%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PHI005^2 : TPTP v9.3.1. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 08:20:20 AM UTC 2026
% Result : Theorem 35.79s 5.47s
% Output : Refutation 35.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 21
% Syntax : Number of formulae : 193 ( 114 unt; 0 typ; 4 def)
% Number of atoms : 1152 ( 251 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 2502 ( 142 ~; 146 |; 11 &;1874 @)
% ( 4 <=>; 137 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 1024 (1024 >; 0 *; 0 +; 0 <<)
% Number of symbols : 266 ( 261 usr; 10 con; 0-5 aty)
% ( 152 !!; 36 ??; 0 @@+; 0 @@-)
% Number of variables : 966 ( 112 sgn 191 !; 4 ?; 966 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
mtrue: $i > $o ).
thf(func_def_2,type,
mfalse: $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mforall_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists_indset: ( ( mu > $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mbox_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mdia_generic: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_19,type,
rel: $i > $i > $o ).
thf(func_def_20,type,
mbox: ( $i > $o ) > $i > $o ).
thf(func_def_21,type,
mdia: ( $i > $o ) > $i > $o ).
thf(func_def_22,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_23,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_24,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
positive: ( mu > $i > $o ) > $i > $o ).
thf(func_def_26,type,
god: mu > $i > $o ).
thf(func_def_27,type,
essence: ( mu > $i > $o ) > mu > $i > $o ).
thf(func_def_28,type,
necessary_existence: mu > $i > $o ).
thf(func_def_29,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_30,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_32,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_35,type,
vNOT: $o > $o ).
thf(func_def_36,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vOR: $o > $o > $o ).
thf(func_def_38,type,
vAND: $o > $o > $o ).
thf(func_def_39,type,
vIMP: $o > $o > $o ).
thf(func_def_40,type,
vIFF: $o > $o > $o ).
thf(func_def_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_43,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
sK2: mu > mu > $i > $o ).
thf(func_def_47,type,
sK3: $i > mu > mu > $i > $o ).
thf(func_def_48,type,
sK4: $i > $i ).
thf(func_def_49,type,
sK5: $i > mu ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sK7: ( mu > $i > mu ) > $i > ( mu > $i > mu > $i > $o ) > ( mu > $i > mu ) > mu ).
thf(func_def_53,type,
sK8: ( mu > $i > mu ) > $i > ( mu > $i > mu > $i > $o ) > ( mu > $i > mu ) > mu ).
thf(func_def_54,type,
sK9: $i > ( mu > $i > mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > mu ).
thf(func_def_55,type,
sK10: $i > ( mu > $i > mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > mu ).
thf(func_def_56,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_57,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_58,type,
sK11: ( mu > $i > $o ) > $i > mu ).
thf(func_def_59,type,
sK12: ( mu > $i > $o ) > $i > mu ).
thf(func_def_60,type,
sK13: $i > ( mu > $i > mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > mu ).
thf(func_def_61,type,
sK14: $i > ( mu > $i > mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > mu ).
thf(func_def_62,type,
sK15: ( mu > $i > mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > $i > mu ).
thf(func_def_63,type,
sK16: ( mu > $i > mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > $i > mu ).
thf(func_def_64,type,
sK17: $i > mu ).
thf(func_def_65,type,
sK18: $i > mu ).
thf(func_def_66,type,
sK19: $i > $i ).
thf(func_def_67,type,
sK20: ( mu > $i > mu > $i > $o ) > ( mu > $i > $i ) > ( mu > $i > mu > $i > $o ) > $i > mu ).
thf(func_def_68,type,
sK21: ( mu > $i > mu > $i > $o ) > ( mu > $i > $i ) > ( mu > $i > mu > $i > $o ) > $i > mu ).
thf(func_def_69,type,
sK22: ( mu > $i > mu ) > ( mu > $i > mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > $i > mu ).
thf(func_def_70,type,
sK23: ( mu > $i > mu ) > ( mu > $i > mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > $i > mu ).
thf(func_def_71,type,
sK24: ( mu > $i > mu ) > ( mu > $i > mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > ( mu > $i > $i ) > $i > mu ).
thf(func_def_72,type,
sK25: ( mu > $i > mu ) > ( mu > $i > mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > ( mu > $i > $i ) > $i > mu ).
thf(func_def_73,type,
sK26: ( mu > $i > mu > $i > $o ) > mu > $i > mu ).
thf(func_def_74,type,
sK27: ( mu > $i > mu > $i > $o ) > mu > $i > mu ).
thf(func_def_75,type,
sK28: $i > ( mu > $i > mu > $i > mu ) > mu ).
thf(func_def_76,type,
sK29: $i > ( mu > $i > mu > $i > mu ) > mu ).
thf(func_def_77,type,
sK30: ( mu > $i > mu > $i > mu ) > $i > mu ).
thf(func_def_78,type,
sK31: ( mu > $i > mu > $i > $o ) > mu > $i > mu ).
thf(func_def_79,type,
sK32: ( mu > $i > mu > $i > $o ) > mu > $i > mu ).
thf(func_def_80,type,
sK33: ( mu > $i > mu > $i > $o ) > mu > $i > $i ).
thf(func_def_81,type,
sK34: ( mu > $i > mu > $i > mu ) > $i > ( mu > $i > mu > $i > mu ) > mu ).
thf(func_def_82,type,
sK35: ( mu > $i > mu > $i > mu ) > $i > ( mu > $i > mu > $i > mu ) > mu ).
thf(func_def_83,type,
sK36: ( mu > $i > mu > $i > $o ) > mu > $i > mu ).
thf(func_def_84,type,
sK37: ( mu > $i > mu > $i > $o ) > mu > $i > mu ).
thf(func_def_85,type,
sK38: ( mu > $i > mu > $i > $o ) > mu > $i > $i ).
thf(func_def_86,type,
sK39: ( mu > $i > mu > $i > mu ) > $i > ( mu > $i > mu > $i > mu ) > mu ).
thf(func_def_87,type,
sK40: ( mu > $i > mu > $i > mu ) > $i > ( mu > $i > mu > $i > mu ) > mu ).
thf(func_def_88,type,
sK41: ( mu > $i > mu > $i > mu ) > $i > ( mu > $i > mu > $i > mu ) > mu ).
thf(func_def_89,type,
sK42: ( mu > $i > mu > $i > mu ) > $i > ( mu > $i > mu > $i > mu ) > mu ).
thf(func_def_90,type,
sK43: ( mu > $i > mu > $i > $o ) > $i > mu ).
thf(func_def_91,type,
sK44: ( mu > $i > mu > $i > $o ) > $i > mu ).
thf(func_def_92,type,
sK45: ( mu > $i > mu > $i > $o ) > $i > $i ).
thf(func_def_93,type,
sK46: $i > ( mu > $i > mu > $i > $i ) > mu ).
thf(func_def_94,type,
sK47: $i > ( mu > $i > mu > $i > $i ) > mu ).
thf(func_def_95,type,
sK48: $i > ( mu > $i > mu > $i > $i ) > mu ).
thf(func_def_96,type,
sK49: ( mu > $i > mu > $i > $i ) > mu ).
thf(func_def_97,type,
sK50: ( mu > $i > mu > $i > $i ) > $i > mu ).
thf(func_def_98,type,
sK51: ( mu > $i > mu > $i > $i ) > $i > mu ).
thf(func_def_99,type,
sK52: mu > mu ).
thf(func_def_100,type,
sK53: mu > $i ).
thf(func_def_101,type,
sK54: ( mu > $i > mu > $i > $o ) > mu ).
thf(func_def_102,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_103,type,
sK55: ( mu > $i > mu > $i > $o ) > mu > mu ).
thf(func_def_104,type,
sK56: ( mu > $i > mu > $i > $o ) > mu ).
thf(func_def_105,type,
sK57: ( mu > $i > mu > $i > $o ) > $i ).
thf(func_def_106,type,
sK58: ( mu > $i > mu > $i > $o ) > mu > $i > $o ).
thf(func_def_107,type,
sK59: ( mu > $i > mu > $i > $o ) > $i ).
thf(func_def_108,type,
sK60: ( mu > $i > mu > $i > $o ) > mu > $i > $o ).
thf(func_def_109,type,
sK61: ( mu > $i > mu > $i > $o ) > $i ).
thf(func_def_110,type,
sK62: ( mu > $i > mu > $i > $o ) > mu > $i > $o ).
thf(func_def_111,type,
sK63: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu ).
thf(func_def_112,type,
sK64: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu ).
thf(func_def_113,type,
sK65: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > mu ).
thf(func_def_114,type,
db8:
!>[X0: $tType] : X0 ).
thf(func_def_115,type,
sK66: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu ).
thf(func_def_116,type,
sK67: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > mu ).
thf(func_def_117,type,
sK68: ( mu > $i > mu > $i > $o ) > mu ).
thf(func_def_118,type,
sK69: ( mu > $i > mu > $i > $o ) > mu > mu ).
thf(func_def_119,type,
sK70: ( mu > $i > mu > $i > $o ) > mu > $i ).
thf(func_def_120,type,
sK71: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu ).
thf(func_def_121,type,
sK72: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu ).
thf(func_def_122,type,
sK73: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > $o ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu ).
thf(func_def_123,type,
sK74: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu ).
thf(func_def_124,type,
sK75: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu ).
thf(func_def_125,type,
sK76: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_126,type,
sK77: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_127,type,
sK78: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_128,type,
sK79: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu ).
thf(func_def_129,type,
sK80: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_130,type,
sK81: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_131,type,
sK82: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu > $i > $o ).
thf(func_def_132,type,
sK83: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu > $i > $o ).
thf(func_def_133,type,
sK84: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu > $i > $o ).
thf(func_def_134,type,
sK85: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > ( mu > $i > ( mu > $i > $o ) > $o ) > mu ).
thf(func_def_135,type,
sK86: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > mu ).
thf(func_def_136,type,
sK87: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > ( mu > $i > ( mu > $i > $o ) > $o ) > mu ).
thf(func_def_137,type,
sK88: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > mu ).
thf(func_def_138,type,
sK89: ( mu > $i > ( mu > $i > $o ) > mu ) > mu ).
thf(func_def_139,type,
sK90: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu ).
thf(func_def_140,type,
sK91: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_141,type,
sK92: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_142,type,
sK93: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu > $i > $o ).
thf(func_def_143,type,
sK94: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu > $i > $o ).
thf(func_def_144,type,
sK95: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu > $i > $o ).
thf(func_def_145,type,
sK96: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_146,type,
db10:
!>[X0: $tType] : X0 ).
thf(func_def_147,type,
db9:
!>[X0: $tType] : X0 ).
thf(func_def_148,type,
sK97: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu > $i > $o ).
thf(func_def_149,type,
sK98: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > ( mu > $i > ( mu > $i > $o ) > $o ) > mu ).
thf(func_def_150,type,
sK99: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu ).
thf(func_def_151,type,
sK100: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > mu ).
thf(func_def_152,type,
sK101: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > ( mu > $i > ( mu > $i > $o ) > $o ) > mu ).
thf(func_def_153,type,
sK102: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu ).
thf(func_def_154,type,
sK103: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_155,type,
sK104: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_156,type,
sK105: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu > $i > $o ).
thf(func_def_157,type,
sK106: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu ).
thf(func_def_158,type,
db12:
!>[X0: $tType] : X0 ).
thf(func_def_159,type,
db11:
!>[X0: $tType] : X0 ).
thf(func_def_160,type,
sK107: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu > $i > $o ).
thf(func_def_161,type,
sK108: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu > $i > $o ).
thf(func_def_162,type,
sK109: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu ).
thf(func_def_163,type,
sK110: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_164,type,
sK111: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_165,type,
sK112: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu ).
thf(func_def_166,type,
sK113: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu ).
thf(func_def_167,type,
sK114: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_168,type,
sK115: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_169,type,
sK116: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_170,type,
sK117: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > $i ).
thf(func_def_171,type,
sK118: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > ( mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_172,type,
sK119: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > ( mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_173,type,
sK120: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu ).
thf(func_def_174,type,
sK121: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_175,type,
sK122: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_176,type,
sK123: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu > $i > $o ).
thf(func_def_177,type,
sK124: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu ).
thf(func_def_178,type,
sK125: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_179,type,
sK126: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > $i ).
thf(func_def_180,type,
sK127: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > $i ).
thf(func_def_181,type,
sK128: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu > $i > $o ).
thf(func_def_182,type,
sK129: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu > $i > $o ).
thf(func_def_183,type,
sK130: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu ).
thf(func_def_184,type,
sK131: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_185,type,
sK132: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > ( mu > $i > ( mu > $i > $o ) > $o ) > mu ).
thf(func_def_186,type,
sK133: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > ( mu > $i > ( mu > $i > $o ) > $o ) > mu ).
thf(func_def_187,type,
sK134: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > ( mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_188,type,
sK135: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > ( mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu ).
thf(func_def_189,type,
sK136: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > mu ).
thf(func_def_190,type,
sK137: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > mu ).
thf(func_def_191,type,
sK138: ( mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > mu ).
thf(func_def_192,type,
sK139: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > ( mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu ).
thf(func_def_193,type,
sK140: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > $i ).
thf(func_def_194,type,
db13:
!>[X0: $tType] : X0 ).
thf(func_def_195,type,
sK141: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu > $i > $o ).
thf(func_def_196,type,
sK142: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu ).
thf(func_def_197,type,
sK143: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > mu > $i > $o ).
thf(func_def_198,type,
sK144: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > mu > $i > $o ).
thf(func_def_199,type,
sK145: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > mu > $i > $o ).
thf(func_def_200,type,
sK146: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > mu > $i > $o ).
thf(func_def_201,type,
sK147: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > mu ).
thf(func_def_202,type,
sK148: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_203,type,
sK149: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_204,type,
sK150: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_205,type,
sK151: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > $i ).
thf(func_def_206,type,
sK152: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_207,type,
sK153: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > $i ).
thf(func_def_208,type,
sK154: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_209,type,
sK155: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_210,type,
sK156: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu > $i > $o ).
thf(func_def_211,type,
sK157: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_212,type,
sK158: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu > $i > $o ).
thf(func_def_213,type,
sK159: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_214,type,
sK160: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > $i ).
thf(func_def_215,type,
sK161: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_216,type,
sK162: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > $i ).
thf(func_def_217,type,
sK163: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_218,type,
sK164: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > $i ).
thf(func_def_219,type,
db14:
!>[X0: $tType] : X0 ).
thf(func_def_220,type,
db19:
!>[X0: $tType] : X0 ).
thf(func_def_221,type,
db18:
!>[X0: $tType] : X0 ).
thf(func_def_222,type,
db17:
!>[X0: $tType] : X0 ).
thf(func_def_223,type,
db16:
!>[X0: $tType] : X0 ).
thf(func_def_224,type,
db15:
!>[X0: $tType] : X0 ).
thf(func_def_225,type,
sK165: $i > ( mu > $i > mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > mu ).
thf(func_def_226,type,
sK166: $i > ( mu > $i > mu > $i > $o ) > ( mu > $i > mu > $i > $o ) > mu ).
thf(func_def_227,type,
sK167: $i > ( mu > $i > mu > $i > mu ) > mu ).
thf(func_def_228,type,
sK168: ( mu > $i > mu > $i > $i ) > $i > mu ).
thf(func_def_229,type,
sK169: ( mu > $i > mu > $i > $i ) > $i > mu ).
thf(func_def_230,type,
sK170: ( mu > $i > mu > $i > mu ) > $i > mu ).
thf(func_def_231,type,
sK171: ( mu > $i > mu > $i > mu > $i > $o ) > ( mu > $i > mu > $i > $i ) > ( mu > $i > $i ) > $i > mu ).
thf(func_def_232,type,
sK172: ( mu > $i > mu > $i > mu > $i > $o ) > ( mu > $i > mu > $i > $i ) > ( mu > $i > $i ) > $i > mu ).
thf(func_def_233,type,
sK173: ( mu > $i > mu > $i > mu ) > ( mu > $i > mu > $i > $i ) > $i > ( mu > $i > mu > $i > mu ) > ( mu > $i > $i ) > mu ).
thf(func_def_234,type,
sK174: ( mu > $i > mu > $i > mu ) > ( mu > $i > mu > $i > $i ) > $i > ( mu > $i > mu > $i > mu ) > ( mu > $i > $i ) > mu ).
thf(func_def_235,type,
sK175: mu > mu ).
thf(func_def_236,type,
sK176: mu > $i ).
thf(func_def_237,type,
sK177: ( mu > $i > mu > $i > $o ) > mu ).
thf(func_def_238,type,
sK178: ( mu > $i > mu > $i > $o ) > $i ).
thf(func_def_239,type,
sK179: ( mu > $i > mu > $i > $o ) > mu > $i > $o ).
thf(func_def_240,type,
sK180: ( mu > $i > mu > $i > $o ) > $i ).
thf(func_def_241,type,
sK181: ( mu > $i > mu > $i > $o ) > mu > $i > $o ).
thf(func_def_242,type,
sK182: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu ).
thf(func_def_243,type,
sK183: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > $o ) > mu ).
thf(func_def_244,type,
sK184: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_245,type,
sK185: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_246,type,
sK186: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_247,type,
sK187: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > $i ).
thf(func_def_248,type,
sK188: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_249,type,
sK189: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > $i ).
thf(func_def_250,type,
sK190: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_251,type,
sK191: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_252,type,
sK192: ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > mu > $i > $o ).
thf(func_def_253,type,
sK193: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_254,type,
sK194: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > mu > $i > $o ).
thf(func_def_255,type,
sK195: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(func_def_256,type,
sK196: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > $i ).
thf(func_def_257,type,
sK197: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o ) > $i ).
thf(func_def_258,type,
sK198: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu ) > $i ).
thf(func_def_259,type,
sK199: ( mu > $i > mu > $i > ( mu > $i > $o ) > mu ) > ( mu > $i > mu > $i > ( mu > $i > $o ) > $o ) > $i ).
thf(f7,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mimplies) ).
thf(f11,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mforall_ind) ).
thf(f12,axiom,
( mforall_indset
= ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mforall_indset) ).
thf(f14,axiom,
( mexists_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
? [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mexists_ind) ).
thf(f17,axiom,
( mbox_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mbox_generic) ).
thf(f18,axiom,
( mdia_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mdia_generic) ).
thf(f19,axiom,
( mbox
= ( mbox_generic @ rel ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mbox) ).
thf(f20,axiom,
( mdia
= ( mdia_generic @ rel ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mdia) ).
thf(f21,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^0.ax',mvalid) ).
thf(f23,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^1.ax',msymmetric) ).
thf(f24,axiom,
msymmetric @ rel,
file('/export/starexec/sandbox/benchmark/Axioms/LCL016^1.ax',sym) ).
thf(f25,axiom,
( god
= ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] : ( mimplies @ ( positive @ X1 ) @ ( X1 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',defD1) ).
thf(f26,axiom,
( necessary_existence
= ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies @ ( essence @ X1 @ X0 )
@ ( mbox
@ ( mexists_ind
@ ^ [X2: mu] : ( X1 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',defD3) ).
thf(f27,axiom,
mvalid @ ( positive @ necessary_existence ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axA5) ).
thf(f28,axiom,
( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X0: mu] : ( god @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corC) ).
thf(f29,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( god @ X0 ) @ ( essence @ god @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thmT2) ).
thf(f30,conjecture,
( mvalid
@ ( mbox
@ ( mexists_ind
@ ^ [X0: mu] : ( god @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thmT3) ).
thf(f31,negated_conjecture,
~ ( mvalid
@ ( mbox
@ ( mexists_ind
@ ^ [X0: mu] : ( god @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f41,plain,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f42,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f49,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f50,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f51,plain,
( mforall_indset
= ( ^ [X0: ( mu > $i > $o ) > $i > $o,X1: $i] :
! [X2: mu > $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f52,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f55,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
? [X2: mu] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f14]) ).
thf(f56,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f61,plain,
( mbox_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f62,plain,
( mbox_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f63,plain,
( mdia_generic
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
? [X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f64,plain,
( mdia_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f65,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f21]) ).
thf(f66,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f69,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f70,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f71,plain,
msymmetric @ rel,
inference(rectify,[],[f24]) ).
thf(f72,plain,
( ( msymmetric @ rel )
= $true ),
inference(fool_elimination,[],[f71]) ).
thf(f73,plain,
( god
= ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] : ( mimplies @ ( positive @ X1 ) @ ( X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f74,plain,
( god
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] : ( mimplies @ ( positive @ Y1 ) @ ( Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f75,plain,
( necessary_existence
= ( ^ [X0: mu] :
( mforall_indset
@ ^ [X1: mu > $i > $o] :
( mimplies @ ( essence @ X1 @ X0 )
@ ( mbox
@ ( mexists_ind
@ ^ [X2: mu] : ( X1 @ X2 ) ) ) ) ) ) ),
inference(rectify,[],[f26]) ).
thf(f76,plain,
( necessary_existence
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] :
( mimplies @ ( essence @ Y1 @ Y0 )
@ ( mbox
@ ( mexists_ind
@ ^ [Y2: mu] : ( Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f77,plain,
mvalid @ ( positive @ necessary_existence ),
inference(rectify,[],[f27]) ).
thf(f78,plain,
( ( mvalid @ ( positive @ necessary_existence ) )
= $true ),
inference(fool_elimination,[],[f77]) ).
thf(f79,plain,
( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [X0: mu] : ( god @ X0 ) ) ) ),
inference(rectify,[],[f28]) ).
thf(f80,plain,
( $true
= ( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [Y0: mu] : ( god @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f81,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( god @ X0 ) @ ( essence @ god @ X0 ) ) ) ),
inference(rectify,[],[f29]) ).
thf(f82,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( god @ Y0 ) @ ( essence @ god @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f83,plain,
~ ( mvalid
@ ( mbox
@ ( mexists_ind
@ ^ [X0: mu] : ( god @ X0 ) ) ) ),
inference(rectify,[],[f31]) ).
thf(f84,plain,
( $true
!= ( mvalid
@ ( mbox
@ ( mexists_ind
@ ^ [Y0: mu] : ( god @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f85,plain,
( $true
!= ( mvalid
@ ( mbox
@ ( mexists_ind
@ ^ [Y0: mu] : ( god @ Y0 ) ) ) ) ),
inference(flattening,[],[f84]) ).
thf(f92,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f96,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f97,plain,
( mforall_indset
= ( ^ [Y0: ( mu > $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f99,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f102,plain,
( mbox_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f103,plain,
( mdia_generic
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f104,plain,
( mbox
= ( mbox_generic @ rel ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f105,plain,
( mdia
= ( mdia_generic @ rel ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f106,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f108,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f109,plain,
( ( msymmetric @ rel )
= $true ),
inference(cnf_transformation,[],[f72]) ).
thf(f110,plain,
( god
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] : ( mimplies @ ( positive @ Y1 ) @ ( Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f111,plain,
( necessary_existence
= ( ^ [Y0: mu] :
( mforall_indset
@ ^ [Y1: mu > $i > $o] :
( mimplies @ ( essence @ Y1 @ Y0 )
@ ( mbox
@ ( mexists_ind
@ ^ [Y2: mu] : ( Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f112,plain,
( ( mvalid @ ( positive @ necessary_existence ) )
= $true ),
inference(cnf_transformation,[],[f78]) ).
thf(f113,plain,
( $true
= ( mvalid
@ ( mdia
@ ( mexists_ind
@ ^ [Y0: mu] : ( god @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f114,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( god @ Y0 ) @ ( essence @ god @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f115,plain,
( $true
!= ( mvalid
@ ( mbox
@ ( mexists_ind
@ ^ [Y0: mu] : ( god @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f118,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ rel ) ),
inference(definition_unfolding,[],[f104,f102]) ).
thf(f119,plain,
( mdia
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ rel ) ),
inference(definition_unfolding,[],[f105,f103]) ).
thf(f120,plain,
( god
= ( ^ [Y0: mu] :
( ^ [Y1: ( mu > $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( positive @ Y1 )
@ ( Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f110,f97,f92]) ).
thf(f121,plain,
( necessary_existence
= ( ^ [Y0: mu] :
( ^ [Y1: ( mu > $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( essence @ Y1 @ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu] : ( Y1 @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f111,f97,f92,f118,f99]) ).
thf(f122,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ rel ) ),
inference(definition_unfolding,[],[f109,f108]) ).
thf(f123,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( positive
@ ^ [Y0: mu] :
( ^ [Y1: ( mu > $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( essence @ Y1 @ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ rel
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu] : ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f112,f106,f121]) ).
thf(f124,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ rel
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu] :
( ^ [Y2: ( mu > $i > $o ) > $i > $o,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu > $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( positive @ Y2 )
@ ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f113,f106,f119,f99,f120]) ).
thf(f125,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] :
( ( Y1 @ Y3 )
=> ( Y2 @ Y3 ) )
@ ( ^ [Y1: mu] :
( ^ [Y2: ( mu > $i > $o ) > $i > $o,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu > $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( positive @ Y2 )
@ ( Y2 @ Y1 ) ) )
@ Y0 )
@ ( essence
@ ^ [Y1: mu] :
( ^ [Y2: ( mu > $i > $o ) > $i > $o,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu > $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( positive @ Y2 )
@ ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f114,f106,f96,f92,f120,f120]) ).
thf(f126,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ rel
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu] :
( ^ [Y2: ( mu > $i > $o ) > $i > $o,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: mu > $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( positive @ Y2 )
@ ( Y2 @ Y1 ) ) )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f115,f106,f118,f99,f120]) ).
thf(f127,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ Y0 @ Y1 )
| ( ?? @ mu
@ ^ [Y2: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f126]) ).
thf(f128,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ Y0 @ Y1 )
| ( ?? @ mu
@ ^ [Y2: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f127]) ).
thf(f129,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ sK0 @ Y0 )
| ( ?? @ mu
@ ^ [Y1: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f128]) ).
thf(f130,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel @ sK0 @ Y0 )
| ( ?? @ mu
@ ^ [Y1: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f129]) ).
thf(f131,plain,
( $false
= ( ~ ( rel @ sK0 @ sK1 )
| ( ?? @ mu
@ ^ [Y0: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK1 )
=> ( Y1 @ Y0 @ sK1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f130]) ).
thf(f132,plain,
( $false
= ( ?? @ mu
@ ^ [Y0: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK1 )
=> ( Y1 @ Y0 @ sK1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f131]) ).
thf(f135,plain,
! [X1: mu] :
( $false
= ( ^ [Y0: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ sK1 )
=> ( Y1 @ Y0 @ sK1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f132]) ).
thf(f136,plain,
! [X1: mu] :
( $false
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK1 )
=> ( Y0 @ X1 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f137,plain,
! [X1: mu] :
( $false
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ sK1 )
=> ( Y0 @ X1 @ sK1 ) )
@ ( sK2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f136]) ).
thf(f138,plain,
! [X1: mu] :
( $false
= ( ( positive @ ( sK2 @ X1 ) @ sK1 )
=> ( sK2 @ X1 @ X1 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f139,plain,
! [X1: mu] :
( $false
= ( sK2 @ X1 @ X1 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X1: mu] :
( $true
= ( positive @ ( sK2 @ X1 ) @ sK1 ) ),
inference(imp_proxy_clausification,[],[f138]) ).
thf(f141,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( essence
@ ^ [Y2: mu,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( positive @ Y4 @ Y3 )
=> ( Y4 @ Y2 @ Y3 ) ) )
@ Y1
@ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f125]) ).
thf(f142,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) )
=> ( essence
@ ^ [Y2: mu,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( positive @ Y4 @ Y3 )
=> ( Y4 @ Y2 @ Y3 ) ) )
@ Y1
@ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X1: $i] :
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ X1 )
=> ( Y1 @ Y0 @ X1 ) ) )
=> ( essence
@ ^ [Y1: mu,Y2: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y2 )
=> ( Y3 @ Y1 @ Y2 ) ) )
@ Y0
@ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f144,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ X1 )
=> ( Y1 @ Y0 @ X1 ) ) )
=> ( essence
@ ^ [Y1: mu,Y2: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y2 )
=> ( Y3 @ Y1 @ Y2 ) ) )
@ Y0
@ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ X1 )
=> ( Y0 @ X2 @ X1 ) ) )
=> ( essence
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X2
@ X1 ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
! [X2: mu,X1: $i] :
( ( $false
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ X1 )
=> ( Y0 @ X2 @ X1 ) ) ) )
| ( $true
= ( essence
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X2
@ X1 ) ) ),
inference(imp_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X2: mu,X1: $i] :
( ( $false
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ X1 )
=> ( Y0 @ X2 @ X1 ) )
@ ( sK3 @ X1 @ X2 ) ) )
| ( $true
= ( essence
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X2
@ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X2: mu,X1: $i] :
( ( $false
= ( ( positive @ ( sK3 @ X1 @ X2 ) @ X1 )
=> ( sK3 @ X1 @ X2 @ X2 @ X1 ) ) )
| ( $true
= ( essence
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X2
@ X1 ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
! [X2: mu,X1: $i] :
( ( $false
= ( sK3 @ X1 @ X2 @ X2 @ X1 ) )
| ( $true
= ( essence
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X2
@ X1 ) ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( positive @ ( sK3 @ X1 @ X2 ) @ X1 ) )
| ( $true
= ( essence
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X2
@ X1 ) ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
& ( ?? @ mu
@ ^ [Y2: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f124]) ).
thf(f152,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( rel @ Y0 @ Y1 )
& ( ?? @ mu
@ ^ [Y2: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y1 )
=> ( Y3 @ Y2 @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X1: $i] :
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
& ( ?? @ mu
@ ^ [Y1: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel @ X1 @ Y0 )
& ( ?? @ mu
@ ^ [Y1: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y0 )
=> ( Y2 @ Y1 @ Y0 ) ) ) ) )
@ ( sK4 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( $true
= ( ( rel @ X1 @ ( sK4 @ X1 ) )
& ( ?? @ mu
@ ^ [Y0: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( sK4 @ X1 ) )
=> ( Y1 @ Y0 @ ( sK4 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( $true
= ( ?? @ mu
@ ^ [Y0: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( sK4 @ X1 ) )
=> ( Y1 @ Y0 @ ( sK4 @ X1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( $true
= ( rel @ X1 @ ( sK4 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f155]) ).
thf(f158,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: mu] :
( !! @ ( mu > $i > $o )
@ ^ [Y1: mu > $i > $o] :
( ( positive @ Y1 @ ( sK4 @ X1 ) )
=> ( Y1 @ Y0 @ ( sK4 @ X1 ) ) ) )
@ ( sK5 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f156]) ).
thf(f159,plain,
! [X1: $i] :
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ ( sK4 @ X1 ) )
=> ( Y0 @ ( sK5 @ X1 ) @ ( sK4 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ ( sK4 @ X1 ) )
=> ( Y0 @ ( sK5 @ X1 ) @ ( sK4 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: mu > $i > $o,X1: $i] :
( $true
= ( ( positive @ X2 @ ( sK4 @ X1 ) )
=> ( X2 @ ( sK5 @ X1 ) @ ( sK4 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
! [X2: mu > $i > $o,X1: $i] :
( ( $false
= ( positive @ X2 @ ( sK4 @ X1 ) ) )
| ( $true
= ( X2 @ ( sK5 @ X1 ) @ ( sK4 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( $true
= ( !! @ $i
@ ( positive
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( essence @ Y2 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel @ Y1 @ Y3 )
| ( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f123]) ).
thf(f164,plain,
! [X1: $i] :
( $true
= ( positive
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( essence @ Y2 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel @ Y1 @ Y3 )
| ( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y1 @ Y0 )
=> ( rel @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f122]) ).
thf(f166,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel @ Y1 @ Y0 )
=> ( rel @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel @ Y0 @ X1 )
=> ( rel @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel @ Y0 @ X1 )
=> ( rel @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel @ X2 @ X1 )
=> ( rel @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel @ X2 @ X1 ) )
| ( $true
= ( rel @ X1 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f628,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( essence @ Y2 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel @ Y1 @ Y3 )
| ( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ ( sK5 @ X0 )
@ ( sK4 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f162,f164]) ).
thf(f629,plain,
! [X0: $i] :
( $true
= ( ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( essence @ Y2 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel @ Y1 @ Y3 )
| ( ?? @ mu
@ ^ [Y4: mu] : ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ ( sK5 @ X0 )
@ ( sK4 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f628]) ).
thf(f630,plain,
! [X0: $i] :
( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( essence @ Y0 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ ( sK4 @ X0 ) @ Y1 )
| ( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f629]) ).
thf(f631,plain,
! [X0: $i,X1: mu > $i > $o] :
( $true
= ( ^ [Y0: mu > $i > $o] :
( ( essence @ Y0 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel @ ( sK4 @ X0 ) @ Y1 )
| ( ?? @ mu
@ ^ [Y2: mu] : ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f630]) ).
thf(f632,plain,
! [X0: $i,X1: mu > $i > $o] :
( $true
= ( ( essence @ X1 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ ( sK4 @ X0 ) @ Y0 )
| ( ?? @ mu
@ ^ [Y1: mu] : ( X1 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f631]) ).
thf(f633,plain,
! [X0: $i,X1: mu > $i > $o] :
( ( $false
= ( essence @ X1 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel @ ( sK4 @ X0 ) @ Y0 )
| ( ?? @ mu
@ ^ [Y1: mu] : ( X1 @ Y1 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f632]) ).
thf(f634,plain,
! [X2: $i,X0: $i,X1: mu > $i > $o] :
( ( $false
= ( essence @ X1 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel @ ( sK4 @ X0 ) @ Y0 )
| ( ?? @ mu
@ ^ [Y1: mu] : ( X1 @ Y1 @ Y0 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f633]) ).
thf(f635,plain,
! [X2: $i,X0: $i,X1: mu > $i > $o] :
( ( $false
= ( essence @ X1 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( $true
= ( ~ ( rel @ ( sK4 @ X0 ) @ X2 )
| ( ?? @ mu
@ ^ [Y0: mu] : ( X1 @ Y0 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f634]) ).
thf(f636,plain,
! [X2: $i,X0: $i,X1: mu > $i > $o] :
( ( $false
= ( essence @ X1 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( $true
= ( ?? @ mu
@ ^ [Y0: mu] : ( X1 @ Y0 @ X2 ) ) )
| ( $true
= ( ~ ( rel @ ( sK4 @ X0 ) @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f635]) ).
thf(f637,plain,
! [X2: $i,X0: $i,X1: mu > $i > $o] :
( ( $false
= ( essence @ X1 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( $true
= ( ^ [Y0: mu] : ( X1 @ Y0 @ X2 )
@ ( sK11 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel @ ( sK4 @ X0 ) @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f636]) ).
thf(f638,plain,
! [X2: $i,X0: $i,X1: mu > $i > $o] :
( ( $false
= ( essence @ X1 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( $true
= ( ^ [Y0: mu] : ( X1 @ Y0 @ X2 )
@ ( sK11 @ X1 @ X2 ) ) )
| ( $false
= ( rel @ ( sK4 @ X0 ) @ X2 ) ) ),
inference(not_proxy_clausification,[],[f637]) ).
thf(f639,plain,
! [X2: $i,X0: $i,X1: mu > $i > $o] :
( ( $false
= ( essence @ X1 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( $true
= ( X1 @ ( sK11 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( rel @ ( sK4 @ X0 ) @ X2 ) ) ),
inference(beta-eta_normalization,[],[f638]) ).
thf(f2150,plain,
! [X0: $i,X1: mu] :
( ( $true = $false )
| ( $true
= ( sK3 @ ( sK4 @ X0 ) @ X1 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( $true
= ( essence
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X1
@ ( sK4 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f162,f150]) ).
thf(f2163,plain,
! [X0: $i,X1: mu] :
( ( $true
= ( sK3 @ ( sK4 @ X0 ) @ X1 @ ( sK5 @ X0 ) @ ( sK4 @ X0 ) ) )
| ( $true
= ( essence
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X1
@ ( sK4 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f2150]) ).
thf(f8816,definition,
( spl6_142
<=> ! [X2: mu > $i > ( mu > $i > $o ) > $o,X1: mu > $i > mu > $i > ( mu > $i > $o ) > $o] :
( ( ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : ( Y2 @ Y0 @ Y1 ) ) )
| ( ( ^ [Y0: mu,Y1: $i] : X2 )
!= X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_142])],[avatar_definition]) ).
thf(f8817,plain,
( ! [X2: mu > $i > ( mu > $i > $o ) > $o,X1: mu > $i > mu > $i > ( mu > $i > $o ) > $o] :
( ( ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : ( Y2 @ Y0 @ Y1 ) ) )
| ( ( ^ [Y0: mu,Y1: $i] : X2 )
!= X1 ) )
| ~ spl6_142 ),
inference(avatar_component_clause,[],[f8816]) ).
thf(f8819,definition,
( spl6_143
<=> ! [X0: mu > $i > mu > $i > ( mu > $i > $o ) > $o,X3: mu > $i > ( mu > $i > $o ) > $o] :
( ( ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : ( positive @ Y2 @ Y1 ) )
!= ( X0
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 ) )
| ( ( ^ [Y0: mu,Y1: $i] : X3 )
!= X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_143])],[avatar_definition]) ).
thf(f8820,plain,
( ! [X3: mu > $i > ( mu > $i > $o ) > $o,X0: mu > $i > mu > $i > ( mu > $i > $o ) > $o] :
( ( ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : ( positive @ Y2 @ Y1 ) )
!= ( X0
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 ) )
| ( ( ^ [Y0: mu,Y1: $i] : X3 )
!= X0 ) )
| ~ spl6_143 ),
inference(avatar_component_clause,[],[f8819]) ).
thf(f8825,plain,
( ! [X0: mu > $i > ( mu > $i > $o ) > $o,X1: mu > $i > mu > $i > ( mu > $i > $o ) > mu] :
( ( ( ^ [Y0: mu,Y1: $i] : X0 )
!= ( ^ [Y0: mu,Y1: $i,Y2: mu,Y3: $i,Y4: mu > $i > $o] :
( Y4 @ ( X1 @ Y0 @ Y1 @ Y2 @ Y3 @ Y4 )
@ ( ^ [Y5: mu,Y6: $i,Y7: mu,Y8: $i,Y9: mu > $i > $o] : Y8
@ Y0
@ Y1
@ Y2
@ Y3
@ Y4 ) ) ) )
| ( ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : Y0 )
!= ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 ) ) )
| ~ spl6_142 ),
inference(equality_resolution,[],[f8817]) ).
thf(f8826,plain,
( ! [X0: mu > $i > ( mu > $i > $o ) > $o,X1: mu > $i > mu > $i > ( mu > $i > $o ) > mu] :
( ( ( ^ [Y0: mu,Y1: $i] : X0 )
!= ( ^ [Y0: mu,Y1: $i,Y2: mu,Y3: $i,Y4: mu > $i > $o] : ( Y4 @ ( X1 @ Y0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
| ( ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : Y0 )
!= ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 ) ) )
| ~ spl6_142 ),
inference(beta-eta_normalization,[],[f8825]) ).
thf(f8879,plain,
( ! [X0: mu > $i > mu > $i > ( mu > $i > $o ) > mu,X1: mu > $i > ( mu > $i > $o ) > mu] :
( ( ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : Y0 )
!= ( X0
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 ) )
| ( ( ^ [Y0: mu,Y1: $i] : X1 )
!= X0 ) )
| ~ spl6_142 ),
inference(equality_resolution,[],[f8826]) ).
thf(f8894,plain,
( ! [X0: mu > $i > ( mu > $i > $o ) > mu] :
( ( ^ [Y0: mu,Y1: $i,Y2: mu,Y3: $i,Y4: mu > $i > $o] : Y2 )
!= ( ^ [Y0: mu,Y1: $i] : X0 ) )
| ~ spl6_142 ),
inference(equality_resolution,[],[f8879]) ).
thf(f8899,plain,
( $false
| ~ spl6_142 ),
inference(equality_resolution,[],[f8894]) ).
thf(f8900,plain,
~ spl6_142,
inference(avatar_contradiction_clause,[],[f8899]) ).
thf(f8903,plain,
( ! [X0: mu > $i > ( mu > $i > $o ) > $o,X1: mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o] :
( ( ( ^ [Y0: mu,Y1: $i] : X0 )
!= ( ^ [Y0: mu,Y1: $i,Y2: mu,Y3: $i,Y4: mu > $i > $o] :
( positive @ ( X1 @ Y0 @ Y1 @ Y2 @ Y3 @ Y4 )
@ ( ^ [Y5: mu,Y6: $i,Y7: mu,Y8: $i,Y9: mu > $i > $o] : Y8
@ Y0
@ Y1
@ Y2
@ Y3
@ Y4 ) ) ) )
| ( ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : Y2 )
!= ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 ) ) )
| ~ spl6_143 ),
inference(equality_resolution,[],[f8820]) ).
thf(f8904,plain,
( ! [X0: mu > $i > ( mu > $i > $o ) > $o,X1: mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o] :
( ( ( ^ [Y0: mu,Y1: $i] : X0 )
!= ( ^ [Y0: mu,Y1: $i,Y2: mu,Y3: $i,Y4: mu > $i > $o] : ( positive @ ( X1 @ Y0 @ Y1 @ Y2 @ Y3 @ Y4 ) @ Y3 ) ) )
| ( ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : Y2 )
!= ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 ) ) )
| ~ spl6_143 ),
inference(beta-eta_normalization,[],[f8903]) ).
thf(f9151,plain,
( ! [X0: mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > $o,X1: mu > $i > ( mu > $i > $o ) > mu > $i > $o] :
( ( ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : Y2 )
!= ( X0
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 ) )
| ( ( ^ [Y0: mu,Y1: $i] : X1 )
!= X0 ) )
| ~ spl6_143 ),
inference(equality_resolution,[],[f8904]) ).
thf(f9209,plain,
( ! [X0: mu > $i > ( mu > $i > $o ) > mu > $i > $o,X1: mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu] :
( ( ( ^ [Y0: mu,Y1: $i] : X0 )
!= ( ^ [Y0: mu,Y1: $i,Y2: mu,Y3: $i,Y4: mu > $i > $o,Y5: mu,Y6: $i] :
( Y4 @ ( X1 @ Y0 @ Y1 @ Y2 @ Y3 @ Y4 @ Y5 @ Y6 )
@ ( ^ [Y7: mu,Y8: $i,Y9: mu,Y10: $i,Y11: mu > $i > $o,Y12: mu,Y13: $i] : Y13
@ Y0
@ Y1
@ Y2
@ Y3
@ Y4
@ Y5
@ Y6 ) ) ) )
| ( ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o,Y3: mu,Y4: $i] : Y3 )
!= ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 ) ) )
| ~ spl6_143 ),
inference(equality_resolution,[],[f9151]) ).
thf(f9210,plain,
( ! [X0: mu > $i > ( mu > $i > $o ) > mu > $i > $o,X1: mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu] :
( ( ( ^ [Y0: mu,Y1: $i] : X0 )
!= ( ^ [Y0: mu,Y1: $i,Y2: mu,Y3: $i,Y4: mu > $i > $o,Y5: mu,Y6: $i] : ( Y4 @ ( X1 @ Y0 @ Y1 @ Y2 @ Y3 @ Y4 @ Y5 @ Y6 ) @ Y6 ) ) )
| ( ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o,Y3: mu,Y4: $i] : Y3 )
!= ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 ) ) )
| ~ spl6_143 ),
inference(beta-eta_normalization,[],[f9209]) ).
thf(f9387,plain,
( ! [X0: mu > $i > mu > $i > ( mu > $i > $o ) > mu > $i > mu,X1: mu > $i > ( mu > $i > $o ) > mu > $i > mu] :
( ( ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o,Y3: mu,Y4: $i] : Y3 )
!= ( X0
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 ) )
| ( ( ^ [Y0: mu,Y1: $i] : X1 )
!= X0 ) )
| ~ spl6_143 ),
inference(equality_resolution,[],[f9210]) ).
thf(f9397,plain,
( ! [X0: mu > $i > ( mu > $i > $o ) > mu > $i > mu] :
( ( ^ [Y0: mu,Y1: $i,Y2: mu,Y3: $i,Y4: mu > $i > $o,Y5: mu,Y6: $i] : Y5 )
!= ( ^ [Y0: mu,Y1: $i] : X0 ) )
| ~ spl6_143 ),
inference(equality_resolution,[],[f9387]) ).
thf(f9402,plain,
( $false
| ~ spl6_143 ),
inference(equality_resolution,[],[f9397]) ).
thf(f9403,plain,
~ spl6_143,
inference(avatar_contradiction_clause,[],[f9402]) ).
thf(f17501,definition,
( spl6_199
<=> ! [X0: $i] :
( $false
= ( rel @ ( sK4 @ X0 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_199])],[avatar_definition]) ).
thf(f17502,plain,
( ! [X0: $i] :
( $false
= ( rel @ ( sK4 @ X0 ) @ sK1 ) )
| ~ spl6_199 ),
inference(avatar_component_clause,[],[f17501]) ).
thf(f17764,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel @ sK1 @ ( sK4 @ X0 ) ) ) )
| ~ spl6_199 ),
inference(constrained_superposition,[],[f170,f17502]) ).
thf(f17819,plain,
( ! [X0: $i] :
( $false
= ( rel @ sK1 @ ( sK4 @ X0 ) ) )
| ~ spl6_199 ),
inference(trivial_inequality_removal,[],[f17764]) ).
thf(f17852,plain,
( ( $true = $false )
| ~ spl6_199 ),
inference(constrained_superposition,[],[f17819,f157]) ).
thf(f17924,plain,
( $false
| ~ spl6_199 ),
inference(trivial_inequality_removal,[],[f17852]) ).
thf(f17925,plain,
~ spl6_199,
inference(avatar_contradiction_clause,[],[f17924]) ).
thf(f23445,definition,
( spl6_207
<=> ! [X0: mu > $i > mu,X1: mu > $i > mu,X3: mu] :
( ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) @ Y1 )
@ sK1 ) )
| ( ( X0
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= X3 )
| ( ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_207])],[avatar_definition]) ).
thf(f23446,plain,
( ! [X3: mu,X0: mu > $i > mu,X1: mu > $i > mu] :
( ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) @ Y1 )
@ sK1 ) )
| ( ( X0
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= X3 )
| ( ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= X3 ) )
| ~ spl6_207 ),
inference(avatar_component_clause,[],[f23445]) ).
thf(f23489,plain,
( ! [X2: mu,X0: mu,X1: mu > $i > mu] :
( ( $true = $false )
| ( ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= X2 )
| ( ( ^ [Y0: mu,Y1: $i] : Y0
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= X2 )
| ( ( ^ [Y0: mu,Y1: $i] : X0 )
!= X1 ) )
| ~ spl6_207 ),
inference(constrained_superposition,[],[f140,f23446]) ).
thf(f23490,plain,
( ! [X2: mu,X0: mu,X1: mu > $i > mu] :
( ( ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= X2 )
| ( ( ^ [Y0: mu,Y1: $i] : Y0
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= X2 )
| ( ( ^ [Y0: mu,Y1: $i] : X0 )
!= X1 ) )
| ~ spl6_207 ),
inference(trivial_inequality_removal,[],[f23489]) ).
thf(f23491,plain,
( ! [X2: mu,X0: mu,X1: mu > $i > mu] :
( ( ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
!= X2 )
| ( ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= X2 )
| ( ( ^ [Y0: mu,Y1: $i] : X0 )
!= X1 ) )
| ~ spl6_207 ),
inference(beta-eta_normalization,[],[f23490]) ).
thf(f23573,plain,
( ! [X0: mu > $i > mu,X1: mu] :
( ( ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
!= ( X0
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 ) )
| ( ( ^ [Y0: mu,Y1: $i] : X1 )
!= X0 ) )
| ~ spl6_207 ),
inference(equality_resolution,[],[f23491]) ).
thf(f23576,plain,
( ! [X0: mu,X1: mu > $i > mu > $i > $o] :
( ( ( ^ [Y0: mu,Y1: $i] : X0 )
!= ( ^ [Y0: mu,Y1: $i] :
( sK11 @ ( X1 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : sK1
@ Y0
@ Y1 ) ) ) )
| ( ( ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 ) ) )
| ~ spl6_207 ),
inference(equality_resolution,[],[f23573]) ).
thf(f23577,plain,
( ! [X0: mu,X1: mu > $i > mu > $i > $o] :
( ( ( ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 ) )
| ( ( ^ [Y0: mu,Y1: $i] : X0 )
!= ( ^ [Y0: mu,Y1: $i] : ( sK11 @ ( X1 @ Y0 @ Y1 ) @ sK1 ) ) ) )
| ~ spl6_207 ),
inference(beta-eta_normalization,[],[f23576]) ).
thf(f23585,plain,
( ! [X2: mu > $i > mu > $i > ( mu > $i > $o ) > $o,X0: mu,X1: mu > $i > mu > $i > ( mu > $i > $o ) > $o] :
( ( ( ^ [Y0: mu,Y1: $i] : X0 )
!= ( ^ [Y0: mu,Y1: $i] :
( sK11
@ ( ^ [Y2: mu,Y3: $i,Y4: mu,Y5: $i] :
( !! @ ( mu > $i > $o )
@ ( ^ [Y6: mu,Y7: $i,Y8: mu,Y9: $i,Y10: mu > $i > $o] :
( ( X1 @ Y6 @ Y7 @ Y8 @ Y9 @ Y10 )
=> ( X2 @ Y6 @ Y7 @ Y8 @ Y9 @ Y10 ) )
@ Y2
@ Y3
@ Y4
@ Y5 ) )
@ Y0
@ Y1 )
@ sK1 ) ) )
| ( ( X2
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : ( Y2 @ Y0 @ Y1 ) ) )
| ( ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : ( positive @ Y2 @ Y1 ) ) ) )
| ~ spl6_207 ),
inference(equality_resolution,[],[f23577]) ).
thf(f23586,plain,
( ! [X2: mu > $i > mu > $i > ( mu > $i > $o ) > $o,X0: mu,X1: mu > $i > mu > $i > ( mu > $i > $o ) > $o] :
( ( ( ^ [Y0: mu,Y1: $i] : X0 )
!= ( ^ [Y0: mu,Y1: $i] :
( sK11
@ ^ [Y2: mu,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( X1 @ Y0 @ Y1 @ Y2 @ Y3 @ Y4 )
=> ( X2 @ Y0 @ Y1 @ Y2 @ Y3 @ Y4 ) ) )
@ sK1 ) ) )
| ( ( X2
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : ( Y2 @ Y0 @ Y1 ) ) )
| ( ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : ( positive @ Y2 @ Y1 ) ) ) )
| ~ spl6_207 ),
inference(beta-eta_normalization,[],[f23585]) ).
thf(f23620,plain,
( ! [X2: mu > $i > $o,X0: mu > $i > mu > $i > ( mu > $i > $o ) > $o,X1: mu > $i > mu > $i > ( mu > $i > $o ) > $o] :
( ( ( ^ [Y0: mu,Y1: $i,Y2: mu,Y3: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y4: mu > $i > $o] :
( ( X1 @ Y0 @ Y1 @ Y2 @ Y3 @ Y4 )
=> ( X0 @ Y0 @ Y1 @ Y2 @ Y3 @ Y4 ) ) ) )
!= ( ^ [Y0: mu,Y1: $i] : X2 ) )
| ( ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : ( positive @ Y2 @ Y1 ) ) )
| ( ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : ( Y2 @ Y0 @ Y1 ) )
!= ( X0
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 ) ) )
| ~ spl6_207 ),
inference(equality_resolution,[],[f23586]) ).
thf(f23623,plain,
( ! [X2: mu > $i > ( mu > $i > $o ) > $o,X3: mu > $i > ( mu > $i > $o ) > $o,X0: mu > $i > mu > $i > ( mu > $i > $o ) > $o,X1: mu > $i > mu > $i > ( mu > $i > $o ) > $o] :
( ( ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : ( positive @ Y2 @ Y1 ) )
!= ( X0
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 ) )
| ( ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= ( ^ [Y0: mu,Y1: $i,Y2: mu > $i > $o] : ( Y2 @ Y0 @ Y1 ) ) )
| ( ( ^ [Y0: mu,Y1: $i] : X2 )
!= X1 )
| ( ( ^ [Y0: mu,Y1: $i] : X3 )
!= X0 ) )
| ~ spl6_207 ),
inference(equality_resolution,[],[f23620]) ).
thf(f23625,plain,
( spl6_142
| spl6_143
| ~ spl6_207 ),
inference(avatar_split_clause,[],[f23623,f23445,f8819,f8816]) ).
thf(f23724,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( essence
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ ( sK5 @ X0 )
@ ( sK4 @ X0 ) ) )
| ( $true
= ( essence
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ ( sK5 @ X0 )
@ ( sK4 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f149,f2163]) ).
thf(f23813,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( essence
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ ( sK5 @ X0 )
@ ( sK4 @ X0 ) ) ) ),
inference(duplicate_literal_removal,[],[f23724]) ).
thf(f23814,plain,
! [X0: $i] :
( $true
= ( essence
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ ( sK5 @ X0 )
@ ( sK4 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f23813]) ).
thf(f25404,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X1 )
@ X1 ) )
| ( $false
= ( rel @ ( sK4 @ X0 ) @ X1 ) ) ),
inference(constrained_superposition,[],[f639,f23814]) ).
thf(f25405,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X1 )
@ X1 ) )
| ( $false
= ( rel @ ( sK4 @ X0 ) @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f25404]) ).
thf(f25406,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( !! @ ( mu > $i > $o )
@ ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ X1 )
=> ( Y0
@ ( sK11
@ ^ [Y1: mu,Y2: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y2 )
=> ( Y3 @ Y1 @ Y2 ) ) )
@ X1 )
@ X1 ) ) ) )
| ( $false
= ( rel @ ( sK4 @ X0 ) @ X1 ) ) ),
inference(beta-eta_normalization,[],[f25405]) ).
thf(f25407,plain,
! [X2: mu > $i > $o,X0: $i,X1: $i] :
( ( $true
= ( ^ [Y0: mu > $i > $o] :
( ( positive @ Y0 @ X1 )
=> ( Y0
@ ( sK11
@ ^ [Y1: mu,Y2: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y3: mu > $i > $o] :
( ( positive @ Y3 @ Y2 )
=> ( Y3 @ Y1 @ Y2 ) ) )
@ X1 )
@ X1 ) )
@ X2 ) )
| ( $false
= ( rel @ ( sK4 @ X0 ) @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f25406]) ).
thf(f25408,plain,
! [X2: mu > $i > $o,X0: $i,X1: $i] :
( ( $true
= ( ( positive @ X2 @ X1 )
=> ( X2
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X1 )
@ X1 ) ) )
| ( $false
= ( rel @ ( sK4 @ X0 ) @ X1 ) ) ),
inference(beta-eta_normalization,[],[f25407]) ).
thf(f25409,plain,
! [X2: mu > $i > $o,X0: $i,X1: $i] :
( ( $true
= ( X2
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X1 )
@ X1 ) )
| ( $false
= ( rel @ ( sK4 @ X0 ) @ X1 ) )
| ( $false
= ( positive @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f25408]) ).
thf(f25913,plain,
! [X2: mu > $i > mu,X3: $i,X0: mu,X1: mu > $i > mu,X4: $i] :
( ( $true = $false )
| ( $false
= ( rel @ ( sK4 @ X4 ) @ X3 ) )
| ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] :
( sK2 @ ( X1 @ Y0 @ Y1 ) @ ( X2 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ X3 ) )
| ( ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X3 )
@ X3 )
!= X0 )
| ( ( X2
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X3 )
@ X3 )
!= X0 )
| ( sK1 != X3 ) ),
inference(constrained_superposition,[],[f139,f25409]) ).
thf(f26007,plain,
! [X2: mu > $i > mu,X3: $i,X0: mu,X1: mu > $i > mu,X4: $i] :
( ( $false
= ( rel @ ( sK4 @ X4 ) @ X3 ) )
| ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] :
( sK2 @ ( X1 @ Y0 @ Y1 ) @ ( X2 @ Y0 @ Y1 )
@ ( ^ [Y2: mu,Y3: $i] : Y3
@ Y0
@ Y1 ) )
@ X3 ) )
| ( ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X3 )
@ X3 )
!= X0 )
| ( ( X2
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X3 )
@ X3 )
!= X0 )
| ( sK1 != X3 ) ),
inference(trivial_inequality_removal,[],[f25913]) ).
thf(f26008,plain,
! [X2: mu > $i > mu,X3: $i,X0: mu,X1: mu > $i > mu,X4: $i] :
( ( sK1 != X3 )
| ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X1 @ Y0 @ Y1 ) @ ( X2 @ Y0 @ Y1 ) @ Y1 )
@ X3 ) )
| ( $false
= ( rel @ ( sK4 @ X4 ) @ X3 ) )
| ( ( X2
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X3 )
@ X3 )
!= X0 )
| ( ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X3 )
@ X3 )
!= X0 ) ),
inference(beta-eta_normalization,[],[f26007]) ).
thf(f26865,plain,
! [X2: $i,X3: mu,X0: mu > $i > mu,X1: mu > $i > mu] :
( ( $false
= ( positive
@ ^ [Y0: mu,Y1: $i] : ( sK2 @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) @ Y1 )
@ sK1 ) )
| ( $false
= ( rel @ ( sK4 @ X2 ) @ sK1 ) )
| ( ( X1
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= X3 )
| ( ( X0
@ ( sK11
@ ^ [Y0: mu,Y1: $i] :
( !! @ ( mu > $i > $o )
@ ^ [Y2: mu > $i > $o] :
( ( positive @ Y2 @ Y1 )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK1 )
@ sK1 )
!= X3 ) ),
inference(equality_resolution,[],[f26008]) ).
thf(f26866,plain,
( spl6_199
| spl6_207 ),
inference(avatar_split_clause,[],[f26865,f23445,f17501]) ).
cnf(s1819,plain,
~ spl6_142,
inference(sat_conversion,[],[f8900]) ).
cnf(s2054,plain,
~ spl6_143,
inference(sat_conversion,[],[f9403]) ).
cnf(s2599,plain,
~ spl6_199,
inference(sat_conversion,[],[f17925]) ).
cnf(s3433,plain,
( spl6_142
| spl6_143
| ~ spl6_207 ),
inference(sat_conversion,[],[f23625]) ).
cnf(s4202,plain,
( spl6_199
| spl6_207 ),
inference(sat_conversion,[],[f26866]) ).
cnf(s4203,plain,
spl6_207,
inference(rat,[],[s4202,s2599]) ).
cnf(s4204,plain,
spl6_142,
inference(rat,[],[s3433,s4203,s2054]) ).
cnf(s4205,plain,
$false,
inference(rat,[],[s1819,s4204]) ).
thf(f26867,plain,
$false,
inference(avatar_sat_refutation,[],[s4205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI005^2 : TPTP v9.3.1. Released v6.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 % Computer : n013.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 13:17:06 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.27 Running first-order model finding
% 0.10/0.27 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.15/1.53 % (2083288)Will run a generic schedule for satisfiability detection.
% 8.15/1.53 % (2083297)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3303291942:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 8.15/1.53 % (2083297)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.15/1.53 % (2083294)% WARNING: option uhcvi not known.
% 8.15/1.53 % (2083294)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1448059416:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 8.15/1.53 % (2083293)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2458295732_2999 on theBenchmark for (2999ds/0Mi)
% 8.15/1.53 % (2083295)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3412152227:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 8.15/1.53 % (2083296)dis+10_1_sil=32000:sp=arity:random_seed=783737925:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 8.15/1.53 % (2083298)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1382217018:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 8.15/1.53 % (2083299)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1028265561:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 8.15/1.53 % (2083294)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.15/1.53 % Exception at run slice level
% 8.15/1.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs% (2083294)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.15/1.53
% 8.15/1.53 % (2083307)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2804053397:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 8.15/1.53 % (2083297)Instruction limit reached!
% 8.15/1.53 % (2083297)------------------------------
% 8.15/1.53 % (2083297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.15/1.53 % (2083297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.15/1.53 % (2083297)CaDiCaL version: 2.1.3
% 8.15/1.53 % (2083297)Termination reason: Instruction limit
% 8.15/1.53 % (2083297)Termination phase: Saturation
% 8.15/1.53 % (2083297)Time elapsed: 0.054 s
% 8.15/1.53 % (2083297)Peak memory usage: 12 MB
% 8.15/1.53 % (2083297)Instructions burned: 116 (million)
% 8.15/1.53 % Exception at run slice level
% 8.15/1.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 8.15/1.53 % (2083309)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2210150847:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 8.15/1.53 % (2083310)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=3093624180:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 8.15/1.53 % (2083310)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 8.15/1.53 % (2083310)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 8.15/1.53 % (2083296)Instruction limit reached!
% 8.15/1.53 % (2083296)------------------------------
% 8.15/1.53 % (2083296)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.15/1.53 % (2083296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.15/1.53 % (2083296)CaDiCaL version: 2.1.3
% 8.15/1.53 % (2083296)Termination reason: Instruction limit
% 8.15/1.53 % (2083296)Termination phase: Saturation
% 8.15/1.53 % (2083296)Time elapsed: 0.105 s
% 8.15/1.53 % (2083296)Peak memory usage: 12 MB
% 8.15/1.53 % (2083296)Instructions burned: 103 (million)
% 8.15/1.53 % (2083298)Instruction limit reached!
% 8.15/1.53 % (2083298)------------------------------
% 8.15/1.53 % (2083298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 8.15/1.53 % (2083298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.15/1.53 % (2083298)CaDiCaL version: 2.1.3
% 8.15/1.53 % (2083298)Termination reason: Instruction limit
% 8.15/1.53 % (2083298)Termination phase: Saturation
% 8.15/1.53 % (2083298)Time elapsed: 0.115 s
% 8.15/1.53 % (2083298)Peak memory usage: 12 MB
% 8.15/1.53 % (2083298)Instructions burned: 131 (million)
% 8.15/1.53 % (2083309)Instruction limit reached!
% 8.15/1.53 % (2083309)------------------------------
% 8.15/1.53 % (2083309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.00/4.45 % (2083309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.00/4.45 % (2083309)CaDiCaL version: 2.1.3
% 29.00/4.45 % (2083309)Termination reason: Instruction limit
% 29.00/4.45 % (2083309)Termination phase: Saturation
% 29.00/4.45 % (2083309)Time elapsed: 0.065 s
% 29.00/4.45 % (2083309)Peak memory usage: 13 MB
% 29.00/4.45 % (2083309)Instructions burned: 134 (million)
% 29.00/4.45 % (2083299)Instruction limit reached!
% 29.00/4.45 % (2083299)------------------------------
% 29.00/4.45 % (2083299)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.00/4.45 % (2083299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.00/4.45 % (2083299)CaDiCaL version: 2.1.3
% 29.00/4.45 % (2083299)Termination reason: Instruction limit
% 29.00/4.45 % (2083299)Termination phase: Saturation
% 29.00/4.45 % (2083299)Time elapsed: 0.139 s
% 29.00/4.45 % (2083299)Peak memory usage: 14 MB
% 29.00/4.45 % (2083299)Instructions burned: 160 (million)
% 29.00/4.45 % (2083313)ott-21_1_sil=16000:fs=off:random_seed=1437503646:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 29.00/4.45 % (2083315)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3213607660:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 29.00/4.45 % Exception at run slice level
% 29.00/4.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.00/4.45 % (2083314)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1286013152:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 29.00/4.45 % (2083320)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=4153392996:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 29.00/4.45 % Exception at run slice level
% 29.00/4.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.00/4.45 % (2083316)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3622498752:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 29.00/4.45 % (2083322)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=2935633805: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)
% 29.00/4.45 % (2083322)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 29.00/4.45 % (2083313)Instruction limit reached!
% 29.00/4.45 % (2083313)------------------------------
% 29.00/4.45 % (2083313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.00/4.45 % (2083313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.00/4.45 % (2083313)CaDiCaL version: 2.1.3
% 29.00/4.45 % (2083313)Termination reason: Instruction limit
% 29.00/4.45 % (2083313)Termination phase: Saturation
% 29.00/4.45 % (2083313)Time elapsed: 0.164 s
% 29.00/4.45 % (2083313)Peak memory usage: 12 MB
% 29.00/4.45 % (2083313)Instructions burned: 180 (million)
% 29.00/4.45 % (2083325)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1213352055:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 29.00/4.45 % (2083325)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 29.00/4.45 % (2083322)Instruction limit reached!
% 29.00/4.45 % (2083322)------------------------------
% 29.00/4.45 % (2083322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.00/4.45 % (2083322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 29.00/4.45 % (2083322)CaDiCaL version: 2.1.3
% 29.00/4.45 % (2083322)Termination reason: Instruction limit
% 29.00/4.45 % (2083322)Termination phase: Saturation
% 29.00/4.45 % (2083322)Time elapsed: 0.308 s
% 29.00/4.45 % (2083322)Peak memory usage: 17 MB
% 29.00/4.45 % (2083322)Instructions burned: 693 (million)
% 29.00/4.45 % (2083327)fmb+10_1_sil=64000:random_seed=2952271988:i=22061:nm=2:gsp=on_2994 on theBenchmark for (2994ds/22061Mi)
% 29.00/4.45 % (2083327)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 29.00/4.45 % Exception at run slice level
% 29.00/4.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 29.00/4.45 % (2083314)Instruction limit reached!
% 29.00/4.45 % (2083314)------------------------------
% 29.00/4.45 % (2083314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 29.00/4.45 % (2083314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.79/5.47 % (2083314)CaDiCaL version: 2.1.3
% 35.79/5.47 % (2083314)Termination reason: Instruction limit
% 35.79/5.47 % (2083314)Termination phase: Saturation
% 35.79/5.47 % (2083314)Time elapsed: 0.427 s
% 35.79/5.47 % (2083314)Peak memory usage: 13 MB
% 35.79/5.47 % (2083314)Instructions burned: 478 (million)
% 35.79/5.47 % (2083329)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2888334395:i=9515:nm=5_2994 on theBenchmark for (2994ds/9515Mi)
% 35.79/5.47 % Exception at run slice level
% 35.79/5.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 35.79/5.47 % (2083330)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3849685958:fmbsr=1.7:i=920_2993 on theBenchmark for (2993ds/920Mi)
% 35.79/5.47 % (2083332)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=3347600948:i=5131_2993 on theBenchmark for (2993ds/5131Mi)
% 35.79/5.47 % (2083332)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 35.79/5.47 % Exception at run slice level
% 35.79/5.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 35.79/5.47 % (2083335)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1683693077:i=1472:ins=7:fdi=8:gsp=on_2993 on theBenchmark for (2993ds/1472Mi)
% 35.79/5.47 % (2083335)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 35.79/5.47 % (2083335)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 35.79/5.47 % (2083310)Instruction limit reached!
% 35.79/5.47 % (2083310)------------------------------
% 35.79/5.47 % (2083310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.79/5.47 % (2083310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.79/5.47 % (2083310)CaDiCaL version: 2.1.3
% 35.79/5.47 % (2083310)Termination reason: Instruction limit
% 35.79/5.47 % (2083310)Termination phase: Saturation
% 35.79/5.47 % (2083310)Time elapsed: 0.582 s
% 35.79/5.47 % (2083310)Peak memory usage: 16 MB
% 35.79/5.47 % (2083310)Instructions burned: 685 (million)
% 35.79/5.47 % (2083337)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=1847759921:i=6324_2992 on theBenchmark for (2992ds/6324Mi)
% 35.79/5.47 % Exception at run slice level
% 35.79/5.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 35.79/5.47 % (2083339)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=4079128451:fmbsr=2.30978:i=2174_2992 on theBenchmark for (2992ds/2174Mi)
% 35.79/5.47 % Exception at run slice level
% 35.79/5.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 35.79/5.47 % (2083341)ott-2_1_sil=16000:newcnf=on:random_seed=2731400402:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2992 on theBenchmark for (2992ds/869Mi)
% 35.79/5.47 % (2083341)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 35.79/5.47 % (2083325)Instruction limit reached!
% 35.79/5.47 % (2083325)------------------------------
% 35.79/5.47 % (2083325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.79/5.47 % (2083325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.79/5.47 % (2083325)CaDiCaL version: 2.1.3
% 35.79/5.47 % (2083325)Termination reason: Instruction limit
% 35.79/5.47 % (2083325)Termination phase: Saturation
% 35.79/5.47 % (2083325)Time elapsed: 0.734 s
% 35.79/5.47 % (2083325)Peak memory usage: 16 MB
% 35.79/5.47 % (2083325)Instructions burned: 880 (million)
% 35.79/5.47 % (2083344)ott+10_1_sil=32000:tgt=ground:random_seed=1293156289:i=5114:av=off_2988 on theBenchmark for (2988ds/5114Mi)
% 35.79/5.47 % (2083316)Instruction limit reached!
% 35.79/5.47 % (2083316)------------------------------
% 35.79/5.47 % (2083316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.79/5.47 % (2083316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.79/5.47 % (2083316)CaDiCaL version: 2.1.3
% 35.79/5.47 % (2083316)Termination reason: Instruction limit
% 35.79/5.47 % (2083316)Termination phase: Saturation
% 35.79/5.47 % (2083316)Time elapsed: 0.980 s
% 35.79/5.47 % (2083316)Peak memory usage: 17 MB
% 35.79/5.47 % (2083316)Instructions burned: 1180 (million)
% 35.79/5.47 % (2083346)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3548357835:i=54282_2987 on theBenchmark for (2987ds/54282Mi)
% 35.79/5.47 % Exception at run slice level
% 35.79/5.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 35.79/5.47 % (2083348)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=769535712:i=3512:aac=none_2987 on theBenchmark for (2987ds/3512Mi)
% 35.79/5.47 % (2083348)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 35.79/5.47 % (2083341)Instruction limit reached!
% 35.79/5.47 % (2083341)------------------------------
% 35.79/5.47 % (2083341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.79/5.47 % (2083341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.79/5.47 % (2083341)CaDiCaL version: 2.1.3
% 35.79/5.47 % (2083341)Termination reason: Instruction limit
% 35.79/5.47 % (2083341)Termination phase: Saturation
% 35.79/5.47 % (2083341)Time elapsed: 0.715 s
% 35.79/5.47 % (2083341)Peak memory usage: 16 MB
% 35.79/5.47 % (2083341)Instructions burned: 869 (million)
% 35.79/5.47 % (2083350)dis+21_1_sil=32000:sas=cadical:random_seed=1531358196:i=3773:amm=off_2984 on theBenchmark for (2984ds/3773Mi)
% 35.79/5.47 % (2083335)Instruction limit reached!
% 35.79/5.47 % (2083335)------------------------------
% 35.79/5.47 % (2083335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.79/5.47 % (2083335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.79/5.47 % (2083335)CaDiCaL version: 2.1.3
% 35.79/5.47 % (2083335)Termination reason: Instruction limit
% 35.79/5.47 % (2083335)Termination phase: Saturation
% 35.79/5.47 % (2083335)Time elapsed: 1.298 s
% 35.79/5.47 % (2083335)Peak memory usage: 17 MB
% 35.79/5.47 % (2083335)Instructions burned: 1472 (million)
% 35.79/5.47 % (2083352)ott+11_1_sil=16000:gs=on:random_seed=1084421702:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2979 on theBenchmark for (2979ds/2251Mi)
% 35.79/5.47 % (2083352)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 35.79/5.47 % (2083332)Instruction limit reached!
% 35.79/5.47 % (2083332)------------------------------
% 35.79/5.47 % (2083332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.79/5.47 % (2083332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.79/5.47 % (2083332)CaDiCaL version: 2.1.3
% 35.79/5.47 % (2083332)Termination reason: Instruction limit
% 35.79/5.47 % (2083332)Termination phase: Saturation
% 35.79/5.47 % (2083332)Time elapsed: 2.180 s
% 35.79/5.47 % (2083332)Peak memory usage: 21 MB
% 35.79/5.47 % (2083332)Instructions burned: 5133 (million)
% 35.79/5.47 % (2083354)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=570064555:fmbsr=1.6:i=67534_2971 on theBenchmark for (2971ds/67534Mi)
% 35.79/5.47 % Exception at run slice level
% 35.79/5.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 35.79/5.47 % (2083356)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=1421839267:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2971 on theBenchmark for (2971ds/4591Mi)
% 35.79/5.47 % (2083352)Instruction limit reached!
% 35.79/5.47 % (2083352)------------------------------
% 35.79/5.47 % (2083352)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.79/5.47 % (2083352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.79/5.47 % (2083352)CaDiCaL version: 2.1.3
% 35.79/5.47 % (2083352)Termination reason: Instruction limit
% 35.79/5.47 % (2083352)Termination phase: Saturation
% 35.79/5.47 % (2083352)Time elapsed: 1.875 s
% 35.79/5.47 % (2083352)Peak memory usage: 19 MB
% 35.79/5.47 % (2083352)Instructions burned: 2252 (million)
% 35.79/5.47 % (2083358)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=2774409419:i=29340_2960 on theBenchmark for (2960ds/29340Mi)
% 35.79/5.47 % (2083348)Instruction limit reached!
% 35.79/5.47 % (2083348)------------------------------
% 35.79/5.47 % (2083348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.79/5.47 % (2083348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.79/5.47 % (2083348)CaDiCaL version: 2.1.3
% 35.79/5.47 % (2083348)Termination reason: Instruction limit
% 35.79/5.47 % (2083348)Termination phase: Saturation
% 35.79/5.47 % (2083348)Time elapsed: 2.839 s
% 35.79/5.47 % (2083348)Peak memory usage: 19 MB
% 35.79/5.47 % (2083348)Instructions burned: 3513 (million)
% 35.79/5.47 % (2083360)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=4108689161:i=5211_2958 on theBenchmark for (2958ds/5211Mi)
% 35.79/5.47 % (2083350)Instruction limit reached!
% 35.79/5.47 % (2083350)------------------------------
% 35.79/5.47 % (2083350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.79/5.47 % (2083350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.79/5.47 % (2083350)CaDiCaL version: 2.1.3
% 35.79/5.47 % (2083350)Termination reason: Instruction limit
% 35.79/5.47 % (2083350)Termination phase: Saturation
% 35.79/5.47 % (2083350)Time elapsed: 3.048 s
% 35.79/5.47 % (2083350)Peak memory usage: 20 MB
% 35.79/5.47 % (2083350)Instructions burned: 3773 (million)
% 35.79/5.47 % (2083362)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=48196142:i=5497:nm=2_2953 on theBenchmark for (2953ds/5497Mi)
% 35.79/5.47 % Exception at run slice level
% 35.79/5.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 35.79/5.47 % (2083364)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=3703280984:fmbsr=2:i=46332_2953 on theBenchmark for (2953ds/46332Mi)
% 35.79/5.47 % Exception at run slice level
% 35.79/5.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 35.79/5.47 % (2083366)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=142450013:i=14071_2952 on theBenchmark for (2952ds/14071Mi)
% 35.79/5.47 % Exception at run slice level
% 35.79/5.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 35.79/5.47 % (2083368)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1062501238:i=22565:add=on:rawr=on_2952 on theBenchmark for (2952ds/22565Mi)
% 35.79/5.47 % (2083356)Instruction limit reached!
% 35.79/5.47 % (2083356)------------------------------
% 35.79/5.47 % (2083356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.79/5.47 % (2083356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.79/5.47 % (2083356)CaDiCaL version: 2.1.3
% 35.79/5.47 % (2083356)Termination reason: Instruction limit
% 35.79/5.47 % (2083356)Termination phase: Saturation
% 35.79/5.47 % (2083356)Time elapsed: 2.016 s
% 35.79/5.47 % (2083356)Peak memory usage: 30 MB
% 35.79/5.47 % (2083356)Instructions burned: 4593 (million)
% 35.79/5.47 % (2083370)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=110541115:i=8173:av=off_2950 on theBenchmark for (2950ds/8173Mi)
% 35.79/5.47 % (2083295) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2083288-2083295"...
% 35.79/5.47 % (2083295)...printing done.
% 35.79/5.47 % (2083295)Refutation found. Thanks to Tanya!
% 35.79/5.47 % SZS status Theorem for theBenchmark
% 35.79/5.47 % SZS output start Proof for theBenchmark
% See solution above
% 35.79/5.48 % (2083295)------------------------------
% 35.79/5.48 % (2083295)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 35.79/5.48 % (2083295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 35.79/5.48 % (2083295)CaDiCaL version: 2.1.3
% 35.79/5.48 % (2083295)Termination reason: Refutation
% 35.79/5.48 % (2083295)Time elapsed: 5.124 s
% 35.79/5.48 % (2083295)Peak memory usage: 27 MB
% 35.79/5.48 % (2083295)Instructions burned: 6254 (million)
% 35.79/5.48 % (2083288)Success in time 5.189 s
% 35.79/5.48 % Vampire exiting
%------------------------------------------------------------------------------