%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP076^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:10:36 AM UTC 2026
% Result : Theorem 2.54s 0.59s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 66 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 303 ( 107 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1703 ( 8 ~; 16 |; 12 &;1584 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 214 ( 209 usr; 22 con; 0-4 aty)
% ( 35 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 266 ( 210 ^; 52 !; 4 ?; 266 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
set_HF_Mirabelle_hf: $tType ).
thf(type_def_6,type,
hF_Mirabelle_hf: $tType ).
thf(type_def_7,type,
set_nat: $tType ).
thf(type_def_8,type,
nat: $tType ).
thf(type_def_9,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_1,type,
zero_z189798548lle_hf: hF_Mirabelle_hf ).
thf(func_def_2,type,
zero_zero_nat: nat ).
thf(func_def_3,type,
hF_Mir818139703ollect: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_4,type,
hF_Mirabelle_HF: set_HF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_5,type,
hF_Mirabelle_HInter: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_6,type,
hF_Mirabelle_HUnion: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_7,type,
hF_Mir1248913145eplace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(func_def_8,type,
hF_Mirabelle_RepFun: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf ).
thf(func_def_9,type,
hF_Mirabelle_Replace: hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(func_def_10,type,
hF_Mirabelle_hcard: hF_Mirabelle_hf > nat ).
thf(func_def_11,type,
hF_Mirabelle_Abs_hf: nat > hF_Mirabelle_hf ).
thf(func_def_12,type,
hF_Mirabelle_Rep_hf: hF_Mirabelle_hf > nat ).
thf(func_def_13,type,
hF_Mirabelle_hfset: hF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(func_def_14,type,
hF_Mirabelle_hfst: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_15,type,
hF_Mir199975595nction: hF_Mirabelle_hf > $o ).
thf(func_def_16,type,
hF_Mirabelle_hinsert: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_17,type,
hF_Mirabelle_hmem: hF_Mirabelle_hf > hF_Mirabelle_hf > $o ).
thf(func_def_18,type,
hF_Mirabelle_hpair: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_19,type,
hF_Mir434065167lation: hF_Mirabelle_hf > $o ).
thf(func_def_20,type,
hF_Mir1653039215strict: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_21,type,
hF_Mirabelle_hsnd: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_22,type,
hF_Mir137170979_hpair: hF_Mirabelle_hf > $o ).
thf(func_def_23,type,
inf_in307783154e_hf_o: ( hF_Mirabelle_hf > $o ) > ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > $o ).
thf(func_def_24,type,
inf_inf_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
thf(func_def_25,type,
inf_in956532509lle_hf: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_26,type,
inf_in923488851lle_hf: set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(func_def_27,type,
inf_inf_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_28,type,
sup_su1199008216e_hf_o: ( hF_Mirabelle_hf > $o ) > ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > $o ).
thf(func_def_29,type,
sup_sup_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
thf(func_def_30,type,
sup_su638957495lle_hf: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_31,type,
sup_su1790843629lle_hf: set_HF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(func_def_32,type,
sup_sup_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_33,type,
suc: nat > nat ).
thf(func_def_34,type,
top_to22270292e_hf_o: hF_Mirabelle_hf > $o ).
thf(func_def_35,type,
top_top_nat_o: nat > $o ).
thf(func_def_36,type,
top_top_o: $o ).
thf(func_def_37,type,
top_to489427057lle_hf: set_HF_Mirabelle_hf ).
thf(func_def_38,type,
top_top_set_nat: set_nat ).
thf(func_def_39,type,
collec2046588256lle_hf: ( hF_Mirabelle_hf > $o ) > set_HF_Mirabelle_hf ).
thf(func_def_40,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_41,type,
insert9649339lle_hf: hF_Mirabelle_hf > set_HF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(func_def_42,type,
insert_nat: nat > set_nat > set_nat ).
thf(func_def_43,type,
type_d1794767497hf_nat: ( hF_Mirabelle_hf > nat ) > ( nat > hF_Mirabelle_hf ) > set_nat > $o ).
thf(func_def_44,type,
member1367349282lle_hf: hF_Mirabelle_hf > set_HF_Mirabelle_hf > $o ).
thf(func_def_45,type,
member_nat: nat > set_nat > $o ).
thf(func_def_46,type,
r: hF_Mirabelle_hf ).
thf(func_def_47,type,
x: hF_Mirabelle_hf ).
thf(func_def_51,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_52,type,
vIMP: $o > $o > $o ).
thf(func_def_53,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_56,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_57,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_58,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_59,type,
vAND: $o > $o > $o ).
thf(func_def_60,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_61,type,
vOR: $o > $o > $o ).
thf(func_def_62,type,
vNOT: $o > $o ).
thf(func_def_63,type,
sK0: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_64,type,
sK1: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_65,type,
sK2: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_66,type,
sK3: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_67,type,
sK4: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_68,type,
sK5: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_69,type,
sK6: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_70,type,
sK7: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_71,type,
sK8: ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_72,type,
sK9: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_73,type,
sK10: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_74,type,
sK11: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_75,type,
sK12: ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_76,type,
sK13: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_77,type,
sK14: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_78,type,
sK15: ( hF_Mirabelle_hf > $o ) > ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(func_def_79,type,
sK16: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_80,type,
sK17: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(func_def_81,type,
sK18: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(func_def_82,type,
sK19: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_83,type,
sK20: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_84,type,
sK21: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(func_def_85,type,
sK22: ( hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(func_def_86,type,
sK23: nat > hF_Mirabelle_hf ).
thf(func_def_87,type,
sK24: ( nat > $o ) > hF_Mirabelle_hf ).
thf(func_def_88,type,
sK25: hF_Mirabelle_hf > nat ).
thf(func_def_89,type,
sK26: ( hF_Mirabelle_hf > $o ) > nat ).
thf(func_def_90,type,
sK27: hF_Mirabelle_hf ).
thf(func_def_91,type,
sK28: hF_Mirabelle_hf ).
thf(func_def_92,type,
sK29: hF_Mirabelle_hf ).
thf(func_def_93,type,
sK30: hF_Mirabelle_hf ).
thf(func_def_94,type,
sK31: hF_Mirabelle_hf ).
thf(func_def_95,type,
sK32: hF_Mirabelle_hf ).
thf(func_def_96,type,
sK33: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_97,type,
sK34: set_HF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_98,type,
sK35: set_nat > nat ).
thf(func_def_99,type,
sK36: hF_Mirabelle_hf ).
thf(func_def_100,type,
sK37: nat ).
thf(func_def_101,type,
sK38: hF_Mirabelle_hf > ( nat > hF_Mirabelle_hf ) > nat ).
thf(func_def_102,type,
sK39: ( nat > $o ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_103,type,
sK40: ( hF_Mirabelle_hf > $o ) > set_nat > ( nat > hF_Mirabelle_hf ) > nat ).
thf(func_def_104,type,
sK41: nat > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_105,type,
sK42: hF_Mirabelle_hf > set_nat > ( nat > hF_Mirabelle_hf ) > nat ).
thf(func_def_106,type,
sK43: ( nat > hF_Mirabelle_hf ) > set_nat > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_107,type,
sK44: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_108,type,
sK45: set_nat > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_109,type,
sK46: set_nat > nat > set_nat ).
thf(func_def_110,type,
sK47: set_HF_Mirabelle_hf > hF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(func_def_111,type,
sK48: set_nat > nat > set_nat ).
thf(func_def_112,type,
sK49: set_HF_Mirabelle_hf > hF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(func_def_113,type,
sK50: hF_Mirabelle_hf ).
thf(func_def_114,type,
sK51: hF_Mirabelle_hf ).
thf(func_def_115,type,
sK52: hF_Mirabelle_hf ).
thf(func_def_116,type,
sK53: set_HF_Mirabelle_hf > hF_Mirabelle_hf > set_HF_Mirabelle_hf > hF_Mirabelle_hf > set_HF_Mirabelle_hf ).
thf(func_def_117,type,
sK54: set_nat > nat > set_nat > nat > set_nat ).
thf(func_def_118,type,
sK55: ( nat > hF_Mirabelle_hf ) > set_nat > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_119,type,
sK56: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_120,type,
sK57: set_nat > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_121,type,
sK58: ( nat > hF_Mirabelle_hf ) > set_nat > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_122,type,
sK59: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_123,type,
sK60: set_nat > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_124,type,
sK61: ( nat > hF_Mirabelle_hf ) > set_nat > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_125,type,
sK62: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_126,type,
sK63: set_nat > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_127,type,
sK64: ( nat > hF_Mirabelle_hf ) > set_nat > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_128,type,
sK65: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_129,type,
sK66: set_nat > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_130,type,
sK67: ( nat > hF_Mirabelle_hf ) > set_nat > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_131,type,
sK68: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_132,type,
sK69: set_nat > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_133,type,
sK70: ( nat > hF_Mirabelle_hf ) > set_nat > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_134,type,
sK71: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_135,type,
sK72: set_nat > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_136,type,
sK73: ( nat > hF_Mirabelle_hf ) > set_nat > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_137,type,
sK74: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_138,type,
sK75: set_nat > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_139,type,
sK76: ( nat > hF_Mirabelle_hf ) > set_nat > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_140,type,
sK77: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_141,type,
sK78: set_nat > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_142,type,
sK79: ( nat > hF_Mirabelle_hf ) > set_nat > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_143,type,
sK80: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_144,type,
sK81: set_nat > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_145,type,
sK82: ( nat > hF_Mirabelle_hf ) > set_nat > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_146,type,
sK83: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_147,type,
sK84: set_nat > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_148,type,
sK85: ( nat > hF_Mirabelle_hf ) > set_nat > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_149,type,
sK86: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_150,type,
sK87: set_nat > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_151,type,
sK88: ( nat > hF_Mirabelle_hf ) > set_nat > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_152,type,
sK89: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_153,type,
sK90: set_nat > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_154,type,
sK91: ( nat > hF_Mirabelle_hf ) > set_nat > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_155,type,
sK92: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_156,type,
sK93: set_nat > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_157,type,
sK94: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_158,type,
sK95: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_159,type,
sK96: ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_160,type,
sK97: ( nat > $o ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_161,type,
sK98: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_162,type,
sK99: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_163,type,
sK100: ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_164,type,
sK101: ( nat > $o ) > nat ).
thf(func_def_165,type,
sK102: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > nat ).
thf(func_def_166,type,
sK103: ( nat > hF_Mirabelle_hf ) > ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_167,type,
sK104: ( hF_Mirabelle_hf > nat ) > hF_Mirabelle_hf ).
thf(func_def_168,type,
sK105: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_169,type,
sK106: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_170,type,
sK107: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_171,type,
sK108: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_172,type,
sK109: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_173,type,
sK110: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_174,type,
sK111: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_175,type,
sK112: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_176,type,
sK113: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_177,type,
sK114: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_178,type,
sK115: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_179,type,
sK116: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_180,type,
sK117: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_181,type,
sK118: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_182,type,
sK119: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_183,type,
sK120: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_184,type,
sK121: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_185,type,
sK122: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_186,type,
sK123: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_187,type,
sK124: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_188,type,
sK125: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_189,type,
sK126: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_190,type,
sK127: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_191,type,
sK128: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_192,type,
sK129: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_193,type,
sK130: hF_Mirabelle_hf > hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf ).
thf(func_def_194,type,
sK131: hF_Mirabelle_hf > hF_Mirabelle_hf > ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf ).
thf(func_def_195,type,
sK132: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_196,type,
sK133: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_197,type,
sK134: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_198,type,
sK135: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_199,type,
sK136: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_200,type,
sK137: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_201,type,
sK138: ( hF_Mirabelle_hf > hF_Mirabelle_hf ) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_202,type,
sK139: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_203,type,
sK140: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_204,type,
sK141: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_205,type,
sK142: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_206,type,
sK143: ( hF_Mirabelle_hf > hF_Mirabelle_hf > $o ) > hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_207,type,
sK144: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_208,type,
sK145: hF_Mirabelle_hf > hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_209,type,
sK146: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(func_def_210,type,
sK147: hF_Mirabelle_hf > hF_Mirabelle_hf ).
thf(f2,axiom,
( hF_Mir199975595nction
= ( ^ [X0: hF_Mirabelle_hf] :
! [X1: hF_Mirabelle_hf,X2: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ X1 @ X2 ) @ X0 )
=> ! [X3: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ X1 @ X3 ) @ X0 )
=> ( X2 = X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_hfunction__def) ).
thf(f3,axiom,
! [X0: hF_Mirabelle_hf,X1: hF_Mirabelle_hf,X2: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ X0 @ ( hF_Mir1653039215strict @ X1 @ X2 ) )
= ( ? [X3: hF_Mirabelle_hf,X4: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X3 @ X2 )
& ( X0
= ( hF_Mirabelle_hpair @ X3 @ X4 ) ) ) ) )
& ( hF_Mirabelle_hmem @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_hrestrict__iff) ).
thf(f34,axiom,
( hF_Mirabelle_hmem
= ( ^ [X0: hF_Mirabelle_hf,X1: hF_Mirabelle_hf] : ( member1367349282lle_hf @ X0 @ ( hF_Mirabelle_hfset @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_hmem__def) ).
thf(f65,axiom,
( hF_Mirabelle_hpair
= ( ^ [X0: hF_Mirabelle_hf,X1: hF_Mirabelle_hf] : ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ X0 @ zero_z189798548lle_hf ) @ ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ X0 @ ( hF_Mirabelle_hinsert @ X1 @ zero_z189798548lle_hf ) ) @ zero_z189798548lle_hf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_hpair__def) ).
thf(f287,axiom,
( hF_Mirabelle_hinsert
= ( ^ [X0: hF_Mirabelle_hf,X1: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X0 @ ( hF_Mirabelle_hfset @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_hinsert__def) ).
thf(f355,axiom,
hF_Mir199975595nction @ r,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(f356,conjecture,
hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(f357,negated_conjecture,
~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) ),
inference(negated_conjecture,[status(cth)],[f356]) ).
thf(f360,plain,
( hF_Mir199975595nction
= ( ^ [X0: hF_Mirabelle_hf] :
! [X1: hF_Mirabelle_hf,X2: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ X1 @ X2 ) @ X0 )
=> ! [X3: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ X1 @ X3 ) @ X0 )
=> ( X2 = X3 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f361,plain,
( hF_Mir199975595nction
= ( ^ [Y0: hF_Mirabelle_hf] :
( !! @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( !! @ hF_Mirabelle_hf
@ ^ [Y2: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ Y2 @ Y1 ) @ Y0 )
=> ( !! @ hF_Mirabelle_hf
@ ^ [Y3: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ Y2 @ Y3 ) @ Y0 )
=> ( Y1 = Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f360]) ).
thf(f362,plain,
! [X0: hF_Mirabelle_hf,X1: hF_Mirabelle_hf,X2: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hmem @ X0 @ ( hF_Mir1653039215strict @ X1 @ X2 ) )
= ( ? [X3: hF_Mirabelle_hf,X4: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X3 @ X2 )
& ( X0
= ( hF_Mirabelle_hpair @ X3 @ X4 ) ) ) ) )
& ( hF_Mirabelle_hmem @ X0 @ X1 ) ),
inference(rectify,[],[f3]) ).
thf(f363,plain,
! [X0: hF_Mirabelle_hf,X1: hF_Mirabelle_hf,X2: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X0 @ ( hF_Mir1653039215strict @ X1 @ X2 ) )
= ( ( hF_Mirabelle_hmem @ X0 @ X1 )
& ( ?? @ hF_Mirabelle_hf
@ ^ [Y0: hF_Mirabelle_hf] :
( ?? @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ Y1 @ Y0 )
= X0 )
& ( hF_Mirabelle_hmem @ Y1 @ X2 ) ) ) ) ) ),
inference(fool_elimination,[],[f362]) ).
thf(f406,plain,
( hF_Mirabelle_hmem
= ( ^ [Y0: hF_Mirabelle_hf,Y1: hF_Mirabelle_hf] : ( member1367349282lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ Y1 ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f426,plain,
( hF_Mirabelle_hpair
= ( ^ [Y0: hF_Mirabelle_hf,Y1: hF_Mirabelle_hf] : ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ Y0 @ zero_z189798548lle_hf ) @ ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ Y0 @ ( hF_Mirabelle_hinsert @ Y1 @ zero_z189798548lle_hf ) ) @ zero_z189798548lle_hf ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f565,plain,
( hF_Mirabelle_hinsert
= ( ^ [Y0: hF_Mirabelle_hf,Y1: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f287]) ).
thf(f660,plain,
hF_Mir199975595nction @ r,
inference(rectify,[],[f355]) ).
thf(f661,plain,
( ( hF_Mir199975595nction @ r )
= $true ),
inference(fool_elimination,[],[f660]) ).
thf(f662,plain,
~ ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) ),
inference(rectify,[],[f357]) ).
thf(f663,plain,
( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) )
!= $true ),
inference(fool_elimination,[],[f662]) ).
thf(f696,plain,
( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) )
!= $true ),
inference(flattening,[],[f663]) ).
thf(f861,plain,
( hF_Mir199975595nction
= ( ^ [Y0: hF_Mirabelle_hf] :
( !! @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( !! @ hF_Mirabelle_hf
@ ^ [Y2: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ Y2 @ Y1 ) @ Y0 )
=> ( !! @ hF_Mirabelle_hf
@ ^ [Y3: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ ( hF_Mirabelle_hpair @ Y2 @ Y3 ) @ Y0 )
=> ( Y1 = Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f361]) ).
thf(f862,plain,
! [X2: hF_Mirabelle_hf,X0: hF_Mirabelle_hf,X1: hF_Mirabelle_hf] :
( ( hF_Mirabelle_hmem @ X0 @ ( hF_Mir1653039215strict @ X1 @ X2 ) )
= ( ( hF_Mirabelle_hmem @ X0 @ X1 )
& ( ?? @ hF_Mirabelle_hf
@ ^ [Y0: hF_Mirabelle_hf] :
( ?? @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( ( ( hF_Mirabelle_hpair @ Y1 @ Y0 )
= X0 )
& ( hF_Mirabelle_hmem @ Y1 @ X2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f363]) ).
thf(f902,plain,
( hF_Mirabelle_hmem
= ( ^ [Y0: hF_Mirabelle_hf,Y1: hF_Mirabelle_hf] : ( member1367349282lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f406]) ).
thf(f939,plain,
( hF_Mirabelle_hpair
= ( ^ [Y0: hF_Mirabelle_hf,Y1: hF_Mirabelle_hf] : ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ Y0 @ zero_z189798548lle_hf ) @ ( hF_Mirabelle_hinsert @ ( hF_Mirabelle_hinsert @ Y0 @ ( hF_Mirabelle_hinsert @ Y1 @ zero_z189798548lle_hf ) ) @ zero_z189798548lle_hf ) ) ) ),
inference(cnf_transformation,[],[f426]) ).
thf(f1171,plain,
( hF_Mirabelle_hinsert
= ( ^ [Y0: hF_Mirabelle_hf,Y1: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f565]) ).
thf(f1252,plain,
( ( hF_Mir199975595nction @ r )
= $true ),
inference(cnf_transformation,[],[f661]) ).
thf(f1253,plain,
( ( hF_Mir199975595nction @ ( hF_Mir1653039215strict @ r @ x ) )
!= $true ),
inference(cnf_transformation,[],[f696]) ).
thf(f1256,plain,
( hF_Mirabelle_hpair
= ( ^ [Y0: hF_Mirabelle_hf,Y1: hF_Mirabelle_hf] :
( ^ [Y2: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y2 @ ( hF_Mirabelle_hfset @ Y3 ) ) )
@ ( ^ [Y2: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y2 @ ( hF_Mirabelle_hfset @ Y3 ) ) )
@ Y0
@ zero_z189798548lle_hf )
@ ( ^ [Y2: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y2 @ ( hF_Mirabelle_hfset @ Y3 ) ) )
@ ( ^ [Y2: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y2 @ ( hF_Mirabelle_hfset @ Y3 ) ) )
@ Y0
@ ( ^ [Y2: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y2 @ ( hF_Mirabelle_hfset @ Y3 ) ) )
@ Y1
@ zero_z189798548lle_hf ) )
@ zero_z189798548lle_hf ) ) ) ),
inference(definition_unfolding,[],[f939,f1171,f1171,f1171,f1171,f1171]) ).
thf(f1257,plain,
( hF_Mir199975595nction
= ( ^ [Y0: hF_Mirabelle_hf] :
( !! @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( !! @ hF_Mirabelle_hf
@ ^ [Y2: hF_Mirabelle_hf] :
( ( ^ [Y3: hF_Mirabelle_hf,Y4: hF_Mirabelle_hf] : ( member1367349282lle_hf @ Y3 @ ( hF_Mirabelle_hfset @ Y4 ) )
@ ( ^ [Y3: hF_Mirabelle_hf,Y4: hF_Mirabelle_hf] :
( ^ [Y5: hF_Mirabelle_hf,Y6: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y5 @ ( hF_Mirabelle_hfset @ Y6 ) ) )
@ ( ^ [Y5: hF_Mirabelle_hf,Y6: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y5 @ ( hF_Mirabelle_hfset @ Y6 ) ) )
@ Y3
@ zero_z189798548lle_hf )
@ ( ^ [Y5: hF_Mirabelle_hf,Y6: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y5 @ ( hF_Mirabelle_hfset @ Y6 ) ) )
@ ( ^ [Y5: hF_Mirabelle_hf,Y6: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y5 @ ( hF_Mirabelle_hfset @ Y6 ) ) )
@ Y3
@ ( ^ [Y5: hF_Mirabelle_hf,Y6: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y5 @ ( hF_Mirabelle_hfset @ Y6 ) ) )
@ Y4
@ zero_z189798548lle_hf ) )
@ zero_z189798548lle_hf ) )
@ Y2
@ Y1 )
@ Y0 )
=> ( !! @ hF_Mirabelle_hf
@ ^ [Y3: hF_Mirabelle_hf] :
( ( ^ [Y4: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] : ( member1367349282lle_hf @ Y4 @ ( hF_Mirabelle_hfset @ Y5 ) )
@ ( ^ [Y4: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] :
( ^ [Y6: hF_Mirabelle_hf,Y7: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y6 @ ( hF_Mirabelle_hfset @ Y7 ) ) )
@ ( ^ [Y6: hF_Mirabelle_hf,Y7: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y6 @ ( hF_Mirabelle_hfset @ Y7 ) ) )
@ Y4
@ zero_z189798548lle_hf )
@ ( ^ [Y6: hF_Mirabelle_hf,Y7: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y6 @ ( hF_Mirabelle_hfset @ Y7 ) ) )
@ ( ^ [Y6: hF_Mirabelle_hf,Y7: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y6 @ ( hF_Mirabelle_hfset @ Y7 ) ) )
@ Y4
@ ( ^ [Y6: hF_Mirabelle_hf,Y7: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y6 @ ( hF_Mirabelle_hfset @ Y7 ) ) )
@ Y5
@ zero_z189798548lle_hf ) )
@ zero_z189798548lle_hf ) )
@ Y2
@ Y3 )
@ Y0 )
=> ( Y1 = Y3 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f861,f902,f1256,f902,f1256]) ).
thf(f1261,plain,
! [X2: hF_Mirabelle_hf,X0: hF_Mirabelle_hf,X1: hF_Mirabelle_hf] :
( ( ^ [Y0: hF_Mirabelle_hf,Y1: hF_Mirabelle_hf] : ( member1367349282lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ Y1 ) )
@ X0
@ ( hF_Mir1653039215strict @ X1 @ X2 ) )
= ( ( ^ [Y0: hF_Mirabelle_hf,Y1: hF_Mirabelle_hf] : ( member1367349282lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ Y1 ) )
@ X0
@ X1 )
& ( ?? @ hF_Mirabelle_hf
@ ^ [Y0: hF_Mirabelle_hf] :
( ?? @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( ( ( ^ [Y2: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
( ^ [Y4: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y4 @ ( hF_Mirabelle_hfset @ Y5 ) ) )
@ ( ^ [Y4: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y4 @ ( hF_Mirabelle_hfset @ Y5 ) ) )
@ Y2
@ zero_z189798548lle_hf )
@ ( ^ [Y4: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y4 @ ( hF_Mirabelle_hfset @ Y5 ) ) )
@ ( ^ [Y4: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y4 @ ( hF_Mirabelle_hfset @ Y5 ) ) )
@ Y2
@ ( ^ [Y4: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y4 @ ( hF_Mirabelle_hfset @ Y5 ) ) )
@ Y3
@ zero_z189798548lle_hf ) )
@ zero_z189798548lle_hf ) )
@ Y1
@ Y0 )
= X0 )
& ( ^ [Y2: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] : ( member1367349282lle_hf @ Y2 @ ( hF_Mirabelle_hfset @ Y3 ) )
@ Y1
@ X2 ) ) ) ) ) ),
inference(definition_unfolding,[],[f862,f902,f902,f1256,f902]) ).
thf(f1368,plain,
( $true
= ( ^ [Y0: hF_Mirabelle_hf] :
( !! @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( !! @ hF_Mirabelle_hf
@ ^ [Y2: hF_Mirabelle_hf] :
( ( ^ [Y3: hF_Mirabelle_hf,Y4: hF_Mirabelle_hf] : ( member1367349282lle_hf @ Y3 @ ( hF_Mirabelle_hfset @ Y4 ) )
@ ( ^ [Y3: hF_Mirabelle_hf,Y4: hF_Mirabelle_hf] :
( ^ [Y5: hF_Mirabelle_hf,Y6: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y5 @ ( hF_Mirabelle_hfset @ Y6 ) ) )
@ ( ^ [Y5: hF_Mirabelle_hf,Y6: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y5 @ ( hF_Mirabelle_hfset @ Y6 ) ) )
@ Y3
@ zero_z189798548lle_hf )
@ ( ^ [Y5: hF_Mirabelle_hf,Y6: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y5 @ ( hF_Mirabelle_hfset @ Y6 ) ) )
@ ( ^ [Y5: hF_Mirabelle_hf,Y6: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y5 @ ( hF_Mirabelle_hfset @ Y6 ) ) )
@ Y3
@ ( ^ [Y5: hF_Mirabelle_hf,Y6: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y5 @ ( hF_Mirabelle_hfset @ Y6 ) ) )
@ Y4
@ zero_z189798548lle_hf ) )
@ zero_z189798548lle_hf ) )
@ Y2
@ Y1 )
@ Y0 )
=> ( !! @ hF_Mirabelle_hf
@ ^ [Y3: hF_Mirabelle_hf] :
( ( ^ [Y4: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] : ( member1367349282lle_hf @ Y4 @ ( hF_Mirabelle_hfset @ Y5 ) )
@ ( ^ [Y4: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] :
( ^ [Y6: hF_Mirabelle_hf,Y7: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y6 @ ( hF_Mirabelle_hfset @ Y7 ) ) )
@ ( ^ [Y6: hF_Mirabelle_hf,Y7: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y6 @ ( hF_Mirabelle_hfset @ Y7 ) ) )
@ Y4
@ zero_z189798548lle_hf )
@ ( ^ [Y6: hF_Mirabelle_hf,Y7: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y6 @ ( hF_Mirabelle_hfset @ Y7 ) ) )
@ ( ^ [Y6: hF_Mirabelle_hf,Y7: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y6 @ ( hF_Mirabelle_hfset @ Y7 ) ) )
@ Y4
@ ( ^ [Y6: hF_Mirabelle_hf,Y7: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y6 @ ( hF_Mirabelle_hfset @ Y7 ) ) )
@ Y5
@ zero_z189798548lle_hf ) )
@ zero_z189798548lle_hf ) )
@ Y2
@ Y3 )
@ Y0 )
=> ( Y1 = Y3 ) ) ) ) ) )
@ r ) ),
inference(definition_unfolding,[],[f1252,f1257]) ).
thf(f1369,plain,
( $true
!= ( ^ [Y0: hF_Mirabelle_hf] :
( !! @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( !! @ hF_Mirabelle_hf
@ ^ [Y2: hF_Mirabelle_hf] :
( ( ^ [Y3: hF_Mirabelle_hf,Y4: hF_Mirabelle_hf] : ( member1367349282lle_hf @ Y3 @ ( hF_Mirabelle_hfset @ Y4 ) )
@ ( ^ [Y3: hF_Mirabelle_hf,Y4: hF_Mirabelle_hf] :
( ^ [Y5: hF_Mirabelle_hf,Y6: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y5 @ ( hF_Mirabelle_hfset @ Y6 ) ) )
@ ( ^ [Y5: hF_Mirabelle_hf,Y6: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y5 @ ( hF_Mirabelle_hfset @ Y6 ) ) )
@ Y3
@ zero_z189798548lle_hf )
@ ( ^ [Y5: hF_Mirabelle_hf,Y6: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y5 @ ( hF_Mirabelle_hfset @ Y6 ) ) )
@ ( ^ [Y5: hF_Mirabelle_hf,Y6: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y5 @ ( hF_Mirabelle_hfset @ Y6 ) ) )
@ Y3
@ ( ^ [Y5: hF_Mirabelle_hf,Y6: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y5 @ ( hF_Mirabelle_hfset @ Y6 ) ) )
@ Y4
@ zero_z189798548lle_hf ) )
@ zero_z189798548lle_hf ) )
@ Y2
@ Y1 )
@ Y0 )
=> ( !! @ hF_Mirabelle_hf
@ ^ [Y3: hF_Mirabelle_hf] :
( ( ^ [Y4: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] : ( member1367349282lle_hf @ Y4 @ ( hF_Mirabelle_hfset @ Y5 ) )
@ ( ^ [Y4: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] :
( ^ [Y6: hF_Mirabelle_hf,Y7: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y6 @ ( hF_Mirabelle_hfset @ Y7 ) ) )
@ ( ^ [Y6: hF_Mirabelle_hf,Y7: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y6 @ ( hF_Mirabelle_hfset @ Y7 ) ) )
@ Y4
@ zero_z189798548lle_hf )
@ ( ^ [Y6: hF_Mirabelle_hf,Y7: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y6 @ ( hF_Mirabelle_hfset @ Y7 ) ) )
@ ( ^ [Y6: hF_Mirabelle_hf,Y7: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y6 @ ( hF_Mirabelle_hfset @ Y7 ) ) )
@ Y4
@ ( ^ [Y6: hF_Mirabelle_hf,Y7: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y6 @ ( hF_Mirabelle_hfset @ Y7 ) ) )
@ Y5
@ zero_z189798548lle_hf ) )
@ zero_z189798548lle_hf ) )
@ Y2
@ Y3 )
@ Y0 )
=> ( Y1 = Y3 ) ) ) ) ) )
@ ( hF_Mir1653039215strict @ r @ x ) ) ),
inference(definition_unfolding,[],[f1253,f1257]) ).
thf(f1394,plain,
( $true
!= ( !! @ hF_Mirabelle_hf
@ ^ [Y0: hF_Mirabelle_hf] :
( !! @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mir1653039215strict @ r @ x ) ) )
=> ( !! @ hF_Mirabelle_hf
@ ^ [Y2: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y2 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mir1653039215strict @ r @ x ) ) )
=> ( Y0 = Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1369]) ).
thf(f1395,plain,
( $false
= ( ^ [Y0: hF_Mirabelle_hf] :
( !! @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mir1653039215strict @ r @ x ) ) )
=> ( !! @ hF_Mirabelle_hf
@ ^ [Y2: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y2 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mir1653039215strict @ r @ x ) ) )
=> ( Y0 = Y2 ) ) ) ) )
@ sK50 ) ),
inference(sigma_proxy_clausification,[],[f1394]) ).
thf(f1396,plain,
( $false
= ( !! @ hF_Mirabelle_hf
@ ^ [Y0: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK50 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mir1653039215strict @ r @ x ) ) )
=> ( !! @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mir1653039215strict @ r @ x ) ) )
=> ( sK50 = Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1395]) ).
thf(f1397,plain,
( $false
= ( ^ [Y0: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK50 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mir1653039215strict @ r @ x ) ) )
=> ( !! @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mir1653039215strict @ r @ x ) ) )
=> ( sK50 = Y1 ) ) ) )
@ sK51 ) ),
inference(sigma_proxy_clausification,[],[f1396]) ).
thf(f1398,plain,
( $false
= ( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK50 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mir1653039215strict @ r @ x ) ) )
=> ( !! @ hF_Mirabelle_hf
@ ^ [Y0: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mir1653039215strict @ r @ x ) ) )
=> ( sK50 = Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1397]) ).
thf(f1399,plain,
( $false
= ( !! @ hF_Mirabelle_hf
@ ^ [Y0: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mir1653039215strict @ r @ x ) ) )
=> ( sK50 = Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f1398]) ).
thf(f1400,plain,
( $true
= ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK50 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(imp_proxy_clausification,[],[f1398]) ).
thf(f1401,plain,
( $false
= ( ^ [Y0: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mir1653039215strict @ r @ x ) ) )
=> ( sK50 = Y0 ) )
@ sK52 ) ),
inference(sigma_proxy_clausification,[],[f1399]) ).
thf(f1402,plain,
( $false
= ( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK52 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mir1653039215strict @ r @ x ) ) )
=> ( sK50 = sK52 ) ) ),
inference(beta-eta_normalization,[],[f1401]) ).
thf(f1403,plain,
( $false
= ( sK50 = sK52 ) ),
inference(imp_proxy_clausification,[],[f1402]) ).
thf(f1404,plain,
( $true
= ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK52 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mir1653039215strict @ r @ x ) ) ) ),
inference(imp_proxy_clausification,[],[f1402]) ).
thf(f1405,plain,
sK50 != sK52,
inference(equality_proxy_clausification,[],[f1403]) ).
thf(f1406,plain,
( $true
= ( !! @ hF_Mirabelle_hf
@ ^ [Y0: hF_Mirabelle_hf] :
( !! @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) )
=> ( !! @ hF_Mirabelle_hf
@ ^ [Y2: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y2 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) )
=> ( Y0 = Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1368]) ).
thf(f1407,plain,
! [X1: hF_Mirabelle_hf] :
( $true
= ( ^ [Y0: hF_Mirabelle_hf] :
( !! @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) )
=> ( !! @ hF_Mirabelle_hf
@ ^ [Y2: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y2 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) )
=> ( Y0 = Y2 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1406]) ).
thf(f1408,plain,
! [X1: hF_Mirabelle_hf] :
( $true
= ( !! @ hF_Mirabelle_hf
@ ^ [Y0: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) )
=> ( !! @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) )
=> ( X1 = Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f1407]) ).
thf(f1409,plain,
! [X2: hF_Mirabelle_hf,X1: hF_Mirabelle_hf] :
( $true
= ( ^ [Y0: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) )
=> ( !! @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) )
=> ( X1 = Y1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f1408]) ).
thf(f1410,plain,
! [X2: hF_Mirabelle_hf,X1: hF_Mirabelle_hf] :
( $true
= ( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) )
=> ( !! @ hF_Mirabelle_hf
@ ^ [Y0: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) )
=> ( X1 = Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1409]) ).
thf(f1411,plain,
! [X2: hF_Mirabelle_hf,X1: hF_Mirabelle_hf] :
( ( $false
= ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) ) )
| ( $true
= ( !! @ hF_Mirabelle_hf
@ ^ [Y0: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) )
=> ( X1 = Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f1410]) ).
thf(f1412,plain,
! [X2: hF_Mirabelle_hf,X3: hF_Mirabelle_hf,X1: hF_Mirabelle_hf] :
( ( $false
= ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) ) )
| ( $true
= ( ^ [Y0: hF_Mirabelle_hf] :
( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) )
=> ( X1 = Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f1411]) ).
thf(f1413,plain,
! [X2: hF_Mirabelle_hf,X3: hF_Mirabelle_hf,X1: hF_Mirabelle_hf] :
( ( $false
= ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) ) )
| ( $true
= ( ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X3 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) )
=> ( X1 = X3 ) ) ) ),
inference(beta-eta_normalization,[],[f1412]) ).
thf(f1414,plain,
! [X2: hF_Mirabelle_hf,X3: hF_Mirabelle_hf,X1: hF_Mirabelle_hf] :
( ( $false
= ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) ) )
| ( $false
= ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X3 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) ) )
| ( $true
= ( X1 = X3 ) ) ),
inference(imp_proxy_clausification,[],[f1413]) ).
thf(f1415,plain,
! [X2: hF_Mirabelle_hf,X3: hF_Mirabelle_hf,X1: hF_Mirabelle_hf] :
( ( $false
= ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X1 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) ) )
| ( $false
= ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X2 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X3 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) ) )
| ( X1 = X3 ) ),
inference(equality_proxy_clausification,[],[f1414]) ).
thf(f2526,plain,
! [X2: hF_Mirabelle_hf,X0: hF_Mirabelle_hf,X1: hF_Mirabelle_hf] :
( ( $false
= ( ^ [Y0: hF_Mirabelle_hf,Y1: hF_Mirabelle_hf] : ( member1367349282lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ Y1 ) )
@ X0
@ ( hF_Mir1653039215strict @ X1 @ X2 ) ) )
| ( $true
= ( ( ^ [Y0: hF_Mirabelle_hf,Y1: hF_Mirabelle_hf] : ( member1367349282lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ Y1 ) )
@ X0
@ X1 )
& ( ?? @ hF_Mirabelle_hf
@ ^ [Y0: hF_Mirabelle_hf] :
( ?? @ hF_Mirabelle_hf
@ ^ [Y1: hF_Mirabelle_hf] :
( ( ( ^ [Y2: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] :
( ^ [Y4: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y4 @ ( hF_Mirabelle_hfset @ Y5 ) ) )
@ ( ^ [Y4: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y4 @ ( hF_Mirabelle_hfset @ Y5 ) ) )
@ Y2
@ zero_z189798548lle_hf )
@ ( ^ [Y4: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y4 @ ( hF_Mirabelle_hfset @ Y5 ) ) )
@ ( ^ [Y4: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y4 @ ( hF_Mirabelle_hfset @ Y5 ) ) )
@ Y2
@ ( ^ [Y4: hF_Mirabelle_hf,Y5: hF_Mirabelle_hf] : ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ Y4 @ ( hF_Mirabelle_hfset @ Y5 ) ) )
@ Y3
@ zero_z189798548lle_hf ) )
@ zero_z189798548lle_hf ) )
@ Y1
@ Y0 )
= X0 )
& ( ^ [Y2: hF_Mirabelle_hf,Y3: hF_Mirabelle_hf] : ( member1367349282lle_hf @ Y2 @ ( hF_Mirabelle_hfset @ Y3 ) )
@ Y1
@ X2 ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f1261]) ).
thf(f2528,plain,
! [X2: hF_Mirabelle_hf,X0: hF_Mirabelle_hf,X1: hF_Mirabelle_hf] :
( ( $false
= ( ^ [Y0: hF_Mirabelle_hf,Y1: hF_Mirabelle_hf] : ( member1367349282lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ Y1 ) )
@ X0
@ ( hF_Mir1653039215strict @ X1 @ X2 ) ) )
| ( $true
= ( ^ [Y0: hF_Mirabelle_hf,Y1: hF_Mirabelle_hf] : ( member1367349282lle_hf @ Y0 @ ( hF_Mirabelle_hfset @ Y1 ) )
@ X0
@ X1 ) ) ),
inference(and_proxy_clausification,[],[f2526]) ).
thf(f2529,plain,
! [X2: hF_Mirabelle_hf,X0: hF_Mirabelle_hf,X1: hF_Mirabelle_hf] :
( ( $false
= ( member1367349282lle_hf @ X0 @ ( hF_Mirabelle_hfset @ ( hF_Mir1653039215strict @ X1 @ X2 ) ) ) )
| ( ( member1367349282lle_hf @ X0 @ ( hF_Mirabelle_hfset @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f2528]) ).
thf(f2589,plain,
( ( $true = $false )
| ( $true
= ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK50 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) ) ) ),
inference(constrained_superposition,[],[f1400,f2529]) ).
thf(f2590,plain,
( ( $true = $false )
| ( $true
= ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK52 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) ) ) ),
inference(constrained_superposition,[],[f1404,f2529]) ).
thf(f2591,plain,
( $true
= ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK52 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) ) ),
inference(trivial_inequality_removal,[],[f2590]) ).
thf(f2592,plain,
( $true
= ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK50 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) ) ),
inference(trivial_inequality_removal,[],[f2589]) ).
thf(f4144,plain,
! [X0: hF_Mirabelle_hf] :
( ( $true = $false )
| ( $false
= ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) ) )
| ( sK50 = X0 ) ),
inference(constrained_superposition,[],[f2592,f1415]) ).
thf(f4147,plain,
! [X0: hF_Mirabelle_hf] :
( ( $false
= ( member1367349282lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ sK51 @ ( hF_Mirabelle_hfset @ ( hF_Mirabelle_HF @ ( insert9649339lle_hf @ X0 @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ zero_z189798548lle_hf ) ) ) ) ) ) @ ( hF_Mirabelle_hfset @ r ) ) )
| ( sK50 = X0 ) ),
inference(trivial_inequality_removal,[],[f4144]) ).
thf(f4211,plain,
( ( $true = $false )
| ( sK50 = sK52 ) ),
inference(constrained_superposition,[],[f2591,f4147]) ).
thf(f4212,plain,
sK50 = sK52,
inference(trivial_inequality_removal,[],[f4211]) ).
thf(f4215,plain,
$false,
inference(forward_subsumption_resolution,[],[f4212,f1405]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP076^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n002.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 19:50:38 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 Running first-order model finding
% 0.09/0.20 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.54/0.59 % (1759302)Will run a generic schedule for satisfiability detection.
% 2.54/0.59 % (1759308)% WARNING: option uhcvi not known.
% 2.54/0.59 % (1759308)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3610823795:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.54/0.59 % (1759308)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.54/0.59 % (1759307)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1430137680_2999 on theBenchmark for (2999ds/0Mi)
% 2.54/0.59 % (1759310)dis+10_1_sil=32000:sp=arity:random_seed=3882919609:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.54/0.59 % (1759309)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=811929992:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.54/0.59 % (1759311)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3930890588:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.54/0.59 % (1759313)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2610203278:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.54/0.59 % (1759308)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.54/0.59 % (1759311)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.54/0.59 % (1759312)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=407451117:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.54/0.59 % Exception at run slice level
% 2.54/0.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.54/0.59 % (1759310)Instruction limit reached!
% 2.54/0.59 % (1759310)------------------------------
% 2.54/0.59 % (1759310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.59 % (1759310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.59 % (1759310)CaDiCaL version: 2.1.3
% 2.54/0.59 % (1759310)Termination reason: Instruction limit
% 2.54/0.59 % (1759310)Termination phase: Saturation
% 2.54/0.59 % (1759310)Time elapsed: 0.044 s
% 2.54/0.59 % (1759310)Peak memory usage: 12 MB
% 2.54/0.59 % (1759310)Instructions burned: 103 (million)
% 2.54/0.59 % (1759311)Instruction limit reached!
% 2.54/0.59 % (1759311)------------------------------
% 2.54/0.59 % (1759311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.59 % (1759311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.59 % (1759311)CaDiCaL version: 2.1.3
% 2.54/0.59 % (1759311)Termination reason: Instruction limit
% 2.54/0.59 % (1759311)Termination phase: Saturation
% 2.54/0.59 % (1759311)Time elapsed: 0.050 s
% 2.54/0.59 % (1759311)Peak memory usage: 12 MB
% 2.54/0.59 % (1759311)Instructions burned: 116 (million)
% 2.54/0.59 % (1759321)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2868973035:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.54/0.59 % (1759322)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4024215962:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.54/0.59 % (1759324)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1777186413:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 2.54/0.59 % (1759313)Instruction limit reached!
% 2.54/0.59 % (1759313)------------------------------
% 2.54/0.59 % (1759313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.59 % (1759313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.59 % (1759313)CaDiCaL version: 2.1.3
% 2.54/0.59 % (1759313)Termination reason: Instruction limit
% 2.54/0.59 % (1759313)Termination phase: Saturation
% 2.54/0.59 % (1759313)Time elapsed: 0.072 s
% 2.54/0.59 % (1759313)Peak memory usage: 14 MB
% 2.54/0.59 % (1759313)Instructions burned: 160 (million)
% 2.54/0.59 % Exception at run slice level
% 2.54/0.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.54/0.59 % (1759324)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.54/0.59 % (1759327)ott-21_1_sil=16000:fs=off:random_seed=754207820:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.54/0.59 % (1759328)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1242233969:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.54/0.59 % (1759324)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.54/0.59 % (1759312)Instruction limit reached!
% 2.54/0.59 % (1759312)------------------------------
% 2.54/0.59 % (1759312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.59 % (1759312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.59 % (1759312)CaDiCaL version: 2.1.3
% 2.54/0.59 % (1759312)Termination reason: Instruction limit
% 2.54/0.59 % (1759312)Termination phase: Saturation
% 2.54/0.59 % (1759312)Time elapsed: 0.106 s
% 2.54/0.59 % (1759312)Peak memory usage: 13 MB
% 2.54/0.59 % (1759312)Instructions burned: 131 (million)
% 2.54/0.59 % (1759322)Instruction limit reached!
% 2.54/0.59 % (1759322)------------------------------
% 2.54/0.59 % (1759322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.59 % (1759322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.59 % (1759322)CaDiCaL version: 2.1.3
% 2.54/0.59 % (1759322)Termination reason: Instruction limit
% 2.54/0.59 % (1759322)Termination phase: Saturation
% 2.54/0.59 % (1759322)Time elapsed: 0.058 s
% 2.54/0.59 % (1759322)Peak memory usage: 13 MB
% 2.54/0.59 % (1759322)Instructions burned: 132 (million)
% 2.54/0.59 % (1759332)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=854182949:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.54/0.59 % (1759331)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2156095629:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.54/0.59 % (1759327)Instruction limit reached!
% 2.54/0.59 % (1759327)------------------------------
% 2.54/0.59 % (1759327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.59 % (1759327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.59 % (1759327)CaDiCaL version: 2.1.3
% 2.54/0.59 % (1759327)Termination reason: Instruction limit
% 2.54/0.59 % (1759327)Termination phase: Saturation
% 2.54/0.59 % (1759327)Time elapsed: 0.079 s
% 2.54/0.59 % (1759327)Peak memory usage: 13 MB
% 2.54/0.59 % (1759327)Instructions burned: 181 (million)
% 2.54/0.59 % Exception at run slice level
% 2.54/0.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.54/0.59 % (1759335)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2289596613:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 2.54/0.59 % (1759336)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3900940368:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 2.54/0.59 % (1759336)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.54/0.59 % Exception at run slice level
% 2.54/0.59 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.54/0.59 % (1759328)Instruction limit reached!
% 2.54/0.59 % (1759328)------------------------------
% 2.54/0.59 % (1759328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.59 % (1759328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.59 % (1759328)CaDiCaL version: 2.1.3
% 2.54/0.59 % (1759328)Termination reason: Instruction limit
% 2.54/0.59 % (1759328)Termination phase: Saturation
% 2.54/0.59 % (1759328)Time elapsed: 0.185 s
% 2.54/0.59 % (1759328)Peak memory usage: 14 MB
% 2.54/0.59 % (1759328)Instructions burned: 477 (million)
% 2.54/0.59 % (1759339)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1866995215:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 2.54/0.59 % (1759340)fmb+10_1_sil=64000:random_seed=3465996617:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 2.54/0.59 % (1759339)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.54/0.59 % (1759324) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1759302-1759324"...
% 2.54/0.59 % (1759340)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.54/0.59 % (1759324)...printing done.
% 2.54/0.59 % (1759324)Refutation found. Thanks to Tanya!
% 2.54/0.59 % SZS status Theorem for theBenchmark
% 2.54/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/0.60 % (1759324)------------------------------
% 2.54/0.60 % (1759324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.54/0.60 % (1759324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/0.60 % (1759324)CaDiCaL version: 2.1.3
% 2.54/0.60 % (1759324)Termination reason: Refutation
% 2.54/0.60 % (1759324)Time elapsed: 0.264 s
% 2.54/0.60 % (1759324)Peak memory usage: 15 MB
% 2.54/0.60 % (1759324)Instructions burned: 602 (million)
% 2.54/0.60 % (1759302)Success in time 0.384 s
% 2.54/0.60 % Vampire exiting
%------------------------------------------------------------------------------