ ( sup_sup_set_a @ R @ S ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % sup_Un_eq
% 0.28/0.45 thf(fact_327_Collect__empty__eq__bot,axiom,
% 0.28/0.45 ! [P: a > $o] :
% 0.28/0.45 ( ( ( collect_a @ P )
% 0.28/0.45 = bot_bot_set_a )
% 0.28/0.45 = ( P = bot_bot_a_o ) ) ).
% 0.28/0.45
% 0.28/0.45 % Collect_empty_eq_bot
% 0.28/0.45 thf(fact_328_is__singleton__the__elem,axiom,
% 0.28/0.45 ( is_singleton_a
% 0.28/0.45 = ( ^ [A5: set_a] :
% 0.28/0.45 ( A5
% 0.28/0.45 = ( insert_a @ ( the_elem_a @ A5 ) @ bot_bot_set_a ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % is_singleton_the_elem
% 0.28/0.45 thf(fact_329_is__singletonI,axiom,
% 0.28/0.45 ! [X3: a] : ( is_singleton_a @ ( insert_a @ X3 @ bot_bot_set_a ) ) ).
% 0.28/0.45
% 0.28/0.45 % is_singletonI
% 0.28/0.45 thf(fact_330_is__singletonI_H,axiom,
% 0.28/0.45 ! [A3: set_a] :
% 0.28/0.45 ( ( A3 != bot_bot_set_a )
% 0.28/0.45 => ( ! [X2: a,Y2: a] :
% 0.28/0.45 ( ( member_a @ X2 @ A3 )
% 0.28/0.45 => ( ( member_a @ Y2 @ A3 )
% 0.28/0.45 => ( X2 = Y2 ) ) )
% 0.28/0.45 => ( is_singleton_a @ A3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % is_singletonI'
% 0.28/0.45 thf(fact_331_is__singleton__def,axiom,
% 0.28/0.45 ( is_singleton_a
% 0.28/0.45 = ( ^ [A5: set_a] :
% 0.28/0.45 ? [X4: a] :
% 0.28/0.45 ( A5
% 0.28/0.45 = ( insert_a @ X4 @ bot_bot_set_a ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % is_singleton_def
% 0.28/0.45 thf(fact_332_is__singletonE,axiom,
% 0.28/0.45 ! [A3: set_a] :
% 0.28/0.45 ( ( is_singleton_a @ A3 )
% 0.28/0.45 => ~ ! [X2: a] :
% 0.28/0.45 ( A3
% 0.28/0.45 != ( insert_a @ X2 @ bot_bot_set_a ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % is_singletonE
% 0.28/0.45 thf(fact_333_diff__strict__right__mono,axiom,
% 0.28/0.45 ! [A2: int,B2: int,C: int] :
% 0.28/0.45 ( ( ord_less_int @ A2 @ B2 )
% 0.28/0.45 => ( ord_less_int @ ( minus_minus_int @ A2 @ C ) @ ( minus_minus_int @ B2 @ C ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % diff_strict_right_mono
% 0.28/0.45 thf(fact_334_diff__strict__left__mono,axiom,
% 0.28/0.45 ! [B2: int,A2: int,C: int] :
% 0.28/0.45 ( ( ord_less_int @ B2 @ A2 )
% 0.28/0.45 => ( ord_less_int @ ( minus_minus_int @ C @ A2 ) @ ( minus_minus_int @ C @ B2 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % diff_strict_left_mono
% 0.28/0.45 thf(fact_335_diff__strict__mono,axiom,
% 0.28/0.45 ! [A2: int,B2: int,D: int,C: int] :
% 0.28/0.45 ( ( ord_less_int @ A2 @ B2 )
% 0.28/0.45 => ( ( ord_less_int @ D @ C )
% 0.28/0.45 => ( ord_less_int @ ( minus_minus_int @ A2 @ C ) @ ( minus_minus_int @ B2 @ D ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % diff_strict_mono
% 0.28/0.45 thf(fact_336_diff__eq__diff__less,axiom,
% 0.28/0.45 ! [A2: int,B2: int,C: int,D: int] :
% 0.28/0.45 ( ( ( minus_minus_int @ A2 @ B2 )
% 0.28/0.45 = ( minus_minus_int @ C @ D ) )
% 0.28/0.45 => ( ( ord_less_int @ A2 @ B2 )
% 0.28/0.45 = ( ord_less_int @ C @ D ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % diff_eq_diff_less
% 0.28/0.45 thf(fact_337_remove__def,axiom,
% 0.28/0.45 ( remove_a
% 0.28/0.45 = ( ^ [X4: a,A5: set_a] : ( minus_minus_set_a @ A5 @ ( insert_a @ X4 @ bot_bot_set_a ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % remove_def
% 0.28/0.45 thf(fact_338_Tree_Osimps_I15_J,axiom,
% 0.28/0.45 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 0.28/0.45 ( ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) )
% 0.28/0.45 = ( sup_sup_set_a @ ( sup_sup_set_a @ ( binary256242811Tree_a @ X21 ) @ ( insert_a @ X22 @ bot_bot_set_a ) ) @ ( binary256242811Tree_a @ X23 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Tree.simps(15)
% 0.28/0.45 thf(fact_339_member__remove,axiom,
% 0.28/0.45 ! [X3: a,Y: a,A3: set_a] :
% 0.28/0.45 ( ( member_a @ X3 @ ( remove_a @ Y @ A3 ) )
% 0.28/0.45 = ( ( member_a @ X3 @ A3 )
% 0.28/0.45 & ( X3 != Y ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % member_remove
% 0.28/0.45 thf(fact_340_Tree_Osimps_I14_J,axiom,
% 0.28/0.45 ( ( binary256242811Tree_a @ binary476621312_Tip_a )
% 0.28/0.45 = bot_bot_set_a ) ).
% 0.28/0.45
% 0.28/0.45 % Tree.simps(14)
% 0.28/0.45 thf(fact_341_Tree_Oset__intros_I3_J,axiom,
% 0.28/0.45 ! [Ya: a,X23: binary1439146945Tree_a,X21: binary1439146945Tree_a,X22: a] :
% 0.28/0.45 ( ( member_a @ Ya @ ( binary256242811Tree_a @ X23 ) )
% 0.28/0.45 => ( member_a @ Ya @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Tree.set_intros(3)
% 0.28/0.45 thf(fact_342_Tree_Oset__intros_I2_J,axiom,
% 0.28/0.45 ! [X22: a,X21: binary1439146945Tree_a,X23: binary1439146945Tree_a] : ( member_a @ X22 @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Tree.set_intros(2)
% 0.28/0.45 thf(fact_343_Tree_Oset__intros_I1_J,axiom,
% 0.28/0.45 ! [Y: a,X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 0.28/0.45 ( ( member_a @ Y @ ( binary256242811Tree_a @ X21 ) )
% 0.28/0.45 => ( member_a @ Y @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Tree.set_intros(1)
% 0.28/0.45 thf(fact_344_Tree_Oset__cases,axiom,
% 0.28/0.45 ! [E: a,A2: binary1439146945Tree_a] :
% 0.28/0.45 ( ( member_a @ E @ ( binary256242811Tree_a @ A2 ) )
% 0.28/0.45 => ( ! [Z1: binary1439146945Tree_a] :
% 0.28/0.45 ( ? [Z22: a,Z32: binary1439146945Tree_a] :
% 0.28/0.45 ( A2
% 0.28/0.45 = ( binary717961607le_T_a @ Z1 @ Z22 @ Z32 ) )
% 0.28/0.45 => ~ ( member_a @ E @ ( binary256242811Tree_a @ Z1 ) ) )
% 0.28/0.45 => ( ! [Z1: binary1439146945Tree_a,Z32: binary1439146945Tree_a] :
% 0.28/0.45 ( A2
% 0.28/0.45 != ( binary717961607le_T_a @ Z1 @ E @ Z32 ) )
% 0.28/0.45 => ~ ! [Z1: binary1439146945Tree_a,Z22: a,Z32: binary1439146945Tree_a] :
% 0.28/0.45 ( ( A2
% 0.28/0.45 = ( binary717961607le_T_a @ Z1 @ Z22 @ Z32 ) )
% 0.28/0.45 => ~ ( member_a @ E @ ( binary256242811Tree_a @ Z32 ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Tree.set_cases
% 0.28/0.45 thf(fact_345_Tree_Opred__cong,axiom,
% 0.28/0.45 ! [X3: binary1439146945Tree_a,Ya: binary1439146945Tree_a,P: a > $o,Pa: a > $o] :
% 0.28/0.45 ( ( X3 = Ya )
% 0.28/0.45 => ( ! [Z: a] :
% 0.28/0.45 ( ( member_a @ Z @ ( binary256242811Tree_a @ Ya ) )
% 0.28/0.45 => ( ( P @ Z )
% 0.28/0.45 = ( Pa @ Z ) ) )
% 0.28/0.45 => ( ( binary1452917696Tree_a @ P @ X3 )
% 0.28/0.45 = ( binary1452917696Tree_a @ Pa @ Ya ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Tree.pred_cong
% 0.28/0.45 thf(fact_346_Tree_Opred__mono__strong,axiom,
% 0.28/0.45 ! [P: a > $o,X3: binary1439146945Tree_a,Pa: a > $o] :
% 0.28/0.45 ( ( binary1452917696Tree_a @ P @ X3 )
% 0.28/0.45 => ( ! [Z: a] :
% 0.28/0.45 ( ( member_a @ Z @ ( binary256242811Tree_a @ X3 ) )
% 0.28/0.45 => ( ( P @ Z )
% 0.28/0.45 => ( Pa @ Z ) ) )
% 0.28/0.45 => ( binary1452917696Tree_a @ Pa @ X3 ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Tree.pred_mono_strong
% 0.28/0.45 thf(fact_347_Set_Ois__empty__def,axiom,
% 0.28/0.45 ( is_empty_a
% 0.28/0.45 = ( ^ [A5: set_a] : ( A5 = bot_bot_set_a ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % Set.is_empty_def
% 0.28/0.45 thf(fact_348_the__elem__def,axiom,
% 0.28/0.45 ( the_elem_a
% 0.28/0.45 = ( ^ [X5: set_a] :
% 0.28/0.45 ( the_a
% 0.28/0.45 @ ^ [X4: a] :
% 0.28/0.45 ( X5
% 0.28/0.45 = ( insert_a @ X4 @ bot_bot_set_a ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % the_elem_def
% 0.28/0.45 thf(fact_349_psubset__insert__iff,axiom,
% 0.28/0.45 ! [A3: set_a,X3: a,B4: set_a] :
% 0.28/0.45 ( ( ord_less_set_a @ A3 @ ( insert_a @ X3 @ B4 ) )
% 0.28/0.45 = ( ( ( member_a @ X3 @ B4 )
% 0.28/0.45 => ( ord_less_set_a @ A3 @ B4 ) )
% 0.28/0.45 & ( ~ ( member_a @ X3 @ B4 )
% 0.28/0.45 => ( ( ( member_a @ X3 @ A3 )
% 0.28/0.45 => ( ord_less_set_a @ ( minus_minus_set_a @ A3 @ ( insert_a @ X3 @ bot_bot_set_a ) ) @ B4 ) )
% 0.28/0.45 & ( ~ ( member_a @ X3 @ A3 )
% 0.28/0.45 => ( ord_less_eq_set_a @ A3 @ B4 ) ) ) ) ) ) ).
% 0.28/0.45
% 0.28/0.45 % psubset_insert_iff
% 0.28/0.45
% 0.28/0.45 % Conjectures (1)
% 0.28/0.45 thf(conj_0,conjecture,
% 0.28/0.45 ord_less_int @ ( h @ w ) @ ( h @ x ) ).
% 0.28/0.45
% 0.28/0.45 %------------------------------------------------------------------------------
% 0.28/0.45 ------------------------
% 2.59/1.68 ---- Embedded in THF ---
% 2.59/1.68 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.59/1.68 %%% Generated on Tue Feb 24 08:24:14 EST 2026
% 2.59/1.68 %%% using '$$dhol' embedding, version 1.3.0.
% 2.59/1.68 %%% Logic specification used:
% 2.59/1.68 %%% thf(spec, logic, $$dhol).
% 2.59/1.68
% 2.59/1.68 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xPc2I3SSGn/DTF2DTF929.p
% See solution above
% 2.59/1.68 ------------------------
% 2.87/1.70 ---- Cleaned THF ---
% 2.87/1.70 thf(ty_n_t__BinaryTree____Mirabelle____mlzyzwgbkd__OTree_Itf__a_J,type,
% 2.87/1.70 binary1439146945Tree_a: $tType ).
% 2.87/1.70
% 2.87/1.70 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 2.87/1.70 set_a: $tType ).
% 2.87/1.70
% 2.87/1.70 thf(ty_n_t__Int__Oint,type,
% 2.87/1.70 int: $tType ).
% 2.87/1.70
% 2.87/1.70 thf(ty_n_tf__a,type,
% 2.87/1.70 a: $tType ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OT_001tf__a,type,
% 2.87/1.70 binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_OTip_001tf__a,type,
% 2.87/1.70 binary476621312_Tip_a: binary1439146945Tree_a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_Opred__Tree_001tf__a,type,
% 2.87/1.70 binary1452917696Tree_a: ( a > $o ) > binary1439146945Tree_a > $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OTree_Oset__Tree_001tf__a,type,
% 2.87/1.70 binary256242811Tree_a: binary1439146945Tree_a > set_a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Obinsert_001tf__a,type,
% 2.87/1.70 binary1226383794sert_a: ( a > int ) > a > binary1439146945Tree_a > binary1439146945Tree_a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Oeqs_001tf__a,type,
% 2.87/1.70 binary504661350_eqs_a: ( a > int ) > a > set_a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Omemb_001tf__a,type,
% 2.87/1.70 binary2053421120memb_a: ( a > int ) > a > binary1439146945Tree_a > $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsetOf_001tf__a,type,
% 2.87/1.70 binary945792244etOf_a: binary1439146945Tree_a > set_a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_OsortedTree_001tf__a,type,
% 2.87/1.70 binary1721989714Tree_a: ( a > int ) > binary1439146945Tree_a > $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_BinaryTree__Mirabelle__mlzyzwgbkd_Osorted__distinct__pred_001tf__a,type,
% 2.87/1.70 binary670562003pred_a: ( a > int ) > a > a > binary1439146945Tree_a > $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Groups_Ominus__class_Ominus_001_062_Itf__a_M_Eo_J,type,
% 2.87/1.70 minus_minus_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Groups_Ominus__class_Ominus_001_Eo,type,
% 2.87/1.70 minus_minus_o: $o > $o > $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
% 2.87/1.70 minus_minus_int: int > int > int ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_Itf__a_J,type,
% 2.87/1.70 minus_minus_set_a: set_a > set_a > set_a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_HOL_OThe_001tf__a,type,
% 2.87/1.70 the_a: ( a > $o ) > a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Lattices_Osup__class_Osup_001_062_Itf__a_M_Eo_J,type,
% 2.87/1.70 sup_sup_a_o: ( a > $o ) > ( a > $o ) > a > $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Lattices_Osup__class_Osup_001_Eo,type,
% 2.87/1.70 sup_sup_o: $o > $o > $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 2.87/1.70 sup_sup_int: int > int > int ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_Itf__a_J,type,
% 2.87/1.70 sup_sup_set_a: set_a > set_a > set_a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Orderings_Obot__class_Obot_001_062_Itf__a_M_Eo_J,type,
% 2.87/1.70 bot_bot_a_o: a > $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Orderings_Obot__class_Obot_001_Eo,type,
% 2.87/1.70 bot_bot_o: $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_Itf__a_J,type,
% 2.87/1.70 bot_bot_set_a: set_a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Orderings_Oord__class_Oless_001_062_Itf__a_M_Eo_J,type,
% 2.87/1.70 ord_less_a_o: ( a > $o ) > ( a > $o ) > $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 2.87/1.70 ord_less_int: int > int > $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__a_J,type,
% 2.87/1.70 ord_less_set_a: set_a > set_a > $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 2.87/1.70 ord_less_eq_set_a: set_a > set_a > $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Set_OCollect_001tf__a,type,
% 2.87/1.70 collect_a: ( a > $o ) > set_a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Set_Oinsert_001tf__a,type,
% 2.87/1.70 insert_a: a > set_a > set_a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Set_Ois__empty_001tf__a,type,
% 2.87/1.70 is_empty_a: set_a > $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Set_Ois__singleton_001tf__a,type,
% 2.87/1.70 is_singleton_a: set_a > $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Set_Oremove_001tf__a,type,
% 2.87/1.70 remove_a: a > set_a > set_a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_Set_Othe__elem_001tf__a,type,
% 2.87/1.70 the_elem_a: set_a > a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_c_member_001tf__a,type,
% 2.87/1.70 member_a: a > set_a > $o ).
% 2.87/1.70
% 2.87/1.70 thf(sy_v_e,type,
% 2.87/1.70 e: a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_v_h,type,
% 2.87/1.70 h: a > int ).
% 2.87/1.70
% 2.87/1.70 thf(sy_v_t1____,type,
% 2.87/1.70 t1: binary1439146945Tree_a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_v_t2____,type,
% 2.87/1.70 t2: binary1439146945Tree_a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_v_w____,type,
% 2.87/1.70 w: a ).
% 2.87/1.70
% 2.87/1.70 thf(sy_v_x____,type,
% 2.87/1.70 x: a ).
% 2.87/1.70
% 2.87/1.70 thf(fact_0_whSet,axiom,
% 2.87/1.70 member_a @ w @ ( binary945792244etOf_a @ t1 ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_1_s,axiom,
% 2.87/1.70 binary1721989714Tree_a @ h @ ( binary717961607le_T_a @ t1 @ x @ t2 ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_2_s2,axiom,
% 2.87/1.70 binary1721989714Tree_a @ h @ t2 ).
% 2.87/1.70
% 2.87/1.70 thf(fact_3_s1,axiom,
% 2.87/1.70 binary1721989714Tree_a @ h @ t1 ).
% 2.87/1.70
% 2.87/1.70 thf(fact_4_eNotLess,axiom,
% 2.87/1.70 ~ ( ord_less_int @ ( h @ e ) @ ( h @ x ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_5_xNotLess,axiom,
% 2.87/1.70 ~ ( ord_less_int @ ( h @ x ) @ ( h @ e ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_6_whEq,axiom,
% 2.87/1.70 member_a @ w @ ( binary504661350_eqs_a @ h @ e ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_7_xeqe,axiom,
% 2.87/1.70 ( ( h @ x )
% 2.87/1.70 = ( h @ e ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_8_Tree_Oinject,axiom,
% 2.87/1.70 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a,Y21: binary1439146945Tree_a,Y22: a,Y23: binary1439146945Tree_a] :
% 2.87/1.70 ( ( ( binary717961607le_T_a @ X21 @ X22 @ X23 )
% 2.87/1.70 = ( binary717961607le_T_a @ Y21 @ Y22 @ Y23 ) )
% 2.87/1.70 = ( ( X21 = Y21 )
% 2.87/1.70 & ( X22 = Y22 )
% 2.87/1.70 & ( X23 = Y23 ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_9_calculation,axiom,
% 2.87/1.70 member_a @ x @ ( binary504661350_eqs_a @ h @ e ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_10_minf_I7_J,axiom,
% 2.87/1.70 ! [T: int] :
% 2.87/1.70 ? [Z: int] :
% 2.87/1.70 ! [X: int] :
% 2.87/1.70 ( ( ord_less_int @ X @ Z )
% 2.87/1.70 => ~ ( ord_less_int @ T @ X ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_11_minf_I5_J,axiom,
% 2.87/1.70 ! [T: int] :
% 2.87/1.70 ? [Z: int] :
% 2.87/1.70 ! [X: int] :
% 2.87/1.70 ( ( ord_less_int @ X @ Z )
% 2.87/1.70 => ( ord_less_int @ X @ T ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_12_minf_I4_J,axiom,
% 2.87/1.70 ! [T: int] :
% 2.87/1.70 ? [Z: int] :
% 2.87/1.70 ! [X: int] :
% 2.87/1.70 ( ( ord_less_int @ X @ Z )
% 2.87/1.70 => ( X != T ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_13_minf_I3_J,axiom,
% 2.87/1.70 ! [T: int] :
% 2.87/1.70 ? [Z: int] :
% 2.87/1.70 ! [X: int] :
% 2.87/1.70 ( ( ord_less_int @ X @ Z )
% 2.87/1.70 => ( X != T ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_14_minf_I2_J,axiom,
% 2.87/1.70 ! [P: int > $o,P2: int > $o,Q: int > $o,Q2: int > $o] :
% 2.87/1.70 ( ? [Z2: int] :
% 2.87/1.70 ! [X2: int] :
% 2.87/1.70 ( ( ord_less_int @ X2 @ Z2 )
% 2.87/1.70 => ( ( P @ X2 )
% 2.87/1.70 = ( P2 @ X2 ) ) )
% 2.87/1.70 => ( ? [Z2: int] :
% 2.87/1.70 ! [X2: int] :
% 2.87/1.70 ( ( ord_less_int @ X2 @ Z2 )
% 2.87/1.70 => ( ( Q @ X2 )
% 2.87/1.70 = ( Q2 @ X2 ) ) )
% 2.87/1.70 => ? [Z: int] :
% 2.87/1.70 ! [X: int] :
% 2.87/1.70 ( ( ord_less_int @ X @ Z )
% 2.87/1.70 => ( ( ( P @ X )
% 2.87/1.70 | ( Q @ X ) )
% 2.87/1.70 = ( ( P2 @ X )
% 2.87/1.70 | ( Q2 @ X ) ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_15_minf_I1_J,axiom,
% 2.87/1.70 ! [P: int > $o,P2: int > $o,Q: int > $o,Q2: int > $o] :
% 2.87/1.70 ( ? [Z2: int] :
% 2.87/1.70 ! [X2: int] :
% 2.87/1.70 ( ( ord_less_int @ X2 @ Z2 )
% 2.87/1.70 => ( ( P @ X2 )
% 2.87/1.70 = ( P2 @ X2 ) ) )
% 2.87/1.70 => ( ? [Z2: int] :
% 2.87/1.70 ! [X2: int] :
% 2.87/1.70 ( ( ord_less_int @ X2 @ Z2 )
% 2.87/1.70 => ( ( Q @ X2 )
% 2.87/1.70 = ( Q2 @ X2 ) ) )
% 2.87/1.70 => ? [Z: int] :
% 2.87/1.70 ! [X: int] :
% 2.87/1.70 ( ( ord_less_int @ X @ Z )
% 2.87/1.70 => ( ( ( P @ X )
% 2.87/1.70 & ( Q @ X ) )
% 2.87/1.70 = ( ( P2 @ X )
% 2.87/1.70 & ( Q2 @ X ) ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_16_res,axiom,
% 2.87/1.70 ( ( binary1226383794sert_a @ h @ e @ ( binary717961607le_T_a @ t1 @ x @ t2 ) )
% 2.87/1.70 = ( binary717961607le_T_a @ t1 @ e @ t2 ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_17_sortLemmaR,axiom,
% 2.87/1.70 ! [H: a > int,T1: binary1439146945Tree_a,X3: a,T2: binary1439146945Tree_a] :
% 2.87/1.70 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X3 @ T2 ) )
% 2.87/1.70 => ( binary1721989714Tree_a @ H @ T2 ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_18_sortLemmaL,axiom,
% 2.87/1.70 ! [H: a > int,T1: binary1439146945Tree_a,X3: a,T2: binary1439146945Tree_a] :
% 2.87/1.70 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X3 @ T2 ) )
% 2.87/1.70 => ( binary1721989714Tree_a @ H @ T1 ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_19_sortedTree_Osimps_I2_J,axiom,
% 2.87/1.70 ! [H: a > int,T1: binary1439146945Tree_a,X3: a,T2: binary1439146945Tree_a] :
% 2.87/1.70 ( ( binary1721989714Tree_a @ H @ ( binary717961607le_T_a @ T1 @ X3 @ T2 ) )
% 2.87/1.70 = ( ( binary1721989714Tree_a @ H @ T1 )
% 2.87/1.70 & ! [X4: a] :
% 2.87/1.70 ( ( member_a @ X4 @ ( binary945792244etOf_a @ T1 ) )
% 2.87/1.70 => ( ord_less_int @ ( H @ X4 ) @ ( H @ X3 ) ) )
% 2.87/1.70 & ! [X4: a] :
% 2.87/1.70 ( ( member_a @ X4 @ ( binary945792244etOf_a @ T2 ) )
% 2.87/1.70 => ( ord_less_int @ ( H @ X3 ) @ ( H @ X4 ) ) )
% 2.87/1.70 & ( binary1721989714Tree_a @ H @ T2 ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_20_pinf_I1_J,axiom,
% 2.87/1.70 ! [P: int > $o,P2: int > $o,Q: int > $o,Q2: int > $o] :
% 2.87/1.70 ( ? [Z2: int] :
% 2.87/1.70 ! [X2: int] :
% 2.87/1.70 ( ( ord_less_int @ Z2 @ X2 )
% 2.87/1.70 => ( ( P @ X2 )
% 2.87/1.70 = ( P2 @ X2 ) ) )
% 2.87/1.70 => ( ? [Z2: int] :
% 2.87/1.70 ! [X2: int] :
% 2.87/1.70 ( ( ord_less_int @ Z2 @ X2 )
% 2.87/1.70 => ( ( Q @ X2 )
% 2.87/1.70 = ( Q2 @ X2 ) ) )
% 2.87/1.70 => ? [Z: int] :
% 2.87/1.70 ! [X: int] :
% 2.87/1.70 ( ( ord_less_int @ Z @ X )
% 2.87/1.70 => ( ( ( P @ X )
% 2.87/1.70 & ( Q @ X ) )
% 2.87/1.70 = ( ( P2 @ X )
% 2.87/1.70 & ( Q2 @ X ) ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_21_pinf_I2_J,axiom,
% 2.87/1.70 ! [P: int > $o,P2: int > $o,Q: int > $o,Q2: int > $o] :
% 2.87/1.70 ( ? [Z2: int] :
% 2.87/1.70 ! [X2: int] :
% 2.87/1.70 ( ( ord_less_int @ Z2 @ X2 )
% 2.87/1.70 => ( ( P @ X2 )
% 2.87/1.70 = ( P2 @ X2 ) ) )
% 2.87/1.70 => ( ? [Z2: int] :
% 2.87/1.70 ! [X2: int] :
% 2.87/1.70 ( ( ord_less_int @ Z2 @ X2 )
% 2.87/1.70 => ( ( Q @ X2 )
% 2.87/1.70 = ( Q2 @ X2 ) ) )
% 2.87/1.70 => ? [Z: int] :
% 2.87/1.70 ! [X: int] :
% 2.87/1.70 ( ( ord_less_int @ Z @ X )
% 2.87/1.70 => ( ( ( P @ X )
% 2.87/1.70 | ( Q @ X ) )
% 2.87/1.70 = ( ( P2 @ X )
% 2.87/1.70 | ( Q2 @ X ) ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_22_pinf_I3_J,axiom,
% 2.87/1.70 ! [T: int] :
% 2.87/1.70 ? [Z: int] :
% 2.87/1.70 ! [X: int] :
% 2.87/1.70 ( ( ord_less_int @ Z @ X )
% 2.87/1.70 => ( X != T ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_23_pinf_I4_J,axiom,
% 2.87/1.70 ! [T: int] :
% 2.87/1.70 ? [Z: int] :
% 2.87/1.70 ! [X: int] :
% 2.87/1.70 ( ( ord_less_int @ Z @ X )
% 2.87/1.70 => ( X != T ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_24_pinf_I5_J,axiom,
% 2.87/1.70 ! [T: int] :
% 2.87/1.70 ? [Z: int] :
% 2.87/1.70 ! [X: int] :
% 2.87/1.70 ( ( ord_less_int @ Z @ X )
% 2.87/1.70 => ~ ( ord_less_int @ X @ T ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_25_pinf_I7_J,axiom,
% 2.87/1.70 ! [T: int] :
% 2.87/1.70 ? [Z: int] :
% 2.87/1.70 ! [X: int] :
% 2.87/1.70 ( ( ord_less_int @ Z @ X )
% 2.87/1.70 => ( ord_less_int @ T @ X ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_26_sorted__distinct__pred__def,axiom,
% 2.87/1.70 ( binary670562003pred_a
% 2.87/1.70 = ( ^ [H2: a > int,A: a,B: a,T3: binary1439146945Tree_a] :
% 2.87/1.70 ( ( ( binary1721989714Tree_a @ H2 @ T3 )
% 2.87/1.70 & ( member_a @ A @ ( binary945792244etOf_a @ T3 ) )
% 2.87/1.70 & ( member_a @ B @ ( binary945792244etOf_a @ T3 ) )
% 2.87/1.70 & ( ( H2 @ A )
% 2.87/1.70 = ( H2 @ B ) ) )
% 2.87/1.70 => ( A = B ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_27_memb__spec,axiom,
% 2.87/1.70 ! [H: a > int,T: binary1439146945Tree_a,X3: a] :
% 2.87/1.70 ( ( binary1721989714Tree_a @ H @ T )
% 2.87/1.70 => ( ( binary2053421120memb_a @ H @ X3 @ T )
% 2.87/1.70 = ( member_a @ X3 @ ( binary945792244etOf_a @ T ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_28_binsert_Osimps_I2_J,axiom,
% 2.87/1.70 ! [H: a > int,E: a,X3: a,T1: binary1439146945Tree_a,T2: binary1439146945Tree_a] :
% 2.87/1.70 ( ( ( ord_less_int @ ( H @ E ) @ ( H @ X3 ) )
% 2.87/1.70 => ( ( binary1226383794sert_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X3 @ T2 ) )
% 2.87/1.70 = ( binary717961607le_T_a @ ( binary1226383794sert_a @ H @ E @ T1 ) @ X3 @ T2 ) ) )
% 2.87/1.70 & ( ~ ( ord_less_int @ ( H @ E ) @ ( H @ X3 ) )
% 2.87/1.70 => ( ( ( ord_less_int @ ( H @ X3 ) @ ( H @ E ) )
% 2.87/1.70 => ( ( binary1226383794sert_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X3 @ T2 ) )
% 2.87/1.70 = ( binary717961607le_T_a @ T1 @ X3 @ ( binary1226383794sert_a @ H @ E @ T2 ) ) ) )
% 2.87/1.70 & ( ~ ( ord_less_int @ ( H @ X3 ) @ ( H @ E ) )
% 2.87/1.70 => ( ( binary1226383794sert_a @ H @ E @ ( binary717961607le_T_a @ T1 @ X3 @ T2 ) )
% 2.87/1.70 = ( binary717961607le_T_a @ T1 @ E @ T2 ) ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_29_linorder__neqE__linordered__idom,axiom,
% 2.87/1.70 ! [X3: int,Y: int] :
% 2.87/1.70 ( ( X3 != Y )
% 2.87/1.70 => ( ~ ( ord_less_int @ X3 @ Y )
% 2.87/1.70 => ( ord_less_int @ Y @ X3 ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_30_dual__order_Ostrict__implies__not__eq,axiom,
% 2.87/1.70 ! [B2: set_a,A2: set_a] :
% 2.87/1.70 ( ( ord_less_set_a @ B2 @ A2 )
% 2.87/1.70 => ( A2 != B2 ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_31_dual__order_Ostrict__implies__not__eq,axiom,
% 2.87/1.70 ! [B2: a > $o,A2: a > $o] :
% 2.87/1.70 ( ( ord_less_a_o @ B2 @ A2 )
% 2.87/1.70 => ( A2 != B2 ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_32_dual__order_Ostrict__implies__not__eq,axiom,
% 2.87/1.70 ! [B2: int,A2: int] :
% 2.87/1.70 ( ( ord_less_int @ B2 @ A2 )
% 2.87/1.70 => ( A2 != B2 ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_33_order_Ostrict__implies__not__eq,axiom,
% 2.87/1.70 ! [A2: set_a,B2: set_a] :
% 2.87/1.70 ( ( ord_less_set_a @ A2 @ B2 )
% 2.87/1.70 => ( A2 != B2 ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_34_order_Ostrict__implies__not__eq,axiom,
% 2.87/1.70 ! [A2: a > $o,B2: a > $o] :
% 2.87/1.70 ( ( ord_less_a_o @ A2 @ B2 )
% 2.87/1.70 => ( A2 != B2 ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_35_order_Ostrict__implies__not__eq,axiom,
% 2.87/1.70 ! [A2: int,B2: int] :
% 2.87/1.70 ( ( ord_less_int @ A2 @ B2 )
% 2.87/1.70 => ( A2 != B2 ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_36_sorted__distinct,axiom,
% 2.87/1.70 ! [H: a > int,A2: a,B2: a,T: binary1439146945Tree_a] : ( binary670562003pred_a @ H @ A2 @ B2 @ T ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_37_ord__eq__less__subst,axiom,
% 2.87/1.70 ! [A2: set_a,F: int > set_a,B2: int,C: int] :
% 2.87/1.70 ( ( A2
% 2.87/1.70 = ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_int @ B2 @ C )
% 2.87/1.70 => ( ! [X2: int,Y2: int] :
% 2.87/1.70 ( ( ord_less_int @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_38_ord__eq__less__subst,axiom,
% 2.87/1.70 ! [A2: a > $o,F: int > a > $o,B2: int,C: int] :
% 2.87/1.70 ( ( A2
% 2.87/1.70 = ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_int @ B2 @ C )
% 2.87/1.70 => ( ! [X2: int,Y2: int] :
% 2.87/1.70 ( ( ord_less_int @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_39_ord__eq__less__subst,axiom,
% 2.87/1.70 ! [A2: int,F: set_a > int,B2: set_a,C: set_a] :
% 2.87/1.70 ( ( A2
% 2.87/1.70 = ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_set_a @ B2 @ C )
% 2.87/1.70 => ( ! [X2: set_a,Y2: set_a] :
% 2.87/1.70 ( ( ord_less_set_a @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_40_ord__eq__less__subst,axiom,
% 2.87/1.70 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 2.87/1.70 ( ( A2
% 2.87/1.70 = ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_set_a @ B2 @ C )
% 2.87/1.70 => ( ! [X2: set_a,Y2: set_a] :
% 2.87/1.70 ( ( ord_less_set_a @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_41_ord__eq__less__subst,axiom,
% 2.87/1.70 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 2.87/1.70 ( ( A2
% 2.87/1.70 = ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_set_a @ B2 @ C )
% 2.87/1.70 => ( ! [X2: set_a,Y2: set_a] :
% 2.87/1.70 ( ( ord_less_set_a @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_42_ord__eq__less__subst,axiom,
% 2.87/1.70 ! [A2: int,F: ( a > $o ) > int,B2: a > $o,C: a > $o] :
% 2.87/1.70 ( ( A2
% 2.87/1.70 = ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_a_o @ B2 @ C )
% 2.87/1.70 => ( ! [X2: a > $o,Y2: a > $o] :
% 2.87/1.70 ( ( ord_less_a_o @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_43_ord__eq__less__subst,axiom,
% 2.87/1.70 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 2.87/1.70 ( ( A2
% 2.87/1.70 = ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_a_o @ B2 @ C )
% 2.87/1.70 => ( ! [X2: a > $o,Y2: a > $o] :
% 2.87/1.70 ( ( ord_less_a_o @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_44_ord__eq__less__subst,axiom,
% 2.87/1.70 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 2.87/1.70 ( ( A2
% 2.87/1.70 = ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_a_o @ B2 @ C )
% 2.87/1.70 => ( ! [X2: a > $o,Y2: a > $o] :
% 2.87/1.70 ( ( ord_less_a_o @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_45_ord__eq__less__subst,axiom,
% 2.87/1.70 ! [A2: int,F: int > int,B2: int,C: int] :
% 2.87/1.70 ( ( A2
% 2.87/1.70 = ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_int @ B2 @ C )
% 2.87/1.70 => ( ! [X2: int,Y2: int] :
% 2.87/1.70 ( ( ord_less_int @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_46_ord__less__eq__subst,axiom,
% 2.87/1.70 ! [A2: int,B2: int,F: int > set_a,C: set_a] :
% 2.87/1.70 ( ( ord_less_int @ A2 @ B2 )
% 2.87/1.70 => ( ( ( F @ B2 )
% 2.87/1.70 = C )
% 2.87/1.70 => ( ! [X2: int,Y2: int] :
% 2.87/1.70 ( ( ord_less_int @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_47_ord__less__eq__subst,axiom,
% 2.87/1.70 ! [A2: int,B2: int,F: int > a > $o,C: a > $o] :
% 2.87/1.70 ( ( ord_less_int @ A2 @ B2 )
% 2.87/1.70 => ( ( ( F @ B2 )
% 2.87/1.70 = C )
% 2.87/1.70 => ( ! [X2: int,Y2: int] :
% 2.87/1.70 ( ( ord_less_int @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_48_ord__less__eq__subst,axiom,
% 2.87/1.70 ! [A2: set_a,B2: set_a,F: set_a > int,C: int] :
% 2.87/1.70 ( ( ord_less_set_a @ A2 @ B2 )
% 2.87/1.70 => ( ( ( F @ B2 )
% 2.87/1.70 = C )
% 2.87/1.70 => ( ! [X2: set_a,Y2: set_a] :
% 2.87/1.70 ( ( ord_less_set_a @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_49_ord__less__eq__subst,axiom,
% 2.87/1.70 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 2.87/1.70 ( ( ord_less_set_a @ A2 @ B2 )
% 2.87/1.70 => ( ( ( F @ B2 )
% 2.87/1.70 = C )
% 2.87/1.70 => ( ! [X2: set_a,Y2: set_a] :
% 2.87/1.70 ( ( ord_less_set_a @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_50_ord__less__eq__subst,axiom,
% 2.87/1.70 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 2.87/1.70 ( ( ord_less_set_a @ A2 @ B2 )
% 2.87/1.70 => ( ( ( F @ B2 )
% 2.87/1.70 = C )
% 2.87/1.70 => ( ! [X2: set_a,Y2: set_a] :
% 2.87/1.70 ( ( ord_less_set_a @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_51_ord__less__eq__subst,axiom,
% 2.87/1.70 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > int,C: int] :
% 2.87/1.70 ( ( ord_less_a_o @ A2 @ B2 )
% 2.87/1.70 => ( ( ( F @ B2 )
% 2.87/1.70 = C )
% 2.87/1.70 => ( ! [X2: a > $o,Y2: a > $o] :
% 2.87/1.70 ( ( ord_less_a_o @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_52_ord__less__eq__subst,axiom,
% 2.87/1.70 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 2.87/1.70 ( ( ord_less_a_o @ A2 @ B2 )
% 2.87/1.70 => ( ( ( F @ B2 )
% 2.87/1.70 = C )
% 2.87/1.70 => ( ! [X2: a > $o,Y2: a > $o] :
% 2.87/1.70 ( ( ord_less_a_o @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_53_ord__less__eq__subst,axiom,
% 2.87/1.70 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 2.87/1.70 ( ( ord_less_a_o @ A2 @ B2 )
% 2.87/1.70 => ( ( ( F @ B2 )
% 2.87/1.70 = C )
% 2.87/1.70 => ( ! [X2: a > $o,Y2: a > $o] :
% 2.87/1.70 ( ( ord_less_a_o @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_54_ord__less__eq__subst,axiom,
% 2.87/1.70 ! [A2: int,B2: int,F: int > int,C: int] :
% 2.87/1.70 ( ( ord_less_int @ A2 @ B2 )
% 2.87/1.70 => ( ( ( F @ B2 )
% 2.87/1.70 = C )
% 2.87/1.70 => ( ! [X2: int,Y2: int] :
% 2.87/1.70 ( ( ord_less_int @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_55_order__less__subst1,axiom,
% 2.87/1.70 ! [A2: int,F: set_a > int,B2: set_a,C: set_a] :
% 2.87/1.70 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_set_a @ B2 @ C )
% 2.87/1.70 => ( ! [X2: set_a,Y2: set_a] :
% 2.87/1.70 ( ( ord_less_set_a @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_56_order__less__subst1,axiom,
% 2.87/1.70 ! [A2: int,F: ( a > $o ) > int,B2: a > $o,C: a > $o] :
% 2.87/1.70 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_a_o @ B2 @ C )
% 2.87/1.70 => ( ! [X2: a > $o,Y2: a > $o] :
% 2.87/1.70 ( ( ord_less_a_o @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_57_order__less__subst1,axiom,
% 2.87/1.70 ! [A2: set_a,F: int > set_a,B2: int,C: int] :
% 2.87/1.70 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_int @ B2 @ C )
% 2.87/1.70 => ( ! [X2: int,Y2: int] :
% 2.87/1.70 ( ( ord_less_int @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_58_order__less__subst1,axiom,
% 2.87/1.70 ! [A2: set_a,F: set_a > set_a,B2: set_a,C: set_a] :
% 2.87/1.70 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_set_a @ B2 @ C )
% 2.87/1.70 => ( ! [X2: set_a,Y2: set_a] :
% 2.87/1.70 ( ( ord_less_set_a @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_59_order__less__subst1,axiom,
% 2.87/1.70 ! [A2: set_a,F: ( a > $o ) > set_a,B2: a > $o,C: a > $o] :
% 2.87/1.70 ( ( ord_less_set_a @ A2 @ ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_a_o @ B2 @ C )
% 2.87/1.70 => ( ! [X2: a > $o,Y2: a > $o] :
% 2.87/1.70 ( ( ord_less_a_o @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_set_a @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_60_order__less__subst1,axiom,
% 2.87/1.70 ! [A2: a > $o,F: int > a > $o,B2: int,C: int] :
% 2.87/1.70 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_int @ B2 @ C )
% 2.87/1.70 => ( ! [X2: int,Y2: int] :
% 2.87/1.70 ( ( ord_less_int @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_61_order__less__subst1,axiom,
% 2.87/1.70 ! [A2: a > $o,F: set_a > a > $o,B2: set_a,C: set_a] :
% 2.87/1.70 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_set_a @ B2 @ C )
% 2.87/1.70 => ( ! [X2: set_a,Y2: set_a] :
% 2.87/1.70 ( ( ord_less_set_a @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_62_order__less__subst1,axiom,
% 2.87/1.70 ! [A2: a > $o,F: ( a > $o ) > a > $o,B2: a > $o,C: a > $o] :
% 2.87/1.70 ( ( ord_less_a_o @ A2 @ ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_a_o @ B2 @ C )
% 2.87/1.70 => ( ! [X2: a > $o,Y2: a > $o] :
% 2.87/1.70 ( ( ord_less_a_o @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_a_o @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.70
% 2.87/1.70 thf(fact_63_order__less__subst1,axiom,
% 2.87/1.70 ! [A2: int,F: int > int,B2: int,C: int] :
% 2.87/1.70 ( ( ord_less_int @ A2 @ ( F @ B2 ) )
% 2.87/1.70 => ( ( ord_less_int @ B2 @ C )
% 2.87/1.70 => ( ! [X2: int,Y2: int] :
% 2.87/1.70 ( ( ord_less_int @ X2 @ Y2 )
% 2.87/1.70 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.70 => ( ord_less_int @ A2 @ ( F @ C ) ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_64_order__less__subst2,axiom,
% 2.87/1.71 ! [A2: int,B2: int,F: int > set_a,C: set_a] :
% 2.87/1.71 ( ( ord_less_int @ A2 @ B2 )
% 2.87/1.71 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 2.87/1.71 => ( ! [X2: int,Y2: int] :
% 2.87/1.71 ( ( ord_less_int @ X2 @ Y2 )
% 2.87/1.71 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.71 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_65_order__less__subst2,axiom,
% 2.87/1.71 ! [A2: int,B2: int,F: int > a > $o,C: a > $o] :
% 2.87/1.71 ( ( ord_less_int @ A2 @ B2 )
% 2.87/1.71 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 2.87/1.71 => ( ! [X2: int,Y2: int] :
% 2.87/1.71 ( ( ord_less_int @ X2 @ Y2 )
% 2.87/1.71 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.71 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_66_order__less__subst2,axiom,
% 2.87/1.71 ! [A2: set_a,B2: set_a,F: set_a > int,C: int] :
% 2.87/1.71 ( ( ord_less_set_a @ A2 @ B2 )
% 2.87/1.71 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 2.87/1.71 => ( ! [X2: set_a,Y2: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ X2 @ Y2 )
% 2.87/1.71 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.71 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_67_order__less__subst2,axiom,
% 2.87/1.71 ! [A2: set_a,B2: set_a,F: set_a > set_a,C: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ A2 @ B2 )
% 2.87/1.71 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 2.87/1.71 => ( ! [X2: set_a,Y2: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ X2 @ Y2 )
% 2.87/1.71 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.71 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_68_order__less__subst2,axiom,
% 2.87/1.71 ! [A2: set_a,B2: set_a,F: set_a > a > $o,C: a > $o] :
% 2.87/1.71 ( ( ord_less_set_a @ A2 @ B2 )
% 2.87/1.71 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 2.87/1.71 => ( ! [X2: set_a,Y2: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ X2 @ Y2 )
% 2.87/1.71 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.71 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_69_order__less__subst2,axiom,
% 2.87/1.71 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > int,C: int] :
% 2.87/1.71 ( ( ord_less_a_o @ A2 @ B2 )
% 2.87/1.71 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 2.87/1.71 => ( ! [X2: a > $o,Y2: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ X2 @ Y2 )
% 2.87/1.71 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.71 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_70_order__less__subst2,axiom,
% 2.87/1.71 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > set_a,C: set_a] :
% 2.87/1.71 ( ( ord_less_a_o @ A2 @ B2 )
% 2.87/1.71 => ( ( ord_less_set_a @ ( F @ B2 ) @ C )
% 2.87/1.71 => ( ! [X2: a > $o,Y2: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ X2 @ Y2 )
% 2.87/1.71 => ( ord_less_set_a @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.71 => ( ord_less_set_a @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_71_order__less__subst2,axiom,
% 2.87/1.71 ! [A2: a > $o,B2: a > $o,F: ( a > $o ) > a > $o,C: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ A2 @ B2 )
% 2.87/1.71 => ( ( ord_less_a_o @ ( F @ B2 ) @ C )
% 2.87/1.71 => ( ! [X2: a > $o,Y2: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ X2 @ Y2 )
% 2.87/1.71 => ( ord_less_a_o @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.71 => ( ord_less_a_o @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_72_order__less__subst2,axiom,
% 2.87/1.71 ! [A2: int,B2: int,F: int > int,C: int] :
% 2.87/1.71 ( ( ord_less_int @ A2 @ B2 )
% 2.87/1.71 => ( ( ord_less_int @ ( F @ B2 ) @ C )
% 2.87/1.71 => ( ! [X2: int,Y2: int] :
% 2.87/1.71 ( ( ord_less_int @ X2 @ Y2 )
% 2.87/1.71 => ( ord_less_int @ ( F @ X2 ) @ ( F @ Y2 ) ) )
% 2.87/1.71 => ( ord_less_int @ ( F @ A2 ) @ C ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_73_lt__ex,axiom,
% 2.87/1.71 ! [X3: int] :
% 2.87/1.71 ? [Y2: int] : ( ord_less_int @ Y2 @ X3 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_74_gt__ex,axiom,
% 2.87/1.71 ! [X3: int] :
% 2.87/1.71 ? [X_1: int] : ( ord_less_int @ X3 @ X_1 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_75_mem__Collect__eq,axiom,
% 2.87/1.71 ! [A2: a,P: a > $o] :
% 2.87/1.71 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 2.87/1.71 = ( P @ A2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_76_Collect__mem__eq,axiom,
% 2.87/1.71 ! [A3: set_a] :
% 2.87/1.71 ( ( collect_a
% 2.87/1.71 @ ^ [X4: a] : ( member_a @ X4 @ A3 ) )
% 2.87/1.71 = A3 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_77_Collect__cong,axiom,
% 2.87/1.71 ! [P: a > $o,Q: a > $o] :
% 2.87/1.71 ( ! [X2: a] :
% 2.87/1.71 ( ( P @ X2 )
% 2.87/1.71 = ( Q @ X2 ) )
% 2.87/1.71 => ( ( collect_a @ P )
% 2.87/1.71 = ( collect_a @ Q ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_78_neqE,axiom,
% 2.87/1.71 ! [X3: int,Y: int] :
% 2.87/1.71 ( ( X3 != Y )
% 2.87/1.71 => ( ~ ( ord_less_int @ X3 @ Y )
% 2.87/1.71 => ( ord_less_int @ Y @ X3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_79_neq__iff,axiom,
% 2.87/1.71 ! [X3: int,Y: int] :
% 2.87/1.71 ( ( X3 != Y )
% 2.87/1.71 = ( ( ord_less_int @ X3 @ Y )
% 2.87/1.71 | ( ord_less_int @ Y @ X3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_80_order_Oasym,axiom,
% 2.87/1.71 ! [A2: set_a,B2: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ A2 @ B2 )
% 2.87/1.71 => ~ ( ord_less_set_a @ B2 @ A2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_81_order_Oasym,axiom,
% 2.87/1.71 ! [A2: a > $o,B2: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ A2 @ B2 )
% 2.87/1.71 => ~ ( ord_less_a_o @ B2 @ A2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_82_order_Oasym,axiom,
% 2.87/1.71 ! [A2: int,B2: int] :
% 2.87/1.71 ( ( ord_less_int @ A2 @ B2 )
% 2.87/1.71 => ~ ( ord_less_int @ B2 @ A2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_83_less__imp__neq,axiom,
% 2.87/1.71 ! [X3: set_a,Y: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ X3 @ Y )
% 2.87/1.71 => ( X3 != Y ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_84_less__imp__neq,axiom,
% 2.87/1.71 ! [X3: a > $o,Y: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ X3 @ Y )
% 2.87/1.71 => ( X3 != Y ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_85_less__imp__neq,axiom,
% 2.87/1.71 ! [X3: int,Y: int] :
% 2.87/1.71 ( ( ord_less_int @ X3 @ Y )
% 2.87/1.71 => ( X3 != Y ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_86_less__asym,axiom,
% 2.87/1.71 ! [X3: set_a,Y: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ X3 @ Y )
% 2.87/1.71 => ~ ( ord_less_set_a @ Y @ X3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_87_less__asym,axiom,
% 2.87/1.71 ! [X3: a > $o,Y: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ X3 @ Y )
% 2.87/1.71 => ~ ( ord_less_a_o @ Y @ X3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_88_less__asym,axiom,
% 2.87/1.71 ! [X3: int,Y: int] :
% 2.87/1.71 ( ( ord_less_int @ X3 @ Y )
% 2.87/1.71 => ~ ( ord_less_int @ Y @ X3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_89_less__asym_H,axiom,
% 2.87/1.71 ! [A2: set_a,B2: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ A2 @ B2 )
% 2.87/1.71 => ~ ( ord_less_set_a @ B2 @ A2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_90_less__asym_H,axiom,
% 2.87/1.71 ! [A2: a > $o,B2: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ A2 @ B2 )
% 2.87/1.71 => ~ ( ord_less_a_o @ B2 @ A2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_91_less__asym_H,axiom,
% 2.87/1.71 ! [A2: int,B2: int] :
% 2.87/1.71 ( ( ord_less_int @ A2 @ B2 )
% 2.87/1.71 => ~ ( ord_less_int @ B2 @ A2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_92_less__trans,axiom,
% 2.87/1.71 ! [X3: set_a,Y: set_a,Z3: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ X3 @ Y )
% 2.87/1.71 => ( ( ord_less_set_a @ Y @ Z3 )
% 2.87/1.71 => ( ord_less_set_a @ X3 @ Z3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_93_less__trans,axiom,
% 2.87/1.71 ! [X3: a > $o,Y: a > $o,Z3: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ X3 @ Y )
% 2.87/1.71 => ( ( ord_less_a_o @ Y @ Z3 )
% 2.87/1.71 => ( ord_less_a_o @ X3 @ Z3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_94_less__trans,axiom,
% 2.87/1.71 ! [X3: int,Y: int,Z3: int] :
% 2.87/1.71 ( ( ord_less_int @ X3 @ Y )
% 2.87/1.71 => ( ( ord_less_int @ Y @ Z3 )
% 2.87/1.71 => ( ord_less_int @ X3 @ Z3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_95_less__linear,axiom,
% 2.87/1.71 ! [X3: int,Y: int] :
% 2.87/1.71 ( ( ord_less_int @ X3 @ Y )
% 2.87/1.71 | ( X3 = Y )
% 2.87/1.71 | ( ord_less_int @ Y @ X3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_96_less__irrefl,axiom,
% 2.87/1.71 ! [X3: set_a] :
% 2.87/1.71 ~ ( ord_less_set_a @ X3 @ X3 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_97_less__irrefl,axiom,
% 2.87/1.71 ! [X3: a > $o] :
% 2.87/1.71 ~ ( ord_less_a_o @ X3 @ X3 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_98_less__irrefl,axiom,
% 2.87/1.71 ! [X3: int] :
% 2.87/1.71 ~ ( ord_less_int @ X3 @ X3 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_99_ord__eq__less__trans,axiom,
% 2.87/1.71 ! [A2: set_a,B2: set_a,C: set_a] :
% 2.87/1.71 ( ( A2 = B2 )
% 2.87/1.71 => ( ( ord_less_set_a @ B2 @ C )
% 2.87/1.71 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_100_ord__eq__less__trans,axiom,
% 2.87/1.71 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 2.87/1.71 ( ( A2 = B2 )
% 2.87/1.71 => ( ( ord_less_a_o @ B2 @ C )
% 2.87/1.71 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_101_ord__eq__less__trans,axiom,
% 2.87/1.71 ! [A2: int,B2: int,C: int] :
% 2.87/1.71 ( ( A2 = B2 )
% 2.87/1.71 => ( ( ord_less_int @ B2 @ C )
% 2.87/1.71 => ( ord_less_int @ A2 @ C ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_102_ord__less__eq__trans,axiom,
% 2.87/1.71 ! [A2: set_a,B2: set_a,C: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ A2 @ B2 )
% 2.87/1.71 => ( ( B2 = C )
% 2.87/1.71 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_103_ord__less__eq__trans,axiom,
% 2.87/1.71 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ A2 @ B2 )
% 2.87/1.71 => ( ( B2 = C )
% 2.87/1.71 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_104_ord__less__eq__trans,axiom,
% 2.87/1.71 ! [A2: int,B2: int,C: int] :
% 2.87/1.71 ( ( ord_less_int @ A2 @ B2 )
% 2.87/1.71 => ( ( B2 = C )
% 2.87/1.71 => ( ord_less_int @ A2 @ C ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_105_dual__order_Oasym,axiom,
% 2.87/1.71 ! [B2: set_a,A2: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ B2 @ A2 )
% 2.87/1.71 => ~ ( ord_less_set_a @ A2 @ B2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_106_dual__order_Oasym,axiom,
% 2.87/1.71 ! [B2: a > $o,A2: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ B2 @ A2 )
% 2.87/1.71 => ~ ( ord_less_a_o @ A2 @ B2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_107_dual__order_Oasym,axiom,
% 2.87/1.71 ! [B2: int,A2: int] :
% 2.87/1.71 ( ( ord_less_int @ B2 @ A2 )
% 2.87/1.71 => ~ ( ord_less_int @ A2 @ B2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_108_less__imp__not__eq,axiom,
% 2.87/1.71 ! [X3: set_a,Y: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ X3 @ Y )
% 2.87/1.71 => ( X3 != Y ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_109_less__imp__not__eq,axiom,
% 2.87/1.71 ! [X3: a > $o,Y: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ X3 @ Y )
% 2.87/1.71 => ( X3 != Y ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_110_less__imp__not__eq,axiom,
% 2.87/1.71 ! [X3: int,Y: int] :
% 2.87/1.71 ( ( ord_less_int @ X3 @ Y )
% 2.87/1.71 => ( X3 != Y ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_111_less__not__sym,axiom,
% 2.87/1.71 ! [X3: set_a,Y: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ X3 @ Y )
% 2.87/1.71 => ~ ( ord_less_set_a @ Y @ X3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_112_less__not__sym,axiom,
% 2.87/1.71 ! [X3: a > $o,Y: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ X3 @ Y )
% 2.87/1.71 => ~ ( ord_less_a_o @ Y @ X3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_113_less__not__sym,axiom,
% 2.87/1.71 ! [X3: int,Y: int] :
% 2.87/1.71 ( ( ord_less_int @ X3 @ Y )
% 2.87/1.71 => ~ ( ord_less_int @ Y @ X3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_114_antisym__conv3,axiom,
% 2.87/1.71 ! [Y: int,X3: int] :
% 2.87/1.71 ( ~ ( ord_less_int @ Y @ X3 )
% 2.87/1.71 => ( ( ~ ( ord_less_int @ X3 @ Y ) )
% 2.87/1.71 = ( X3 = Y ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_115_less__imp__not__eq2,axiom,
% 2.87/1.71 ! [X3: set_a,Y: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ X3 @ Y )
% 2.87/1.71 => ( Y != X3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_116_less__imp__not__eq2,axiom,
% 2.87/1.71 ! [X3: a > $o,Y: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ X3 @ Y )
% 2.87/1.71 => ( Y != X3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_117_less__imp__not__eq2,axiom,
% 2.87/1.71 ! [X3: int,Y: int] :
% 2.87/1.71 ( ( ord_less_int @ X3 @ Y )
% 2.87/1.71 => ( Y != X3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_118_less__imp__triv,axiom,
% 2.87/1.71 ! [X3: set_a,Y: set_a,P: $o] :
% 2.87/1.71 ( ( ord_less_set_a @ X3 @ Y )
% 2.87/1.71 => ( ( ord_less_set_a @ Y @ X3 )
% 2.87/1.71 => P ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_119_less__imp__triv,axiom,
% 2.87/1.71 ! [X3: a > $o,Y: a > $o,P: $o] :
% 2.87/1.71 ( ( ord_less_a_o @ X3 @ Y )
% 2.87/1.71 => ( ( ord_less_a_o @ Y @ X3 )
% 2.87/1.71 => P ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_120_less__imp__triv,axiom,
% 2.87/1.71 ! [X3: int,Y: int,P: $o] :
% 2.87/1.71 ( ( ord_less_int @ X3 @ Y )
% 2.87/1.71 => ( ( ord_less_int @ Y @ X3 )
% 2.87/1.71 => P ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_121_linorder__cases,axiom,
% 2.87/1.71 ! [X3: int,Y: int] :
% 2.87/1.71 ( ~ ( ord_less_int @ X3 @ Y )
% 2.87/1.71 => ( ( X3 != Y )
% 2.87/1.71 => ( ord_less_int @ Y @ X3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_122_dual__order_Oirrefl,axiom,
% 2.87/1.71 ! [A2: set_a] :
% 2.87/1.71 ~ ( ord_less_set_a @ A2 @ A2 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_123_dual__order_Oirrefl,axiom,
% 2.87/1.71 ! [A2: a > $o] :
% 2.87/1.71 ~ ( ord_less_a_o @ A2 @ A2 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_124_dual__order_Oirrefl,axiom,
% 2.87/1.71 ! [A2: int] :
% 2.87/1.71 ~ ( ord_less_int @ A2 @ A2 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_125_order_Ostrict__trans,axiom,
% 2.87/1.71 ! [A2: set_a,B2: set_a,C: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ A2 @ B2 )
% 2.87/1.71 => ( ( ord_less_set_a @ B2 @ C )
% 2.87/1.71 => ( ord_less_set_a @ A2 @ C ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_126_order_Ostrict__trans,axiom,
% 2.87/1.71 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ A2 @ B2 )
% 2.87/1.71 => ( ( ord_less_a_o @ B2 @ C )
% 2.87/1.71 => ( ord_less_a_o @ A2 @ C ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_127_order_Ostrict__trans,axiom,
% 2.87/1.71 ! [A2: int,B2: int,C: int] :
% 2.87/1.71 ( ( ord_less_int @ A2 @ B2 )
% 2.87/1.71 => ( ( ord_less_int @ B2 @ C )
% 2.87/1.71 => ( ord_less_int @ A2 @ C ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_128_less__imp__not__less,axiom,
% 2.87/1.71 ! [X3: set_a,Y: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ X3 @ Y )
% 2.87/1.71 => ~ ( ord_less_set_a @ Y @ X3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_129_less__imp__not__less,axiom,
% 2.87/1.71 ! [X3: a > $o,Y: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ X3 @ Y )
% 2.87/1.71 => ~ ( ord_less_a_o @ Y @ X3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_130_less__imp__not__less,axiom,
% 2.87/1.71 ! [X3: int,Y: int] :
% 2.87/1.71 ( ( ord_less_int @ X3 @ Y )
% 2.87/1.71 => ~ ( ord_less_int @ Y @ X3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_131_linorder__less__wlog,axiom,
% 2.87/1.71 ! [P: int > int > $o,A2: int,B2: int] :
% 2.87/1.71 ( ! [A4: int,B3: int] :
% 2.87/1.71 ( ( ord_less_int @ A4 @ B3 )
% 2.87/1.71 => ( P @ A4 @ B3 ) )
% 2.87/1.71 => ( ! [A4: int] : ( P @ A4 @ A4 )
% 2.87/1.71 => ( ! [A4: int,B3: int] :
% 2.87/1.71 ( ( P @ B3 @ A4 )
% 2.87/1.71 => ( P @ A4 @ B3 ) )
% 2.87/1.71 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_132_dual__order_Ostrict__trans,axiom,
% 2.87/1.71 ! [B2: set_a,A2: set_a,C: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ B2 @ A2 )
% 2.87/1.71 => ( ( ord_less_set_a @ C @ B2 )
% 2.87/1.71 => ( ord_less_set_a @ C @ A2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_133_dual__order_Ostrict__trans,axiom,
% 2.87/1.71 ! [B2: a > $o,A2: a > $o,C: a > $o] :
% 2.87/1.71 ( ( ord_less_a_o @ B2 @ A2 )
% 2.87/1.71 => ( ( ord_less_a_o @ C @ B2 )
% 2.87/1.71 => ( ord_less_a_o @ C @ A2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_134_dual__order_Ostrict__trans,axiom,
% 2.87/1.71 ! [B2: int,A2: int,C: int] :
% 2.87/1.71 ( ( ord_less_int @ B2 @ A2 )
% 2.87/1.71 => ( ( ord_less_int @ C @ B2 )
% 2.87/1.71 => ( ord_less_int @ C @ A2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_135_not__less__iff__gr__or__eq,axiom,
% 2.87/1.71 ! [X3: int,Y: int] :
% 2.87/1.71 ( ( ~ ( ord_less_int @ X3 @ Y ) )
% 2.87/1.71 = ( ( ord_less_int @ Y @ X3 )
% 2.87/1.71 | ( X3 = Y ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_136_binsert_Osimps_I1_J,axiom,
% 2.87/1.71 ! [H: a > int,E: a] :
% 2.87/1.71 ( ( binary1226383794sert_a @ H @ E @ binary476621312_Tip_a )
% 2.87/1.71 = ( binary717961607le_T_a @ binary476621312_Tip_a @ E @ binary476621312_Tip_a ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_137_verit__comp__simplify1_I1_J,axiom,
% 2.87/1.71 ! [A2: set_a] :
% 2.87/1.71 ~ ( ord_less_set_a @ A2 @ A2 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_138_verit__comp__simplify1_I1_J,axiom,
% 2.87/1.71 ! [A2: a > $o] :
% 2.87/1.71 ~ ( ord_less_a_o @ A2 @ A2 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_139_verit__comp__simplify1_I1_J,axiom,
% 2.87/1.71 ! [A2: int] :
% 2.87/1.71 ~ ( ord_less_int @ A2 @ A2 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_140_c2,axiom,
% 2.87/1.71 ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t2 ) )
% 2.87/1.71 = ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t2 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_141_c1,axiom,
% 2.87/1.71 ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t1 ) )
% 2.87/1.71 = ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t1 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_142_Tree_Opred__inject_I2_J,axiom,
% 2.87/1.71 ! [P: a > $o,A2: binary1439146945Tree_a,Aa: a,Ab: binary1439146945Tree_a] :
% 2.87/1.71 ( ( binary1452917696Tree_a @ P @ ( binary717961607le_T_a @ A2 @ Aa @ Ab ) )
% 2.87/1.71 = ( ( binary1452917696Tree_a @ P @ A2 )
% 2.87/1.71 & ( P @ Aa )
% 2.87/1.71 & ( binary1452917696Tree_a @ P @ Ab ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_143_bot__apply,axiom,
% 2.87/1.71 ( bot_bot_a_o
% 2.87/1.71 = ( ^ [X4: a] : bot_bot_o ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_144_bot__fun__def,axiom,
% 2.87/1.71 ( bot_bot_a_o
% 2.87/1.71 = ( ^ [X4: a] : bot_bot_o ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_145_Tree_Opred__inject_I1_J,axiom,
% 2.87/1.71 ! [P: a > $o] : ( binary1452917696Tree_a @ P @ binary476621312_Tip_a ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_146_setOf_Osimps_I2_J,axiom,
% 2.87/1.71 ! [T1: binary1439146945Tree_a,X3: a,T2: binary1439146945Tree_a] :
% 2.87/1.71 ( ( binary945792244etOf_a @ ( binary717961607le_T_a @ T1 @ X3 @ T2 ) )
% 2.87/1.71 = ( sup_sup_set_a @ ( sup_sup_set_a @ ( binary945792244etOf_a @ T1 ) @ ( binary945792244etOf_a @ T2 ) ) @ ( insert_a @ X3 @ bot_bot_set_a ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_147_setOf_Osimps_I1_J,axiom,
% 2.87/1.71 ( ( binary945792244etOf_a @ binary476621312_Tip_a )
% 2.87/1.71 = bot_bot_set_a ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_148_bot_Onot__eq__extremum,axiom,
% 2.87/1.71 ! [A2: a > $o] :
% 2.87/1.71 ( ( A2 != bot_bot_a_o )
% 2.87/1.71 = ( ord_less_a_o @ bot_bot_a_o @ A2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_149_bot_Onot__eq__extremum,axiom,
% 2.87/1.71 ! [A2: set_a] :
% 2.87/1.71 ( ( A2 != bot_bot_set_a )
% 2.87/1.71 = ( ord_less_set_a @ bot_bot_set_a @ A2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_150_bot_Oextremum__strict,axiom,
% 2.87/1.71 ! [A2: a > $o] :
% 2.87/1.71 ~ ( ord_less_a_o @ A2 @ bot_bot_a_o ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_151_bot_Oextremum__strict,axiom,
% 2.87/1.71 ! [A2: set_a] :
% 2.87/1.71 ~ ( ord_less_set_a @ A2 @ bot_bot_set_a ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_152_Tree_Odistinct_I1_J,axiom,
% 2.87/1.71 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 2.87/1.71 ( binary476621312_Tip_a
% 2.87/1.71 != ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_153_Tree_Oinduct,axiom,
% 2.87/1.71 ! [P: binary1439146945Tree_a > $o,Tree: binary1439146945Tree_a] :
% 2.87/1.71 ( ( P @ binary476621312_Tip_a )
% 2.87/1.71 => ( ! [X1: binary1439146945Tree_a,X24: a,X32: binary1439146945Tree_a] :
% 2.87/1.71 ( ( P @ X1 )
% 2.87/1.71 => ( ( P @ X32 )
% 2.87/1.71 => ( P @ ( binary717961607le_T_a @ X1 @ X24 @ X32 ) ) ) )
% 2.87/1.71 => ( P @ Tree ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_154_Tree_Oexhaust,axiom,
% 2.87/1.71 ! [Y: binary1439146945Tree_a] :
% 2.87/1.71 ( ( Y != binary476621312_Tip_a )
% 2.87/1.71 => ~ ! [X212: binary1439146945Tree_a,X222: a,X232: binary1439146945Tree_a] :
% 2.87/1.71 ( Y
% 2.87/1.71 != ( binary717961607le_T_a @ X212 @ X222 @ X232 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_155_sortedTree_Osimps_I1_J,axiom,
% 2.87/1.71 ! [H: a > int] : ( binary1721989714Tree_a @ H @ binary476621312_Tip_a ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_156_insert__Diff__single,axiom,
% 2.87/1.71 ! [A2: a,A3: set_a] :
% 2.87/1.71 ( ( insert_a @ A2 @ ( minus_minus_set_a @ A3 @ ( insert_a @ A2 @ bot_bot_set_a ) ) )
% 2.87/1.71 = ( insert_a @ A2 @ A3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_157_Un__Diff__cancel,axiom,
% 2.87/1.71 ! [A3: set_a,B4: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ A3 @ ( minus_minus_set_a @ B4 @ A3 ) )
% 2.87/1.71 = ( sup_sup_set_a @ A3 @ B4 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_158_Un__Diff__cancel2,axiom,
% 2.87/1.71 ! [B4: set_a,A3: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ ( minus_minus_set_a @ B4 @ A3 ) @ A3 )
% 2.87/1.71 = ( sup_sup_set_a @ B4 @ A3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_159_Diff__insert0,axiom,
% 2.87/1.71 ! [X3: a,A3: set_a,B4: set_a] :
% 2.87/1.71 ( ~ ( member_a @ X3 @ A3 )
% 2.87/1.71 => ( ( minus_minus_set_a @ A3 @ ( insert_a @ X3 @ B4 ) )
% 2.87/1.71 = ( minus_minus_set_a @ A3 @ B4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_160_insert__Diff1,axiom,
% 2.87/1.71 ! [X3: a,B4: set_a,A3: set_a] :
% 2.87/1.71 ( ( member_a @ X3 @ B4 )
% 2.87/1.71 => ( ( minus_minus_set_a @ ( insert_a @ X3 @ A3 ) @ B4 )
% 2.87/1.71 = ( minus_minus_set_a @ A3 @ B4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_161_Un__insert__left,axiom,
% 2.87/1.71 ! [A2: a,B4: set_a,C2: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ ( insert_a @ A2 @ B4 ) @ C2 )
% 2.87/1.71 = ( insert_a @ A2 @ ( sup_sup_set_a @ B4 @ C2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_162_empty__Collect__eq,axiom,
% 2.87/1.71 ! [P: a > $o] :
% 2.87/1.71 ( ( bot_bot_set_a
% 2.87/1.71 = ( collect_a @ P ) )
% 2.87/1.71 = ( ! [X4: a] :
% 2.87/1.71 ~ ( P @ X4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_163_Collect__empty__eq,axiom,
% 2.87/1.71 ! [P: a > $o] :
% 2.87/1.71 ( ( ( collect_a @ P )
% 2.87/1.71 = bot_bot_set_a )
% 2.87/1.71 = ( ! [X4: a] :
% 2.87/1.71 ~ ( P @ X4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_164_all__not__in__conv,axiom,
% 2.87/1.71 ! [A3: set_a] :
% 2.87/1.71 ( ( ! [X4: a] :
% 2.87/1.71 ~ ( member_a @ X4 @ A3 ) )
% 2.87/1.71 = ( A3 = bot_bot_set_a ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_165_empty__iff,axiom,
% 2.87/1.71 ! [C: a] :
% 2.87/1.71 ~ ( member_a @ C @ bot_bot_set_a ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_166_insert__absorb2,axiom,
% 2.87/1.71 ! [X3: a,A3: set_a] :
% 2.87/1.71 ( ( insert_a @ X3 @ ( insert_a @ X3 @ A3 ) )
% 2.87/1.71 = ( insert_a @ X3 @ A3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_167_insert__iff,axiom,
% 2.87/1.71 ! [A2: a,B2: a,A3: set_a] :
% 2.87/1.71 ( ( member_a @ A2 @ ( insert_a @ B2 @ A3 ) )
% 2.87/1.71 = ( ( A2 = B2 )
% 2.87/1.71 | ( member_a @ A2 @ A3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_168_insertCI,axiom,
% 2.87/1.71 ! [A2: a,B4: set_a,B2: a] :
% 2.87/1.71 ( ( ~ ( member_a @ A2 @ B4 )
% 2.87/1.71 => ( A2 = B2 ) )
% 2.87/1.71 => ( member_a @ A2 @ ( insert_a @ B2 @ B4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_169_Un__iff,axiom,
% 2.87/1.71 ! [C: a,A3: set_a,B4: set_a] :
% 2.87/1.71 ( ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) )
% 2.87/1.71 = ( ( member_a @ C @ A3 )
% 2.87/1.71 | ( member_a @ C @ B4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_170_UnCI,axiom,
% 2.87/1.71 ! [C: a,B4: set_a,A3: set_a] :
% 2.87/1.71 ( ( ~ ( member_a @ C @ B4 )
% 2.87/1.71 => ( member_a @ C @ A3 ) )
% 2.87/1.71 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_171_Diff__idemp,axiom,
% 2.87/1.71 ! [A3: set_a,B4: set_a] :
% 2.87/1.71 ( ( minus_minus_set_a @ ( minus_minus_set_a @ A3 @ B4 ) @ B4 )
% 2.87/1.71 = ( minus_minus_set_a @ A3 @ B4 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_172_Diff__iff,axiom,
% 2.87/1.71 ! [C: a,A3: set_a,B4: set_a] :
% 2.87/1.71 ( ( member_a @ C @ ( minus_minus_set_a @ A3 @ B4 ) )
% 2.87/1.71 = ( ( member_a @ C @ A3 )
% 2.87/1.71 & ~ ( member_a @ C @ B4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_173_DiffI,axiom,
% 2.87/1.71 ! [C: a,A3: set_a,B4: set_a] :
% 2.87/1.71 ( ( member_a @ C @ A3 )
% 2.87/1.71 => ( ~ ( member_a @ C @ B4 )
% 2.87/1.71 => ( member_a @ C @ ( minus_minus_set_a @ A3 @ B4 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_174_singletonI,axiom,
% 2.87/1.71 ! [A2: a] : ( member_a @ A2 @ ( insert_a @ A2 @ bot_bot_set_a ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_175_Un__empty,axiom,
% 2.87/1.71 ! [A3: set_a,B4: set_a] :
% 2.87/1.71 ( ( ( sup_sup_set_a @ A3 @ B4 )
% 2.87/1.71 = bot_bot_set_a )
% 2.87/1.71 = ( ( A3 = bot_bot_set_a )
% 2.87/1.71 & ( B4 = bot_bot_set_a ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_176_Diff__cancel,axiom,
% 2.87/1.71 ! [A3: set_a] :
% 2.87/1.71 ( ( minus_minus_set_a @ A3 @ A3 )
% 2.87/1.71 = bot_bot_set_a ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_177_empty__Diff,axiom,
% 2.87/1.71 ! [A3: set_a] :
% 2.87/1.71 ( ( minus_minus_set_a @ bot_bot_set_a @ A3 )
% 2.87/1.71 = bot_bot_set_a ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_178_Diff__empty,axiom,
% 2.87/1.71 ! [A3: set_a] :
% 2.87/1.71 ( ( minus_minus_set_a @ A3 @ bot_bot_set_a )
% 2.87/1.71 = A3 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_179_Un__insert__right,axiom,
% 2.87/1.71 ! [A3: set_a,A2: a,B4: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ A3 @ ( insert_a @ A2 @ B4 ) )
% 2.87/1.71 = ( insert_a @ A2 @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_180_bot__set__def,axiom,
% 2.87/1.71 ( bot_bot_set_a
% 2.87/1.71 = ( collect_a @ bot_bot_a_o ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_181_not__psubset__empty,axiom,
% 2.87/1.71 ! [A3: set_a] :
% 2.87/1.71 ~ ( ord_less_set_a @ A3 @ bot_bot_set_a ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_182_ex__in__conv,axiom,
% 2.87/1.71 ! [A3: set_a] :
% 2.87/1.71 ( ( ? [X4: a] : ( member_a @ X4 @ A3 ) )
% 2.87/1.71 = ( A3 != bot_bot_set_a ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_183_equals0I,axiom,
% 2.87/1.71 ! [A3: set_a] :
% 2.87/1.71 ( ! [Y2: a] :
% 2.87/1.71 ~ ( member_a @ Y2 @ A3 )
% 2.87/1.71 => ( A3 = bot_bot_set_a ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_184_equals0D,axiom,
% 2.87/1.71 ! [A3: set_a,A2: a] :
% 2.87/1.71 ( ( A3 = bot_bot_set_a )
% 2.87/1.71 => ~ ( member_a @ A2 @ A3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_185_emptyE,axiom,
% 2.87/1.71 ! [A2: a] :
% 2.87/1.71 ~ ( member_a @ A2 @ bot_bot_set_a ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_186_mk__disjoint__insert,axiom,
% 2.87/1.71 ! [A2: a,A3: set_a] :
% 2.87/1.71 ( ( member_a @ A2 @ A3 )
% 2.87/1.71 => ? [B5: set_a] :
% 2.87/1.71 ( ( A3
% 2.87/1.71 = ( insert_a @ A2 @ B5 ) )
% 2.87/1.71 & ~ ( member_a @ A2 @ B5 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_187_insert__commute,axiom,
% 2.87/1.71 ! [X3: a,Y: a,A3: set_a] :
% 2.87/1.71 ( ( insert_a @ X3 @ ( insert_a @ Y @ A3 ) )
% 2.87/1.71 = ( insert_a @ Y @ ( insert_a @ X3 @ A3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_188_insert__eq__iff,axiom,
% 2.87/1.71 ! [A2: a,A3: set_a,B2: a,B4: set_a] :
% 2.87/1.71 ( ~ ( member_a @ A2 @ A3 )
% 2.87/1.71 => ( ~ ( member_a @ B2 @ B4 )
% 2.87/1.71 => ( ( ( insert_a @ A2 @ A3 )
% 2.87/1.71 = ( insert_a @ B2 @ B4 ) )
% 2.87/1.71 = ( ( ( A2 = B2 )
% 2.87/1.71 => ( A3 = B4 ) )
% 2.87/1.71 & ( ( A2 != B2 )
% 2.87/1.71 => ? [C3: set_a] :
% 2.87/1.71 ( ( A3
% 2.87/1.71 = ( insert_a @ B2 @ C3 ) )
% 2.87/1.71 & ~ ( member_a @ B2 @ C3 )
% 2.87/1.71 & ( B4
% 2.87/1.71 = ( insert_a @ A2 @ C3 ) )
% 2.87/1.71 & ~ ( member_a @ A2 @ C3 ) ) ) ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_189_insert__absorb,axiom,
% 2.87/1.71 ! [A2: a,A3: set_a] :
% 2.87/1.71 ( ( member_a @ A2 @ A3 )
% 2.87/1.71 => ( ( insert_a @ A2 @ A3 )
% 2.87/1.71 = A3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_190_insert__ident,axiom,
% 2.87/1.71 ! [X3: a,A3: set_a,B4: set_a] :
% 2.87/1.71 ( ~ ( member_a @ X3 @ A3 )
% 2.87/1.71 => ( ~ ( member_a @ X3 @ B4 )
% 2.87/1.71 => ( ( ( insert_a @ X3 @ A3 )
% 2.87/1.71 = ( insert_a @ X3 @ B4 ) )
% 2.87/1.71 = ( A3 = B4 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_191_Set_Oset__insert,axiom,
% 2.87/1.71 ! [X3: a,A3: set_a] :
% 2.87/1.71 ( ( member_a @ X3 @ A3 )
% 2.87/1.71 => ~ ! [B5: set_a] :
% 2.87/1.71 ( ( A3
% 2.87/1.71 = ( insert_a @ X3 @ B5 ) )
% 2.87/1.71 => ( member_a @ X3 @ B5 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_192_insertI2,axiom,
% 2.87/1.71 ! [A2: a,B4: set_a,B2: a] :
% 2.87/1.71 ( ( member_a @ A2 @ B4 )
% 2.87/1.71 => ( member_a @ A2 @ ( insert_a @ B2 @ B4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_193_insertI1,axiom,
% 2.87/1.71 ! [A2: a,B4: set_a] : ( member_a @ A2 @ ( insert_a @ A2 @ B4 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_194_insertE,axiom,
% 2.87/1.71 ! [A2: a,B2: a,A3: set_a] :
% 2.87/1.71 ( ( member_a @ A2 @ ( insert_a @ B2 @ A3 ) )
% 2.87/1.71 => ( ( A2 != B2 )
% 2.87/1.71 => ( member_a @ A2 @ A3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_195_Un__left__commute,axiom,
% 2.87/1.71 ! [A3: set_a,B4: set_a,C2: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ A3 @ ( sup_sup_set_a @ B4 @ C2 ) )
% 2.87/1.71 = ( sup_sup_set_a @ B4 @ ( sup_sup_set_a @ A3 @ C2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_196_Un__left__absorb,axiom,
% 2.87/1.71 ! [A3: set_a,B4: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ A3 @ ( sup_sup_set_a @ A3 @ B4 ) )
% 2.87/1.71 = ( sup_sup_set_a @ A3 @ B4 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_197_Un__commute,axiom,
% 2.87/1.71 ( sup_sup_set_a
% 2.87/1.71 = ( ^ [A5: set_a,B6: set_a] : ( sup_sup_set_a @ B6 @ A5 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_198_Un__absorb,axiom,
% 2.87/1.71 ! [A3: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ A3 @ A3 )
% 2.87/1.71 = A3 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_199_Un__assoc,axiom,
% 2.87/1.71 ! [A3: set_a,B4: set_a,C2: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ ( sup_sup_set_a @ A3 @ B4 ) @ C2 )
% 2.87/1.71 = ( sup_sup_set_a @ A3 @ ( sup_sup_set_a @ B4 @ C2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_200_ball__Un,axiom,
% 2.87/1.71 ! [A3: set_a,B4: set_a,P: a > $o] :
% 2.87/1.71 ( ( ! [X4: a] :
% 2.87/1.71 ( ( member_a @ X4 @ ( sup_sup_set_a @ A3 @ B4 ) )
% 2.87/1.71 => ( P @ X4 ) ) )
% 2.87/1.71 = ( ! [X4: a] :
% 2.87/1.71 ( ( member_a @ X4 @ A3 )
% 2.87/1.71 => ( P @ X4 ) )
% 2.87/1.71 & ! [X4: a] :
% 2.87/1.71 ( ( member_a @ X4 @ B4 )
% 2.87/1.71 => ( P @ X4 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_201_bex__Un,axiom,
% 2.87/1.71 ! [A3: set_a,B4: set_a,P: a > $o] :
% 2.87/1.71 ( ( ? [X4: a] :
% 2.87/1.71 ( ( member_a @ X4 @ ( sup_sup_set_a @ A3 @ B4 ) )
% 2.87/1.71 & ( P @ X4 ) ) )
% 2.87/1.71 = ( ? [X4: a] :
% 2.87/1.71 ( ( member_a @ X4 @ A3 )
% 2.87/1.71 & ( P @ X4 ) )
% 2.87/1.71 | ? [X4: a] :
% 2.87/1.71 ( ( member_a @ X4 @ B4 )
% 2.87/1.71 & ( P @ X4 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_202_UnI2,axiom,
% 2.87/1.71 ! [C: a,B4: set_a,A3: set_a] :
% 2.87/1.71 ( ( member_a @ C @ B4 )
% 2.87/1.71 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_203_UnI1,axiom,
% 2.87/1.71 ! [C: a,A3: set_a,B4: set_a] :
% 2.87/1.71 ( ( member_a @ C @ A3 )
% 2.87/1.71 => ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_204_UnE,axiom,
% 2.87/1.71 ! [C: a,A3: set_a,B4: set_a] :
% 2.87/1.71 ( ( member_a @ C @ ( sup_sup_set_a @ A3 @ B4 ) )
% 2.87/1.71 => ( ~ ( member_a @ C @ A3 )
% 2.87/1.71 => ( member_a @ C @ B4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_205_psubset__imp__ex__mem,axiom,
% 2.87/1.71 ! [A3: set_a,B4: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ A3 @ B4 )
% 2.87/1.71 => ? [B3: a] : ( member_a @ B3 @ ( minus_minus_set_a @ B4 @ A3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_206_DiffD2,axiom,
% 2.87/1.71 ! [C: a,A3: set_a,B4: set_a] :
% 2.87/1.71 ( ( member_a @ C @ ( minus_minus_set_a @ A3 @ B4 ) )
% 2.87/1.71 => ~ ( member_a @ C @ B4 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_207_DiffD1,axiom,
% 2.87/1.71 ! [C: a,A3: set_a,B4: set_a] :
% 2.87/1.71 ( ( member_a @ C @ ( minus_minus_set_a @ A3 @ B4 ) )
% 2.87/1.71 => ( member_a @ C @ A3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_208_DiffE,axiom,
% 2.87/1.71 ! [C: a,A3: set_a,B4: set_a] :
% 2.87/1.71 ( ( member_a @ C @ ( minus_minus_set_a @ A3 @ B4 ) )
% 2.87/1.71 => ~ ( ( member_a @ C @ A3 )
% 2.87/1.71 => ( member_a @ C @ B4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_209_singleton__inject,axiom,
% 2.87/1.71 ! [A2: a,B2: a] :
% 2.87/1.71 ( ( ( insert_a @ A2 @ bot_bot_set_a )
% 2.87/1.71 = ( insert_a @ B2 @ bot_bot_set_a ) )
% 2.87/1.71 => ( A2 = B2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_210_insert__not__empty,axiom,
% 2.87/1.71 ! [A2: a,A3: set_a] :
% 2.87/1.71 ( ( insert_a @ A2 @ A3 )
% 2.87/1.71 != bot_bot_set_a ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_211_doubleton__eq__iff,axiom,
% 2.87/1.71 ! [A2: a,B2: a,C: a,D: a] :
% 2.87/1.71 ( ( ( insert_a @ A2 @ ( insert_a @ B2 @ bot_bot_set_a ) )
% 2.87/1.71 = ( insert_a @ C @ ( insert_a @ D @ bot_bot_set_a ) ) )
% 2.87/1.71 = ( ( ( A2 = C )
% 2.87/1.71 & ( B2 = D ) )
% 2.87/1.71 | ( ( A2 = D )
% 2.87/1.71 & ( B2 = C ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_212_singleton__iff,axiom,
% 2.87/1.71 ! [B2: a,A2: a] :
% 2.87/1.71 ( ( member_a @ B2 @ ( insert_a @ A2 @ bot_bot_set_a ) )
% 2.87/1.71 = ( B2 = A2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_213_singletonD,axiom,
% 2.87/1.71 ! [B2: a,A2: a] :
% 2.87/1.71 ( ( member_a @ B2 @ ( insert_a @ A2 @ bot_bot_set_a ) )
% 2.87/1.71 => ( B2 = A2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_214_Un__empty__right,axiom,
% 2.87/1.71 ! [A3: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ A3 @ bot_bot_set_a )
% 2.87/1.71 = A3 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_215_Un__empty__left,axiom,
% 2.87/1.71 ! [B4: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ bot_bot_set_a @ B4 )
% 2.87/1.71 = B4 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_216_insert__Diff__if,axiom,
% 2.87/1.71 ! [X3: a,B4: set_a,A3: set_a] :
% 2.87/1.71 ( ( ( member_a @ X3 @ B4 )
% 2.87/1.71 => ( ( minus_minus_set_a @ ( insert_a @ X3 @ A3 ) @ B4 )
% 2.87/1.71 = ( minus_minus_set_a @ A3 @ B4 ) ) )
% 2.87/1.71 & ( ~ ( member_a @ X3 @ B4 )
% 2.87/1.71 => ( ( minus_minus_set_a @ ( insert_a @ X3 @ A3 ) @ B4 )
% 2.87/1.71 = ( insert_a @ X3 @ ( minus_minus_set_a @ A3 @ B4 ) ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_217_Un__Diff,axiom,
% 2.87/1.71 ! [A3: set_a,B4: set_a,C2: set_a] :
% 2.87/1.71 ( ( minus_minus_set_a @ ( sup_sup_set_a @ A3 @ B4 ) @ C2 )
% 2.87/1.71 = ( sup_sup_set_a @ ( minus_minus_set_a @ A3 @ C2 ) @ ( minus_minus_set_a @ B4 @ C2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_218_singleton__Un__iff,axiom,
% 2.87/1.71 ! [X3: a,A3: set_a,B4: set_a] :
% 2.87/1.71 ( ( ( insert_a @ X3 @ bot_bot_set_a )
% 2.87/1.71 = ( sup_sup_set_a @ A3 @ B4 ) )
% 2.87/1.71 = ( ( ( A3 = bot_bot_set_a )
% 2.87/1.71 & ( B4
% 2.87/1.71 = ( insert_a @ X3 @ bot_bot_set_a ) ) )
% 2.87/1.71 | ( ( A3
% 2.87/1.71 = ( insert_a @ X3 @ bot_bot_set_a ) )
% 2.87/1.71 & ( B4 = bot_bot_set_a ) )
% 2.87/1.71 | ( ( A3
% 2.87/1.71 = ( insert_a @ X3 @ bot_bot_set_a ) )
% 2.87/1.71 & ( B4
% 2.87/1.71 = ( insert_a @ X3 @ bot_bot_set_a ) ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_219_Un__singleton__iff,axiom,
% 2.87/1.71 ! [A3: set_a,B4: set_a,X3: a] :
% 2.87/1.71 ( ( ( sup_sup_set_a @ A3 @ B4 )
% 2.87/1.71 = ( insert_a @ X3 @ bot_bot_set_a ) )
% 2.87/1.71 = ( ( ( A3 = bot_bot_set_a )
% 2.87/1.71 & ( B4
% 2.87/1.71 = ( insert_a @ X3 @ bot_bot_set_a ) ) )
% 2.87/1.71 | ( ( A3
% 2.87/1.71 = ( insert_a @ X3 @ bot_bot_set_a ) )
% 2.87/1.71 & ( B4 = bot_bot_set_a ) )
% 2.87/1.71 | ( ( A3
% 2.87/1.71 = ( insert_a @ X3 @ bot_bot_set_a ) )
% 2.87/1.71 & ( B4
% 2.87/1.71 = ( insert_a @ X3 @ bot_bot_set_a ) ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_220_insert__is__Un,axiom,
% 2.87/1.71 ( insert_a
% 2.87/1.71 = ( ^ [A: a] : ( sup_sup_set_a @ ( insert_a @ A @ bot_bot_set_a ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_221_Diff__insert__absorb,axiom,
% 2.87/1.71 ! [X3: a,A3: set_a] :
% 2.87/1.71 ( ~ ( member_a @ X3 @ A3 )
% 2.87/1.71 => ( ( minus_minus_set_a @ ( insert_a @ X3 @ A3 ) @ ( insert_a @ X3 @ bot_bot_set_a ) )
% 2.87/1.71 = A3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_222_Diff__insert2,axiom,
% 2.87/1.71 ! [A3: set_a,A2: a,B4: set_a] :
% 2.87/1.71 ( ( minus_minus_set_a @ A3 @ ( insert_a @ A2 @ B4 ) )
% 2.87/1.71 = ( minus_minus_set_a @ ( minus_minus_set_a @ A3 @ ( insert_a @ A2 @ bot_bot_set_a ) ) @ B4 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_223_insert__Diff,axiom,
% 2.87/1.71 ! [A2: a,A3: set_a] :
% 2.87/1.71 ( ( member_a @ A2 @ A3 )
% 2.87/1.71 => ( ( insert_a @ A2 @ ( minus_minus_set_a @ A3 @ ( insert_a @ A2 @ bot_bot_set_a ) ) )
% 2.87/1.71 = A3 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_224_Diff__insert,axiom,
% 2.87/1.71 ! [A3: set_a,A2: a,B4: set_a] :
% 2.87/1.71 ( ( minus_minus_set_a @ A3 @ ( insert_a @ A2 @ B4 ) )
% 2.87/1.71 = ( minus_minus_set_a @ ( minus_minus_set_a @ A3 @ B4 ) @ ( insert_a @ A2 @ bot_bot_set_a ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_225_sup__bot_Oright__neutral,axiom,
% 2.87/1.71 ! [A2: a > $o] :
% 2.87/1.71 ( ( sup_sup_a_o @ A2 @ bot_bot_a_o )
% 2.87/1.71 = A2 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_226_sup__bot_Oright__neutral,axiom,
% 2.87/1.71 ! [A2: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ A2 @ bot_bot_set_a )
% 2.87/1.71 = A2 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_227_sup__bot_Oneutr__eq__iff,axiom,
% 2.87/1.71 ! [A2: a > $o,B2: a > $o] :
% 2.87/1.71 ( ( bot_bot_a_o
% 2.87/1.71 = ( sup_sup_a_o @ A2 @ B2 ) )
% 2.87/1.71 = ( ( A2 = bot_bot_a_o )
% 2.87/1.71 & ( B2 = bot_bot_a_o ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_228_sup__bot_Oneutr__eq__iff,axiom,
% 2.87/1.71 ! [A2: set_a,B2: set_a] :
% 2.87/1.71 ( ( bot_bot_set_a
% 2.87/1.71 = ( sup_sup_set_a @ A2 @ B2 ) )
% 2.87/1.71 = ( ( A2 = bot_bot_set_a )
% 2.87/1.71 & ( B2 = bot_bot_set_a ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_229_sup__bot_Oleft__neutral,axiom,
% 2.87/1.71 ! [A2: a > $o] :
% 2.87/1.71 ( ( sup_sup_a_o @ bot_bot_a_o @ A2 )
% 2.87/1.71 = A2 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_230_sup__bot_Oleft__neutral,axiom,
% 2.87/1.71 ! [A2: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ bot_bot_set_a @ A2 )
% 2.87/1.71 = A2 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_231_sup__bot_Oeq__neutr__iff,axiom,
% 2.87/1.71 ! [A2: a > $o,B2: a > $o] :
% 2.87/1.71 ( ( ( sup_sup_a_o @ A2 @ B2 )
% 2.87/1.71 = bot_bot_a_o )
% 2.87/1.71 = ( ( A2 = bot_bot_a_o )
% 2.87/1.71 & ( B2 = bot_bot_a_o ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_232_sup__bot_Oeq__neutr__iff,axiom,
% 2.87/1.71 ! [A2: set_a,B2: set_a] :
% 2.87/1.71 ( ( ( sup_sup_set_a @ A2 @ B2 )
% 2.87/1.71 = bot_bot_set_a )
% 2.87/1.71 = ( ( A2 = bot_bot_set_a )
% 2.87/1.71 & ( B2 = bot_bot_set_a ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_233_sup__eq__bot__iff,axiom,
% 2.87/1.71 ! [X3: a > $o,Y: a > $o] :
% 2.87/1.71 ( ( ( sup_sup_a_o @ X3 @ Y )
% 2.87/1.71 = bot_bot_a_o )
% 2.87/1.71 = ( ( X3 = bot_bot_a_o )
% 2.87/1.71 & ( Y = bot_bot_a_o ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_234_sup__eq__bot__iff,axiom,
% 2.87/1.71 ! [X3: set_a,Y: set_a] :
% 2.87/1.71 ( ( ( sup_sup_set_a @ X3 @ Y )
% 2.87/1.71 = bot_bot_set_a )
% 2.87/1.71 = ( ( X3 = bot_bot_set_a )
% 2.87/1.71 & ( Y = bot_bot_set_a ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_235_minus__apply,axiom,
% 2.87/1.71 ( minus_minus_a_o
% 2.87/1.71 = ( ^ [A5: a > $o,B6: a > $o,X4: a] : ( minus_minus_o @ ( A5 @ X4 ) @ ( B6 @ X4 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_236_sup__apply,axiom,
% 2.87/1.71 ( sup_sup_a_o
% 2.87/1.71 = ( ^ [F2: a > $o,G: a > $o,X4: a] : ( sup_sup_o @ ( F2 @ X4 ) @ ( G @ X4 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_237_sup_Oidem,axiom,
% 2.87/1.71 ! [A2: int] :
% 2.87/1.71 ( ( sup_sup_int @ A2 @ A2 )
% 2.87/1.71 = A2 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_238_sup_Oidem,axiom,
% 2.87/1.71 ! [A2: a > $o] :
% 2.87/1.71 ( ( sup_sup_a_o @ A2 @ A2 )
% 2.87/1.71 = A2 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_239_sup_Oidem,axiom,
% 2.87/1.71 ! [A2: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ A2 @ A2 )
% 2.87/1.71 = A2 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_240_sup__idem,axiom,
% 2.87/1.71 ! [X3: int] :
% 2.87/1.71 ( ( sup_sup_int @ X3 @ X3 )
% 2.87/1.71 = X3 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_241_sup__idem,axiom,
% 2.87/1.71 ! [X3: a > $o] :
% 2.87/1.71 ( ( sup_sup_a_o @ X3 @ X3 )
% 2.87/1.71 = X3 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_242_sup__idem,axiom,
% 2.87/1.71 ! [X3: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ X3 @ X3 )
% 2.87/1.71 = X3 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_243_sup_Oleft__idem,axiom,
% 2.87/1.71 ! [A2: int,B2: int] :
% 2.87/1.71 ( ( sup_sup_int @ A2 @ ( sup_sup_int @ A2 @ B2 ) )
% 2.87/1.71 = ( sup_sup_int @ A2 @ B2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_244_sup_Oleft__idem,axiom,
% 2.87/1.71 ! [A2: a > $o,B2: a > $o] :
% 2.87/1.71 ( ( sup_sup_a_o @ A2 @ ( sup_sup_a_o @ A2 @ B2 ) )
% 2.87/1.71 = ( sup_sup_a_o @ A2 @ B2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_245_sup_Oleft__idem,axiom,
% 2.87/1.71 ! [A2: set_a,B2: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ A2 @ ( sup_sup_set_a @ A2 @ B2 ) )
% 2.87/1.71 = ( sup_sup_set_a @ A2 @ B2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_246_sup__left__idem,axiom,
% 2.87/1.71 ! [X3: int,Y: int] :
% 2.87/1.71 ( ( sup_sup_int @ X3 @ ( sup_sup_int @ X3 @ Y ) )
% 2.87/1.71 = ( sup_sup_int @ X3 @ Y ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_247_sup__left__idem,axiom,
% 2.87/1.71 ! [X3: a > $o,Y: a > $o] :
% 2.87/1.71 ( ( sup_sup_a_o @ X3 @ ( sup_sup_a_o @ X3 @ Y ) )
% 2.87/1.71 = ( sup_sup_a_o @ X3 @ Y ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_248_sup__left__idem,axiom,
% 2.87/1.71 ! [X3: set_a,Y: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ X3 @ Y ) )
% 2.87/1.71 = ( sup_sup_set_a @ X3 @ Y ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_249_sup_Oright__idem,axiom,
% 2.87/1.71 ! [A2: int,B2: int] :
% 2.87/1.71 ( ( sup_sup_int @ ( sup_sup_int @ A2 @ B2 ) @ B2 )
% 2.87/1.71 = ( sup_sup_int @ A2 @ B2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_250_sup_Oright__idem,axiom,
% 2.87/1.71 ! [A2: a > $o,B2: a > $o] :
% 2.87/1.71 ( ( sup_sup_a_o @ ( sup_sup_a_o @ A2 @ B2 ) @ B2 )
% 2.87/1.71 = ( sup_sup_a_o @ A2 @ B2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_251_sup_Oright__idem,axiom,
% 2.87/1.71 ! [A2: set_a,B2: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ ( sup_sup_set_a @ A2 @ B2 ) @ B2 )
% 2.87/1.71 = ( sup_sup_set_a @ A2 @ B2 ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_252_sup__bot__left,axiom,
% 2.87/1.71 ! [X3: a > $o] :
% 2.87/1.71 ( ( sup_sup_a_o @ bot_bot_a_o @ X3 )
% 2.87/1.71 = X3 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_253_sup__bot__left,axiom,
% 2.87/1.71 ! [X3: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ bot_bot_set_a @ X3 )
% 2.87/1.71 = X3 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_254_sup__bot__right,axiom,
% 2.87/1.71 ! [X3: a > $o] :
% 2.87/1.71 ( ( sup_sup_a_o @ X3 @ bot_bot_a_o )
% 2.87/1.71 = X3 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_255_sup__bot__right,axiom,
% 2.87/1.71 ! [X3: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ X3 @ bot_bot_set_a )
% 2.87/1.71 = X3 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_256_bot__eq__sup__iff,axiom,
% 2.87/1.71 ! [X3: a > $o,Y: a > $o] :
% 2.87/1.71 ( ( bot_bot_a_o
% 2.87/1.71 = ( sup_sup_a_o @ X3 @ Y ) )
% 2.87/1.71 = ( ( X3 = bot_bot_a_o )
% 2.87/1.71 & ( Y = bot_bot_a_o ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_257_bot__eq__sup__iff,axiom,
% 2.87/1.71 ! [X3: set_a,Y: set_a] :
% 2.87/1.71 ( ( bot_bot_set_a
% 2.87/1.71 = ( sup_sup_set_a @ X3 @ Y ) )
% 2.87/1.71 = ( ( X3 = bot_bot_set_a )
% 2.87/1.71 & ( Y = bot_bot_set_a ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_258_psubsetD,axiom,
% 2.87/1.71 ! [A3: set_a,B4: set_a,C: a] :
% 2.87/1.71 ( ( ord_less_set_a @ A3 @ B4 )
% 2.87/1.71 => ( ( member_a @ C @ A3 )
% 2.87/1.71 => ( member_a @ C @ B4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_259_psubset__trans,axiom,
% 2.87/1.71 ! [A3: set_a,B4: set_a,C2: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ A3 @ B4 )
% 2.87/1.71 => ( ( ord_less_set_a @ B4 @ C2 )
% 2.87/1.71 => ( ord_less_set_a @ A3 @ C2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_260_fun__diff__def,axiom,
% 2.87/1.71 ( minus_minus_a_o
% 2.87/1.71 = ( ^ [A5: a > $o,B6: a > $o,X4: a] : ( minus_minus_o @ ( A5 @ X4 ) @ ( B6 @ X4 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_261_inf__sup__aci_I8_J,axiom,
% 2.87/1.71 ! [X3: int,Y: int] :
% 2.87/1.71 ( ( sup_sup_int @ X3 @ ( sup_sup_int @ X3 @ Y ) )
% 2.87/1.71 = ( sup_sup_int @ X3 @ Y ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_262_inf__sup__aci_I8_J,axiom,
% 2.87/1.71 ! [X3: a > $o,Y: a > $o] :
% 2.87/1.71 ( ( sup_sup_a_o @ X3 @ ( sup_sup_a_o @ X3 @ Y ) )
% 2.87/1.71 = ( sup_sup_a_o @ X3 @ Y ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_263_inf__sup__aci_I8_J,axiom,
% 2.87/1.71 ! [X3: set_a,Y: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ X3 @ Y ) )
% 2.87/1.71 = ( sup_sup_set_a @ X3 @ Y ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_264_inf__sup__aci_I7_J,axiom,
% 2.87/1.71 ! [X3: int,Y: int,Z3: int] :
% 2.87/1.71 ( ( sup_sup_int @ X3 @ ( sup_sup_int @ Y @ Z3 ) )
% 2.87/1.71 = ( sup_sup_int @ Y @ ( sup_sup_int @ X3 @ Z3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_265_inf__sup__aci_I7_J,axiom,
% 2.87/1.71 ! [X3: a > $o,Y: a > $o,Z3: a > $o] :
% 2.87/1.71 ( ( sup_sup_a_o @ X3 @ ( sup_sup_a_o @ Y @ Z3 ) )
% 2.87/1.71 = ( sup_sup_a_o @ Y @ ( sup_sup_a_o @ X3 @ Z3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_266_inf__sup__aci_I7_J,axiom,
% 2.87/1.71 ! [X3: set_a,Y: set_a,Z3: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ Y @ Z3 ) )
% 2.87/1.71 = ( sup_sup_set_a @ Y @ ( sup_sup_set_a @ X3 @ Z3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_267_inf__sup__aci_I6_J,axiom,
% 2.87/1.71 ! [X3: int,Y: int,Z3: int] :
% 2.87/1.71 ( ( sup_sup_int @ ( sup_sup_int @ X3 @ Y ) @ Z3 )
% 2.87/1.71 = ( sup_sup_int @ X3 @ ( sup_sup_int @ Y @ Z3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_268_inf__sup__aci_I6_J,axiom,
% 2.87/1.71 ! [X3: a > $o,Y: a > $o,Z3: a > $o] :
% 2.87/1.71 ( ( sup_sup_a_o @ ( sup_sup_a_o @ X3 @ Y ) @ Z3 )
% 2.87/1.71 = ( sup_sup_a_o @ X3 @ ( sup_sup_a_o @ Y @ Z3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_269_inf__sup__aci_I6_J,axiom,
% 2.87/1.71 ! [X3: set_a,Y: set_a,Z3: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ ( sup_sup_set_a @ X3 @ Y ) @ Z3 )
% 2.87/1.71 = ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ Y @ Z3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_270_inf__sup__aci_I5_J,axiom,
% 2.87/1.71 ( sup_sup_int
% 2.87/1.71 = ( ^ [X4: int,Y3: int] : ( sup_sup_int @ Y3 @ X4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_271_inf__sup__aci_I5_J,axiom,
% 2.87/1.71 ( sup_sup_a_o
% 2.87/1.71 = ( ^ [X4: a > $o,Y3: a > $o] : ( sup_sup_a_o @ Y3 @ X4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_272_inf__sup__aci_I5_J,axiom,
% 2.87/1.71 ( sup_sup_set_a
% 2.87/1.71 = ( ^ [X4: set_a,Y3: set_a] : ( sup_sup_set_a @ Y3 @ X4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_273_sup__fun__def,axiom,
% 2.87/1.71 ( sup_sup_a_o
% 2.87/1.71 = ( ^ [F2: a > $o,G: a > $o,X4: a] : ( sup_sup_o @ ( F2 @ X4 ) @ ( G @ X4 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_274_boolean__algebra__cancel_Osup1,axiom,
% 2.87/1.71 ! [A3: int,K: int,A2: int,B2: int] :
% 2.87/1.71 ( ( A3
% 2.87/1.71 = ( sup_sup_int @ K @ A2 ) )
% 2.87/1.71 => ( ( sup_sup_int @ A3 @ B2 )
% 2.87/1.71 = ( sup_sup_int @ K @ ( sup_sup_int @ A2 @ B2 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_275_boolean__algebra__cancel_Osup1,axiom,
% 2.87/1.71 ! [A3: a > $o,K: a > $o,A2: a > $o,B2: a > $o] :
% 2.87/1.71 ( ( A3
% 2.87/1.71 = ( sup_sup_a_o @ K @ A2 ) )
% 2.87/1.71 => ( ( sup_sup_a_o @ A3 @ B2 )
% 2.87/1.71 = ( sup_sup_a_o @ K @ ( sup_sup_a_o @ A2 @ B2 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_276_boolean__algebra__cancel_Osup1,axiom,
% 2.87/1.71 ! [A3: set_a,K: set_a,A2: set_a,B2: set_a] :
% 2.87/1.71 ( ( A3
% 2.87/1.71 = ( sup_sup_set_a @ K @ A2 ) )
% 2.87/1.71 => ( ( sup_sup_set_a @ A3 @ B2 )
% 2.87/1.71 = ( sup_sup_set_a @ K @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_277_boolean__algebra__cancel_Osup2,axiom,
% 2.87/1.71 ! [B4: int,K: int,B2: int,A2: int] :
% 2.87/1.71 ( ( B4
% 2.87/1.71 = ( sup_sup_int @ K @ B2 ) )
% 2.87/1.71 => ( ( sup_sup_int @ A2 @ B4 )
% 2.87/1.71 = ( sup_sup_int @ K @ ( sup_sup_int @ A2 @ B2 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_278_boolean__algebra__cancel_Osup2,axiom,
% 2.87/1.71 ! [B4: a > $o,K: a > $o,B2: a > $o,A2: a > $o] :
% 2.87/1.71 ( ( B4
% 2.87/1.71 = ( sup_sup_a_o @ K @ B2 ) )
% 2.87/1.71 => ( ( sup_sup_a_o @ A2 @ B4 )
% 2.87/1.71 = ( sup_sup_a_o @ K @ ( sup_sup_a_o @ A2 @ B2 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_279_boolean__algebra__cancel_Osup2,axiom,
% 2.87/1.71 ! [B4: set_a,K: set_a,B2: set_a,A2: set_a] :
% 2.87/1.71 ( ( B4
% 2.87/1.71 = ( sup_sup_set_a @ K @ B2 ) )
% 2.87/1.71 => ( ( sup_sup_set_a @ A2 @ B4 )
% 2.87/1.71 = ( sup_sup_set_a @ K @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_280_sup_Oassoc,axiom,
% 2.87/1.71 ! [A2: int,B2: int,C: int] :
% 2.87/1.71 ( ( sup_sup_int @ ( sup_sup_int @ A2 @ B2 ) @ C )
% 2.87/1.71 = ( sup_sup_int @ A2 @ ( sup_sup_int @ B2 @ C ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_281_sup_Oassoc,axiom,
% 2.87/1.71 ! [A2: a > $o,B2: a > $o,C: a > $o] :
% 2.87/1.71 ( ( sup_sup_a_o @ ( sup_sup_a_o @ A2 @ B2 ) @ C )
% 2.87/1.71 = ( sup_sup_a_o @ A2 @ ( sup_sup_a_o @ B2 @ C ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_282_sup_Oassoc,axiom,
% 2.87/1.71 ! [A2: set_a,B2: set_a,C: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ ( sup_sup_set_a @ A2 @ B2 ) @ C )
% 2.87/1.71 = ( sup_sup_set_a @ A2 @ ( sup_sup_set_a @ B2 @ C ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_283_sup__assoc,axiom,
% 2.87/1.71 ! [X3: int,Y: int,Z3: int] :
% 2.87/1.71 ( ( sup_sup_int @ ( sup_sup_int @ X3 @ Y ) @ Z3 )
% 2.87/1.71 = ( sup_sup_int @ X3 @ ( sup_sup_int @ Y @ Z3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_284_sup__assoc,axiom,
% 2.87/1.71 ! [X3: a > $o,Y: a > $o,Z3: a > $o] :
% 2.87/1.71 ( ( sup_sup_a_o @ ( sup_sup_a_o @ X3 @ Y ) @ Z3 )
% 2.87/1.71 = ( sup_sup_a_o @ X3 @ ( sup_sup_a_o @ Y @ Z3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_285_sup__assoc,axiom,
% 2.87/1.71 ! [X3: set_a,Y: set_a,Z3: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ ( sup_sup_set_a @ X3 @ Y ) @ Z3 )
% 2.87/1.71 = ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ Y @ Z3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_286_sup_Ocommute,axiom,
% 2.87/1.71 ( sup_sup_int
% 2.87/1.71 = ( ^ [A: int,B: int] : ( sup_sup_int @ B @ A ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_287_sup_Ocommute,axiom,
% 2.87/1.71 ( sup_sup_a_o
% 2.87/1.71 = ( ^ [A: a > $o,B: a > $o] : ( sup_sup_a_o @ B @ A ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_288_sup_Ocommute,axiom,
% 2.87/1.71 ( sup_sup_set_a
% 2.87/1.71 = ( ^ [A: set_a,B: set_a] : ( sup_sup_set_a @ B @ A ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_289_sup__commute,axiom,
% 2.87/1.71 ( sup_sup_int
% 2.87/1.71 = ( ^ [X4: int,Y3: int] : ( sup_sup_int @ Y3 @ X4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_290_sup__commute,axiom,
% 2.87/1.71 ( sup_sup_a_o
% 2.87/1.71 = ( ^ [X4: a > $o,Y3: a > $o] : ( sup_sup_a_o @ Y3 @ X4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_291_sup__commute,axiom,
% 2.87/1.71 ( sup_sup_set_a
% 2.87/1.71 = ( ^ [X4: set_a,Y3: set_a] : ( sup_sup_set_a @ Y3 @ X4 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_292_sup_Oleft__commute,axiom,
% 2.87/1.71 ! [B2: set_a,A2: set_a,C: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ B2 @ ( sup_sup_set_a @ A2 @ C ) )
% 2.87/1.71 = ( sup_sup_set_a @ A2 @ ( sup_sup_set_a @ B2 @ C ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_293_sup__left__commute,axiom,
% 2.87/1.71 ! [X3: set_a,Y: set_a,Z3: set_a] :
% 2.87/1.71 ( ( sup_sup_set_a @ X3 @ ( sup_sup_set_a @ Y @ Z3 ) )
% 2.87/1.71 = ( sup_sup_set_a @ Y @ ( sup_sup_set_a @ X3 @ Z3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_294_less__supI1,axiom,
% 2.87/1.71 ! [X3: set_a,A2: set_a,B2: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ X3 @ A2 )
% 2.87/1.71 => ( ord_less_set_a @ X3 @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_295_less__supI1,axiom,
% 2.87/1.71 ! [X3: int,A2: int,B2: int] :
% 2.87/1.71 ( ( ord_less_int @ X3 @ A2 )
% 2.87/1.71 => ( ord_less_int @ X3 @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_296_less__supI2,axiom,
% 2.87/1.71 ! [X3: set_a,B2: set_a,A2: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ X3 @ B2 )
% 2.87/1.71 => ( ord_less_set_a @ X3 @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_297_less__supI2,axiom,
% 2.87/1.71 ! [X3: int,B2: int,A2: int] :
% 2.87/1.71 ( ( ord_less_int @ X3 @ B2 )
% 2.87/1.71 => ( ord_less_int @ X3 @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_298_sup_Ostrict__boundedE,axiom,
% 2.87/1.71 ! [B2: set_a,C: set_a,A2: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ ( sup_sup_set_a @ B2 @ C ) @ A2 )
% 2.87/1.71 => ~ ( ( ord_less_set_a @ B2 @ A2 )
% 2.87/1.71 => ~ ( ord_less_set_a @ C @ A2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_299_sup_Ostrict__boundedE,axiom,
% 2.87/1.71 ! [B2: int,C: int,A2: int] :
% 2.87/1.71 ( ( ord_less_int @ ( sup_sup_int @ B2 @ C ) @ A2 )
% 2.87/1.71 => ~ ( ( ord_less_int @ B2 @ A2 )
% 2.87/1.71 => ~ ( ord_less_int @ C @ A2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_300_sup_Ostrict__order__iff,axiom,
% 2.87/1.71 ( ord_less_set_a
% 2.87/1.71 = ( ^ [B: set_a,A: set_a] :
% 2.87/1.71 ( ( A
% 2.87/1.71 = ( sup_sup_set_a @ A @ B ) )
% 2.87/1.71 & ( A != B ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_301_sup_Ostrict__order__iff,axiom,
% 2.87/1.71 ( ord_less_int
% 2.87/1.71 = ( ^ [B: int,A: int] :
% 2.87/1.71 ( ( A
% 2.87/1.71 = ( sup_sup_int @ A @ B ) )
% 2.87/1.71 & ( A != B ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_302_sup_Ostrict__coboundedI1,axiom,
% 2.87/1.71 ! [C: set_a,A2: set_a,B2: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ C @ A2 )
% 2.87/1.71 => ( ord_less_set_a @ C @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_303_sup_Ostrict__coboundedI1,axiom,
% 2.87/1.71 ! [C: int,A2: int,B2: int] :
% 2.87/1.71 ( ( ord_less_int @ C @ A2 )
% 2.87/1.71 => ( ord_less_int @ C @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_304_sup_Ostrict__coboundedI2,axiom,
% 2.87/1.71 ! [C: set_a,B2: set_a,A2: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ C @ B2 )
% 2.87/1.71 => ( ord_less_set_a @ C @ ( sup_sup_set_a @ A2 @ B2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_305_sup_Ostrict__coboundedI2,axiom,
% 2.87/1.71 ! [C: int,B2: int,A2: int] :
% 2.87/1.71 ( ( ord_less_int @ C @ B2 )
% 2.87/1.71 => ( ord_less_int @ C @ ( sup_sup_int @ A2 @ B2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_306_h2,axiom,
% 2.87/1.71 ( ( binary1721989714Tree_a @ h @ t2 )
% 2.87/1.71 => ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t2 ) )
% 2.87/1.71 = ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t2 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_307_h1,axiom,
% 2.87/1.71 ( ( binary1721989714Tree_a @ h @ t1 )
% 2.87/1.71 => ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ t1 ) )
% 2.87/1.71 = ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ t1 ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_308__092_060open_062sortedTree_Ah_ATip_A_092_060longrightarrow_062_AsetOf_A_Ibinsert_Ah_Ae_ATip_J_A_061_AsetOf_ATip_A_N_Aeqs_Ah_Ae_A_092_060union_062_A_123e_125_092_060close_062,axiom,
% 2.87/1.71 ( ( binary1721989714Tree_a @ h @ binary476621312_Tip_a )
% 2.87/1.71 => ( ( binary945792244etOf_a @ ( binary1226383794sert_a @ h @ e @ binary476621312_Tip_a ) )
% 2.87/1.71 = ( sup_sup_set_a @ ( minus_minus_set_a @ ( binary945792244etOf_a @ binary476621312_Tip_a ) @ ( binary504661350_eqs_a @ h @ e ) ) @ ( insert_a @ e @ bot_bot_set_a ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_309_singleton__conv,axiom,
% 2.87/1.71 ! [A2: a] :
% 2.87/1.71 ( ( collect_a
% 2.87/1.71 @ ^ [X4: a] : ( X4 = A2 ) )
% 2.87/1.71 = ( insert_a @ A2 @ bot_bot_set_a ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_310_singleton__conv2,axiom,
% 2.87/1.71 ! [A2: a] :
% 2.87/1.71 ( ( collect_a
% 2.87/1.71 @ ( ^ [Y4: a,Z4: a] : ( Y4 = Z4 )
% 2.87/1.71 @ A2 ) )
% 2.87/1.71 = ( insert_a @ A2 @ bot_bot_set_a ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_311_Un__def,axiom,
% 2.87/1.71 ( sup_sup_set_a
% 2.87/1.71 = ( ^ [A5: set_a,B6: set_a] :
% 2.87/1.71 ( collect_a
% 2.87/1.71 @ ^ [X4: a] :
% 2.87/1.71 ( ( member_a @ X4 @ A5 )
% 2.87/1.71 | ( member_a @ X4 @ B6 ) ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_312_empty__def,axiom,
% 2.87/1.71 ( bot_bot_set_a
% 2.87/1.71 = ( collect_a
% 2.87/1.71 @ ^ [X4: a] : $false ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_313_insert__def,axiom,
% 2.87/1.71 ( insert_a
% 2.87/1.71 = ( ^ [A: a] :
% 2.87/1.71 ( sup_sup_set_a
% 2.87/1.71 @ ( collect_a
% 2.87/1.71 @ ^ [X4: a] : ( X4 = A ) ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_314_sup__set__def,axiom,
% 2.87/1.71 ( sup_sup_set_a
% 2.87/1.71 = ( ^ [A5: set_a,B6: set_a] :
% 2.87/1.71 ( collect_a
% 2.87/1.71 @ ( sup_sup_a_o
% 2.87/1.71 @ ^ [X4: a] : ( member_a @ X4 @ A5 )
% 2.87/1.71 @ ^ [X4: a] : ( member_a @ X4 @ B6 ) ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_315_Collect__conv__if,axiom,
% 2.87/1.71 ! [P: a > $o,A2: a] :
% 2.87/1.71 ( ( ( P @ A2 )
% 2.87/1.71 => ( ( collect_a
% 2.87/1.71 @ ^ [X4: a] :
% 2.87/1.71 ( ( X4 = A2 )
% 2.87/1.71 & ( P @ X4 ) ) )
% 2.87/1.71 = ( insert_a @ A2 @ bot_bot_set_a ) ) )
% 2.87/1.71 & ( ~ ( P @ A2 )
% 2.87/1.71 => ( ( collect_a
% 2.87/1.71 @ ^ [X4: a] :
% 2.87/1.71 ( ( X4 = A2 )
% 2.87/1.71 & ( P @ X4 ) ) )
% 2.87/1.71 = bot_bot_set_a ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_316_Collect__disj__eq,axiom,
% 2.87/1.71 ! [P: a > $o,Q: a > $o] :
% 2.87/1.71 ( ( collect_a
% 2.87/1.71 @ ^ [X4: a] :
% 2.87/1.71 ( ( P @ X4 )
% 2.87/1.71 | ( Q @ X4 ) ) )
% 2.87/1.71 = ( sup_sup_set_a @ ( collect_a @ P ) @ ( collect_a @ Q ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_317_Collect__conv__if2,axiom,
% 2.87/1.71 ! [P: a > $o,A2: a] :
% 2.87/1.71 ( ( ( P @ A2 )
% 2.87/1.71 => ( ( collect_a
% 2.87/1.71 @ ^ [X4: a] :
% 2.87/1.71 ( ( A2 = X4 )
% 2.87/1.71 & ( P @ X4 ) ) )
% 2.87/1.71 = ( insert_a @ A2 @ bot_bot_set_a ) ) )
% 2.87/1.71 & ( ~ ( P @ A2 )
% 2.87/1.71 => ( ( collect_a
% 2.87/1.71 @ ^ [X4: a] :
% 2.87/1.71 ( ( A2 = X4 )
% 2.87/1.71 & ( P @ X4 ) ) )
% 2.87/1.71 = bot_bot_set_a ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_318_less__set__def,axiom,
% 2.87/1.71 ( ord_less_set_a
% 2.87/1.71 = ( ^ [A5: set_a,B6: set_a] :
% 2.87/1.71 ( ord_less_a_o
% 2.87/1.71 @ ^ [X4: a] : ( member_a @ X4 @ A5 )
% 2.87/1.71 @ ^ [X4: a] : ( member_a @ X4 @ B6 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_319_eqs__def,axiom,
% 2.87/1.71 ( binary504661350_eqs_a
% 2.87/1.71 = ( ^ [H2: a > int,X4: a] :
% 2.87/1.71 ( collect_a
% 2.87/1.71 @ ^ [Y3: a] :
% 2.87/1.71 ( ( H2 @ Y3 )
% 2.87/1.71 = ( H2 @ X4 ) ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_320_insert__Collect,axiom,
% 2.87/1.71 ! [A2: a,P: a > $o] :
% 2.87/1.71 ( ( insert_a @ A2 @ ( collect_a @ P ) )
% 2.87/1.71 = ( collect_a
% 2.87/1.71 @ ^ [U: a] :
% 2.87/1.71 ( ( U != A2 )
% 2.87/1.71 => ( P @ U ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_321_minus__set__def,axiom,
% 2.87/1.71 ( minus_minus_set_a
% 2.87/1.71 = ( ^ [A5: set_a,B6: set_a] :
% 2.87/1.71 ( collect_a
% 2.87/1.71 @ ( minus_minus_a_o
% 2.87/1.71 @ ^ [X4: a] : ( member_a @ X4 @ A5 )
% 2.87/1.71 @ ^ [X4: a] : ( member_a @ X4 @ B6 ) ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_322_insert__compr,axiom,
% 2.87/1.71 ( insert_a
% 2.87/1.71 = ( ^ [A: a,B6: set_a] :
% 2.87/1.71 ( collect_a
% 2.87/1.71 @ ^ [X4: a] :
% 2.87/1.71 ( ( X4 = A )
% 2.87/1.71 | ( member_a @ X4 @ B6 ) ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_323_set__diff__eq,axiom,
% 2.87/1.71 ( minus_minus_set_a
% 2.87/1.71 = ( ^ [A5: set_a,B6: set_a] :
% 2.87/1.71 ( collect_a
% 2.87/1.71 @ ^ [X4: a] :
% 2.87/1.71 ( ( member_a @ X4 @ A5 )
% 2.87/1.71 & ~ ( member_a @ X4 @ B6 ) ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_324_the__elem__eq,axiom,
% 2.87/1.71 ! [X3: a] :
% 2.87/1.71 ( ( the_elem_a @ ( insert_a @ X3 @ bot_bot_set_a ) )
% 2.87/1.71 = X3 ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_325_bot__empty__eq,axiom,
% 2.87/1.71 ( bot_bot_a_o
% 2.87/1.71 = ( ^ [X4: a] : ( member_a @ X4 @ bot_bot_set_a ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_326_sup__Un__eq,axiom,
% 2.87/1.71 ! [R: set_a,S: set_a] :
% 2.87/1.71 ( ( sup_sup_a_o
% 2.87/1.71 @ ^ [X4: a] : ( member_a @ X4 @ R )
% 2.87/1.71 @ ^ [X4: a] : ( member_a @ X4 @ S ) )
% 2.87/1.71 = ( ^ [X4: a] : ( member_a @ X4 @ ( sup_sup_set_a @ R @ S ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_327_Collect__empty__eq__bot,axiom,
% 2.87/1.71 ! [P: a > $o] :
% 2.87/1.71 ( ( ( collect_a @ P )
% 2.87/1.71 = bot_bot_set_a )
% 2.87/1.71 = ( P = bot_bot_a_o ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_328_is__singleton__the__elem,axiom,
% 2.87/1.71 ( is_singleton_a
% 2.87/1.71 = ( ^ [A5: set_a] :
% 2.87/1.71 ( A5
% 2.87/1.71 = ( insert_a @ ( the_elem_a @ A5 ) @ bot_bot_set_a ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_329_is__singletonI,axiom,
% 2.87/1.71 ! [X3: a] : ( is_singleton_a @ ( insert_a @ X3 @ bot_bot_set_a ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_330_is__singletonI_H,axiom,
% 2.87/1.71 ! [A3: set_a] :
% 2.87/1.71 ( ( A3 != bot_bot_set_a )
% 2.87/1.71 => ( ! [X2: a,Y2: a] :
% 2.87/1.71 ( ( member_a @ X2 @ A3 )
% 2.87/1.71 => ( ( member_a @ Y2 @ A3 )
% 2.87/1.71 => ( X2 = Y2 ) ) )
% 2.87/1.71 => ( is_singleton_a @ A3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_331_is__singleton__def,axiom,
% 2.87/1.71 ( is_singleton_a
% 2.87/1.71 = ( ^ [A5: set_a] :
% 2.87/1.71 ? [X4: a] :
% 2.87/1.71 ( A5
% 2.87/1.71 = ( insert_a @ X4 @ bot_bot_set_a ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_332_is__singletonE,axiom,
% 2.87/1.71 ! [A3: set_a] :
% 2.87/1.71 ( ( is_singleton_a @ A3 )
% 2.87/1.71 => ~ ! [X2: a] :
% 2.87/1.71 ( A3
% 2.87/1.71 != ( insert_a @ X2 @ bot_bot_set_a ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_333_diff__strict__right__mono,axiom,
% 2.87/1.71 ! [A2: int,B2: int,C: int] :
% 2.87/1.71 ( ( ord_less_int @ A2 @ B2 )
% 2.87/1.71 => ( ord_less_int @ ( minus_minus_int @ A2 @ C ) @ ( minus_minus_int @ B2 @ C ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_334_diff__strict__left__mono,axiom,
% 2.87/1.71 ! [B2: int,A2: int,C: int] :
% 2.87/1.71 ( ( ord_less_int @ B2 @ A2 )
% 2.87/1.71 => ( ord_less_int @ ( minus_minus_int @ C @ A2 ) @ ( minus_minus_int @ C @ B2 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_335_diff__strict__mono,axiom,
% 2.87/1.71 ! [A2: int,B2: int,D: int,C: int] :
% 2.87/1.71 ( ( ord_less_int @ A2 @ B2 )
% 2.87/1.71 => ( ( ord_less_int @ D @ C )
% 2.87/1.71 => ( ord_less_int @ ( minus_minus_int @ A2 @ C ) @ ( minus_minus_int @ B2 @ D ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_336_diff__eq__diff__less,axiom,
% 2.87/1.71 ! [A2: int,B2: int,C: int,D: int] :
% 2.87/1.71 ( ( ( minus_minus_int @ A2 @ B2 )
% 2.87/1.71 = ( minus_minus_int @ C @ D ) )
% 2.87/1.71 => ( ( ord_less_int @ A2 @ B2 )
% 2.87/1.71 = ( ord_less_int @ C @ D ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_337_remove__def,axiom,
% 2.87/1.71 ( remove_a
% 2.87/1.71 = ( ^ [X4: a,A5: set_a] : ( minus_minus_set_a @ A5 @ ( insert_a @ X4 @ bot_bot_set_a ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_338_Tree_Osimps_I15_J,axiom,
% 2.87/1.71 ! [X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 2.87/1.71 ( ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) )
% 2.87/1.71 = ( sup_sup_set_a @ ( sup_sup_set_a @ ( binary256242811Tree_a @ X21 ) @ ( insert_a @ X22 @ bot_bot_set_a ) ) @ ( binary256242811Tree_a @ X23 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_339_member__remove,axiom,
% 2.87/1.71 ! [X3: a,Y: a,A3: set_a] :
% 2.87/1.71 ( ( member_a @ X3 @ ( remove_a @ Y @ A3 ) )
% 2.87/1.71 = ( ( member_a @ X3 @ A3 )
% 2.87/1.71 & ( X3 != Y ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_340_Tree_Osimps_I14_J,axiom,
% 2.87/1.71 ( ( binary256242811Tree_a @ binary476621312_Tip_a )
% 2.87/1.71 = bot_bot_set_a ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_341_Tree_Oset__intros_I3_J,axiom,
% 2.87/1.71 ! [Ya: a,X23: binary1439146945Tree_a,X21: binary1439146945Tree_a,X22: a] :
% 2.87/1.71 ( ( member_a @ Ya @ ( binary256242811Tree_a @ X23 ) )
% 2.87/1.71 => ( member_a @ Ya @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_342_Tree_Oset__intros_I2_J,axiom,
% 2.87/1.71 ! [X22: a,X21: binary1439146945Tree_a,X23: binary1439146945Tree_a] : ( member_a @ X22 @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_343_Tree_Oset__intros_I1_J,axiom,
% 2.87/1.71 ! [Y: a,X21: binary1439146945Tree_a,X22: a,X23: binary1439146945Tree_a] :
% 2.87/1.71 ( ( member_a @ Y @ ( binary256242811Tree_a @ X21 ) )
% 2.87/1.71 => ( member_a @ Y @ ( binary256242811Tree_a @ ( binary717961607le_T_a @ X21 @ X22 @ X23 ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_344_Tree_Oset__cases,axiom,
% 2.87/1.71 ! [E: a,A2: binary1439146945Tree_a] :
% 2.87/1.71 ( ( member_a @ E @ ( binary256242811Tree_a @ A2 ) )
% 2.87/1.71 => ( ! [Z1: binary1439146945Tree_a] :
% 2.87/1.71 ( ? [Z22: a,Z32: binary1439146945Tree_a] :
% 2.87/1.71 ( A2
% 2.87/1.71 = ( binary717961607le_T_a @ Z1 @ Z22 @ Z32 ) )
% 2.87/1.71 => ~ ( member_a @ E @ ( binary256242811Tree_a @ Z1 ) ) )
% 2.87/1.71 => ( ! [Z1: binary1439146945Tree_a,Z32: binary1439146945Tree_a] :
% 2.87/1.71 ( A2
% 2.87/1.71 != ( binary717961607le_T_a @ Z1 @ E @ Z32 ) )
% 2.87/1.71 => ~ ! [Z1: binary1439146945Tree_a,Z22: a,Z32: binary1439146945Tree_a] :
% 2.87/1.71 ( ( A2
% 2.87/1.71 = ( binary717961607le_T_a @ Z1 @ Z22 @ Z32 ) )
% 2.87/1.71 => ~ ( member_a @ E @ ( binary256242811Tree_a @ Z32 ) ) ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_345_Tree_Opred__cong,axiom,
% 2.87/1.71 ! [X3: binary1439146945Tree_a,Ya: binary1439146945Tree_a,P: a > $o,Pa: a > $o] :
% 2.87/1.71 ( ( X3 = Ya )
% 2.87/1.71 => ( ! [Z: a] :
% 2.87/1.71 ( ( member_a @ Z @ ( binary256242811Tree_a @ Ya ) )
% 2.87/1.71 => ( ( P @ Z )
% 2.87/1.71 = ( Pa @ Z ) ) )
% 2.87/1.71 => ( ( binary1452917696Tree_a @ P @ X3 )
% 2.87/1.71 = ( binary1452917696Tree_a @ Pa @ Ya ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_346_Tree_Opred__mono__strong,axiom,
% 2.87/1.71 ! [P: a > $o,X3: binary1439146945Tree_a,Pa: a > $o] :
% 2.87/1.71 ( ( binary1452917696Tree_a @ P @ X3 )
% 2.87/1.71 => ( ! [Z: a] :
% 2.87/1.71 ( ( member_a @ Z @ ( binary256242811Tree_a @ X3 ) )
% 2.87/1.71 => ( ( P @ Z )
% 2.87/1.71 => ( Pa @ Z ) ) )
% 2.87/1.71 => ( binary1452917696Tree_a @ Pa @ X3 ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_347_Set_Ois__empty__def,axiom,
% 2.87/1.71 ( is_empty_a
% 2.87/1.71 = ( ^ [A5: set_a] : ( A5 = bot_bot_set_a ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_348_the__elem__def,axiom,
% 2.87/1.71 ( the_elem_a
% 2.87/1.71 = ( ^ [X5: set_a] :
% 2.87/1.71 ( the_a
% 2.87/1.71 @ ^ [X4: a] :
% 2.87/1.71 ( X5
% 2.87/1.71 = ( insert_a @ X4 @ bot_bot_set_a ) ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(fact_349_psubset__insert__iff,axiom,
% 2.87/1.71 ! [A3: set_a,X3: a,B4: set_a] :
% 2.87/1.71 ( ( ord_less_set_a @ A3 @ ( insert_a @ X3 @ B4 ) )
% 2.87/1.71 = ( ( ( member_a @ X3 @ B4 )
% 2.87/1.71 => ( ord_less_set_a @ A3 @ B4 ) )
% 2.87/1.71 & ( ~ ( member_a @ X3 @ B4 )
% 2.87/1.71 => ( ( ( member_a @ X3 @ A3 )
% 2.87/1.71 => ( ord_less_set_a @ ( minus_minus_set_a @ A3 @ ( insert_a @ X3 @ bot_bot_set_a ) ) @ B4 ) )
% 2.87/1.71 & ( ~ ( member_a @ X3 @ A3 )
% 2.87/1.71 => ( ord_less_eq_set_a @ A3 @ B4 ) ) ) ) ) ) ).
% 2.87/1.71
% 2.87/1.71 thf(conj_0,conjecture,
% 2.87/1.71 ord_less_int @ ( h @ w ) @ ( h @ x ) ).
% 2.87/1.71 ------------------------
% 2.87/1.72 % (1186)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_929 for (2999ds/27Mi)
% 2.87/1.72 % (1184)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/183Mi)
% 2.87/1.72 % (1185)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_929 for (2999ds/4Mi)
% 2.87/1.72 % (1189)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_929 for (2999ds/275Mi)
% 2.87/1.72 % (1190)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/18Mi)
% 2.87/1.73 % (1185)Instruction limit reached!
% 2.87/1.73 % (1185)------------------------------
% 2.87/1.73 % (1185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.73 % (1185)Termination reason: Unknown
% 2.87/1.73 % (1185)Termination phase: shuffling
% 2.87/1.73
% 2.87/1.73 % (1185)Memory used [KB]: 1407
% 2.87/1.73 % (1185)Time elapsed: 0.003 s
% 2.87/1.73 % (1185)Instructions burned: 6 (million)
% 2.87/1.73 % (1185)------------------------------
% 2.87/1.73 % (1185)------------------------------
% 2.87/1.73 % (1190)Instruction limit reached!
% 2.87/1.73 % (1190)------------------------------
% 2.87/1.73 % (1190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.73 % (1190)Termination reason: Unknown
% 2.87/1.73 % (1190)Termination phase: shuffling
% 2.87/1.73
% 2.87/1.73 % (1190)Memory used [KB]: 1663
% 2.87/1.73 % (1190)Time elapsed: 0.007 s
% 2.87/1.73 % (1190)Instructions burned: 18 (million)
% 2.87/1.73 % (1190)------------------------------
% 2.87/1.73 % (1190)------------------------------
% 2.87/1.73 % (1187)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/2Mi)
% 2.87/1.73 % (1188)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_929 for (2999ds/2Mi)
% 2.87/1.73 % (1186)Instruction limit reached!
% 2.87/1.73 % (1186)------------------------------
% 2.87/1.73 % (1186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.73 % (1186)Termination reason: Unknown
% 2.87/1.73 % (1186)Termination phase: Property scanning
% 2.87/1.73
% 2.87/1.73 % (1186)Memory used [KB]: 1791
% 2.87/1.73 % (1186)Time elapsed: 0.010 s
% 2.87/1.73 % (1186)Instructions burned: 28 (million)
% 2.87/1.73 % (1186)------------------------------
% 2.87/1.73 % (1186)------------------------------
% 2.87/1.73 % (1187)Instruction limit reached!
% 2.87/1.73 % (1187)------------------------------
% 2.87/1.73 % (1187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.73 % (1187)Termination reason: Unknown
% 2.87/1.73 % (1187)Termination phase: shuffling
% 2.87/1.73
% 2.87/1.73 % (1187)Memory used [KB]: 1407
% 2.87/1.73 % (1187)Time elapsed: 0.004 s
% 2.87/1.73 % (1187)Instructions burned: 3 (million)
% 2.87/1.73 % (1187)------------------------------
% 2.87/1.73 % (1187)------------------------------
% 2.87/1.73 % (1188)Instruction limit reached!
% 2.87/1.73 % (1188)------------------------------
% 2.87/1.73 % (1188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.73 % (1188)Termination reason: Unknown
% 2.87/1.73 % (1188)Termination phase: shuffling
% 2.87/1.73
% 2.87/1.73 % (1188)Memory used [KB]: 1407
% 2.87/1.73 % (1188)Time elapsed: 0.004 s
% 2.87/1.73 % (1188)Instructions burned: 3 (million)
% 2.87/1.73 % (1188)------------------------------
% 2.87/1.73 % (1188)------------------------------
% 2.87/1.74 % (1198)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/3Mi)
% 2.87/1.74 % (1198)Instruction limit reached!
% 2.87/1.74 % (1198)------------------------------
% 2.87/1.74 % (1198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.74 % (1198)Termination reason: Unknown
% 2.87/1.74 % (1198)Termination phase: shuffling
% 2.87/1.74
% 2.87/1.74 % (1198)Memory used [KB]: 1407
% 2.87/1.74 % (1198)Time elapsed: 0.002 s
% 2.87/1.74 % (1198)Instructions burned: 3 (million)
% 2.87/1.74 % (1198)------------------------------
% 2.87/1.74 % (1198)------------------------------
% 2.87/1.74 % (1199)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_929 for (2999ds/37Mi)
% 2.87/1.74 % (1200)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_929 for (2999ds/15Mi)
% 2.87/1.75 % (1203)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/7Mi)
% 2.87/1.75 % (1200)Instruction limit reached!
% 2.87/1.75 % (1200)------------------------------
% 2.87/1.75 % (1200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.75 % (1200)Termination reason: Unknown
% 2.87/1.75 % (1200)Termination phase: shuffling
% 2.87/1.75
% 2.87/1.75 % (1200)Memory used [KB]: 1663
% 2.87/1.75 % (1200)Time elapsed: 0.007 s
% 2.87/1.75 % (1200)Instructions burned: 17 (million)
% 2.87/1.75 % (1200)------------------------------
% 2.87/1.75 % (1200)------------------------------
% 2.87/1.75 % (1203)Instruction limit reached!
% 2.87/1.75 % (1203)------------------------------
% 2.87/1.75 % (1203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.75 % (1203)Termination reason: Unknown
% 2.87/1.75 % (1203)Termination phase: shuffling
% 2.87/1.75
% 2.87/1.75 % (1203)Memory used [KB]: 1535
% 2.87/1.75 % (1203)Time elapsed: 0.004 s
% 2.87/1.75 % (1203)Instructions burned: 8 (million)
% 2.87/1.75 % (1203)------------------------------
% 2.87/1.75 % (1203)------------------------------
% 2.87/1.75 % (1199)Instruction limit reached!
% 2.87/1.75 % (1199)------------------------------
% 2.87/1.75 % (1199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.75 % (1199)Termination reason: Unknown
% 2.87/1.75 % (1199)Termination phase: shuffling
% 2.87/1.75
% 2.87/1.75 % (1199)Memory used [KB]: 2174
% 2.87/1.75 % (1199)Time elapsed: 0.012 s
% 2.87/1.75 % (1199)Instructions burned: 39 (million)
% 2.87/1.75 % (1199)------------------------------
% 2.87/1.75 % (1199)------------------------------
% 2.87/1.75 % (1201)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_929 for (2999ds/3Mi)
% 2.87/1.75 % (1202)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_929 for (2999ds/1041Mi)
% 2.87/1.75 % (1201)Instruction limit reached!
% 2.87/1.75 % (1201)------------------------------
% 2.87/1.75 % (1201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.75 % (1201)Termination reason: Unknown
% 2.87/1.75 % (1201)Termination phase: shuffling
% 2.87/1.75
% 2.87/1.75 % (1201)Memory used [KB]: 1407
% 2.87/1.75 % (1201)Time elapsed: 0.004 s
% 2.87/1.75 % (1201)Instructions burned: 3 (million)
% 2.87/1.75 % (1201)------------------------------
% 2.87/1.75 % (1201)------------------------------
% 2.87/1.76 % (1211)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/16Mi)
% 2.87/1.76 % (1213)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_929 for (2999ds/3Mi)
% 2.87/1.76 % (1213)Instruction limit reached!
% 2.87/1.76 % (1213)------------------------------
% 2.87/1.76 % (1213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.76 % (1213)Termination reason: Unknown
% 2.87/1.76 % (1213)Termination phase: shuffling
% 2.87/1.76
% 2.87/1.76 % (1213)Memory used [KB]: 1407
% 2.87/1.76 % (1213)Time elapsed: 0.002 s
% 2.87/1.76 % (1213)Instructions burned: 3 (million)
% 2.87/1.76 % (1213)------------------------------
% 2.87/1.76 % (1213)------------------------------
% 2.87/1.76 % (1215)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_929 for (2999ds/3Mi)
% 2.87/1.76 % (1215)Instruction limit reached!
% 2.87/1.76 % (1215)------------------------------
% 2.87/1.76 % (1215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.76 % (1215)Termination reason: Unknown
% 2.87/1.76 % (1215)Termination phase: shuffling
% 2.87/1.76
% 2.87/1.76 % (1215)Memory used [KB]: 1407
% 2.87/1.76 % (1215)Time elapsed: 0.002 s
% 2.87/1.76 % (1215)Instructions burned: 3 (million)
% 2.87/1.76 % (1215)------------------------------
% 2.87/1.76 % (1215)------------------------------
% 2.87/1.76 % (1211)Instruction limit reached!
% 2.87/1.76 % (1211)------------------------------
% 2.87/1.76 % (1211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.76 % (1211)Termination reason: Unknown
% 2.87/1.76 % (1211)Termination phase: shuffling
% 2.87/1.76
% 2.87/1.76 % (1211)Memory used [KB]: 1663
% 2.87/1.76 % (1211)Time elapsed: 0.006 s
% 2.87/1.76 % (1211)Instructions burned: 16 (million)
% 2.87/1.76 % (1211)------------------------------
% 2.87/1.76 % (1211)------------------------------
% 2.87/1.77 % (1220)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/3Mi)
% 2.87/1.77 % (1220)Instruction limit reached!
% 2.87/1.77 % (1220)------------------------------
% 2.87/1.77 % (1220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.77 % (1220)Termination reason: Unknown
% 2.87/1.77 % (1220)Termination phase: shuffling
% 2.87/1.77
% 2.87/1.77 % (1220)Memory used [KB]: 1407
% 2.87/1.77 % (1220)Time elapsed: 0.002 s
% 2.87/1.77 % (1220)Instructions burned: 4 (million)
% 2.87/1.77 % (1220)------------------------------
% 2.87/1.77 % (1220)------------------------------
% 2.87/1.77 % (1223)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/4Mi)
% 2.87/1.77 % (1218)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/7Mi)
% 2.87/1.77 % (1225)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/18Mi)
% 2.87/1.77 % (1223)Instruction limit reached!
% 2.87/1.77 % (1223)------------------------------
% 2.87/1.77 % (1223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.77 % (1223)Termination reason: Unknown
% 2.87/1.77 % (1223)Termination phase: shuffling
% 2.87/1.77
% 2.87/1.77 % (1223)Memory used [KB]: 1407
% 2.87/1.77 % (1223)Time elapsed: 0.003 s
% 2.87/1.77 % (1223)Instructions burned: 6 (million)
% 2.87/1.77 % (1223)------------------------------
% 2.87/1.77 % (1223)------------------------------
% 2.87/1.77 % (1184)Instruction limit reached!
% 2.87/1.77 % (1184)------------------------------
% 2.87/1.77 % (1184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.77 % (1184)Termination reason: Unknown
% 2.87/1.77 % (1184)Termination phase: Saturation
% 2.87/1.77
% 2.87/1.77 % (1184)Memory used [KB]: 7036
% 2.87/1.77 % (1184)Time elapsed: 0.050 s
% 2.87/1.77 % (1184)Instructions burned: 184 (million)
% 2.87/1.77 % (1184)------------------------------
% 2.87/1.77 % (1184)------------------------------
% 2.87/1.78 % (1218)Instruction limit reached!
% 2.87/1.78 % (1218)------------------------------
% 2.87/1.78 % (1218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.78 % (1218)Termination reason: Unknown
% 2.87/1.78 % (1218)Termination phase: shuffling
% 2.87/1.78
% 2.87/1.78 % (1218)Memory used [KB]: 1407
% 2.87/1.78 % (1218)Time elapsed: 0.006 s
% 2.87/1.78 % (1218)Instructions burned: 7 (million)
% 2.87/1.78 % (1218)------------------------------
% 2.87/1.78 % (1218)------------------------------
% 2.87/1.78 % (1225)Instruction limit reached!
% 2.87/1.78 % (1225)------------------------------
% 2.87/1.78 % (1225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.78 % (1225)Termination reason: Unknown
% 2.87/1.78 % (1225)Termination phase: shuffling
% 2.87/1.78
% 2.87/1.78 % (1225)Memory used [KB]: 1791
% 2.87/1.78 % (1225)Time elapsed: 0.007 s
% 2.87/1.78 % (1225)Instructions burned: 18 (million)
% 2.87/1.78 % (1225)------------------------------
% 2.87/1.78 % (1225)------------------------------
% 2.87/1.78 % (1231)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/710Mi)
% 2.87/1.78 % (1232)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/6Mi)
% 2.87/1.78 % (1233)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/902Mi)
% 2.87/1.78 % (1232)Instruction limit reached!
% 2.87/1.78 % (1232)------------------------------
% 2.87/1.78 % (1232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.78 % (1232)Termination reason: Unknown
% 2.87/1.78 % (1232)Termination phase: shuffling
% 2.87/1.78
% 2.87/1.78 % (1232)Memory used [KB]: 1407
% 2.87/1.78 % (1232)Time elapsed: 0.003 s
% 2.87/1.78 % (1232)Instructions burned: 6 (million)
% 2.87/1.78 % (1232)------------------------------
% 2.87/1.78 % (1232)------------------------------
% 2.87/1.79 % (1235)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/5Mi)
% 2.87/1.79 % (1235)Instruction limit reached!
% 2.87/1.79 % (1235)------------------------------
% 2.87/1.79 % (1235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.79 % (1235)Termination reason: Unknown
% 2.87/1.79 % (1235)Termination phase: shuffling
% 2.87/1.79
% 2.87/1.79 % (1235)Memory used [KB]: 1407
% 2.87/1.79 % (1235)Time elapsed: 0.003 s
% 2.87/1.79 % (1235)Instructions burned: 6 (million)
% 2.87/1.79 % (1235)------------------------------
% 2.87/1.79 % (1235)------------------------------
% 2.87/1.79 % (1234)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/21Mi)
% 2.87/1.79 % (1236)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/6Mi)
% 2.87/1.80 % (1236)Instruction limit reached!
% 2.87/1.80 % (1236)------------------------------
% 2.87/1.80 % (1236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.80 % (1236)Termination reason: Unknown
% 2.87/1.80 % (1236)Termination phase: shuffling
% 2.87/1.80
% 2.87/1.80 % (1236)Memory used [KB]: 1407
% 2.87/1.80 % (1236)Time elapsed: 0.003 s
% 2.87/1.80 % (1236)Instructions burned: 6 (million)
% 2.87/1.80 % (1236)------------------------------
% 2.87/1.80 % (1236)------------------------------
% 2.89/1.80 % (1239)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/377Mi)
% 2.89/1.80 % (1247)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/779Mi)
% 2.89/1.81 % (1234)Instruction limit reached!
% 2.89/1.81 % (1234)------------------------------
% 2.89/1.81 % (1234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.81 % (1234)Termination reason: Unknown
% 2.89/1.81 % (1234)Termination phase: shuffling
% 2.89/1.81
% 2.89/1.81 % (1234)Memory used [KB]: 1791
% 2.89/1.81 % (1234)Time elapsed: 0.015 s
% 2.89/1.81 % (1234)Instructions burned: 22 (million)
% 2.89/1.81 % (1234)------------------------------
% 2.89/1.81 % (1234)------------------------------
% 2.89/1.81 % (1189)Instruction limit reached!
% 2.89/1.81 % (1189)------------------------------
% 2.89/1.81 % (1189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.81 % (1189)Termination reason: Unknown
% 2.89/1.81 % (1189)Termination phase: Saturation
% 2.89/1.81
% 2.89/1.81 % (1189)Memory used [KB]: 6908
% 2.89/1.81 % (1189)Time elapsed: 0.085 s
% 2.89/1.81 % (1189)Instructions burned: 277 (million)
% 2.89/1.81 % (1189)------------------------------
% 2.89/1.81 % (1189)------------------------------
% 2.89/1.82 % (1257)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/879Mi)
% 2.89/1.82 % (1255)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_929 for (2999ds/19Mi)
% 2.89/1.83 % (1255)Instruction limit reached!
% 2.89/1.83 % (1255)------------------------------
% 2.89/1.83 % (1255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.83 % (1255)Termination reason: Unknown
% 2.89/1.83 % (1255)Termination phase: shuffling
% 2.89/1.83
% 2.89/1.83 % (1255)Memory used [KB]: 1663
% 2.89/1.83 % (1255)Time elapsed: 0.012 s
% 2.89/1.83 % (1255)Instructions burned: 19 (million)
% 2.89/1.83 % (1255)------------------------------
% 2.89/1.83 % (1255)------------------------------
% 2.89/1.85 % (1265)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_929 for (2998ds/17Mi)
% 2.89/1.85 % (1265)Instruction limit reached!
% 2.89/1.85 % (1265)------------------------------
% 2.89/1.85 % (1265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.85 % (1265)Termination reason: Unknown
% 2.89/1.85 % (1265)Termination phase: shuffling
% 2.89/1.85
% 2.89/1.85 % (1265)Memory used [KB]: 1663
% 2.89/1.85 % (1265)Time elapsed: 0.007 s
% 2.89/1.85 % (1265)Instructions burned: 17 (million)
% 2.89/1.85 % (1265)------------------------------
% 2.89/1.85 % (1265)------------------------------
% 2.89/1.86 % (1281)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_929 for (2998ds/3Mi)
% 2.89/1.86 % (1281)Instruction limit reached!
% 2.89/1.86 % (1281)------------------------------
% 2.89/1.86 % (1281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.86 % (1281)Termination reason: Unknown
% 2.89/1.86 % (1281)Termination phase: shuffling
% 2.89/1.86
% 2.89/1.86 % (1281)Memory used [KB]: 1407
% 2.89/1.86 % (1281)Time elapsed: 0.002 s
% 2.89/1.86 % (1281)Instructions burned: 3 (million)
% 2.89/1.86 % (1281)------------------------------
% 2.89/1.86 % (1281)------------------------------
% 2.89/1.87 % (1283)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_929 for (2998ds/30Mi)
% 2.89/1.88 % (1283)Instruction limit reached!
% 2.89/1.88 % (1283)------------------------------
% 2.89/1.88 % (1283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.88 % (1283)Termination reason: Unknown
% 2.89/1.88 % (1283)Termination phase: Property scanning
% 2.89/1.88
% 2.89/1.88 % (1283)Memory used [KB]: 1791
% 2.89/1.88 % (1283)Time elapsed: 0.011 s
% 2.89/1.88 % (1283)Instructions burned: 32 (million)
% 2.89/1.88 % (1283)------------------------------
% 2.89/1.88 % (1283)------------------------------
% 2.89/1.89 % (1294)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_929 for (2998ds/127Mi)
% 2.89/1.91 % (1239)Instruction limit reached!
% 2.89/1.91 % (1239)------------------------------
% 2.89/1.91 % (1239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.91 % (1239)Termination reason: Unknown
% 2.89/1.91 % (1239)Termination phase: Saturation
% 2.89/1.91
% 2.89/1.91 % (1239)Memory used [KB]: 8059
% 2.89/1.91 % (1239)Time elapsed: 0.108 s
% 2.89/1.91 % (1239)Instructions burned: 377 (million)
% 2.89/1.91 % (1239)------------------------------
% 2.89/1.91 % (1239)------------------------------
% 2.89/1.92 % (1302)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_929 for (2998ds/100Mi)
% 2.89/1.93 % (1294)Instruction limit reached!
% 2.89/1.93 % (1294)------------------------------
% 2.89/1.93 % (1294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.93 % (1294)Termination reason: Unknown
% 2.89/1.93 % (1294)Termination phase: Property scanning
% 2.89/1.93
% 2.89/1.93 % (1294)Memory used [KB]: 2302
% 2.89/1.93 % (1294)Time elapsed: 0.036 s
% 2.89/1.93 % (1294)Instructions burned: 129 (million)
% 2.89/1.93 % (1294)------------------------------
% 2.89/1.93 % (1294)------------------------------
% 2.89/1.94 % (1310)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_929 for (2997ds/3Mi)
% 2.89/1.94 % (1310)Instruction limit reached!
% 2.89/1.94 % (1310)------------------------------
% 2.89/1.94 % (1310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.94 % (1310)Termination reason: Unknown
% 2.89/1.94 % (1310)Termination phase: shuffling
% 2.89/1.94
% 2.89/1.94 % (1310)Memory used [KB]: 1407
% 2.89/1.94 % (1310)Time elapsed: 0.002 s
% 2.89/1.94 % (1310)Instructions burned: 4 (million)
% 2.89/1.94 % (1310)------------------------------
% 2.89/1.94 % (1310)------------------------------
% 2.89/1.94 % (1302)Instruction limit reached!
% 2.89/1.94 % (1302)------------------------------
% 2.89/1.94 % (1302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.94 % (1302)Termination reason: Unknown
% 2.89/1.94 % (1302)Termination phase: Property scanning
% 2.89/1.94
% 2.89/1.94 % (1302)Memory used [KB]: 2302
% 2.89/1.94 % (1302)Time elapsed: 0.027 s
% 2.89/1.94 % (1302)Instructions burned: 102 (million)
% 2.89/1.94 % (1302)------------------------------
% 2.89/1.94 % (1302)------------------------------
% 2.89/1.95 % (1315)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_929 for (2997ds/20Mi)
% 2.89/1.95 % (1316)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_929 for (2997ds/86Mi)
% 2.89/1.95 % (1315)Instruction limit reached!
% 2.89/1.95 % (1315)------------------------------
% 2.89/1.95 % (1315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.95 % (1315)Termination reason: Unknown
% 2.89/1.95 % (1315)Termination phase: shuffling
% 2.89/1.95
% 2.89/1.95 % (1315)Memory used [KB]: 1663
% 2.89/1.95 % (1315)Time elapsed: 0.008 s
% 2.89/1.95 % (1315)Instructions burned: 21 (million)
% 2.89/1.95 % (1315)------------------------------
% 2.89/1.95 % (1315)------------------------------
% 2.89/1.96 % (1323)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_929 for (2997ds/107Mi)
% 2.89/1.97 % (1231)Refutation not found, non-redundant clauses discarded% (1231)------------------------------
% 2.89/1.97 % (1231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.97 % (1231)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.89/1.97
% 2.89/1.97 % (1231)Memory used [KB]: 8187
% 2.89/1.97 % (1231)Time elapsed: 0.194 s
% 2.89/1.97 % (1231)Instructions burned: 648 (million)
% 2.89/1.97 % (1231)------------------------------
% 2.89/1.97 % (1231)------------------------------
% 2.89/1.98 % (1316)Instruction limit reached!
% 2.89/1.98 % (1316)------------------------------
% 2.89/1.98 % (1316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.98 % (1316)Termination reason: Unknown
% 2.89/1.98 % (1316)Termination phase: Property scanning
% 2.89/1.98
% 2.89/1.98 % (1316)Memory used [KB]: 2302
% 2.89/1.98 % (1316)Time elapsed: 0.026 s
% 2.89/1.98 % (1316)Instructions burned: 89 (million)
% 2.89/1.98 % (1316)------------------------------
% 2.89/1.98 % (1316)------------------------------
% 2.89/1.98 % (1331)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_929 for (2997ds/39Mi)
% 2.89/1.99 % (1333)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_929 for (2997ds/448Mi)
% 2.89/1.99 % (1331)Instruction limit reached!
% 2.89/1.99 % (1331)------------------------------
% 2.89/1.99 % (1331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.99 % (1331)Termination reason: Unknown
% 2.89/1.99 % (1331)Termination phase: shuffling
% 2.89/1.99
% 2.89/1.99 % (1331)Memory used [KB]: 2174
% 2.89/1.99 % (1331)Time elapsed: 0.012 s
% 2.89/1.99 % (1331)Instructions burned: 40 (million)
% 2.89/1.99 % (1323)Instruction limit reached!
% 2.89/1.99 % (1323)------------------------------
% 2.89/1.99 % (1323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.99 % (1331)------------------------------
% 2.89/1.99 % (1331)------------------------------
% 2.89/1.99 % (1323)Termination reason: Unknown
% 2.89/1.99 % (1323)Termination phase: Property scanning
% 2.89/1.99
% 2.89/1.99 % (1323)Memory used [KB]: 2302
% 2.89/1.99 % (1323)Time elapsed: 0.031 s
% 2.89/1.99 % (1323)Instructions burned: 109 (million)
% 2.89/1.99 % (1323)------------------------------
% 2.89/1.99 % (1323)------------------------------
% 2.89/2.00 % (1338)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_929 for (2997ds/46Mi)
% 2.89/2.00 % (1339)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_929 for (2997ds/98Mi)
% 4.89/2.02 % (1338)Instruction limit reached!
% 4.89/2.02 % (1338)------------------------------
% 4.89/2.02 % (1338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.89/2.02 % (1338)Termination reason: Unknown
% 4.89/2.02 % (1338)Termination phase: Preprocessing 1
% 4.89/2.02
% 4.89/2.02 % (1338)Memory used [KB]: 1791
% 4.89/2.02 % (1338)Time elapsed: 0.015 s
% 4.89/2.02 % (1338)Instructions burned: 48 (million)
% 4.89/2.02 % (1338)------------------------------
% 4.89/2.02 % (1338)------------------------------
% 4.89/2.02 % (1247)Instruction limit reached!
% 4.89/2.02 % (1247)------------------------------
% 4.89/2.02 % (1247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.89/2.02 % (1247)Termination reason: Unknown
% 4.89/2.02 % (1247)Termination phase: Saturation
% 4.89/2.02
% 4.89/2.02 % (1247)Memory used [KB]: 9722
% 4.89/2.02 % (1247)Time elapsed: 0.217 s
% 4.89/2.02 % (1247)Instructions burned: 779 (million)
% 4.89/2.02 % (1247)------------------------------
% 4.89/2.02 % (1247)------------------------------
% 4.89/2.03 % (1345)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_929 for (2997ds/507Mi)
% 4.89/2.03 % (1339)Instruction limit reached!
% 4.89/2.03 % (1339)------------------------------
% 4.89/2.03 % (1339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.89/2.03 % (1339)Termination reason: Unknown
% 4.89/2.03 % (1339)Termination phase: Property scanning
% 4.89/2.03
% 4.89/2.03 % (1339)Memory used [KB]: 2302
% 4.89/2.03 % (1339)Time elapsed: 0.027 s
% 4.89/2.03 % (1339)Instructions burned: 101 (million)
% 4.89/2.03 % (1339)------------------------------
% 4.89/2.03 % (1339)------------------------------
% 4.89/2.03 % (1347)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_929 for (2997ds/149Mi)
% 4.89/2.04 % (1352)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_929 for (2996ds/39Mi)
% 4.89/2.04 % (1233)Instruction limit reached!
% 4.89/2.04 % (1233)------------------------------
% 4.89/2.04 % (1233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.89/2.04 % (1233)Termination reason: Unknown
% 4.89/2.04 % (1233)Termination phase: Saturation
% 4.89/2.04
% 4.89/2.04 % (1233)Memory used [KB]: 8443
% 4.89/2.04 % (1233)Time elapsed: 0.259 s
% 4.89/2.04 % (1233)Instructions burned: 903 (million)
% 4.89/2.04 % (1233)------------------------------
% 4.89/2.04 % (1233)------------------------------
% 4.89/2.05 % (1352)Instruction limit reached!
% 4.89/2.05 % (1352)------------------------------
% 4.89/2.05 % (1352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.89/2.05 % (1352)Termination reason: Unknown
% 4.89/2.05 % (1352)Termination phase: Preprocessing 1
% 4.89/2.05
% 4.89/2.05 % (1352)Memory used [KB]: 1791
% 4.89/2.05 % (1352)Time elapsed: 0.013 s
% 4.89/2.05 % (1352)Instructions burned: 40 (million)
% 4.89/2.05 % (1352)------------------------------
% 4.89/2.05 % (1352)------------------------------
% 4.89/2.05 % (1354)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_929 for (2996ds/6Mi)
% 4.89/2.05 % (1354)Instruction limit reached!
% 4.89/2.05 % (1354)------------------------------
% 4.89/2.05 % (1354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.89/2.05 % (1354)Termination reason: Unknown
% 4.89/2.05 % (1354)Termination phase: shuffling
% 4.89/2.05
% 4.89/2.05 % (1354)Memory used [KB]: 1407
% 4.89/2.05 % (1354)Time elapsed: 0.003 s
% 4.89/2.05 % (1354)Instructions burned: 7 (million)
% 4.89/2.05 % (1354)------------------------------
% 4.89/2.05 % (1354)------------------------------
% 4.89/2.06 % (1358)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_929 for (2996ds/1087Mi)
% 4.89/2.06 % (1360)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_929 for (2996ds/47Mi)
% 4.89/2.07 % (1347)Instruction limit reached!
% 4.89/2.07 % (1347)------------------------------
% 4.89/2.07 % (1347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.89/2.07 % (1347)Termination reason: Unknown
% 4.89/2.07 % (1347)Termination phase: Property scanning
% 4.89/2.07
% 4.89/2.07 % (1347)Memory used [KB]: 2302
% 4.89/2.07 % (1347)Time elapsed: 0.041 s
% 4.89/2.07 % (1347)Instructions burned: 151 (million)
% 4.89/2.07 % (1347)------------------------------
% 4.89/2.07 % (1347)------------------------------
% 4.89/2.08 % (1360)Instruction limit reached!
% 4.89/2.08 % (1360)------------------------------
% 4.89/2.08 % (1360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.89/2.08 % (1360)Termination reason: Unknown
% 4.89/2.08 % (1360)Termination phase: Preprocessing 3
% 4.89/2.08
% 4.89/2.08 % (1360)Memory used [KB]: 2046
% 4.89/2.08 % (1360)Time elapsed: 0.015 s
% 4.89/2.08 % (1360)Instructions burned: 48 (million)
% 4.89/2.08 % (1360)------------------------------
% 4.89/2.08 % (1360)------------------------------
% 4.89/2.08 % (1364)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_929 for (2996ds/44Mi)
% 4.89/2.09 % (1367)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_929 for (2996ds/432Mi)
% 4.89/2.09 % (1364)Instruction limit reached!
% 4.89/2.09 % (1364)------------------------------
% 4.89/2.09 % (1364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.89/2.09 % (1364)Termination reason: Unknown
% 4.89/2.09 % (1364)Termination phase: shuffling
% 4.89/2.09
% 4.89/2.09 % (1364)Memory used [KB]: 2302
% 4.89/2.09 % (1364)Time elapsed: 0.014 s
% 4.89/2.09 % (1364)Instructions burned: 47 (million)
% 4.89/2.09 % (1364)------------------------------
% 4.89/2.09 % (1364)------------------------------
% 4.89/2.10 % (1374)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_929 for (2996ds/62Mi)
% 4.89/2.10 % (1202)Instruction limit reached!
% 4.89/2.10 % (1202)------------------------------
% 4.89/2.10 % (1202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.89/2.10 % (1202)Termination reason: Unknown
% 4.89/2.10 % (1202)Termination phase: Saturation
% 4.89/2.10
% 4.89/2.10 % (1202)Memory used [KB]: 9594
% 4.89/2.10 % (1202)Time elapsed: 0.353 s
% 4.89/2.10 % (1202)Instructions burned: 1043 (million)
% 4.89/2.10 % (1202)------------------------------
% 4.89/2.10 % (1202)------------------------------
% 4.89/2.11 % (1333)Instruction limit reached!
% 4.89/2.11 % (1333)------------------------------
% 4.89/2.11 % (1333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.89/2.11 % (1333)Termination reason: Unknown
% 4.89/2.11 % (1333)Termination phase: Saturation
% 4.89/2.11
% 4.89/2.11 % (1333)Memory used [KB]: 8699
% 4.89/2.11 % (1333)Time elapsed: 0.121 s
% 4.89/2.11 % (1333)Instructions burned: 448 (million)
% 4.89/2.11 % (1333)------------------------------
% 4.89/2.11 % (1333)------------------------------
% 5.42/2.11 % (1380)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_929 for (2996ds/31Mi)
% 5.42/2.12 % (1383)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_929 for (2996ds/96Mi)
% 5.42/2.12 % (1374)Instruction limit reached!
% 5.42/2.12 % (1374)------------------------------
% 5.42/2.12 % (1374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.12 % (1374)Termination reason: Unknown
% 5.42/2.12 % (1374)Termination phase: Property scanning
% 5.42/2.12
% 5.42/2.12 % (1374)Memory used [KB]: 2302
% 5.42/2.12 % (1374)Time elapsed: 0.018 s
% 5.42/2.12 % (1374)Instructions burned: 62 (million)
% 5.42/2.12 % (1374)------------------------------
% 5.42/2.12 % (1374)------------------------------
% 5.42/2.12 % (1380)Instruction limit reached!
% 5.42/2.12 % (1380)------------------------------
% 5.42/2.12 % (1380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.12 % (1380)Termination reason: Unknown
% 5.42/2.12 % (1380)Termination phase: Property scanning
% 5.42/2.12
% 5.42/2.12 % (1380)Memory used [KB]: 1791
% 5.42/2.12 % (1380)Time elapsed: 0.011 s
% 5.42/2.12 % (1380)Instructions burned: 31 (million)
% 5.42/2.12 % (1380)------------------------------
% 5.42/2.12 % (1380)------------------------------
% 5.42/2.13 % (1391)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_929 for (2995ds/453Mi)
% 5.42/2.13 % (1257)Refutation not found, non-redundant clauses discarded% (1257)------------------------------
% 5.42/2.13 % (1257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.13 % (1257)Termination reason: Refutation not found, non-redundant clauses discarded
% 5.42/2.13
% 5.42/2.13 % (1257)Memory used [KB]: 7931
% 5.42/2.13 % (1257)Time elapsed: 0.312 s
% 5.42/2.13 % (1257)Instructions burned: 854 (million)
% 5.42/2.13 % (1257)------------------------------
% 5.42/2.13 % (1257)------------------------------
% 5.42/2.13 % (1395)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_929 for (2995ds/71Mi)
% 5.42/2.14 % (1400)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_929 for (2995ds/83Mi)
% 5.42/2.14 % (1383)Instruction limit reached!
% 5.42/2.14 % (1383)------------------------------
% 5.42/2.14 % (1383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.14 % (1383)Termination reason: Unknown
% 5.42/2.14 % (1383)Termination phase: Property scanning
% 5.42/2.14
% 5.42/2.14 % (1383)Memory used [KB]: 2302
% 5.42/2.14 % (1383)Time elapsed: 0.028 s
% 5.42/2.14 % (1383)Instructions burned: 97 (million)
% 5.42/2.14 % (1383)------------------------------
% 5.42/2.14 % (1383)------------------------------
% 5.42/2.15 % (1407)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_929 for (2995ds/11Mi)
% 5.42/2.15 % (1395)Instruction limit reached!
% 5.42/2.15 % (1395)------------------------------
% 5.42/2.15 % (1395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.15 % (1395)Termination reason: Unknown
% 5.42/2.15 % (1395)Termination phase: Property scanning
% 5.42/2.15
% 5.42/2.15 % (1395)Memory used [KB]: 2174
% 5.42/2.15 % (1395)Time elapsed: 0.022 s
% 5.42/2.15 % (1395)Instructions burned: 73 (million)
% 5.42/2.15 % (1395)------------------------------
% 5.42/2.15 % (1395)------------------------------
% 5.42/2.15 % (1407)Instruction limit reached!
% 5.42/2.15 % (1407)------------------------------
% 5.42/2.15 % (1407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.15 % (1407)Termination reason: Unknown
% 5.42/2.15 % (1407)Termination phase: shuffling
% 5.42/2.15
% 5.42/2.15 % (1407)Memory used [KB]: 1535
% 5.42/2.15 % (1407)Time elapsed: 0.004 s
% 5.42/2.15 % (1407)Instructions burned: 11 (million)
% 5.42/2.15 % (1407)------------------------------
% 5.42/2.15 % (1407)------------------------------
% 5.42/2.16 % (1411)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_929 for (2995ds/41Mi)
% 5.42/2.16 % (1400)Instruction limit reached!
% 5.42/2.16 % (1400)------------------------------
% 5.42/2.16 % (1400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.16 % (1400)Termination reason: Unknown
% 5.42/2.16 % (1400)Termination phase: Function definition elimination
% 5.42/2.16
% 5.42/2.16 % (1400)Memory used [KB]: 2174
% 5.42/2.16 % (1400)Time elapsed: 0.025 s
% 5.42/2.16 % (1400)Instructions burned: 86 (million)
% 5.42/2.16 % (1400)------------------------------
% 5.42/2.16 % (1400)------------------------------
% 5.42/2.16 % (1412)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_929 for (2995ds/6Mi)
% 5.42/2.17 % (1412)Instruction limit reached!
% 5.42/2.17 % (1412)------------------------------
% 5.42/2.17 % (1412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.17 % (1412)Termination reason: Unknown
% 5.42/2.17 % (1412)Termination phase: shuffling
% 5.42/2.17
% 5.42/2.17 % (1412)Memory used [KB]: 1407
% 5.42/2.17 % (1412)Time elapsed: 0.003 s
% 5.42/2.17 % (1412)Instructions burned: 6 (million)
% 5.42/2.17 % (1412)------------------------------
% 5.42/2.17 % (1412)------------------------------
% 5.42/2.17 % (1416)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_929 for (2995ds/150Mi)
% 5.42/2.17 % (1411)Instruction limit reached!
% 5.42/2.17 % (1411)------------------------------
% 5.42/2.17 % (1411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.17 % (1411)Termination reason: Unknown
% 5.42/2.17 % (1411)Termination phase: shuffling
% 5.42/2.17
% 5.42/2.17 % (1411)Memory used [KB]: 2174
% 5.42/2.17 % (1411)Time elapsed: 0.013 s
% 5.42/2.17 % (1411)Instructions burned: 44 (million)
% 5.42/2.17 % (1411)------------------------------
% 5.42/2.17 % (1411)------------------------------
% 5.42/2.18 % (1418)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_929 for (2995ds/343Mi)
% 5.42/2.18 % (1345)Instruction limit reached!
% 5.42/2.18 % (1345)------------------------------
% 5.42/2.18 % (1345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.18 % (1345)Termination reason: Unknown
% 5.42/2.18 % (1345)Termination phase: Saturation
% 5.42/2.18
% 5.42/2.18 % (1345)Memory used [KB]: 8571
% 5.42/2.18 % (1345)Time elapsed: 0.173 s
% 5.42/2.18 % (1345)Instructions burned: 507 (million)
% 5.42/2.18 % (1345)------------------------------
% 5.42/2.18 % (1345)------------------------------
% 5.42/2.18 % (1419)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_929 for (2995ds/109Mi)
% 5.42/2.19 % (1420)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_929 for (2995ds/253Mi)
% 5.81/2.20 % (1367)Instruction limit reached!
% 5.81/2.20 % (1367)------------------------------
% 5.81/2.20 % (1367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.20 % (1367)Termination reason: Unknown
% 5.81/2.20 % (1367)Termination phase: Saturation
% 5.81/2.20
% 5.81/2.20 % (1367)Memory used [KB]: 4349
% 5.81/2.20 % (1367)Time elapsed: 0.120 s
% 5.81/2.20 % (1367)Instructions burned: 432 (million)
% 5.81/2.20 % (1367)------------------------------
% 5.81/2.20 % (1367)------------------------------
% 5.81/2.21 % (1416)Instruction limit reached!
% 5.81/2.21 % (1416)------------------------------
% 5.81/2.21 % (1416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.21 % (1416)Termination reason: Unknown
% 5.81/2.21 % (1416)Termination phase: Property scanning
% 5.81/2.21
% 5.81/2.21 % (1416)Memory used [KB]: 2430
% 5.81/2.21 % (1416)Time elapsed: 0.041 s
% 5.81/2.21 % (1416)Instructions burned: 150 (million)
% 5.81/2.21 % (1416)------------------------------
% 5.81/2.21 % (1416)------------------------------
% 5.81/2.21 % (1421)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_929 for (2995ds/140Mi)
% 5.81/2.21 % (1419)Instruction limit reached!
% 5.81/2.21 % (1419)------------------------------
% 5.81/2.21 % (1419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.21 % (1419)Termination reason: Unknown
% 5.81/2.21 % (1419)Termination phase: Property scanning
% 5.81/2.21
% 5.81/2.21 % (1419)Memory used [KB]: 2302
% 5.81/2.21 % (1419)Time elapsed: 0.031 s
% 5.81/2.21 % (1419)Instructions burned: 110 (million)
% 5.81/2.21 % (1419)------------------------------
% 5.81/2.21 % (1419)------------------------------
% 5.81/2.22 % (1422)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_929 for (2995ds/614Mi)
% 5.81/2.22 % (1423)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_929 for (2995ds/202Mi)
% 5.81/2.25 % (1391)Instruction limit reached!
% 5.81/2.25 % (1391)------------------------------
% 5.81/2.25 % (1391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.25 % (1391)Termination reason: Unknown
% 5.81/2.25 % (1391)Termination phase: Saturation
% 5.81/2.25
% 5.81/2.25 % (1391)Memory used [KB]: 8571
% 5.81/2.25 % (1391)Time elapsed: 0.125 s
% 5.81/2.25 % (1391)Instructions burned: 455 (million)
% 5.81/2.25 % (1391)------------------------------
% 5.81/2.25 % (1391)------------------------------
% 5.81/2.25 % (1423)Refutation not found, incomplete strategy
% 5.81/2.25 % (1423)------------------------------
% 5.81/2.25 % (1423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.25 % (1423)Termination reason: Refutation not found, incomplete strategy
% 5.81/2.25
% 5.81/2.25
% 5.81/2.25 % (1423)Memory used [KB]: 6908
% 5.81/2.25 % (1423)Time elapsed: 0.032 s
% 5.81/2.25 % (1423)Instructions burned: 103 (million)
% 5.81/2.25 % (1423)------------------------------
% 5.81/2.25 % (1423)------------------------------
% 5.81/2.26 % (1421)Instruction limit reached!
% 5.81/2.26 % (1421)------------------------------
% 5.81/2.26 % (1421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.26 % (1421)Termination reason: Unknown
% 5.81/2.26 % (1421)Termination phase: Saturation
% 5.81/2.26
% 5.81/2.26 % (1421)Memory used [KB]: 6780
% 5.81/2.26 % (1421)Time elapsed: 0.045 s
% 5.81/2.26 % (1421)Instructions burned: 141 (million)
% 5.81/2.26 % (1421)------------------------------
% 5.81/2.26 % (1421)------------------------------
% 5.81/2.26 % (1420)Instruction limit reached!
% 5.81/2.26 % (1420)------------------------------
% 5.81/2.26 % (1420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.26 % (1420)Termination reason: Unknown
% 5.81/2.26 % (1420)Termination phase: Saturation
% 5.81/2.26
% 5.81/2.26 % (1420)Memory used [KB]: 8059
% 5.81/2.26 % (1420)Time elapsed: 0.074 s
% 5.81/2.26 % (1420)Instructions burned: 253 (million)
% 5.81/2.26 % (1420)------------------------------
% 5.81/2.26 % (1420)------------------------------
% 5.81/2.26 % (1424)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_929 for (2994ds/339Mi)
% 5.81/2.26 % (1425)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_929 for (2994ds/283Mi)
% 5.81/2.27 % (1426)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_929 for (2994ds/134Mi)
% 5.81/2.27 % (1427)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_929 for (2994ds/298Mi)
% 5.81/2.27 % (1418)Instruction limit reached!
% 5.81/2.27 % (1418)------------------------------
% 5.81/2.27 % (1418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.81/2.27 % (1418)Termination reason: Unknown
% 5.81/2.27 % (1418)Termination phase: Saturation
% 5.81/2.27
% 5.81/2.27 % (1418)Memory used [KB]: 7675
% 5.81/2.27 % (1418)Time elapsed: 0.098 s
% 5.81/2.27 % (1418)Instructions burned: 345 (million)
% 5.81/2.27 % (1418)------------------------------
% 5.81/2.27 % (1418)------------------------------
% 5.81/2.28 % (1428)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_929 for (2994ds/192Mi)
% 6.44/2.30 % (1426)Instruction limit reached!
% 6.44/2.30 % (1426)------------------------------
% 6.44/2.30 % (1426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.30 % (1426)Termination reason: Unknown
% 6.44/2.30 % (1426)Termination phase: Property scanning
% 6.44/2.30
% 6.44/2.30 % (1426)Memory used [KB]: 2302
% 6.44/2.30 % (1426)Time elapsed: 0.037 s
% 6.44/2.30 % (1426)Instructions burned: 138 (million)
% 6.44/2.30 % (1426)------------------------------
% 6.44/2.30 % (1426)------------------------------
% 6.44/2.31 % (1429)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_929 for (2994ds/258Mi)
% 6.44/2.33 % (1428)Instruction limit reached!
% 6.44/2.33 % (1428)------------------------------
% 6.44/2.33 % (1428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.33 % (1428)Termination reason: Unknown
% 6.44/2.33 % (1428)Termination phase: Saturation
% 6.44/2.33
% 6.44/2.33 % (1428)Memory used [KB]: 2942
% 6.44/2.33 % (1428)Time elapsed: 0.052 s
% 6.44/2.33 % (1428)Instructions burned: 194 (million)
% 6.44/2.33 % (1428)------------------------------
% 6.44/2.33 % (1428)------------------------------
% 6.44/2.34 % (1425)Instruction limit reached!
% 6.44/2.34 % (1425)------------------------------
% 6.44/2.34 % (1425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.34 % (1425)Termination reason: Unknown
% 6.44/2.34 % (1425)Termination phase: Saturation
% 6.44/2.34
% 6.44/2.34 % (1425)Memory used [KB]: 7547
% 6.44/2.34 % (1425)Time elapsed: 0.072 s
% 6.44/2.34 % (1425)Instructions burned: 283 (million)
% 6.44/2.34 % (1425)------------------------------
% 6.44/2.34 % (1425)------------------------------
% 6.44/2.34 % (1430)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_929 for (2993ds/90Mi)
% 6.44/2.34 % (1427)Instruction limit reached!
% 6.44/2.34 % (1427)------------------------------
% 6.44/2.34 % (1427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.34 % (1427)Termination reason: Unknown
% 6.44/2.34 % (1427)Termination phase: Saturation
% 6.44/2.34
% 6.44/2.34 % (1427)Memory used [KB]: 8187
% 6.44/2.34 % (1427)Time elapsed: 0.077 s
% 6.44/2.34 % (1427)Instructions burned: 299 (million)
% 6.44/2.34 % (1427)------------------------------
% 6.44/2.34 % (1427)------------------------------
% 6.44/2.34 % (1431)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_929 for (2993ds/231Mi)
% 6.44/2.35 % (1432)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_929 for (2993ds/458Mi)
% 6.44/2.36 % (1424)Instruction limit reached!
% 6.44/2.36 % (1424)------------------------------
% 6.44/2.36 % (1424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.36 % (1424)Termination reason: Unknown
% 6.44/2.36 % (1424)Termination phase: Saturation
% 6.44/2.36
% 6.44/2.36 % (1424)Memory used [KB]: 7164
% 6.44/2.36 % (1424)Time elapsed: 0.098 s
% 6.44/2.36 % (1424)Instructions burned: 340 (million)
% 6.44/2.36 % (1424)------------------------------
% 6.44/2.36 % (1424)------------------------------
% 6.44/2.37 % (1430)Instruction limit reached!
% 6.44/2.37 % (1430)------------------------------
% 6.44/2.37 % (1430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.37 % (1430)Termination reason: Unknown
% 6.44/2.37 % (1430)Termination phase: Property scanning
% 6.44/2.37
% 6.44/2.37 % (1430)Memory used [KB]: 2302
% 6.44/2.37 % (1430)Time elapsed: 0.026 s
% 6.44/2.37 % (1430)Instructions burned: 91 (million)
% 6.44/2.37 % (1430)------------------------------
% 6.44/2.37 % (1430)------------------------------
% 6.44/2.37 % (1433)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_929 for (2993ds/31Mi)
% 6.44/2.38 % (1434)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_929 for (2993ds/297Mi)
% 6.44/2.38 % (1433)Instruction limit reached!
% 6.44/2.38 % (1433)------------------------------
% 6.44/2.38 % (1433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.38 % (1433)Termination reason: Unknown
% 6.44/2.38 % (1433)Termination phase: Property scanning
% 6.44/2.38
% 6.44/2.38 % (1433)Memory used [KB]: 1791
% 6.44/2.38 % (1433)Time elapsed: 0.011 s
% 6.44/2.38 % (1433)Instructions burned: 34 (million)
% 6.44/2.38 % (1433)------------------------------
% 6.44/2.38 % (1433)------------------------------
% 6.44/2.39 % (1435)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_929 for (2993ds/987Mi)
% 6.44/2.39 % (1429)Instruction limit reached!
% 6.44/2.39 % (1429)------------------------------
% 6.44/2.39 % (1429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.39 % (1429)Termination reason: Unknown
% 6.44/2.39 % (1429)Termination phase: Saturation
% 6.44/2.39
% 6.44/2.39 % (1429)Memory used [KB]: 7164
% 6.44/2.39 % (1429)Time elapsed: 0.078 s
% 6.44/2.39 % (1429)Instructions burned: 260 (million)
% 6.44/2.39 % (1429)------------------------------
% 6.44/2.39 % (1429)------------------------------
% 6.44/2.40 % (1422)Instruction limit reached!
% 6.44/2.40 % (1422)------------------------------
% 6.44/2.40 % (1422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.40 % (1422)Termination reason: Unknown
% 6.44/2.40 % (1422)Termination phase: Saturation
% 6.44/2.40
% 6.44/2.40 % (1422)Memory used [KB]: 9210
% 6.44/2.40 % (1422)Time elapsed: 0.174 s
% 6.44/2.40 % (1422)Instructions burned: 616 (million)
% 6.44/2.40 % (1422)------------------------------
% 6.44/2.40 % (1422)------------------------------
% 7.14/2.40 % (1436)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_929 for (2993ds/182Mi)
% 7.14/2.40 % (1431)Instruction limit reached!
% 7.14/2.40 % (1431)------------------------------
% 7.14/2.40 % (1431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.40 % (1431)Termination reason: Unknown
% 7.14/2.40 % (1431)Termination phase: Saturation
% 7.14/2.40
% 7.14/2.40 % (1431)Memory used [KB]: 7291
% 7.14/2.40 % (1431)Time elapsed: 0.059 s
% 7.14/2.40 % (1431)Instructions burned: 232 (million)
% 7.14/2.40 % (1431)------------------------------
% 7.14/2.40 % (1431)------------------------------
% 7.14/2.40 % (1437)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_929 for (2993ds/182Mi)
% 7.14/2.41 % (1358)Instruction limit reached!
% 7.14/2.41 % (1358)------------------------------
% 7.14/2.41 % (1358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.41 % (1358)Termination reason: Unknown
% 7.14/2.41 % (1358)Termination phase: Saturation
% 7.14/2.41
% 7.14/2.41 % (1358)Memory used [KB]: 8827
% 7.14/2.41 % (1358)Time elapsed: 0.371 s
% 7.14/2.41 % (1358)Instructions burned: 1087 (million)
% 7.14/2.41 % (1358)------------------------------
% 7.14/2.41 % (1358)------------------------------
% 7.14/2.41 % (1438)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_929 for (2993ds/154Mi)
% 7.14/2.42 % (1439)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_929 for (2993ds/79Mi)
% 7.14/2.44 % (1439)Instruction limit reached!
% 7.14/2.44 % (1439)------------------------------
% 7.14/2.44 % (1439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.44 % (1439)Termination reason: Unknown
% 7.14/2.44 % (1439)Termination phase: Function definition elimination
% 7.14/2.44
% 7.14/2.44 % (1439)Memory used [KB]: 2302
% 7.14/2.44 % (1439)Time elapsed: 0.024 s
% 7.14/2.44 % (1439)Instructions burned: 79 (million)
% 7.14/2.44 % (1439)------------------------------
% 7.14/2.44 % (1439)------------------------------
% 7.14/2.45 % (1440)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_929 for (2992ds/216Mi)
% 7.14/2.45 % (1436)Instruction limit reached!
% 7.14/2.45 % (1436)------------------------------
% 7.14/2.45 % (1436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.45 % (1436)Termination reason: Unknown
% 7.14/2.45 % (1436)Termination phase: Saturation
% 7.14/2.45
% 7.14/2.45 % (1436)Memory used [KB]: 7164
% 7.14/2.45 % (1436)Time elapsed: 0.051 s
% 7.14/2.45 % (1436)Instructions burned: 184 (million)
% 7.14/2.45 % (1436)------------------------------
% 7.14/2.45 % (1436)------------------------------
% 7.14/2.45 % (1438)Instruction limit reached!
% 7.14/2.45 % (1438)------------------------------
% 7.14/2.45 % (1438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.45 % (1438)Termination reason: Unknown
% 7.14/2.45 % (1438)Termination phase: Property scanning
% 7.14/2.45
% 7.14/2.45 % (1438)Memory used [KB]: 2686
% 7.14/2.45 % (1438)Time elapsed: 0.041 s
% 7.14/2.45 % (1438)Instructions burned: 156 (million)
% 7.14/2.45 % (1438)------------------------------
% 7.14/2.45 % (1438)------------------------------
% 7.14/2.45 % (1434)Instruction limit reached!
% 7.14/2.45 % (1434)------------------------------
% 7.14/2.45 % (1434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.45 % (1434)Termination reason: Unknown
% 7.14/2.45 % (1434)Termination phase: Saturation
% 7.14/2.45
% 7.14/2.45 % (1434)Memory used [KB]: 7547
% 7.14/2.45 % (1434)Time elapsed: 0.079 s
% 7.14/2.45 % (1434)Instructions burned: 298 (million)
% 7.14/2.45 % (1434)------------------------------
% 7.14/2.45 % (1434)------------------------------
% 7.14/2.46 % (1441)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_929 for (2992ds/114Mi)
% 7.14/2.46 % (1437)Instruction limit reached!
% 7.14/2.46 % (1437)------------------------------
% 7.14/2.46 % (1437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.46 % (1437)Termination reason: Unknown
% 7.14/2.46 % (1437)Termination phase: Saturation
% 7.14/2.46
% 7.14/2.46 % (1437)Memory used [KB]: 7291
% 7.14/2.46 % (1437)Time elapsed: 0.077 s
% 7.14/2.46 % (1437)Instructions burned: 182 (million)
% 7.14/2.46 % (1437)------------------------------
% 7.14/2.46 % (1437)------------------------------
% 7.14/2.46 % (1442)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_929 for (2992ds/922Mi)
% 7.14/2.46 % (1443)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_929 for (2992ds/182Mi)
% 7.14/2.47 % (1444)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_929 for (2992ds/164Mi)
% 7.14/2.48 % (1432)Instruction limit reached!
% 7.14/2.48 % (1432)------------------------------
% 7.14/2.48 % (1432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.48 % (1432)Termination reason: Unknown
% 7.14/2.48 % (1432)Termination phase: Saturation
% 7.14/2.48
% 7.14/2.48 % (1432)Memory used [KB]: 8187
% 7.14/2.48 % (1432)Time elapsed: 0.130 s
% 7.14/2.48 % (1432)Instructions burned: 458 (million)
% 7.14/2.48 % (1432)------------------------------
% 7.14/2.48 % (1432)------------------------------
% 7.14/2.49 % (1441)Instruction limit reached!
% 7.14/2.49 % (1441)------------------------------
% 7.14/2.49 % (1441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.14/2.49 % (1441)Termination reason: Unknown
% 7.14/2.49 % (1441)Termination phase: Property scanning
% 7.14/2.49
% 7.14/2.49 % (1441)Memory used [KB]: 2302
% 7.14/2.49 % (1441)Time elapsed: 0.032 s
% 7.14/2.49 % (1441)Instructions burned: 117 (million)
% 7.14/2.49 % (1441)------------------------------
% 7.14/2.49 % (1441)------------------------------
% 7.14/2.49 % (1445)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_929 for (2992ds/50Mi)
% 8.06/2.50 % (1446)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_929 for (2992ds/368Mi)
% 8.06/2.50 % (1440)Instruction limit reached!
% 8.06/2.50 % (1440)------------------------------
% 8.06/2.50 % (1440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.50 % (1440)Termination reason: Unknown
% 8.06/2.50 % (1440)Termination phase: Saturation
% 8.06/2.50
% 8.06/2.50 % (1440)Memory used [KB]: 7291
% 8.06/2.50 % (1440)Time elapsed: 0.056 s
% 8.06/2.50 % (1440)Instructions burned: 218 (million)
% 8.06/2.50 % (1440)------------------------------
% 8.06/2.50 % (1440)------------------------------
% 8.06/2.51 % (1445)Instruction limit reached!
% 8.06/2.51 % (1445)------------------------------
% 8.06/2.51 % (1445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.51 % (1445)Termination reason: Unknown
% 8.06/2.51 % (1445)Termination phase: Property scanning
% 8.06/2.51
% 8.06/2.51 % (1445)Memory used [KB]: 2302
% 8.06/2.51 % (1445)Time elapsed: 0.015 s
% 8.06/2.51 % (1445)Instructions burned: 51 (million)
% 8.06/2.51 % (1445)------------------------------
% 8.06/2.51 % (1445)------------------------------
% 8.06/2.51 % (1443)Instruction limit reached!
% 8.06/2.51 % (1443)------------------------------
% 8.06/2.51 % (1443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.51 % (1443)Termination reason: Unknown
% 8.06/2.51 % (1443)Termination phase: Property scanning
% 8.06/2.51
% 8.06/2.51 % (1443)Memory used [KB]: 2686
% 8.06/2.51 % (1443)Time elapsed: 0.047 s
% 8.06/2.51 % (1443)Instructions burned: 183 (million)
% 8.06/2.51 % (1443)------------------------------
% 8.06/2.51 % (1443)------------------------------
% 8.06/2.51 % (1444)Instruction limit reached!
% 8.06/2.51 % (1444)------------------------------
% 8.06/2.51 % (1444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.51 % (1444)Termination reason: Unknown
% 8.06/2.51 % (1444)Termination phase: Property scanning
% 8.06/2.51
% 8.06/2.51 % (1444)Memory used [KB]: 2430
% 8.06/2.51 % (1444)Time elapsed: 0.043 s
% 8.06/2.51 % (1444)Instructions burned: 165 (million)
% 8.06/2.51 % (1444)------------------------------
% 8.06/2.51 % (1444)------------------------------
% 8.06/2.51 % (1447)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_929 for (2992ds/1021Mi)
% 8.06/2.52 % (1448)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_929 for (2992ds/267Mi)
% 8.06/2.52 % (1449)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_929 for (2991ds/204Mi)
% 8.06/2.52 % (1450)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_929 for (2991ds/26Mi)
% 8.06/2.53 % (1450)Instruction limit reached!
% 8.06/2.53 % (1450)------------------------------
% 8.06/2.53 % (1450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.53 % (1450)Termination reason: Unknown
% 8.06/2.53 % (1450)Termination phase: shuffling
% 8.06/2.53
% 8.06/2.53 % (1450)Memory used [KB]: 1791
% 8.06/2.53 % (1450)Time elapsed: 0.008 s
% 8.06/2.53 % (1450)Instructions burned: 26 (million)
% 8.06/2.53 % (1450)------------------------------
% 8.06/2.53 % (1450)------------------------------
% 8.06/2.54 % (1451)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_929 for (2991ds/53Mi)
% 8.06/2.55 % (1451)Instruction limit reached!
% 8.06/2.55 % (1451)------------------------------
% 8.06/2.55 % (1451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.55 % (1451)Termination reason: Unknown
% 8.06/2.55 % (1451)Termination phase: Property scanning
% 8.06/2.55
% 8.06/2.55 % (1451)Memory used [KB]: 2302
% 8.06/2.55 % (1451)Time elapsed: 0.016 s
% 8.06/2.55 % (1451)Instructions burned: 54 (million)
% 8.06/2.55 % (1451)------------------------------
% 8.06/2.55 % (1451)------------------------------
% 8.06/2.56 % (1452)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_929 for (2991ds/4436Mi)
% 8.06/2.58 % (1449)Instruction limit reached!
% 8.06/2.58 % (1449)------------------------------
% 8.06/2.58 % (1449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.58 % (1449)Termination reason: Unknown
% 8.06/2.58 % (1449)Termination phase: Saturation
% 8.06/2.58
% 8.06/2.58 % (1449)Memory used [KB]: 7164
% 8.06/2.58 % (1449)Time elapsed: 0.057 s
% 8.06/2.58 % (1449)Instructions burned: 205 (million)
% 8.06/2.58 % (1449)------------------------------
% 8.06/2.58 % (1449)------------------------------
% 8.06/2.58 % (1448)Instruction limit reached!
% 8.06/2.58 % (1448)------------------------------
% 8.06/2.58 % (1448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.06/2.58 % (1448)Termination reason: Unknown
% 8.06/2.58 % (1448)Termination phase: Saturation
% 8.06/2.58
% 8.06/2.58 % (1448)Memory used [KB]: 7547
% 8.06/2.58 % (1448)Time elapsed: 0.069 s
% 8.06/2.58 % (1448)Instructions burned: 268 (million)
% 8.06/2.58 % (1448)------------------------------
% 8.06/2.58 % (1448)------------------------------
% 8.06/2.58 % (1453)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_929 for (2991ds/1539Mi)
% 8.06/2.59 % (1454)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_929 for (2991ds/408Mi)
% 8.43/2.60 % (1446)Instruction limit reached!
% 8.43/2.60 % (1446)------------------------------
% 8.43/2.60 % (1446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.60 % (1446)Termination reason: Unknown
% 8.43/2.60 % (1446)Termination phase: Saturation
% 8.43/2.60
% 8.43/2.60 % (1446)Memory used [KB]: 8059
% 8.43/2.60 % (1446)Time elapsed: 0.104 s
% 8.43/2.60 % (1446)Instructions burned: 369 (million)
% 8.43/2.60 % (1446)------------------------------
% 8.43/2.60 % (1446)------------------------------
% 8.43/2.61 % (1455)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_929 for (2991ds/5205Mi)
% 8.43/2.68 % (1435)Instruction limit reached!
% 8.43/2.68 % (1435)------------------------------
% 8.43/2.68 % (1435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.68 % (1435)Termination reason: Unknown
% 8.43/2.68 % (1435)Termination phase: Saturation
% 8.43/2.68
% 8.43/2.68 % (1435)Memory used [KB]: 9722
% 8.43/2.68 % (1435)Time elapsed: 0.297 s
% 8.43/2.68 % (1435)Instructions burned: 990 (million)
% 8.43/2.68 % (1435)------------------------------
% 8.43/2.68 % (1435)------------------------------
% 8.43/2.69 % (1456)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_929 for (2990ds/1913Mi)
% 8.84/2.71 % (1454)Instruction limit reached!
% 8.84/2.71 % (1454)------------------------------
% 8.84/2.71 % (1454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.84/2.71 % (1454)Termination reason: Unknown
% 8.84/2.71 % (1454)Termination phase: Saturation
% 8.84/2.71
% 8.84/2.71 % (1454)Memory used [KB]: 8315
% 8.84/2.71 % (1454)Time elapsed: 0.119 s
% 8.84/2.71 % (1454)Instructions burned: 408 (million)
% 8.84/2.71 % (1454)------------------------------
% 8.84/2.71 % (1454)------------------------------
% 8.84/2.72 % (1457)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_929 for (2989ds/4350Mi)
% 8.84/2.74 % (1442)Instruction limit reached!
% 8.84/2.74 % (1442)------------------------------
% 8.84/2.74 % (1442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.84/2.74 % (1442)Termination reason: Unknown
% 8.84/2.74 % (1442)Termination phase: Saturation
% 8.84/2.74
% 8.84/2.74 % (1442)Memory used [KB]: 8827
% 8.84/2.74 % (1442)Time elapsed: 0.307 s
% 8.84/2.74 % (1442)Instructions burned: 922 (million)
% 8.84/2.74 % (1442)------------------------------
% 8.84/2.74 % (1442)------------------------------
% 8.84/2.75 % (1458)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_929 for (2989ds/68Mi)
% 8.84/2.77 % (1458)Instruction limit reached!
% 8.84/2.77 % (1458)------------------------------
% 8.84/2.77 % (1458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.84/2.77 % (1458)Termination reason: Unknown
% 8.84/2.77 % (1458)Termination phase: Property scanning
% 8.84/2.77
% 8.84/2.77 % (1458)Memory used [KB]: 2174
% 8.84/2.77 % (1458)Time elapsed: 0.021 s
% 8.84/2.77 % (1458)Instructions burned: 69 (million)
% 8.84/2.77 % (1458)------------------------------
% 8.84/2.77 % (1458)------------------------------
% 8.84/2.78 % (1460)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_929 for (2989ds/358Mi)
% 9.30/2.81 % (1447)Instruction limit reached!
% 9.30/2.81 % (1447)------------------------------
% 9.30/2.81 % (1447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.30/2.81 % (1447)Termination reason: Unknown
% 9.30/2.81 % (1447)Termination phase: Saturation
% 9.30/2.81
% 9.30/2.81 % (1447)Memory used [KB]: 9850
% 9.30/2.81 % (1447)Time elapsed: 0.298 s
% 9.30/2.81 % (1447)Instructions burned: 1023 (million)
% 9.30/2.81 % (1447)------------------------------
% 9.30/2.81 % (1447)------------------------------
% 9.30/2.82 % (1461)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_929 for (2989ds/31Mi)
% 9.30/2.83 % (1461)Instruction limit reached!
% 9.30/2.83 % (1461)------------------------------
% 9.30/2.83 % (1461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.30/2.83 % (1461)Termination reason: Unknown
% 9.30/2.83 % (1461)Termination phase: Property scanning
% 9.30/2.83
% 9.30/2.83 % (1461)Memory used [KB]: 1791
% 9.30/2.83 % (1461)Time elapsed: 0.011 s
% 9.30/2.83 % (1461)Instructions burned: 33 (million)
% 9.30/2.83 % (1461)------------------------------
% 9.30/2.83 % (1461)------------------------------
% 9.30/2.84 % (1462)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_929 for (2988ds/279Mi)
% 9.30/2.88 % (1460)Instruction limit reached!
% 9.30/2.88 % (1460)------------------------------
% 9.30/2.88 % (1460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.30/2.88 % (1460)Termination reason: Unknown
% 9.30/2.88 % (1460)Termination phase: Saturation
% 9.30/2.88
% 9.30/2.88 % (1460)Memory used [KB]: 7675
% 9.30/2.88 % (1460)Time elapsed: 0.101 s
% 9.30/2.88 % (1460)Instructions burned: 359 (million)
% 9.30/2.88 % (1460)------------------------------
% 9.30/2.88 % (1460)------------------------------
% 9.30/2.89 % (1463)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_929 for (2988ds/258Mi)
% 9.75/2.90 % (1462)Refutation not found, incomplete strategy
% 9.75/2.90 % (1462)------------------------------
% 9.75/2.90 % (1462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.90 % (1462)Termination reason: Refutation not found, incomplete strategy
% 9.75/2.90
% 9.75/2.90
% 9.75/2.90 % (1462)Memory used [KB]: 7547
% 9.75/2.90 % (1462)Time elapsed: 0.067 s
% 9.75/2.90 % (1462)Instructions burned: 251 (million)
% 9.75/2.90 % (1462)------------------------------
% 9.75/2.90 % (1462)------------------------------
% 9.75/2.91 % (1464)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_929 for (2988ds/26Mi)
% 9.75/2.92 % (1464)Instruction limit reached!
% 9.75/2.92 % (1464)------------------------------
% 9.75/2.92 % (1464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.92 % (1464)Termination reason: Unknown
% 9.75/2.92 % (1464)Termination phase: shuffling
% 9.75/2.92
% 9.75/2.92 % (1464)Memory used [KB]: 1918
% 9.75/2.92 % (1464)Time elapsed: 0.008 s
% 9.75/2.92 % (1464)Instructions burned: 27 (million)
% 9.75/2.92 % (1464)------------------------------
% 9.75/2.92 % (1464)------------------------------
% 9.75/2.93 % (1465)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_929 for (2987ds/995Mi)
% 9.75/2.97 % (1463)Instruction limit reached!
% 9.75/2.97 % (1463)------------------------------
% 9.75/2.97 % (1463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.97 % (1463)Termination reason: Unknown
% 9.75/2.97 % (1463)Termination phase: Saturation
% 9.75/2.97
% 9.75/2.97 % (1463)Memory used [KB]: 7547
% 9.75/2.97 % (1463)Time elapsed: 0.078 s
% 9.75/2.97 % (1463)Instructions burned: 259 (million)
% 9.75/2.97 % (1463)------------------------------
% 9.75/2.97 % (1463)------------------------------
% 9.75/2.98 % (1466)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_929 for (2987ds/373Mi)
% 9.75/3.02 % (1453)Instruction limit reached!
% 9.75/3.02 % (1453)------------------------------
% 9.75/3.02 % (1453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/3.02 % (1453)Termination reason: Unknown
% 9.75/3.02 % (1453)Termination phase: Saturation
% 9.75/3.02
% 9.75/3.02 % (1453)Memory used [KB]: 10106
% 9.75/3.02 % (1453)Time elapsed: 0.439 s
% 9.75/3.02 % (1453)Instructions burned: 1541 (million)
% 9.75/3.02 % (1453)------------------------------
% 9.75/3.02 % (1453)------------------------------
% 11.98/3.03 % (1467)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_929 for (2986ds/253Mi)
% 11.98/3.09 % (1466)Instruction limit reached!
% 11.98/3.09 % (1466)------------------------------
% 11.98/3.09 % (1466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.98/3.09 % (1466)Termination reason: Unknown
% 11.98/3.09 % (1466)Termination phase: Saturation
% 11.98/3.09
% 11.98/3.09 % (1466)Memory used [KB]: 8187
% 11.98/3.09 % (1466)Time elapsed: 0.107 s
% 11.98/3.09 % (1466)Instructions burned: 374 (million)
% 11.98/3.09 % (1466)------------------------------
% 11.98/3.09 % (1466)------------------------------
% 11.98/3.10 % (1468)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_929 for (2986ds/832Mi)
% 11.98/3.10 % (1467)Instruction limit reached!
% 11.98/3.10 % (1467)------------------------------
% 11.98/3.10 % (1467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.98/3.10 % (1467)Termination reason: Unknown
% 11.98/3.10 % (1467)Termination phase: Saturation
% 11.98/3.10
% 11.98/3.10 % (1467)Memory used [KB]: 7419
% 11.98/3.10 % (1467)Time elapsed: 0.065 s
% 11.98/3.10 % (1467)Instructions burned: 256 (million)
% 11.98/3.10 % (1467)------------------------------
% 11.98/3.10 % (1467)------------------------------
% 11.98/3.11 % (1469)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_929 for (2986ds/668Mi)
% 13.05/3.22 % (1465)Instruction limit reached!
% 13.05/3.22 % (1465)------------------------------
% 13.05/3.22 % (1465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.05/3.22 % (1465)Termination reason: Unknown
% 13.05/3.22 % (1465)Termination phase: Saturation
% 13.05/3.22
% 13.05/3.22 % (1465)Memory used [KB]: 9594
% 13.05/3.22 % (1465)Time elapsed: 0.286 s
% 13.05/3.22 % (1465)Instructions burned: 998 (million)
% 13.05/3.22 % (1465)------------------------------
% 13.05/3.22 % (1465)------------------------------
% 13.05/3.23 % (1470)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_929 for (2984ds/40Mi)
% 13.05/3.24 % (1470)Instruction limit reached!
% 13.05/3.24 % (1470)------------------------------
% 13.05/3.24 % (1470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.05/3.24 % (1470)Termination reason: Unknown
% 13.05/3.24 % (1470)Termination phase: shuffling
% 13.05/3.24
% 13.05/3.24 % (1470)Memory used [KB]: 2174
% 13.05/3.24 % (1470)Time elapsed: 0.012 s
% 13.05/3.24 % (1470)Instructions burned: 40 (million)
% 13.05/3.24 % (1470)------------------------------
% 13.05/3.24 % (1470)------------------------------
% 13.05/3.25 % (1471)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_929 for (2984ds/294Mi)
% 13.05/3.27 % (1471)Refutation not found, incomplete strategy
% 13.05/3.27 % (1471)------------------------------
% 13.05/3.27 % (1471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.05/3.27 % (1471)Termination reason: Refutation not found, incomplete strategy
% 13.05/3.27
% 13.05/3.27
% 13.05/3.27 % (1471)Memory used [KB]: 6908
% 13.05/3.27 % (1471)Time elapsed: 0.026 s
% 13.05/3.27 % (1471)Instructions burned: 96 (million)
% 13.05/3.27 % (1471)------------------------------
% 13.05/3.27 % (1471)------------------------------
% 13.05/3.28 % (1456)Instruction limit reached!
% 13.05/3.28 % (1456)------------------------------
% 13.05/3.28 % (1456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.05/3.28 % (1456)Termination reason: Unknown
% 13.05/3.28 % (1456)Termination phase: Saturation
% 13.05/3.28
% 13.05/3.28 % (1456)Memory used [KB]: 4861
% 13.05/3.28 % (1456)Time elapsed: 0.586 s
% 13.05/3.28 % (1456)Instructions burned: 1915 (million)
% 13.05/3.28 % (1456)------------------------------
% 13.05/3.28 % (1456)------------------------------
% 13.05/3.28 % (1472)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_929 for (2984ds/187Mi)
% 13.05/3.29 % (1473)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_929 for (2984ds/371Mi)
% 13.05/3.29 % (1469)Instruction limit reached!
% 13.05/3.29 % (1469)------------------------------
% 13.05/3.29 % (1469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.05/3.29 % (1469)Termination reason: Unknown
% 13.05/3.29 % (1469)Termination phase: Saturation
% 13.05/3.29
% 13.05/3.29 % (1469)Memory used [KB]: 13816
% 13.05/3.29 % (1469)Time elapsed: 0.188 s
% 13.05/3.29 % (1469)Instructions burned: 668 (million)
% 13.05/3.29 % (1469)------------------------------
% 13.05/3.29 % (1469)------------------------------
% 13.71/3.30 % (1474)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_929 for (2984ds/1827Mi)
% 13.71/3.33 % (1472)Instruction limit reached!
% 13.71/3.33 % (1472)------------------------------
% 13.71/3.33 % (1472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.71/3.33 % (1472)Termination reason: Unknown
% 13.71/3.33 % (1472)Termination phase: Saturation
% 13.71/3.33
% 13.71/3.33 % (1472)Memory used [KB]: 7164
% 13.71/3.33 % (1472)Time elapsed: 0.052 s
% 13.71/3.33 % (1472)Instructions burned: 189 (million)
% 13.71/3.33 % (1472)------------------------------
% 13.71/3.33 % (1472)------------------------------
% 13.71/3.34 % (1468)Instruction limit reached!
% 13.71/3.34 % (1468)------------------------------
% 13.71/3.34 % (1468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.71/3.34 % (1468)Termination reason: Unknown
% 13.71/3.34 % (1468)Termination phase: Saturation
% 13.71/3.34
% 13.71/3.34 % (1468)Memory used [KB]: 7931
% 13.71/3.34 % (1468)Time elapsed: 0.248 s
% 13.71/3.34 % (1468)Instructions burned: 833 (million)
% 13.71/3.34 % (1468)------------------------------
% 13.71/3.34 % (1468)------------------------------
% 13.71/3.34 % (1475)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_929 for (2983ds/70Mi)
% 13.71/3.35 % (1476)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_929 for (2983ds/316Mi)
% 13.71/3.36 % (1475)Instruction limit reached!
% 13.71/3.36 % (1475)------------------------------
% 13.71/3.36 % (1475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.71/3.36 % (1475)Termination reason: Unknown
% 13.71/3.36 % (1475)Termination phase: Property scanning
% 13.71/3.36
% 13.71/3.36 % (1475)Memory used [KB]: 2302
% 13.71/3.36 % (1475)Time elapsed: 0.020 s
% 13.71/3.36 % (1475)Instructions burned: 70 (million)
% 13.71/3.36 % (1475)------------------------------
% 13.71/3.36 % (1475)------------------------------
% 13.71/3.37 % (1477)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_929 for (2983ds/932Mi)
% 13.71/3.39 % (1473)Instruction limit reached!
% 13.71/3.39 % (1473)------------------------------
% 13.71/3.39 % (1473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.71/3.39 % (1473)Termination reason: Unknown
% 13.71/3.39 % (1473)Termination phase: Saturation
% 13.71/3.39
% 13.71/3.39 % (1473)Memory used [KB]: 7803
% 13.71/3.39 % (1473)Time elapsed: 0.106 s
% 13.71/3.39 % (1473)Instructions burned: 371 (million)
% 13.71/3.39 % (1473)------------------------------
% 13.71/3.39 % (1473)------------------------------
% 14.47/3.40 % (1478)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_929 for (2983ds/4714Mi)
% 14.47/3.43 % (1476)Refutation not found, incomplete strategy
% 14.47/3.43 % (1476)------------------------------
% 14.47/3.43 % (1476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.47/3.43 % (1476)Termination reason: Refutation not found, incomplete strategy
% 14.47/3.43
% 14.47/3.43
% 14.47/3.43 % (1476)Memory used [KB]: 7803
% 14.47/3.43 % (1476)Time elapsed: 0.081 s
% 14.47/3.43 % (1476)Instructions burned: 302 (million)
% 14.47/3.43 % (1476)------------------------------
% 14.47/3.43 % (1476)------------------------------
% 14.47/3.44 % (1479)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_929 for (2982ds/8250Mi)
% 14.47/3.49 % (1478)Refutation not found, incomplete strategy
% 14.47/3.49 % (1478)------------------------------
% 14.47/3.49 % (1478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.47/3.49 % (1478)Termination reason: Refutation not found, incomplete strategy
% 14.47/3.49
% 14.47/3.49
% 14.47/3.49 % (1478)Memory used [KB]: 8059
% 14.47/3.49 % (1478)Time elapsed: 0.090 s
% 14.47/3.49 % (1478)Instructions burned: 332 (million)
% 14.47/3.49 % (1478)------------------------------
% 14.47/3.49 % (1478)------------------------------
% 14.96/3.50 % (1480)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_929 for (2982ds/770Mi)
% 15.25/3.64 % (1477)Instruction limit reached!
% 15.25/3.64 % (1477)------------------------------
% 15.25/3.64 % (1477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.25/3.64 % (1477)Termination reason: Unknown
% 15.25/3.64 % (1477)Termination phase: Saturation
% 15.25/3.64
% 15.25/3.64 % (1477)Memory used [KB]: 9722
% 15.25/3.64 % (1477)Time elapsed: 0.270 s
% 15.25/3.64 % (1477)Instructions burned: 935 (million)
% 15.25/3.64 % (1477)------------------------------
% 15.25/3.64 % (1477)------------------------------
% 15.25/3.65 % (1481)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_929 for (2980ds/794Mi)
% 15.83/3.73 % (1480)Refutation not found, non-redundant clauses discarded% (1480)------------------------------
% 15.83/3.73 % (1480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.83/3.73 % (1480)Termination reason: Refutation not found, non-redundant clauses discarded
% 15.83/3.73
% 15.83/3.73 % (1480)Memory used [KB]: 7291
% 15.83/3.73 % (1480)Time elapsed: 0.227 s
% 15.83/3.73 % (1480)Instructions burned: 758 (million)
% 15.83/3.73 % (1480)------------------------------
% 15.83/3.73 % (1480)------------------------------
% 15.83/3.74 % (1482)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_929 for (2979ds/464Mi)
% 16.37/3.85 % (1457)Refutation not found, non-redundant clauses discarded% (1457)------------------------------
% 16.37/3.85 % (1457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.37/3.85 % (1457)Termination reason: Refutation not found, non-redundant clauses discarded
% 16.37/3.85
% 16.37/3.85 % (1457)Memory used [KB]: 9594
% 16.37/3.85 % (1457)Time elapsed: 1.129 s
% 16.37/3.85 % (1457)Instructions burned: 4120 (million)
% 16.37/3.85 % (1457)------------------------------
% 16.37/3.85 % (1457)------------------------------
% 16.37/3.86 % (1483)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_929 for (2978ds/1376Mi)
% 16.37/3.86 % (1482)Instruction limit reached!
% 16.37/3.86 % (1482)------------------------------
% 16.37/3.86 % (1482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.37/3.86 % (1482)Termination reason: Unknown
% 16.37/3.86 % (1482)Termination phase: Saturation
% 16.37/3.86
% 16.37/3.86 % (1482)Memory used [KB]: 7803
% 16.37/3.86 % (1482)Time elapsed: 0.125 s
% 16.37/3.86 % (1482)Instructions burned: 466 (million)
% 16.37/3.86 % (1482)------------------------------
% 16.37/3.86 % (1482)------------------------------
% 16.37/3.87 % (1474)Instruction limit reached!
% 16.37/3.87 % (1474)------------------------------
% 16.37/3.87 % (1474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.37/3.87 % (1474)Termination reason: Unknown
% 16.37/3.87 % (1474)Termination phase: Saturation
% 16.37/3.87
% 16.37/3.87 % (1474)Memory used [KB]: 10106
% 16.37/3.87 % (1474)Time elapsed: 0.568 s
% 16.37/3.87 % (1474)Instructions burned: 1830 (million)
% 16.37/3.87 % (1474)------------------------------
% 16.37/3.87 % (1474)------------------------------
% 16.37/3.87 % (1484)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_929 for (2978ds/906Mi)
% 16.37/3.88 % (1481)Instruction limit reached!
% 16.37/3.88 % (1481)------------------------------
% 16.37/3.88 % (1481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.37/3.88 % (1481)Termination reason: Unknown
% 16.37/3.88 % (1481)Termination phase: Saturation
% 16.37/3.88
% 16.37/3.88 % (1481)Memory used [KB]: 4989
% 16.37/3.88 % (1481)Time elapsed: 0.227 s
% 16.37/3.88 % (1481)Instructions burned: 795 (million)
% 16.37/3.88 % (1481)------------------------------
% 16.37/3.88 % (1481)------------------------------
% 16.37/3.88 % (1485)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_929 for (2978ds/434Mi)
% 16.37/3.89 % (1486)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_929 for (2978ds/865Mi)
% 17.58/3.94 % (1452)Instruction limit reached!
% 17.58/3.94 % (1452)------------------------------
% 17.58/3.94 % (1452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.58/3.94 % (1452)Termination reason: Unknown
% 17.58/3.94 % (1452)Termination phase: Saturation
% 17.58/3.94
% 17.58/3.94 % (1452)Memory used [KB]: 12537
% 17.58/3.94 % (1452)Time elapsed: 1.382 s
% 17.58/3.94 % (1452)Instructions burned: 4438 (million)
% 17.58/3.94 % (1452)------------------------------
% 17.58/3.94 % (1452)------------------------------
% 17.58/3.95 % (1487)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_929 for (2977ds/593Mi)
% 17.58/4.01 % (1485)Instruction limit reached!
% 17.58/4.01 % (1485)------------------------------
% 17.58/4.01 % (1485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.58/4.01 % (1485)Termination reason: Unknown
% 17.58/4.01 % (1485)Termination phase: Saturation
% 17.58/4.01
% 17.58/4.01 % (1485)Memory used [KB]: 8059
% 17.58/4.01 % (1485)Time elapsed: 0.150 s
% 17.58/4.01 % (1485)Instructions burned: 435 (million)
% 17.58/4.01 % (1485)------------------------------
% 17.58/4.01 % (1485)------------------------------
% 17.58/4.02 % (1488)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_929 for (2977ds/443Mi)
% 18.98/4.11 % (1487)Instruction limit reached!
% 18.98/4.11 % (1487)------------------------------
% 18.98/4.11 % (1487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.98/4.11 % (1487)Termination reason: Unknown
% 18.98/4.11 % (1487)Termination phase: Saturation
% 18.98/4.11
% 18.98/4.11 % (1487)Memory used [KB]: 8955
% 18.98/4.11 % (1487)Time elapsed: 0.158 s
% 18.98/4.11 % (1487)Instructions burned: 595 (million)
% 18.98/4.11 % (1487)------------------------------
% 18.98/4.11 % (1487)------------------------------
% 18.98/4.12 % (1489)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_929 for (2975ds/594Mi)
% 19.61/4.13 % (1486)Instruction limit reached!
% 19.61/4.13 % (1486)------------------------------
% 19.61/4.13 % (1486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.61/4.13 % (1486)Termination reason: Unknown
% 19.61/4.13 % (1486)Termination phase: Saturation
% 19.61/4.13
% 19.61/4.13 % (1486)Memory used [KB]: 9083
% 19.61/4.13 % (1486)Time elapsed: 0.245 s
% 19.61/4.13 % (1486)Instructions burned: 866 (million)
% 19.61/4.13 % (1486)------------------------------
% 19.61/4.13 % (1486)------------------------------
% 19.61/4.14 % (1490)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_929 for (2975ds/327Mi)
% 19.61/4.14 % (1455)Instruction limit reached!
% 19.61/4.14 % (1455)------------------------------
% 19.61/4.14 % (1455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.61/4.14 % (1455)Termination reason: Unknown
% 19.61/4.14 % (1455)Termination phase: Saturation
% 19.61/4.14
% 19.61/4.14 % (1455)Memory used [KB]: 13688
% 19.61/4.14 % (1455)Time elapsed: 1.533 s
% 19.61/4.14 % (1455)Instructions burned: 5208 (million)
% 19.61/4.14 % (1455)------------------------------
% 19.61/4.14 % (1455)------------------------------
% 19.61/4.14 % (1488)Instruction limit reached!
% 19.61/4.14 % (1488)------------------------------
% 19.61/4.14 % (1488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.61/4.14 % (1488)Termination reason: Unknown
% 19.61/4.14 % (1488)Termination phase: Saturation
% 19.61/4.14
% 19.61/4.14 % (1488)Memory used [KB]: 8187
% 19.61/4.14 % (1488)Time elapsed: 0.127 s
% 19.61/4.14 % (1488)Instructions burned: 444 (million)
% 19.61/4.14 % (1488)------------------------------
% 19.61/4.14 % (1488)------------------------------
% 19.61/4.15 % (1491)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_929 for (2975ds/5411Mi)
% 19.61/4.15 % (1492)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_929 for (2975ds/1762Mi)
% 19.61/4.18 % (1484)Instruction limit reached!
% 19.61/4.18 % (1484)------------------------------
% 19.61/4.18 % (1484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.61/4.18 % (1484)Termination reason: Unknown
% 19.61/4.18 % (1484)Termination phase: Saturation
% 19.61/4.18
% 19.61/4.18 % (1484)Memory used [KB]: 10362
% 19.61/4.18 % (1484)Time elapsed: 0.308 s
% 19.61/4.18 % (1484)Instructions burned: 908 (million)
% 19.61/4.18 % (1484)------------------------------
% 19.61/4.18 % (1484)------------------------------
% 19.61/4.19 % (1493)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_929 for (2975ds/96Mi)
% 20.01/4.21 % (1493)Instruction limit reached!
% 20.01/4.21 % (1493)------------------------------
% 20.01/4.21 % (1493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.01/4.21 % (1493)Termination reason: Unknown
% 20.01/4.21 % (1493)Termination phase: Property scanning
% 20.01/4.21
% 20.01/4.21 % (1493)Memory used [KB]: 2302
% 20.01/4.21 % (1493)Time elapsed: 0.026 s
% 20.01/4.21 % (1493)Instructions burned: 98 (million)
% 20.01/4.21 % (1493)------------------------------
% 20.01/4.21 % (1493)------------------------------
% 20.01/4.22 % (1494)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_929 for (2974ds/503Mi)
% 20.01/4.24 % (1490)Instruction limit reached!
% 20.01/4.24 % (1490)------------------------------
% 20.01/4.24 % (1490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.01/4.24 % (1490)Termination reason: Unknown
% 20.01/4.24 % (1490)Termination phase: Saturation
% 20.01/4.24
% 20.01/4.24 % (1490)Memory used [KB]: 7803
% 20.01/4.24 % (1490)Time elapsed: 0.100 s
% 20.01/4.24 % (1490)Instructions burned: 329 (million)
% 20.01/4.24 % (1490)------------------------------
% 20.01/4.24 % (1490)------------------------------
% 20.01/4.25 % (1495)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_929 for (2974ds/90Mi)
% 20.01/4.25 % (1483)Instruction limit reached!
% 20.01/4.25 % (1483)------------------------------
% 20.01/4.25 % (1483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.01/4.25 % (1483)Termination reason: Unknown
% 20.01/4.25 % (1483)Termination phase: Saturation
% 20.01/4.25
% 20.01/4.25 % (1483)Memory used [KB]: 11513
% 20.01/4.25 % (1483)Time elapsed: 0.415 s
% 20.01/4.25 % (1483)Instructions burned: 1376 (million)
% 20.01/4.25 % (1483)------------------------------
% 20.01/4.25 % (1483)------------------------------
% 20.01/4.26 % (1496)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_929 for (2974ds/593Mi)
% 20.01/4.27 % (1495)Instruction limit reached!
% 20.01/4.27 % (1495)------------------------------
% 20.01/4.27 % (1495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.01/4.27 % (1495)Termination reason: Unknown
% 20.01/4.27 % (1495)Termination phase: Property scanning
% 20.01/4.27
% 20.01/4.27 % (1495)Memory used [KB]: 2430
% 20.01/4.27 % (1495)Time elapsed: 0.026 s
% 20.01/4.27 % (1495)Instructions burned: 92 (million)
% 20.01/4.27 % (1495)------------------------------
% 20.01/4.27 % (1495)------------------------------
% 20.01/4.28 % (1497)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_929 for (2974ds/1512Mi)
% 20.35/4.30 % (1489)Instruction limit reached!
% 20.35/4.30 % (1489)------------------------------
% 20.35/4.30 % (1489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.35/4.30 % (1489)Termination reason: Unknown
% 20.35/4.30 % (1489)Termination phase: Saturation
% 20.35/4.30
% 20.35/4.30 % (1489)Memory used [KB]: 8443
% 20.35/4.30 % (1489)Time elapsed: 0.180 s
% 20.35/4.30 % (1489)Instructions burned: 596 (million)
% 20.35/4.30 % (1489)------------------------------
% 20.35/4.30 % (1489)------------------------------
% 20.35/4.31 % (1494)Refutation not found, incomplete strategy
% 20.35/4.31 % (1494)------------------------------
% 20.35/4.31 % (1494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.35/4.31 % (1494)Termination reason: Refutation not found, incomplete strategy
% 20.35/4.31
% 20.35/4.31
% 20.35/4.31 % (1494)Memory used [KB]: 8443
% 20.35/4.31 % (1494)Time elapsed: 0.084 s
% 20.35/4.31 % (1494)Instructions burned: 288 (million)
% 20.35/4.31 % (1494)------------------------------
% 20.35/4.31 % (1494)------------------------------
% 20.35/4.31 % (1498)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_929 for (2974ds/569Mi)
% 20.35/4.32 % (1499)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_929 for (2974ds/501Mi)
% 20.73/4.42 % (1499)First to succeed.
% 20.73/4.42 % (1499)Refutation found. Thanks to Tanya!
% 20.73/4.42 % SZS status Theorem for DTF2THF_929
% 20.73/4.42 % SZS output start Proof for DTF2THF_929
% 20.73/4.42 thf(type_def_5, type, binary1439146945Tree_a: $tType).
% 20.73/4.42 thf(type_def_6, type, a: $tType).
% 20.73/4.42 thf(type_def_8, type, set_a: $tType).
% 20.73/4.42 thf(type_def_9, type, int: $tType).
% 20.73/4.42 thf(func_def_0, type, binary1439146945Tree_a: $tType).
% 20.73/4.42 thf(func_def_1, type, set_a: $tType).
% 20.73/4.42 thf(func_def_2, type, int: $tType).
% 20.73/4.42 thf(func_def_3, type, a: $tType).
% 20.73/4.42 thf(func_def_4, type, binary717961607le_T_a: binary1439146945Tree_a > a > binary1439146945Tree_a > binary1439146945Tree_a).
% 20.73/4.42 thf(func_def_5, type, binary476621312_Tip_a: binary1439146945Tree_a).
% 20.73/4.42 thf(func_def_6, type, binary1452917696Tree_a: (a > $o) > binary1439146945Tree_a > $o).
% 20.73/4.42 thf(func_def_7, type, binary256242811Tree_a: binary1439146945Tree_a > set_a).
% 20.73/4.42 thf(func_def_8, type, binary1226383794sert_a: (a > int) > a > binary1439146945Tree_a > binary1439146945Tree_a).
% 20.73/4.42 thf(func_def_9, type, binary504661350_eqs_a: (a > int) > a > set_a).
% 20.73/4.42 thf(func_def_10, type, binary2053421120memb_a: (a > int) > a > binary1439146945Tree_a > $o).
% 20.73/4.42 thf(func_def_11, type, binary945792244etOf_a: binary1439146945Tree_a > set_a).
% 20.73/4.42 thf(func_def_12, type, binary1721989714Tree_a: (a > int) > binary1439146945Tree_a > $o).
% 20.73/4.42 thf(func_def_13, type, binary670562003pred_a: (a > int) > a > a > binary1439146945Tree_a > $o).
% 20.73/4.42 thf(func_def_14, type, minus_minus_a_o: (a > $o) > (a > $o) > a > $o).
% 20.73/4.42 thf(func_def_15, type, minus_minus_o: $o > $o > $o).
% 20.73/4.42 thf(func_def_16, type, minus_minus_int: int > int > int).
% 20.73/4.42 thf(func_def_17, type, minus_minus_set_a: set_a > set_a > set_a).
% 20.73/4.42 thf(func_def_18, type, the_a: (a > $o) > a).
% 20.73/4.42 thf(func_def_19, type, sup_sup_a_o: (a > $o) > (a > $o) > a > $o).
% 20.73/4.42 thf(func_def_20, type, sup_sup_o: $o > $o > $o).
% 20.73/4.42 thf(func_def_21, type, sup_sup_int: int > int > int).
% 20.73/4.42 thf(func_def_22, type, sup_sup_set_a: set_a > set_a > set_a).
% 20.73/4.42 thf(func_def_23, type, bot_bot_a_o: a > $o).
% 20.73/4.42 thf(func_def_25, type, bot_bot_set_a: set_a).
% 20.73/4.42 thf(func_def_26, type, ord_less_a_o: (a > $o) > (a > $o) > $o).
% 20.73/4.42 thf(func_def_27, type, ord_less_int: int > int > $o).
% 20.73/4.42 thf(func_def_28, type, ord_less_set_a: set_a > set_a > $o).
% 20.73/4.42 thf(func_def_29, type, ord_less_eq_set_a: set_a > set_a > $o).
% 20.73/4.42 thf(func_def_30, type, collect_a: (a > $o) > set_a).
% 20.73/4.42 thf(func_def_31, type, insert_a: a > set_a > set_a).
% 20.73/4.42 thf(func_def_32, type, is_empty_a: set_a > $o).
% 20.73/4.42 thf(func_def_33, type, is_singleton_a: set_a > $o).
% 20.73/4.42 thf(func_def_34, type, remove_a: a > set_a > set_a).
% 20.73/4.42 thf(func_def_35, type, the_elem_a: set_a > a).
% 20.73/4.42 thf(func_def_36, type, member_a: a > set_a > $o).
% 20.73/4.42 thf(func_def_37, type, e: a).
% 20.73/4.42 thf(func_def_38, type, h: a > int).
% 20.73/4.42 thf(func_def_39, type, t1: binary1439146945Tree_a).
% 20.73/4.42 thf(func_def_40, type, t2: binary1439146945Tree_a).
% 20.73/4.42 thf(func_def_41, type, w: a).
% 20.73/4.42 thf(func_def_42, type, x: a).
% 20.73/4.42 thf(func_def_57, type, diff: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1) > X0)).
% 20.73/4.42 thf(func_def_58, type, sP0: set_a > a > set_a > $o).
% 20.73/4.42 thf(func_def_59, type, sP1: (int > $o) > (int > $o) > (int > $o) > (int > $o) > $o).
% 20.73/4.42 thf(func_def_60, type, sP2: a > a > set_a > set_a > $o).
% 20.73/4.42 thf(func_def_61, type, sP3: a > a > set_a > set_a > $o).
% 20.73/4.42 thf(func_def_62, type, sP4: (int > $o) > (int > $o) > (int > $o) > (int > $o) > $o).
% 20.73/4.42 thf(func_def_63, type, sP5: (int > $o) > (int > $o) > (int > $o) > (int > $o) > $o).
% 20.73/4.42 thf(func_def_64, type, sP6: set_a > a > set_a > $o).
% 20.73/4.42 thf(func_def_65, type, sP7: set_a > a > set_a > $o).
% 20.73/4.42 thf(func_def_66, type, sP8: (int > $o) > (int > $o) > (int > $o) > (int > $o) > $o).
% 20.73/4.42 thf(func_def_67, type, sK9: int > int).
% 20.73/4.42 thf(func_def_68, type, sK10: (int > set_a) > int).
% 20.73/4.42 thf(func_def_69, type, sK11: (int > set_a) > int).
% 20.73/4.42 thf(func_def_70, type, sK12: (a > $o) > binary1439146945Tree_a > (a > $o) > a).
% 20.73/4.42 thf(func_def_71, type, sK13: ((a > $o) > int) > a > $o).
% 20.73/4.42 thf(func_def_72, type, sK14: ((a > $o) > int) > a > $o).
% 20.73/4.42 thf(func_def_73, type, sK15: set_a > a).
% 20.73/4.42 thf(func_def_74, type, sK16: ((a > $o) > int) > a > $o).
% 20.73/4.42 thf(func_def_75, type, sK17: ((a > $o) > int) > a > $o).
% 20.73/4.42 thf(func_def_76, type, sK18: ((a > $o) > set_a) > a > $o).
% 20.73/4.42 thf(func_def_77, type, sK19: ((a > $o) > set_a) > a > $o).
% 20.73/4.42 thf(func_def_78, type, sK20: (int > int) > int).
% 20.73/4.42 thf(func_def_79, type, sK21: (int > int) > int).
% 20.73/4.42 thf(func_def_80, type, sK22: (int > $o) > (int > $o) > (int > $o) > (int > $o) > int).
% 20.73/4.42 thf(func_def_81, type, sK23: int > (int > $o) > (int > $o) > int).
% 20.73/4.42 thf(func_def_82, type, sK24: int > (int > $o) > (int > $o) > int).
% 20.73/4.42 thf(func_def_83, type, sK25: int > int).
% 20.73/4.42 thf(func_def_84, type, sK26: (int > int > $o) > int).
% 20.73/4.42 thf(func_def_85, type, sK27: (int > int > $o) > int).
% 20.73/4.42 thf(func_def_86, type, sK28: (int > int > $o) > int).
% 20.73/4.42 thf(func_def_87, type, sK29: (int > int > $o) > int).
% 20.73/4.42 thf(func_def_88, type, sK30: (int > int > $o) > int).
% 20.73/4.42 thf(func_def_89, type, sK31: (int > a > $o) > int).
% 20.73/4.42 thf(func_def_90, type, sK32: (int > a > $o) > int).
% 20.73/4.42 thf(func_def_91, type, sK33: int > int).
% 20.73/4.42 thf(func_def_92, type, sK34: (a > $o) > (a > $o) > binary1439146945Tree_a > a).
% 20.73/4.42 thf(func_def_93, type, sK35: a > a > set_a > set_a > set_a).
% 20.73/4.42 thf(func_def_94, type, sK36: (binary1439146945Tree_a > $o) > binary1439146945Tree_a).
% 20.73/4.42 thf(func_def_95, type, sK37: (binary1439146945Tree_a > $o) > a).
% 20.73/4.42 thf(func_def_96, type, sK38: (binary1439146945Tree_a > $o) > binary1439146945Tree_a).
% 20.73/4.42 thf(func_def_97, type, sK39: set_a > a).
% 20.73/4.42 thf(func_def_98, type, sK40: int > int).
% 20.73/4.42 thf(func_def_99, type, sK41: (int > $o) > (int > $o) > (int > $o) > (int > $o) > int).
% 20.73/4.42 thf(func_def_100, type, sK42: int > (int > $o) > (int > $o) > int).
% 20.73/4.42 thf(func_def_101, type, sK43: int > (int > $o) > (int > $o) > int).
% 20.73/4.42 thf(func_def_102, type, sK44: (int > $o) > (int > $o) > (int > $o) > (int > $o) > int).
% 20.73/4.42 thf(func_def_103, type, sK45: int > (int > $o) > (int > $o) > int).
% 20.73/4.42 thf(func_def_104, type, sK46: int > (int > $o) > (int > $o) > int).
% 20.73/4.42 thf(func_def_105, type, sK47: int > int).
% 20.73/4.42 thf(func_def_106, type, sK48: (set_a > a > $o) > set_a).
% 20.73/4.42 thf(func_def_107, type, sK49: (set_a > a > $o) > set_a).
% 20.73/4.42 thf(func_def_108, type, sK50: ((a > $o) > a > $o) > a > $o).
% 20.73/4.42 thf(func_def_109, type, sK51: ((a > $o) > a > $o) > a > $o).
% 20.73/4.42 thf(func_def_110, type, sK52: (int > set_a) > int).
% 20.73/4.42 thf(func_def_111, type, sK53: (int > set_a) > int).
% 20.73/4.42 thf(func_def_112, type, sK54: set_a > a).
% 20.73/4.42 thf(func_def_113, type, sK55: (set_a > int) > set_a).
% 20.73/4.42 thf(func_def_114, type, sK56: (set_a > int) > set_a).
% 20.73/4.42 thf(func_def_115, type, sK57: (set_a > int) > set_a).
% 20.73/4.42 thf(func_def_116, type, sK58: (set_a > int) > set_a).
% 20.73/4.42 thf(func_def_117, type, sK59: (set_a > a > $o) > set_a).
% 20.73/4.42 thf(func_def_118, type, sK60: (set_a > a > $o) > set_a).
% 20.73/4.42 thf(func_def_119, type, sK61: (int > int) > int).
% 20.73/4.42 thf(func_def_120, type, sK62: (int > int) > int).
% 20.73/4.42 thf(func_def_121, type, sK63: (int > a > $o) > int).
% 20.73/4.42 thf(func_def_122, type, sK64: (int > a > $o) > int).
% 20.73/4.42 thf(func_def_123, type, sK65: ((a > $o) > int) > a > $o).
% 20.73/4.42 thf(func_def_124, type, sK66: ((a > $o) > int) > a > $o).
% 20.73/4.42 thf(func_def_125, type, sK67: int > int).
% 20.73/4.42 thf(func_def_126, type, sK68: set_a > (a > $o) > set_a > a).
% 20.73/4.42 thf(func_def_127, type, sK69: (a > $o) > set_a > a).
% 20.73/4.42 thf(func_def_128, type, sK70: set_a > (a > $o) > a).
% 20.73/4.42 thf(func_def_129, type, sK71: a > set_a > set_a).
% 20.73/4.42 thf(func_def_130, type, sK72: (set_a > set_a) > set_a).
% 20.73/4.42 thf(func_def_131, type, sK73: (set_a > set_a) > set_a).
% 20.73/4.42 thf(func_def_132, type, sK74: ((a > $o) > set_a) > a > $o).
% 20.73/4.42 thf(func_def_133, type, sK75: ((a > $o) > set_a) > a > $o).
% 20.73/4.42 thf(func_def_134, type, sK76: set_a > set_a > a).
% 20.73/4.42 thf(func_def_135, type, sK77: (set_a > set_a) > set_a).
% 20.73/4.42 thf(func_def_136, type, sK78: (set_a > set_a) > set_a).
% 20.73/4.42 thf(func_def_137, type, sK79: (set_a > a > $o) > set_a).
% 20.73/4.42 thf(func_def_138, type, sK80: (set_a > a > $o) > set_a).
% 20.73/4.42 thf(func_def_139, type, sK81: (int > set_a) > int).
% 20.73/4.42 thf(func_def_140, type, sK82: (int > set_a) > int).
% 20.73/4.42 thf(func_def_141, type, sK83: set_a > a > set_a).
% 20.73/4.42 thf(func_def_142, type, sK84: binary1439146945Tree_a > binary1439146945Tree_a).
% 20.73/4.42 thf(func_def_143, type, sK85: binary1439146945Tree_a > binary1439146945Tree_a).
% 20.73/4.42 thf(func_def_144, type, sK86: binary1439146945Tree_a > a).
% 20.73/4.42 thf(func_def_145, type, sK87: (int > int) > int).
% 20.73/4.42 thf(func_def_146, type, sK88: (int > int) > int).
% 20.73/4.42 thf(func_def_147, type, sK89: ((a > $o) > a > $o) > a > $o).
% 20.73/4.42 thf(func_def_148, type, sK90: ((a > $o) > a > $o) > a > $o).
% 20.73/4.42 thf(func_def_149, type, sK91: ((a > $o) > a > $o) > a > $o).
% 20.73/4.42 thf(func_def_150, type, sK92: ((a > $o) > a > $o) > a > $o).
% 20.73/4.42 thf(func_def_151, type, sK93: (a > $o) > (a > $o) > a).
% 20.73/4.42 thf(func_def_152, type, sK94: set_a > a).
% 20.73/4.42 thf(func_def_153, type, sK95: (int > a > $o) > int).
% 20.73/4.42 thf(func_def_154, type, sK96: (int > a > $o) > int).
% 20.73/4.42 thf(func_def_155, type, sK97: (a > $o) > a).
% 20.73/4.42 thf(func_def_156, type, sK98: ((a > $o) > a > $o) > a > $o).
% 20.73/4.42 thf(func_def_157, type, sK99: ((a > $o) > a > $o) > a > $o).
% 20.73/4.42 thf(func_def_158, type, sK100: ((a > $o) > set_a) > a > $o).
% 20.73/4.42 thf(func_def_159, type, sK101: ((a > $o) > set_a) > a > $o).
% 20.73/4.42 thf(func_def_160, type, sK102: (a > $o) > a).
% 20.73/4.42 thf(func_def_161, type, sK103: int > int).
% 20.73/4.42 thf(func_def_162, type, sK104: binary1439146945Tree_a > a > a).
% 20.73/4.42 thf(func_def_163, type, sK105: binary1439146945Tree_a > a > binary1439146945Tree_a).
% 20.73/4.42 thf(func_def_164, type, sK106: binary1439146945Tree_a > a > binary1439146945Tree_a).
% 20.73/4.42 thf(func_def_165, type, sK107: binary1439146945Tree_a > a > binary1439146945Tree_a).
% 20.73/4.42 thf(func_def_166, type, sK108: binary1439146945Tree_a > a > binary1439146945Tree_a).
% 20.73/4.42 thf(func_def_167, type, sK109: binary1439146945Tree_a > a > binary1439146945Tree_a).
% 20.73/4.42 thf(func_def_168, type, sK110: binary1439146945Tree_a > a > a).
% 20.73/4.42 thf(func_def_169, type, sK111: binary1439146945Tree_a > a > binary1439146945Tree_a).
% 20.73/4.42 thf(func_def_170, type, sK112: (int > set_a) > int).
% 20.73/4.42 thf(func_def_171, type, sK113: (int > set_a) > int).
% 20.73/4.42 thf(func_def_172, type, sK114: (int > a > $o) > int).
% 20.73/4.42 thf(func_def_173, type, sK115: (int > a > $o) > int).
% 20.73/4.42 thf(func_def_174, type, sK116: (set_a > a > $o) > set_a).
% 20.73/4.42 thf(func_def_175, type, sK117: (set_a > a > $o) > set_a).
% 20.73/4.42 thf(func_def_176, type, sK118: ((a > $o) > set_a) > a > $o).
% 20.73/4.42 thf(func_def_177, type, sK119: ((a > $o) > set_a) > a > $o).
% 20.73/4.42 thf(func_def_178, type, sK120: (set_a > int) > set_a).
% 20.73/4.42 thf(func_def_179, type, sK121: (set_a > int) > set_a).
% 20.73/4.42 thf(func_def_180, type, sK122: a > (a > int) > binary1439146945Tree_a > a).
% 20.73/4.42 thf(func_def_181, type, sK123: a > (a > int) > binary1439146945Tree_a > a).
% 20.73/4.42 thf(func_def_182, type, sK124: int > int).
% 20.73/4.42 thf(func_def_183, type, sK125: (set_a > int) > set_a).
% 20.73/4.42 thf(func_def_184, type, sK126: (set_a > int) > set_a).
% 20.73/4.42 thf(func_def_185, type, sK127: ((a > $o) > int) > a > $o).
% 20.73/4.42 thf(func_def_186, type, sK128: ((a > $o) > int) > a > $o).
% 20.73/4.42 thf(func_def_187, type, sK129: set_a > a).
% 20.73/4.42 thf(func_def_188, type, sK130: set_a > a).
% 20.73/4.42 thf(func_def_189, type, sK131: (int > int) > int).
% 20.73/4.42 thf(func_def_190, type, sK132: (int > int) > int).
% 20.73/4.42 thf(func_def_191, type, sK133: set_a > (a > $o) > set_a > a).
% 20.73/4.42 thf(func_def_192, type, sK134: set_a > (a > $o) > a).
% 20.73/4.42 thf(func_def_193, type, sK135: (a > $o) > set_a > a).
% 20.73/4.42 thf(func_def_194, type, sK136: int > int).
% 20.73/4.42 thf(func_def_195, type, sK137: int > int).
% 20.73/4.42 thf(func_def_196, type, sK138: (int > $o) > (int > $o) > (int > $o) > (int > $o) > int).
% 20.73/4.42 thf(func_def_197, type, sK139: int > (int > $o) > (int > $o) > int).
% 20.73/4.42 thf(func_def_198, type, sK140: int > (int > $o) > (int > $o) > int).
% 20.73/4.42 thf(func_def_199, type, sK141: (set_a > set_a) > set_a).
% 20.73/4.42 thf(func_def_200, type, sK142: (set_a > set_a) > set_a).
% 20.73/4.42 thf(func_def_201, type, sK143: (set_a > set_a) > set_a).
% 20.73/4.42 thf(func_def_202, type, sK144: (set_a > set_a) > set_a).
% 20.73/4.42 thf(func_def_204, type, ph146: !>[X0: $tType]:(X0)).
% 20.73/4.42 thf(f3340,plain,(
% 20.73/4.42 $false),
% 20.73/4.42 inference(subsumption_resolution,[status(thm)],[f3326,f2027])).
% 20.73/4.42 thf(f2027,plain,(
% 20.73/4.42 ((member_a @ w @ (binary945792244etOf_a @ t1)) = $true)),
% 20.73/4.42 inference(cnf_transformation,[status(thm)],[f533])).
% 20.73/4.42 thf(f533,plain,(
% 20.73/4.42 ((member_a @ w @ (binary945792244etOf_a @ t1)) = $true)),
% 20.73/4.42 inference(fool_elimination,[status(thm)],[f532])).
% 20.73/4.42 thf(f532,plain,(
% 20.73/4.42 (member_a @ w @ (binary945792244etOf_a @ t1))),
% 20.73/4.42 inference(rectify,[status(thm)],[f1])).
% 20.73/4.42 thf(f1,axiom,(
% 20.73/4.42 (member_a @ w @ (binary945792244etOf_a @ t1))),
% 20.73/4.42 file('/export/starexec/sandbox/tmp/tmp.xPc2I3SSGn/DTF2THF_929.p',fact_0_whSet)).
% 20.73/4.42 thf(f3326,plain,(
% 20.73/4.42 ((member_a @ w @ (binary945792244etOf_a @ t1)) != $true)),
% 20.73/4.42 inference(trivial_inequality_removal,[status(thm)],[f3319])).
% 20.73/4.42 thf(f3319,plain,(
% 20.73/4.42 ((member_a @ w @ (binary945792244etOf_a @ t1)) != $true) | ($true != $true)),
% 20.73/4.42 inference(superposition,[status(thm)],[f3266,f2000])).
% 20.73/4.42 thf(f2000,plain,(
% 20.73/4.42 ((binary1721989714Tree_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2)) = $true)),
% 20.73/4.42 inference(cnf_transformation,[status(thm)],[f761])).
% 20.73/4.42 thf(f761,plain,(
% 20.73/4.42 ((binary1721989714Tree_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2)) = $true)),
% 20.73/4.42 inference(fool_elimination,[status(thm)],[f760])).
% 20.73/4.42 thf(f760,plain,(
% 20.73/4.42 (binary1721989714Tree_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))),
% 20.73/4.42 inference(rectify,[status(thm)],[f2])).
% 20.73/4.42 thf(f2,axiom,(
% 20.73/4.42 (binary1721989714Tree_a @ h @ (binary717961607le_T_a @ t1 @ x @ t2))),
% 20.73/4.42 file('/export/starexec/sandbox/tmp/tmp.xPc2I3SSGn/DTF2THF_929.p',fact_1_s)).
% 20.73/4.42 thf(f3266,plain,(
% 20.73/4.42 ( ! [X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a] : (($true != (binary1721989714Tree_a @ h @ (binary717961607le_T_a @ X0 @ x @ X1))) | ($true != (member_a @ w @ (binary945792244etOf_a @ X0)))) )),
% 20.73/4.42 inference(beta_eta_normalization,[status(thm)],[f3265])).
% 20.73/4.42 thf(f3265,plain,(
% 20.73/4.42 ( ! [X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a] : (((binary1721989714Tree_a @ (^[Y0 : a]: (h @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (binary717961607le_T_a @ X0 @ x @ X1)) != $true) | ($true != (member_a @ w @ (binary945792244etOf_a @ X0)))) )),
% 20.73/4.42 inference(trivial_inequality_removal,[status(thm)],[f3248])).
% 20.73/4.42 thf(f3248,plain,(
% 20.73/4.42 ( ! [X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a] : (((binary1721989714Tree_a @ (^[Y0 : a]: (h @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (binary717961607le_T_a @ X0 @ x @ X1)) != $true) | ($true != (member_a @ w @ (binary945792244etOf_a @ X0))) | ($true != $true)) )),
% 20.73/4.42 inference(superposition,[status(thm)],[f3239,f2956])).
% 20.73/4.42 thf(f2956,plain,(
% 20.73/4.42 ( ! [X2 : a > int,X3 : a,X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a,X7 : a] : (($true = (((sup_sup_int @ (X2 @ X3) @ (X2 @ X7)) = (X2 @ X3)) & (~ ((X2 @ X7) = (X2 @ X3))))) | ((member_a @ X7 @ (binary945792244etOf_a @ X0)) != $true) | ((binary1721989714Tree_a @ X2 @ (binary717961607le_T_a @ X0 @ X3 @ X1)) != $true)) )),
% 20.73/4.42 inference(beta_eta_normalization,[status(thm)],[f2562])).
% 20.73/4.42 thf(f2562,plain,(
% 20.73/4.42 ( ! [X2 : a > int,X3 : a,X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a,X7 : a] : ((((^[Y0 : int]: ((^[Y1 : int]: (((sup_sup_int @ Y1 @ Y0) = Y1) & (~ (Y0 = Y1)))))) @ (X2 @ X7) @ (X2 @ X3)) = $true) | ((member_a @ X7 @ (binary945792244etOf_a @ X0)) != $true) | ((binary1721989714Tree_a @ X2 @ (binary717961607le_T_a @ X0 @ X3 @ X1)) != $true)) )),
% 20.73/4.42 inference(definition_unfolding,[status(thm)],[f2107,f1702])).
% 20.73/4.42 thf(f1702,plain,(
% 20.73/4.42 (ord_less_int = (^[Y0 : int]: ((^[Y1 : int]: (((sup_sup_int @ Y1 @ Y0) = Y1) & (~ (Y0 = Y1)))))))),
% 20.73/4.42 inference(cnf_transformation,[status(thm)],[f670])).
% 20.73/4.42 thf(f670,plain,(
% 20.73/4.42 (ord_less_int = (^[Y0 : int]: ((^[Y1 : int]: (((sup_sup_int @ Y1 @ Y0) = Y1) & (~ (Y0 = Y1)))))))),
% 20.73/4.42 inference(fool_elimination,[status(thm)],[f669])).
% 20.73/4.42 thf(f669,plain,(
% 20.73/4.42 (ord_less_int = (^[X0 : int, X1 : int] : ((X0 != X1) & ((sup_sup_int @ X1 @ X0) = X1))))),
% 20.73/4.42 inference(rectify,[status(thm)],[f302])).
% 20.73/4.42 thf(f302,axiom,(
% 20.73/4.42 (ord_less_int = (^[X22 : int, X21 : int] : ((X21 != X22) & ((sup_sup_int @ X21 @ X22) = X21))))),
% 20.73/4.42 file('/export/starexec/sandbox/tmp/tmp.xPc2I3SSGn/DTF2THF_929.p',fact_301_sup_Ostrict__order__iff)).
% 20.73/4.42 thf(f2107,plain,(
% 20.73/4.42 ( ! [X2 : a > int,X3 : a,X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a,X7 : a] : (($true = (ord_less_int @ (X2 @ X7) @ (X2 @ X3))) | ((member_a @ X7 @ (binary945792244etOf_a @ X0)) != $true) | ((binary1721989714Tree_a @ X2 @ (binary717961607le_T_a @ X0 @ X3 @ X1)) != $true)) )),
% 20.73/4.42 inference(cnf_transformation,[status(thm)],[f1599])).
% 20.73/4.42 thf(f1599,plain,(
% 20.73/4.42 ! [X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a,X2 : a > int,X3 : a] : ((((binary1721989714Tree_a @ X2 @ (binary717961607le_T_a @ X0 @ X3 @ X1)) = $true) | (($true != (ord_less_int @ (X2 @ X3) @ (X2 @ (sK122 @ X3 @ X2 @ X1)))) & ($true = (member_a @ (sK122 @ X3 @ X2 @ X1) @ (binary945792244etOf_a @ X1)))) | ((binary1721989714Tree_a @ X2 @ X0) != $true) | ((binary1721989714Tree_a @ X2 @ X1) != $true) | (((ord_less_int @ (X2 @ (sK123 @ X3 @ X2 @ X0)) @ (X2 @ X3)) != $true) & ($true = (member_a @ (sK123 @ X3 @ X2 @ X0) @ (binary945792244etOf_a @ X0))))) & ((! [X6 : a] : (((ord_less_int @ (X2 @ X3) @ (X2 @ X6)) = $true) | ($true != (member_a @ X6 @ (binary945792244etOf_a @ X1)))) & ((binary1721989714Tree_a @ X2 @ X0) = $true) & ((binary1721989714Tree_a @ X2 @ X1) = $true) & ! [X7 : a] : (($true = (ord_less_int @ (X2 @ X7) @ (X2 @ X3))) | ((member_a @ X7 @ (binary945792244etOf_a @ X0)) != $true))) | ((binary1721989714Tree_a @ X2 @ (binary717961607le_T_a @ X0 @ X3 @ X1)) != $true)))),
% 20.73/4.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK122,sK123])],[f1596,f1598,f1597])).
% 20.73/4.42 thf(f1597,plain,(
% 20.73/4.42 ! [X1 : binary1439146945Tree_a,X2 : a > int,X3 : a] : (? [X4 : a] : (($true != (ord_less_int @ (X2 @ X3) @ (X2 @ X4))) & ((member_a @ X4 @ (binary945792244etOf_a @ X1)) = $true)) => (($true != (ord_less_int @ (X2 @ X3) @ (X2 @ (sK122 @ X3 @ X2 @ X1)))) & ($true = (member_a @ (sK122 @ X3 @ X2 @ X1) @ (binary945792244etOf_a @ X1)))))),
% 20.73/4.42 introduced(definition,[],[choice_axiom])).
% 20.73/4.42 thf(f1598,plain,(
% 20.73/4.42 ! [X0 : binary1439146945Tree_a,X2 : a > int,X3 : a] : (? [X5 : a] : (($true != (ord_less_int @ (X2 @ X5) @ (X2 @ X3))) & ($true = (member_a @ X5 @ (binary945792244etOf_a @ X0)))) => (((ord_less_int @ (X2 @ (sK123 @ X3 @ X2 @ X0)) @ (X2 @ X3)) != $true) & ($true = (member_a @ (sK123 @ X3 @ X2 @ X0) @ (binary945792244etOf_a @ X0)))))),
% 20.73/4.42 introduced(definition,[],[choice_axiom])).
% 20.73/4.42 thf(f1596,plain,(
% 20.73/4.42 ! [X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a,X2 : a > int,X3 : a] : ((((binary1721989714Tree_a @ X2 @ (binary717961607le_T_a @ X0 @ X3 @ X1)) = $true) | ? [X4 : a] : (($true != (ord_less_int @ (X2 @ X3) @ (X2 @ X4))) & ((member_a @ X4 @ (binary945792244etOf_a @ X1)) = $true)) | ((binary1721989714Tree_a @ X2 @ X0) != $true) | ((binary1721989714Tree_a @ X2 @ X1) != $true) | ? [X5 : a] : (($true != (ord_less_int @ (X2 @ X5) @ (X2 @ X3))) & ($true = (member_a @ X5 @ (binary945792244etOf_a @ X0))))) & ((! [X6 : a] : (((ord_less_int @ (X2 @ X3) @ (X2 @ X6)) = $true) | ($true != (member_a @ X6 @ (binary945792244etOf_a @ X1)))) & ((binary1721989714Tree_a @ X2 @ X0) = $true) & ((binary1721989714Tree_a @ X2 @ X1) = $true) & ! [X7 : a] : (($true = (ord_less_int @ (X2 @ X7) @ (X2 @ X3))) | ((member_a @ X7 @ (binary945792244etOf_a @ X0)) != $true))) | ((binary1721989714Tree_a @ X2 @ (binary717961607le_T_a @ X0 @ X3 @ X1)) != $true)))),
% 20.73/4.42 inference(rectify,[status(thm)],[f1595])).
% 20.73/4.42 thf(f1595,plain,(
% 20.73/4.42 ! [X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a,X2 : a > int,X3 : a] : ((((binary1721989714Tree_a @ X2 @ (binary717961607le_T_a @ X0 @ X3 @ X1)) = $true) | ? [X5 : a] : (((ord_less_int @ (X2 @ X3) @ (X2 @ X5)) != $true) & ((member_a @ X5 @ (binary945792244etOf_a @ X1)) = $true)) | ((binary1721989714Tree_a @ X2 @ X0) != $true) | ((binary1721989714Tree_a @ X2 @ X1) != $true) | ? [X4 : a] : (($true != (ord_less_int @ (X2 @ X4) @ (X2 @ X3))) & ($true = (member_a @ X4 @ (binary945792244etOf_a @ X0))))) & ((! [X5 : a] : (((ord_less_int @ (X2 @ X3) @ (X2 @ X5)) = $true) | ((member_a @ X5 @ (binary945792244etOf_a @ X1)) != $true)) & ((binary1721989714Tree_a @ X2 @ X0) = $true) & ((binary1721989714Tree_a @ X2 @ X1) = $true) & ! [X4 : a] : (($true = (ord_less_int @ (X2 @ X4) @ (X2 @ X3))) | ($true != (member_a @ X4 @ (binary945792244etOf_a @ X0))))) | ((binary1721989714Tree_a @ X2 @ (binary717961607le_T_a @ X0 @ X3 @ X1)) != $true)))),
% 20.73/4.42 inference(flattening,[status(thm)],[f1594])).
% 20.73/4.42 thf(f1594,plain,(
% 20.73/4.42 ! [X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a,X2 : a > int,X3 : a] : ((((binary1721989714Tree_a @ X2 @ (binary717961607le_T_a @ X0 @ X3 @ X1)) = $true) | (? [X5 : a] : (((ord_less_int @ (X2 @ X3) @ (X2 @ X5)) != $true) & ((member_a @ X5 @ (binary945792244etOf_a @ X1)) = $true)) | ((binary1721989714Tree_a @ X2 @ X0) != $true) | ((binary1721989714Tree_a @ X2 @ X1) != $true) | ? [X4 : a] : (($true != (ord_less_int @ (X2 @ X4) @ (X2 @ X3))) & ($true = (member_a @ X4 @ (binary945792244etOf_a @ X0)))))) & ((! [X5 : a] : (((ord_less_int @ (X2 @ X3) @ (X2 @ X5)) = $true) | ((member_a @ X5 @ (binary945792244etOf_a @ X1)) != $true)) & ((binary1721989714Tree_a @ X2 @ X0) = $true) & ((binary1721989714Tree_a @ X2 @ X1) = $true) & ! [X4 : a] : (($true = (ord_less_int @ (X2 @ X4) @ (X2 @ X3))) | ($true != (member_a @ X4 @ (binary945792244etOf_a @ X0))))) | ((binary1721989714Tree_a @ X2 @ (binary717961607le_T_a @ X0 @ X3 @ X1)) != $true)))),
% 20.73/4.42 inference(nnf_transformation,[status(thm)],[f1179])).
% 20.73/4.42 thf(f1179,plain,(
% 20.73/4.42 ! [X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a,X2 : a > int,X3 : a] : (((binary1721989714Tree_a @ X2 @ (binary717961607le_T_a @ X0 @ X3 @ X1)) = $true) <=> (! [X5 : a] : (((ord_less_int @ (X2 @ X3) @ (X2 @ X5)) = $true) | ((member_a @ X5 @ (binary945792244etOf_a @ X1)) != $true)) & ((binary1721989714Tree_a @ X2 @ X0) = $true) & ((binary1721989714Tree_a @ X2 @ X1) = $true) & ! [X4 : a] : (($true = (ord_less_int @ (X2 @ X4) @ (X2 @ X3))) | ($true != (member_a @ X4 @ (binary945792244etOf_a @ X0))))))),
% 20.73/4.42 inference(ennf_transformation,[status(thm)],[f858])).
% 20.73/4.42 thf(f858,plain,(
% 20.73/4.42 ! [X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a,X2 : a > int,X3 : a] : ((! [X4 : a] : (($true = (member_a @ X4 @ (binary945792244etOf_a @ X0))) => ($true = (ord_less_int @ (X2 @ X4) @ (X2 @ X3)))) & ((binary1721989714Tree_a @ X2 @ X1) = $true) & ! [X5 : a] : (((member_a @ X5 @ (binary945792244etOf_a @ X1)) = $true) => ((ord_less_int @ (X2 @ X3) @ (X2 @ X5)) = $true)) & ((binary1721989714Tree_a @ X2 @ X0) = $true)) <=> ((binary1721989714Tree_a @ X2 @ (binary717961607le_T_a @ X0 @ X3 @ X1)) = $true))),
% 20.73/4.42 inference(fool_elimination,[status(thm)],[f857])).
% 20.73/4.42 thf(f857,plain,(
% 20.73/4.42 ! [X0 : binary1439146945Tree_a,X1 : binary1439146945Tree_a,X2 : a > int,X3 : a] : ((binary1721989714Tree_a @ X2 @ (binary717961607le_T_a @ X0 @ X3 @ X1)) = ! [X4 : a] : ((member_a @ X4 @ (binary945792244etOf_a @ X0)) => (ord_less_int @ (X2 @ X4) @ (X2 @ X3))) & (binary1721989714Tree_a @ X2 @ X1) & ! [X5 : a] : ((member_a @ X5 @ (binary945792244etOf_a @ X1)) => (ord_less_int @ (X2 @ X3) @ (X2 @ X5))) & (binary1721989714Tree_a @ X2 @ X0))),
% 20.73/4.42 inference(rectify,[status(thm)],[f20])).
% 20.73/4.42 thf(f20,axiom,(
% 20.73/4.42 ! [X16 : binary1439146945Tree_a,X18 : binary1439146945Tree_a,X15 : a > int,X17 : a] : ((binary1721989714Tree_a @ X15 @ (binary717961607le_T_a @ X16 @ X17 @ X18)) = ! [X19 : a] : ((member_a @ X19 @ (binary945792244etOf_a @ X16)) => (ord_less_int @ (X15 @ X19) @ (X15 @ X17))) & (binary1721989714Tree_a @ X15 @ X18) & ! [X19 : a] : ((member_a @ X19 @ (binary945792244etOf_a @ X18)) => (ord_less_int @ (X15 @ X17) @ (X15 @ X19))) & (binary1721989714Tree_a @ X15 @ X16))),
% 20.73/4.42 file('/export/starexec/sandbox/tmp/tmp.xPc2I3SSGn/DTF2THF_929.p',fact_19_sortedTree_Osimps_I2_J)).
% 20.73/4.42 thf(f3239,plain,(
% 20.73/4.42 ((((sup_sup_int @ (h @ x) @ (h @ w)) = (h @ x)) & (~ ((h @ w) = (h @ x)))) != $true)),
% 20.73/4.42 inference(beta_eta_normalization,[status(thm)],[f2382])).
% 20.73/4.42 thf(f2382,plain,(
% 20.73/4.42 (((^[Y0 : int]: ((^[Y1 : int]: (((sup_sup_int @ Y1 @ Y0) = Y1) & (~ (Y0 = Y1)))))) @ (h @ w) @ (h @ x)) != $true)),
% 20.73/4.42 inference(definition_unfolding,[status(thm)],[f1876,f1702])).
% 20.73/4.42 thf(f1876,plain,(
% 20.73/4.42 ((ord_less_int @ (h @ w) @ (h @ x)) != $true)),
% 20.73/4.42 inference(cnf_transformation,[status(thm)],[f1067])).
% 20.73/4.42 thf(f1067,plain,(
% 20.73/4.42 ((ord_less_int @ (h @ w) @ (h @ x)) != $true)),
% 20.73/4.42 inference(flattening,[status(thm)],[f529])).
% 20.73/4.42 thf(f529,plain,(
% 20.73/4.42 ~((ord_less_int @ (h @ w) @ (h @ x)) = $true)),
% 20.73/4.42 inference(fool_elimination,[status(thm)],[f528])).
% 20.73/4.42 thf(f528,plain,(
% 20.73/4.42 ~(ord_less_int @ (h @ w) @ (h @ x))),
% 20.73/4.42 inference(rectify,[status(thm)],[f352])).
% 20.73/4.42 thf(f352,negated_conjecture,(
% 20.73/4.42 ~(ord_less_int @ (h @ w) @ (h @ x))),
% 20.73/4.42 inference(negated_conjecture,[status(cth)],[f351])).
% 20.73/4.42 thf(f351,conjecture,(
% 20.73/4.42 (ord_less_int @ (h @ w) @ (h @ x))),
% 20.73/4.42 file('/export/starexec/sandbox/tmp/tmp.xPc2I3SSGn/DTF2THF_929.p',conj_0)).
% 20.73/4.42 % SZS output end Proof for DTF2THF_929
% 20.73/4.42 % (1499)------------------------------
% 20.73/4.42 % (1499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.73/4.42 % (1499)Termination reason: Refutation
% 20.73/4.42
% 20.73/4.42 % (1499)Memory used [KB]: 8699
% 20.73/4.42 % (1499)Time elapsed: 0.102 s
% 20.73/4.42 % (1499)Instructions burned: 344 (million)
% 20.73/4.42 % (1499)------------------------------
% 20.73/4.42 % (1499)------------------------------
% 20.73/4.42 % (1181)Success in time 2.707 s
%------------------------------------------------------------------------------