TSTP Solution File: ITP114^2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP114^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 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 : Mon May 20 22:52:21 EDT 2024
% Result : Theorem 0.20s 0.51s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 535
% Syntax : Number of formulae : 1235 ( 535 unt; 218 typ; 0 def)
% Number of atoms : 4008 (1036 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 1051 ( 372 ~; 366 |; 25 &; 0 @)
% ( 161 <=>; 127 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 384 ( 383 >; 1 *; 0 +; 0 <<)
% Number of symbols : 376 ( 373 usr; 166 con; 0-6 aty)
% Number of variables : 742 ( 0 ^ 610 !; 33 ?; 742 :)
% ( 99 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
nat: $tType ).
thf(type_def_6,type,
extended_enat: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_8,type,
extended_ereal: $tType ).
thf(type_def_9,type,
real: $tType ).
thf(type_def_10,type,
num: $tType ).
thf(type_def_11,type,
set: $tType > $tType ).
thf(type_def_12,type,
a: $tType ).
thf(func_def_0,type,
extended_ereal: $tType ).
thf(func_def_1,type,
extended_enat: $tType ).
thf(func_def_2,type,
real: $tType ).
thf(func_def_3,type,
set: $tType > $tType ).
thf(func_def_4,type,
num: $tType ).
thf(func_def_5,type,
nat: $tType ).
thf(func_def_6,type,
a: $tType ).
thf(func_def_7,type,
type:
!>[X0: $tType] : $o ).
thf(func_def_8,type,
zero:
!>[X0: $tType] : $o ).
thf(func_def_9,type,
numeral:
!>[X0: $tType] : $o ).
thf(func_def_10,type,
uminus:
!>[X0: $tType] : $o ).
thf(func_def_11,type,
ord:
!>[X0: $tType] : $o ).
thf(func_def_12,type,
ring_char_0:
!>[X0: $tType] : $o ).
thf(func_def_13,type,
neg_numeral:
!>[X0: $tType] : $o ).
thf(func_def_14,type,
order:
!>[X0: $tType] : $o ).
thf(func_def_15,type,
group_add:
!>[X0: $tType] : $o ).
thf(func_def_16,type,
linorder:
!>[X0: $tType] : $o ).
thf(func_def_17,type,
preorder:
!>[X0: $tType] : $o ).
thf(func_def_18,type,
semiring_char_0:
!>[X0: $tType] : $o ).
thf(func_def_19,type,
linordered_idom:
!>[X0: $tType] : $o ).
thf(func_def_20,type,
linordered_field:
!>[X0: $tType] : $o ).
thf(func_def_21,type,
boolean_algebra:
!>[X0: $tType] : $o ).
thf(func_def_22,type,
ordered_ab_group_add:
!>[X0: $tType] : $o ).
thf(func_def_23,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
thf(func_def_24,type,
ordere142940540dd_abs:
!>[X0: $tType] : $o ).
thf(func_def_25,type,
real_V2090557954_space:
!>[X0: $tType] : $o ).
thf(func_def_26,type,
linord1659791738miring:
!>[X0: $tType] : $o ).
thf(func_def_27,type,
topolo259154727pology:
!>[X0: $tType] : $o ).
thf(func_def_28,type,
topolo503727757_space:
!>[X0: $tType] : $o ).
thf(func_def_29,type,
canoni770627133id_add:
!>[X0: $tType] : $o ).
thf(func_def_30,type,
extended_enat2: nat > extended_enat ).
thf(func_def_31,type,
extended_case_enat:
!>[X0: $tType] : ( ( nat > X0 ) > X0 > extended_enat > X0 ) ).
thf(func_def_32,type,
extended_rec_enat:
!>[X0: $tType] : ( ( nat > X0 ) > X0 > extended_enat > X0 ) ).
thf(func_def_33,type,
extend1396239628finity:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
extended_the_enat: extended_enat > nat ).
thf(func_def_35,type,
extended_MInfty: extended_ereal ).
thf(func_def_36,type,
extended_PInfty: extended_ereal ).
thf(func_def_37,type,
extended_ereal2: real > extended_ereal ).
thf(func_def_38,type,
extended_size_ereal: extended_ereal > nat ).
thf(func_def_39,type,
extend1771934483f_enat: extended_enat > extended_ereal ).
thf(func_def_40,type,
extend1716541707_ereal: extended_ereal > real ).
thf(func_def_41,type,
abs_abs:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_42,type,
uminus_uminus:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_43,type,
zero_zero:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
lower_107104146le_lsc:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > $o ) ).
thf(func_def_45,type,
lower_582600101lsc_at:
!>[X0: $tType,X1: $tType] : ( X0 > ( X0 > X1 ) > $o ) ).
thf(func_def_46,type,
lower_1879122655c_hull:
!>[X0: $tType] : ( ( X0 > extended_ereal ) > X0 > extended_ereal ) ).
thf(func_def_47,type,
neg_numeral_dbl:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_48,type,
neg_numeral_sub:
!>[X0: $tType] : ( num > num > X0 ) ).
thf(func_def_49,type,
numeral_numeral:
!>[X0: $tType] : ( num > X0 ) ).
thf(func_def_50,type,
ord_less_eq:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
order_Greatest:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_52,type,
order_antimono:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > $o ) ).
thf(func_def_53,type,
order_strict_mono:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > $o ) ).
thf(func_def_54,type,
divide_divide:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_55,type,
member:
!>[X0: $tType] : ( X0 > set(X0) > $o ) ).
thf(func_def_56,type,
f: a > extended_ereal ).
thf(func_def_57,type,
g: a > extended_ereal ).
thf(func_def_58,type,
x: a ).
thf(func_def_62,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_63,type,
vAND: $o > $o > $o ).
thf(func_def_64,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_65,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_66,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_67,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_68,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_69,type,
vOR: $o > $o > $o ).
thf(func_def_70,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_71,type,
vNOT: $o > $o ).
thf(func_def_72,type,
vIMP: $o > $o > $o ).
thf(func_def_73,type,
sP0:
!>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).
thf(func_def_74,type,
sP1:
!>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).
thf(func_def_75,type,
sP2:
!>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).
thf(func_def_76,type,
sP3:
!>[X0: $tType] : ( X0 > X0 > X0 > $o ) ).
thf(func_def_77,type,
sP4:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_78,type,
sP5: extended_ereal > real > $o ).
thf(func_def_79,type,
sP6: extended_ereal > extended_ereal > $o ).
thf(func_def_80,type,
sP7: extended_ereal > extended_ereal > $o ).
thf(func_def_81,type,
sP8: extended_ereal > extended_ereal > $o ).
thf(func_def_82,type,
sP9: extended_ereal > extended_ereal > $o ).
thf(func_def_83,type,
sP10: extended_ereal > extended_ereal > $o ).
thf(func_def_84,type,
sP11: extended_ereal > extended_ereal > $o ).
thf(func_def_85,type,
sP12: extended_ereal > extended_ereal > $o ).
thf(func_def_86,type,
sP13: extended_ereal > extended_ereal > $o ).
thf(func_def_87,type,
sP14: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_88,type,
sP15: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_89,type,
sP16: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_90,type,
sP17: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_91,type,
sP18: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_92,type,
sP19: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_93,type,
sP20: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_94,type,
sP21: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_95,type,
sP22: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_96,type,
sP23: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_97,type,
sP24: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_98,type,
sP25: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_99,type,
sP26: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_100,type,
sP27: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_101,type,
sP28: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_102,type,
sP29: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_103,type,
sP30: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_104,type,
sP31: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_105,type,
sP32: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_106,type,
sP33: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_107,type,
sP34: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_108,type,
sP35: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_109,type,
sP36: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_110,type,
sP37: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_111,type,
sP38: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_112,type,
sP39: extended_ereal > extended_ereal > extended_ereal > $o ).
thf(func_def_113,type,
sK40: extended_ereal > real ).
thf(func_def_114,type,
sK41: extended_ereal > real ).
thf(func_def_115,type,
sK42: extended_ereal > real ).
thf(func_def_116,type,
sK43: extended_ereal > real ).
thf(func_def_117,type,
sK44: extended_ereal > real ).
thf(func_def_118,type,
sK45: extended_ereal > real ).
thf(func_def_119,type,
sK46: extended_ereal > real ).
thf(func_def_120,type,
sK47: extended_ereal > real ).
thf(func_def_121,type,
sK48:
!>[X0: $tType] : ( ( X0 > extended_ereal ) > ( X0 > extended_ereal ) > X0 ) ).
thf(func_def_122,type,
sK49:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_123,type,
sK50:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_124,type,
sK51:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_125,type,
sK52:
!>[X0: $tType] : ( ( X0 > X0 > $o ) > X0 ) ).
thf(func_def_126,type,
sK53:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 ) ).
thf(func_def_127,type,
sK54:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_128,type,
sK55:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 ) ).
thf(func_def_129,type,
sK56: set(extended_ereal) > extended_ereal ).
thf(func_def_130,type,
sK57: extended_ereal > set(extended_ereal) > extended_ereal ).
thf(func_def_131,type,
sK58: set(extended_ereal) > extended_ereal ).
thf(func_def_132,type,
sK59: extended_ereal > set(extended_ereal) > extended_ereal ).
thf(func_def_133,type,
sK60: extended_ereal > real > real ).
thf(func_def_134,type,
sK61: extended_ereal > extended_ereal > real ).
thf(func_def_135,type,
sK62:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_136,type,
sK63:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_137,type,
sK64:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_138,type,
sK65:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_139,type,
sK66:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_140,type,
sK67:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_141,type,
sK68:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_142,type,
sK69:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > X0 ) ).
thf(func_def_143,type,
sK70:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_144,type,
sK71:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > X1 ) ).
thf(func_def_145,type,
sK72: extended_ereal > real ).
thf(func_def_146,type,
sK73: extended_ereal > real ).
thf(func_def_147,type,
sK74: extended_ereal > real ).
thf(func_def_148,type,
sK75: extended_ereal > real ).
thf(func_def_149,type,
sK76: extended_ereal > real ).
thf(func_def_150,type,
sK77: extended_ereal > real ).
thf(func_def_151,type,
sK78: extended_ereal > extended_ereal > real ).
thf(func_def_152,type,
sK79: ( extended_ereal > $o ) > real ).
thf(func_def_153,type,
sK80: ( extended_ereal > $o ) > real ).
thf(func_def_154,type,
sK81: ( extended_ereal > $o ) > real ).
thf(func_def_155,type,
sK82: ( extended_ereal > $o ) > real ).
thf(func_def_156,type,
sK83: nat > ( nat > $o ) > nat ).
thf(func_def_157,type,
sK84:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_158,type,
sK85: extended_enat > nat ).
thf(func_def_159,type,
sK86: extended_ereal > real ).
thf(func_def_160,type,
sK87: extended_ereal > real ).
thf(func_def_161,type,
sK88: extended_ereal > real ).
thf(func_def_162,type,
sK89: extended_ereal > real ).
thf(func_def_163,type,
sK90: extended_ereal > real ).
thf(func_def_164,type,
sK91: extended_ereal > real ).
thf(func_def_165,type,
sK92: extended_ereal > real ).
thf(func_def_166,type,
sK93: extended_ereal > real ).
thf(func_def_167,type,
sK94: extended_ereal > real ).
thf(func_def_168,type,
sK95: extended_ereal > real ).
thf(func_def_169,type,
sK96: extended_ereal > real ).
thf(func_def_170,type,
sK97: extended_ereal > real ).
thf(func_def_171,type,
sK98: extended_ereal > real ).
thf(func_def_172,type,
sK99: extended_ereal > real ).
thf(func_def_173,type,
sK100: extended_ereal > real ).
thf(func_def_174,type,
sK101: extended_ereal > real ).
thf(func_def_175,type,
sK102: extended_ereal > real ).
thf(func_def_176,type,
sK103: extended_ereal > real ).
thf(func_def_177,type,
sK104: extended_ereal > real ).
thf(func_def_178,type,
sK105: extended_ereal > real ).
thf(func_def_179,type,
sK106: extended_ereal > real ).
thf(func_def_180,type,
sK107: extended_ereal > real ).
thf(func_def_181,type,
sK108: extended_ereal > real ).
thf(func_def_182,type,
sK109: extended_ereal > real ).
thf(func_def_183,type,
sK110: extended_ereal > real ).
thf(func_def_184,type,
sK111: extended_ereal > real ).
thf(func_def_185,type,
sK112: extended_ereal > real ).
thf(func_def_186,type,
sK113: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_187,type,
sK114: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_188,type,
sK115: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_189,type,
sK116: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_190,type,
sK117: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_191,type,
sK118: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_192,type,
sK119: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_193,type,
sK120: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_194,type,
sK121: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_195,type,
sK122: ( extended_ereal > extended_ereal > $o ) > extended_ereal ).
thf(func_def_196,type,
sK123: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_197,type,
sK124: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_198,type,
sK125: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_199,type,
sK126: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_200,type,
sK127: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_201,type,
sK128: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_202,type,
sK129: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_203,type,
sK130: ( extended_ereal > extended_ereal > $o ) > real ).
thf(func_def_204,type,
sK131: ( nat > $o ) > nat ).
thf(func_def_205,type,
sK132: nat > ( nat > $o ) > nat ).
thf(func_def_206,type,
sK133: nat > ( nat > $o ) > nat ).
thf(func_def_207,type,
sK134: nat > ( nat > $o ) > nat ).
thf(func_def_208,type,
sK135:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_210,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_211,type,
sK137:
!>[X0: $tType] : ( ( X0 > extended_ereal ) > ( X0 > extended_ereal ) > X0 > extended_ereal ) ).
thf(func_def_212,type,
sK138:
!>[X0: $tType] : ( ( X0 > extended_ereal ) > ( X0 > extended_ereal ) > X0 ) ).
thf(func_def_213,type,
sK139: extended_ereal > real ).
thf(f3523,plain,
$false,
inference(avatar_sat_refutation,[],[f2481,f2486,f2491,f2496,f2501,f2506,f2511,f2516,f2521,f2526,f2531,f2536,f2541,f2546,f2551,f2556,f2561,f2566,f2571,f2576,f2581,f2586,f2591,f2596,f2601,f2606,f2611,f2616,f2621,f2626,f2631,f2636,f2641,f2646,f2651,f2656,f2661,f2666,f2671,f2676,f2681,f2686,f2691,f2696,f2701,f2706,f2711,f2716,f2721,f2726,f2731,f2736,f2741,f2746,f2751,f2756,f2761,f2766,f2771,f2776,f2781,f2786,f2791,f2796,f2801,f2806,f2811,f2816,f2821,f2826,f2830,f2864,f2868,f2873,f2878,f2883,f2888,f2893,f2897,f2901,f2906,f2911,f2919,f2924,f2941,f2946,f2951,f2956,f2961,f2968,f2973,f2978,f2982,f2986,f2990,f2994,f2998,f3002,f3072,f3076,f3084,f3089,f3093,f3101,f3105,f3109,f3113,f3118,f3122,f3126,f3142,f3146,f3150,f3154,f3159,f3165,f3169,f3173,f3177,f3181,f3185,f3189,f3193,f3197,f3201,f3209,f3225,f3229,f3233,f3237,f3241,f3245,f3249,f3253,f3257,f3261,f3287,f3305,f3309,f3313,f3317,f3330,f3362,f3366,f3370,f3374,f3378,f3382,f3396,f3417,f3421,f3425,f3449,f3453,f3457,f3476,f3480,f3484,f3488,f3492,f3501,f3518,f3520,f3522]) ).
thf(f3522,plain,
( ~ spl136_74
| ~ spl136_160 ),
inference(avatar_contradiction_clause,[],[f3521]) ).
thf(f3521,plain,
( $false
| ~ spl136_74
| ~ spl136_160 ),
inference(trivial_inequality_removal,[],[f3514]) ).
thf(f3514,plain,
( ( $true = $false )
| ~ spl136_74
| ~ spl136_160 ),
inference(superposition,[],[f3491,f2872]) ).
thf(f2872,plain,
( ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) = $false )
| ~ spl136_74 ),
inference(avatar_component_clause,[],[f2870]) ).
thf(f2870,plain,
( spl136_74
<=> ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_74])]) ).
thf(f3491,plain,
( ! [X0: a] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,X0)),vAPP(a,extended_ereal,f,X0)) )
| ~ spl136_160 ),
inference(avatar_component_clause,[],[f3490]) ).
thf(f3490,plain,
( spl136_160
<=> ! [X0: a] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,X0)),vAPP(a,extended_ereal,f,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_160])]) ).
thf(f3520,plain,
( ~ spl136_74
| ~ spl136_160 ),
inference(avatar_contradiction_clause,[],[f3519]) ).
thf(f3519,plain,
( $false
| ~ spl136_74
| ~ spl136_160 ),
inference(trivial_inequality_removal,[],[f3515]) ).
thf(f3515,plain,
( ( $true = $false )
| ~ spl136_74
| ~ spl136_160 ),
inference(superposition,[],[f2872,f3491]) ).
thf(f3518,plain,
( spl136_70
| ~ spl136_160 ),
inference(avatar_contradiction_clause,[],[f3517]) ).
thf(f3517,plain,
( $false
| spl136_70
| ~ spl136_160 ),
inference(trivial_inequality_removal,[],[f3516]) ).
thf(f3516,plain,
( ( $true != $true )
| spl136_70
| ~ spl136_160 ),
inference(superposition,[],[f2825,f3491]) ).
thf(f2825,plain,
( ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) != $true )
| spl136_70 ),
inference(avatar_component_clause,[],[f2823]) ).
thf(f2823,plain,
( spl136_70
<=> ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_70])]) ).
thf(f3501,plain,
( spl136_161
| ~ spl136_38
| ~ spl136_95 ),
inference(avatar_split_clause,[],[f3025,f2988,f2663,f3499]) ).
thf(f3499,plain,
( spl136_161
<=> ! [X0: $tType] : ( $true = topolo503727757_space(sTfun(X0,nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_161])]) ).
thf(f2663,plain,
( spl136_38
<=> ( topolo503727757_space(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_38])]) ).
thf(f2988,plain,
( spl136_95
<=> ! [X1: $tType,X0: $tType] :
( ( $true = topolo503727757_space(sTfun(X0,X1)) )
| ( $true != topolo503727757_space(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_95])]) ).
thf(f3025,plain,
( ! [X0: $tType] : ( $true = topolo503727757_space(sTfun(X0,nat)) )
| ~ spl136_38
| ~ spl136_95 ),
inference(trivial_inequality_removal,[],[f3016]) ).
thf(f3016,plain,
( ! [X0: $tType] :
( ( $true != $true )
| ( $true = topolo503727757_space(sTfun(X0,nat)) ) )
| ~ spl136_38
| ~ spl136_95 ),
inference(superposition,[],[f2989,f2665]) ).
thf(f2665,plain,
( ( topolo503727757_space(nat) = $true )
| ~ spl136_38 ),
inference(avatar_component_clause,[],[f2663]) ).
thf(f2989,plain,
( ! [X1: $tType,X0: $tType] :
( ( $true != topolo503727757_space(X1) )
| ( $true = topolo503727757_space(sTfun(X0,X1)) ) )
| ~ spl136_95 ),
inference(avatar_component_clause,[],[f2988]) ).
thf(f3492,plain,
spl136_160,
inference(avatar_split_clause,[],[f1624,f3490]) ).
thf(f1624,plain,
! [X0: a] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,X0)),vAPP(a,extended_ereal,f,X0)) ),
inference(cnf_transformation,[],[f604]) ).
thf(f604,plain,
! [X0: a] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,X0)),vAPP(a,extended_ereal,f,X0)) ),
inference(fool_elimination,[],[f603]) ).
thf(f603,plain,
! [X0: a] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,X0)),vAPP(a,extended_ereal,f,X0)),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
! [X3: a] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,X3)),vAPP(a,extended_ereal,f,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms) ).
thf(f3488,plain,
spl136_159,
inference(avatar_split_clause,[],[f1568,f3486]) ).
thf(f3486,plain,
( spl136_159
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) )
| ( ordere142940540dd_abs(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_159])]) ).
thf(f1568,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) )
| ( ordere142940540dd_abs(X0) != $true ) ),
inference(cnf_transformation,[],[f992]) ).
thf(f992,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) )
| ( ordere142940540dd_abs(X0) != $true ) ),
inference(ennf_transformation,[],[f510]) ).
thf(f510,plain,
! [X0: $tType] :
( ( ordere142940540dd_abs(X0) = $true )
=> ! [X1: X0] : ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) ) ),
inference(fool_elimination,[],[f509]) ).
thf(f509,plain,
! [X0: $tType] :
( ordere142940540dd_abs(X0)
=> ! [X1: X0] : ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) ) ),
inference(rectify,[],[f218]) ).
thf(f218,axiom,
! [X0: $tType] :
( ordere142940540dd_abs(X0)
=> ! [X15: X0] : ( vAPP(X0,X0,abs_abs(X0),X15) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,uminus_uminus(X0),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_abs__minus__cancel) ).
thf(f3484,plain,
spl136_158,
inference(avatar_split_clause,[],[f1567,f3482]) ).
thf(f3482,plain,
( spl136_158
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,abs_abs(X0),X1)) )
| ( ordere142940540dd_abs(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_158])]) ).
thf(f1567,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,abs_abs(X0),X1)) )
| ( ordere142940540dd_abs(X0) != $true ) ),
inference(cnf_transformation,[],[f991]) ).
thf(f991,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,abs_abs(X0),X1)) )
| ( ordere142940540dd_abs(X0) != $true ) ),
inference(ennf_transformation,[],[f508]) ).
thf(f508,plain,
! [X0: $tType] :
( ( ordere142940540dd_abs(X0) = $true )
=> ! [X1: X0] : ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,abs_abs(X0),X1)) ) ),
inference(fool_elimination,[],[f507]) ).
thf(f507,plain,
! [X0: $tType] :
( ordere142940540dd_abs(X0)
=> ! [X1: X0] : ( vAPP(X0,X0,abs_abs(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,abs_abs(X0),X1)) ) ),
inference(rectify,[],[f213]) ).
thf(f213,axiom,
! [X0: $tType] :
( ordere142940540dd_abs(X0)
=> ! [X15: X0] : ( vAPP(X0,X0,abs_abs(X0),X15) = vAPP(X0,X0,abs_abs(X0),vAPP(X0,X0,abs_abs(X0),X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_abs__idempotent) ).
thf(f3480,plain,
spl136_157,
inference(avatar_split_clause,[],[f1534,f3478]) ).
thf(f3478,plain,
( spl136_157
<=> ! [X0: $tType,X1: num] :
( ( vAPP(num,X0,numeral_numeral(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(num,X0,numeral_numeral(X0),X1)) )
| ( linordered_idom(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_157])]) ).
thf(f1534,plain,
! [X0: $tType,X1: num] :
( ( vAPP(num,X0,numeral_numeral(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(num,X0,numeral_numeral(X0),X1)) )
| ( linordered_idom(X0) != $true ) ),
inference(cnf_transformation,[],[f969]) ).
thf(f969,plain,
! [X0: $tType] :
( ! [X1: num] : ( vAPP(num,X0,numeral_numeral(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(num,X0,numeral_numeral(X0),X1)) )
| ( linordered_idom(X0) != $true ) ),
inference(ennf_transformation,[],[f470]) ).
thf(f470,plain,
! [X0: $tType] :
( ( linordered_idom(X0) = $true )
=> ! [X1: num] : ( vAPP(num,X0,numeral_numeral(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(num,X0,numeral_numeral(X0),X1)) ) ),
inference(fool_elimination,[],[f469]) ).
thf(f469,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: num] : ( vAPP(num,X0,numeral_numeral(X0),X1) = vAPP(X0,X0,abs_abs(X0),vAPP(num,X0,numeral_numeral(X0),X1)) ) ),
inference(rectify,[],[f217]) ).
thf(f217,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X36: num] : ( vAPP(num,X0,numeral_numeral(X0),X36) = vAPP(X0,X0,abs_abs(X0),vAPP(num,X0,numeral_numeral(X0),X36)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_abs__numeral) ).
thf(f3476,plain,
spl136_156,
inference(avatar_split_clause,[],[f1499,f3474]) ).
thf(f3474,plain,
( spl136_156
<=> ! [X0: $tType,X2: num,X1: num] :
( ( vAPP(num,X0,numeral_numeral(X0),X1) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X2)) )
| ( ring_char_0(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_156])]) ).
thf(f1499,plain,
! [X0: $tType,X2: num,X1: num] :
( ( vAPP(num,X0,numeral_numeral(X0),X1) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X2)) )
| ( ring_char_0(X0) != $true ) ),
inference(cnf_transformation,[],[f933]) ).
thf(f933,plain,
! [X0: $tType] :
( ! [X1: num,X2: num] : ( vAPP(num,X0,numeral_numeral(X0),X1) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X2)) )
| ( ring_char_0(X0) != $true ) ),
inference(ennf_transformation,[],[f400]) ).
thf(f400,plain,
! [X0: $tType] :
( ( ring_char_0(X0) = $true )
=> ! [X1: num,X2: num] : ( vAPP(num,X0,numeral_numeral(X0),X1) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X2)) ) ),
inference(fool_elimination,[],[f399]) ).
thf(f399,plain,
! [X0: $tType] :
( ring_char_0(X0)
=> ! [X1: num,X2: num] : ( vAPP(num,X0,numeral_numeral(X0),X1) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X2)) ) ),
inference(rectify,[],[f113]) ).
thf(f113,axiom,
! [X0: $tType] :
( ring_char_0(X0)
=> ! [X35: num,X36: num] : ( vAPP(num,X0,numeral_numeral(X0),X35) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X36)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_numeral__neq__neg__numeral) ).
thf(f3457,plain,
spl136_155,
inference(avatar_split_clause,[],[f1452,f3455]) ).
thf(f3455,plain,
( spl136_155
<=> ! [X0: real] : ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),vAPP(real,extended_ereal,extended_ereal2,X0)) = vAPP(real,extended_ereal,extended_ereal2,vAPP(real,real,uminus_uminus(real),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_155])]) ).
thf(f1452,plain,
! [X0: real] : ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),vAPP(real,extended_ereal,extended_ereal2,X0)) = vAPP(real,extended_ereal,extended_ereal2,vAPP(real,real,uminus_uminus(real),X0)) ),
inference(cnf_transformation,[],[f861]) ).
thf(f861,plain,
! [X0: real] : ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),vAPP(real,extended_ereal,extended_ereal2,X0)) = vAPP(real,extended_ereal,extended_ereal2,vAPP(real,real,uminus_uminus(real),X0)) ),
inference(rectify,[],[f195]) ).
thf(f195,axiom,
! [X41: real] : ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),vAPP(real,extended_ereal,extended_ereal2,X41)) = vAPP(real,extended_ereal,extended_ereal2,vAPP(real,real,uminus_uminus(real),X41)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_uminus__ereal_Osimps_I1_J) ).
thf(f3453,plain,
spl136_154,
inference(avatar_split_clause,[],[f1451,f3451]) ).
thf(f3451,plain,
( spl136_154
<=> ! [X0: extended_ereal] : ( vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) = vAPP(real,real,uminus_uminus(real),vAPP(extended_ereal,real,extend1716541707_ereal,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_154])]) ).
thf(f1451,plain,
! [X0: extended_ereal] : ( vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) = vAPP(real,real,uminus_uminus(real),vAPP(extended_ereal,real,extend1716541707_ereal,X0)) ),
inference(cnf_transformation,[],[f860]) ).
thf(f860,plain,
! [X0: extended_ereal] : ( vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) = vAPP(real,real,uminus_uminus(real),vAPP(extended_ereal,real,extend1716541707_ereal,X0)) ),
inference(rectify,[],[f87]) ).
thf(f87,axiom,
! [X4: extended_ereal] : ( vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X4)) = vAPP(real,real,uminus_uminus(real),vAPP(extended_ereal,real,extend1716541707_ereal,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_real__of__ereal) ).
thf(f3449,plain,
( spl136_153
| ~ spl136_37
| ~ spl136_95 ),
inference(avatar_split_clause,[],[f3024,f2988,f2658,f3447]) ).
thf(f3447,plain,
( spl136_153
<=> ! [X0: $tType] : ( $true = topolo503727757_space(sTfun(X0,extended_enat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_153])]) ).
thf(f2658,plain,
( spl136_37
<=> ( topolo503727757_space(extended_enat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_37])]) ).
thf(f3024,plain,
( ! [X0: $tType] : ( $true = topolo503727757_space(sTfun(X0,extended_enat)) )
| ~ spl136_37
| ~ spl136_95 ),
inference(trivial_inequality_removal,[],[f3017]) ).
thf(f3017,plain,
( ! [X0: $tType] :
( ( $true != $true )
| ( $true = topolo503727757_space(sTfun(X0,extended_enat)) ) )
| ~ spl136_37
| ~ spl136_95 ),
inference(superposition,[],[f2989,f2660]) ).
thf(f2660,plain,
( ( topolo503727757_space(extended_enat) = $true )
| ~ spl136_37 ),
inference(avatar_component_clause,[],[f2658]) ).
thf(f3425,plain,
spl136_152,
inference(avatar_split_clause,[],[f2285,f3423]) ).
thf(f3423,plain,
( spl136_152
<=> ! [X0: extended_ereal] :
( ( extended_PInfty != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
| ( zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_152])]) ).
thf(f2285,plain,
! [X0: extended_ereal] :
( ( extended_PInfty != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
| ( zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) ) ),
inference(forward_demodulation,[],[f1472,f1416]) ).
thf(f1416,plain,
extend1396239628finity(extended_ereal) = extended_PInfty,
inference(cnf_transformation,[],[f203]) ).
thf(f203,axiom,
extend1396239628finity(extended_ereal) = extended_PInfty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_infinity__ereal__def) ).
thf(f1472,plain,
! [X0: extended_ereal] :
( ( zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) )
| ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ),
inference(cnf_transformation,[],[f901]) ).
thf(f901,plain,
! [X0: extended_ereal] :
( ( ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) = X0 )
| ( extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) )
& ( ( zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) )
| ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ) ),
inference(ennf_transformation,[],[f867]) ).
thf(f867,plain,
! [X0: extended_ereal] :
( ( ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
=> ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) = X0 ) )
& ( ( extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
=> ( zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) ) ) ),
inference(rectify,[],[f250]) ).
thf(f250,axiom,
! [X4: extended_ereal] :
( ( ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X4) )
=> ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X4)) = X4 ) )
& ( ( extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X4) )
=> ( zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_ereal__real) ).
thf(f3421,plain,
spl136_151,
inference(avatar_split_clause,[],[f1622,f3419]) ).
thf(f3419,plain,
( spl136_151
<=> ! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_151])]) ).
thf(f1622,plain,
! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0)) ),
inference(cnf_transformation,[],[f600]) ).
thf(f600,plain,
! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0)) ),
inference(fool_elimination,[],[f599]) ).
thf(f599,plain,
! [X0: extended_ereal] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0)),
inference(rectify,[],[f237]) ).
thf(f237,axiom,
! [X4: extended_ereal] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_abs__ereal__pos) ).
thf(f3417,plain,
spl136_150,
inference(avatar_split_clause,[],[f1506,f3415]) ).
thf(f3415,plain,
( spl136_150
<=> ! [X0: $tType] :
( ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) = $true )
| ( linord1659791738miring(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_150])]) ).
thf(f1506,plain,
! [X0: $tType] :
( ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) = $true )
| ( linord1659791738miring(X0) != $true ) ),
inference(cnf_transformation,[],[f940]) ).
thf(f940,plain,
! [X0: $tType] :
( ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) = $true )
| ( linord1659791738miring(X0) != $true ) ),
inference(ennf_transformation,[],[f414]) ).
thf(f414,plain,
! [X0: $tType] :
( ( linord1659791738miring(X0) = $true )
=> ( vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) = $true ) ),
inference(fool_elimination,[],[f413]) ).
thf(f413,plain,
! [X0: $tType] :
( linord1659791738miring(X0)
=> vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) ),
inference(rectify,[],[f71]) ).
thf(f71,axiom,
! [X0: $tType] :
( linord1659791738miring(X0)
=> vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),zero_zero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_le__numeral__extra_I3_J) ).
thf(f3396,plain,
( spl136_149
| ~ spl136_42
| ~ spl136_95 ),
inference(avatar_split_clause,[],[f3023,f2988,f2683,f3394]) ).
thf(f3394,plain,
( spl136_149
<=> ! [X0: $tType] : ( $true = topolo503727757_space(sTfun(X0,extended_ereal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_149])]) ).
thf(f2683,plain,
( spl136_42
<=> ( topolo503727757_space(extended_ereal) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_42])]) ).
thf(f3023,plain,
( ! [X0: $tType] : ( $true = topolo503727757_space(sTfun(X0,extended_ereal)) )
| ~ spl136_42
| ~ spl136_95 ),
inference(trivial_inequality_removal,[],[f3018]) ).
thf(f3018,plain,
( ! [X0: $tType] :
( ( $true != $true )
| ( $true = topolo503727757_space(sTfun(X0,extended_ereal)) ) )
| ~ spl136_42
| ~ spl136_95 ),
inference(superposition,[],[f2989,f2685]) ).
thf(f2685,plain,
( ( topolo503727757_space(extended_ereal) = $true )
| ~ spl136_42 ),
inference(avatar_component_clause,[],[f2683]) ).
thf(f3382,plain,
spl136_148,
inference(avatar_split_clause,[],[f2293,f3380]) ).
thf(f3380,plain,
( spl136_148
<=> ! [X0: extended_ereal] :
( ( extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK40,X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_148])]) ).
thf(f2293,plain,
! [X0: extended_ereal] :
( ( extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK40,X0)) = X0 ) ),
inference(forward_demodulation,[],[f1478,f1416]) ).
thf(f1478,plain,
! [X0: extended_ereal] :
( ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK40,X0)) = X0 )
| ( extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ),
inference(cnf_transformation,[],[f1180]) ).
thf(f1180,plain,
! [X0: extended_ereal] :
( ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK40,X0)) = X0 )
| ( extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f906,f1179]) ).
thf(f1179,plain,
! [X0: extended_ereal] :
( ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 )
=> ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK40,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f906,plain,
! [X0: extended_ereal] :
( ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 )
| ( extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ),
inference(ennf_transformation,[],[f871]) ).
thf(f871,plain,
! [X0: extended_ereal] :
( ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
=> ~ ! [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) != X0 ) ),
inference(rectify,[],[f232]) ).
thf(f232,axiom,
! [X4: extended_ereal] :
( ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X4) )
=> ~ ! [X58: real] : ( vAPP(real,extended_ereal,extended_ereal2,X58) != X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_abs__neq__infinity__cases) ).
thf(f3378,plain,
spl136_147,
inference(avatar_split_clause,[],[f2291,f3376]) ).
thf(f3376,plain,
( spl136_147
<=> ! [X0: extended_ereal] :
( ( extended_PInfty = X0 )
| ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
| ( extended_PInfty != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_147])]) ).
thf(f2291,plain,
! [X0: extended_ereal] :
( ( extended_PInfty = X0 )
| ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
| ( extended_PInfty != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ),
inference(forward_demodulation,[],[f2290,f1416]) ).
thf(f2290,plain,
! [X0: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
| ( extended_PInfty != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
| ( extend1396239628finity(extended_ereal) = X0 ) ),
inference(forward_demodulation,[],[f2289,f1416]) ).
thf(f2289,plain,
! [X0: extended_ereal] :
( ( extended_PInfty != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
| ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( extend1396239628finity(extended_ereal) = X0 ) ),
inference(forward_demodulation,[],[f1476,f1416]) ).
thf(f1476,plain,
! [X0: extended_ereal] :
( ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
| ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( extend1396239628finity(extended_ereal) = X0 ) ),
inference(cnf_transformation,[],[f904]) ).
thf(f904,plain,
! [X0: extended_ereal] :
( ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
| ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( extend1396239628finity(extended_ereal) = X0 ) ),
inference(flattening,[],[f903]) ).
thf(f903,plain,
! [X0: extended_ereal] :
( ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
| ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( extend1396239628finity(extended_ereal) = X0 ) ),
inference(ennf_transformation,[],[f869]) ).
thf(f869,plain,
! [X0: extended_ereal] :
( ( extend1396239628finity(extended_ereal) != X0 )
=> ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X0 )
=> ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ) ),
inference(rectify,[],[f234]) ).
thf(f234,axiom,
! [X15: extended_ereal] :
( ( extend1396239628finity(extended_ereal) != X15 )
=> ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X15 )
=> ( extend1396239628finity(extended_ereal) != vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_ereal__infinity__cases) ).
thf(f3374,plain,
spl136_146,
inference(avatar_split_clause,[],[f2284,f3372]) ).
thf(f3372,plain,
( spl136_146
<=> ! [X0: extended_ereal] :
( ( extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_146])]) ).
thf(f2284,plain,
! [X0: extended_ereal] :
( ( extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) = X0 ) ),
inference(forward_demodulation,[],[f1473,f1416]) ).
thf(f1473,plain,
! [X0: extended_ereal] :
( ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,extend1716541707_ereal,X0)) = X0 )
| ( extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) ) ),
inference(cnf_transformation,[],[f901]) ).
thf(f3370,plain,
spl136_145,
inference(avatar_split_clause,[],[f1621,f3368]) ).
thf(f3368,plain,
( spl136_145
<=> ! [X0: extended_enat] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_enat,extended_ereal,extend1771934483f_enat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_145])]) ).
thf(f1621,plain,
! [X0: extended_enat] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_enat,extended_ereal,extend1771934483f_enat,X0)) ),
inference(cnf_transformation,[],[f598]) ).
thf(f598,plain,
! [X0: extended_enat] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_enat,extended_ereal,extend1771934483f_enat,X0)) ),
inference(fool_elimination,[],[f597]) ).
thf(f597,plain,
! [X0: extended_enat] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_enat,extended_ereal,extend1771934483f_enat,X0)),
inference(rectify,[],[f49]) ).
thf(f49,axiom,
! [X36: extended_enat] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_enat,extended_ereal,extend1771934483f_enat,X36)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_ereal__of__enat__nonneg) ).
thf(f3366,plain,
spl136_144,
inference(avatar_split_clause,[],[f1605,f3364]) ).
thf(f3364,plain,
( spl136_144
<=> ! [X0: nat] :
( ( zero_zero(nat) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_144])]) ).
thf(f1605,plain,
! [X0: nat] :
( ( zero_zero(nat) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)) ) ),
inference(cnf_transformation,[],[f1035]) ).
thf(f1035,plain,
! [X0: nat] :
( ( zero_zero(nat) = X0 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)) ) ),
inference(ennf_transformation,[],[f574]) ).
thf(f574,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat)) )
=> ( zero_zero(nat) = X0 ) ),
inference(fool_elimination,[],[f573]) ).
thf(f573,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),zero_zero(nat))
=> ( zero_zero(nat) = X0 ) ),
inference(rectify,[],[f144]) ).
thf(f144,axiom,
! [X15: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X15),zero_zero(nat))
=> ( zero_zero(nat) = X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_bot__nat__0_Oextremum__uniqueI) ).
thf(f3362,plain,
spl136_143,
inference(avatar_split_clause,[],[f1491,f3360]) ).
thf(f3360,plain,
( spl136_143
<=> ! [X0: $tType,X1: X0] :
( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1) )
| ( canoni770627133id_add(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_143])]) ).
thf(f1491,plain,
! [X0: $tType,X1: X0] :
( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1) )
| ( canoni770627133id_add(X0) != $true ) ),
inference(cnf_transformation,[],[f925]) ).
thf(f925,plain,
! [X0: $tType] :
( ! [X1: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1) )
| ( canoni770627133id_add(X0) != $true ) ),
inference(ennf_transformation,[],[f384]) ).
thf(f384,plain,
! [X0: $tType] :
( ( canoni770627133id_add(X0) = $true )
=> ! [X1: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1) ) ),
inference(fool_elimination,[],[f383]) ).
thf(f383,plain,
! [X0: $tType] :
( canoni770627133id_add(X0)
=> ! [X1: X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X1) ),
inference(rectify,[],[f70]) ).
thf(f70,axiom,
! [X0: $tType] :
( canoni770627133id_add(X0)
=> ! [X4: X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),zero_zero(X0)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_zero__le) ).
thf(f3330,plain,
( spl136_142
| ~ spl136_40
| ~ spl136_95 ),
inference(avatar_split_clause,[],[f3022,f2988,f2673,f3328]) ).
thf(f3328,plain,
( spl136_142
<=> ! [X0: $tType] : ( $true = topolo503727757_space(sTfun(X0,real)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_142])]) ).
thf(f2673,plain,
( spl136_40
<=> ( topolo503727757_space(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_40])]) ).
thf(f3022,plain,
( ! [X0: $tType] : ( $true = topolo503727757_space(sTfun(X0,real)) )
| ~ spl136_40
| ~ spl136_95 ),
inference(trivial_inequality_removal,[],[f3019]) ).
thf(f3019,plain,
( ! [X0: $tType] :
( ( $true != $true )
| ( $true = topolo503727757_space(sTfun(X0,real)) ) )
| ~ spl136_40
| ~ spl136_95 ),
inference(superposition,[],[f2989,f2675]) ).
thf(f2675,plain,
( ( topolo503727757_space(real) = $true )
| ~ spl136_40 ),
inference(avatar_component_clause,[],[f2673]) ).
thf(f3317,plain,
spl136_141,
inference(avatar_split_clause,[],[f1590,f3315]) ).
thf(f3315,plain,
( spl136_141
<=> ! [X0: $tType,X1: X0] :
( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) )
| ( order(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_141])]) ).
thf(f1590,plain,
! [X0: $tType,X1: X0] :
( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) )
| ( order(X0) != $true ) ),
inference(cnf_transformation,[],[f1017]) ).
thf(f1017,plain,
! [X0: $tType] :
( ! [X1: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) )
| ( order(X0) != $true ) ),
inference(ennf_transformation,[],[f554]) ).
thf(f554,plain,
! [X0: $tType] :
( ( order(X0) = $true )
=> ! [X1: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) ) ),
inference(fool_elimination,[],[f553]) ).
thf(f553,plain,
! [X0: $tType] :
( order(X0)
=> ! [X1: X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) ),
inference(rectify,[],[f20]) ).
thf(f20,axiom,
! [X0: $tType] :
( order(X0)
=> ! [X15: X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X15),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_dual__order_Orefl) ).
thf(f3313,plain,
spl136_140,
inference(avatar_split_clause,[],[f1544,f3311]) ).
thf(f3311,plain,
( spl136_140
<=> ! [X0: $tType,X1: X0] :
( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) )
| ( preorder(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_140])]) ).
thf(f1544,plain,
! [X0: $tType,X1: X0] :
( ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) )
| ( preorder(X0) != $true ) ),
inference(cnf_transformation,[],[f979]) ).
thf(f979,plain,
! [X0: $tType] :
( ! [X1: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) )
| ( preorder(X0) != $true ) ),
inference(ennf_transformation,[],[f490]) ).
thf(f490,plain,
! [X0: $tType] :
( ( preorder(X0) = $true )
=> ! [X1: X0] : ( $true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) ) ),
inference(fool_elimination,[],[f489]) ).
thf(f489,plain,
! [X0: $tType] :
( preorder(X0)
=> ! [X1: X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1) ),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
! [X0: $tType] :
( preorder(X0)
=> ! [X4: X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X4),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_order__refl) ).
thf(f3309,plain,
spl136_139,
inference(avatar_split_clause,[],[f1493,f3307]) ).
thf(f3307,plain,
( spl136_139
<=> ! [X0: $tType,X1: num] :
( ( zero_zero(X0) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X1)) )
| ( ring_char_0(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_139])]) ).
thf(f1493,plain,
! [X0: $tType,X1: num] :
( ( zero_zero(X0) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X1)) )
| ( ring_char_0(X0) != $true ) ),
inference(cnf_transformation,[],[f927]) ).
thf(f927,plain,
! [X0: $tType] :
( ! [X1: num] : ( zero_zero(X0) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X1)) )
| ( ring_char_0(X0) != $true ) ),
inference(ennf_transformation,[],[f388]) ).
thf(f388,plain,
! [X0: $tType] :
( ( ring_char_0(X0) = $true )
=> ! [X1: num] : ( zero_zero(X0) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X1)) ) ),
inference(fool_elimination,[],[f387]) ).
thf(f387,plain,
! [X0: $tType] :
( ring_char_0(X0)
=> ! [X1: num] : ( zero_zero(X0) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X1)) ) ),
inference(rectify,[],[f126]) ).
thf(f126,axiom,
! [X0: $tType] :
( ring_char_0(X0)
=> ! [X36: num] : ( zero_zero(X0) != vAPP(X0,X0,uminus_uminus(X0),vAPP(num,X0,numeral_numeral(X0),X36)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_zero__neq__neg__numeral) ).
thf(f3305,plain,
spl136_138,
inference(avatar_split_clause,[],[f1449,f3303]) ).
thf(f3303,plain,
( spl136_138
<=> ! [X0: extended_ereal] : ( vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_138])]) ).
thf(f1449,plain,
! [X0: extended_ereal] : ( vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) ),
inference(cnf_transformation,[],[f858]) ).
thf(f858,plain,
! [X0: extended_ereal] : ( vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X0) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) ),
inference(rectify,[],[f219]) ).
thf(f219,axiom,
! [X4: extended_ereal] : ( vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X4)) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_abs__ereal__uminus) ).
thf(f3287,plain,
( spl136_137
| ~ spl136_36
| ~ spl136_94 ),
inference(avatar_split_clause,[],[f3014,f2984,f2653,f3285]) ).
thf(f3285,plain,
( spl136_137
<=> ! [X0: $tType] : ( $true = boolean_algebra(sTfun(X0,$o)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_137])]) ).
thf(f2653,plain,
( spl136_36
<=> ( boolean_algebra($o) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_36])]) ).
thf(f2984,plain,
( spl136_94
<=> ! [X1: $tType,X0: $tType] :
( ( $true = boolean_algebra(sTfun(X0,X1)) )
| ( $true != boolean_algebra(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_94])]) ).
thf(f3014,plain,
( ! [X0: $tType] : ( $true = boolean_algebra(sTfun(X0,$o)) )
| ~ spl136_36
| ~ spl136_94 ),
inference(trivial_inequality_removal,[],[f3011]) ).
thf(f3011,plain,
( ! [X0: $tType] :
( ( $true != $true )
| ( $true = boolean_algebra(sTfun(X0,$o)) ) )
| ~ spl136_36
| ~ spl136_94 ),
inference(superposition,[],[f2985,f2655]) ).
thf(f2655,plain,
( ( boolean_algebra($o) = $true )
| ~ spl136_36 ),
inference(avatar_component_clause,[],[f2653]) ).
thf(f2985,plain,
( ! [X1: $tType,X0: $tType] :
( ( $true != boolean_algebra(X1) )
| ( $true = boolean_algebra(sTfun(X0,X1)) ) )
| ~ spl136_94 ),
inference(avatar_component_clause,[],[f2984]) ).
thf(f3261,plain,
spl136_136,
inference(avatar_split_clause,[],[f2365,f3259]) ).
thf(f3259,plain,
( spl136_136
<=> ! [X0: extended_ereal] :
( ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),extended_MInfty) )
| ( extended_MInfty = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_136])]) ).
thf(f2365,plain,
! [X0: extended_ereal] :
( ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),extended_MInfty) )
| ( extended_MInfty = X0 ) ),
inference(forward_demodulation,[],[f2364,f1419]) ).
thf(f1419,plain,
extended_MInfty = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty),
inference(cnf_transformation,[],[f209]) ).
thf(f209,axiom,
extended_MInfty = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_uminus__ereal_Osimps_I2_J) ).
thf(f2364,plain,
! [X0: extended_ereal] :
( ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty)) )
| ( extended_MInfty = X0 ) ),
inference(forward_demodulation,[],[f2363,f1416]) ).
thf(f2363,plain,
! [X0: extended_ereal] :
( ( extended_MInfty = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))) ) ),
inference(forward_demodulation,[],[f2362,f1419]) ).
thf(f2362,plain,
! [X0: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))) ) ),
inference(forward_demodulation,[],[f1903,f1416]) ).
thf(f1903,plain,
! [X0: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))) ) ),
inference(equality_resolution,[],[f1715]) ).
thf(f1715,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),X1) ) ),
inference(cnf_transformation,[],[f1104]) ).
thf(f1104,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),X1) ) ),
inference(flattening,[],[f1103]) ).
thf(f1103,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),X1) ) ),
inference(ennf_transformation,[],[f692]) ).
thf(f692,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),X1) )
=> ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 )
=> ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 ) ) ),
inference(fool_elimination,[],[f691]) ).
thf(f691,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),X1)
=> ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 )
=> ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 ) ) ),
inference(rectify,[],[f128]) ).
thf(f128,axiom,
! [X15: extended_ereal,X16: extended_ereal] :
( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X15),X16)
=> ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X16 )
=> ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X15 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_ereal__infty__less__eq2_I2_J) ).
thf(f3257,plain,
spl136_135,
inference(avatar_split_clause,[],[f2327,f3255]) ).
thf(f3255,plain,
( spl136_135
<=> ! [X0: extended_ereal] :
( ( extended_PInfty = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),extended_PInfty),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_135])]) ).
thf(f2327,plain,
! [X0: extended_ereal] :
( ( extended_PInfty = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),extended_PInfty),X0) ) ),
inference(forward_demodulation,[],[f2326,f1416]) ).
thf(f2326,plain,
! [X0: extended_ereal] :
( ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),extended_PInfty),X0) )
| ( extend1396239628finity(extended_ereal) = X0 ) ),
inference(forward_demodulation,[],[f1889,f1416]) ).
thf(f1889,plain,
! [X0: extended_ereal] :
( ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),extend1396239628finity(extended_ereal)),X0) )
| ( extend1396239628finity(extended_ereal) = X0 ) ),
inference(equality_resolution,[],[f1644]) ).
thf(f1644,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extend1396239628finity(extended_ereal) != X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X1),X0) )
| ( extend1396239628finity(extended_ereal) = X0 ) ),
inference(cnf_transformation,[],[f1044]) ).
thf(f1044,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extend1396239628finity(extended_ereal) != X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X1),X0) )
| ( extend1396239628finity(extended_ereal) = X0 ) ),
inference(flattening,[],[f1043]) ).
thf(f1043,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extend1396239628finity(extended_ereal) != X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X1),X0) )
| ( extend1396239628finity(extended_ereal) = X0 ) ),
inference(ennf_transformation,[],[f624]) ).
thf(f624,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extend1396239628finity(extended_ereal) != X0 )
=> ( ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X1),X0) )
=> ( extend1396239628finity(extended_ereal) != X1 ) ) ),
inference(fool_elimination,[],[f623]) ).
thf(f623,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extend1396239628finity(extended_ereal) != X0 )
=> ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X1),X0)
=> ( extend1396239628finity(extended_ereal) != X1 ) ) ),
inference(rectify,[],[f58]) ).
thf(f58,axiom,
! [X27: extended_ereal,X4: extended_ereal] :
( ( extend1396239628finity(extended_ereal) != X27 )
=> ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X4),X27)
=> ( extend1396239628finity(extended_ereal) != X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_neq__PInf__trans) ).
thf(f3253,plain,
spl136_134,
inference(avatar_split_clause,[],[f2305,f3251]) ).
thf(f3251,plain,
( spl136_134
<=> ! [X0: extended_ereal] :
( ( extended_MInfty = X0 )
| ( extended_PInfty = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK45,X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_134])]) ).
thf(f2305,plain,
! [X0: extended_ereal] :
( ( extended_MInfty = X0 )
| ( extended_PInfty = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK45,X0)) = X0 ) ),
inference(forward_demodulation,[],[f2304,f1419]) ).
thf(f2304,plain,
! [X0: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
| ( extended_PInfty = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK45,X0)) = X0 ) ),
inference(forward_demodulation,[],[f2303,f1416]) ).
thf(f2303,plain,
! [X0: extended_ereal] :
( ( extended_PInfty = X0 )
| ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK45,X0)) = X0 ) ),
inference(forward_demodulation,[],[f1484,f1416]) ).
thf(f1484,plain,
! [X0: extended_ereal] :
( ( extend1396239628finity(extended_ereal) = X0 )
| ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK45,X0)) = X0 ) ),
inference(cnf_transformation,[],[f1190]) ).
thf(f1190,plain,
! [X0: extended_ereal] :
( ( extend1396239628finity(extended_ereal) = X0 )
| ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK45,X0)) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f918,f1189]) ).
thf(f1189,plain,
! [X0: extended_ereal] :
( ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 )
=> ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK45,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f918,plain,
! [X0: extended_ereal] :
( ( extend1396239628finity(extended_ereal) = X0 )
| ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
inference(flattening,[],[f917]) ).
thf(f917,plain,
! [X0: extended_ereal] :
( ( extend1396239628finity(extended_ereal) = X0 )
| ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
inference(ennf_transformation,[],[f877]) ).
thf(f877,plain,
! [X0: extended_ereal] :
( ! [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) != X0 )
=> ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X0 )
=> ( extend1396239628finity(extended_ereal) = X0 ) ) ),
inference(rectify,[],[f188]) ).
thf(f188,axiom,
! [X4: extended_ereal] :
( ! [X58: real] : ( vAPP(real,extended_ereal,extended_ereal2,X58) != X4 )
=> ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X4 )
=> ( extend1396239628finity(extended_ereal) = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_abs__ereal_Ocases) ).
thf(f3249,plain,
spl136_133,
inference(avatar_split_clause,[],[f2302,f3247]) ).
thf(f3247,plain,
( spl136_133
<=> ! [X0: extended_ereal] :
( ( extended_PInfty = X0 )
| ( extended_MInfty = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK44,X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_133])]) ).
thf(f2302,plain,
! [X0: extended_ereal] :
( ( extended_PInfty = X0 )
| ( extended_MInfty = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK44,X0)) = X0 ) ),
inference(forward_demodulation,[],[f2301,f1416]) ).
thf(f2301,plain,
! [X0: extended_ereal] :
( ( extended_MInfty = X0 )
| ( extend1396239628finity(extended_ereal) = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK44,X0)) = X0 ) ),
inference(forward_demodulation,[],[f2300,f1419]) ).
thf(f2300,plain,
! [X0: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
| ( extend1396239628finity(extended_ereal) = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK44,X0)) = X0 ) ),
inference(forward_demodulation,[],[f1483,f1416]) ).
thf(f1483,plain,
! [X0: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( extend1396239628finity(extended_ereal) = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK44,X0)) = X0 ) ),
inference(cnf_transformation,[],[f1188]) ).
thf(f1188,plain,
! [X0: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( extend1396239628finity(extended_ereal) = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK44,X0)) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f916,f1187]) ).
thf(f1187,plain,
! [X0: extended_ereal] :
( ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 )
=> ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK44,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f916,plain,
! [X0: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( extend1396239628finity(extended_ereal) = X0 )
| ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
inference(flattening,[],[f915]) ).
thf(f915,plain,
! [X0: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( extend1396239628finity(extended_ereal) = X0 )
| ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
inference(ennf_transformation,[],[f876]) ).
thf(f876,plain,
! [X0: extended_ereal] :
( ! [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) != X0 )
=> ( ( extend1396239628finity(extended_ereal) != X0 )
=> ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 ) ) ),
inference(rectify,[],[f192]) ).
thf(f192,axiom,
! [X4: extended_ereal] :
( ! [X58: real] : ( vAPP(real,extended_ereal,extended_ereal2,X58) != X4 )
=> ( ( extend1396239628finity(extended_ereal) != X4 )
=> ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_ereal__cases) ).
thf(f3245,plain,
spl136_132,
inference(avatar_split_clause,[],[f2299,f3243]) ).
thf(f3243,plain,
( spl136_132
<=> ! [X0: extended_ereal] :
( ( extended_PInfty = X0 )
| ( extended_MInfty = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK43,X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_132])]) ).
thf(f2299,plain,
! [X0: extended_ereal] :
( ( extended_PInfty = X0 )
| ( extended_MInfty = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK43,X0)) = X0 ) ),
inference(forward_demodulation,[],[f2298,f1416]) ).
thf(f2298,plain,
! [X0: extended_ereal] :
( ( extended_MInfty = X0 )
| ( extend1396239628finity(extended_ereal) = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK43,X0)) = X0 ) ),
inference(forward_demodulation,[],[f2297,f1419]) ).
thf(f2297,plain,
! [X0: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
| ( extend1396239628finity(extended_ereal) = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK43,X0)) = X0 ) ),
inference(forward_demodulation,[],[f1482,f1416]) ).
thf(f1482,plain,
! [X0: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( extend1396239628finity(extended_ereal) = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK43,X0)) = X0 ) ),
inference(cnf_transformation,[],[f1186]) ).
thf(f1186,plain,
! [X0: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( extend1396239628finity(extended_ereal) = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK43,X0)) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f914,f1185]) ).
thf(f1185,plain,
! [X0: extended_ereal] :
( ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 )
=> ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK43,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f914,plain,
! [X0: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( extend1396239628finity(extended_ereal) = X0 )
| ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
inference(flattening,[],[f913]) ).
thf(f913,plain,
! [X0: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( extend1396239628finity(extended_ereal) = X0 )
| ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
inference(ennf_transformation,[],[f875]) ).
thf(f875,plain,
! [X0: extended_ereal] :
( ! [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) != X0 )
=> ( ( extend1396239628finity(extended_ereal) != X0 )
=> ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 ) ) ),
inference(rectify,[],[f182]) ).
thf(f182,axiom,
! [X4: extended_ereal] :
( ! [X58: real] : ( vAPP(real,extended_ereal,extended_ereal2,X58) != X4 )
=> ( ( extend1396239628finity(extended_ereal) != X4 )
=> ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_real__of__ereal_Ocases) ).
thf(f3241,plain,
( spl136_131
| ~ spl136_29
| ~ spl136_93 ),
inference(avatar_split_clause,[],[f3010,f2980,f2618,f3239]) ).
thf(f3239,plain,
( spl136_131
<=> ! [X0: $tType] : ( $true = uminus(sTfun(X0,real)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_131])]) ).
thf(f2618,plain,
( spl136_29
<=> ( uminus(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_29])]) ).
thf(f2980,plain,
( spl136_93
<=> ! [X1: $tType,X0: $tType] :
( ( $true = uminus(sTfun(X0,X1)) )
| ( $true != uminus(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_93])]) ).
thf(f3010,plain,
( ! [X0: $tType] : ( $true = uminus(sTfun(X0,real)) )
| ~ spl136_29
| ~ spl136_93 ),
inference(trivial_inequality_removal,[],[f3003]) ).
thf(f3003,plain,
( ! [X0: $tType] :
( ( $true != $true )
| ( $true = uminus(sTfun(X0,real)) ) )
| ~ spl136_29
| ~ spl136_93 ),
inference(superposition,[],[f2981,f2620]) ).
thf(f2620,plain,
( ( uminus(real) = $true )
| ~ spl136_29 ),
inference(avatar_component_clause,[],[f2618]) ).
thf(f2981,plain,
( ! [X1: $tType,X0: $tType] :
( ( $true != uminus(X1) )
| ( $true = uminus(sTfun(X0,X1)) ) )
| ~ spl136_93 ),
inference(avatar_component_clause,[],[f2980]) ).
thf(f3237,plain,
spl136_130,
inference(avatar_split_clause,[],[f1523,f3235]) ).
thf(f3235,plain,
( spl136_130
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 )
| ( boolean_algebra(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_130])]) ).
thf(f1523,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 )
| ( boolean_algebra(X0) != $true ) ),
inference(cnf_transformation,[],[f958]) ).
thf(f958,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 )
| ( boolean_algebra(X0) != $true ) ),
inference(ennf_transformation,[],[f448]) ).
thf(f448,plain,
! [X0: $tType] :
( ( boolean_algebra(X0) = $true )
=> ! [X1: X0] : ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 ) ),
inference(fool_elimination,[],[f447]) ).
thf(f447,plain,
! [X0: $tType] :
( boolean_algebra(X0)
=> ! [X1: X0] : ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 ) ),
inference(rectify,[],[f151]) ).
thf(f151,axiom,
! [X0: $tType] :
( boolean_algebra(X0)
=> ! [X4: X0] : ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X4)) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_double__compl) ).
thf(f3233,plain,
spl136_129,
inference(avatar_split_clause,[],[f1521,f3231]) ).
thf(f3231,plain,
( spl136_129
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 )
| ( group_add(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_129])]) ).
thf(f1521,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 )
| ( group_add(X0) != $true ) ),
inference(cnf_transformation,[],[f956]) ).
thf(f956,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 )
| ( group_add(X0) != $true ) ),
inference(ennf_transformation,[],[f444]) ).
thf(f444,plain,
! [X0: $tType] :
( ( group_add(X0) = $true )
=> ! [X1: X0] : ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 ) ),
inference(fool_elimination,[],[f443]) ).
thf(f443,plain,
! [X0: $tType] :
( group_add(X0)
=> ! [X1: X0] : ( vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)) = X1 ) ),
inference(rectify,[],[f82]) ).
thf(f82,axiom,
! [X2: $tType] :
( group_add(X2)
=> ! [X16: X2] : ( vAPP(X2,X2,uminus_uminus(X2),vAPP(X2,X2,uminus_uminus(X2),X16)) = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_verit__minus__simplify_I4_J) ).
thf(f3229,plain,
spl136_128,
inference(avatar_split_clause,[],[f1481,f3227]) ).
thf(f3227,plain,
( spl136_128
<=> ! [X0: extended_ereal] :
( ( extended_MInfty = X0 )
| ( extended_PInfty = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK42,X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_128])]) ).
thf(f1481,plain,
! [X0: extended_ereal] :
( ( extended_MInfty = X0 )
| ( extended_PInfty = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK42,X0)) = X0 ) ),
inference(cnf_transformation,[],[f1184]) ).
thf(f1184,plain,
! [X0: extended_ereal] :
( ( extended_MInfty = X0 )
| ( extended_PInfty = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK42,X0)) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42])],[f912,f1183]) ).
thf(f1183,plain,
! [X0: extended_ereal] :
( ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 )
=> ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK42,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f912,plain,
! [X0: extended_ereal] :
( ( extended_MInfty = X0 )
| ( extended_PInfty = X0 )
| ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
inference(flattening,[],[f911]) ).
thf(f911,plain,
! [X0: extended_ereal] :
( ( extended_MInfty = X0 )
| ( extended_PInfty = X0 )
| ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
inference(ennf_transformation,[],[f874]) ).
thf(f874,plain,
! [X0: extended_ereal] :
( ! [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) != X0 )
=> ( ( extended_PInfty != X0 )
=> ( extended_MInfty = X0 ) ) ),
inference(rectify,[],[f207]) ).
thf(f207,axiom,
! [X27: extended_ereal] :
( ! [X70: real] : ( vAPP(real,extended_ereal,extended_ereal2,X70) != X27 )
=> ( ( extended_PInfty != X27 )
=> ( extended_MInfty = X27 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_ereal_Oexhaust) ).
thf(f3225,plain,
spl136_127,
inference(avatar_split_clause,[],[f1480,f3223]) ).
thf(f3223,plain,
( spl136_127
<=> ! [X0: extended_ereal] :
( ( extended_MInfty = X0 )
| ( extended_PInfty = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK41,X0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_127])]) ).
thf(f1480,plain,
! [X0: extended_ereal] :
( ( extended_MInfty = X0 )
| ( extended_PInfty = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK41,X0)) = X0 ) ),
inference(cnf_transformation,[],[f1182]) ).
thf(f1182,plain,
! [X0: extended_ereal] :
( ( extended_MInfty = X0 )
| ( extended_PInfty = X0 )
| ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK41,X0)) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f910,f1181]) ).
thf(f1181,plain,
! [X0: extended_ereal] :
( ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 )
=> ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK41,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f910,plain,
! [X0: extended_ereal] :
( ( extended_MInfty = X0 )
| ( extended_PInfty = X0 )
| ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
inference(flattening,[],[f909]) ).
thf(f909,plain,
! [X0: extended_ereal] :
( ( extended_MInfty = X0 )
| ( extended_PInfty = X0 )
| ? [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) = X0 ) ),
inference(ennf_transformation,[],[f873]) ).
thf(f873,plain,
! [X0: extended_ereal] :
( ! [X1: real] : ( vAPP(real,extended_ereal,extended_ereal2,X1) != X0 )
=> ( ( extended_PInfty != X0 )
=> ( extended_MInfty = X0 ) ) ),
inference(rectify,[],[f206]) ).
thf(f206,axiom,
! [X4: extended_ereal] :
( ! [X58: real] : ( vAPP(real,extended_ereal,extended_ereal2,X58) != X4 )
=> ( ( extended_PInfty != X4 )
=> ( extended_MInfty = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_uminus__ereal_Ocases) ).
thf(f3209,plain,
( spl136_126
| ~ spl136_31
| ~ spl136_93 ),
inference(avatar_split_clause,[],[f3009,f2980,f2628,f3207]) ).
thf(f3207,plain,
( spl136_126
<=> ! [X0: $tType] : ( $true = uminus(sTfun(X0,$o)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_126])]) ).
thf(f2628,plain,
( spl136_31
<=> ( uminus($o) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_31])]) ).
thf(f3009,plain,
( ! [X0: $tType] : ( $true = uminus(sTfun(X0,$o)) )
| ~ spl136_31
| ~ spl136_93 ),
inference(trivial_inequality_removal,[],[f3004]) ).
thf(f3004,plain,
( ! [X0: $tType] :
( ( $true != $true )
| ( $true = uminus(sTfun(X0,$o)) ) )
| ~ spl136_31
| ~ spl136_93 ),
inference(superposition,[],[f2981,f2630]) ).
thf(f2630,plain,
( ( uminus($o) = $true )
| ~ spl136_31 ),
inference(avatar_component_clause,[],[f2628]) ).
thf(f3201,plain,
spl136_125,
inference(avatar_split_clause,[],[f2341,f3199]) ).
thf(f3199,plain,
( spl136_125
<=> ! [X0: extended_ereal,X1: extended_ereal] :
( ( extended_PInfty = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP8,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_125])]) ).
thf(f2341,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extended_PInfty = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP8,X1),X0) ) ),
inference(forward_demodulation,[],[f1685,f1416]) ).
thf(f1685,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extend1396239628finity(extended_ereal) = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP8,X1),X0) ) ),
inference(cnf_transformation,[],[f1261]) ).
thf(f1261,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( ( extend1396239628finity(extended_ereal) = X0 )
& ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK75,X1)) = X1 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP8,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK75])],[f1259,f1260]) ).
thf(f1260,plain,
! [X1: extended_ereal] :
( ? [X2: real] : ( vAPP(real,extended_ereal,extended_ereal2,X2) = X1 )
=> ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK75,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
thf(f1259,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( ( extend1396239628finity(extended_ereal) = X0 )
& ? [X2: real] : ( vAPP(real,extended_ereal,extended_ereal2,X2) = X1 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP8,X1),X0) ) ),
inference(rectify,[],[f1258]) ).
thf(f1258,plain,
! [X1: extended_ereal,X0: extended_ereal] :
( ( ( extend1396239628finity(extended_ereal) = X1 )
& ? [X4: real] : ( vAPP(real,extended_ereal,extended_ereal2,X4) = X0 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP8,X0),X1) ) ),
inference(nnf_transformation,[],[f1145]) ).
thf(f1145,plain,
! [X1: extended_ereal,X0: extended_ereal] :
( ( ( extend1396239628finity(extended_ereal) = X1 )
& ? [X4: real] : ( vAPP(real,extended_ereal,extended_ereal2,X4) = X0 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP8,X0),X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3197,plain,
spl136_124,
inference(avatar_split_clause,[],[f2340,f3195]) ).
thf(f3195,plain,
( spl136_124
<=> ! [X0: extended_ereal,X1: extended_ereal] :
( ( extended_MInfty = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP9,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_124])]) ).
thf(f2340,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extended_MInfty = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP9,X1),X0) ) ),
inference(forward_demodulation,[],[f2339,f1419]) ).
thf(f2339,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP9,X1),X0) ) ),
inference(forward_demodulation,[],[f1683,f1416]) ).
thf(f1683,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP9,X1),X0) ) ),
inference(cnf_transformation,[],[f1257]) ).
thf(f1257,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
& ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK74,X1)) = X1 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP9,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK74])],[f1255,f1256]) ).
thf(f1256,plain,
! [X1: extended_ereal] :
( ? [X2: real] : ( vAPP(real,extended_ereal,extended_ereal2,X2) = X1 )
=> ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK74,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
thf(f1255,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
& ? [X2: real] : ( vAPP(real,extended_ereal,extended_ereal2,X2) = X1 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP9,X1),X0) ) ),
inference(rectify,[],[f1254]) ).
thf(f1254,plain,
! [X1: extended_ereal,X0: extended_ereal] :
( ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 )
& ? [X5: real] : ( vAPP(real,extended_ereal,extended_ereal2,X5) = X0 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP9,X0),X1) ) ),
inference(nnf_transformation,[],[f1146]) ).
thf(f1146,plain,
! [X1: extended_ereal,X0: extended_ereal] :
( ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 )
& ? [X5: real] : ( vAPP(real,extended_ereal,extended_ereal2,X5) = X0 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP9,X0),X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3193,plain,
spl136_123,
inference(avatar_split_clause,[],[f2338,f3191]) ).
thf(f3191,plain,
( spl136_123
<=> ! [X0: extended_ereal,X1: extended_ereal] :
( ( extended_PInfty = X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP10,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_123])]) ).
thf(f2338,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extended_PInfty = X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP10,X1),X0) ) ),
inference(forward_demodulation,[],[f1680,f1416]) ).
thf(f1680,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extend1396239628finity(extended_ereal) = X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP10,X1),X0) ) ),
inference(cnf_transformation,[],[f1253]) ).
thf(f1253,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK73,X0)) = X0 )
& ( extend1396239628finity(extended_ereal) = X1 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP10,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK73])],[f1251,f1252]) ).
thf(f1252,plain,
! [X0: extended_ereal] :
( ? [X2: real] : ( vAPP(real,extended_ereal,extended_ereal2,X2) = X0 )
=> ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK73,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f1251,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( ? [X2: real] : ( vAPP(real,extended_ereal,extended_ereal2,X2) = X0 )
& ( extend1396239628finity(extended_ereal) = X1 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP10,X1),X0) ) ),
inference(rectify,[],[f1250]) ).
thf(f1250,plain,
! [X1: extended_ereal,X0: extended_ereal] :
( ( ? [X6: real] : ( vAPP(real,extended_ereal,extended_ereal2,X6) = X1 )
& ( extend1396239628finity(extended_ereal) = X0 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP10,X0),X1) ) ),
inference(nnf_transformation,[],[f1147]) ).
thf(f1147,plain,
! [X1: extended_ereal,X0: extended_ereal] :
( ( ? [X6: real] : ( vAPP(real,extended_ereal,extended_ereal2,X6) = X1 )
& ( extend1396239628finity(extended_ereal) = X0 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP10,X0),X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3189,plain,
spl136_122,
inference(avatar_split_clause,[],[f2337,f3187]) ).
thf(f3187,plain,
( spl136_122
<=> ! [X0: extended_ereal,X1: extended_ereal] :
( ( extended_PInfty = X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_122])]) ).
thf(f2337,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extended_PInfty = X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X1),X0) ) ),
inference(forward_demodulation,[],[f1678,f1416]) ).
thf(f1678,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extend1396239628finity(extended_ereal) = X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X1),X0) ) ),
inference(cnf_transformation,[],[f1249]) ).
thf(f1249,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( ( extend1396239628finity(extended_ereal) = X0 )
& ( extend1396239628finity(extended_ereal) = X1 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X1),X0) ) ),
inference(rectify,[],[f1248]) ).
thf(f1248,plain,
! [X1: extended_ereal,X0: extended_ereal] :
( ( ( extend1396239628finity(extended_ereal) = X1 )
& ( extend1396239628finity(extended_ereal) = X0 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X0),X1) ) ),
inference(nnf_transformation,[],[f1148]) ).
thf(f1148,plain,
! [X1: extended_ereal,X0: extended_ereal] :
( ( ( extend1396239628finity(extended_ereal) = X1 )
& ( extend1396239628finity(extended_ereal) = X0 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X0),X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3185,plain,
spl136_121,
inference(avatar_split_clause,[],[f2336,f3183]) ).
thf(f3183,plain,
( spl136_121
<=> ! [X0: extended_ereal,X1: extended_ereal] :
( ( extended_PInfty = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_121])]) ).
thf(f2336,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extended_PInfty = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X1),X0) ) ),
inference(forward_demodulation,[],[f1679,f1416]) ).
thf(f1679,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extend1396239628finity(extended_ereal) = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP11,X1),X0) ) ),
inference(cnf_transformation,[],[f1249]) ).
thf(f3181,plain,
spl136_120,
inference(avatar_split_clause,[],[f2335,f3179]) ).
thf(f3179,plain,
( spl136_120
<=> ! [X0: extended_ereal,X1: extended_ereal] :
( ( extended_PInfty = X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_120])]) ).
thf(f2335,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extended_PInfty = X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X1),X0) ) ),
inference(forward_demodulation,[],[f1676,f1416]) ).
thf(f1676,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extend1396239628finity(extended_ereal) = X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X1),X0) ) ),
inference(cnf_transformation,[],[f1247]) ).
thf(f1247,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
& ( extend1396239628finity(extended_ereal) = X1 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X1),X0) ) ),
inference(rectify,[],[f1246]) ).
thf(f1246,plain,
! [X1: extended_ereal,X0: extended_ereal] :
( ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 )
& ( extend1396239628finity(extended_ereal) = X0 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X0),X1) ) ),
inference(nnf_transformation,[],[f1149]) ).
thf(f1149,plain,
! [X1: extended_ereal,X0: extended_ereal] :
( ( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 )
& ( extend1396239628finity(extended_ereal) = X0 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X0),X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3177,plain,
spl136_119,
inference(avatar_split_clause,[],[f2334,f3175]) ).
thf(f3175,plain,
( spl136_119
<=> ! [X0: extended_ereal,X1: extended_ereal] :
( ( extended_MInfty = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_119])]) ).
thf(f2334,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extended_MInfty = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X1),X0) ) ),
inference(forward_demodulation,[],[f2333,f1419]) ).
thf(f2333,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X1),X0) ) ),
inference(forward_demodulation,[],[f1677,f1416]) ).
thf(f1677,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP12,X1),X0) ) ),
inference(cnf_transformation,[],[f1247]) ).
thf(f3173,plain,
( spl136_118
| ~ spl136_32
| ~ spl136_93 ),
inference(avatar_split_clause,[],[f3008,f2980,f2633,f3171]) ).
thf(f3171,plain,
( spl136_118
<=> ! [X0: $tType] : ( $true = uminus(sTfun(X0,extended_ereal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_118])]) ).
thf(f2633,plain,
( spl136_32
<=> ( uminus(extended_ereal) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_32])]) ).
thf(f3008,plain,
( ! [X0: $tType] : ( $true = uminus(sTfun(X0,extended_ereal)) )
| ~ spl136_32
| ~ spl136_93 ),
inference(trivial_inequality_removal,[],[f3005]) ).
thf(f3005,plain,
( ! [X0: $tType] :
( ( $true != $true )
| ( $true = uminus(sTfun(X0,extended_ereal)) ) )
| ~ spl136_32
| ~ spl136_93 ),
inference(superposition,[],[f2981,f2635]) ).
thf(f2635,plain,
( ( uminus(extended_ereal) = $true )
| ~ spl136_32 ),
inference(avatar_component_clause,[],[f2633]) ).
thf(f3169,plain,
spl136_117,
inference(avatar_split_clause,[],[f2332,f3167]) ).
thf(f3167,plain,
( spl136_117
<=> ! [X0: extended_ereal,X1: extended_ereal] :
( ( extended_MInfty = X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP13,X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_117])]) ).
thf(f2332,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( extended_MInfty = X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP13,X1),X0) ) ),
inference(forward_demodulation,[],[f2331,f1419]) ).
thf(f2331,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) = X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP13,X1),X0) ) ),
inference(forward_demodulation,[],[f1674,f1416]) ).
thf(f1674,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP13,X1),X0) ) ),
inference(cnf_transformation,[],[f1245]) ).
thf(f1245,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK72,X0)) = X0 )
& ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP13,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72])],[f1243,f1244]) ).
thf(f1244,plain,
! [X0: extended_ereal] :
( ? [X2: real] : ( vAPP(real,extended_ereal,extended_ereal2,X2) = X0 )
=> ( vAPP(real,extended_ereal,extended_ereal2,vAPP(extended_ereal,real,sK72,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f1243,plain,
! [X0: extended_ereal,X1: extended_ereal] :
( ( ? [X2: real] : ( vAPP(real,extended_ereal,extended_ereal2,X2) = X0 )
& ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X1 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP13,X1),X0) ) ),
inference(rectify,[],[f1242]) ).
thf(f1242,plain,
! [X1: extended_ereal,X0: extended_ereal] :
( ( ? [X7: real] : ( vAPP(real,extended_ereal,extended_ereal2,X7) = X1 )
& ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP13,X0),X1) ) ),
inference(nnf_transformation,[],[f1150]) ).
thf(f1150,plain,
! [X1: extended_ereal,X0: extended_ereal] :
( ( ? [X7: real] : ( vAPP(real,extended_ereal,extended_ereal2,X7) = X1 )
& ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) = X0 ) )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),sP13,X0),X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3165,plain,
spl136_116,
inference(avatar_split_clause,[],[f1448,f3163]) ).
thf(f3163,plain,
( spl136_116
<=> ! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),zero_zero(extended_ereal)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_116])]) ).
thf(f1448,plain,
! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),zero_zero(extended_ereal)),X0) ),
inference(cnf_transformation,[],[f857]) ).
thf(f857,plain,
! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),zero_zero(extended_ereal)),X0) ),
inference(rectify,[],[f222]) ).
thf(f222,axiom,
! [X15: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),zero_zero(extended_ereal)),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_ereal__divide__zero__left) ).
thf(f3159,plain,
~ spl136_115,
inference(avatar_split_clause,[],[f2312,f3156]) ).
thf(f3156,plain,
( spl136_115
<=> ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),extended_MInfty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_115])]) ).
thf(f2312,plain,
$true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),extended_MInfty),
inference(forward_demodulation,[],[f2311,f1419]) ).
thf(f2311,plain,
$true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty)),
inference(forward_demodulation,[],[f1886,f1416]) ).
thf(f1886,plain,
$true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),
inference(equality_resolution,[],[f1607]) ).
thf(f1607,plain,
! [X0: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),X0) ) ),
inference(cnf_transformation,[],[f1037]) ).
thf(f1037,plain,
! [X0: extended_ereal] :
( ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X0 )
| ( $true != vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),X0) ) ),
inference(ennf_transformation,[],[f578]) ).
thf(f578,plain,
! [X0: extended_ereal] :
( ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),X0) )
=> ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X0 ) ),
inference(fool_elimination,[],[f577]) ).
thf(f577,plain,
! [X0: extended_ereal] :
( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),X0)
=> ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X0 ) ),
inference(rectify,[],[f133]) ).
thf(f133,axiom,
! [X4: extended_ereal] :
( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),zero_zero(extended_ereal)),X4)
=> ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)) != X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_not__MInfty__nonneg) ).
thf(f3154,plain,
spl136_114,
inference(avatar_split_clause,[],[f2263,f3152]) ).
thf(f3152,plain,
( spl136_114
<=> ! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),extended_MInfty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_114])]) ).
thf(f2263,plain,
! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),extended_MInfty) ),
inference(forward_demodulation,[],[f2262,f1419]) ).
thf(f2262,plain,
! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty)) ),
inference(forward_demodulation,[],[f1450,f1416]) ).
thf(f1450,plain,
! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))) ),
inference(cnf_transformation,[],[f859]) ).
thf(f859,plain,
! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))) ),
inference(rectify,[],[f230]) ).
thf(f230,axiom,
! [X4: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X4),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_ereal__divide__Infty_I2_J) ).
thf(f3150,plain,
spl136_113,
inference(avatar_split_clause,[],[f2261,f3148]) ).
thf(f3148,plain,
( spl136_113
<=> ! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),extended_PInfty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_113])]) ).
thf(f2261,plain,
! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),extended_PInfty) ),
inference(forward_demodulation,[],[f1447,f1416]) ).
thf(f1447,plain,
! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),extend1396239628finity(extended_ereal)) ),
inference(cnf_transformation,[],[f856]) ).
thf(f856,plain,
! [X0: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X0),extend1396239628finity(extended_ereal)) ),
inference(rectify,[],[f228]) ).
thf(f228,axiom,
! [X4: extended_ereal] : ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,vAPP(extended_ereal,sTfun(extended_ereal,extended_ereal),divide_divide(extended_ereal),X4),extend1396239628finity(extended_ereal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_ereal__divide__Infty_I1_J) ).
thf(f3146,plain,
spl136_112,
inference(avatar_split_clause,[],[f1617,f3144]) ).
thf(f3144,plain,
( spl136_112
<=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_112])]) ).
thf(f1617,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0) ),
inference(cnf_transformation,[],[f590]) ).
thf(f590,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0) ),
inference(fool_elimination,[],[f589]) ).
thf(f589,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X0),
inference(rectify,[],[f147]) ).
thf(f147,axiom,
! [X36: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),zero_zero(nat)),X36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_less__eq__nat_Osimps_I1_J) ).
thf(f3142,plain,
spl136_111,
inference(avatar_split_clause,[],[f1616,f3140]) ).
thf(f3140,plain,
( spl136_111
<=> ! [X0: extended_enat] : ( $true = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less_eq(extended_enat),zero_zero(extended_enat)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_111])]) ).
thf(f1616,plain,
! [X0: extended_enat] : ( $true = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less_eq(extended_enat),zero_zero(extended_enat)),X0) ),
inference(cnf_transformation,[],[f588]) ).
thf(f588,plain,
! [X0: extended_enat] : ( $true = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less_eq(extended_enat),zero_zero(extended_enat)),X0) ),
inference(fool_elimination,[],[f587]) ).
thf(f587,plain,
! [X0: extended_enat] : vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less_eq(extended_enat),zero_zero(extended_enat)),X0),
inference(rectify,[],[f67]) ).
thf(f67,axiom,
! [X36: extended_enat] : vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less_eq(extended_enat),zero_zero(extended_enat)),X36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_i0__lb) ).
thf(f3126,plain,
spl136_110,
inference(avatar_split_clause,[],[f2315,f3124]) ).
thf(f3124,plain,
( spl136_110
<=> ! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),extended_MInfty),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_110])]) ).
thf(f2315,plain,
! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),extended_MInfty),X0) ),
inference(forward_demodulation,[],[f2314,f1419]) ).
thf(f2314,plain,
! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty)),X0) ),
inference(forward_demodulation,[],[f1623,f1416]) ).
thf(f1623,plain,
! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),X0) ),
inference(cnf_transformation,[],[f602]) ).
thf(f602,plain,
! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),X0) ),
inference(fool_elimination,[],[f601]) ).
thf(f601,plain,
! [X0: extended_ereal] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),X0),
inference(rectify,[],[f129]) ).
thf(f129,axiom,
! [X4: extended_ereal] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_ereal__less__eq_I2_J) ).
thf(f3122,plain,
spl136_109,
inference(avatar_split_clause,[],[f2313,f3120]) ).
thf(f3120,plain,
( spl136_109
<=> ! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),extended_PInfty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_109])]) ).
thf(f2313,plain,
! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),extended_PInfty) ),
inference(forward_demodulation,[],[f1620,f1416]) ).
thf(f1620,plain,
! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),extend1396239628finity(extended_ereal)) ),
inference(cnf_transformation,[],[f596]) ).
thf(f596,plain,
! [X0: extended_ereal] : ( $true = vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),extend1396239628finity(extended_ereal)) ),
inference(fool_elimination,[],[f595]) ).
thf(f595,plain,
! [X0: extended_ereal] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X0),extend1396239628finity(extended_ereal)),
inference(rectify,[],[f60]) ).
thf(f60,axiom,
! [X4: extended_ereal] : vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),X4),extend1396239628finity(extended_ereal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_ereal__less__eq_I1_J) ).
thf(f3118,plain,
( spl136_108
| ~ spl136_34
| ~ spl136_79 ),
inference(avatar_split_clause,[],[f2929,f2895,f2643,f3115]) ).
thf(f3115,plain,
( spl136_108
<=> ( $true = type(real) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_108])]) ).
thf(f2643,plain,
( spl136_34
<=> ( real_V2090557954_space(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_34])]) ).
thf(f2895,plain,
( spl136_79
<=> ! [X0: $tType] :
( ( type(X0) = $true )
| ( real_V2090557954_space(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_79])]) ).
thf(f2929,plain,
( ( $true = type(real) )
| ~ spl136_34
| ~ spl136_79 ),
inference(trivial_inequality_removal,[],[f2926]) ).
thf(f2926,plain,
( ( $true != $true )
| ( $true = type(real) )
| ~ spl136_34
| ~ spl136_79 ),
inference(superposition,[],[f2896,f2645]) ).
thf(f2645,plain,
( ( real_V2090557954_space(real) = $true )
| ~ spl136_34 ),
inference(avatar_component_clause,[],[f2643]) ).
thf(f2896,plain,
( ! [X0: $tType] :
( ( real_V2090557954_space(X0) != $true )
| ( type(X0) = $true ) )
| ~ spl136_79 ),
inference(avatar_component_clause,[],[f2895]) ).
thf(f3113,plain,
spl136_107,
inference(avatar_split_clause,[],[f1615,f3111]) ).
thf(f3111,plain,
( spl136_107
<=> ! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_107])]) ).
thf(f1615,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0) ),
inference(cnf_transformation,[],[f586]) ).
thf(f586,plain,
! [X0: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0) ),
inference(fool_elimination,[],[f585]) ).
thf(f585,plain,
! [X0: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0),
inference(rectify,[],[f134]) ).
thf(f134,axiom,
! [X36: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X36),X36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_le__refl) ).
thf(f3109,plain,
spl136_106,
inference(avatar_split_clause,[],[f1566,f3107]) ).
thf(f3107,plain,
( spl136_106
<=> ! [X0: $tType] :
( ( zero_zero(X0) = vAPP(X0,X0,abs_abs(X0),zero_zero(X0)) )
| ( ordere142940540dd_abs(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_106])]) ).
thf(f1566,plain,
! [X0: $tType] :
( ( zero_zero(X0) = vAPP(X0,X0,abs_abs(X0),zero_zero(X0)) )
| ( ordere142940540dd_abs(X0) != $true ) ),
inference(cnf_transformation,[],[f990]) ).
thf(f990,plain,
! [X0: $tType] :
( ( zero_zero(X0) = vAPP(X0,X0,abs_abs(X0),zero_zero(X0)) )
| ( ordere142940540dd_abs(X0) != $true ) ),
inference(ennf_transformation,[],[f506]) ).
thf(f506,plain,
! [X0: $tType] :
( ( ordere142940540dd_abs(X0) = $true )
=> ( zero_zero(X0) = vAPP(X0,X0,abs_abs(X0),zero_zero(X0)) ) ),
inference(fool_elimination,[],[f505]) ).
thf(f505,plain,
! [X0: $tType] :
( ordere142940540dd_abs(X0)
=> ( zero_zero(X0) = vAPP(X0,X0,abs_abs(X0),zero_zero(X0)) ) ),
inference(rectify,[],[f214]) ).
thf(f214,axiom,
! [X0: $tType] :
( ordere142940540dd_abs(X0)
=> ( zero_zero(X0) = vAPP(X0,X0,abs_abs(X0),zero_zero(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_abs__zero) ).
thf(f3105,plain,
spl136_105,
inference(avatar_split_clause,[],[f1520,f3103]) ).
thf(f3103,plain,
( spl136_105
<=> ! [X0: $tType] :
( ( zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0)) )
| ( group_add(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_105])]) ).
thf(f1520,plain,
! [X0: $tType] :
( ( zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0)) )
| ( group_add(X0) != $true ) ),
inference(cnf_transformation,[],[f955]) ).
thf(f955,plain,
! [X0: $tType] :
( ( zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0)) )
| ( group_add(X0) != $true ) ),
inference(ennf_transformation,[],[f442]) ).
thf(f442,plain,
! [X0: $tType] :
( ( group_add(X0) = $true )
=> ( zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0)) ) ),
inference(fool_elimination,[],[f441]) ).
thf(f441,plain,
! [X0: $tType] :
( group_add(X0)
=> ( zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0)) ) ),
inference(rectify,[],[f93]) ).
thf(f93,axiom,
! [X0: $tType] :
( group_add(X0)
=> ( zero_zero(X0) = vAPP(X0,X0,uminus_uminus(X0),zero_zero(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add_Oinverse__neutral) ).
thf(f3101,plain,
spl136_104,
inference(avatar_split_clause,[],[f1488,f3099]) ).
thf(f3099,plain,
( spl136_104
<=> ! [X0: $tType] :
( ( zero_zero(X0) = vAPP(X0,X0,neg_numeral_dbl(X0),zero_zero(X0)) )
| ( neg_numeral(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_104])]) ).
thf(f1488,plain,
! [X0: $tType] :
( ( zero_zero(X0) = vAPP(X0,X0,neg_numeral_dbl(X0),zero_zero(X0)) )
| ( neg_numeral(X0) != $true ) ),
inference(cnf_transformation,[],[f922]) ).
thf(f922,plain,
! [X0: $tType] :
( ( zero_zero(X0) = vAPP(X0,X0,neg_numeral_dbl(X0),zero_zero(X0)) )
| ( neg_numeral(X0) != $true ) ),
inference(ennf_transformation,[],[f378]) ).
thf(f378,plain,
! [X0: $tType] :
( ( neg_numeral(X0) = $true )
=> ( zero_zero(X0) = vAPP(X0,X0,neg_numeral_dbl(X0),zero_zero(X0)) ) ),
inference(fool_elimination,[],[f377]) ).
thf(f377,plain,
! [X0: $tType] :
( neg_numeral(X0)
=> ( zero_zero(X0) = vAPP(X0,X0,neg_numeral_dbl(X0),zero_zero(X0)) ) ),
inference(rectify,[],[f164]) ).
thf(f164,axiom,
! [X0: $tType] :
( neg_numeral(X0)
=> ( zero_zero(X0) = vAPP(X0,X0,neg_numeral_dbl(X0),zero_zero(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_dbl__simps_I2_J) ).
thf(f3093,plain,
spl136_103,
inference(avatar_split_clause,[],[f1492,f3091]) ).
thf(f3091,plain,
( spl136_103
<=> ! [X0: $tType,X1: num] :
( ( zero_zero(X0) != vAPP(num,X0,numeral_numeral(X0),X1) )
| ( semiring_char_0(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_103])]) ).
thf(f1492,plain,
! [X0: $tType,X1: num] :
( ( zero_zero(X0) != vAPP(num,X0,numeral_numeral(X0),X1) )
| ( semiring_char_0(X0) != $true ) ),
inference(cnf_transformation,[],[f926]) ).
thf(f926,plain,
! [X0: $tType] :
( ! [X1: num] : ( zero_zero(X0) != vAPP(num,X0,numeral_numeral(X0),X1) )
| ( semiring_char_0(X0) != $true ) ),
inference(ennf_transformation,[],[f386]) ).
thf(f386,plain,
! [X0: $tType] :
( ( semiring_char_0(X0) = $true )
=> ! [X1: num] : ( zero_zero(X0) != vAPP(num,X0,numeral_numeral(X0),X1) ) ),
inference(fool_elimination,[],[f385]) ).
thf(f385,plain,
! [X0: $tType] :
( semiring_char_0(X0)
=> ! [X1: num] : ( zero_zero(X0) != vAPP(num,X0,numeral_numeral(X0),X1) ) ),
inference(rectify,[],[f72]) ).
thf(f72,axiom,
! [X0: $tType] :
( semiring_char_0(X0)
=> ! [X36: num] : ( vAPP(num,X0,numeral_numeral(X0),X36) != zero_zero(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_zero__neq__numeral) ).
thf(f3089,plain,
spl136_102,
inference(avatar_split_clause,[],[f1446,f3087]) ).
thf(f3087,plain,
( spl136_102
<=> ! [X0: extended_ereal] : ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_102])]) ).
thf(f1446,plain,
! [X0: extended_ereal] : ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) = X0 ),
inference(cnf_transformation,[],[f855]) ).
thf(f855,plain,
! [X0: extended_ereal] : ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X0)) = X0 ),
inference(rectify,[],[f154]) ).
thf(f154,axiom,
! [X15: extended_ereal] : ( vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),X15)) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_ereal__uminus__uminus) ).
thf(f3084,plain,
spl136_101,
inference(avatar_split_clause,[],[f1444,f3082]) ).
thf(f3082,plain,
( spl136_101
<=> ! [X0: real] : ( zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,vAPP(real,extended_ereal,extended_ereal2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_101])]) ).
thf(f1444,plain,
! [X0: real] : ( zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,vAPP(real,extended_ereal,extended_ereal2,X0)) ),
inference(cnf_transformation,[],[f853]) ).
thf(f853,plain,
! [X0: real] : ( zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,vAPP(real,extended_ereal,extended_ereal2,X0)) ),
inference(rectify,[],[f199]) ).
thf(f199,axiom,
! [X52: real] : ( zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,vAPP(real,extended_ereal,extended_ereal2,X52)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_ereal_Osize__gen_I1_J) ).
thf(f3076,plain,
spl136_100,
inference(avatar_split_clause,[],[f1443,f3074]) ).
thf(f3074,plain,
( spl136_100
<=> ! [X0: real] : ( vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(real,extended_ereal,extended_ereal2,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_100])]) ).
thf(f1443,plain,
! [X0: real] : ( vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(real,extended_ereal,extended_ereal2,X0)) = X0 ),
inference(cnf_transformation,[],[f852]) ).
thf(f852,plain,
! [X0: real] : ( vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(real,extended_ereal,extended_ereal2,X0)) = X0 ),
inference(rectify,[],[f175]) ).
thf(f175,axiom,
! [X41: real] : ( vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(real,extended_ereal,extended_ereal2,X41)) = X41 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_real__of__ereal_Osimps_I1_J) ).
thf(f3072,plain,
spl136_99,
inference(avatar_split_clause,[],[f1442,f3070]) ).
thf(f3070,plain,
( spl136_99
<=> ! [X0: nat] : ( vAPP(extended_enat,nat,extended_the_enat,vAPP(nat,extended_enat,extended_enat2,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_99])]) ).
thf(f1442,plain,
! [X0: nat] : ( vAPP(extended_enat,nat,extended_the_enat,vAPP(nat,extended_enat,extended_enat2,X0)) = X0 ),
inference(cnf_transformation,[],[f851]) ).
thf(f851,plain,
! [X0: nat] : ( vAPP(extended_enat,nat,extended_the_enat,vAPP(nat,extended_enat,extended_enat2,X0)) = X0 ),
inference(rectify,[],[f149]) ).
thf(f149,axiom,
! [X36: nat] : ( vAPP(extended_enat,nat,extended_the_enat,vAPP(nat,extended_enat,extended_enat2,X36)) = X36 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_the__enat_Osimps) ).
thf(f3002,plain,
spl136_98,
inference(avatar_split_clause,[],[f1711,f3000]) ).
thf(f3000,plain,
( spl136_98
<=> ! [X1: $tType,X0: $tType] :
( ( $true = order(sTfun(X0,X1)) )
| ( $true != order(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_98])]) ).
thf(f1711,plain,
! [X1: $tType,X0: $tType] :
( ( $true = order(sTfun(X0,X1)) )
| ( $true != order(X1) ) ),
inference(cnf_transformation,[],[f1097]) ).
thf(f1097,plain,
! [X0: $tType,X1: $tType] :
( ( $true = order(sTfun(X0,X1)) )
| ( $true != order(X1) ) ),
inference(ennf_transformation,[],[f684]) ).
thf(f684,plain,
! [X0: $tType,X1: $tType] :
( ( $true = order(X1) )
=> ( $true = order(sTfun(X0,X1)) ) ),
inference(fool_elimination,[],[f683]) ).
thf(f683,plain,
! [X0: $tType,X1: $tType] :
( order(X1)
=> order(sTfun(X0,X1)) ),
inference(rectify,[],[f258]) ).
thf(f258,axiom,
! [X73: $tType,X74: $tType] :
( order(X74)
=> order(sTfun(X73,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(f2998,plain,
spl136_97,
inference(avatar_split_clause,[],[f1710,f2996]) ).
thf(f2996,plain,
( spl136_97
<=> ! [X1: $tType,X0: $tType] :
( ( $true = ord(sTfun(X0,X1)) )
| ( $true != ord(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_97])]) ).
thf(f1710,plain,
! [X1: $tType,X0: $tType] :
( ( $true = ord(sTfun(X0,X1)) )
| ( $true != ord(X1) ) ),
inference(cnf_transformation,[],[f1096]) ).
thf(f1096,plain,
! [X0: $tType,X1: $tType] :
( ( $true = ord(sTfun(X0,X1)) )
| ( $true != ord(X1) ) ),
inference(ennf_transformation,[],[f682]) ).
thf(f682,plain,
! [X0: $tType,X1: $tType] :
( ( $true = ord(X1) )
=> ( $true = ord(sTfun(X0,X1)) ) ),
inference(fool_elimination,[],[f681]) ).
thf(f681,plain,
! [X0: $tType,X1: $tType] :
( ord(X1)
=> ord(sTfun(X0,X1)) ),
inference(rectify,[],[f259]) ).
thf(f259,axiom,
! [X73: $tType,X74: $tType] :
( ord(X74)
=> ord(sTfun(X73,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(f2994,plain,
spl136_96,
inference(avatar_split_clause,[],[f1705,f2992]) ).
thf(f2992,plain,
( spl136_96
<=> ! [X1: $tType,X0: $tType] :
( ( $true = preorder(sTfun(X0,X1)) )
| ( $true != preorder(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_96])]) ).
thf(f1705,plain,
! [X1: $tType,X0: $tType] :
( ( $true = preorder(sTfun(X0,X1)) )
| ( $true != preorder(X1) ) ),
inference(cnf_transformation,[],[f1091]) ).
thf(f1091,plain,
! [X0: $tType,X1: $tType] :
( ( $true = preorder(sTfun(X0,X1)) )
| ( $true != preorder(X1) ) ),
inference(ennf_transformation,[],[f672]) ).
thf(f672,plain,
! [X0: $tType,X1: $tType] :
( ( $true = preorder(X1) )
=> ( $true = preorder(sTfun(X0,X1)) ) ),
inference(fool_elimination,[],[f671]) ).
thf(f671,plain,
! [X0: $tType,X1: $tType] :
( preorder(X1)
=> preorder(sTfun(X0,X1)) ),
inference(rectify,[],[f257]) ).
thf(f257,axiom,
! [X73: $tType,X74: $tType] :
( preorder(X74)
=> preorder(sTfun(X73,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(f2990,plain,
spl136_95,
inference(avatar_split_clause,[],[f1704,f2988]) ).
thf(f1704,plain,
! [X1: $tType,X0: $tType] :
( ( $true = topolo503727757_space(sTfun(X0,X1)) )
| ( $true != topolo503727757_space(X1) ) ),
inference(cnf_transformation,[],[f1090]) ).
thf(f1090,plain,
! [X0: $tType,X1: $tType] :
( ( $true = topolo503727757_space(sTfun(X0,X1)) )
| ( $true != topolo503727757_space(X1) ) ),
inference(ennf_transformation,[],[f670]) ).
thf(f670,plain,
! [X0: $tType,X1: $tType] :
( ( $true = topolo503727757_space(X1) )
=> ( $true = topolo503727757_space(sTfun(X0,X1)) ) ),
inference(fool_elimination,[],[f669]) ).
thf(f669,plain,
! [X0: $tType,X1: $tType] :
( topolo503727757_space(X1)
=> topolo503727757_space(sTfun(X0,X1)) ),
inference(rectify,[],[f255]) ).
thf(f255,axiom,
! [X73: $tType,X74: $tType] :
( topolo503727757_space(X74)
=> topolo503727757_space(sTfun(X73,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Topological__Spaces_Otopological__space) ).
thf(f2986,plain,
spl136_94,
inference(avatar_split_clause,[],[f1703,f2984]) ).
thf(f1703,plain,
! [X1: $tType,X0: $tType] :
( ( $true = boolean_algebra(sTfun(X0,X1)) )
| ( $true != boolean_algebra(X1) ) ),
inference(cnf_transformation,[],[f1089]) ).
thf(f1089,plain,
! [X0: $tType,X1: $tType] :
( ( $true = boolean_algebra(sTfun(X0,X1)) )
| ( $true != boolean_algebra(X1) ) ),
inference(ennf_transformation,[],[f668]) ).
thf(f668,plain,
! [X0: $tType,X1: $tType] :
( ( $true = boolean_algebra(X1) )
=> ( $true = boolean_algebra(sTfun(X0,X1)) ) ),
inference(fool_elimination,[],[f667]) ).
thf(f667,plain,
! [X0: $tType,X1: $tType] :
( boolean_algebra(X1)
=> boolean_algebra(sTfun(X0,X1)) ),
inference(rectify,[],[f256]) ).
thf(f256,axiom,
! [X73: $tType,X74: $tType] :
( boolean_algebra(X74)
=> boolean_algebra(sTfun(X73,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Oboolean__algebra) ).
thf(f2982,plain,
spl136_93,
inference(avatar_split_clause,[],[f1702,f2980]) ).
thf(f1702,plain,
! [X1: $tType,X0: $tType] :
( ( $true = uminus(sTfun(X0,X1)) )
| ( $true != uminus(X1) ) ),
inference(cnf_transformation,[],[f1088]) ).
thf(f1088,plain,
! [X0: $tType,X1: $tType] :
( ( $true = uminus(sTfun(X0,X1)) )
| ( $true != uminus(X1) ) ),
inference(ennf_transformation,[],[f666]) ).
thf(f666,plain,
! [X0: $tType,X1: $tType] :
( ( $true = uminus(X1) )
=> ( $true = uminus(sTfun(X0,X1)) ) ),
inference(fool_elimination,[],[f665]) ).
thf(f665,plain,
! [X0: $tType,X1: $tType] :
( uminus(X1)
=> uminus(sTfun(X0,X1)) ),
inference(rectify,[],[f260]) ).
thf(f260,axiom,
! [X73: $tType,X74: $tType] :
( uminus(X74)
=> uminus(sTfun(X73,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Groups_Ouminus) ).
thf(f2978,plain,
spl136_92,
inference(avatar_split_clause,[],[f1431,f2975]) ).
thf(f2975,plain,
( spl136_92
<=> ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),zero_zero(extended_ereal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_92])]) ).
thf(f1431,plain,
zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),zero_zero(extended_ereal)),
inference(cnf_transformation,[],[f84]) ).
thf(f84,axiom,
zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),zero_zero(extended_ereal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_ereal__uminus__zero) ).
thf(f2973,plain,
spl136_91,
inference(avatar_split_clause,[],[f1430,f2970]) ).
thf(f2970,plain,
( spl136_91
<=> ( zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),zero_zero(extended_ereal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_91])]) ).
thf(f1430,plain,
zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),zero_zero(extended_ereal)),
inference(cnf_transformation,[],[f220]) ).
thf(f220,axiom,
zero_zero(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),zero_zero(extended_ereal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_abs__ereal__zero) ).
thf(f2968,plain,
( spl136_90
| ~ spl136_3
| ~ spl136_80 ),
inference(avatar_split_clause,[],[f2936,f2899,f2488,f2965]) ).
thf(f2965,plain,
( spl136_90
<=> ( $true = topolo503727757_space(a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_90])]) ).
thf(f2488,plain,
( spl136_3
<=> ( real_V2090557954_space(a) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_3])]) ).
thf(f2899,plain,
( spl136_80
<=> ! [X0: $tType] :
( ( topolo503727757_space(X0) = $true )
| ( real_V2090557954_space(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_80])]) ).
thf(f2936,plain,
( ( $true = topolo503727757_space(a) )
| ~ spl136_3
| ~ spl136_80 ),
inference(trivial_inequality_removal,[],[f2931]) ).
thf(f2931,plain,
( ( $true != $true )
| ( $true = topolo503727757_space(a) )
| ~ spl136_3
| ~ spl136_80 ),
inference(superposition,[],[f2900,f2490]) ).
thf(f2490,plain,
( ( real_V2090557954_space(a) = $true )
| ~ spl136_3 ),
inference(avatar_component_clause,[],[f2488]) ).
thf(f2900,plain,
( ! [X0: $tType] :
( ( real_V2090557954_space(X0) != $true )
| ( topolo503727757_space(X0) = $true ) )
| ~ spl136_80 ),
inference(avatar_component_clause,[],[f2899]) ).
thf(f2961,plain,
spl136_89,
inference(avatar_split_clause,[],[f1426,f2958]) ).
thf(f2958,plain,
( spl136_89
<=> ( zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,zero_zero(real)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_89])]) ).
thf(f1426,plain,
zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,zero_zero(real)),
inference(cnf_transformation,[],[f178]) ).
thf(f178,axiom,
zero_zero(extended_ereal) = vAPP(real,extended_ereal,extended_ereal2,zero_zero(real)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_zero__ereal__def) ).
thf(f2956,plain,
spl136_88,
inference(avatar_split_clause,[],[f1425,f2953]) ).
thf(f2953,plain,
( spl136_88
<=> ( zero_zero(extended_ereal) = vAPP(extended_enat,extended_ereal,extend1771934483f_enat,zero_zero(extended_enat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_88])]) ).
thf(f1425,plain,
zero_zero(extended_ereal) = vAPP(extended_enat,extended_ereal,extend1771934483f_enat,zero_zero(extended_enat)),
inference(cnf_transformation,[],[f54]) ).
thf(f54,axiom,
zero_zero(extended_ereal) = vAPP(extended_enat,extended_ereal,extend1771934483f_enat,zero_zero(extended_enat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_ereal__of__enat__zero) ).
thf(f2951,plain,
spl136_87,
inference(avatar_split_clause,[],[f1423,f2948]) ).
thf(f2948,plain,
( spl136_87
<=> ( zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,zero_zero(extended_ereal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_87])]) ).
thf(f1423,plain,
zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,zero_zero(extended_ereal)),
inference(cnf_transformation,[],[f102]) ).
thf(f102,axiom,
zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,zero_zero(extended_ereal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_real__of__ereal__0) ).
thf(f2946,plain,
spl136_86,
inference(avatar_split_clause,[],[f1422,f2943]) ).
thf(f2943,plain,
( spl136_86
<=> ( zero_zero(extended_enat) = vAPP(nat,extended_enat,extended_enat2,zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_86])]) ).
thf(f1422,plain,
zero_zero(extended_enat) = vAPP(nat,extended_enat,extended_enat2,zero_zero(nat)),
inference(cnf_transformation,[],[f115]) ).
thf(f115,axiom,
zero_zero(extended_enat) = vAPP(nat,extended_enat,extended_enat2,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_zero__enat__def) ).
thf(f2941,plain,
( spl136_85
| ~ spl136_3
| ~ spl136_79 ),
inference(avatar_split_clause,[],[f2930,f2895,f2488,f2938]) ).
thf(f2938,plain,
( spl136_85
<=> ( $true = type(a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_85])]) ).
thf(f2930,plain,
( ( $true = type(a) )
| ~ spl136_3
| ~ spl136_79 ),
inference(trivial_inequality_removal,[],[f2925]) ).
thf(f2925,plain,
( ( $true != $true )
| ( $true = type(a) )
| ~ spl136_3
| ~ spl136_79 ),
inference(superposition,[],[f2896,f2490]) ).
thf(f2924,plain,
spl136_84,
inference(avatar_split_clause,[],[f2253,f2921]) ).
thf(f2921,plain,
( spl136_84
<=> ( extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),extended_MInfty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_84])]) ).
thf(f2253,plain,
extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),extended_MInfty),
inference(forward_demodulation,[],[f2252,f1419]) ).
thf(f2252,plain,
extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty)),
inference(forward_demodulation,[],[f1434,f1416]) ).
thf(f1434,plain,
extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),
inference(cnf_transformation,[],[f233]) ).
thf(f233,axiom,
extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_abs__ereal_Osimps_I2_J) ).
thf(f2919,plain,
spl136_83,
inference(avatar_split_clause,[],[f2251,f2916]) ).
thf(f2916,plain,
( spl136_83
<=> ( zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,extended_MInfty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_83])]) ).
thf(f2251,plain,
zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,extended_MInfty),
inference(forward_demodulation,[],[f2250,f1419]) ).
thf(f2250,plain,
zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty)),
inference(forward_demodulation,[],[f1433,f1416]) ).
thf(f1433,plain,
zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),
inference(cnf_transformation,[],[f104]) ).
thf(f104,axiom,
zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_real__of__ereal_Osimps_I3_J) ).
thf(f2911,plain,
spl136_82,
inference(avatar_split_clause,[],[f2249,f2908]) ).
thf(f2908,plain,
( spl136_82
<=> ( extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),extended_PInfty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_82])]) ).
thf(f2249,plain,
extended_PInfty = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),extended_PInfty),
inference(forward_demodulation,[],[f1432,f1416]) ).
thf(f1432,plain,
extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),extend1396239628finity(extended_ereal)),
inference(cnf_transformation,[],[f245]) ).
thf(f245,axiom,
extend1396239628finity(extended_ereal) = vAPP(extended_ereal,extended_ereal,abs_abs(extended_ereal),extend1396239628finity(extended_ereal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_abs__ereal_Osimps_I3_J) ).
thf(f2906,plain,
spl136_81,
inference(avatar_split_clause,[],[f2243,f2903]) ).
thf(f2903,plain,
( spl136_81
<=> ( zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,extended_PInfty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_81])]) ).
thf(f2243,plain,
zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,extended_PInfty),
inference(forward_demodulation,[],[f1424,f1416]) ).
thf(f1424,plain,
zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,extend1396239628finity(extended_ereal)),
inference(cnf_transformation,[],[f109]) ).
thf(f109,axiom,
zero_zero(real) = vAPP(extended_ereal,real,extend1716541707_ereal,extend1396239628finity(extended_ereal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_real__of__ereal_Osimps_I2_J) ).
thf(f2901,plain,
spl136_80,
inference(avatar_split_clause,[],[f1519,f2899]) ).
thf(f1519,plain,
! [X0: $tType] :
( ( topolo503727757_space(X0) = $true )
| ( real_V2090557954_space(X0) != $true ) ),
inference(cnf_transformation,[],[f954]) ).
thf(f954,plain,
! [X0: $tType] :
( ( topolo503727757_space(X0) = $true )
| ( real_V2090557954_space(X0) != $true ) ),
inference(ennf_transformation,[],[f440]) ).
thf(f440,plain,
! [X0: $tType] :
( ( real_V2090557954_space(X0) = $true )
=> ( topolo503727757_space(X0) = $true ) ),
inference(fool_elimination,[],[f439]) ).
thf(f439,plain,
! [X0: $tType] :
( real_V2090557954_space(X0)
=> topolo503727757_space(X0) ),
inference(rectify,[],[f254]) ).
thf(f254,axiom,
! [X0: $tType] :
( real_V2090557954_space(X0)
=> topolo503727757_space(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Real__Vector__Spaces_Ometric__space___Topological__Spaces_Otopological__space) ).
thf(f2897,plain,
spl136_79,
inference(avatar_split_clause,[],[f1518,f2895]) ).
thf(f1518,plain,
! [X0: $tType] :
( ( type(X0) = $true )
| ( real_V2090557954_space(X0) != $true ) ),
inference(cnf_transformation,[],[f953]) ).
thf(f953,plain,
! [X0: $tType] :
( ( type(X0) = $true )
| ( real_V2090557954_space(X0) != $true ) ),
inference(ennf_transformation,[],[f438]) ).
thf(f438,plain,
! [X0: $tType] :
( ( real_V2090557954_space(X0) = $true )
=> ( type(X0) = $true ) ),
inference(fool_elimination,[],[f437]) ).
thf(f437,plain,
! [X0: $tType] :
( real_V2090557954_space(X0)
=> type(X0) ),
inference(rectify,[],[f253]) ).
thf(f253,axiom,
! [X0: $tType] :
( real_V2090557954_space(X0)
=> type(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Real__Vector__Spaces_Ometric__space___HOL_Otype) ).
thf(f2893,plain,
spl136_78,
inference(avatar_split_clause,[],[f1421,f2890]) ).
thf(f2890,plain,
( spl136_78
<=> ( zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,extended_PInfty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_78])]) ).
thf(f1421,plain,
zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,extended_PInfty),
inference(cnf_transformation,[],[f202]) ).
thf(f202,axiom,
zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,extended_PInfty),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_ereal_Osize__gen_I2_J) ).
thf(f2888,plain,
spl136_77,
inference(avatar_split_clause,[],[f1420,f2885]) ).
thf(f2885,plain,
( spl136_77
<=> ( zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,extended_MInfty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_77])]) ).
thf(f1420,plain,
zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,extended_MInfty),
inference(cnf_transformation,[],[f198]) ).
thf(f198,axiom,
zero_zero(nat) = vAPP(extended_ereal,nat,extended_size_ereal,extended_MInfty),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_ereal_Osize__gen_I3_J) ).
thf(f2883,plain,
spl136_76,
inference(avatar_split_clause,[],[f1419,f2880]) ).
thf(f2880,plain,
( spl136_76
<=> ( extended_MInfty = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_76])]) ).
thf(f2878,plain,
spl136_75,
inference(avatar_split_clause,[],[f1418,f2875]) ).
thf(f2875,plain,
( spl136_75
<=> ( extended_PInfty = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_MInfty) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_75])]) ).
thf(f1418,plain,
extended_PInfty = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_MInfty),
inference(cnf_transformation,[],[f210]) ).
thf(f210,axiom,
extended_PInfty = vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_MInfty),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_uminus__ereal_Osimps_I3_J) ).
thf(f2873,plain,
( spl136_74
| spl136_70
| ~ spl136_71 ),
inference(avatar_split_clause,[],[f2842,f2828,f2823,f2870]) ).
thf(f2828,plain,
( spl136_71
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_71])]) ).
thf(f2842,plain,
( ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) = $false )
| spl136_70
| ~ spl136_71 ),
inference(trivial_inequality_removal,[],[f2840]) ).
thf(f2840,plain,
( ( $true != $true )
| ( vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) = $false )
| spl136_70
| ~ spl136_71 ),
inference(superposition,[],[f2825,f2829]) ).
thf(f2829,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) )
| ~ spl136_71 ),
inference(avatar_component_clause,[],[f2828]) ).
thf(f2868,plain,
spl136_73,
inference(avatar_split_clause,[],[f1440,f2866]) ).
thf(f2866,plain,
( spl136_73
<=> ! [X0: real] : ( extended_PInfty != vAPP(real,extended_ereal,extended_ereal2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_73])]) ).
thf(f1440,plain,
! [X0: real] : ( extended_PInfty != vAPP(real,extended_ereal,extended_ereal2,X0) ),
inference(cnf_transformation,[],[f849]) ).
thf(f849,plain,
! [X0: real] : ( extended_PInfty != vAPP(real,extended_ereal,extended_ereal2,X0) ),
inference(rectify,[],[f201]) ).
thf(f201,axiom,
! [X52: real] : ( vAPP(real,extended_ereal,extended_ereal2,X52) != extended_PInfty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_ereal_Odistinct_I1_J) ).
thf(f2864,plain,
spl136_72,
inference(avatar_split_clause,[],[f1439,f2862]) ).
thf(f2862,plain,
( spl136_72
<=> ! [X0: real] : ( extended_MInfty != vAPP(real,extended_ereal,extended_ereal2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_72])]) ).
thf(f1439,plain,
! [X0: real] : ( extended_MInfty != vAPP(real,extended_ereal,extended_ereal2,X0) ),
inference(cnf_transformation,[],[f848]) ).
thf(f848,plain,
! [X0: real] : ( extended_MInfty != vAPP(real,extended_ereal,extended_ereal2,X0) ),
inference(rectify,[],[f174]) ).
thf(f174,axiom,
! [X52: real] : ( extended_MInfty != vAPP(real,extended_ereal,extended_ereal2,X52) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_ereal_Odistinct_I3_J) ).
thf(f2830,plain,
spl136_71,
inference(avatar_split_clause,[],[f328,f2828]) ).
thf(f328,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f2826,plain,
~ spl136_70,
inference(avatar_split_clause,[],[f1413,f2823]) ).
thf(f1413,plain,
vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) != $true,
inference(cnf_transformation,[],[f847]) ).
thf(f847,plain,
vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) != $true,
inference(flattening,[],[f330]) ).
thf(f330,plain,
vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)) != $true,
inference(fool_elimination,[],[f329]) ).
thf(f329,plain,
~ vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)),
inference(rectify,[],[f326]) ).
thf(f326,negated_conjecture,
~ vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)),
inference(negated_conjecture,[],[f325]) ).
thf(f325,conjecture,
vAPP(extended_ereal,$o,vAPP(extended_ereal,sTfun(extended_ereal,$o),ord_less_eq(extended_ereal),vAPP(a,extended_ereal,g,x)),vAPP(a,extended_ereal,f,x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f2821,plain,
~ spl136_69,
inference(avatar_split_clause,[],[f2246,f2818]) ).
thf(f2818,plain,
( spl136_69
<=> ( zero_zero(extended_ereal) = extended_MInfty ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_69])]) ).
thf(f2246,plain,
zero_zero(extended_ereal) != extended_MInfty,
inference(forward_demodulation,[],[f2245,f1419]) ).
thf(f2245,plain,
zero_zero(extended_ereal) != vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extended_PInfty),
inference(forward_demodulation,[],[f1428,f1416]) ).
thf(f1428,plain,
zero_zero(extended_ereal) != vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)),
inference(cnf_transformation,[],[f127]) ).
thf(f127,axiom,
zero_zero(extended_ereal) != vAPP(extended_ereal,extended_ereal,uminus_uminus(extended_ereal),extend1396239628finity(extended_ereal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Infty__neq__0_I3_J) ).
thf(f2816,plain,
~ spl136_68,
inference(avatar_split_clause,[],[f2242,f2813]) ).
thf(f2813,plain,
( spl136_68
<=> ( zero_zero(extended_ereal) = extended_PInfty ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_68])]) ).
thf(f2242,plain,
zero_zero(extended_ereal) != extended_PInfty,
inference(forward_demodulation,[],[f1417,f1416]) ).
thf(f1417,plain,
zero_zero(extended_ereal) != extend1396239628finity(extended_ereal),
inference(cnf_transformation,[],[f56]) ).
thf(f56,axiom,
zero_zero(extended_ereal) != extend1396239628finity(extended_ereal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Infty__neq__0_I1_J) ).
thf(f2811,plain,
spl136_67,
inference(avatar_split_clause,[],[f1880,f2808]) ).
thf(f2808,plain,
( spl136_67
<=> ( order(extended_ereal) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_67])]) ).
thf(f1880,plain,
order(extended_ereal) = $true,
inference(cnf_transformation,[],[f844]) ).
thf(f844,plain,
order(extended_ereal) = $true,
inference(fool_elimination,[],[f843]) ).
thf(f843,plain,
order(extended_ereal),
inference(rectify,[],[f319]) ).
thf(f319,axiom,
order(extended_ereal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Orderings_Oorder_43) ).
thf(f2806,plain,
spl136_66,
inference(avatar_split_clause,[],[f1879,f2803]) ).
thf(f2803,plain,
( spl136_66
<=> ( order($o) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_66])]) ).
thf(f1879,plain,
order($o) = $true,
inference(cnf_transformation,[],[f842]) ).
thf(f842,plain,
order($o) = $true,
inference(fool_elimination,[],[f841]) ).
thf(f841,plain,
order($o),
inference(rectify,[],[f281]) ).
thf(f281,axiom,
order($o),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_14) ).
thf(f2801,plain,
spl136_65,
inference(avatar_split_clause,[],[f1878,f2798]) ).
thf(f2798,plain,
( spl136_65
<=> ( order(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_65])]) ).
thf(f1878,plain,
order(real) = $true,
inference(cnf_transformation,[],[f840]) ).
thf(f840,plain,
order(real) = $true,
inference(fool_elimination,[],[f839]) ).
thf(f839,plain,
order(real),
inference(rectify,[],[f297]) ).
thf(f297,axiom,
order(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oorder_23) ).
thf(f2796,plain,
spl136_64,
inference(avatar_split_clause,[],[f1877,f2793]) ).
thf(f2793,plain,
( spl136_64
<=> ( order(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_64])]) ).
thf(f1877,plain,
order(nat) = $true,
inference(cnf_transformation,[],[f838]) ).
thf(f838,plain,
order(nat) = $true,
inference(fool_elimination,[],[f837]) ).
thf(f837,plain,
order(nat),
inference(rectify,[],[f268]) ).
thf(f268,axiom,
order(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_3) ).
thf(f2791,plain,
spl136_63,
inference(avatar_split_clause,[],[f1876,f2788]) ).
thf(f2788,plain,
( spl136_63
<=> ( order(extended_enat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_63])]) ).
thf(f1876,plain,
order(extended_enat) = $true,
inference(cnf_transformation,[],[f836]) ).
thf(f836,plain,
order(extended_enat) = $true,
inference(fool_elimination,[],[f835]) ).
thf(f835,plain,
order(extended_enat),
inference(rectify,[],[f311]) ).
thf(f311,axiom,
order(extended_enat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oorder_35) ).
thf(f2786,plain,
spl136_62,
inference(avatar_split_clause,[],[f1875,f2783]) ).
thf(f2783,plain,
( spl136_62
<=> ( order(num) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_62])]) ).
thf(f1875,plain,
order(num) = $true,
inference(cnf_transformation,[],[f834]) ).
thf(f834,plain,
order(num) = $true,
inference(fool_elimination,[],[f833]) ).
thf(f833,plain,
order(num),
inference(rectify,[],[f274]) ).
thf(f274,axiom,
order(num),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Oorder_7) ).
thf(f2781,plain,
spl136_61,
inference(avatar_split_clause,[],[f1874,f2778]) ).
thf(f2778,plain,
( spl136_61
<=> ( ord(extended_ereal) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_61])]) ).
thf(f1874,plain,
ord(extended_ereal) = $true,
inference(cnf_transformation,[],[f832]) ).
thf(f832,plain,
ord(extended_ereal) = $true,
inference(fool_elimination,[],[f831]) ).
thf(f831,plain,
ord(extended_ereal),
inference(rectify,[],[f320]) ).
thf(f320,axiom,
ord(extended_ereal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Orderings_Oord_44) ).
thf(f2776,plain,
spl136_60,
inference(avatar_split_clause,[],[f1873,f2773]) ).
thf(f2773,plain,
( spl136_60
<=> ( ord($o) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_60])]) ).
thf(f1873,plain,
ord($o) = $true,
inference(cnf_transformation,[],[f830]) ).
thf(f830,plain,
ord($o) = $true,
inference(fool_elimination,[],[f829]) ).
thf(f829,plain,
ord($o),
inference(rectify,[],[f282]) ).
thf(f282,axiom,
ord($o),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_15) ).
thf(f2771,plain,
spl136_59,
inference(avatar_split_clause,[],[f1872,f2768]) ).
thf(f2768,plain,
( spl136_59
<=> ( ord(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_59])]) ).
thf(f1872,plain,
ord(real) = $true,
inference(cnf_transformation,[],[f828]) ).
thf(f828,plain,
ord(real) = $true,
inference(fool_elimination,[],[f827]) ).
thf(f827,plain,
ord(real),
inference(rectify,[],[f300]) ).
thf(f300,axiom,
ord(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oord_24) ).
thf(f2766,plain,
spl136_58,
inference(avatar_split_clause,[],[f1871,f2763]) ).
thf(f2763,plain,
( spl136_58
<=> ( ord(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_58])]) ).
thf(f1871,plain,
ord(nat) = $true,
inference(cnf_transformation,[],[f826]) ).
thf(f826,plain,
ord(nat) = $true,
inference(fool_elimination,[],[f825]) ).
thf(f825,plain,
ord(nat),
inference(rectify,[],[f269]) ).
thf(f269,axiom,
ord(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_4) ).
thf(f2761,plain,
spl136_57,
inference(avatar_split_clause,[],[f1870,f2758]) ).
thf(f2758,plain,
( spl136_57
<=> ( ord(extended_enat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_57])]) ).
thf(f1870,plain,
ord(extended_enat) = $true,
inference(cnf_transformation,[],[f824]) ).
thf(f824,plain,
ord(extended_enat) = $true,
inference(fool_elimination,[],[f823]) ).
thf(f823,plain,
ord(extended_enat),
inference(rectify,[],[f312]) ).
thf(f312,axiom,
ord(extended_enat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oord_36) ).
thf(f2756,plain,
spl136_56,
inference(avatar_split_clause,[],[f1869,f2753]) ).
thf(f2753,plain,
( spl136_56
<=> ( ord(num) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_56])]) ).
thf(f1869,plain,
ord(num) = $true,
inference(cnf_transformation,[],[f822]) ).
thf(f822,plain,
ord(num) = $true,
inference(fool_elimination,[],[f821]) ).
thf(f821,plain,
ord(num),
inference(rectify,[],[f275]) ).
thf(f275,axiom,
ord(num),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Oord_8) ).
thf(f2751,plain,
spl136_55,
inference(avatar_split_clause,[],[f1868,f2748]) ).
thf(f2748,plain,
( spl136_55
<=> ( ordere142940540dd_abs(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_55])]) ).
thf(f1868,plain,
ordere142940540dd_abs(real) = $true,
inference(cnf_transformation,[],[f820]) ).
thf(f820,plain,
ordere142940540dd_abs(real) = $true,
inference(fool_elimination,[],[f819]) ).
thf(f819,plain,
ordere142940540dd_abs(real),
inference(rectify,[],[f288]) ).
thf(f288,axiom,
ordere142940540dd_abs(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add__abs) ).
thf(f2746,plain,
spl136_54,
inference(avatar_split_clause,[],[f1867,f2743]) ).
thf(f2743,plain,
( spl136_54
<=> ( linorder(extended_ereal) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_54])]) ).
thf(f1867,plain,
linorder(extended_ereal) = $true,
inference(cnf_transformation,[],[f818]) ).
thf(f818,plain,
linorder(extended_ereal) = $true,
inference(fool_elimination,[],[f817]) ).
thf(f817,plain,
linorder(extended_ereal),
inference(rectify,[],[f318]) ).
thf(f318,axiom,
linorder(extended_ereal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Orderings_Olinorder_42) ).
thf(f2741,plain,
spl136_53,
inference(avatar_split_clause,[],[f1866,f2738]) ).
thf(f2738,plain,
( spl136_53
<=> ( linorder($o) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_53])]) ).
thf(f1866,plain,
linorder($o) = $true,
inference(cnf_transformation,[],[f816]) ).
thf(f816,plain,
linorder($o) = $true,
inference(fool_elimination,[],[f815]) ).
thf(f815,plain,
linorder($o),
inference(rectify,[],[f280]) ).
thf(f280,axiom,
linorder($o),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_13) ).
thf(f2736,plain,
spl136_52,
inference(avatar_split_clause,[],[f1865,f2733]) ).
thf(f2733,plain,
( spl136_52
<=> ( linorder(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_52])]) ).
thf(f1865,plain,
linorder(real) = $true,
inference(cnf_transformation,[],[f814]) ).
thf(f814,plain,
linorder(real) = $true,
inference(fool_elimination,[],[f813]) ).
thf(f813,plain,
linorder(real),
inference(rectify,[],[f295]) ).
thf(f295,axiom,
linorder(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Olinorder_22) ).
thf(f2731,plain,
spl136_51,
inference(avatar_split_clause,[],[f1864,f2728]) ).
thf(f2728,plain,
( spl136_51
<=> ( linorder(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_51])]) ).
thf(f1864,plain,
linorder(nat) = $true,
inference(cnf_transformation,[],[f812]) ).
thf(f812,plain,
linorder(nat) = $true,
inference(fool_elimination,[],[f811]) ).
thf(f811,plain,
linorder(nat),
inference(rectify,[],[f267]) ).
thf(f267,axiom,
linorder(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(f2726,plain,
spl136_50,
inference(avatar_split_clause,[],[f1863,f2723]) ).
thf(f2723,plain,
( spl136_50
<=> ( linorder(extended_enat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_50])]) ).
thf(f1863,plain,
linorder(extended_enat) = $true,
inference(cnf_transformation,[],[f810]) ).
thf(f810,plain,
linorder(extended_enat) = $true,
inference(fool_elimination,[],[f809]) ).
thf(f809,plain,
linorder(extended_enat),
inference(rectify,[],[f310]) ).
thf(f310,axiom,
linorder(extended_enat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Olinorder_34) ).
thf(f2721,plain,
spl136_49,
inference(avatar_split_clause,[],[f1862,f2718]) ).
thf(f2718,plain,
( spl136_49
<=> ( linorder(num) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_49])]) ).
thf(f1862,plain,
linorder(num) = $true,
inference(cnf_transformation,[],[f808]) ).
thf(f808,plain,
linorder(num) = $true,
inference(fool_elimination,[],[f807]) ).
thf(f807,plain,
linorder(num),
inference(rectify,[],[f273]) ).
thf(f273,axiom,
linorder(num),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Olinorder_6) ).
thf(f2716,plain,
spl136_48,
inference(avatar_split_clause,[],[f1861,f2713]) ).
thf(f2713,plain,
( spl136_48
<=> ( preorder(extended_ereal) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_48])]) ).
thf(f1861,plain,
preorder(extended_ereal) = $true,
inference(cnf_transformation,[],[f806]) ).
thf(f806,plain,
preorder(extended_ereal) = $true,
inference(fool_elimination,[],[f805]) ).
thf(f805,plain,
preorder(extended_ereal),
inference(rectify,[],[f317]) ).
thf(f317,axiom,
preorder(extended_ereal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Orderings_Opreorder_41) ).
thf(f2711,plain,
spl136_47,
inference(avatar_split_clause,[],[f1860,f2708]) ).
thf(f2708,plain,
( spl136_47
<=> ( preorder($o) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_47])]) ).
thf(f1860,plain,
preorder($o) = $true,
inference(cnf_transformation,[],[f804]) ).
thf(f804,plain,
preorder($o) = $true,
inference(fool_elimination,[],[f803]) ).
thf(f803,plain,
preorder($o),
inference(rectify,[],[f279]) ).
thf(f279,axiom,
preorder($o),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_12) ).
thf(f2706,plain,
spl136_46,
inference(avatar_split_clause,[],[f1859,f2703]) ).
thf(f2703,plain,
( spl136_46
<=> ( preorder(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_46])]) ).
thf(f1859,plain,
preorder(real) = $true,
inference(cnf_transformation,[],[f802]) ).
thf(f802,plain,
preorder(real) = $true,
inference(fool_elimination,[],[f801]) ).
thf(f801,plain,
preorder(real),
inference(rectify,[],[f294]) ).
thf(f294,axiom,
preorder(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Opreorder_21) ).
thf(f2701,plain,
spl136_45,
inference(avatar_split_clause,[],[f1858,f2698]) ).
thf(f2698,plain,
( spl136_45
<=> ( preorder(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_45])]) ).
thf(f1858,plain,
preorder(nat) = $true,
inference(cnf_transformation,[],[f800]) ).
thf(f800,plain,
preorder(nat) = $true,
inference(fool_elimination,[],[f799]) ).
thf(f799,plain,
preorder(nat),
inference(rectify,[],[f266]) ).
thf(f266,axiom,
preorder(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_2) ).
thf(f2696,plain,
spl136_44,
inference(avatar_split_clause,[],[f1857,f2693]) ).
thf(f2693,plain,
( spl136_44
<=> ( preorder(extended_enat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_44])]) ).
thf(f1857,plain,
preorder(extended_enat) = $true,
inference(cnf_transformation,[],[f798]) ).
thf(f798,plain,
preorder(extended_enat) = $true,
inference(fool_elimination,[],[f797]) ).
thf(f797,plain,
preorder(extended_enat),
inference(rectify,[],[f309]) ).
thf(f309,axiom,
preorder(extended_enat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Opreorder_33) ).
thf(f2691,plain,
spl136_43,
inference(avatar_split_clause,[],[f1856,f2688]) ).
thf(f2688,plain,
( spl136_43
<=> ( preorder(num) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_43])]) ).
thf(f1856,plain,
preorder(num) = $true,
inference(cnf_transformation,[],[f796]) ).
thf(f796,plain,
preorder(num) = $true,
inference(fool_elimination,[],[f795]) ).
thf(f795,plain,
preorder(num),
inference(rectify,[],[f272]) ).
thf(f272,axiom,
preorder(num),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Opreorder_5) ).
thf(f2686,plain,
spl136_42,
inference(avatar_split_clause,[],[f1855,f2683]) ).
thf(f1855,plain,
topolo503727757_space(extended_ereal) = $true,
inference(cnf_transformation,[],[f794]) ).
thf(f794,plain,
topolo503727757_space(extended_ereal) = $true,
inference(fool_elimination,[],[f793]) ).
thf(f793,plain,
topolo503727757_space(extended_ereal),
inference(rectify,[],[f315]) ).
thf(f315,axiom,
topolo503727757_space(extended_ereal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Topological__Spaces_Otopological__space_39) ).
thf(f2681,plain,
spl136_41,
inference(avatar_split_clause,[],[f1854,f2678]) ).
thf(f2678,plain,
( spl136_41
<=> ( topolo503727757_space($o) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_41])]) ).
thf(f1854,plain,
topolo503727757_space($o) = $true,
inference(cnf_transformation,[],[f792]) ).
thf(f792,plain,
topolo503727757_space($o) = $true,
inference(fool_elimination,[],[f791]) ).
thf(f791,plain,
topolo503727757_space($o),
inference(rectify,[],[f276]) ).
thf(f276,axiom,
topolo503727757_space($o),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Otopological__space_9) ).
thf(f2676,plain,
spl136_40,
inference(avatar_split_clause,[],[f1853,f2673]) ).
thf(f1853,plain,
topolo503727757_space(real) = $true,
inference(cnf_transformation,[],[f790]) ).
thf(f790,plain,
topolo503727757_space(real) = $true,
inference(fool_elimination,[],[f789]) ).
thf(f789,plain,
topolo503727757_space(real),
inference(rectify,[],[f284]) ).
thf(f284,axiom,
topolo503727757_space(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Otopological__space_17) ).
thf(f2671,plain,
spl136_39,
inference(avatar_split_clause,[],[f1852,f2668]) ).
thf(f2668,plain,
( spl136_39
<=> ( linordered_idom(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_39])]) ).
thf(f1852,plain,
linordered_idom(real) = $true,
inference(cnf_transformation,[],[f788]) ).
thf(f788,plain,
linordered_idom(real) = $true,
inference(fool_elimination,[],[f787]) ).
thf(f787,plain,
linordered_idom(real),
inference(rectify,[],[f292]) ).
thf(f292,axiom,
linordered_idom(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__idom) ).
thf(f2666,plain,
spl136_38,
inference(avatar_split_clause,[],[f1851,f2663]) ).
thf(f1851,plain,
topolo503727757_space(nat) = $true,
inference(cnf_transformation,[],[f786]) ).
thf(f786,plain,
topolo503727757_space(nat) = $true,
inference(fool_elimination,[],[f785]) ).
thf(f785,plain,
topolo503727757_space(nat),
inference(rectify,[],[f262]) ).
thf(f262,axiom,
topolo503727757_space(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Topological__Spaces_Otopological__space_1) ).
thf(f2661,plain,
spl136_37,
inference(avatar_split_clause,[],[f1850,f2658]) ).
thf(f1850,plain,
topolo503727757_space(extended_enat) = $true,
inference(cnf_transformation,[],[f784]) ).
thf(f784,plain,
topolo503727757_space(extended_enat) = $true,
inference(fool_elimination,[],[f783]) ).
thf(f783,plain,
topolo503727757_space(extended_enat),
inference(rectify,[],[f305]) ).
thf(f305,axiom,
topolo503727757_space(extended_enat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Topological__Spaces_Otopological__space_29) ).
thf(f2656,plain,
spl136_36,
inference(avatar_split_clause,[],[f1849,f2653]) ).
thf(f1849,plain,
boolean_algebra($o) = $true,
inference(cnf_transformation,[],[f782]) ).
thf(f782,plain,
boolean_algebra($o) = $true,
inference(fool_elimination,[],[f781]) ).
thf(f781,plain,
boolean_algebra($o),
inference(rectify,[],[f278]) ).
thf(f278,axiom,
boolean_algebra($o),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Oboolean__algebra_11) ).
thf(f2651,plain,
spl136_35,
inference(avatar_split_clause,[],[f1848,f2648]) ).
thf(f2648,plain,
( spl136_35
<=> ( group_add(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_35])]) ).
thf(f1848,plain,
group_add(real) = $true,
inference(cnf_transformation,[],[f780]) ).
thf(f780,plain,
group_add(real) = $true,
inference(fool_elimination,[],[f779]) ).
thf(f779,plain,
group_add(real),
inference(rectify,[],[f296]) ).
thf(f296,axiom,
group_add(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ogroup__add) ).
thf(f2646,plain,
spl136_34,
inference(avatar_split_clause,[],[f1847,f2643]) ).
thf(f1847,plain,
real_V2090557954_space(real) = $true,
inference(cnf_transformation,[],[f778]) ).
thf(f778,plain,
real_V2090557954_space(real) = $true,
inference(fool_elimination,[],[f777]) ).
thf(f777,plain,
real_V2090557954_space(real),
inference(rectify,[],[f287]) ).
thf(f287,axiom,
real_V2090557954_space(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space) ).
thf(f2641,plain,
spl136_33,
inference(avatar_split_clause,[],[f1846,f2638]) ).
thf(f2638,plain,
( spl136_33
<=> ( ordered_ab_group_add(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_33])]) ).
thf(f1846,plain,
ordered_ab_group_add(real) = $true,
inference(cnf_transformation,[],[f776]) ).
thf(f776,plain,
ordered_ab_group_add(real) = $true,
inference(fool_elimination,[],[f775]) ).
thf(f775,plain,
ordered_ab_group_add(real),
inference(rectify,[],[f290]) ).
thf(f290,axiom,
ordered_ab_group_add(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add) ).
thf(f2636,plain,
spl136_32,
inference(avatar_split_clause,[],[f1845,f2633]) ).
thf(f1845,plain,
uminus(extended_ereal) = $true,
inference(cnf_transformation,[],[f774]) ).
thf(f774,plain,
uminus(extended_ereal) = $true,
inference(fool_elimination,[],[f773]) ).
thf(f773,plain,
uminus(extended_ereal),
inference(rectify,[],[f321]) ).
thf(f321,axiom,
uminus(extended_ereal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Groups_Ouminus_45) ).
thf(f2631,plain,
spl136_31,
inference(avatar_split_clause,[],[f1844,f2628]) ).
thf(f1844,plain,
uminus($o) = $true,
inference(cnf_transformation,[],[f772]) ).
thf(f772,plain,
uminus($o) = $true,
inference(fool_elimination,[],[f771]) ).
thf(f771,plain,
uminus($o),
inference(rectify,[],[f283]) ).
thf(f283,axiom,
uminus($o),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ouminus_16) ).
thf(f2626,plain,
spl136_30,
inference(avatar_split_clause,[],[f1843,f2623]) ).
thf(f2623,plain,
( spl136_30
<=> ( linord1659791738miring(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_30])]) ).
thf(f1843,plain,
linord1659791738miring(real) = $true,
inference(cnf_transformation,[],[f770]) ).
thf(f770,plain,
linord1659791738miring(real) = $true,
inference(fool_elimination,[],[f769]) ).
thf(f769,plain,
linord1659791738miring(real),
inference(rectify,[],[f286]) ).
thf(f286,axiom,
linord1659791738miring(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_19) ).
thf(f2621,plain,
spl136_29,
inference(avatar_split_clause,[],[f1842,f2618]) ).
thf(f1842,plain,
uminus(real) = $true,
inference(cnf_transformation,[],[f768]) ).
thf(f768,plain,
uminus(real) = $true,
inference(fool_elimination,[],[f767]) ).
thf(f767,plain,
uminus(real),
inference(rectify,[],[f301]) ).
thf(f301,axiom,
uminus(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ouminus_25) ).
thf(f2616,plain,
spl136_28,
inference(avatar_split_clause,[],[f1841,f2613]) ).
thf(f2613,plain,
( spl136_28
<=> ( linord1659791738miring(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_28])]) ).
thf(f1841,plain,
linord1659791738miring(nat) = $true,
inference(cnf_transformation,[],[f766]) ).
thf(f766,plain,
linord1659791738miring(nat) = $true,
inference(fool_elimination,[],[f765]) ).
thf(f765,plain,
linord1659791738miring(nat),
inference(rectify,[],[f264]) ).
thf(f264,axiom,
linord1659791738miring(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring) ).
thf(f2611,plain,
spl136_27,
inference(avatar_split_clause,[],[f1840,f2608]) ).
thf(f2608,plain,
( spl136_27
<=> ( linord1659791738miring(extended_enat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_27])]) ).
thf(f1840,plain,
linord1659791738miring(extended_enat) = $true,
inference(cnf_transformation,[],[f764]) ).
thf(f764,plain,
linord1659791738miring(extended_enat) = $true,
inference(fool_elimination,[],[f763]) ).
thf(f763,plain,
linord1659791738miring(extended_enat),
inference(rectify,[],[f307]) ).
thf(f307,axiom,
linord1659791738miring(extended_enat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Olinordered__nonzero__semiring_31) ).
thf(f2606,plain,
spl136_26,
inference(avatar_split_clause,[],[f1839,f2603]) ).
thf(f2603,plain,
( spl136_26
<=> ( topolo259154727pology(extended_ereal) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_26])]) ).
thf(f1839,plain,
topolo259154727pology(extended_ereal) = $true,
inference(cnf_transformation,[],[f762]) ).
thf(f762,plain,
topolo259154727pology(extended_ereal) = $true,
inference(fool_elimination,[],[f761]) ).
thf(f761,plain,
topolo259154727pology(extended_ereal),
inference(rectify,[],[f316]) ).
thf(f316,axiom,
topolo259154727pology(extended_ereal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Topological__Spaces_Oorder__topology_40) ).
thf(f2601,plain,
spl136_25,
inference(avatar_split_clause,[],[f1838,f2598]) ).
thf(f2598,plain,
( spl136_25
<=> ( topolo259154727pology($o) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_25])]) ).
thf(f1838,plain,
topolo259154727pology($o) = $true,
inference(cnf_transformation,[],[f760]) ).
thf(f760,plain,
topolo259154727pology($o) = $true,
inference(fool_elimination,[],[f759]) ).
thf(f759,plain,
topolo259154727pology($o),
inference(rectify,[],[f277]) ).
thf(f277,axiom,
topolo259154727pology($o),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Oorder__topology_10) ).
thf(f2596,plain,
spl136_24,
inference(avatar_split_clause,[],[f1837,f2593]) ).
thf(f2593,plain,
( spl136_24
<=> ( topolo259154727pology(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_24])]) ).
thf(f1837,plain,
topolo259154727pology(real) = $true,
inference(cnf_transformation,[],[f758]) ).
thf(f758,plain,
topolo259154727pology(real) = $true,
inference(fool_elimination,[],[f757]) ).
thf(f757,plain,
topolo259154727pology(real),
inference(rectify,[],[f285]) ).
thf(f285,axiom,
topolo259154727pology(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Oorder__topology_18) ).
thf(f2591,plain,
spl136_23,
inference(avatar_split_clause,[],[f1836,f2588]) ).
thf(f2588,plain,
( spl136_23
<=> ( topolo259154727pology(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_23])]) ).
thf(f1836,plain,
topolo259154727pology(nat) = $true,
inference(cnf_transformation,[],[f756]) ).
thf(f756,plain,
topolo259154727pology(nat) = $true,
inference(fool_elimination,[],[f755]) ).
thf(f755,plain,
topolo259154727pology(nat),
inference(rectify,[],[f263]) ).
thf(f263,axiom,
topolo259154727pology(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Topological__Spaces_Oorder__topology) ).
thf(f2586,plain,
spl136_22,
inference(avatar_split_clause,[],[f1835,f2583]) ).
thf(f2583,plain,
( spl136_22
<=> ( topolo259154727pology(extended_enat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_22])]) ).
thf(f1835,plain,
topolo259154727pology(extended_enat) = $true,
inference(cnf_transformation,[],[f754]) ).
thf(f754,plain,
topolo259154727pology(extended_enat) = $true,
inference(fool_elimination,[],[f753]) ).
thf(f753,plain,
topolo259154727pology(extended_enat),
inference(rectify,[],[f306]) ).
thf(f306,axiom,
topolo259154727pology(extended_enat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Topological__Spaces_Oorder__topology_30) ).
thf(f2581,plain,
spl136_21,
inference(avatar_split_clause,[],[f1834,f2578]) ).
thf(f2578,plain,
( spl136_21
<=> ( zero(extended_ereal) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_21])]) ).
thf(f1834,plain,
zero(extended_ereal) = $true,
inference(cnf_transformation,[],[f752]) ).
thf(f752,plain,
zero(extended_ereal) = $true,
inference(fool_elimination,[],[f751]) ).
thf(f751,plain,
zero(extended_ereal),
inference(rectify,[],[f323]) ).
thf(f323,axiom,
zero(extended_ereal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Groups_Ozero_47) ).
thf(f2576,plain,
spl136_20,
inference(avatar_split_clause,[],[f1833,f2573]) ).
thf(f2573,plain,
( spl136_20
<=> ( ring_char_0(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_20])]) ).
thf(f1833,plain,
ring_char_0(real) = $true,
inference(cnf_transformation,[],[f750]) ).
thf(f750,plain,
ring_char_0(real) = $true,
inference(fool_elimination,[],[f749]) ).
thf(f749,plain,
ring_char_0(real),
inference(rectify,[],[f299]) ).
thf(f299,axiom,
ring_char_0(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Oring__char__0) ).
thf(f2571,plain,
spl136_19,
inference(avatar_split_clause,[],[f1832,f2568]) ).
thf(f2568,plain,
( spl136_19
<=> ( semiring_char_0(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_19])]) ).
thf(f1832,plain,
semiring_char_0(real) = $true,
inference(cnf_transformation,[],[f748]) ).
thf(f748,plain,
semiring_char_0(real) = $true,
inference(fool_elimination,[],[f747]) ).
thf(f747,plain,
semiring_char_0(real),
inference(rectify,[],[f293]) ).
thf(f293,axiom,
semiring_char_0(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Osemiring__char__0_20) ).
thf(f2566,plain,
spl136_18,
inference(avatar_split_clause,[],[f1831,f2563]) ).
thf(f2563,plain,
( spl136_18
<=> ( zero(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_18])]) ).
thf(f1831,plain,
zero(real) = $true,
inference(cnf_transformation,[],[f746]) ).
thf(f746,plain,
zero(real) = $true,
inference(fool_elimination,[],[f745]) ).
thf(f745,plain,
zero(real),
inference(rectify,[],[f303]) ).
thf(f303,axiom,
zero(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_27) ).
thf(f2561,plain,
spl136_17,
inference(avatar_split_clause,[],[f1830,f2558]) ).
thf(f2558,plain,
( spl136_17
<=> ( linord219039673up_add(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_17])]) ).
thf(f1830,plain,
linord219039673up_add(real) = $true,
inference(cnf_transformation,[],[f744]) ).
thf(f744,plain,
linord219039673up_add(real) = $true,
inference(fool_elimination,[],[f743]) ).
thf(f743,plain,
linord219039673up_add(real),
inference(rectify,[],[f289]) ).
thf(f289,axiom,
linord219039673up_add(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Olinordered__ab__group__add) ).
thf(f2556,plain,
spl136_16,
inference(avatar_split_clause,[],[f1829,f2553]) ).
thf(f2553,plain,
( spl136_16
<=> ( zero(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_16])]) ).
thf(f1829,plain,
zero(nat) = $true,
inference(cnf_transformation,[],[f742]) ).
thf(f742,plain,
zero(nat) = $true,
inference(fool_elimination,[],[f741]) ).
thf(f741,plain,
zero(nat),
inference(rectify,[],[f271]) ).
thf(f271,axiom,
zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).
thf(f2551,plain,
spl136_15,
inference(avatar_split_clause,[],[f1828,f2548]) ).
thf(f2548,plain,
( spl136_15
<=> ( semiring_char_0(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_15])]) ).
thf(f1828,plain,
semiring_char_0(nat) = $true,
inference(cnf_transformation,[],[f740]) ).
thf(f740,plain,
semiring_char_0(nat) = $true,
inference(fool_elimination,[],[f739]) ).
thf(f739,plain,
semiring_char_0(nat),
inference(rectify,[],[f265]) ).
thf(f265,axiom,
semiring_char_0(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osemiring__char__0) ).
thf(f2546,plain,
spl136_14,
inference(avatar_split_clause,[],[f1827,f2543]) ).
thf(f2543,plain,
( spl136_14
<=> ( semiring_char_0(extended_enat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_14])]) ).
thf(f1827,plain,
semiring_char_0(extended_enat) = $true,
inference(cnf_transformation,[],[f738]) ).
thf(f738,plain,
semiring_char_0(extended_enat) = $true,
inference(fool_elimination,[],[f737]) ).
thf(f737,plain,
semiring_char_0(extended_enat),
inference(rectify,[],[f308]) ).
thf(f308,axiom,
semiring_char_0(extended_enat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_32) ).
thf(f2541,plain,
spl136_13,
inference(avatar_split_clause,[],[f1826,f2538]) ).
thf(f2538,plain,
( spl136_13
<=> ( zero(extended_enat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_13])]) ).
thf(f1826,plain,
zero(extended_enat) = $true,
inference(cnf_transformation,[],[f736]) ).
thf(f736,plain,
zero(extended_enat) = $true,
inference(fool_elimination,[],[f735]) ).
thf(f735,plain,
zero(extended_enat),
inference(rectify,[],[f314]) ).
thf(f314,axiom,
zero(extended_enat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ozero_38) ).
thf(f2536,plain,
spl136_12,
inference(avatar_split_clause,[],[f1825,f2533]) ).
thf(f2533,plain,
( spl136_12
<=> ( numeral(extended_ereal) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_12])]) ).
thf(f1825,plain,
numeral(extended_ereal) = $true,
inference(cnf_transformation,[],[f734]) ).
thf(f734,plain,
numeral(extended_ereal) = $true,
inference(fool_elimination,[],[f733]) ).
thf(f733,plain,
numeral(extended_ereal),
inference(rectify,[],[f322]) ).
thf(f322,axiom,
numeral(extended_ereal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Num_Onumeral_46) ).
thf(f2531,plain,
spl136_11,
inference(avatar_split_clause,[],[f1824,f2528]) ).
thf(f2528,plain,
( spl136_11
<=> ( numeral(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_11])]) ).
thf(f1824,plain,
numeral(real) = $true,
inference(cnf_transformation,[],[f732]) ).
thf(f732,plain,
numeral(real) = $true,
inference(fool_elimination,[],[f731]) ).
thf(f731,plain,
numeral(real),
inference(rectify,[],[f302]) ).
thf(f302,axiom,
numeral(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Num_Onumeral_26) ).
thf(f2526,plain,
spl136_10,
inference(avatar_split_clause,[],[f1823,f2523]) ).
thf(f2523,plain,
( spl136_10
<=> ( numeral(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_10])]) ).
thf(f1823,plain,
numeral(nat) = $true,
inference(cnf_transformation,[],[f730]) ).
thf(f730,plain,
numeral(nat) = $true,
inference(fool_elimination,[],[f729]) ).
thf(f729,plain,
numeral(nat),
inference(rectify,[],[f270]) ).
thf(f270,axiom,
numeral(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Num_Onumeral) ).
thf(f2521,plain,
spl136_9,
inference(avatar_split_clause,[],[f1822,f2518]) ).
thf(f2518,plain,
( spl136_9
<=> ( canoni770627133id_add(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_9])]) ).
thf(f1822,plain,
canoni770627133id_add(nat) = $true,
inference(cnf_transformation,[],[f728]) ).
thf(f728,plain,
canoni770627133id_add(nat) = $true,
inference(fool_elimination,[],[f727]) ).
thf(f727,plain,
canoni770627133id_add(nat),
inference(rectify,[],[f261]) ).
thf(f261,axiom,
canoni770627133id_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(f2516,plain,
spl136_8,
inference(avatar_split_clause,[],[f1821,f2513]) ).
thf(f2513,plain,
( spl136_8
<=> ( canoni770627133id_add(extended_enat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_8])]) ).
thf(f1821,plain,
canoni770627133id_add(extended_enat) = $true,
inference(cnf_transformation,[],[f726]) ).
thf(f726,plain,
canoni770627133id_add(extended_enat) = $true,
inference(fool_elimination,[],[f725]) ).
thf(f725,plain,
canoni770627133id_add(extended_enat),
inference(rectify,[],[f304]) ).
thf(f304,axiom,
canoni770627133id_add(extended_enat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_28) ).
thf(f2511,plain,
spl136_7,
inference(avatar_split_clause,[],[f1820,f2508]) ).
thf(f2508,plain,
( spl136_7
<=> ( numeral(extended_enat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_7])]) ).
thf(f1820,plain,
numeral(extended_enat) = $true,
inference(cnf_transformation,[],[f724]) ).
thf(f724,plain,
numeral(extended_enat) = $true,
inference(fool_elimination,[],[f723]) ).
thf(f723,plain,
numeral(extended_enat),
inference(rectify,[],[f313]) ).
thf(f313,axiom,
numeral(extended_enat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Num_Onumeral_37) ).
thf(f2506,plain,
spl136_6,
inference(avatar_split_clause,[],[f1819,f2503]) ).
thf(f2503,plain,
( spl136_6
<=> ( neg_numeral(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_6])]) ).
thf(f1819,plain,
neg_numeral(real) = $true,
inference(cnf_transformation,[],[f722]) ).
thf(f722,plain,
neg_numeral(real) = $true,
inference(fool_elimination,[],[f721]) ).
thf(f721,plain,
neg_numeral(real),
inference(rectify,[],[f298]) ).
thf(f298,axiom,
neg_numeral(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Num_Oneg__numeral) ).
thf(f2501,plain,
spl136_5,
inference(avatar_split_clause,[],[f1818,f2498]) ).
thf(f2498,plain,
( spl136_5
<=> ( linordered_field(real) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_5])]) ).
thf(f1818,plain,
linordered_field(real) = $true,
inference(cnf_transformation,[],[f720]) ).
thf(f720,plain,
linordered_field(real) = $true,
inference(fool_elimination,[],[f719]) ).
thf(f719,plain,
linordered_field(real),
inference(rectify,[],[f291]) ).
thf(f291,axiom,
linordered_field(real),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Olinordered__field) ).
thf(f2496,plain,
spl136_4,
inference(avatar_split_clause,[],[f1416,f2493]) ).
thf(f2493,plain,
( spl136_4
<=> ( extend1396239628finity(extended_ereal) = extended_PInfty ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_4])]) ).
thf(f2491,plain,
spl136_3,
inference(avatar_split_clause,[],[f1414,f2488]) ).
thf(f1414,plain,
real_V2090557954_space(a) = $true,
inference(cnf_transformation,[],[f332]) ).
thf(f332,plain,
real_V2090557954_space(a) = $true,
inference(fool_elimination,[],[f331]) ).
thf(f331,plain,
real_V2090557954_space(a),
inference(rectify,[],[f324]) ).
thf(f324,axiom,
real_V2090557954_space(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
thf(f2486,plain,
~ spl136_2,
inference(avatar_split_clause,[],[f1415,f2483]) ).
thf(f2483,plain,
( spl136_2
<=> ( extended_MInfty = extended_PInfty ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_2])]) ).
thf(f1415,plain,
extended_MInfty != extended_PInfty,
inference(cnf_transformation,[],[f204]) ).
thf(f204,axiom,
extended_MInfty != extended_PInfty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_ereal_Odistinct_I5_J) ).
thf(f2481,plain,
~ spl136_1,
inference(avatar_split_clause,[],[f327,f2478]) ).
thf(f2478,plain,
( spl136_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl136_1])]) ).
thf(f327,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : ITP114^2 : TPTP v8.2.0. Released v7.5.0.
% 0.02/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat May 18 17:28:52 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (27737)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.38 % (27739)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.38 % (27741)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.38 % (27744)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.38 % (27743)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.38 % (27742)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.38 % (27738)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.39 % (27740)WARNING: value z3 for option sas not known
% 0.20/0.39 % (27740)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.41 % (27744)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.42 % Exception at run slice level
% 0.20/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.44 % (27745)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.47 % (27745)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.47 % Exception at run slice level
% 0.20/0.47 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.49 % (27746)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.20/0.49 % (27742)First to succeed.
% 0.20/0.51 % (27742)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-27737"
% 0.20/0.51 % (27742)Refutation found. Thanks to Tanya!
% 0.20/0.51 % SZS status Theorem for theBenchmark
% 0.20/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52 % (27742)------------------------------
% 0.20/0.52 % (27742)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.52 % (27742)Termination reason: Refutation
% 0.20/0.52
% 0.20/0.52 % (27742)Memory used [KB]: 2787
% 0.20/0.52 % (27742)Time elapsed: 0.124 s
% 0.20/0.52 % (27742)Instructions burned: 253 (million)
% 0.20/0.52 % (27737)Success in time 0.162 s
%------------------------------------------------------------------------------