TSTP Solution File: ITP166^2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP166^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:54:18 EDT 2024
% Result : Theorem 2.70s 0.80s
% Output : Refutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 637
% Syntax : Number of formulae : 1357 ( 557 unt; 278 typ; 0 def)
% Number of atoms : 8198 (1396 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 1612 ( 585 ~; 517 |; 102 &; 0 @)
% ( 180 <=>; 228 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 1244 (1235 >; 9 *; 0 +; 0 <<)
% Number of symbols : 483 ( 480 usr; 188 con; 0-9 aty)
% Number of variables : 2607 ( 12 ^2013 !; 176 ?;2607 :)
% ( 406 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
bexp: $tType ).
thf(type_def_6,type,
char: $tType ).
thf(type_def_7,type,
list: $tType > $tType ).
thf(type_def_8,type,
int: $tType ).
thf(type_def_9,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_10,type,
set: $tType > $tType ).
thf(type_def_11,type,
product_prod: ( $tType * $tType ) > $tType ).
thf(type_def_12,type,
nat: $tType ).
thf(type_def_13,type,
sum_sum: ( $tType * $tType ) > $tType ).
thf(type_def_14,type,
com: $tType ).
thf(type_def_15,type,
aexp: $tType ).
thf(type_def_16,type,
option: $tType > $tType ).
thf(type_def_17,type,
tuple_isomorphism: ( $tType * $tType * $tType ) > $tType ).
thf(type_def_18,type,
literal: $tType ).
thf(type_def_19,type,
typerep: $tType ).
thf(func_def_0,type,
tuple_isomorphism: ( $tType * $tType * $tType ) > $tType ).
thf(func_def_1,type,
product_prod: ( $tType * $tType ) > $tType ).
thf(func_def_2,type,
typerep: $tType ).
thf(func_def_3,type,
literal: $tType ).
thf(func_def_4,type,
sum_sum: ( $tType * $tType ) > $tType ).
thf(func_def_5,type,
option: $tType > $tType ).
thf(func_def_6,type,
char: $tType ).
thf(func_def_7,type,
list: $tType > $tType ).
thf(func_def_8,type,
bexp: $tType ).
thf(func_def_9,type,
aexp: $tType ).
thf(func_def_10,type,
set: $tType > $tType ).
thf(func_def_11,type,
nat: $tType ).
thf(func_def_12,type,
int: $tType ).
thf(func_def_13,type,
com: $tType ).
thf(func_def_14,type,
type:
!>[X0: $tType] : $o ).
thf(func_def_15,type,
size:
!>[X0: $tType] : $o ).
thf(func_def_16,type,
zero:
!>[X0: $tType] : $o ).
thf(func_def_17,type,
neg_numeral:
!>[X0: $tType] : $o ).
thf(func_def_18,type,
group_add:
!>[X0: $tType] : $o ).
thf(func_def_19,type,
monoid_add:
!>[X0: $tType] : $o ).
thf(func_def_20,type,
semigroup_add:
!>[X0: $tType] : $o ).
thf(func_def_21,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
thf(func_def_22,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
thf(func_def_23,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
thf(func_def_24,type,
cancel1352612707id_add:
!>[X0: $tType] : $o ).
thf(func_def_25,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
thf(func_def_26,type,
ordere779506340up_add:
!>[X0: $tType] : $o ).
thf(func_def_27,type,
canoni770627133id_add:
!>[X0: $tType] : $o ).
thf(func_def_28,type,
unique1598680935umeral:
!>[X0: $tType] : $o ).
thf(func_def_29,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
thf(func_def_30,type,
bval: bexp > ( list(char) > int ) > $o ).
thf(func_def_31,type,
bNF_Greatest_Shift:
!>[X0: $tType] : ( set(list(X0)) > X0 > set(list(X0)) ) ).
thf(func_def_32,type,
bNF_Greatest_Succ:
!>[X0: $tType] : ( set(list(X0)) > list(X0) > set(X0) ) ).
thf(func_def_33,type,
bNF_Greatest_image2:
!>[X0: $tType,X1: $tType,X2: $tType] : ( set(X0) > ( X0 > X1 ) > ( X0 > X2 ) > set(product_prod(X1,X2)) ) ).
thf(func_def_34,type,
bNF_Greatest_image2p:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( X0 > X1 ) > ( X2 > X3 ) > ( X0 > X2 > $o ) > X1 > X3 > $o ) ).
thf(func_def_35,type,
bNF_Gr1317331620lImage:
!>[X0: $tType,X1: $tType] : ( set(product_prod(X0,X0)) > ( X0 > X1 ) > set(product_prod(X1,X1)) ) ).
thf(func_def_36,type,
bNF_Gr2107612801vImage:
!>[X0: $tType,X1: $tType] : ( set(X0) > set(product_prod(X1,X1)) > ( X0 > X1 ) > set(product_prod(X0,X0)) ) ).
thf(func_def_37,type,
bNF_Greatest_shift:
!>[X0: $tType,X1: $tType] : ( ( list(X0) > X1 ) > X0 > list(X0) > X1 ) ).
thf(func_def_38,type,
basic_BNF_size_sum:
!>[X0: $tType,X1: $tType] : ( ( X0 > nat ) > ( X1 > nat ) > sum_sum(X0,X1) > nat ) ).
thf(func_def_39,type,
big_big_step: product_prod(com,sTfun(list(char),int)) > ( list(char) > int ) > $o ).
thf(func_def_40,type,
assign: list(char) > aexp > com ).
thf(func_def_41,type,
if: bexp > com > com > com ).
thf(func_def_42,type,
skip: com ).
thf(func_def_43,type,
seq: com > com > com ).
thf(func_def_44,type,
while: bexp > com > com ).
thf(func_def_45,type,
size_com: com > nat ).
thf(func_def_46,type,
unique455577585es_aux:
!>[X0: $tType] : ( product_prod(X0,X0) > $o ) ).
thf(func_def_47,type,
plus_plus:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_48,type,
zero_zero:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
append:
!>[X0: $tType] : ( list(X0) > list(X0) > list(X0) ) ).
thf(func_def_50,type,
gen_length:
!>[X0: $tType] : ( nat > list(X0) > nat ) ).
thf(func_def_51,type,
lex:
!>[X0: $tType] : ( set(product_prod(X0,X0)) > set(product_prod(list(X0),list(X0))) ) ).
thf(func_def_52,type,
lexn:
!>[X0: $tType] : ( set(product_prod(X0,X0)) > nat > set(product_prod(list(X0),list(X0))) ) ).
thf(func_def_53,type,
lexord:
!>[X0: $tType] : ( set(product_prod(X0,X0)) > set(product_prod(list(X0),list(X0))) ) ).
thf(func_def_54,type,
cons:
!>[X0: $tType] : ( X0 > list(X0) > list(X0) ) ).
thf(func_def_55,type,
size_list:
!>[X0: $tType] : ( ( X0 > nat ) > list(X0) > nat ) ).
thf(func_def_56,type,
listrel1:
!>[X0: $tType] : ( set(product_prod(X0,X0)) > set(product_prod(list(X0),list(X0))) ) ).
thf(func_def_57,type,
set_Cons:
!>[X0: $tType] : ( set(X0) > set(list(X0)) > set(list(X0)) ) ).
thf(func_def_58,type,
splice:
!>[X0: $tType] : ( list(X0) > list(X0) > list(X0) ) ).
thf(func_def_59,type,
suc: nat > nat ).
thf(func_def_60,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
thf(func_def_61,type,
none:
!>[X0: $tType] : option(X0) ).
thf(func_def_62,type,
some:
!>[X0: $tType] : ( X0 > option(X0) ) ).
thf(func_def_63,type,
case_option:
!>[X0: $tType,X1: $tType] : ( X0 > ( X1 > X0 ) > option(X1) > X0 ) ).
thf(func_def_64,type,
size_option:
!>[X0: $tType] : ( ( X0 > nat ) > option(X0) > nat ) ).
thf(func_def_65,type,
product_Pair:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > product_prod(X0,X1) ) ).
thf(func_def_66,type,
produc2004651681e_prod:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > product_prod(X0,X1) > X2 ) ).
thf(func_def_67,type,
product_rec_prod:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > product_prod(X0,X1) > X2 ) ).
thf(func_def_68,type,
tuple_742722141rphism:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > product_prod(X1,X2) ) > ( product_prod(X1,X2) > X0 ) > tuple_isomorphism(X0,X1,X2) ) ).
thf(func_def_69,type,
tuple_1907371454rphism:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > nat ) > ( X1 > nat ) > ( X2 > nat ) > tuple_isomorphism(X0,X1,X2) > nat ) ).
thf(func_def_70,type,
relati1716060877e_flip: ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( list(char) > int ) > ( list(char) > int ) > $o ).
thf(func_def_71,type,
relati1010904253t_back:
!>[X0: $tType] : ( ( ( list(char) > int ) > X0 > $o ) > bexp > com > nat > ( list(char) > int ) > X0 > $o ) ).
thf(func_def_72,type,
relati1493963588_hoare: ( ( list(char) > int ) > ( list(char) > int ) > $o ) > com > com > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > $o ).
thf(func_def_73,type,
relati167478067_valid: ( ( list(char) > int ) > ( list(char) > int ) > $o ) > com > com > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > $o ).
thf(func_def_74,type,
collect:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) ) ).
thf(func_def_75,type,
sum_Inl:
!>[X0: $tType,X1: $tType] : ( X0 > sum_sum(X0,X1) ) ).
thf(func_def_76,type,
sum_Inr:
!>[X0: $tType,X1: $tType] : ( X0 > sum_sum(X1,X0) ) ).
thf(func_def_77,type,
typerep2: literal > list(typerep) > typerep ).
thf(func_def_78,type,
size_typerep: typerep > nat ).
thf(func_def_79,type,
member:
!>[X0: $tType] : ( X0 > set(X0) > $o ) ).
thf(func_def_80,type,
p: ( list(char) > int ) > ( list(char) > int ) > $o ).
thf(func_def_81,type,
q: ( list(char) > int ) > ( list(char) > int ) > $o ).
thf(func_def_82,type,
b: bexp ).
thf(func_def_83,type,
c: com ).
thf(func_def_84,type,
c2: com ).
thf(func_def_85,type,
k: nat ).
thf(func_def_86,type,
ka: nat ).
thf(func_def_87,type,
s: list(char) > int ).
thf(func_def_88,type,
s_a: list(char) > int ).
thf(func_def_89,type,
s2: list(char) > int ).
thf(func_def_90,type,
sa: list(char) > int ).
thf(func_def_91,type,
t: list(char) > int ).
thf(func_def_92,type,
t_a: list(char) > int ).
thf(func_def_93,type,
t2: list(char) > int ).
thf(func_def_94,type,
ta: list(char) > int ).
thf(func_def_95,type,
u: list(char) > int ).
thf(func_def_96,type,
ua: list(char) > int ).
thf(func_def_100,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_101,type,
vIMP: $o > $o > $o ).
thf(func_def_102,type,
vAND: $o > $o > $o ).
thf(func_def_103,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_104,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_105,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_106,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_107,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_108,type,
vNOT: $o > $o ).
thf(func_def_109,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_110,type,
vOR: $o > $o > $o ).
thf(func_def_111,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_112,type,
sP0: ( com > $o ) > $o ).
thf(func_def_113,type,
sP1: ( com > $o ) > $o ).
thf(func_def_114,type,
sP2: ( list(char) > int ) > bexp > com > ( list(char) > int ) > $o ).
thf(func_def_115,type,
sP3: ( nat > ( list(char) > int ) > ( list(char) > int ) > $o ) > nat > bexp > com > ( list(char) > int ) > com > ( list(char) > int ) > $o ).
thf(func_def_116,type,
sK4: com > bexp ).
thf(func_def_117,type,
sK5: com > com ).
thf(func_def_118,type,
sK6: com > bexp ).
thf(func_def_119,type,
sK7: com > com ).
thf(func_def_120,type,
sK8: com > com ).
thf(func_def_121,type,
sK9: com > com ).
thf(func_def_122,type,
sK10: com > com ).
thf(func_def_123,type,
sK11: com > list(char) ).
thf(func_def_124,type,
sK12: com > aexp ).
thf(func_def_125,type,
sK13: nat > nat ).
thf(func_def_126,type,
sK14: nat > nat ).
thf(func_def_127,type,
sK15: ( com > $o ) > bexp ).
thf(func_def_128,type,
sK16: ( com > $o ) > com ).
thf(func_def_129,type,
sK17: ( com > $o ) > com ).
thf(func_def_130,type,
sK18: ( com > $o ) > com ).
thf(func_def_131,type,
sK19: ( com > $o ) > com ).
thf(func_def_132,type,
sK20: ( com > $o ) > bexp ).
thf(func_def_133,type,
sK21: ( com > $o ) > com ).
thf(func_def_134,type,
sK22: ( com > $o ) > list(char) ).
thf(func_def_135,type,
sK23: ( com > $o ) > aexp ).
thf(func_def_136,type,
sK24: ( nat > $o ) > nat ).
thf(func_def_137,type,
sK25: ( nat > $o ) > nat ).
thf(func_def_138,type,
sK26: ( nat > $o ) > nat ).
thf(func_def_139,type,
sK27:
!>[X0: $tType] : ( nat > list(X0) ) ).
thf(func_def_140,type,
sK28:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_141,type,
sK29:
!>[X0: $tType,X1: $tType] : ( sum_sum(X0,X1) > X1 ) ).
thf(func_def_142,type,
sK30:
!>[X0: $tType,X1: $tType] : ( sum_sum(X0,X1) > X0 ) ).
thf(func_def_143,type,
sK31:
!>[X0: $tType] : ( set(product_prod(X0,X0)) > X0 ) ).
thf(func_def_144,type,
sK32: ( nat > nat > $o ) > nat ).
thf(func_def_145,type,
sK33: ( nat > nat > $o ) > nat ).
thf(func_def_146,type,
sK34: ( nat > nat > $o ) > nat ).
thf(func_def_147,type,
sK35: ( nat > nat > $o ) > nat ).
thf(func_def_148,type,
sK36: ( nat > nat > $o ) > nat ).
thf(func_def_149,type,
sK37: ( nat > nat > $o ) > nat ).
thf(func_def_150,type,
sK38: ( nat > nat > $o ) > nat ).
thf(func_def_151,type,
sK39: ( nat > nat > $o ) > nat ).
thf(func_def_152,type,
sK40: ( nat > nat > $o ) > nat ).
thf(func_def_153,type,
sK41: com > com > list(char) > int ).
thf(func_def_154,type,
sK42: com > com > list(char) > int ).
thf(func_def_155,type,
sK43: com > com > list(char) > int ).
thf(func_def_156,type,
sK44: com > com > list(char) > int ).
thf(func_def_157,type,
sK45: com > com > list(char) > int ).
thf(func_def_158,type,
sK46: com > com > list(char) > int ).
thf(func_def_159,type,
sK47: com > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_160,type,
sK48: com > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_161,type,
sK49: com > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_162,type,
sK50: com > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_163,type,
sK51:
!>[X0: $tType] : ( ( nat > X0 > X0 > $o ) > ( nat > X0 > $o ) > nat > X0 ) ).
thf(func_def_164,type,
sK52:
!>[X0: $tType] : ( ( nat > X0 > X0 > $o ) > ( nat > X0 > $o ) > X0 ) ).
thf(func_def_165,type,
sK53:
!>[X0: $tType] : ( ( nat > X0 > X0 > $o ) > ( nat > X0 > $o ) > nat ) ).
thf(func_def_166,type,
sK54:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
thf(func_def_167,type,
sK55:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
thf(func_def_168,type,
sK56:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
thf(func_def_169,type,
sK57:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
thf(func_def_170,type,
sK58:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_171,type,
sK59:
!>[X0: $tType] : ( set(product_prod(X0,X0)) > X0 ) ).
thf(func_def_172,type,
sK60:
!>[X0: $tType] : ( set(product_prod(X0,X0)) > X0 ) ).
thf(func_def_173,type,
sK61:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X1 ) ).
thf(func_def_174,type,
sK62:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X0 ) ).
thf(func_def_175,type,
sK63:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X1 ) ).
thf(func_def_176,type,
sK64:
!>[X0: $tType,X1: $tType] : ( ( product_prod(X1,X0) > $o ) > X0 ) ).
thf(func_def_177,type,
sK65:
!>[X0: $tType] : ( option(X0) > ( X0 > $o ) > X0 ) ).
thf(func_def_178,type,
sK66: ( list(char) > int ) > bexp > com > ( list(char) > int ) > list(char) > int ).
thf(func_def_179,type,
sK67: ( list(char) > int ) > ( list(char) > int ) > com > com > list(char) > int ).
thf(func_def_180,type,
sK68:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).
thf(func_def_181,type,
sK69:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).
thf(func_def_182,type,
sK70:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).
thf(func_def_183,type,
sK71:
!>[X0: $tType] : ( set(product_prod(X0,X0)) > X0 ) ).
thf(func_def_184,type,
sK72: com > bexp > ( nat > ( list(char) > int ) > ( list(char) > int ) > $o ) > nat ).
thf(func_def_185,type,
sK73: com > bexp > ( nat > ( list(char) > int ) > ( list(char) > int ) > $o ) > nat ).
thf(func_def_186,type,
sK74:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X2 ) ).
thf(func_def_187,type,
sK75:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X1 ) ).
thf(func_def_188,type,
sK76:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X2,product_prod(X1,X0)) > $o ) > X0 ) ).
thf(func_def_189,type,
sK77: com > com > list(char) > int ).
thf(func_def_190,type,
sK78: com > com > list(char) > int ).
thf(func_def_191,type,
sK79: ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_192,type,
sK80: ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_193,type,
sK81: ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_194,type,
sK82: ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_195,type,
sK83:
!>[X0: $tType] : ( set(product_prod(X0,X0)) > list(X0) > X0 > list(X0) > list(X0) ) ).
thf(func_def_196,type,
sK84:
!>[X0: $tType] : ( set(product_prod(X0,X0)) > list(X0) > X0 > list(X0) > X0 ) ).
thf(func_def_197,type,
sK85:
!>[X0: $tType] : ( set(product_prod(X0,X0)) > list(X0) > list(X0) > X0 > list(X0) ) ).
thf(func_def_198,type,
sK86:
!>[X0: $tType] : ( set(product_prod(X0,X0)) > list(X0) > list(X0) > X0 > X0 ) ).
thf(func_def_199,type,
sK87: ( list(char) > int ) > ( list(char) > int ) > list(char) > int ).
thf(func_def_200,type,
sK88: ( list(char) > int ) > ( list(char) > int ) > list(char) > int ).
thf(func_def_201,type,
sK89:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).
thf(func_def_202,type,
sK90:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).
thf(func_def_203,type,
sK91:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).
thf(func_def_204,type,
sK92:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).
thf(func_def_205,type,
sK93:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X3 ) ).
thf(func_def_206,type,
sK94:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X2 ) ).
thf(func_def_207,type,
sK95:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X1 ) ).
thf(func_def_208,type,
sK96:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o ) > X0 ) ).
thf(func_def_209,type,
sK97: ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_210,type,
sK98: ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_211,type,
sK99: ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_212,type,
sK100: ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_213,type,
sK101: ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_214,type,
sK102: ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_215,type,
sK103: ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_216,type,
sK104: ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_217,type,
sK105:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X0 ) ).
thf(func_def_218,type,
sK106:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X1 ) ).
thf(func_def_219,type,
sK107:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X2 ) ).
thf(func_def_220,type,
sK108:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X3 ) ).
thf(func_def_221,type,
sK109:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X4 ) ).
thf(func_def_222,type,
sK110:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X4 ) ).
thf(func_def_223,type,
sK111:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X3 ) ).
thf(func_def_224,type,
sK112:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X2 ) ).
thf(func_def_225,type,
sK113:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X1 ) ).
thf(func_def_226,type,
sK114:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( ( product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o ) > X0 ) ).
thf(func_def_227,type,
sK115:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X0 ) ).
thf(func_def_228,type,
sK116:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X1 ) ).
thf(func_def_229,type,
sK117:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X2 ) ).
thf(func_def_230,type,
sK118:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X3 ) ).
thf(func_def_231,type,
sK119:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X4 ) ).
thf(func_def_232,type,
sK120:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X5 ) ).
thf(func_def_233,type,
sK121: ( nat > ( list(char) > int ) > ( list(char) > int ) > $o ) > nat > bexp > com > ( list(char) > int ) > com > ( list(char) > int ) > list(char) > int ).
thf(func_def_234,type,
sK122: ( nat > ( list(char) > int ) > ( list(char) > int ) > $o ) > nat > bexp > com > ( list(char) > int ) > com > ( list(char) > int ) > list(char) > int ).
thf(func_def_235,type,
sK123: com > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > com > bexp > nat > ( nat > ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_236,type,
sK124: com > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > com > bexp > nat > ( nat > ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_237,type,
sK125: com > bexp > nat > ( nat > ( list(char) > int ) > ( list(char) > int ) > $o ) > nat ).
thf(func_def_238,type,
sK126: com > bexp > nat > ( nat > ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_239,type,
sK127: com > bexp > nat > ( nat > ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(func_def_240,type,
sK128:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X5 ) ).
thf(func_def_241,type,
sK129:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X4 ) ).
thf(func_def_242,type,
sK130:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X3 ) ).
thf(func_def_243,type,
sK131:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X2 ) ).
thf(func_def_244,type,
sK132:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X1 ) ).
thf(func_def_245,type,
sK133:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( ( product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o ) > X0 ) ).
thf(func_def_246,type,
sK134:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X0 > $o ) > ( X1 > $o ) > X1 ) ).
thf(func_def_247,type,
sK135:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X0 ) ).
thf(func_def_248,type,
sK136:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X1 ) ).
thf(func_def_249,type,
sK137:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X2 ) ).
thf(func_def_250,type,
sK138:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X3 ) ).
thf(func_def_251,type,
sK139:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X4 ) ).
thf(func_def_252,type,
sK140:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X5 ) ).
thf(func_def_253,type,
sK141:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X6 ) ).
thf(func_def_254,type,
sK142:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X6 ) ).
thf(func_def_255,type,
sK143:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X5 ) ).
thf(func_def_256,type,
sK144:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X4 ) ).
thf(func_def_257,type,
sK145:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X3 ) ).
thf(func_def_258,type,
sK146:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X2 ) ).
thf(func_def_259,type,
sK147:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X1 ) ).
thf(func_def_260,type,
sK148:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType,X6: $tType] : ( ( product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o ) > X0 ) ).
thf(func_def_261,type,
sK149:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( X0 > X1 > ( X2 > X3 > $o ) > ( X3 > X0 ) > ( X2 > X1 ) > X2 ) ).
thf(func_def_262,type,
sK150:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( X0 > X1 > ( X2 > X3 > $o ) > ( X3 > X0 ) > ( X2 > X1 ) > X3 ) ).
thf(func_def_264,type,
sK152:
!>[X0: $tType] : ( nat > list(X0) > list(X0) ) ).
thf(func_def_265,type,
sK153:
!>[X0: $tType] : ( list(X0) > nat > list(X0) ) ).
thf(func_def_266,type,
sK154: ( ( list(char) > int ) > ( list(char) > int ) > $o ) > ( ( list(char) > int ) > ( list(char) > int ) > $o ) > list(char) > int ).
thf(f3774,plain,
$false,
inference(avatar_sat_refutation,[],[f1919,f1924,f1929,f1934,f1939,f1944,f1949,f1954,f1959,f1964,f1969,f1974,f1979,f1984,f1989,f1994,f1999,f2004,f2009,f2014,f2019,f2024,f2029,f2034,f2039,f2044,f2049,f2054,f2059,f2064,f2069,f2073,f2077,f2081,f2085,f2089,f2121,f2125,f2130,f2134,f2139,f2143,f2147,f2151,f2155,f2159,f2163,f2167,f2171,f2175,f2179,f2183,f2187,f2191,f2199,f2203,f2208,f2212,f2218,f2222,f2226,f2230,f2234,f2238,f2242,f2247,f2251,f2256,f2294,f2298,f2302,f2307,f2311,f2315,f2319,f2324,f2329,f2341,f2345,f2349,f2353,f2357,f2361,f2366,f2370,f2381,f2385,f2389,f2393,f2433,f2437,f2441,f2445,f2449,f2453,f2457,f2471,f2493,f2497,f2515,f2525,f2529,f2533,f2537,f2541,f2545,f2578,f2582,f2593,f2598,f2602,f2609,f2613,f2625,f2629,f2633,f2637,f2651,f2658,f2662,f2666,f2670,f2674,f2678,f2682,f2686,f2690,f2694,f2698,f2765,f2769,f2773,f2777,f2869,f2876,f2908,f2912,f2917,f2922,f2927,f2932,f2936,f2981,f2987,f2993,f2997,f3003,f3009,f3013,f3022,f3027,f3032,f3036,f3050,f3054,f3061,f3074,f3078,f3217,f3221,f3233,f3237,f3245,f3249,f3423,f3434,f3438,f3450,f3464,f3468,f3478,f3489,f3500,f3528,f3539,f3560,f3577,f3581,f3671,f3772,f3773]) ).
thf(f3773,plain,
( ~ spl151_141
| ~ spl151_68
| ~ spl151_139
| ~ spl151_147
| ~ spl151_176 ),
inference(avatar_split_clause,[],[f3571,f3557,f3001,f2919,f2253,f2929]) ).
thf(f2929,plain,
( spl151_141
<=> ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),sa)),ta) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_141])]) ).
thf(f2253,plain,
( spl151_68
<=> ( vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),sa) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_68])]) ).
thf(f2919,plain,
( spl151_139
<=> ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),s_a)),t_a) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_139])]) ).
thf(f3001,plain,
( spl151_147
<=> ! [X0: list(char) > int,X1: list(char) > int] :
( ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),X1)),t_a) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),X0)),ta) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),X0) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),vAPP(nat,nat,suc,ka)),X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_147])]) ).
thf(f3557,plain,
( spl151_176
<=> ( vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),vAPP(nat,nat,suc,ka)),sa),s_a) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_176])]) ).
thf(f3571,plain,
( ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),sa)),ta) != $true )
| ~ spl151_68
| ~ spl151_139
| ~ spl151_147
| ~ spl151_176 ),
inference(trivial_inequality_removal,[],[f3570]) ).
thf(f3570,plain,
( ( $true != $true )
| ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),sa)),ta) != $true )
| ~ spl151_68
| ~ spl151_139
| ~ spl151_147
| ~ spl151_176 ),
inference(forward_demodulation,[],[f3569,f2921]) ).
thf(f2921,plain,
( ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),s_a)),t_a) = $true )
| ~ spl151_139 ),
inference(avatar_component_clause,[],[f2919]) ).
thf(f3569,plain,
( ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),sa)),ta) != $true )
| ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),s_a)),t_a) != $true )
| ~ spl151_68
| ~ spl151_147
| ~ spl151_176 ),
inference(trivial_inequality_removal,[],[f3568]) ).
thf(f3568,plain,
( ( $true != $true )
| ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),sa)),ta) != $true )
| ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),s_a)),t_a) != $true )
| ~ spl151_68
| ~ spl151_147
| ~ spl151_176 ),
inference(forward_demodulation,[],[f3567,f2255]) ).
thf(f2255,plain,
( ( vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),sa) = $true )
| ~ spl151_68 ),
inference(avatar_component_clause,[],[f2253]) ).
thf(f3567,plain,
( ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),sa)),ta) != $true )
| ( vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),sa) != $true )
| ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),s_a)),t_a) != $true )
| ~ spl151_147
| ~ spl151_176 ),
inference(trivial_inequality_removal,[],[f3561]) ).
thf(f3561,plain,
( ( $true != $true )
| ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),sa)),ta) != $true )
| ( vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),sa) != $true )
| ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),s_a)),t_a) != $true )
| ~ spl151_147
| ~ spl151_176 ),
inference(superposition,[],[f3002,f3559]) ).
thf(f3559,plain,
( ( vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),vAPP(nat,nat,suc,ka)),sa),s_a) = $true )
| ~ spl151_176 ),
inference(avatar_component_clause,[],[f3557]) ).
thf(f3002,plain,
( ! [X0: list(char) > int,X1: list(char) > int] :
( ( $true != vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),vAPP(nat,nat,suc,ka)),X0),X1) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),X0)),ta) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),X0) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),X1)),t_a) ) )
| ~ spl151_147 ),
inference(avatar_component_clause,[],[f3001]) ).
thf(f3772,plain,
spl151_180,
inference(avatar_split_clause,[],[f1295,f3770]) ).
thf(f3770,plain,
( spl151_180
<=> ! [X0: com,X3: list(char) > int,X2: list(char) > int,X1: list(char) > int] :
( ( X2 = X3 )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X0),X1)),X3) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X0),X1)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_180])]) ).
thf(f1295,plain,
! [X2: list(char) > int,X3: list(char) > int,X0: com,X1: list(char) > int] :
( ( X2 = X3 )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X0),X1)),X3) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X0),X1)),X2) ) ),
inference(cnf_transformation,[],[f865]) ).
thf(f865,plain,
! [X0: com,X1: list(char) > int,X2: list(char) > int,X3: list(char) > int] :
( ( X2 = X3 )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X0),X1)),X3) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X0),X1)),X2) ) ),
inference(flattening,[],[f864]) ).
thf(f864,plain,
! [X0: com,X1: list(char) > int,X2: list(char) > int,X3: list(char) > int] :
( ( X2 = X3 )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X0),X1)),X3) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X0),X1)),X2) ) ),
inference(ennf_transformation,[],[f466]) ).
thf(f466,plain,
! [X0: com,X1: list(char) > int,X2: list(char) > int,X3: list(char) > int] :
( ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X0),X1)),X2) )
=> ( ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X0),X1)),X3) )
=> ( X2 = X3 ) ) ),
inference(fool_elimination,[],[f465]) ).
thf(f465,plain,
! [X0: com,X1: list(char) > int,X2: list(char) > int,X3: list(char) > int] :
( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X0),X1)),X2)
=> ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X0),X1)),X3)
=> ( X2 = X3 ) ) ),
inference(rectify,[],[f52]) ).
thf(f52,axiom,
! [X22: com,X17: list(char) > int,X15: list(char) > int,X16: list(char) > int] :
( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X22),X17)),X15)
=> ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X22),X17)),X16)
=> ( X15 = X16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_big__step__determ) ).
thf(f3671,plain,
spl151_179,
inference(avatar_split_clause,[],[f1411,f3669]) ).
thf(f3669,plain,
( spl151_179
<=> ! [X1: $tType,X0: $tType,X5: X0 > $o,X3: X1 > $o,X4: option(X1),X2: $o,X7: X1 > X0,X6: X0] :
( ( $true = vAPP(X0,$o,X5,vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),case_option(X0,X1),X6),X7),X4)) )
| ( $true != vAPP(X0,$o,X5,vAPP(X1,X0,X7,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1),vAPP(sTfun(X1,X0),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1)),sK134(X0,X1),X7),X5),X3))) )
| ( $true != vAPP(X0,$o,X5,X6) )
| ( $true != vAPP(option(X1),$o,vAPP(sTfun(X1,$o),sTfun(option(X1),$o),vAPP($o,sTfun(sTfun(X1,$o),sTfun(option(X1),$o)),case_option($o,X1),X2),X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_179])]) ).
thf(f1411,plain,
! [X1: $tType,X0: $tType,X2: $o,X3: X1 > $o,X6: X0,X7: X1 > X0,X4: option(X1),X5: X0 > $o] :
( ( $true = vAPP(X0,$o,X5,vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),case_option(X0,X1),X6),X7),X4)) )
| ( $true != vAPP(X0,$o,X5,vAPP(X1,X0,X7,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1),vAPP(sTfun(X1,X0),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1)),sK134(X0,X1),X7),X5),X3))) )
| ( $true != vAPP(X0,$o,X5,X6) )
| ( $true != vAPP(option(X1),$o,vAPP(sTfun(X1,$o),sTfun(option(X1),$o),vAPP($o,sTfun(sTfun(X1,$o),sTfun(option(X1),$o)),case_option($o,X1),X2),X3),X4) ) ),
inference(cnf_transformation,[],[f1105]) ).
thf(f1105,plain,
! [X0: $tType,X1: $tType,X2: $o,X3: X1 > $o,X4: option(X1),X5: X0 > $o,X6: X0,X7: X1 > X0] :
( ( $true = vAPP(X0,$o,X5,vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),case_option(X0,X1),X6),X7),X4)) )
| ( ( $true != vAPP(X0,$o,X5,vAPP(X1,X0,X7,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1),vAPP(sTfun(X1,X0),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1)),sK134(X0,X1),X7),X5),X3))) )
& ( $true = vAPP(X1,$o,X3,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1),vAPP(sTfun(X1,X0),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1)),sK134(X0,X1),X7),X5),X3)) ) )
| ( ( $true != vAPP(X0,$o,X5,X6) )
& ( $true = X2 ) )
| ( $true != vAPP(option(X1),$o,vAPP(sTfun(X1,$o),sTfun(option(X1),$o),vAPP($o,sTfun(sTfun(X1,$o),sTfun(option(X1),$o)),case_option($o,X1),X2),X3),X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK134])],[f951,f1104]) ).
thf(f1104,plain,
! [X1: $tType,X0: $tType,X3: X1 > $o,X5: X0 > $o,X7: X1 > X0] :
( ? [X8: X1] :
( ( $true != vAPP(X0,$o,X5,vAPP(X1,X0,X7,X8)) )
& ( $true = vAPP(X1,$o,X3,X8) ) )
=> ( ( $true != vAPP(X0,$o,X5,vAPP(X1,X0,X7,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1),vAPP(sTfun(X1,X0),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1)),sK134(X0,X1),X7),X5),X3))) )
& ( $true = vAPP(X1,$o,X3,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1),vAPP(sTfun(X1,X0),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1)),sK134(X0,X1),X7),X5),X3)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f951,plain,
! [X0: $tType,X1: $tType,X2: $o,X3: X1 > $o,X4: option(X1),X5: X0 > $o,X6: X0,X7: X1 > X0] :
( ( $true = vAPP(X0,$o,X5,vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),case_option(X0,X1),X6),X7),X4)) )
| ? [X8: X1] :
( ( $true != vAPP(X0,$o,X5,vAPP(X1,X0,X7,X8)) )
& ( $true = vAPP(X1,$o,X3,X8) ) )
| ( ( $true != vAPP(X0,$o,X5,X6) )
& ( $true = X2 ) )
| ( $true != vAPP(option(X1),$o,vAPP(sTfun(X1,$o),sTfun(option(X1),$o),vAPP($o,sTfun(sTfun(X1,$o),sTfun(option(X1),$o)),case_option($o,X1),X2),X3),X4) ) ),
inference(flattening,[],[f950]) ).
thf(f950,plain,
! [X0: $tType,X1: $tType,X2: $o,X3: X1 > $o,X4: option(X1),X5: X0 > $o,X6: X0,X7: X1 > X0] :
( ( $true = vAPP(X0,$o,X5,vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),case_option(X0,X1),X6),X7),X4)) )
| ? [X8: X1] :
( ( $true != vAPP(X0,$o,X5,vAPP(X1,X0,X7,X8)) )
& ( $true = vAPP(X1,$o,X3,X8) ) )
| ( ( $true != vAPP(X0,$o,X5,X6) )
& ( $true = X2 ) )
| ( $true != vAPP(option(X1),$o,vAPP(sTfun(X1,$o),sTfun(option(X1),$o),vAPP($o,sTfun(sTfun(X1,$o),sTfun(option(X1),$o)),case_option($o,X1),X2),X3),X4) ) ),
inference(ennf_transformation,[],[f590]) ).
thf(f590,plain,
! [X0: $tType,X1: $tType,X2: $o,X3: X1 > $o,X4: option(X1),X5: X0 > $o,X6: X0,X7: X1 > X0] :
( ( $true = vAPP(option(X1),$o,vAPP(sTfun(X1,$o),sTfun(option(X1),$o),vAPP($o,sTfun(sTfun(X1,$o),sTfun(option(X1),$o)),case_option($o,X1),X2),X3),X4) )
=> ( ( ( $true = X2 )
=> ( $true = vAPP(X0,$o,X5,X6) ) )
=> ( ! [X8: X1] :
( ( $true = vAPP(X1,$o,X3,X8) )
=> ( $true = vAPP(X0,$o,X5,vAPP(X1,X0,X7,X8)) ) )
=> ( $true = vAPP(X0,$o,X5,vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),case_option(X0,X1),X6),X7),X4)) ) ) ) ),
inference(fool_elimination,[],[f589]) ).
thf(f589,plain,
! [X0: $tType,X1: $tType,X2: $o,X3: X1 > $o,X4: option(X1),X5: X0 > $o,X6: X0,X7: X1 > X0] :
( vAPP(option(X1),$o,vAPP(sTfun(X1,$o),sTfun(option(X1),$o),vAPP($o,sTfun(sTfun(X1,$o),sTfun(option(X1),$o)),case_option($o,X1),X2),X3),X4)
=> ( ( X2
=> vAPP(X0,$o,X5,X6) )
=> ( ! [X8: X1] :
( vAPP(X1,$o,X3,X8)
=> vAPP(X0,$o,X5,vAPP(X1,X0,X7,X8)) )
=> vAPP(X0,$o,X5,vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),case_option(X0,X1),X6),X7),X4)) ) ) ),
inference(rectify,[],[f217]) ).
thf(f217,axiom,
! [X2: $tType,X0: $tType,X34: $o,X35: X0 > $o,X55: option(X0),X79: X2 > $o,X65: X2,X66: X0 > X2] :
( vAPP(option(X0),$o,vAPP(sTfun(X0,$o),sTfun(option(X0),$o),vAPP($o,sTfun(sTfun(X0,$o),sTfun(option(X0),$o)),case_option($o,X0),X34),X35),X55)
=> ( ( X34
=> vAPP(X2,$o,X79,X65) )
=> ( ! [X155: X0] :
( vAPP(X0,$o,X35,X155)
=> vAPP(X2,$o,X79,vAPP(X0,X2,X66,X155)) )
=> vAPP(X2,$o,X79,vAPP(option(X0),X2,vAPP(sTfun(X0,X2),sTfun(option(X0),X2),vAPP(X2,sTfun(sTfun(X0,X2),sTfun(option(X0),X2)),case_option(X2,X0),X65),X66),X55)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_disjE__realizer2) ).
thf(f3581,plain,
spl151_178,
inference(avatar_split_clause,[],[f1410,f3579]) ).
thf(f3579,plain,
( spl151_178
<=> ! [X1: $tType,X0: $tType,X5: X0 > $o,X3: X1 > $o,X4: option(X1),X2: $o,X7: X1 > X0,X6: X0] :
( ( $true = vAPP(X0,$o,X5,vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),case_option(X0,X1),X6),X7),X4)) )
| ( $true != vAPP(X0,$o,X5,vAPP(X1,X0,X7,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1),vAPP(sTfun(X1,X0),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1)),sK134(X0,X1),X7),X5),X3))) )
| ( $true = X2 )
| ( $true != vAPP(option(X1),$o,vAPP(sTfun(X1,$o),sTfun(option(X1),$o),vAPP($o,sTfun(sTfun(X1,$o),sTfun(option(X1),$o)),case_option($o,X1),X2),X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_178])]) ).
thf(f1410,plain,
! [X1: $tType,X0: $tType,X2: $o,X3: X1 > $o,X6: X0,X7: X1 > X0,X4: option(X1),X5: X0 > $o] :
( ( $true = vAPP(X0,$o,X5,vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),case_option(X0,X1),X6),X7),X4)) )
| ( $true != vAPP(X0,$o,X5,vAPP(X1,X0,X7,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1),vAPP(sTfun(X1,X0),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1)),sK134(X0,X1),X7),X5),X3))) )
| ( $true = X2 )
| ( $true != vAPP(option(X1),$o,vAPP(sTfun(X1,$o),sTfun(option(X1),$o),vAPP($o,sTfun(sTfun(X1,$o),sTfun(option(X1),$o)),case_option($o,X1),X2),X3),X4) ) ),
inference(cnf_transformation,[],[f1105]) ).
thf(f3577,plain,
spl151_177,
inference(avatar_split_clause,[],[f1409,f3575]) ).
thf(f3575,plain,
( spl151_177
<=> ! [X1: $tType,X0: $tType,X5: X0 > $o,X3: X1 > $o,X4: option(X1),X2: $o,X7: X1 > X0,X6: X0] :
( ( $true = vAPP(X0,$o,X5,vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),case_option(X0,X1),X6),X7),X4)) )
| ( $true = vAPP(X1,$o,X3,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1),vAPP(sTfun(X1,X0),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1)),sK134(X0,X1),X7),X5),X3)) )
| ( $true != vAPP(X0,$o,X5,X6) )
| ( $true != vAPP(option(X1),$o,vAPP(sTfun(X1,$o),sTfun(option(X1),$o),vAPP($o,sTfun(sTfun(X1,$o),sTfun(option(X1),$o)),case_option($o,X1),X2),X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_177])]) ).
thf(f1409,plain,
! [X1: $tType,X0: $tType,X2: $o,X3: X1 > $o,X6: X0,X7: X1 > X0,X4: option(X1),X5: X0 > $o] :
( ( $true = vAPP(X0,$o,X5,vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),case_option(X0,X1),X6),X7),X4)) )
| ( $true = vAPP(X1,$o,X3,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1),vAPP(sTfun(X1,X0),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1)),sK134(X0,X1),X7),X5),X3)) )
| ( $true != vAPP(X0,$o,X5,X6) )
| ( $true != vAPP(option(X1),$o,vAPP(sTfun(X1,$o),sTfun(option(X1),$o),vAPP($o,sTfun(sTfun(X1,$o),sTfun(option(X1),$o)),case_option($o,X1),X2),X3),X4) ) ),
inference(cnf_transformation,[],[f1105]) ).
thf(f3560,plain,
spl151_176,
inference(avatar_split_clause,[],[f1461,f3557]) ).
thf(f1461,plain,
vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),vAPP(nat,nat,suc,ka)),sa),s_a) = $true,
inference(cnf_transformation,[],[f684]) ).
thf(f684,plain,
vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),vAPP(nat,nat,suc,ka)),sa),s_a) = $true,
inference(fool_elimination,[],[f683]) ).
thf(f683,plain,
vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),vAPP(nat,nat,suc,ka)),sa),s_a),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),vAPP(nat,nat,suc,ka)),sa),s_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_Suc_Oprems_I7_J) ).
thf(f3539,plain,
spl151_175,
inference(avatar_split_clause,[],[f1408,f3537]) ).
thf(f3537,plain,
( spl151_175
<=> ! [X1: $tType,X0: $tType,X5: X0 > $o,X3: X1 > $o,X4: option(X1),X2: $o,X7: X1 > X0,X6: X0] :
( ( $true = vAPP(X0,$o,X5,vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),case_option(X0,X1),X6),X7),X4)) )
| ( $true = vAPP(X1,$o,X3,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1),vAPP(sTfun(X1,X0),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1)),sK134(X0,X1),X7),X5),X3)) )
| ( $true = X2 )
| ( $true != vAPP(option(X1),$o,vAPP(sTfun(X1,$o),sTfun(option(X1),$o),vAPP($o,sTfun(sTfun(X1,$o),sTfun(option(X1),$o)),case_option($o,X1),X2),X3),X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_175])]) ).
thf(f1408,plain,
! [X1: $tType,X0: $tType,X2: $o,X3: X1 > $o,X6: X0,X7: X1 > X0,X4: option(X1),X5: X0 > $o] :
( ( $true = vAPP(X0,$o,X5,vAPP(option(X1),X0,vAPP(sTfun(X1,X0),sTfun(option(X1),X0),vAPP(X0,sTfun(sTfun(X1,X0),sTfun(option(X1),X0)),case_option(X0,X1),X6),X7),X4)) )
| ( $true = vAPP(X1,$o,X3,vAPP(sTfun(X1,$o),X1,vAPP(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1),vAPP(sTfun(X1,X0),sTfun(sTfun(X0,$o),sTfun(sTfun(X1,$o),X1)),sK134(X0,X1),X7),X5),X3)) )
| ( $true = X2 )
| ( $true != vAPP(option(X1),$o,vAPP(sTfun(X1,$o),sTfun(option(X1),$o),vAPP($o,sTfun(sTfun(X1,$o),sTfun(option(X1),$o)),case_option($o,X1),X2),X3),X4) ) ),
inference(cnf_transformation,[],[f1105]) ).
thf(f3528,plain,
spl151_174,
inference(avatar_split_clause,[],[f1460,f3525]) ).
thf(f3525,plain,
( spl151_174
<=> ( vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),k),s2),s) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_174])]) ).
thf(f1460,plain,
vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),k),s2),s) = $true,
inference(cnf_transformation,[],[f682]) ).
thf(f682,plain,
vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),k),s2),s) = $true,
inference(fool_elimination,[],[f681]) ).
thf(f681,plain,
vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),k),s2),s),
inference(rectify,[],[f9]) ).
thf(f9,axiom,
vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),k),s2),s),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8__092_060open_062get__back_AP_Ab_Ac_Ak_As_____As_H_____092_060close_062) ).
thf(f3500,plain,
spl151_173,
inference(avatar_split_clause,[],[f1322,f3498]) ).
thf(f3498,plain,
( spl151_173
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: product_prod(X2,product_prod(X1,X0)),X3: product_prod(X2,product_prod(X1,X0)) > $o] :
( ( $true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4) )
| ( $true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X2,sK74(X0,X1,X2),X3)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X1,sK75(X0,X1,X2),X3)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X0,sK76(X0,X1,X2),X3)))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_173])]) ).
thf(f1322,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X2,product_prod(X1,X0)) > $o,X4: product_prod(X2,product_prod(X1,X0))] :
( ( $true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4) )
| ( $true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X2,sK74(X0,X1,X2),X3)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X1,sK75(X0,X1,X2),X3)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X0,sK76(X0,X1,X2),X3)))) ) ),
inference(cnf_transformation,[],[f1059]) ).
thf(f1059,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X2,product_prod(X1,X0)) > $o,X4: product_prod(X2,product_prod(X1,X0))] :
( ( $true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4) )
| ( $true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X2,sK74(X0,X1,X2),X3)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X1,sK75(X0,X1,X2),X3)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X0,sK76(X0,X1,X2),X3)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK74,sK75,sK76])],[f883,f1058]) ).
thf(f1058,plain,
! [X2: $tType,X1: $tType,X0: $tType,X3: product_prod(X2,product_prod(X1,X0)) > $o] :
( ? [X5: X2,X6: X1,X7: X0] : ( $true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X5),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7))) )
=> ( $true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X2,sK74(X0,X1,X2),X3)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X1,sK75(X0,X1,X2),X3)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X0,sK76(X0,X1,X2),X3)))) ) ),
introduced(choice_axiom,[]) ).
thf(f883,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X2,product_prod(X1,X0)) > $o,X4: product_prod(X2,product_prod(X1,X0))] :
( ( $true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4) )
| ? [X5: X2,X6: X1,X7: X0] : ( $true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X5),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7))) ) ),
inference(ennf_transformation,[],[f492]) ).
thf(f492,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X2,product_prod(X1,X0)) > $o,X4: product_prod(X2,product_prod(X1,X0))] :
( ! [X5: X2,X6: X1,X7: X0] : ( $true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X5),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7))) )
=> ( $true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4) ) ),
inference(fool_elimination,[],[f491]) ).
thf(f491,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X2,product_prod(X1,X0)) > $o,X4: product_prod(X2,product_prod(X1,X0))] :
( ! [X5: X2,X6: X1,X7: X0] : vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X5),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7)))
=> vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4) ),
inference(rectify,[],[f37]) ).
thf(f37,axiom,
! [X1: $tType,X2: $tType,X0: $tType,X34: product_prod(X0,product_prod(X2,X1)) > $o,X55: product_prod(X0,product_prod(X2,X1))] :
( ! [X49: X0,X50: X2,X56: X1] : vAPP(product_prod(X0,product_prod(X2,X1)),$o,X34,vAPP(product_prod(X2,X1),product_prod(X0,product_prod(X2,X1)),vAPP(X0,sTfun(product_prod(X2,X1),product_prod(X0,product_prod(X2,X1))),product_Pair(X0,product_prod(X2,X1)),X49),vAPP(X1,product_prod(X2,X1),vAPP(X2,sTfun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X50),X56)))
=> vAPP(product_prod(X0,product_prod(X2,X1)),$o,X34,X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_prod__induct3) ).
thf(f3489,plain,
spl151_172,
inference(avatar_split_clause,[],[f1134,f3487]) ).
thf(f3487,plain,
( spl151_172
<=> ! [X0: com] :
( ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,vAPP(com,bexp,sK4,X0)),vAPP(com,com,sK5,X0)) = X0 )
| ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,vAPP(com,bexp,sK6,X0)),vAPP(com,com,sK7,X0)),vAPP(com,com,sK8,X0)) = X0 )
| ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,vAPP(com,com,sK9,X0)),vAPP(com,com,sK10,X0)) = X0 )
| ( vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,vAPP(com,list(char),sK11,X0)),vAPP(com,aexp,sK12,X0)) = X0 )
| ( skip = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_172])]) ).
thf(f1134,plain,
! [X0: com] :
( ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,vAPP(com,bexp,sK4,X0)),vAPP(com,com,sK5,X0)) = X0 )
| ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,vAPP(com,bexp,sK6,X0)),vAPP(com,com,sK7,X0)),vAPP(com,com,sK8,X0)) = X0 )
| ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,vAPP(com,com,sK9,X0)),vAPP(com,com,sK10,X0)) = X0 )
| ( vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,vAPP(com,list(char),sK11,X0)),vAPP(com,aexp,sK12,X0)) = X0 )
| ( skip = X0 ) ),
inference(cnf_transformation,[],[f972]) ).
thf(f972,plain,
! [X0: com] :
( ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,vAPP(com,bexp,sK4,X0)),vAPP(com,com,sK5,X0)) = X0 )
| ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,vAPP(com,bexp,sK6,X0)),vAPP(com,com,sK7,X0)),vAPP(com,com,sK8,X0)) = X0 )
| ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,vAPP(com,com,sK9,X0)),vAPP(com,com,sK10,X0)) = X0 )
| ( vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,vAPP(com,list(char),sK11,X0)),vAPP(com,aexp,sK12,X0)) = X0 )
| ( skip = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12])],[f967,f971,f970,f969,f968]) ).
thf(f968,plain,
! [X0: com] :
( ? [X1: bexp,X2: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X1),X2) = X0 )
=> ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,vAPP(com,bexp,sK4,X0)),vAPP(com,com,sK5,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f969,plain,
! [X0: com] :
( ? [X3: bexp,X4: com,X5: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X3),X4),X5) = X0 )
=> ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,vAPP(com,bexp,sK6,X0)),vAPP(com,com,sK7,X0)),vAPP(com,com,sK8,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f970,plain,
! [X0: com] :
( ? [X6: com,X7: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X6),X7) = X0 )
=> ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,vAPP(com,com,sK9,X0)),vAPP(com,com,sK10,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f971,plain,
! [X0: com] :
( ? [X8: list(char),X9: aexp] : ( vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X8),X9) = X0 )
=> ( vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,vAPP(com,list(char),sK11,X0)),vAPP(com,aexp,sK12,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f967,plain,
! [X0: com] :
( ? [X1: bexp,X2: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X1),X2) = X0 )
| ? [X3: bexp,X4: com,X5: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X3),X4),X5) = X0 )
| ? [X6: com,X7: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X6),X7) = X0 )
| ? [X8: list(char),X9: aexp] : ( vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X8),X9) = X0 )
| ( skip = X0 ) ),
inference(rectify,[],[f788]) ).
thf(f788,plain,
! [X0: com] :
( ? [X8: bexp,X9: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X8),X9) = X0 )
| ? [X5: bexp,X6: com,X7: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X5),X6),X7) = X0 )
| ? [X3: com,X4: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X3),X4) = X0 )
| ? [X1: list(char),X2: aexp] : ( vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X1),X2) = X0 )
| ( skip = X0 ) ),
inference(flattening,[],[f787]) ).
thf(f787,plain,
! [X0: com] :
( ? [X8: bexp,X9: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X8),X9) = X0 )
| ? [X5: bexp,X6: com,X7: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X5),X6),X7) = X0 )
| ? [X3: com,X4: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X3),X4) = X0 )
| ? [X1: list(char),X2: aexp] : ( vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X1),X2) = X0 )
| ( skip = X0 ) ),
inference(ennf_transformation,[],[f699]) ).
thf(f699,plain,
! [X0: com] :
( ( skip != X0 )
=> ( ! [X1: list(char),X2: aexp] : ( vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X1),X2) != X0 )
=> ( ! [X3: com,X4: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X3),X4) != X0 )
=> ( ! [X5: bexp,X6: com,X7: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X5),X6),X7) != X0 )
=> ~ ! [X8: bexp,X9: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X8),X9) != X0 ) ) ) ) ),
inference(rectify,[],[f126]) ).
thf(f126,axiom,
! [X51: com] :
( ( skip != X51 )
=> ( ! [X114: list(char),X115: aexp] : ( vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X114),X115) != X51 )
=> ( ! [X116: com,X117: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X116),X117) != X51 )
=> ( ! [X118: bexp,X119: com,X120: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X118),X119),X120) != X51 )
=> ~ ! [X121: bexp,X122: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X121),X122) != X51 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_com_Oexhaust) ).
thf(f3478,plain,
spl151_171,
inference(avatar_split_clause,[],[f1249,f3476]) ).
thf(f3476,plain,
( spl151_171
<=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),zero_zero(nat)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_171])]) ).
thf(f1249,plain,
! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),zero_zero(nat)) ) ),
inference(cnf_transformation,[],[f1009]) ).
thf(f1009,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0)) ) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),zero_zero(nat)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33,sK34,sK35])],[f1005,f1008,f1007,f1006]) ).
thf(f1006,plain,
! [X0: nat > nat > $o] :
( ? [X3: nat,X4: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X3)),vAPP(nat,nat,suc,X4)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) ) )
=> ( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0))),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0))) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1007,plain,
! [X0: nat > nat > $o] :
( ? [X5: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,X5)) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f1008,plain,
! [X0: nat > nat > $o] :
( ? [X6: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),zero_zero(nat)) )
=> ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),zero_zero(nat)) ) ),
introduced(choice_axiom,[]) ).
thf(f1005,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ? [X3: nat,X4: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X3)),vAPP(nat,nat,suc,X4)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),X4) ) )
| ? [X5: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,X5)) )
| ? [X6: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X6),zero_zero(nat)) ) ),
inference(rectify,[],[f843]) ).
thf(f843,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ? [X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X5)),vAPP(nat,nat,suc,X6)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) ) )
| ? [X4: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,X4)) )
| ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),zero_zero(nat)) ) ),
inference(flattening,[],[f842]) ).
thf(f842,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ? [X5: nat,X6: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X5)),vAPP(nat,nat,suc,X6)) )
& ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) ) )
| ? [X4: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,X4)) )
| ? [X3: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),zero_zero(nat)) ) ),
inference(ennf_transformation,[],[f430]) ).
thf(f430,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ! [X3: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),zero_zero(nat)) )
=> ( ! [X4: nat] : ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,X4)) )
=> ( ! [X5: nat,X6: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X5)),vAPP(nat,nat,suc,X6)) ) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) ) ) ) ),
inference(fool_elimination,[],[f429]) ).
thf(f429,plain,
! [X0: nat > nat > $o,X1: nat,X2: nat] :
( ! [X3: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X3),zero_zero(nat))
=> ( ! [X4: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,X4))
=> ( ! [X5: nat,X6: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X5),X6)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(nat,nat,suc,X5)),vAPP(nat,nat,suc,X6)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) ) ) ),
inference(rectify,[],[f153]) ).
thf(f153,axiom,
! [X34: nat > nat > $o,X86: nat,X68: nat] :
( ! [X64: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X34,X64),zero_zero(nat))
=> ( ! [X67: nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X34,zero_zero(nat)),vAPP(nat,nat,suc,X67))
=> ( ! [X64: nat,X67: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X34,X64),X67)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X34,vAPP(nat,nat,suc,X64)),vAPP(nat,nat,suc,X67)) )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X34,X86),X68) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_diff__induct) ).
thf(f3468,plain,
( spl151_170
| ~ spl151_34
| ~ spl151_64 ),
inference(avatar_split_clause,[],[f2288,f2236,f2079,f3466]) ).
thf(f3466,plain,
( spl151_170
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( cancel1352612707id_add(X0) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_170])]) ).
thf(f2079,plain,
( spl151_34
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_34])]) ).
thf(f2236,plain,
( spl151_64
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( cancel1352612707id_add(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_64])]) ).
thf(f2288,plain,
( ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( cancel1352612707id_add(X0) = $false ) )
| ~ spl151_34
| ~ spl151_64 ),
inference(trivial_inequality_removal,[],[f2287]) ).
thf(f2287,plain,
( ! [X0: $tType,X1: X0] :
( ( $true != $true )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( cancel1352612707id_add(X0) = $false ) )
| ~ spl151_34
| ~ spl151_64 ),
inference(superposition,[],[f2237,f2080]) ).
thf(f2080,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) )
| ~ spl151_34 ),
inference(avatar_component_clause,[],[f2079]) ).
thf(f2237,plain,
( ! [X0: $tType,X1: X0] :
( ( cancel1352612707id_add(X0) != $true )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 ) )
| ~ spl151_64 ),
inference(avatar_component_clause,[],[f2236]) ).
thf(f3464,plain,
spl151_169,
inference(avatar_split_clause,[],[f1399,f3462]) ).
thf(f3462,plain,
( spl151_169
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X2 > nat,X4: X0 > nat,X6: X2 > product_prod(X0,X1),X5: X1 > nat,X7: product_prod(X0,X1) > X2] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(tuple_isomorphism(X2,X0,X1),nat,vAPP(sTfun(X1,nat),sTfun(tuple_isomorphism(X2,X0,X1),nat),vAPP(sTfun(X0,nat),sTfun(sTfun(X1,nat),sTfun(tuple_isomorphism(X2,X0,X1),nat)),vAPP(sTfun(X2,nat),sTfun(sTfun(X0,nat),sTfun(sTfun(X1,nat),sTfun(tuple_isomorphism(X2,X0,X1),nat))),tuple_1907371454rphism(X2,X0,X1),X3),X4),X5),vAPP(sTfun(product_prod(X0,X1),X2),tuple_isomorphism(X2,X0,X1),vAPP(sTfun(X2,product_prod(X0,X1)),sTfun(sTfun(product_prod(X0,X1),X2),tuple_isomorphism(X2,X0,X1)),tuple_742722141rphism(X2,X0,X1),X6),X7)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_169])]) ).
thf(f1399,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2 > nat,X6: X2 > product_prod(X0,X1),X7: product_prod(X0,X1) > X2,X4: X0 > nat,X5: X1 > nat] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(tuple_isomorphism(X2,X0,X1),nat,vAPP(sTfun(X1,nat),sTfun(tuple_isomorphism(X2,X0,X1),nat),vAPP(sTfun(X0,nat),sTfun(sTfun(X1,nat),sTfun(tuple_isomorphism(X2,X0,X1),nat)),vAPP(sTfun(X2,nat),sTfun(sTfun(X0,nat),sTfun(sTfun(X1,nat),sTfun(tuple_isomorphism(X2,X0,X1),nat))),tuple_1907371454rphism(X2,X0,X1),X3),X4),X5),vAPP(sTfun(product_prod(X0,X1),X2),tuple_isomorphism(X2,X0,X1),vAPP(sTfun(X2,product_prod(X0,X1)),sTfun(sTfun(product_prod(X0,X1),X2),tuple_isomorphism(X2,X0,X1)),tuple_742722141rphism(X2,X0,X1),X6),X7)) ),
inference(cnf_transformation,[],[f783]) ).
thf(f783,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > nat,X4: X0 > nat,X5: X1 > nat,X6: X2 > product_prod(X0,X1),X7: product_prod(X0,X1) > X2] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(tuple_isomorphism(X2,X0,X1),nat,vAPP(sTfun(X1,nat),sTfun(tuple_isomorphism(X2,X0,X1),nat),vAPP(sTfun(X0,nat),sTfun(sTfun(X1,nat),sTfun(tuple_isomorphism(X2,X0,X1),nat)),vAPP(sTfun(X2,nat),sTfun(sTfun(X0,nat),sTfun(sTfun(X1,nat),sTfun(tuple_isomorphism(X2,X0,X1),nat))),tuple_1907371454rphism(X2,X0,X1),X3),X4),X5),vAPP(sTfun(product_prod(X0,X1),X2),tuple_isomorphism(X2,X0,X1),vAPP(sTfun(X2,product_prod(X0,X1)),sTfun(sTfun(product_prod(X0,X1),X2),tuple_isomorphism(X2,X0,X1)),tuple_742722141rphism(X2,X0,X1),X6),X7)) ),
inference(rectify,[],[f205]) ).
thf(f205,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X150: X0 > nat,X151: X2 > nat,X55: X1 > nat,X9: X0 > product_prod(X2,X1),X5: product_prod(X2,X1) > X0] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(tuple_isomorphism(X0,X2,X1),nat,vAPP(sTfun(X1,nat),sTfun(tuple_isomorphism(X0,X2,X1),nat),vAPP(sTfun(X2,nat),sTfun(sTfun(X1,nat),sTfun(tuple_isomorphism(X0,X2,X1),nat)),vAPP(sTfun(X0,nat),sTfun(sTfun(X2,nat),sTfun(sTfun(X1,nat),sTfun(tuple_isomorphism(X0,X2,X1),nat))),tuple_1907371454rphism(X0,X2,X1),X150),X151),X55),vAPP(sTfun(product_prod(X2,X1),X0),tuple_isomorphism(X0,X2,X1),vAPP(sTfun(X0,product_prod(X2,X1)),sTfun(sTfun(product_prod(X2,X1),X0),tuple_isomorphism(X0,X2,X1)),tuple_742722141rphism(X0,X2,X1),X9),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_tuple__isomorphism_Osize__gen) ).
thf(f3450,plain,
spl151_168,
inference(avatar_split_clause,[],[f1214,f3448]) ).
thf(f3448,plain,
( spl151_168
<=> ! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,vAPP(sTfun(com,$o),bexp,sK20,X0)),vAPP(sTfun(com,$o),com,sK21,X0))) )
| ( $true = vAPP(sTfun(com,$o),$o,sP1,X0) )
| ( $true = vAPP(sTfun(com,$o),$o,sP0,X0) )
| ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,vAPP(sTfun(com,$o),list(char),sK22,X0)),vAPP(sTfun(com,$o),aexp,sK23,X0))) )
| ( $true != vAPP(com,$o,X0,skip) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_168])]) ).
thf(f1214,plain,
! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,vAPP(sTfun(com,$o),bexp,sK20,X0)),vAPP(sTfun(com,$o),com,sK21,X0))) )
| ( $true = vAPP(sTfun(com,$o),$o,sP1,X0) )
| ( $true = vAPP(sTfun(com,$o),$o,sP0,X0) )
| ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,vAPP(sTfun(com,$o),list(char),sK22,X0)),vAPP(sTfun(com,$o),aexp,sK23,X0))) )
| ( $true != vAPP(com,$o,X0,skip) ) ),
inference(cnf_transformation,[],[f988]) ).
thf(f988,plain,
! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,vAPP(sTfun(com,$o),bexp,sK20,X0)),vAPP(sTfun(com,$o),com,sK21,X0))) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK21,X0)) ) )
| ( $true = vAPP(sTfun(com,$o),$o,sP1,X0) )
| ( $true = vAPP(sTfun(com,$o),$o,sP0,X0) )
| ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,vAPP(sTfun(com,$o),list(char),sK22,X0)),vAPP(sTfun(com,$o),aexp,sK23,X0))) )
| ( $true != vAPP(com,$o,X0,skip) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23])],[f985,f987,f986]) ).
thf(f986,plain,
! [X0: com > $o] :
( ? [X2: bexp,X3: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X3)) )
& ( $true = vAPP(com,$o,X0,X3) ) )
=> ( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,vAPP(sTfun(com,$o),bexp,sK20,X0)),vAPP(sTfun(com,$o),com,sK21,X0))) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK21,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f987,plain,
! [X0: com > $o] :
( ? [X4: list(char),X5: aexp] : ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X4),X5)) )
=> ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,vAPP(sTfun(com,$o),list(char),sK22,X0)),vAPP(sTfun(com,$o),aexp,sK23,X0))) ) ),
introduced(choice_axiom,[]) ).
thf(f985,plain,
! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ? [X2: bexp,X3: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X3)) )
& ( $true = vAPP(com,$o,X0,X3) ) )
| ( $true = vAPP(sTfun(com,$o),$o,sP1,X0) )
| ( $true = vAPP(sTfun(com,$o),$o,sP0,X0) )
| ? [X4: list(char),X5: aexp] : ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X4),X5)) )
| ( $true != vAPP(com,$o,X0,skip) ) ),
inference(rectify,[],[f962]) ).
thf(f962,plain,
! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ? [X9: bexp,X10: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X9),X10)) )
& ( $true = vAPP(com,$o,X0,X10) ) )
| ( $true = vAPP(sTfun(com,$o),$o,sP1,X0) )
| ( $true = vAPP(sTfun(com,$o),$o,sP0,X0) )
| ? [X2: list(char),X3: aexp] : ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X2),X3)) )
| ( $true != vAPP(com,$o,X0,skip) ) ),
inference(definition_folding,[],[f828,f961,f960]) ).
thf(f960,plain,
! [X0: com > $o] :
( ? [X4: com,X5: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X4),X5)) )
& ( $true = vAPP(com,$o,X0,X5) )
& ( $true = vAPP(com,$o,X0,X4) ) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f961,plain,
! [X0: com > $o] :
( ? [X6: bexp,X7: com,X8: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X6),X7),X8)) )
& ( $true = vAPP(com,$o,X0,X8) )
& ( $true = vAPP(com,$o,X0,X7) ) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f828,plain,
! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ? [X9: bexp,X10: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X9),X10)) )
& ( $true = vAPP(com,$o,X0,X10) ) )
| ? [X6: bexp,X7: com,X8: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X6),X7),X8)) )
& ( $true = vAPP(com,$o,X0,X8) )
& ( $true = vAPP(com,$o,X0,X7) ) )
| ? [X4: com,X5: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X4),X5)) )
& ( $true = vAPP(com,$o,X0,X5) )
& ( $true = vAPP(com,$o,X0,X4) ) )
| ? [X2: list(char),X3: aexp] : ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X2),X3)) )
| ( $true != vAPP(com,$o,X0,skip) ) ),
inference(flattening,[],[f827]) ).
thf(f827,plain,
! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ? [X9: bexp,X10: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X9),X10)) )
& ( $true = vAPP(com,$o,X0,X10) ) )
| ? [X6: bexp,X7: com,X8: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X6),X7),X8)) )
& ( $true = vAPP(com,$o,X0,X8) )
& ( $true = vAPP(com,$o,X0,X7) ) )
| ? [X4: com,X5: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X4),X5)) )
& ( $true = vAPP(com,$o,X0,X5) )
& ( $true = vAPP(com,$o,X0,X4) ) )
| ? [X2: list(char),X3: aexp] : ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X2),X3)) )
| ( $true != vAPP(com,$o,X0,skip) ) ),
inference(ennf_transformation,[],[f406]) ).
thf(f406,plain,
! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,skip) )
=> ( ! [X2: list(char),X3: aexp] : ( $true = vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X2),X3)) )
=> ( ! [X4: com,X5: com] :
( ( $true = vAPP(com,$o,X0,X4) )
=> ( ( $true = vAPP(com,$o,X0,X5) )
=> ( $true = vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X4),X5)) ) ) )
=> ( ! [X6: bexp,X7: com,X8: com] :
( ( $true = vAPP(com,$o,X0,X7) )
=> ( ( $true = vAPP(com,$o,X0,X8) )
=> ( $true = vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X6),X7),X8)) ) ) )
=> ( ! [X9: bexp,X10: com] :
( ( $true = vAPP(com,$o,X0,X10) )
=> ( $true = vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X9),X10)) ) )
=> ( $true = vAPP(com,$o,X0,X1) ) ) ) ) ) ),
inference(fool_elimination,[],[f405]) ).
thf(f405,plain,
! [X0: com > $o,X1: com] :
( vAPP(com,$o,X0,skip)
=> ( ! [X2: list(char),X3: aexp] : vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X2),X3))
=> ( ! [X4: com,X5: com] :
( vAPP(com,$o,X0,X4)
=> ( vAPP(com,$o,X0,X5)
=> vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X4),X5)) ) )
=> ( ! [X6: bexp,X7: com,X8: com] :
( vAPP(com,$o,X0,X7)
=> ( vAPP(com,$o,X0,X8)
=> vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X6),X7),X8)) ) )
=> ( ! [X9: bexp,X10: com] :
( vAPP(com,$o,X0,X10)
=> vAPP(com,$o,X0,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X9),X10)) )
=> vAPP(com,$o,X0,X1) ) ) ) ) ),
inference(rectify,[],[f127]) ).
thf(f127,axiom,
! [X34: com > $o,X123: com] :
( vAPP(com,$o,X34,skip)
=> ( ! [X124: list(char),X125: aexp] : vAPP(com,$o,X34,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X124),X125))
=> ( ! [X124: com,X125: com] :
( vAPP(com,$o,X34,X124)
=> ( vAPP(com,$o,X34,X125)
=> vAPP(com,$o,X34,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X124),X125)) ) )
=> ( ! [X124: bexp,X125: com,X126: com] :
( vAPP(com,$o,X34,X125)
=> ( vAPP(com,$o,X34,X126)
=> vAPP(com,$o,X34,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X124),X125),X126)) ) )
=> ( ! [X124: bexp,X125: com] :
( vAPP(com,$o,X34,X125)
=> vAPP(com,$o,X34,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X124),X125)) )
=> vAPP(com,$o,X34,X123) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_com_Oinduct) ).
thf(f3438,plain,
spl151_167,
inference(avatar_split_clause,[],[f1337,f3436]) ).
thf(f3436,plain,
( spl151_167
<=> ! [X0: $tType,X4: nat,X3: set(product_prod(X0,X0)),X2: list(X0),X1: list(X0)] :
( ( vAPP(list(X0),nat,size_size(list(X0)),X2) = X4 )
| ( $true != vAPP(set(product_prod(list(X0),list(X0))),$o,vAPP(product_prod(list(X0),list(X0)),sTfun(set(product_prod(list(X0),list(X0))),$o),member(product_prod(list(X0),list(X0))),vAPP(list(X0),product_prod(list(X0),list(X0)),vAPP(list(X0),sTfun(list(X0),product_prod(list(X0),list(X0))),product_Pair(list(X0),list(X0)),X1),X2)),vAPP(nat,set(product_prod(list(X0),list(X0))),vAPP(set(product_prod(X0,X0)),sTfun(nat,set(product_prod(list(X0),list(X0)))),lexn(X0),X3),X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_167])]) ).
thf(f1337,plain,
! [X0: $tType,X2: list(X0),X3: set(product_prod(X0,X0)),X1: list(X0),X4: nat] :
( ( vAPP(list(X0),nat,size_size(list(X0)),X2) = X4 )
| ( $true != vAPP(set(product_prod(list(X0),list(X0))),$o,vAPP(product_prod(list(X0),list(X0)),sTfun(set(product_prod(list(X0),list(X0))),$o),member(product_prod(list(X0),list(X0))),vAPP(list(X0),product_prod(list(X0),list(X0)),vAPP(list(X0),sTfun(list(X0),product_prod(list(X0),list(X0))),product_Pair(list(X0),list(X0)),X1),X2)),vAPP(nat,set(product_prod(list(X0),list(X0))),vAPP(set(product_prod(X0,X0)),sTfun(nat,set(product_prod(list(X0),list(X0)))),lexn(X0),X3),X4)) ) ),
inference(cnf_transformation,[],[f899]) ).
thf(f899,plain,
! [X0: $tType,X1: list(X0),X2: list(X0),X3: set(product_prod(X0,X0)),X4: nat] :
( ( ( vAPP(list(X0),nat,size_size(list(X0)),X2) = X4 )
& ( vAPP(list(X0),nat,size_size(list(X0)),X1) = X4 ) )
| ( $true != vAPP(set(product_prod(list(X0),list(X0))),$o,vAPP(product_prod(list(X0),list(X0)),sTfun(set(product_prod(list(X0),list(X0))),$o),member(product_prod(list(X0),list(X0))),vAPP(list(X0),product_prod(list(X0),list(X0)),vAPP(list(X0),sTfun(list(X0),product_prod(list(X0),list(X0))),product_Pair(list(X0),list(X0)),X1),X2)),vAPP(nat,set(product_prod(list(X0),list(X0))),vAPP(set(product_prod(X0,X0)),sTfun(nat,set(product_prod(list(X0),list(X0)))),lexn(X0),X3),X4)) ) ),
inference(ennf_transformation,[],[f510]) ).
thf(f510,plain,
! [X0: $tType,X1: list(X0),X2: list(X0),X3: set(product_prod(X0,X0)),X4: nat] :
( ( $true = vAPP(set(product_prod(list(X0),list(X0))),$o,vAPP(product_prod(list(X0),list(X0)),sTfun(set(product_prod(list(X0),list(X0))),$o),member(product_prod(list(X0),list(X0))),vAPP(list(X0),product_prod(list(X0),list(X0)),vAPP(list(X0),sTfun(list(X0),product_prod(list(X0),list(X0))),product_Pair(list(X0),list(X0)),X1),X2)),vAPP(nat,set(product_prod(list(X0),list(X0))),vAPP(set(product_prod(X0,X0)),sTfun(nat,set(product_prod(list(X0),list(X0)))),lexn(X0),X3),X4)) )
=> ( ( vAPP(list(X0),nat,size_size(list(X0)),X2) = X4 )
& ( vAPP(list(X0),nat,size_size(list(X0)),X1) = X4 ) ) ),
inference(fool_elimination,[],[f509]) ).
thf(f509,plain,
! [X0: $tType,X1: list(X0),X2: list(X0),X3: set(product_prod(X0,X0)),X4: nat] :
( vAPP(set(product_prod(list(X0),list(X0))),$o,vAPP(product_prod(list(X0),list(X0)),sTfun(set(product_prod(list(X0),list(X0))),$o),member(product_prod(list(X0),list(X0))),vAPP(list(X0),product_prod(list(X0),list(X0)),vAPP(list(X0),sTfun(list(X0),product_prod(list(X0),list(X0))),product_Pair(list(X0),list(X0)),X1),X2)),vAPP(nat,set(product_prod(list(X0),list(X0))),vAPP(set(product_prod(X0,X0)),sTfun(nat,set(product_prod(list(X0),list(X0)))),lexn(X0),X3),X4))
=> ( ( vAPP(list(X0),nat,size_size(list(X0)),X2) = X4 )
& ( vAPP(list(X0),nat,size_size(list(X0)),X1) = X4 ) ) ),
inference(rectify,[],[f234]) ).
thf(f234,axiom,
! [X0: $tType,X156: list(X0),X164: list(X0),X145: set(product_prod(X0,X0)),X68: nat] :
( vAPP(set(product_prod(list(X0),list(X0))),$o,vAPP(product_prod(list(X0),list(X0)),sTfun(set(product_prod(list(X0),list(X0))),$o),member(product_prod(list(X0),list(X0))),vAPP(list(X0),product_prod(list(X0),list(X0)),vAPP(list(X0),sTfun(list(X0),product_prod(list(X0),list(X0))),product_Pair(list(X0),list(X0)),X156),X164)),vAPP(nat,set(product_prod(list(X0),list(X0))),vAPP(set(product_prod(X0,X0)),sTfun(nat,set(product_prod(list(X0),list(X0)))),lexn(X0),X145),X68))
=> ( ( vAPP(list(X0),nat,size_size(list(X0)),X164) = X68 )
& ( vAPP(list(X0),nat,size_size(list(X0)),X156) = X68 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_lexn__length) ).
thf(f3434,plain,
spl151_166,
inference(avatar_split_clause,[],[f1336,f3432]) ).
thf(f3432,plain,
( spl151_166
<=> ! [X0: $tType,X2: list(X0),X4: nat,X3: set(product_prod(X0,X0)),X1: list(X0)] :
( ( vAPP(list(X0),nat,size_size(list(X0)),X1) = X4 )
| ( $true != vAPP(set(product_prod(list(X0),list(X0))),$o,vAPP(product_prod(list(X0),list(X0)),sTfun(set(product_prod(list(X0),list(X0))),$o),member(product_prod(list(X0),list(X0))),vAPP(list(X0),product_prod(list(X0),list(X0)),vAPP(list(X0),sTfun(list(X0),product_prod(list(X0),list(X0))),product_Pair(list(X0),list(X0)),X1),X2)),vAPP(nat,set(product_prod(list(X0),list(X0))),vAPP(set(product_prod(X0,X0)),sTfun(nat,set(product_prod(list(X0),list(X0)))),lexn(X0),X3),X4)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_166])]) ).
thf(f1336,plain,
! [X0: $tType,X2: list(X0),X3: set(product_prod(X0,X0)),X1: list(X0),X4: nat] :
( ( vAPP(list(X0),nat,size_size(list(X0)),X1) = X4 )
| ( $true != vAPP(set(product_prod(list(X0),list(X0))),$o,vAPP(product_prod(list(X0),list(X0)),sTfun(set(product_prod(list(X0),list(X0))),$o),member(product_prod(list(X0),list(X0))),vAPP(list(X0),product_prod(list(X0),list(X0)),vAPP(list(X0),sTfun(list(X0),product_prod(list(X0),list(X0))),product_Pair(list(X0),list(X0)),X1),X2)),vAPP(nat,set(product_prod(list(X0),list(X0))),vAPP(set(product_prod(X0,X0)),sTfun(nat,set(product_prod(list(X0),list(X0)))),lexn(X0),X3),X4)) ) ),
inference(cnf_transformation,[],[f899]) ).
thf(f3423,plain,
spl151_165,
inference(avatar_split_clause,[],[f1248,f3421]) ).
thf(f3421,plain,
( spl151_165
<=> ! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),zero_zero(nat)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_165])]) ).
thf(f1248,plain,
! [X2: nat,X0: nat > nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK32,X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK33,X0)) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,zero_zero(nat)),vAPP(nat,nat,suc,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK34,X0))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK35,X0)),zero_zero(nat)) ) ),
inference(cnf_transformation,[],[f1009]) ).
thf(f3249,plain,
( spl151_164
| ~ spl151_34
| ~ spl151_63 ),
inference(avatar_split_clause,[],[f2282,f2232,f2079,f3247]) ).
thf(f3247,plain,
( spl151_164
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( comm_monoid_add(X0) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_164])]) ).
thf(f2232,plain,
( spl151_63
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( comm_monoid_add(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_63])]) ).
thf(f2282,plain,
( ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( comm_monoid_add(X0) = $false ) )
| ~ spl151_34
| ~ spl151_63 ),
inference(trivial_inequality_removal,[],[f2281]) ).
thf(f2281,plain,
( ! [X0: $tType,X1: X0] :
( ( $true != $true )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( comm_monoid_add(X0) = $false ) )
| ~ spl151_34
| ~ spl151_63 ),
inference(superposition,[],[f2233,f2080]) ).
thf(f2233,plain,
( ! [X0: $tType,X1: X0] :
( ( comm_monoid_add(X0) != $true )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 ) )
| ~ spl151_63 ),
inference(avatar_component_clause,[],[f2232]) ).
thf(f3245,plain,
spl151_163,
inference(avatar_split_clause,[],[f1394,f3243]) ).
thf(f3243,plain,
( spl151_163
<=> ! [X1: $tType,X0: $tType,X2: $tType,X5: X2 > X1,X4: X1,X6: option(X2),X3: X1 > X0] : ( vAPP(X1,X0,X3,vAPP(option(X2),X1,vAPP(sTfun(X2,X1),sTfun(option(X2),X1),vAPP(X1,sTfun(sTfun(X2,X1),sTfun(option(X2),X1)),case_option(X1,X2),X4),X5),X6)) = vAPP(option(X2),X0,vAPP(sTfun(X2,X0),sTfun(option(X2),X0),vAPP(X0,sTfun(sTfun(X2,X0),sTfun(option(X2),X0)),case_option(X0,X2),vAPP(X1,X0,X3,X4)),vAPP(sTfun(X2,X1),sTfun(X2,X0),vAPP(sTfun(X1,X0),sTfun(sTfun(X2,X1),sTfun(X2,X0)),bCOMB,X3),X5)),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_163])]) ).
thf(f1394,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X1 > X0,X6: option(X2),X4: X1,X5: X2 > X1] : ( vAPP(X1,X0,X3,vAPP(option(X2),X1,vAPP(sTfun(X2,X1),sTfun(option(X2),X1),vAPP(X1,sTfun(sTfun(X2,X1),sTfun(option(X2),X1)),case_option(X1,X2),X4),X5),X6)) = vAPP(option(X2),X0,vAPP(sTfun(X2,X0),sTfun(option(X2),X0),vAPP(X0,sTfun(sTfun(X2,X0),sTfun(option(X2),X0)),case_option(X0,X2),vAPP(X1,X0,X3,X4)),vAPP(sTfun(X2,X1),sTfun(X2,X0),vAPP(sTfun(X1,X0),sTfun(sTfun(X2,X1),sTfun(X2,X0)),bCOMB,X3),X5)),X6) ),
inference(cnf_transformation,[],[f578]) ).
thf(f578,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X1 > X0,X4: X1,X5: X2 > X1,X6: option(X2)] : ( vAPP(X1,X0,X3,vAPP(option(X2),X1,vAPP(sTfun(X2,X1),sTfun(option(X2),X1),vAPP(X1,sTfun(sTfun(X2,X1),sTfun(option(X2),X1)),case_option(X1,X2),X4),X5),X6)) = vAPP(option(X2),X0,vAPP(sTfun(X2,X0),sTfun(option(X2),X0),vAPP(X0,sTfun(sTfun(X2,X0),sTfun(option(X2),X0)),case_option(X0,X2),vAPP(X1,X0,X3,X4)),vAPP(sTfun(X2,X1),sTfun(X2,X0),vAPP(sTfun(X1,X0),sTfun(sTfun(X2,X1),sTfun(X2,X0)),bCOMB,X3),X5)),X6) ),
inference(fool_elimination,[],[f577]) ).
thf(f577,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X1 > X0,X4: X1,X5: X2 > X1,X6: option(X2)] :
( vAPP(X1,X0,X3,vAPP(option(X2),X1,vAPP(sTfun(X2,X1),sTfun(option(X2),X1),vAPP(X1,sTfun(sTfun(X2,X1),sTfun(option(X2),X1)),case_option(X1,X2),X4),X5),X6)) = vAPP(option(X2),X0,
vAPP(sTfun(X2,X0),sTfun(option(X2),X0),vAPP(X0,sTfun(sTfun(X2,X0),sTfun(option(X2),X0)),case_option(X0,X2),vAPP(X1,X0,X3,X4)),
^ [X7: X2] : vAPP(X1,X0,X3,vAPP(X2,X1,X5,X7))),
X6) ),
inference(rectify,[],[f214]) ).
thf(f214,axiom,
! [X1: $tType,X2: $tType,X0: $tType,X152: X2 > X1,X70: X2,X153: X0 > X2,X154: option(X0)] :
( vAPP(X2,X1,X152,vAPP(option(X0),X2,vAPP(sTfun(X0,X2),sTfun(option(X0),X2),vAPP(X2,sTfun(sTfun(X0,X2),sTfun(option(X0),X2)),case_option(X2,X0),X70),X153),X154)) = vAPP(option(X0),X1,
vAPP(sTfun(X0,X1),sTfun(option(X0),X1),vAPP(X1,sTfun(sTfun(X0,X1),sTfun(option(X0),X1)),case_option(X1,X0),vAPP(X2,X1,X152,X70)),
^ [X63: X0] : vAPP(X2,X1,X152,vAPP(X0,X2,X153,X63))),
X154) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_option_Ocase__distrib) ).
thf(f3237,plain,
spl151_162,
inference(avatar_split_clause,[],[f1303,f3235]) ).
thf(f3235,plain,
( spl151_162
<=> ! [X0: $tType,X3: set(product_prod(X0,X0)),X2: list(X0),X1: list(X0)] :
( ( vAPP(list(X0),nat,size_size(list(X0)),X2) = vAPP(list(X0),nat,size_size(list(X0)),X1) )
| ( $true != vAPP(set(product_prod(list(X0),list(X0))),$o,vAPP(product_prod(list(X0),list(X0)),sTfun(set(product_prod(list(X0),list(X0))),$o),member(product_prod(list(X0),list(X0))),vAPP(list(X0),product_prod(list(X0),list(X0)),vAPP(list(X0),sTfun(list(X0),product_prod(list(X0),list(X0))),product_Pair(list(X0),list(X0)),X1),X2)),vAPP(set(product_prod(X0,X0)),set(product_prod(list(X0),list(X0))),listrel1(X0),X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_162])]) ).
thf(f1303,plain,
! [X0: $tType,X2: list(X0),X3: set(product_prod(X0,X0)),X1: list(X0)] :
( ( vAPP(list(X0),nat,size_size(list(X0)),X2) = vAPP(list(X0),nat,size_size(list(X0)),X1) )
| ( $true != vAPP(set(product_prod(list(X0),list(X0))),$o,vAPP(product_prod(list(X0),list(X0)),sTfun(set(product_prod(list(X0),list(X0))),$o),member(product_prod(list(X0),list(X0))),vAPP(list(X0),product_prod(list(X0),list(X0)),vAPP(list(X0),sTfun(list(X0),product_prod(list(X0),list(X0))),product_Pair(list(X0),list(X0)),X1),X2)),vAPP(set(product_prod(X0,X0)),set(product_prod(list(X0),list(X0))),listrel1(X0),X3)) ) ),
inference(cnf_transformation,[],[f869]) ).
thf(f869,plain,
! [X0: $tType,X1: list(X0),X2: list(X0),X3: set(product_prod(X0,X0))] :
( ( vAPP(list(X0),nat,size_size(list(X0)),X2) = vAPP(list(X0),nat,size_size(list(X0)),X1) )
| ( $true != vAPP(set(product_prod(list(X0),list(X0))),$o,vAPP(product_prod(list(X0),list(X0)),sTfun(set(product_prod(list(X0),list(X0))),$o),member(product_prod(list(X0),list(X0))),vAPP(list(X0),product_prod(list(X0),list(X0)),vAPP(list(X0),sTfun(list(X0),product_prod(list(X0),list(X0))),product_Pair(list(X0),list(X0)),X1),X2)),vAPP(set(product_prod(X0,X0)),set(product_prod(list(X0),list(X0))),listrel1(X0),X3)) ) ),
inference(ennf_transformation,[],[f472]) ).
thf(f472,plain,
! [X0: $tType,X1: list(X0),X2: list(X0),X3: set(product_prod(X0,X0))] :
( ( $true = vAPP(set(product_prod(list(X0),list(X0))),$o,vAPP(product_prod(list(X0),list(X0)),sTfun(set(product_prod(list(X0),list(X0))),$o),member(product_prod(list(X0),list(X0))),vAPP(list(X0),product_prod(list(X0),list(X0)),vAPP(list(X0),sTfun(list(X0),product_prod(list(X0),list(X0))),product_Pair(list(X0),list(X0)),X1),X2)),vAPP(set(product_prod(X0,X0)),set(product_prod(list(X0),list(X0))),listrel1(X0),X3)) )
=> ( vAPP(list(X0),nat,size_size(list(X0)),X2) = vAPP(list(X0),nat,size_size(list(X0)),X1) ) ),
inference(fool_elimination,[],[f471]) ).
thf(f471,plain,
! [X0: $tType,X1: list(X0),X2: list(X0),X3: set(product_prod(X0,X0))] :
( vAPP(set(product_prod(list(X0),list(X0))),$o,vAPP(product_prod(list(X0),list(X0)),sTfun(set(product_prod(list(X0),list(X0))),$o),member(product_prod(list(X0),list(X0))),vAPP(list(X0),product_prod(list(X0),list(X0)),vAPP(list(X0),sTfun(list(X0),product_prod(list(X0),list(X0))),product_Pair(list(X0),list(X0)),X1),X2)),vAPP(set(product_prod(X0,X0)),set(product_prod(list(X0),list(X0))),listrel1(X0),X3))
=> ( vAPP(list(X0),nat,size_size(list(X0)),X2) = vAPP(list(X0),nat,size_size(list(X0)),X1) ) ),
inference(rectify,[],[f243]) ).
thf(f243,axiom,
! [X0: $tType,X156: list(X0),X164: list(X0),X145: set(product_prod(X0,X0))] :
( vAPP(set(product_prod(list(X0),list(X0))),$o,vAPP(product_prod(list(X0),list(X0)),sTfun(set(product_prod(list(X0),list(X0))),$o),member(product_prod(list(X0),list(X0))),vAPP(list(X0),product_prod(list(X0),list(X0)),vAPP(list(X0),sTfun(list(X0),product_prod(list(X0),list(X0))),product_Pair(list(X0),list(X0)),X156),X164)),vAPP(set(product_prod(X0,X0)),set(product_prod(list(X0),list(X0))),listrel1(X0),X145))
=> ( vAPP(list(X0),nat,size_size(list(X0)),X156) = vAPP(list(X0),nat,size_size(list(X0)),X164) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_listrel1__eq__len) ).
thf(f3233,plain,
spl151_161,
inference(avatar_split_clause,[],[f1244,f3231]) ).
thf(f3231,plain,
( spl151_161
<=> ! [X2: com,X0: bexp,X1: list(char) > int] :
( ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X2)),X1)),X1) )
| ( $true = vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_161])]) ).
thf(f1244,plain,
! [X2: com,X0: bexp,X1: list(char) > int] :
( ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X2)),X1)),X1) )
| ( $true = vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,X0),X1) ) ),
inference(cnf_transformation,[],[f838]) ).
thf(f838,plain,
! [X0: bexp,X1: list(char) > int,X2: com] :
( ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X2)),X1)),X1) )
| ( $true = vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,X0),X1) ) ),
inference(ennf_transformation,[],[f739]) ).
thf(f739,plain,
! [X0: bexp,X1: list(char) > int,X2: com] :
( ( $true != vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,X0),X1) )
=> ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X2)),X1)),X1) ) ),
inference(flattening,[],[f426]) ).
thf(f426,plain,
! [X0: bexp,X1: list(char) > int,X2: com] :
( ( $true != vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,X0),X1) )
=> ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X2)),X1)),X1) ) ),
inference(fool_elimination,[],[f425]) ).
thf(f425,plain,
! [X0: bexp,X1: list(char) > int,X2: com] :
( ~ vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,X0),X1)
=> vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X2)),X1)),X1) ),
inference(rectify,[],[f28]) ).
thf(f28,axiom,
! [X12: bexp,X17: list(char) > int,X22: com] :
( ~ vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,X12),X17)
=> vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X12),X22)),X17)),X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_WhileFalse) ).
thf(f3221,plain,
spl151_160,
inference(avatar_split_clause,[],[f1307,f3219]) ).
thf(f3219,plain,
( spl151_160
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: product_prod(X0,product_prod(X1,X2))] : ( vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod(X0,product_prod(X1,X2)),X0,sK68(X0,X1,X2),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X0,product_prod(X1,X2)),X1,sK69(X0,X1,X2),X3)),vAPP(product_prod(X0,product_prod(X1,X2)),X2,sK70(X0,X1,X2),X3))) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_160])]) ).
thf(f1307,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: product_prod(X0,product_prod(X1,X2))] : ( vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod(X0,product_prod(X1,X2)),X0,sK68(X0,X1,X2),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X0,product_prod(X1,X2)),X1,sK69(X0,X1,X2),X3)),vAPP(product_prod(X0,product_prod(X1,X2)),X2,sK70(X0,X1,X2),X3))) = X3 ),
inference(cnf_transformation,[],[f1051]) ).
thf(f1051,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X0,product_prod(X1,X2))] : ( vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod(X0,product_prod(X1,X2)),X0,sK68(X0,X1,X2),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X0,product_prod(X1,X2)),X1,sK69(X0,X1,X2),X3)),vAPP(product_prod(X0,product_prod(X1,X2)),X2,sK70(X0,X1,X2),X3))) = X3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK68,sK69,sK70])],[f873,f1050]) ).
thf(f1050,plain,
! [X2: $tType,X1: $tType,X0: $tType,X3: product_prod(X0,product_prod(X1,X2))] :
( ? [X4: X0,X5: X1,X6: X2] : ( vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),X4),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)) = X3 )
=> ( vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod(X0,product_prod(X1,X2)),X0,sK68(X0,X1,X2),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X0,product_prod(X1,X2)),X1,sK69(X0,X1,X2),X3)),vAPP(product_prod(X0,product_prod(X1,X2)),X2,sK70(X0,X1,X2),X3))) = X3 ) ),
introduced(choice_axiom,[]) ).
thf(f873,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X0,product_prod(X1,X2))] :
? [X4: X0,X5: X1,X6: X2] : ( vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),X4),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)) = X3 ),
inference(ennf_transformation,[],[f763]) ).
thf(f763,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: product_prod(X0,product_prod(X1,X2))] :
~ ! [X4: X0,X5: X1,X6: X2] : ( vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),X4),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)) != X3 ),
inference(rectify,[],[f42]) ).
thf(f42,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X51: product_prod(X0,product_prod(X2,X1))] :
~ ! [X49: X0,X50: X2,X56: X1] : ( vAPP(product_prod(X2,X1),product_prod(X0,product_prod(X2,X1)),vAPP(X0,sTfun(product_prod(X2,X1),product_prod(X0,product_prod(X2,X1))),product_Pair(X0,product_prod(X2,X1)),X49),vAPP(X1,product_prod(X2,X1),vAPP(X2,sTfun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X50),X56)) != X51 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_prod__cases3) ).
thf(f3217,plain,
spl151_159,
inference(avatar_split_clause,[],[f1172,f3215]) ).
thf(f3215,plain,
( spl151_159
<=> ! [X0: ( list(char) > int ) > ( list(char) > int ) > $o] : ( $true = vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o,vAPP(com,sTfun(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o),vAPP(com,sTfun(com,sTfun(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o)),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(com,sTfun(com,sTfun(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o))),relati1493963588_hoare,X0),skip),skip),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_159])]) ).
thf(f1172,plain,
! [X0: ( list(char) > int ) > ( list(char) > int ) > $o] : ( $true = vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o,vAPP(com,sTfun(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o),vAPP(com,sTfun(com,sTfun(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o)),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(com,sTfun(com,sTfun(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o))),relati1493963588_hoare,X0),skip),skip),X0) ),
inference(cnf_transformation,[],[f376]) ).
thf(f376,plain,
! [X0: ( list(char) > int ) > ( list(char) > int ) > $o] : ( $true = vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o,vAPP(com,sTfun(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o),vAPP(com,sTfun(com,sTfun(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o)),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(com,sTfun(com,sTfun(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o))),relati1493963588_hoare,X0),skip),skip),X0) ),
inference(fool_elimination,[],[f375]) ).
thf(f375,plain,
! [X0: ( list(char) > int ) > ( list(char) > int ) > $o] : vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o,vAPP(com,sTfun(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o),vAPP(com,sTfun(com,sTfun(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o)),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(com,sTfun(com,sTfun(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o))),relati1493963588_hoare,X0),skip),skip),X0),
inference(rectify,[],[f94]) ).
thf(f94,axiom,
! [X34: ( list(char) > int ) > ( list(char) > int ) > $o] : vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o,vAPP(com,sTfun(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o),vAPP(com,sTfun(com,sTfun(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o)),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(com,sTfun(com,sTfun(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),$o))),relati1493963588_hoare,X34),skip),skip),X34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_ir__Skip__Skip) ).
thf(f3078,plain,
( spl151_158
| ~ spl151_34
| ~ spl151_62 ),
inference(avatar_split_clause,[],[f2276,f2228,f2079,f3076]) ).
thf(f3076,plain,
( spl151_158
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( comm_monoid_add(X0) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_158])]) ).
thf(f2228,plain,
( spl151_62
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( comm_monoid_add(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_62])]) ).
thf(f2276,plain,
( ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( comm_monoid_add(X0) = $false ) )
| ~ spl151_34
| ~ spl151_62 ),
inference(trivial_inequality_removal,[],[f2275]) ).
thf(f2275,plain,
( ! [X0: $tType,X1: X0] :
( ( $true != $true )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( comm_monoid_add(X0) = $false ) )
| ~ spl151_34
| ~ spl151_62 ),
inference(superposition,[],[f2229,f2080]) ).
thf(f2229,plain,
( ! [X0: $tType,X1: X0] :
( ( comm_monoid_add(X0) != $true )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 ) )
| ~ spl151_62 ),
inference(avatar_component_clause,[],[f2228]) ).
thf(f3074,plain,
spl151_157,
inference(avatar_split_clause,[],[f1274,f3072]) ).
thf(f3072,plain,
( spl151_157
<=> ! [X0: $tType,X3: list(X0),X2: X0,X1: X0 > nat] : ( vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X1),vAPP(list(X0),list(X0),vAPP(X0,sTfun(list(X0),list(X0)),cons(X0),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X1,X2)),vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X1),X3))),vAPP(nat,nat,suc,zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_157])]) ).
thf(f1274,plain,
! [X0: $tType,X2: X0,X3: list(X0),X1: X0 > nat] : ( vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X1),vAPP(list(X0),list(X0),vAPP(X0,sTfun(list(X0),list(X0)),cons(X0),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X1,X2)),vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X1),X3))),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(cnf_transformation,[],[f755]) ).
thf(f755,plain,
! [X0: $tType,X1: X0 > nat,X2: X0,X3: list(X0)] : ( vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X1),vAPP(list(X0),list(X0),vAPP(X0,sTfun(list(X0),list(X0)),cons(X0),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X1,X2)),vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X1),X3))),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(rectify,[],[f220]) ).
thf(f220,axiom,
! [X0: $tType,X55: X0 > nat,X132: X0,X133: list(X0)] : ( vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X55),vAPP(list(X0),list(X0),vAPP(X0,sTfun(list(X0),list(X0)),cons(X0),X132),X133)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X55,X132)),vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X55),X133))),vAPP(nat,nat,suc,zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_list_Osize__gen_I2_J) ).
thf(f3061,plain,
spl151_156,
inference(avatar_split_clause,[],[f1213,f3059]) ).
thf(f3059,plain,
( spl151_156
<=> ! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK21,X0)) )
| ( $true = vAPP(sTfun(com,$o),$o,sP1,X0) )
| ( $true = vAPP(sTfun(com,$o),$o,sP0,X0) )
| ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,vAPP(sTfun(com,$o),list(char),sK22,X0)),vAPP(sTfun(com,$o),aexp,sK23,X0))) )
| ( $true != vAPP(com,$o,X0,skip) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_156])]) ).
thf(f1213,plain,
! [X0: com > $o,X1: com] :
( ( $true = vAPP(com,$o,X0,X1) )
| ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK21,X0)) )
| ( $true = vAPP(sTfun(com,$o),$o,sP1,X0) )
| ( $true = vAPP(sTfun(com,$o),$o,sP0,X0) )
| ( $true != vAPP(com,$o,X0,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,vAPP(sTfun(com,$o),list(char),sK22,X0)),vAPP(sTfun(com,$o),aexp,sK23,X0))) )
| ( $true != vAPP(com,$o,X0,skip) ) ),
inference(cnf_transformation,[],[f988]) ).
thf(f3054,plain,
spl151_155,
inference(avatar_split_clause,[],[f1273,f3052]) ).
thf(f3052,plain,
( spl151_155
<=> ! [X0: $tType,X3: com,X2: bexp,X1: ( list(char) > int ) > X0 > $o] : ( vAPP(nat,sTfun(sTfun(list(char),int),sTfun(X0,$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(X0,$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(X0,$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(X0,$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(X0,$o))))),relati1010904253t_back(X0),X1),X2),X3),zero_zero(nat)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_155])]) ).
thf(f1273,plain,
! [X0: $tType,X2: bexp,X3: com,X1: ( list(char) > int ) > X0 > $o] : ( vAPP(nat,sTfun(sTfun(list(char),int),sTfun(X0,$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(X0,$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(X0,$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(X0,$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(X0,$o))))),relati1010904253t_back(X0),X1),X2),X3),zero_zero(nat)) = X1 ),
inference(cnf_transformation,[],[f754]) ).
thf(f754,plain,
! [X0: $tType,X1: ( list(char) > int ) > X0 > $o,X2: bexp,X3: com] : ( vAPP(nat,sTfun(sTfun(list(char),int),sTfun(X0,$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(X0,$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(X0,$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(X0,$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(X0,$o))))),relati1010904253t_back(X0),X1),X2),X3),zero_zero(nat)) = X1 ),
inference(rectify,[],[f168]) ).
thf(f168,axiom,
! [X0: $tType,X34: ( list(char) > int ) > X0 > $o,X12: bexp,X22: com] : ( vAPP(nat,sTfun(sTfun(list(char),int),sTfun(X0,$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(X0,$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(X0,$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(X0,$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(X0,$o))))),relati1010904253t_back(X0),X34),X12),X22),zero_zero(nat)) = X34 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_get__back_Osimps_I1_J) ).
thf(f3050,plain,
spl151_154,
inference(avatar_split_clause,[],[f1272,f3048]) ).
thf(f3048,plain,
( spl151_154
<=> ! [X0: $tType,X3: list(X0),X2: list(X0),X1: X0 > nat] : ( vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X1),vAPP(list(X0),list(X0),vAPP(list(X0),sTfun(list(X0),list(X0)),append(X0),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X1),X2)),vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_154])]) ).
thf(f1272,plain,
! [X0: $tType,X2: list(X0),X3: list(X0),X1: X0 > nat] : ( vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X1),vAPP(list(X0),list(X0),vAPP(list(X0),sTfun(list(X0),list(X0)),append(X0),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X1),X2)),vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X1),X3)) ),
inference(cnf_transformation,[],[f753]) ).
thf(f753,plain,
! [X0: $tType,X1: X0 > nat,X2: list(X0),X3: list(X0)] : ( vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X1),vAPP(list(X0),list(X0),vAPP(list(X0),sTfun(list(X0),list(X0)),append(X0),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X1),X2)),vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X1),X3)) ),
inference(rectify,[],[f251]) ).
thf(f251,axiom,
! [X0: $tType,X65: X0 > nat,X156: list(X0),X164: list(X0)] : ( vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X65),vAPP(list(X0),list(X0),vAPP(list(X0),sTfun(list(X0),list(X0)),append(X0),X156),X164)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X65),X156)),vAPP(list(X0),nat,vAPP(sTfun(X0,nat),sTfun(list(X0),nat),size_list(X0),X65),X164)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_size__list__append) ).
thf(f3036,plain,
( spl151_153
| ~ spl151_34
| ~ spl151_61 ),
inference(avatar_split_clause,[],[f2270,f2224,f2079,f3034]) ).
thf(f3034,plain,
( spl151_153
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( monoid_add(X0) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_153])]) ).
thf(f2224,plain,
( spl151_61
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( monoid_add(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_61])]) ).
thf(f2270,plain,
( ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( monoid_add(X0) = $false ) )
| ~ spl151_34
| ~ spl151_61 ),
inference(trivial_inequality_removal,[],[f2269]) ).
thf(f2269,plain,
( ! [X0: $tType,X1: X0] :
( ( $true != $true )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( monoid_add(X0) = $false ) )
| ~ spl151_34
| ~ spl151_61 ),
inference(superposition,[],[f2225,f2080]) ).
thf(f2225,plain,
( ! [X0: $tType,X1: X0] :
( ( monoid_add(X0) != $true )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 ) )
| ~ spl151_61 ),
inference(avatar_component_clause,[],[f2224]) ).
thf(f3032,plain,
spl151_152,
inference(avatar_split_clause,[],[f1459,f3029]) ).
thf(f3029,plain,
( spl151_152
<=> ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),ta)),ua) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_152])]) ).
thf(f1459,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),ta)),ua) = $true,
inference(cnf_transformation,[],[f680]) ).
thf(f680,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),ta)),ua) = $true,
inference(fool_elimination,[],[f679]) ).
thf(f679,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),ta)),ua),
inference(rectify,[],[f10]) ).
thf(f10,axiom,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),ta)),ua),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Suc_Oprems_I2_J) ).
thf(f3027,plain,
spl151_151,
inference(avatar_split_clause,[],[f1458,f3024]) ).
thf(f3024,plain,
( spl151_151
<=> ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),t2)),u) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_151])]) ).
thf(f1458,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),t2)),u) = $true,
inference(cnf_transformation,[],[f678]) ).
thf(f678,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),t2)),u) = $true,
inference(fool_elimination,[],[f677]) ).
thf(f677,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),t2)),u),
inference(rectify,[],[f11]) ).
thf(f11,axiom,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,b),c)),t2)),u),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10__092_060open_062_IWHILE_Ab_ADO_Ac_M_At_____J_A_092_060Rightarrow_062_Au_____092_060close_062) ).
thf(f3022,plain,
spl151_150,
inference(avatar_split_clause,[],[f1296,f3020]) ).
thf(f3020,plain,
( spl151_150
<=> ! [X0: list(char) > int,X3: list(char) > int,X2: bexp,X1: com] :
( ( $true = vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,X2),X3) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(com,sTfun(sTfun(list(char),int),$o),vAPP(bexp,sTfun(com,sTfun(sTfun(list(char),int),$o)),vAPP(sTfun(list(char),int),sTfun(bexp,sTfun(com,sTfun(sTfun(list(char),int),$o))),sP2,X3),X2),X1),X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_150])]) ).
thf(f1296,plain,
! [X2: bexp,X3: list(char) > int,X0: list(char) > int,X1: com] :
( ( $true = vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,X2),X3) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(com,sTfun(sTfun(list(char),int),$o),vAPP(bexp,sTfun(com,sTfun(sTfun(list(char),int),$o)),vAPP(sTfun(list(char),int),sTfun(bexp,sTfun(com,sTfun(sTfun(list(char),int),$o))),sP2,X3),X2),X1),X0) ) ),
inference(cnf_transformation,[],[f1047]) ).
thf(f1047,plain,
! [X0: list(char) > int,X1: com,X2: bexp,X3: list(char) > int] :
( ( ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X1)),vAPP(sTfun(list(char),int),sTfun(list(char),int),vAPP(com,sTfun(sTfun(list(char),int),sTfun(list(char),int)),vAPP(bexp,sTfun(com,sTfun(sTfun(list(char),int),sTfun(list(char),int))),vAPP(sTfun(list(char),int),sTfun(bexp,sTfun(com,sTfun(sTfun(list(char),int),sTfun(list(char),int)))),sK66,X3),X2),X1),X0))),X0) )
& ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X1),X3)),vAPP(sTfun(list(char),int),sTfun(list(char),int),vAPP(com,sTfun(sTfun(list(char),int),sTfun(list(char),int)),vAPP(bexp,sTfun(com,sTfun(sTfun(list(char),int),sTfun(list(char),int))),vAPP(sTfun(list(char),int),sTfun(bexp,sTfun(com,sTfun(sTfun(list(char),int),sTfun(list(char),int)))),sK66,X3),X2),X1),X0)) )
& ( $true = vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,X2),X3) ) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(com,sTfun(sTfun(list(char),int),$o),vAPP(bexp,sTfun(com,sTfun(sTfun(list(char),int),$o)),vAPP(sTfun(list(char),int),sTfun(bexp,sTfun(com,sTfun(sTfun(list(char),int),$o))),sP2,X3),X2),X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f1045,f1046]) ).
thf(f1046,plain,
! [X0: list(char) > int,X1: com,X2: bexp,X3: list(char) > int] :
( ? [X4: list(char) > int] :
( ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X1)),X4)),X0) )
& ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X1),X3)),X4) ) )
=> ( ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X1)),vAPP(sTfun(list(char),int),sTfun(list(char),int),vAPP(com,sTfun(sTfun(list(char),int),sTfun(list(char),int)),vAPP(bexp,sTfun(com,sTfun(sTfun(list(char),int),sTfun(list(char),int))),vAPP(sTfun(list(char),int),sTfun(bexp,sTfun(com,sTfun(sTfun(list(char),int),sTfun(list(char),int)))),sK66,X3),X2),X1),X0))),X0) )
& ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X1),X3)),vAPP(sTfun(list(char),int),sTfun(list(char),int),vAPP(com,sTfun(sTfun(list(char),int),sTfun(list(char),int)),vAPP(bexp,sTfun(com,sTfun(sTfun(list(char),int),sTfun(list(char),int))),vAPP(sTfun(list(char),int),sTfun(bexp,sTfun(com,sTfun(sTfun(list(char),int),sTfun(list(char),int)))),sK66,X3),X2),X1),X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f1045,plain,
! [X0: list(char) > int,X1: com,X2: bexp,X3: list(char) > int] :
( ( ? [X4: list(char) > int] :
( ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X1)),X4)),X0) )
& ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X1),X3)),X4) ) )
& ( $true = vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,X2),X3) ) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(com,sTfun(sTfun(list(char),int),$o),vAPP(bexp,sTfun(com,sTfun(sTfun(list(char),int),$o)),vAPP(sTfun(list(char),int),sTfun(bexp,sTfun(com,sTfun(sTfun(list(char),int),$o))),sP2,X3),X2),X1),X0) ) ),
inference(rectify,[],[f1044]) ).
thf(f1044,plain,
! [X3: list(char) > int,X1: com,X0: bexp,X2: list(char) > int] :
( ( ? [X4: list(char) > int] :
( ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X4)),X3) )
& ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X1),X2)),X4) ) )
& ( $true = vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,X0),X2) ) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(com,sTfun(sTfun(list(char),int),$o),vAPP(bexp,sTfun(com,sTfun(sTfun(list(char),int),$o)),vAPP(sTfun(list(char),int),sTfun(bexp,sTfun(com,sTfun(sTfun(list(char),int),$o))),sP2,X2),X0),X1),X3) ) ),
inference(nnf_transformation,[],[f963]) ).
thf(f963,plain,
! [X3: list(char) > int,X1: com,X0: bexp,X2: list(char) > int] :
( ( ? [X4: list(char) > int] :
( ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)),X4)),X3) )
& ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),X1),X2)),X4) ) )
& ( $true = vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,X0),X2) ) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(com,sTfun(sTfun(list(char),int),$o),vAPP(bexp,sTfun(com,sTfun(sTfun(list(char),int),$o)),vAPP(sTfun(list(char),int),sTfun(bexp,sTfun(com,sTfun(sTfun(list(char),int),$o))),sP2,X2),X0),X1),X3) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[=])]) ).
thf(f3013,plain,
spl151_149,
inference(avatar_split_clause,[],[f1290,f3011]) ).
thf(f3011,plain,
( spl151_149
<=> ! [X0: $tType,X3: option(X0),X2: X0 > $o,X1: $o] :
( ( vAPP(X0,option(X0),some(X0),vAPP(sTfun(X0,$o),X0,vAPP(option(X0),sTfun(sTfun(X0,$o),X0),sK65(X0),X3),X2)) = X3 )
| ( none(X0) = X3 )
| ( $true != vAPP(option(X0),$o,vAPP(sTfun(X0,$o),sTfun(option(X0),$o),vAPP($o,sTfun(sTfun(X0,$o),sTfun(option(X0),$o)),case_option($o,X0),X1),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_149])]) ).
thf(f1290,plain,
! [X0: $tType,X2: X0 > $o,X3: option(X0),X1: $o] :
( ( vAPP(X0,option(X0),some(X0),vAPP(sTfun(X0,$o),X0,vAPP(option(X0),sTfun(sTfun(X0,$o),X0),sK65(X0),X3),X2)) = X3 )
| ( none(X0) = X3 )
| ( $true != vAPP(option(X0),$o,vAPP(sTfun(X0,$o),sTfun(option(X0),$o),vAPP($o,sTfun(sTfun(X0,$o),sTfun(option(X0),$o)),case_option($o,X0),X1),X2),X3) ) ),
inference(cnf_transformation,[],[f1043]) ).
thf(f1043,plain,
! [X0: $tType,X1: $o,X2: X0 > $o,X3: option(X0)] :
( ( ( $true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(option(X0),sTfun(sTfun(X0,$o),X0),sK65(X0),X3),X2)) )
& ( vAPP(X0,option(X0),some(X0),vAPP(sTfun(X0,$o),X0,vAPP(option(X0),sTfun(sTfun(X0,$o),X0),sK65(X0),X3),X2)) = X3 ) )
| ( ( $true = X1 )
& ( none(X0) = X3 ) )
| ( $true != vAPP(option(X0),$o,vAPP(sTfun(X0,$o),sTfun(option(X0),$o),vAPP($o,sTfun(sTfun(X0,$o),sTfun(option(X0),$o)),case_option($o,X0),X1),X2),X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f862,f1042]) ).
thf(f1042,plain,
! [X0: $tType,X2: X0 > $o,X3: option(X0)] :
( ? [X4: X0] :
( ( $true = vAPP(X0,$o,X2,X4) )
& ( vAPP(X0,option(X0),some(X0),X4) = X3 ) )
=> ( ( $true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(option(X0),sTfun(sTfun(X0,$o),X0),sK65(X0),X3),X2)) )
& ( vAPP(X0,option(X0),some(X0),vAPP(sTfun(X0,$o),X0,vAPP(option(X0),sTfun(sTfun(X0,$o),X0),sK65(X0),X3),X2)) = X3 ) ) ),
introduced(choice_axiom,[]) ).
thf(f862,plain,
! [X0: $tType,X1: $o,X2: X0 > $o,X3: option(X0)] :
( ? [X4: X0] :
( ( $true = vAPP(X0,$o,X2,X4) )
& ( vAPP(X0,option(X0),some(X0),X4) = X3 ) )
| ( ( $true = X1 )
& ( none(X0) = X3 ) )
| ( $true != vAPP(option(X0),$o,vAPP(sTfun(X0,$o),sTfun(option(X0),$o),vAPP($o,sTfun(sTfun(X0,$o),sTfun(option(X0),$o)),case_option($o,X0),X1),X2),X3) ) ),
inference(flattening,[],[f861]) ).
thf(f861,plain,
! [X0: $tType,X1: $o,X2: X0 > $o,X3: option(X0)] :
( ? [X4: X0] :
( ( $true = vAPP(X0,$o,X2,X4) )
& ( vAPP(X0,option(X0),some(X0),X4) = X3 ) )
| ( ( $true = X1 )
& ( none(X0) = X3 ) )
| ( $true != vAPP(option(X0),$o,vAPP(sTfun(X0,$o),sTfun(option(X0),$o),vAPP($o,sTfun(sTfun(X0,$o),sTfun(option(X0),$o)),case_option($o,X0),X1),X2),X3) ) ),
inference(ennf_transformation,[],[f760]) ).
thf(f760,plain,
! [X0: $tType,X1: $o,X2: X0 > $o,X3: option(X0)] :
( ( $true = vAPP(option(X0),$o,vAPP(sTfun(X0,$o),sTfun(option(X0),$o),vAPP($o,sTfun(sTfun(X0,$o),sTfun(option(X0),$o)),case_option($o,X0),X1),X2),X3) )
=> ( ( ( none(X0) = X3 )
=> ( $true != X1 ) )
=> ~ ! [X4: X0] :
( ( vAPP(X0,option(X0),some(X0),X4) = X3 )
=> ( $true != vAPP(X0,$o,X2,X4) ) ) ) ),
inference(flattening,[],[f462]) ).
thf(f462,plain,
! [X0: $tType,X1: $o,X2: X0 > $o,X3: option(X0)] :
( ( $true = vAPP(option(X0),$o,vAPP(sTfun(X0,$o),sTfun(option(X0),$o),vAPP($o,sTfun(sTfun(X0,$o),sTfun(option(X0),$o)),case_option($o,X0),X1),X2),X3) )
=> ( ( ( none(X0) = X3 )
=> ( $true != X1 ) )
=> ~ ! [X4: X0] :
( ( vAPP(X0,option(X0),some(X0),X4) = X3 )
=> ( $true != vAPP(X0,$o,X2,X4) ) ) ) ),
inference(fool_elimination,[],[f461]) ).
thf(f461,plain,
! [X0: $tType,X1: $o,X2: X0 > $o,X3: option(X0)] :
( vAPP(option(X0),$o,vAPP(sTfun(X0,$o),sTfun(option(X0),$o),vAPP($o,sTfun(sTfun(X0,$o),sTfun(option(X0),$o)),case_option($o,X0),X1),X2),X3)
=> ( ( ( none(X0) = X3 )
=> ~ X1 )
=> ~ ! [X4: X0] :
( ( vAPP(X0,option(X0),some(X0),X4) = X3 )
=> ~ vAPP(X0,$o,X2,X4) ) ) ),
inference(rectify,[],[f212]) ).
thf(f212,axiom,
! [X0: $tType,X34: $o,X35: X0 > $o,X55: option(X0)] :
( vAPP(option(X0),$o,vAPP(sTfun(X0,$o),sTfun(option(X0),$o),vAPP($o,sTfun(sTfun(X0,$o),sTfun(option(X0),$o)),case_option($o,X0),X34),X35),X55)
=> ( ( ( none(X0) = X55 )
=> ~ X34 )
=> ~ ! [X67: X0] :
( ( vAPP(X0,option(X0),some(X0),X67) = X55 )
=> ~ vAPP(X0,$o,X35,X67) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_case__optionE) ).
thf(f3009,plain,
spl151_148,
inference(avatar_split_clause,[],[f1221,f3007]) ).
thf(f3007,plain,
( spl151_148
<=> ! [X0: list(char) > int,X1: list(char) > int] :
( ( X0 = X1 )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),skip),X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_148])]) ).
thf(f1221,plain,
! [X0: list(char) > int,X1: list(char) > int] :
( ( X0 = X1 )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),skip),X0)),X1) ) ),
inference(cnf_transformation,[],[f835]) ).
thf(f835,plain,
! [X0: list(char) > int,X1: list(char) > int] :
( ( X0 = X1 )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),skip),X0)),X1) ) ),
inference(ennf_transformation,[],[f414]) ).
thf(f414,plain,
! [X0: list(char) > int,X1: list(char) > int] :
( ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),skip),X0)),X1) )
=> ( X0 = X1 ) ),
inference(fool_elimination,[],[f413]) ).
thf(f413,plain,
! [X0: list(char) > int,X1: list(char) > int] :
( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),skip),X0)),X1)
=> ( X0 = X1 ) ),
inference(rectify,[],[f82]) ).
thf(f82,axiom,
! [X17: list(char) > int,X15: list(char) > int] :
( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),skip),X17)),X15)
=> ( X15 = X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_SkipE) ).
thf(f3003,plain,
spl151_147,
inference(avatar_split_clause,[],[f1113,f3001]) ).
thf(f1113,plain,
! [X0: list(char) > int,X1: list(char) > int] :
( ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),X1)),t_a) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),X0)),ta) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),X0) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),vAPP(nat,nat,suc,ka)),X0),X1) ) ),
inference(cnf_transformation,[],[f786]) ).
thf(f786,plain,
! [X0: list(char) > int,X1: list(char) > int] :
( ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),X1)),t_a) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),X0)),ta) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),X0) )
| ( $true != vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),vAPP(nat,nat,suc,ka)),X0),X1) ) ),
inference(ennf_transformation,[],[f294]) ).
thf(f294,plain,
~ ? [X0: list(char) > int,X1: list(char) > int] :
( ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),X1)),t_a) )
& ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),X0)),ta) )
& ( $true = vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),X0) )
& ( $true = vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),vAPP(nat,nat,suc,ka)),X0),X1) ) ),
inference(fool_elimination,[],[f293]) ).
thf(f293,plain,
~ ? [X0: list(char) > int,X1: list(char) > int] :
( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),X1)),t_a)
& vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),X0)),ta)
& vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),X0)
& vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),vAPP(nat,nat,suc,ka)),X0),X1) ),
inference(rectify,[],[f290]) ).
thf(f290,negated_conjecture,
~ ? [X26: list(char) > int,X76: list(char) > int] :
( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),X76)),t_a)
& vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),X26)),ta)
& vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),X26)
& vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),vAPP(nat,nat,suc,ka)),X26),X76) ),
inference(negated_conjecture,[],[f289]) ).
thf(f289,conjecture,
? [X26: list(char) > int,X76: list(char) > int] :
( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),X76)),t_a)
& vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),X26)),ta)
& vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),X26)
& vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),vAPP(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),vAPP(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))),vAPP(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)))),vAPP(sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o)),sTfun(bexp,sTfun(com,sTfun(nat,sTfun(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o))))),relati1010904253t_back(sTfun(list(char),int)),p),b),c),vAPP(nat,nat,suc,ka)),X26),X76) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f2997,plain,
( spl151_146
| ~ spl151_34
| ~ spl151_60 ),
inference(avatar_split_clause,[],[f2265,f2220,f2079,f2995]) ).
thf(f2995,plain,
( spl151_146
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( group_add(X0) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_146])]) ).
thf(f2220,plain,
( spl151_60
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( group_add(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_60])]) ).
thf(f2265,plain,
( ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( group_add(X0) = $false ) )
| ~ spl151_34
| ~ spl151_60 ),
inference(trivial_inequality_removal,[],[f2264]) ).
thf(f2264,plain,
( ! [X0: $tType,X1: X0] :
( ( $true != $true )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( group_add(X0) = $false ) )
| ~ spl151_34
| ~ spl151_60 ),
inference(superposition,[],[f2221,f2080]) ).
thf(f2221,plain,
( ! [X0: $tType,X1: X0] :
( ( group_add(X0) != $true )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 ) )
| ~ spl151_60 ),
inference(avatar_component_clause,[],[f2220]) ).
thf(f2993,plain,
spl151_145,
inference(avatar_split_clause,[],[f1291,f2991]) ).
thf(f2991,plain,
( spl151_145
<=> ! [X0: $tType,X3: option(X0),X2: X0 > $o,X1: $o] :
( ( vAPP(X0,option(X0),some(X0),vAPP(sTfun(X0,$o),X0,vAPP(option(X0),sTfun(sTfun(X0,$o),X0),sK65(X0),X3),X2)) = X3 )
| ( $true = X1 )
| ( $true != vAPP(option(X0),$o,vAPP(sTfun(X0,$o),sTfun(option(X0),$o),vAPP($o,sTfun(sTfun(X0,$o),sTfun(option(X0),$o)),case_option($o,X0),X1),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_145])]) ).
thf(f1291,plain,
! [X0: $tType,X2: X0 > $o,X3: option(X0),X1: $o] :
( ( vAPP(X0,option(X0),some(X0),vAPP(sTfun(X0,$o),X0,vAPP(option(X0),sTfun(sTfun(X0,$o),X0),sK65(X0),X3),X2)) = X3 )
| ( $true = X1 )
| ( $true != vAPP(option(X0),$o,vAPP(sTfun(X0,$o),sTfun(option(X0),$o),vAPP($o,sTfun(sTfun(X0,$o),sTfun(option(X0),$o)),case_option($o,X0),X1),X2),X3) ) ),
inference(cnf_transformation,[],[f1043]) ).
thf(f2987,plain,
spl151_144,
inference(avatar_split_clause,[],[f1292,f2985]) ).
thf(f2985,plain,
( spl151_144
<=> ! [X0: $tType,X3: option(X0),X2: X0 > $o,X1: $o] :
( ( $true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(option(X0),sTfun(sTfun(X0,$o),X0),sK65(X0),X3),X2)) )
| ( none(X0) = X3 )
| ( $true != vAPP(option(X0),$o,vAPP(sTfun(X0,$o),sTfun(option(X0),$o),vAPP($o,sTfun(sTfun(X0,$o),sTfun(option(X0),$o)),case_option($o,X0),X1),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_144])]) ).
thf(f1292,plain,
! [X0: $tType,X2: X0 > $o,X3: option(X0),X1: $o] :
( ( $true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(option(X0),sTfun(sTfun(X0,$o),X0),sK65(X0),X3),X2)) )
| ( none(X0) = X3 )
| ( $true != vAPP(option(X0),$o,vAPP(sTfun(X0,$o),sTfun(option(X0),$o),vAPP($o,sTfun(sTfun(X0,$o),sTfun(option(X0),$o)),case_option($o,X0),X1),X2),X3) ) ),
inference(cnf_transformation,[],[f1043]) ).
thf(f2981,plain,
spl151_143,
inference(avatar_split_clause,[],[f1293,f2979]) ).
thf(f2979,plain,
( spl151_143
<=> ! [X0: $tType,X3: option(X0),X2: X0 > $o,X1: $o] :
( ( $true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(option(X0),sTfun(sTfun(X0,$o),X0),sK65(X0),X3),X2)) )
| ( $true = X1 )
| ( $true != vAPP(option(X0),$o,vAPP(sTfun(X0,$o),sTfun(option(X0),$o),vAPP($o,sTfun(sTfun(X0,$o),sTfun(option(X0),$o)),case_option($o,X0),X1),X2),X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_143])]) ).
thf(f1293,plain,
! [X0: $tType,X2: X0 > $o,X3: option(X0),X1: $o] :
( ( $true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(option(X0),sTfun(sTfun(X0,$o),X0),sK65(X0),X3),X2)) )
| ( $true = X1 )
| ( $true != vAPP(option(X0),$o,vAPP(sTfun(X0,$o),sTfun(option(X0),$o),vAPP($o,sTfun(sTfun(X0,$o),sTfun(option(X0),$o)),case_option($o,X0),X1),X2),X3) ) ),
inference(cnf_transformation,[],[f1043]) ).
thf(f2936,plain,
( spl151_142
| ~ spl151_34
| ~ spl151_59 ),
inference(avatar_split_clause,[],[f2260,f2216,f2079,f2934]) ).
thf(f2934,plain,
( spl151_142
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( monoid_add(X0) = $false ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_142])]) ).
thf(f2216,plain,
( spl151_59
<=> ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( monoid_add(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_59])]) ).
thf(f2260,plain,
( ! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( monoid_add(X0) = $false ) )
| ~ spl151_34
| ~ spl151_59 ),
inference(trivial_inequality_removal,[],[f2259]) ).
thf(f2259,plain,
( ! [X0: $tType,X1: X0] :
( ( $true != $true )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( monoid_add(X0) = $false ) )
| ~ spl151_34
| ~ spl151_59 ),
inference(superposition,[],[f2217,f2080]) ).
thf(f2217,plain,
( ! [X0: $tType,X1: X0] :
( ( monoid_add(X0) != $true )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 ) )
| ~ spl151_59 ),
inference(avatar_component_clause,[],[f2216]) ).
thf(f2932,plain,
spl151_141,
inference(avatar_split_clause,[],[f1457,f2929]) ).
thf(f1457,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),sa)),ta) = $true,
inference(cnf_transformation,[],[f676]) ).
thf(f676,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),sa)),ta) = $true,
inference(fool_elimination,[],[f675]) ).
thf(f675,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),sa)),ta),
inference(rectify,[],[f3]) ).
thf(f3,axiom,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),sa)),ta),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Suc_Oprems_I3_J) ).
thf(f2927,plain,
spl151_140,
inference(avatar_split_clause,[],[f1456,f2924]) ).
thf(f2924,plain,
( spl151_140
<=> ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),s2)),t2) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_140])]) ).
thf(f1456,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),s2)),t2) = $true,
inference(cnf_transformation,[],[f674]) ).
thf(f674,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),s2)),t2) = $true,
inference(fool_elimination,[],[f673]) ).
thf(f673,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),s2)),t2),
inference(rectify,[],[f7]) ).
thf(f7,axiom,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c),s2)),t2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__092_060open_062_Ic_M_As_____J_A_092_060Rightarrow_062_At_____092_060close_062) ).
thf(f2922,plain,
spl151_139,
inference(avatar_split_clause,[],[f1455,f2919]) ).
thf(f1455,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),s_a)),t_a) = $true,
inference(cnf_transformation,[],[f672]) ).
thf(f672,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),s_a)),t_a) = $true,
inference(fool_elimination,[],[f671]) ).
thf(f671,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),s_a)),t_a),
inference(rectify,[],[f4]) ).
thf(f4,axiom,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),s_a)),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_Suc_Oprems_I4_J) ).
thf(f2917,plain,
spl151_138,
inference(avatar_split_clause,[],[f1454,f2914]) ).
thf(f2914,plain,
( spl151_138
<=> ( vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),s)),t) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_138])]) ).
thf(f1454,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),s)),t) = $true,
inference(cnf_transformation,[],[f670]) ).
thf(f670,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),s)),t) = $true,
inference(fool_elimination,[],[f669]) ).
thf(f669,plain,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),s)),t),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),c2),s)),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__092_060open_062_Ic_H_M_As_H_____J_A_092_060Rightarrow_062_At_H_____092_060close_062) ).
thf(f2912,plain,
spl151_137,
inference(avatar_split_clause,[],[f1189,f2910]) ).
thf(f2910,plain,
( spl151_137
<=> ! [X0: com,X1: com] : ( vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_size(com),X0)),vAPP(com,nat,size_size(com),X1))),vAPP(nat,nat,suc,zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_137])]) ).
thf(f1189,plain,
! [X0: com,X1: com] : ( vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_size(com),X0)),vAPP(com,nat,size_size(com),X1))),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(cnf_transformation,[],[f718]) ).
thf(f718,plain,
! [X0: com,X1: com] : ( vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_size(com),X0)),vAPP(com,nat,size_size(com),X1))),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(rectify,[],[f182]) ).
thf(f182,axiom,
! [X82: com,X83: com] : ( vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(com,sTfun(com,com),seq,X82),X83)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_size(com),X82)),vAPP(com,nat,size_size(com),X83))),vAPP(nat,nat,suc,zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_com_Osize_I8_J) ).
thf(f2908,plain,
spl151_136,
inference(avatar_split_clause,[],[f1171,f2906]) ).
thf(f2906,plain,
( spl151_136
<=> ! [X0: list(char) > int] : ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),skip),X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_136])]) ).
thf(f1171,plain,
! [X0: list(char) > int] : ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),skip),X0)),X0) ),
inference(cnf_transformation,[],[f374]) ).
thf(f374,plain,
! [X0: list(char) > int] : ( $true = vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),skip),X0)),X0) ),
inference(fool_elimination,[],[f373]) ).
thf(f373,plain,
! [X0: list(char) > int] : vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),skip),X0)),X0),
inference(rectify,[],[f83]) ).
thf(f83,axiom,
! [X17: list(char) > int] : vAPP(sTfun(list(char),int),$o,vAPP(product_prod(com,sTfun(list(char),int)),sTfun(sTfun(list(char),int),$o),big_big_step,vAPP(sTfun(list(char),int),product_prod(com,sTfun(list(char),int)),vAPP(com,sTfun(sTfun(list(char),int),product_prod(com,sTfun(list(char),int))),product_Pair(com,sTfun(list(char),int)),skip),X17)),X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Skip) ).
thf(f2876,plain,
spl151_135,
inference(avatar_split_clause,[],[f1289,f2874]) ).
thf(f2874,plain,
( spl151_135
<=> ! [X1: $tType,X0: $tType,X3: product_prod(X1,X0),X2: product_prod(X1,X0) > $o] :
( ( $true = vAPP(product_prod(X1,X0),$o,X2,X3) )
| ( $true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK63(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK64(X0,X1),X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_135])]) ).
thf(f1289,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X1,X0) > $o,X3: product_prod(X1,X0)] :
( ( $true = vAPP(product_prod(X1,X0),$o,X2,X3) )
| ( $true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK63(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK64(X0,X1),X2))) ) ),
inference(cnf_transformation,[],[f1041]) ).
thf(f1041,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X1,X0) > $o,X3: product_prod(X1,X0)] :
( ( $true = vAPP(product_prod(X1,X0),$o,X2,X3) )
| ( $true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK63(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK64(X0,X1),X2))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63,sK64])],[f860,f1040]) ).
thf(f1040,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X1,X0) > $o] :
( ? [X4: X1,X5: X0] : ( $true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)) )
=> ( $true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK63(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK64(X0,X1),X2))) ) ),
introduced(choice_axiom,[]) ).
thf(f860,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X1,X0) > $o,X3: product_prod(X1,X0)] :
( ( $true = vAPP(product_prod(X1,X0),$o,X2,X3) )
| ? [X4: X1,X5: X0] : ( $true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)) ) ),
inference(ennf_transformation,[],[f460]) ).
thf(f460,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X1,X0) > $o,X3: product_prod(X1,X0)] :
( ! [X4: X1,X5: X0] : ( $true = vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)) )
=> ( $true = vAPP(product_prod(X1,X0),$o,X2,X3) ) ),
inference(fool_elimination,[],[f459]) ).
thf(f459,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X1,X0) > $o,X3: product_prod(X1,X0)] :
( ! [X4: X1,X5: X0] : vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5))
=> vAPP(product_prod(X1,X0),$o,X2,X3) ),
inference(rectify,[],[f31]) ).
thf(f31,axiom,
! [X2: $tType,X0: $tType,X34: product_prod(X0,X2) > $o,X48: product_prod(X0,X2)] :
( ! [X49: X0,X50: X2] : vAPP(product_prod(X0,X2),$o,X34,vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X49),X50))
=> vAPP(product_prod(X0,X2),$o,X34,X48) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_old_Oprod_Oinducts) ).
thf(f2869,plain,
spl151_134,
inference(avatar_split_clause,[],[f1288,f2867]) ).
thf(f2867,plain,
( spl151_134
<=> ! [X1: $tType,X0: $tType,X3: product_prod(X1,X0),X2: product_prod(X1,X0) > $o] :
( ( $true = vAPP(product_prod(X1,X0),$o,X2,X3) )
| ( $true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK61(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK62(X0,X1),X2))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_134])]) ).
thf(f1288,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X1,X0) > $o,X3: product_prod(X1,X0)] :
( ( $true = vAPP(product_prod(X1,X0),$o,X2,X3) )
| ( $true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK61(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK62(X0,X1),X2))) ) ),
inference(cnf_transformation,[],[f1039]) ).
thf(f1039,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X1,X0) > $o,X3: product_prod(X1,X0)] :
( ( $true = vAPP(product_prod(X1,X0),$o,X2,X3) )
| ( $true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK61(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK62(X0,X1),X2))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61,sK62])],[f859,f1038]) ).
thf(f1038,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X1,X0) > $o] :
( ? [X4: X1,X5: X0] : ( $true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)) )
=> ( $true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK61(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK62(X0,X1),X2))) ) ),
introduced(choice_axiom,[]) ).
thf(f859,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X1,X0) > $o,X3: product_prod(X1,X0)] :
( ( $true = vAPP(product_prod(X1,X0),$o,X2,X3) )
| ? [X4: X1,X5: X0] : ( $true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)) ) ),
inference(ennf_transformation,[],[f458]) ).
thf(f458,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X1,X0) > $o,X3: product_prod(X1,X0)] :
( ! [X4: X1,X5: X0] : ( $true = vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)) )
=> ( $true = vAPP(product_prod(X1,X0),$o,X2,X3) ) ),
inference(fool_elimination,[],[f457]) ).
thf(f457,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X1,X0) > $o,X3: product_prod(X1,X0)] :
( ! [X4: X1,X5: X0] : vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5))
=> vAPP(product_prod(X1,X0),$o,X2,X3) ),
inference(rectify,[],[f44]) ).
thf(f44,axiom,
! [X2: $tType,X0: $tType,X34: product_prod(X0,X2) > $o,X61: product_prod(X0,X2)] :
( ! [X49: X0,X50: X2] : vAPP(product_prod(X0,X2),$o,X34,vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X49),X50))
=> vAPP(product_prod(X0,X2),$o,X34,X61) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_prod__cases) ).
thf(f2777,plain,
spl151_133,
inference(avatar_split_clause,[],[f1284,f2775]) ).
thf(f2775,plain,
( spl151_133
<=> ! [X1: $tType,X0: $tType,X3: X1 > X0,X2: X1 > X0] :
( ( X2 = X3 )
| ( vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK58(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK58(X0,X1),X3),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_133])]) ).
thf(f1284,plain,
! [X1: $tType,X0: $tType,X2: X1 > X0,X3: X1 > X0] :
( ( X2 = X3 )
| ( vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK58(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK58(X0,X1),X3),X2)) ) ),
inference(cnf_transformation,[],[f1035]) ).
thf(f1035,plain,
! [X0: $tType,X1: $tType,X2: X1 > X0,X3: X1 > X0] :
( ( X2 = X3 )
| ( vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK58(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK58(X0,X1),X3),X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58])],[f856,f1034]) ).
thf(f1034,plain,
! [X1: $tType,X0: $tType,X2: X1 > X0,X3: X1 > X0] :
( ? [X4: X1] : ( vAPP(X1,X0,X3,X4) != vAPP(X1,X0,X2,X4) )
=> ( vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK58(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK58(X0,X1),X3),X2)) ) ),
introduced(choice_axiom,[]) ).
thf(f856,plain,
! [X0: $tType,X1: $tType,X2: X1 > X0,X3: X1 > X0] :
( ( X2 = X3 )
| ? [X4: X1] : ( vAPP(X1,X0,X3,X4) != vAPP(X1,X0,X2,X4) ) ),
inference(ennf_transformation,[],[f759]) ).
thf(f759,plain,
! [X0: $tType,X1: $tType,X2: X1 > X0,X3: X1 > X0] :
( ! [X4: X1] : ( vAPP(X1,X0,X3,X4) = vAPP(X1,X0,X2,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f48]) ).
thf(f48,axiom,
! [X2: $tType,X0: $tType,X65: X0 > X2,X66: X0 > X2] :
( ! [X64: X0] : ( vAPP(X0,X2,X65,X64) = vAPP(X0,X2,X66,X64) )
=> ( X65 = X66 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_ext) ).
thf(f2773,plain,
spl151_132,
inference(avatar_split_clause,[],[f1209,f2771]) ).
thf(f2771,plain,
( spl151_132
<=> ! [X0: com > $o] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,vAPP(sTfun(com,$o),bexp,sK15,X0)),vAPP(sTfun(com,$o),com,sK16,X0)),vAPP(sTfun(com,$o),com,sK17,X0))) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_132])]) ).
thf(f1209,plain,
! [X0: com > $o] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,vAPP(sTfun(com,$o),bexp,sK15,X0)),vAPP(sTfun(com,$o),com,sK16,X0)),vAPP(sTfun(com,$o),com,sK17,X0))) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f980]) ).
thf(f980,plain,
! [X0: com > $o] :
( ( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,vAPP(sTfun(com,$o),bexp,sK15,X0)),vAPP(sTfun(com,$o),com,sK16,X0)),vAPP(sTfun(com,$o),com,sK17,X0))) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK17,X0)) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK16,X0)) ) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f978,f979]) ).
thf(f979,plain,
! [X0: com > $o] :
( ? [X1: bexp,X2: com,X3: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X1),X2),X3)) )
& ( $true = vAPP(com,$o,X0,X3) )
& ( $true = vAPP(com,$o,X0,X2) ) )
=> ( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,vAPP(sTfun(com,$o),bexp,sK15,X0)),vAPP(sTfun(com,$o),com,sK16,X0)),vAPP(sTfun(com,$o),com,sK17,X0))) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK17,X0)) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK16,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f978,plain,
! [X0: com > $o] :
( ? [X1: bexp,X2: com,X3: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X1),X2),X3)) )
& ( $true = vAPP(com,$o,X0,X3) )
& ( $true = vAPP(com,$o,X0,X2) ) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ),
inference(rectify,[],[f977]) ).
thf(f977,plain,
! [X0: com > $o] :
( ? [X6: bexp,X7: com,X8: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X6),X7),X8)) )
& ( $true = vAPP(com,$o,X0,X8) )
& ( $true = vAPP(com,$o,X0,X7) ) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ),
inference(nnf_transformation,[],[f961]) ).
thf(f2769,plain,
spl151_131,
inference(avatar_split_clause,[],[f1188,f2767]) ).
thf(f2767,plain,
( spl151_131
<=> ! [X0: literal,X1: list(typerep)] : ( vAPP(typerep,nat,size_size(typerep),vAPP(list(typerep),typerep,vAPP(literal,sTfun(list(typerep),typerep),typerep2,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(typerep),nat,vAPP(sTfun(typerep,nat),sTfun(list(typerep),nat),size_list(typerep),size_size(typerep)),X1)),vAPP(nat,nat,suc,zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_131])]) ).
thf(f1188,plain,
! [X0: literal,X1: list(typerep)] : ( vAPP(typerep,nat,size_size(typerep),vAPP(list(typerep),typerep,vAPP(literal,sTfun(list(typerep),typerep),typerep2,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(typerep),nat,vAPP(sTfun(typerep,nat),sTfun(list(typerep),nat),size_list(typerep),size_size(typerep)),X1)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(cnf_transformation,[],[f717]) ).
thf(f717,plain,
! [X0: literal,X1: list(typerep)] : ( vAPP(typerep,nat,size_size(typerep),vAPP(list(typerep),typerep,vAPP(literal,sTfun(list(typerep),typerep),typerep2,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(typerep),nat,vAPP(sTfun(typerep,nat),sTfun(list(typerep),nat),size_list(typerep),size_size(typerep)),X1)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(rectify,[],[f218]) ).
thf(f218,axiom,
! [X9: literal,X5: list(typerep)] : ( vAPP(typerep,nat,size_size(typerep),vAPP(list(typerep),typerep,vAPP(literal,sTfun(list(typerep),typerep),typerep2,X9),X5)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(typerep),nat,vAPP(sTfun(typerep,nat),sTfun(list(typerep),nat),size_list(typerep),size_size(typerep)),X5)),vAPP(nat,nat,suc,zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_typerep_Osize_I2_J) ).
thf(f2765,plain,
spl151_130,
inference(avatar_split_clause,[],[f1187,f2763]) ).
thf(f2763,plain,
( spl151_130
<=> ! [X0: com,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_com,X0)),vAPP(com,nat,size_com,X1))),vAPP(nat,nat,suc,zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_130])]) ).
thf(f1187,plain,
! [X0: com,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_com,X0)),vAPP(com,nat,size_com,X1))),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(cnf_transformation,[],[f716]) ).
thf(f716,plain,
! [X0: com,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_com,X0)),vAPP(com,nat,size_com,X1))),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(rectify,[],[f173]) ).
thf(f173,axiom,
! [X82: com,X83: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X82),X83)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_com,X82)),vAPP(com,nat,size_com,X83))),vAPP(nat,nat,suc,zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_com_Osize__gen_I3_J) ).
thf(f2698,plain,
spl151_129,
inference(avatar_split_clause,[],[f1912,f2696]) ).
thf(f2696,plain,
( spl151_129
<=> ! [X1: $tType,X0: $tType,X2: X0 > nat,X4: X1,X3: X1 > nat] : ( vAPP(sum_sum(X0,X1),nat,vAPP(sTfun(X1,nat),sTfun(sum_sum(X0,X1),nat),vAPP(sTfun(X0,nat),sTfun(sTfun(X1,nat),sTfun(sum_sum(X0,X1),nat)),basic_BNF_size_sum(X0,X1),X2),X3),vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X4)) = vAPP(nat,nat,suc,vAPP(X1,nat,X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_129])]) ).
thf(f1912,plain,
! [X1: $tType,X0: $tType,X2: X0 > nat,X3: X1 > nat,X4: X1] : ( vAPP(sum_sum(X0,X1),nat,vAPP(sTfun(X1,nat),sTfun(sum_sum(X0,X1),nat),vAPP(sTfun(X0,nat),sTfun(sTfun(X1,nat),sTfun(sum_sum(X0,X1),nat)),basic_BNF_size_sum(X0,X1),X2),X3),vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X4)) = vAPP(nat,nat,suc,vAPP(X1,nat,X3,X4)) ),
inference(forward_demodulation,[],[f1911,f1127]) ).
thf(f1127,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),zero_zero(nat)) = X0 ),
inference(cnf_transformation,[],[f697]) ).
thf(f697,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),zero_zero(nat)) = X0 ),
inference(rectify,[],[f143]) ).
thf(f143,axiom,
! [X86: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X86),zero_zero(nat)) = X86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Nat_Oadd__0__right) ).
thf(f1911,plain,
! [X1: $tType,X0: $tType,X2: X0 > nat,X3: X1 > nat,X4: X1] : ( vAPP(sum_sum(X0,X1),nat,vAPP(sTfun(X1,nat),sTfun(sum_sum(X0,X1),nat),vAPP(sTfun(X0,nat),sTfun(sTfun(X1,nat),sTfun(sum_sum(X0,X1),nat)),basic_BNF_size_sum(X0,X1),X2),X3),vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X4)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X1,nat,X3,X4)),zero_zero(nat))) ),
inference(forward_demodulation,[],[f1313,f1182]) ).
thf(f1182,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,suc,X1)) ),
inference(cnf_transformation,[],[f711]) ).
thf(f711,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,suc,X1)) ),
inference(rectify,[],[f65]) ).
thf(f65,axiom,
! [X86: nat,X68: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X86),vAPP(nat,nat,suc,X68)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X86),X68)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_add__Suc__right) ).
thf(f1313,plain,
! [X1: $tType,X0: $tType,X2: X0 > nat,X3: X1 > nat,X4: X1] : ( vAPP(sum_sum(X0,X1),nat,vAPP(sTfun(X1,nat),sTfun(sum_sum(X0,X1),nat),vAPP(sTfun(X0,nat),sTfun(sTfun(X1,nat),sTfun(sum_sum(X0,X1),nat)),basic_BNF_size_sum(X0,X1),X2),X3),vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X1,nat,X3,X4)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(cnf_transformation,[],[f769]) ).
thf(f769,plain,
! [X0: $tType,X1: $tType,X2: X0 > nat,X3: X1 > nat,X4: X1] : ( vAPP(sum_sum(X0,X1),nat,vAPP(sTfun(X1,nat),sTfun(sum_sum(X0,X1),nat),vAPP(sTfun(X0,nat),sTfun(sTfun(X1,nat),sTfun(sum_sum(X0,X1),nat)),basic_BNF_size_sum(X0,X1),X2),X3),vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X1,nat,X3,X4)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(rectify,[],[f210]) ).
thf(f210,axiom,
! [X0: $tType,X2: $tType,X151: X0 > nat,X55: X2 > nat,X5: X2] : ( vAPP(sum_sum(X0,X2),nat,vAPP(sTfun(X2,nat),sTfun(sum_sum(X0,X2),nat),vAPP(sTfun(X0,nat),sTfun(sTfun(X2,nat),sTfun(sum_sum(X0,X2),nat)),basic_BNF_size_sum(X0,X2),X151),X55),vAPP(X2,sum_sum(X0,X2),sum_Inr(X2,X0),X5)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X2,nat,X55,X5)),vAPP(nat,nat,suc,zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_sum_Osize__gen_I2_J) ).
thf(f2694,plain,
( spl151_128
| ~ spl151_52
| ~ spl151_53 ),
inference(avatar_split_clause,[],[f2372,f2185,f2181,f2692]) ).
thf(f2692,plain,
( spl151_128
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X1) != X0 )
| ( vAPP(nat,nat,sK14,X0) = X1 )
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_128])]) ).
thf(f2181,plain,
( spl151_52
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK14,X0)) = X0 )
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_52])]) ).
thf(f2185,plain,
( spl151_53
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) != vAPP(nat,nat,suc,X1) )
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_53])]) ).
thf(f2372,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X1) != X0 )
| ( vAPP(nat,nat,sK14,X0) = X1 )
| ( zero_zero(nat) = X0 ) )
| ~ spl151_52
| ~ spl151_53 ),
inference(superposition,[],[f2186,f2182]) ).
thf(f2182,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK14,X0)) = X0 )
| ( zero_zero(nat) = X0 ) )
| ~ spl151_52 ),
inference(avatar_component_clause,[],[f2181]) ).
thf(f2186,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) != vAPP(nat,nat,suc,X1) )
| ( X0 = X1 ) )
| ~ spl151_53 ),
inference(avatar_component_clause,[],[f2185]) ).
thf(f2690,plain,
spl151_127,
inference(avatar_split_clause,[],[f1910,f2688]) ).
thf(f2688,plain,
( spl151_127
<=> ! [X1: $tType,X0: $tType,X4: X1,X3: X0 > nat,X2: X1 > nat] : ( vAPP(sum_sum(X1,X0),nat,vAPP(sTfun(X0,nat),sTfun(sum_sum(X1,X0),nat),vAPP(sTfun(X1,nat),sTfun(sTfun(X0,nat),sTfun(sum_sum(X1,X0),nat)),basic_BNF_size_sum(X1,X0),X2),X3),vAPP(X1,sum_sum(X1,X0),sum_Inl(X1,X0),X4)) = vAPP(nat,nat,suc,vAPP(X1,nat,X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_127])]) ).
thf(f1910,plain,
! [X1: $tType,X0: $tType,X2: X1 > nat,X3: X0 > nat,X4: X1] : ( vAPP(sum_sum(X1,X0),nat,vAPP(sTfun(X0,nat),sTfun(sum_sum(X1,X0),nat),vAPP(sTfun(X1,nat),sTfun(sTfun(X0,nat),sTfun(sum_sum(X1,X0),nat)),basic_BNF_size_sum(X1,X0),X2),X3),vAPP(X1,sum_sum(X1,X0),sum_Inl(X1,X0),X4)) = vAPP(nat,nat,suc,vAPP(X1,nat,X2,X4)) ),
inference(forward_demodulation,[],[f1909,f1127]) ).
thf(f1909,plain,
! [X1: $tType,X0: $tType,X2: X1 > nat,X3: X0 > nat,X4: X1] : ( vAPP(sum_sum(X1,X0),nat,vAPP(sTfun(X0,nat),sTfun(sum_sum(X1,X0),nat),vAPP(sTfun(X1,nat),sTfun(sTfun(X0,nat),sTfun(sum_sum(X1,X0),nat)),basic_BNF_size_sum(X1,X0),X2),X3),vAPP(X1,sum_sum(X1,X0),sum_Inl(X1,X0),X4)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X1,nat,X2,X4)),zero_zero(nat))) ),
inference(forward_demodulation,[],[f1312,f1182]) ).
thf(f1312,plain,
! [X1: $tType,X0: $tType,X2: X1 > nat,X3: X0 > nat,X4: X1] : ( vAPP(sum_sum(X1,X0),nat,vAPP(sTfun(X0,nat),sTfun(sum_sum(X1,X0),nat),vAPP(sTfun(X1,nat),sTfun(sTfun(X0,nat),sTfun(sum_sum(X1,X0),nat)),basic_BNF_size_sum(X1,X0),X2),X3),vAPP(X1,sum_sum(X1,X0),sum_Inl(X1,X0),X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X1,nat,X2,X4)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(cnf_transformation,[],[f768]) ).
thf(f768,plain,
! [X0: $tType,X1: $tType,X2: X1 > nat,X3: X0 > nat,X4: X1] : ( vAPP(sum_sum(X1,X0),nat,vAPP(sTfun(X0,nat),sTfun(sum_sum(X1,X0),nat),vAPP(sTfun(X1,nat),sTfun(sTfun(X0,nat),sTfun(sum_sum(X1,X0),nat)),basic_BNF_size_sum(X1,X0),X2),X3),vAPP(X1,sum_sum(X1,X0),sum_Inl(X1,X0),X4)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X1,nat,X2,X4)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(rectify,[],[f207]) ).
thf(f207,axiom,
! [X2: $tType,X0: $tType,X151: X0 > nat,X55: X2 > nat,X9: X0] : ( vAPP(sum_sum(X0,X2),nat,vAPP(sTfun(X2,nat),sTfun(sum_sum(X0,X2),nat),vAPP(sTfun(X0,nat),sTfun(sTfun(X2,nat),sTfun(sum_sum(X0,X2),nat)),basic_BNF_size_sum(X0,X2),X151),X55),vAPP(X0,sum_sum(X0,X2),sum_Inl(X0,X2),X9)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X151,X9)),vAPP(nat,nat,suc,zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_sum_Osize__gen_I1_J) ).
thf(f2686,plain,
spl151_126,
inference(avatar_split_clause,[],[f1507,f2684]) ).
thf(f2684,plain,
( spl151_126
<=> ! [X0: $tType,X4: X0,X3: X0,X2: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) )
| ( comm_monoid_add(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_126])]) ).
thf(f1507,plain,
! [X0: $tType,X2: X0,X3: X0,X4: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) )
| ( comm_monoid_add(X0) != $true ) ),
inference(equality_resolution,[],[f1162]) ).
thf(f1162,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X1) )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1 )
| ( comm_monoid_add(X0) != $true ) ),
inference(cnf_transformation,[],[f817]) ).
thf(f817,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X1) )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1 ) )
| ( comm_monoid_add(X0) != $true ) ),
inference(ennf_transformation,[],[f356]) ).
thf(f356,plain,
! [X0: $tType] :
( ( comm_monoid_add(X0) = $true )
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1 )
=> ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X1) ) ) ),
inference(fool_elimination,[],[f355]) ).
thf(f355,plain,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1 )
=> ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X1) ) ) ),
inference(rectify,[],[f113]) ).
thf(f113,axiom,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X112: X0,X38: X0,X12: X0,X11: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X38),X12) = X112 )
=> ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X38),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X11),X12)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X11),X112) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_group__cancel_Oadd2) ).
thf(f2682,plain,
spl151_125,
inference(avatar_split_clause,[],[f1506,f2680]) ).
thf(f2680,plain,
( spl151_125
<=> ! [X0: $tType,X4: X0,X3: X0,X2: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X4) )
| ( comm_monoid_add(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_125])]) ).
thf(f1506,plain,
! [X0: $tType,X2: X0,X3: X0,X4: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X4) )
| ( comm_monoid_add(X0) != $true ) ),
inference(equality_resolution,[],[f1161]) ).
thf(f1161,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X4) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1 )
| ( comm_monoid_add(X0) != $true ) ),
inference(cnf_transformation,[],[f816]) ).
thf(f816,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X4) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) )
| ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1 ) )
| ( comm_monoid_add(X0) != $true ) ),
inference(ennf_transformation,[],[f354]) ).
thf(f354,plain,
! [X0: $tType] :
( ( comm_monoid_add(X0) = $true )
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1 )
=> ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X4) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) ) ) ),
inference(fool_elimination,[],[f353]) ).
thf(f353,plain,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1 )
=> ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X4) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) ) ) ),
inference(rectify,[],[f112]) ).
thf(f112,axiom,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X62: X0,X38: X0,X11: X0,X12: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X38),X11) = X62 )
=> ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X62),X12) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X38),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X11),X12)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_group__cancel_Oadd1) ).
thf(f2678,plain,
spl151_124,
inference(avatar_split_clause,[],[f1235,f2676]) ).
thf(f2676,plain,
( spl151_124
<=> ! [X0: $tType,X2: list(X0),X1: list(X0)] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,size_size(list(X0)),X1)),vAPP(list(X0),nat,size_size(list(X0)),X2)) = vAPP(list(X0),nat,size_size(list(X0)),vAPP(list(X0),list(X0),vAPP(list(X0),sTfun(list(X0),list(X0)),append(X0),X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_124])]) ).
thf(f1235,plain,
! [X0: $tType,X2: list(X0),X1: list(X0)] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,size_size(list(X0)),X1)),vAPP(list(X0),nat,size_size(list(X0)),X2)) = vAPP(list(X0),nat,size_size(list(X0)),vAPP(list(X0),list(X0),vAPP(list(X0),sTfun(list(X0),list(X0)),append(X0),X1),X2)) ),
inference(cnf_transformation,[],[f733]) ).
thf(f733,plain,
! [X0: $tType,X1: list(X0),X2: list(X0)] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,size_size(list(X0)),X1)),vAPP(list(X0),nat,size_size(list(X0)),X2)) = vAPP(list(X0),nat,size_size(list(X0)),vAPP(list(X0),list(X0),vAPP(list(X0),sTfun(list(X0),list(X0)),append(X0),X1),X2)) ),
inference(rectify,[],[f250]) ).
thf(f250,axiom,
! [X0: $tType,X156: list(X0),X164: list(X0)] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,size_size(list(X0)),X156)),vAPP(list(X0),nat,size_size(list(X0)),X164)) = vAPP(list(X0),nat,size_size(list(X0)),vAPP(list(X0),list(X0),vAPP(list(X0),sTfun(list(X0),list(X0)),append(X0),X156),X164)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_length__append) ).
thf(f2674,plain,
spl151_123,
inference(avatar_split_clause,[],[f1234,f2672]) ).
thf(f2672,plain,
( spl151_123
<=> ! [X0: $tType,X2: list(X0),X1: list(X0)] : ( vAPP(list(X0),nat,size_size(list(X0)),vAPP(list(X0),list(X0),vAPP(list(X0),sTfun(list(X0),list(X0)),splice(X0),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,size_size(list(X0)),X1)),vAPP(list(X0),nat,size_size(list(X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_123])]) ).
thf(f1234,plain,
! [X0: $tType,X2: list(X0),X1: list(X0)] : ( vAPP(list(X0),nat,size_size(list(X0)),vAPP(list(X0),list(X0),vAPP(list(X0),sTfun(list(X0),list(X0)),splice(X0),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,size_size(list(X0)),X1)),vAPP(list(X0),nat,size_size(list(X0)),X2)) ),
inference(cnf_transformation,[],[f732]) ).
thf(f732,plain,
! [X0: $tType,X1: list(X0),X2: list(X0)] : ( vAPP(list(X0),nat,size_size(list(X0)),vAPP(list(X0),list(X0),vAPP(list(X0),sTfun(list(X0),list(X0)),splice(X0),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,size_size(list(X0)),X1)),vAPP(list(X0),nat,size_size(list(X0)),X2)) ),
inference(rectify,[],[f238]) ).
thf(f238,axiom,
! [X0: $tType,X156: list(X0),X164: list(X0)] : ( vAPP(list(X0),nat,size_size(list(X0)),vAPP(list(X0),list(X0),vAPP(list(X0),sTfun(list(X0),list(X0)),splice(X0),X156),X164)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,size_size(list(X0)),X156)),vAPP(list(X0),nat,size_size(list(X0)),X164)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_length__splice) ).
thf(f2670,plain,
spl151_122,
inference(avatar_split_clause,[],[f1154,f2668]) ).
thf(f2668,plain,
( spl151_122
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) )
| ( ab_semigroup_add(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_122])]) ).
thf(f1154,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) )
| ( ab_semigroup_add(X0) != $true ) ),
inference(cnf_transformation,[],[f809]) ).
thf(f809,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) )
| ( ab_semigroup_add(X0) != $true ) ),
inference(ennf_transformation,[],[f340]) ).
thf(f340,plain,
! [X0: $tType] :
( ( ab_semigroup_add(X0) = $true )
=> ! [X1: X0,X2: X0,X3: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) ) ),
inference(fool_elimination,[],[f339]) ).
thf(f339,plain,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) ) ),
inference(rectify,[],[f110]) ).
thf(f110,axiom,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X11: X0,X12: X0,X22: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X11),X12)),X22) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X11),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X12),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(f2666,plain,
spl151_121,
inference(avatar_split_clause,[],[f1153,f2664]) ).
thf(f2664,plain,
( spl151_121
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) )
| ( ab_semigroup_add(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_121])]) ).
thf(f1153,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) )
| ( ab_semigroup_add(X0) != $true ) ),
inference(cnf_transformation,[],[f808]) ).
thf(f808,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) )
| ( ab_semigroup_add(X0) != $true ) ),
inference(ennf_transformation,[],[f338]) ).
thf(f338,plain,
! [X0: $tType] :
( ( ab_semigroup_add(X0) = $true )
=> ! [X1: X0,X2: X0,X3: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) ) ),
inference(fool_elimination,[],[f337]) ).
thf(f337,plain,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) ) ),
inference(rectify,[],[f118]) ).
thf(f118,axiom,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X12: X0,X11: X0,X22: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X11),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X12),X22)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X12),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X11),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_add_Oleft__commute) ).
thf(f2662,plain,
spl151_120,
inference(avatar_split_clause,[],[f1144,f2660]) ).
thf(f2660,plain,
( spl151_120
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) )
| ( semigroup_add(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_120])]) ).
thf(f1144,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) )
| ( semigroup_add(X0) != $true ) ),
inference(cnf_transformation,[],[f798]) ).
thf(f798,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) )
| ( semigroup_add(X0) != $true ) ),
inference(ennf_transformation,[],[f320]) ).
thf(f320,plain,
! [X0: $tType] :
( ( semigroup_add(X0) = $true )
=> ! [X1: X0,X2: X0,X3: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) ) ),
inference(fool_elimination,[],[f319]) ).
thf(f319,plain,
! [X0: $tType] :
( semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) ) ),
inference(rectify,[],[f114]) ).
thf(f114,axiom,
! [X0: $tType] :
( semigroup_add(X0)
=> ! [X11: X0,X12: X0,X22: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X11),X12)),X22) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X11),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X12),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_add_Oassoc) ).
thf(f2658,plain,
spl151_119,
inference(avatar_split_clause,[],[f1137,f2656]) ).
thf(f2656,plain,
( spl151_119
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) )
| ( neg_numeral(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_119])]) ).
thf(f1137,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) )
| ( neg_numeral(X0) != $true ) ),
inference(cnf_transformation,[],[f791]) ).
thf(f791,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) )
| ( neg_numeral(X0) != $true ) ),
inference(ennf_transformation,[],[f306]) ).
thf(f306,plain,
! [X0: $tType] :
( ( neg_numeral(X0) = $true )
=> ! [X1: X0,X2: X0,X3: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) ) ),
inference(fool_elimination,[],[f305]) ).
thf(f305,plain,
! [X0: $tType] :
( neg_numeral(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) ) ),
inference(rectify,[],[f130]) ).
thf(f130,axiom,
! [X0: $tType] :
( neg_numeral(X0)
=> ! [X11: X0,X12: X0,X22: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X11),X12)),X22) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X11),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X12),X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_is__num__normalize_I1_J) ).
thf(f2651,plain,
( spl151_118
| ~ spl151_51
| ~ spl151_53 ),
inference(avatar_split_clause,[],[f2371,f2185,f2177,f2649]) ).
thf(f2649,plain,
( spl151_118
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X1) != X0 )
| ( vAPP(nat,nat,sK13,X0) = X1 )
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_118])]) ).
thf(f2177,plain,
( spl151_51
<=> ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK13,X0)) = X0 )
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_51])]) ).
thf(f2371,plain,
( ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X1) != X0 )
| ( vAPP(nat,nat,sK13,X0) = X1 )
| ( zero_zero(nat) = X0 ) )
| ~ spl151_51
| ~ spl151_53 ),
inference(superposition,[],[f2186,f2178]) ).
thf(f2178,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK13,X0)) = X0 )
| ( zero_zero(nat) = X0 ) )
| ~ spl151_51 ),
inference(avatar_component_clause,[],[f2177]) ).
thf(f2637,plain,
spl151_117,
inference(avatar_split_clause,[],[f1358,f2635]) ).
thf(f2635,plain,
( spl151_117
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: X0 > X2 > X1,X4: X0,X5: X2] : ( vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X3,X4),X5) = vAPP(product_prod(X0,X2),X1,vAPP(sTfun(X0,sTfun(X2,X1)),sTfun(product_prod(X0,X2),X1),product_rec_prod(X0,X2,X1),X3),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_117])]) ).
thf(f1358,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X2 > X1,X4: X0,X5: X2] : ( vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X3,X4),X5) = vAPP(product_prod(X0,X2),X1,vAPP(sTfun(X0,sTfun(X2,X1)),sTfun(product_prod(X0,X2),X1),product_rec_prod(X0,X2,X1),X3),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X5)) ),
inference(cnf_transformation,[],[f778]) ).
thf(f778,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X2 > X1,X4: X0,X5: X2] : ( vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X3,X4),X5) = vAPP(product_prod(X0,X2),X1,vAPP(sTfun(X0,sTfun(X2,X1)),sTfun(product_prod(X0,X2),X1),product_rec_prod(X0,X2,X1),X3),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X5)) ),
inference(rectify,[],[f54]) ).
thf(f54,axiom,
! [X0: $tType,X4: $tType,X2: $tType,X70: X0 > X2 > X4,X11: X0,X12: X2] : ( vAPP(product_prod(X0,X2),X4,vAPP(sTfun(X0,sTfun(X2,X4)),sTfun(product_prod(X0,X2),X4),product_rec_prod(X0,X2,X4),X70),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X11),X12)) = vAPP(X2,X4,vAPP(X0,sTfun(X2,X4),X70,X11),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_old_Oprod_Orec) ).
thf(f2633,plain,
spl151_116,
inference(avatar_split_clause,[],[f1357,f2631]) ).
thf(f2631,plain,
( spl151_116
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X2 > X1,X4: X0,X5: X2] : ( vAPP(product_prod(X0,X2),X1,vAPP(sTfun(X0,sTfun(X2,X1)),sTfun(product_prod(X0,X2),X1),produc2004651681e_prod(X0,X2,X1),X3),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X5)) = vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X3,X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_116])]) ).
thf(f1357,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0 > X2 > X1,X4: X0,X5: X2] : ( vAPP(product_prod(X0,X2),X1,vAPP(sTfun(X0,sTfun(X2,X1)),sTfun(product_prod(X0,X2),X1),produc2004651681e_prod(X0,X2,X1),X3),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X5)) = vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X3,X4),X5) ),
inference(cnf_transformation,[],[f777]) ).
thf(f777,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0 > X2 > X1,X4: X0,X5: X2] : ( vAPP(product_prod(X0,X2),X1,vAPP(sTfun(X0,sTfun(X2,X1)),sTfun(product_prod(X0,X2),X1),produc2004651681e_prod(X0,X2,X1),X3),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X5)) = vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X3,X4),X5) ),
inference(rectify,[],[f63]) ).
thf(f63,axiom,
! [X2: $tType,X0: $tType,X1: $tType,X22: X2 > X1 > X0,X11: X2,X12: X1] : ( vAPP(product_prod(X2,X1),X0,vAPP(sTfun(X2,sTfun(X1,X0)),sTfun(product_prod(X2,X1),X0),produc2004651681e_prod(X2,X1,X0),X22),vAPP(X1,product_prod(X2,X1),vAPP(X2,sTfun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X11),X12)) = vAPP(X1,X0,vAPP(X2,sTfun(X1,X0),X22,X11),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_internal__case__prod__conv) ).
thf(f2629,plain,
spl151_115,
inference(avatar_split_clause,[],[f1311,f2627]) ).
thf(f2627,plain,
( spl151_115
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: product_prod(X0,X1) > X2,X3: X2 > product_prod(X0,X1)] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(tuple_isomorphism(X2,X0,X1),nat,size_size(tuple_isomorphism(X2,X0,X1)),vAPP(sTfun(product_prod(X0,X1),X2),tuple_isomorphism(X2,X0,X1),vAPP(sTfun(X2,product_prod(X0,X1)),sTfun(sTfun(product_prod(X0,X1),X2),tuple_isomorphism(X2,X0,X1)),tuple_742722141rphism(X2,X0,X1),X3),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_115])]) ).
thf(f1311,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2 > product_prod(X0,X1),X4: product_prod(X0,X1) > X2] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(tuple_isomorphism(X2,X0,X1),nat,size_size(tuple_isomorphism(X2,X0,X1)),vAPP(sTfun(product_prod(X0,X1),X2),tuple_isomorphism(X2,X0,X1),vAPP(sTfun(X2,product_prod(X0,X1)),sTfun(sTfun(product_prod(X0,X1),X2),tuple_isomorphism(X2,X0,X1)),tuple_742722141rphism(X2,X0,X1),X3),X4)) ),
inference(cnf_transformation,[],[f767]) ).
thf(f767,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > product_prod(X0,X1),X4: product_prod(X0,X1) > X2] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(tuple_isomorphism(X2,X0,X1),nat,size_size(tuple_isomorphism(X2,X0,X1)),vAPP(sTfun(product_prod(X0,X1),X2),tuple_isomorphism(X2,X0,X1),vAPP(sTfun(X2,product_prod(X0,X1)),sTfun(sTfun(product_prod(X0,X1),X2),tuple_isomorphism(X2,X0,X1)),tuple_742722141rphism(X2,X0,X1),X3),X4)) ),
inference(rectify,[],[f203]) ).
thf(f203,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X9: X0 > product_prod(X2,X1),X5: product_prod(X2,X1) > X0] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(tuple_isomorphism(X0,X2,X1),nat,size_size(tuple_isomorphism(X0,X2,X1)),vAPP(sTfun(product_prod(X2,X1),X0),tuple_isomorphism(X0,X2,X1),vAPP(sTfun(X0,product_prod(X2,X1)),sTfun(sTfun(product_prod(X2,X1),X0),tuple_isomorphism(X0,X2,X1)),tuple_742722141rphism(X0,X2,X1),X9),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_tuple__isomorphism_Osize_I2_J) ).
thf(f2625,plain,
spl151_114,
inference(avatar_split_clause,[],[f1186,f2623]) ).
thf(f2623,plain,
( spl151_114
<=> ! [X0: literal,X1: list(typerep)] : ( vAPP(typerep,nat,size_typerep,vAPP(list(typerep),typerep,vAPP(literal,sTfun(list(typerep),typerep),typerep2,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(typerep),nat,vAPP(sTfun(typerep,nat),sTfun(list(typerep),nat),size_list(typerep),size_typerep),X1)),vAPP(nat,nat,suc,zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_114])]) ).
thf(f1186,plain,
! [X0: literal,X1: list(typerep)] : ( vAPP(typerep,nat,size_typerep,vAPP(list(typerep),typerep,vAPP(literal,sTfun(list(typerep),typerep),typerep2,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(typerep),nat,vAPP(sTfun(typerep,nat),sTfun(list(typerep),nat),size_list(typerep),size_typerep),X1)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(cnf_transformation,[],[f715]) ).
thf(f715,plain,
! [X0: literal,X1: list(typerep)] : ( vAPP(typerep,nat,size_typerep,vAPP(list(typerep),typerep,vAPP(literal,sTfun(list(typerep),typerep),typerep2,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(typerep),nat,vAPP(sTfun(typerep,nat),sTfun(list(typerep),nat),size_list(typerep),size_typerep),X1)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(rectify,[],[f219]) ).
thf(f219,axiom,
! [X9: literal,X5: list(typerep)] : ( vAPP(typerep,nat,size_typerep,vAPP(list(typerep),typerep,vAPP(literal,sTfun(list(typerep),typerep),typerep2,X9),X5)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(typerep),nat,vAPP(sTfun(typerep,nat),sTfun(list(typerep),nat),size_list(typerep),size_typerep),X5)),vAPP(nat,nat,suc,zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_typerep_Osize__gen) ).
thf(f2613,plain,
spl151_113,
inference(avatar_split_clause,[],[f1246,f2611]) ).
thf(f2611,plain,
( spl151_113
<=> ! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] :
( ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),vAPP(sum_sum(X0,X1),X1,sK29(X0,X1),X2)) = X2 )
| ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),vAPP(sum_sum(X0,X1),X0,sK30(X0,X1),X2)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_113])]) ).
thf(f1246,plain,
! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] :
( ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),vAPP(sum_sum(X0,X1),X1,sK29(X0,X1),X2)) = X2 )
| ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),vAPP(sum_sum(X0,X1),X0,sK30(X0,X1),X2)) = X2 ) ),
inference(cnf_transformation,[],[f1002]) ).
thf(f1002,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] :
( ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),vAPP(sum_sum(X0,X1),X1,sK29(X0,X1),X2)) = X2 )
| ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),vAPP(sum_sum(X0,X1),X0,sK30(X0,X1),X2)) = X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30])],[f999,f1001,f1000]) ).
thf(f1000,plain,
! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] :
( ? [X3: X1] : ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X3) = X2 )
=> ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),vAPP(sum_sum(X0,X1),X1,sK29(X0,X1),X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
thf(f1001,plain,
! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] :
( ? [X4: X0] : ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X4) = X2 )
=> ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),vAPP(sum_sum(X0,X1),X0,sK30(X0,X1),X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
thf(f999,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] :
( ? [X3: X1] : ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X3) = X2 )
| ? [X4: X0] : ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X4) = X2 ) ),
inference(rectify,[],[f840]) ).
thf(f840,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] :
( ? [X4: X1] : ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X4) = X2 )
| ? [X3: X0] : ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X3) = X2 ) ),
inference(ennf_transformation,[],[f741]) ).
thf(f741,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] :
( ! [X3: X0] : ( vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X3) != X2 )
=> ~ ! [X4: X1] : ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X4) != X2 ) ),
inference(rectify,[],[f209]) ).
thf(f209,axiom,
! [X0: $tType,X2: $tType,X17: sum_sum(X0,X2)] :
( ! [X64: X0] : ( vAPP(X0,sum_sum(X0,X2),sum_Inl(X0,X2),X64) != X17 )
=> ~ ! [X64: X2] : ( vAPP(X2,sum_sum(X0,X2),sum_Inr(X2,X0),X64) != X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_obj__sumE) ).
thf(f2609,plain,
spl151_112,
inference(avatar_split_clause,[],[f1908,f2607]) ).
thf(f2607,plain,
( spl151_112
<=> ! [X2: com,X0: bexp,X1: com] : ( vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2)) = vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(com,sTfun(com,com),seq,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_112])]) ).
thf(f1908,plain,
! [X2: com,X0: bexp,X1: com] : ( vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2)) = vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(com,sTfun(com,com),seq,X1),X2)) ),
inference(forward_demodulation,[],[f1237,f1189]) ).
thf(f1237,plain,
! [X2: com,X0: bexp,X1: com] : ( vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_size(com),X1)),vAPP(com,nat,size_size(com),X2))),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(cnf_transformation,[],[f735]) ).
thf(f735,plain,
! [X0: bexp,X1: com,X2: com] : ( vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_size(com),X1)),vAPP(com,nat,size_size(com),X2))),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(rectify,[],[f175]) ).
thf(f175,axiom,
! [X99: bexp,X100: com,X101: com] : ( vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X99),X100),X101)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_size(com),X100)),vAPP(com,nat,size_size(com),X101))),vAPP(nat,nat,suc,zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_com_Osize_I9_J) ).
thf(f2602,plain,
spl151_111,
inference(avatar_split_clause,[],[f1907,f2600]) ).
thf(f2600,plain,
( spl151_111
<=> ! [X2: com,X0: bexp,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2)) = vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_111])]) ).
thf(f1907,plain,
! [X2: com,X0: bexp,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2)) = vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X1),X2)) ),
inference(forward_demodulation,[],[f1236,f1187]) ).
thf(f1236,plain,
! [X2: com,X0: bexp,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_com,X1)),vAPP(com,nat,size_com,X2))),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(cnf_transformation,[],[f734]) ).
thf(f734,plain,
! [X0: bexp,X1: com,X2: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_com,X1)),vAPP(com,nat,size_com,X2))),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(rectify,[],[f172]) ).
thf(f172,axiom,
! [X99: bexp,X100: com,X101: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X99),X100),X101)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_com,X100)),vAPP(com,nat,size_com,X101))),vAPP(nat,nat,suc,zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_com_Osize__gen_I4_J) ).
thf(f2598,plain,
( spl151_110
| ~ spl151_56
| ~ spl151_106
| ~ spl151_109 ),
inference(avatar_split_clause,[],[f2594,f2591,f2543,f2201,f2596]) ).
thf(f2596,plain,
( spl151_110
<=> ! [X0: bexp,X1: com] : ( vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)) = vAPP(nat,nat,suc,vAPP(com,nat,size_size(com),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_110])]) ).
thf(f2201,plain,
( spl151_56
<=> ! [X0: $tType,X1: nat] : ( vAPP(list(X0),nat,size_size(list(X0)),vAPP(nat,list(X0),sK27(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_56])]) ).
thf(f2543,plain,
( spl151_106
<=> ! [X0: $tType,X2: list(X0)] : ( vAPP(nat,nat,suc,vAPP(list(X0),nat,size_size(list(X0)),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,size_size(list(X0)),X2)),vAPP(nat,nat,suc,zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_106])]) ).
thf(f2591,plain,
( spl151_109
<=> ! [X0: bexp,X1: com] : ( vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_size(com),X1)),vAPP(nat,nat,suc,zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_109])]) ).
thf(f2594,plain,
( ! [X0: bexp,X1: com] : ( vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)) = vAPP(nat,nat,suc,vAPP(com,nat,size_size(com),X1)) )
| ~ spl151_56
| ~ spl151_106
| ~ spl151_109 ),
inference(forward_demodulation,[],[f2592,f2570]) ).
thf(f2570,plain,
( ! [X1: nat] : ( vAPP(nat,nat,suc,X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,suc,zero_zero(nat))) )
| ~ spl151_56
| ~ spl151_106 ),
inference(superposition,[],[f2544,f2202]) ).
thf(f2202,plain,
( ! [X0: $tType,X1: nat] : ( vAPP(list(X0),nat,size_size(list(X0)),vAPP(nat,list(X0),sK27(X0),X1)) = X1 )
| ~ spl151_56 ),
inference(avatar_component_clause,[],[f2201]) ).
thf(f2544,plain,
( ! [X0: $tType,X2: list(X0)] : ( vAPP(nat,nat,suc,vAPP(list(X0),nat,size_size(list(X0)),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,size_size(list(X0)),X2)),vAPP(nat,nat,suc,zero_zero(nat))) )
| ~ spl151_106 ),
inference(avatar_component_clause,[],[f2543]) ).
thf(f2592,plain,
( ! [X0: bexp,X1: com] : ( vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_size(com),X1)),vAPP(nat,nat,suc,zero_zero(nat))) )
| ~ spl151_109 ),
inference(avatar_component_clause,[],[f2591]) ).
thf(f2593,plain,
spl151_109,
inference(avatar_split_clause,[],[f1185,f2591]) ).
thf(f1185,plain,
! [X0: bexp,X1: com] : ( vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_size(com),X1)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(cnf_transformation,[],[f714]) ).
thf(f714,plain,
! [X0: bexp,X1: com] : ( vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_size(com),X1)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(rectify,[],[f181]) ).
thf(f181,axiom,
! [X71: bexp,X72: com] : ( vAPP(com,nat,size_size(com),vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X71),X72)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_size(com),X72)),vAPP(nat,nat,suc,zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_com_Osize_I10_J) ).
thf(f2582,plain,
spl151_108,
inference(avatar_split_clause,[],[f1212,f2580]) ).
thf(f2580,plain,
( spl151_108
<=> ! [X0: com > $o] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,vAPP(sTfun(com,$o),com,sK18,X0)),vAPP(sTfun(com,$o),com,sK19,X0))) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_108])]) ).
thf(f1212,plain,
! [X0: com > $o] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,vAPP(sTfun(com,$o),com,sK18,X0)),vAPP(sTfun(com,$o),com,sK19,X0))) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ),
inference(cnf_transformation,[],[f984]) ).
thf(f984,plain,
! [X0: com > $o] :
( ( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,vAPP(sTfun(com,$o),com,sK18,X0)),vAPP(sTfun(com,$o),com,sK19,X0))) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK19,X0)) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK18,X0)) ) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f982,f983]) ).
thf(f983,plain,
! [X0: com > $o] :
( ? [X1: com,X2: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X1),X2)) )
& ( $true = vAPP(com,$o,X0,X2) )
& ( $true = vAPP(com,$o,X0,X1) ) )
=> ( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,vAPP(sTfun(com,$o),com,sK18,X0)),vAPP(sTfun(com,$o),com,sK19,X0))) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK19,X0)) )
& ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK18,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f982,plain,
! [X0: com > $o] :
( ? [X1: com,X2: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X1),X2)) )
& ( $true = vAPP(com,$o,X0,X2) )
& ( $true = vAPP(com,$o,X0,X1) ) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ),
inference(rectify,[],[f981]) ).
thf(f981,plain,
! [X0: com > $o] :
( ? [X4: com,X5: com] :
( ( $true != vAPP(com,$o,X0,vAPP(com,com,vAPP(com,sTfun(com,com),seq,X4),X5)) )
& ( $true = vAPP(com,$o,X0,X5) )
& ( $true = vAPP(com,$o,X0,X4) ) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ),
inference(nnf_transformation,[],[f960]) ).
thf(f2578,plain,
spl151_107,
inference(avatar_split_clause,[],[f1203,f2576]) ).
thf(f2576,plain,
( spl151_107
<=> ! [X0: $tType,X1: set(X0)] : ( vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_107])]) ).
thf(f1203,plain,
! [X0: $tType,X1: set(X0)] : ( vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1)) = X1 ),
inference(cnf_transformation,[],[f404]) ).
thf(f404,plain,
! [X0: $tType,X1: set(X0)] : ( vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1)) = X1 ),
inference(fool_elimination,[],[f403]) ).
thf(f403,plain,
! [X0: $tType,X1: set(X0)] :
( vAPP(sTfun(X0,$o),set(X0),collect(X0),
^ [X2: X0] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)) = X1 ),
inference(rectify,[],[f46]) ).
thf(f46,axiom,
! [X0: $tType,X62: set(X0)] :
( vAPP(sTfun(X0,$o),set(X0),collect(X0),
^ [X63: X0] : vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X63),X62)) = X62 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_Collect__mem__eq) ).
thf(f2545,plain,
spl151_106,
inference(avatar_split_clause,[],[f1906,f2543]) ).
thf(f1906,plain,
! [X0: $tType,X2: list(X0)] : ( vAPP(nat,nat,suc,vAPP(list(X0),nat,size_size(list(X0)),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,size_size(list(X0)),X2)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(forward_demodulation,[],[f1233,f1231]) ).
thf(f1231,plain,
! [X0: $tType,X2: list(X0),X1: X0] : ( vAPP(list(X0),nat,size_size(list(X0)),vAPP(list(X0),list(X0),vAPP(X0,sTfun(list(X0),list(X0)),cons(X0),X1),X2)) = vAPP(nat,nat,suc,vAPP(list(X0),nat,size_size(list(X0)),X2)) ),
inference(cnf_transformation,[],[f729]) ).
thf(f729,plain,
! [X0: $tType,X1: X0,X2: list(X0)] : ( vAPP(list(X0),nat,size_size(list(X0)),vAPP(list(X0),list(X0),vAPP(X0,sTfun(list(X0),list(X0)),cons(X0),X1),X2)) = vAPP(nat,nat,suc,vAPP(list(X0),nat,size_size(list(X0)),X2)) ),
inference(rectify,[],[f223]) ).
thf(f223,axiom,
! [X0: $tType,X55: X0,X156: list(X0)] : ( vAPP(list(X0),nat,size_size(list(X0)),vAPP(list(X0),list(X0),vAPP(X0,sTfun(list(X0),list(X0)),cons(X0),X55),X156)) = vAPP(nat,nat,suc,vAPP(list(X0),nat,size_size(list(X0)),X156)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_length__Cons) ).
thf(f1233,plain,
! [X0: $tType,X2: list(X0),X1: X0] : ( vAPP(list(X0),nat,size_size(list(X0)),vAPP(list(X0),list(X0),vAPP(X0,sTfun(list(X0),list(X0)),cons(X0),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,size_size(list(X0)),X2)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(cnf_transformation,[],[f731]) ).
thf(f731,plain,
! [X0: $tType,X1: X0,X2: list(X0)] : ( vAPP(list(X0),nat,size_size(list(X0)),vAPP(list(X0),list(X0),vAPP(X0,sTfun(list(X0),list(X0)),cons(X0),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,size_size(list(X0)),X2)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(rectify,[],[f224]) ).
thf(f224,axiom,
! [X0: $tType,X132: X0,X133: list(X0)] : ( vAPP(list(X0),nat,size_size(list(X0)),vAPP(list(X0),list(X0),vAPP(X0,sTfun(list(X0),list(X0)),cons(X0),X132),X133)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(X0),nat,size_size(list(X0)),X133)),vAPP(nat,nat,suc,zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_list_Osize_I4_J) ).
thf(f2541,plain,
spl151_105,
inference(avatar_split_clause,[],[f1264,f2539]) ).
thf(f2539,plain,
( spl151_105
<=> ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK56(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK57(X0,X1),X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_105])]) ).
thf(f1264,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK56(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK57(X0,X1),X2)) = X2 ),
inference(cnf_transformation,[],[f1033]) ).
thf(f1033,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK56(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK57(X0,X1),X2)) = X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57])],[f746,f1032]) ).
thf(f1032,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] :
( ? [X3: X0,X4: X1] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2 )
=> ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK56(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK57(X0,X1),X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
thf(f746,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
? [X3: X0,X4: X1] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2 ),
inference(rectify,[],[f49]) ).
thf(f49,axiom,
! [X0: $tType,X2: $tType,X61: product_prod(X0,X2)] :
? [X64: X0,X67: X2] : ( vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X64),X67) = X61 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_surj__pair) ).
thf(f2537,plain,
spl151_104,
inference(avatar_split_clause,[],[f1263,f2535]) ).
thf(f2535,plain,
( spl151_104
<=> ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK54(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK55(X0,X1),X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_104])]) ).
thf(f1263,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK54(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK55(X0,X1),X2)) = X2 ),
inference(cnf_transformation,[],[f1031]) ).
thf(f1031,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK54(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK55(X0,X1),X2)) = X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55])],[f854,f1030]) ).
thf(f1030,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] :
( ? [X3: X0,X4: X1] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2 )
=> ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK54(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK55(X0,X1),X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
thf(f854,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
? [X3: X0,X4: X1] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2 ),
inference(ennf_transformation,[],[f745]) ).
thf(f745,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] :
~ ! [X3: X0,X4: X1] : ( vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) != X2 ),
inference(rectify,[],[f32]) ).
thf(f32,axiom,
! [X0: $tType,X2: $tType,X51: product_prod(X0,X2)] :
~ ! [X49: X0,X50: X2] : ( vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X49),X50) != X51 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_old_Oprod_Oexhaust) ).
thf(f2533,plain,
spl151_103,
inference(avatar_split_clause,[],[f1184,f2531]) ).
thf(f2531,plain,
( spl151_103
<=> ! [X0: bexp,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_com,X1)),vAPP(nat,nat,suc,zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_103])]) ).
thf(f1184,plain,
! [X0: bexp,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_com,X1)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(cnf_transformation,[],[f713]) ).
thf(f713,plain,
! [X0: bexp,X1: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_com,X1)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(rectify,[],[f174]) ).
thf(f174,axiom,
! [X71: bexp,X72: com] : ( vAPP(com,nat,size_com,vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X71),X72)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(com,nat,size_com,X72)),vAPP(nat,nat,suc,zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_com_Osize__gen_I5_J) ).
thf(f2529,plain,
spl151_102,
inference(avatar_split_clause,[],[f1231,f2527]) ).
thf(f2527,plain,
( spl151_102
<=> ! [X0: $tType,X2: list(X0),X1: X0] : ( vAPP(list(X0),nat,size_size(list(X0)),vAPP(list(X0),list(X0),vAPP(X0,sTfun(list(X0),list(X0)),cons(X0),X1),X2)) = vAPP(nat,nat,suc,vAPP(list(X0),nat,size_size(list(X0)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_102])]) ).
thf(f2525,plain,
( spl151_101
| ~ spl151_16
| ~ spl151_60 ),
inference(avatar_split_clause,[],[f2266,f2220,f1991,f2523]) ).
thf(f2523,plain,
( spl151_101
<=> ! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),zero_zero(int)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_101])]) ).
thf(f1991,plain,
( spl151_16
<=> ( group_add(int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_16])]) ).
thf(f2266,plain,
( ! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),zero_zero(int)),X0) = X0 )
| ~ spl151_16
| ~ spl151_60 ),
inference(trivial_inequality_removal,[],[f2263]) ).
thf(f2263,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),zero_zero(int)),X0) = X0 ) )
| ~ spl151_16
| ~ spl151_60 ),
inference(superposition,[],[f2221,f1993]) ).
thf(f1993,plain,
( ( group_add(int) = $true )
| ~ spl151_16 ),
inference(avatar_component_clause,[],[f1991]) ).
thf(f2515,plain,
spl151_100,
inference(avatar_split_clause,[],[f1512,f2513]) ).
thf(f2513,plain,
( spl151_100
<=> ! [X1: $tType,X0: $tType,X2: $tType,X4: X2] :
( ( vAPP(sTfun(X0,X1),X2,vAPP(X2,sTfun(sTfun(X0,X1),X2),kCOMB,X4),vAPP(X1,sTfun(X0,X1),kCOMB,zero_zero(X1))) = X4 )
| ( $true != zero(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_100])]) ).
thf(f1512,plain,
! [X1: $tType,X0: $tType,X2: $tType,X4: X2] :
( ( vAPP(sTfun(X0,X1),X2,vAPP(X2,sTfun(sTfun(X0,X1),X2),kCOMB,X4),vAPP(X1,sTfun(X0,X1),kCOMB,zero_zero(X1))) = X4 )
| ( $true != zero(X1) ) ),
inference(equality_resolution,[],[f1262]) ).
thf(f1262,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: ( X0 > X1 ) > X2,X4: X2] :
( ( vAPP(sTfun(X0,X1),X2,X3,vAPP(X1,sTfun(X0,X1),kCOMB,zero_zero(X1))) = X4 )
| ( vAPP(X2,sTfun(sTfun(X0,X1),X2),kCOMB,X4) != X3 )
| ( $true != zero(X1) ) ),
inference(cnf_transformation,[],[f853]) ).
thf(f853,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ! [X3: ( X0 > X1 ) > X2,X4: X2] :
( ( vAPP(sTfun(X0,X1),X2,X3,vAPP(X1,sTfun(X0,X1),kCOMB,zero_zero(X1))) = X4 )
| ( vAPP(X2,sTfun(sTfun(X0,X1),X2),kCOMB,X4) != X3 ) )
| ( $true != zero(X1) ) ),
inference(ennf_transformation,[],[f440]) ).
thf(f440,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( ( $true = zero(X1) )
=> ! [X3: ( X0 > X1 ) > X2,X4: X2] :
( ( vAPP(X2,sTfun(sTfun(X0,X1),X2),kCOMB,X4) = X3 )
=> ( vAPP(sTfun(X0,X1),X2,X3,vAPP(X1,sTfun(X0,X1),kCOMB,zero_zero(X1))) = X4 ) ) ),
inference(fool_elimination,[],[f439]) ).
thf(f439,plain,
! [X0: $tType,X1: $tType,X2: $tType] :
( zero(X1)
=> ! [X3: ( X0 > X1 ) > X2,X4: X2] :
( ( X3
= ( ^ [X5: X0 > X1] : X4 ) )
=> ( vAPP(sTfun(X0,X1),X2,X3,
^ [X6: X0] : zero_zero(X1)) = X4 ) ) ),
inference(rectify,[],[f189]) ).
thf(f189,axiom,
! [X0: $tType,X2: $tType,X1: $tType] :
( zero(X2)
=> ! [X65: ( X0 > X2 ) > X1,X66: X1] :
( ( X65
= ( ^ [X63: X0 > X2] : X66 ) )
=> ( vAPP(sTfun(X0,X2),X1,X65,
^ [X63: X0] : zero_zero(X2)) = X66 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_fun__cong__unused__0) ).
thf(f2497,plain,
spl151_99,
inference(avatar_split_clause,[],[f1182,f2495]) ).
thf(f2495,plain,
( spl151_99
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,suc,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_99])]) ).
thf(f2493,plain,
spl151_98,
inference(avatar_split_clause,[],[f1181,f2491]) ).
thf(f2491,plain,
( spl151_98
<=> ! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_98])]) ).
thf(f1181,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0)),X1) ),
inference(cnf_transformation,[],[f710]) ).
thf(f710,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0)),X1) ),
inference(rectify,[],[f75]) ).
thf(f75,axiom,
! [X86: nat,X68: nat] : ( vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X86),X68)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X86)),X68) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_add__Suc) ).
thf(f2471,plain,
( spl151_97
| ~ spl151_15
| ~ spl151_59 ),
inference(avatar_split_clause,[],[f2261,f2216,f1986,f2469]) ).
thf(f2469,plain,
( spl151_97
<=> ! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),zero_zero(int)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_97])]) ).
thf(f1986,plain,
( spl151_15
<=> ( monoid_add(int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_15])]) ).
thf(f2261,plain,
( ! [X0: int] : ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),zero_zero(int)) = X0 )
| ~ spl151_15
| ~ spl151_59 ),
inference(trivial_inequality_removal,[],[f2258]) ).
thf(f2258,plain,
( ! [X0: int] :
( ( $true != $true )
| ( vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),zero_zero(int)) = X0 ) )
| ~ spl151_15
| ~ spl151_59 ),
inference(superposition,[],[f2217,f1988]) ).
thf(f1988,plain,
( ( monoid_add(int) = $true )
| ~ spl151_15 ),
inference(avatar_component_clause,[],[f1986]) ).
thf(f2457,plain,
spl151_96,
inference(avatar_split_clause,[],[f1905,f2455]) ).
thf(f2455,plain,
( spl151_96
<=> ! [X0: $tType,X2: X0,X1: X0 > nat] : ( vAPP(option(X0),nat,vAPP(sTfun(X0,nat),sTfun(option(X0),nat),size_option(X0),X1),vAPP(X0,option(X0),some(X0),X2)) = vAPP(nat,nat,suc,vAPP(X0,nat,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_96])]) ).
thf(f1905,plain,
! [X0: $tType,X2: X0,X1: X0 > nat] : ( vAPP(option(X0),nat,vAPP(sTfun(X0,nat),sTfun(option(X0),nat),size_option(X0),X1),vAPP(X0,option(X0),some(X0),X2)) = vAPP(nat,nat,suc,vAPP(X0,nat,X1,X2)) ),
inference(forward_demodulation,[],[f1904,f1127]) ).
thf(f1904,plain,
! [X0: $tType,X2: X0,X1: X0 > nat] : ( vAPP(option(X0),nat,vAPP(sTfun(X0,nat),sTfun(option(X0),nat),size_option(X0),X1),vAPP(X0,option(X0),some(X0),X2)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X1,X2)),zero_zero(nat))) ),
inference(forward_demodulation,[],[f1232,f1182]) ).
thf(f1232,plain,
! [X0: $tType,X2: X0,X1: X0 > nat] : ( vAPP(option(X0),nat,vAPP(sTfun(X0,nat),sTfun(option(X0),nat),size_option(X0),X1),vAPP(X0,option(X0),some(X0),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X1,X2)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(cnf_transformation,[],[f730]) ).
thf(f730,plain,
! [X0: $tType,X1: X0 > nat,X2: X0] : ( vAPP(option(X0),nat,vAPP(sTfun(X0,nat),sTfun(option(X0),nat),size_option(X0),X1),vAPP(X0,option(X0),some(X0),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X1,X2)),vAPP(nat,nat,suc,zero_zero(nat))) ),
inference(rectify,[],[f198]) ).
thf(f198,axiom,
! [X0: $tType,X55: X0 > nat,X5: X0] : ( vAPP(option(X0),nat,vAPP(sTfun(X0,nat),sTfun(option(X0),nat),size_option(X0),X55),vAPP(X0,option(X0),some(X0),X5)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X55,X5)),vAPP(nat,nat,suc,zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_option_Osize__gen_I2_J) ).
thf(f2453,plain,
spl151_95,
inference(avatar_split_clause,[],[f1310,f2451]) ).
thf(f2451,plain,
( spl151_95
<=> ! [X4: com,X0: list(char),X3: com,X2: bexp,X1: aexp] : ( vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1) != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X2),X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_95])]) ).
thf(f1310,plain,
! [X2: bexp,X3: com,X0: list(char),X1: aexp,X4: com] : ( vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1) != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X2),X3),X4) ),
inference(cnf_transformation,[],[f766]) ).
thf(f766,plain,
! [X0: list(char),X1: aexp,X2: bexp,X3: com,X4: com] : ( vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1) != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X2),X3),X4) ),
inference(rectify,[],[f167]) ).
thf(f167,axiom,
! [X132: list(char),X133: aexp,X99: bexp,X100: com,X101: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X99),X100),X101) != vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X132),X133) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_com_Odistinct_I11_J) ).
thf(f2449,plain,
spl151_94,
inference(avatar_split_clause,[],[f1220,f2447]) ).
thf(f2447,plain,
( spl151_94
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK26,X0))) )
| ( $true != vAPP(nat,$o,X0,zero_zero(nat)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_94])]) ).
thf(f1220,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK26,X0))) )
| ( $true != vAPP(nat,$o,X0,zero_zero(nat)) ) ),
inference(cnf_transformation,[],[f994]) ).
thf(f994,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK26,X0))) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK26,X0)) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero(nat)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f834,f993]) ).
thf(f993,plain,
! [X0: nat > $o] :
( ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
=> ( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK26,X0))) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK26,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f834,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero(nat)) ) ),
inference(flattening,[],[f833]) ).
thf(f833,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero(nat)) ) ),
inference(ennf_transformation,[],[f412]) ).
thf(f412,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero(nat)) )
=> ( ! [X2: nat] :
( ( $true = vAPP(nat,$o,X0,X2) )
=> ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) ) )
=> ( $true = vAPP(nat,$o,X0,X1) ) ) ),
inference(fool_elimination,[],[f411]) ).
thf(f411,plain,
! [X0: nat > $o,X1: nat] :
( vAPP(nat,$o,X0,zero_zero(nat))
=> ( ! [X2: nat] :
( vAPP(nat,$o,X0,X2)
=> vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
=> vAPP(nat,$o,X0,X1) ) ),
inference(rectify,[],[f159]) ).
thf(f159,axiom,
! [X34: nat > $o,X7: nat] :
( vAPP(nat,$o,X34,zero_zero(nat))
=> ( ! [X137: nat] :
( vAPP(nat,$o,X34,X137)
=> vAPP(nat,$o,X34,vAPP(nat,nat,suc,X137)) )
=> vAPP(nat,$o,X34,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_old_Onat_Oinducts) ).
thf(f2445,plain,
spl151_93,
inference(avatar_split_clause,[],[f1218,f2443]) ).
thf(f2443,plain,
( spl151_93
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK25,X0))) )
| ( $true != vAPP(nat,$o,X0,zero_zero(nat)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_93])]) ).
thf(f1218,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK25,X0))) )
| ( $true != vAPP(nat,$o,X0,zero_zero(nat)) ) ),
inference(cnf_transformation,[],[f992]) ).
thf(f992,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK25,X0))) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK25,X0)) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero(nat)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f832,f991]) ).
thf(f991,plain,
! [X0: nat > $o] :
( ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
=> ( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK25,X0))) )
& ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK25,X0)) ) ) ),
introduced(choice_axiom,[]) ).
thf(f832,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero(nat)) ) ),
inference(flattening,[],[f831]) ).
thf(f831,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
& ( $true = vAPP(nat,$o,X0,X2) ) )
| ( $true != vAPP(nat,$o,X0,zero_zero(nat)) ) ),
inference(ennf_transformation,[],[f410]) ).
thf(f410,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero(nat)) )
=> ( ! [X2: nat] :
( ( $true = vAPP(nat,$o,X0,X2) )
=> ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) ) )
=> ( $true = vAPP(nat,$o,X0,X1) ) ) ),
inference(fool_elimination,[],[f409]) ).
thf(f409,plain,
! [X0: nat > $o,X1: nat] :
( vAPP(nat,$o,X0,zero_zero(nat))
=> ( ! [X2: nat] :
( vAPP(nat,$o,X0,X2)
=> vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
=> vAPP(nat,$o,X0,X1) ) ),
inference(rectify,[],[f152]) ).
thf(f152,axiom,
! [X34: nat > $o,X68: nat] :
( vAPP(nat,$o,X34,zero_zero(nat))
=> ( ! [X77: nat] :
( vAPP(nat,$o,X34,X77)
=> vAPP(nat,$o,X34,vAPP(nat,nat,suc,X77)) )
=> vAPP(nat,$o,X34,X68) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_nat__induct) ).
thf(f2441,plain,
spl151_92,
inference(avatar_split_clause,[],[f1215,f2439]) ).
thf(f2439,plain,
( spl151_92
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero(nat)) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK24,X0))) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_92])]) ).
thf(f1215,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero(nat)) )
| ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK24,X0))) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f990]) ).
thf(f990,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero(nat)) )
| ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK24,X0)) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK24,X0))) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f830,f989]) ).
thf(f989,plain,
! [X0: nat > $o] :
( ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,X2) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) ) )
=> ( ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK24,X0)) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK24,X0))) ) ) ),
introduced(choice_axiom,[]) ).
thf(f830,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero(nat)) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,X2) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(flattening,[],[f829]) ).
thf(f829,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero(nat)) )
| ? [X2: nat] :
( ( $true != vAPP(nat,$o,X0,X2) )
& ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) ) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(ennf_transformation,[],[f408]) ).
thf(f408,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
=> ( ! [X2: nat] :
( ( $true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2)) )
=> ( $true = vAPP(nat,$o,X0,X2) ) )
=> ( $true = vAPP(nat,$o,X0,zero_zero(nat)) ) ) ),
inference(fool_elimination,[],[f407]) ).
thf(f407,plain,
! [X0: nat > $o,X1: nat] :
( vAPP(nat,$o,X0,X1)
=> ( ! [X2: nat] :
( vAPP(nat,$o,X0,vAPP(nat,nat,suc,X2))
=> vAPP(nat,$o,X0,X2) )
=> vAPP(nat,$o,X0,zero_zero(nat)) ) ),
inference(rectify,[],[f154]) ).
thf(f154,axiom,
! [X34: nat > $o,X38: nat] :
( vAPP(nat,$o,X34,X38)
=> ( ! [X77: nat] :
( vAPP(nat,$o,X34,vAPP(nat,nat,suc,X77))
=> vAPP(nat,$o,X34,X77) )
=> vAPP(nat,$o,X34,zero_zero(nat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_zero__induct) ).
thf(f2437,plain,
spl151_91,
inference(avatar_split_clause,[],[f1309,f2435]) ).
thf(f2435,plain,
( spl151_91
<=> ! [X4: com,X0: com,X3: com,X2: bexp,X1: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X2),X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_91])]) ).
thf(f1309,plain,
! [X2: bexp,X3: com,X0: com,X1: com,X4: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X2),X3),X4) ),
inference(cnf_transformation,[],[f765]) ).
thf(f765,plain,
! [X0: com,X1: com,X2: bexp,X3: com,X4: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X2),X3),X4) ),
inference(rectify,[],[f105]) ).
thf(f105,axiom,
! [X82: com,X83: com,X99: bexp,X100: com,X101: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X82),X83) != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X99),X100),X101) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_com_Odistinct_I15_J) ).
thf(f2433,plain,
spl151_90,
inference(avatar_split_clause,[],[f1308,f2431]) ).
thf(f2431,plain,
( spl151_90
<=> ! [X4: com,X0: bexp,X3: bexp,X2: com,X1: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2) != vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_90])]) ).
thf(f1308,plain,
! [X2: com,X3: bexp,X0: bexp,X1: com,X4: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2) != vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X3),X4) ),
inference(cnf_transformation,[],[f764]) ).
thf(f764,plain,
! [X0: bexp,X1: com,X2: com,X3: bexp,X4: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2) != vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X3),X4) ),
inference(rectify,[],[f103]) ).
thf(f103,axiom,
! [X99: bexp,X100: com,X101: com,X71: bexp,X72: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X71),X72) != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X99),X100),X101) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_com_Odistinct_I19_J) ).
thf(f2393,plain,
spl151_89,
inference(avatar_split_clause,[],[f1219,f2391]) ).
thf(f2391,plain,
( spl151_89
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK26,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero(nat)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_89])]) ).
thf(f1219,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK26,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero(nat)) ) ),
inference(cnf_transformation,[],[f994]) ).
thf(f2389,plain,
spl151_88,
inference(avatar_split_clause,[],[f1217,f2387]) ).
thf(f2387,plain,
( spl151_88
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK25,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero(nat)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_88])]) ).
thf(f1217,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,X1) )
| ( $true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK25,X0)) )
| ( $true != vAPP(nat,$o,X0,zero_zero(nat)) ) ),
inference(cnf_transformation,[],[f992]) ).
thf(f2385,plain,
spl151_87,
inference(avatar_split_clause,[],[f1216,f2383]) ).
thf(f2383,plain,
( spl151_87
<=> ! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero(nat)) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK24,X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_87])]) ).
thf(f1216,plain,
! [X0: nat > $o,X1: nat] :
( ( $true = vAPP(nat,$o,X0,zero_zero(nat)) )
| ( $true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK24,X0)) )
| ( $true != vAPP(nat,$o,X0,X1) ) ),
inference(cnf_transformation,[],[f990]) ).
thf(f2381,plain,
spl151_86,
inference(avatar_split_clause,[],[f1152,f2379]) ).
thf(f2379,plain,
( spl151_86
<=> ! [X0: $tType] :
( ( plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0)) )
| ( ab_semigroup_add(X0) != $true ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_86])]) ).
thf(f1152,plain,
! [X0: $tType] :
( ( plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0)) )
| ( ab_semigroup_add(X0) != $true ) ),
inference(cnf_transformation,[],[f807]) ).
thf(f807,plain,
! [X0: $tType] :
( ( plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0)) )
| ( ab_semigroup_add(X0) != $true ) ),
inference(ennf_transformation,[],[f336]) ).
thf(f336,plain,
! [X0: $tType] :
( ( ab_semigroup_add(X0) = $true )
=> ( plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0)) ) ),
inference(fool_elimination,[],[f335]) ).
thf(f335,plain,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ( plus_plus(X0)
= ( ^ [X1: X0,X2: X0] : vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X1) ) ) ),
inference(rectify,[],[f117]) ).
thf(f117,axiom,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ( plus_plus(X0)
= ( ^ [X98: X0,X113: X0] : vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X113),X98) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_add_Ocommute) ).
thf(f2370,plain,
spl151_85,
inference(avatar_split_clause,[],[f1229,f2368]) ).
thf(f2368,plain,
( spl151_85
<=> ! [X1: $tType,X0: $tType,X2: X0] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(sum_sum(X1,X0),nat,size_size(sum_sum(X1,X0)),vAPP(X0,sum_sum(X1,X0),sum_Inr(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_85])]) ).
thf(f1229,plain,
! [X1: $tType,X0: $tType,X2: X0] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(sum_sum(X1,X0),nat,size_size(sum_sum(X1,X0)),vAPP(X0,sum_sum(X1,X0),sum_Inr(X0,X1),X2)) ),
inference(cnf_transformation,[],[f727]) ).
thf(f727,plain,
! [X0: $tType,X1: $tType,X2: X0] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(sum_sum(X1,X0),nat,size_size(sum_sum(X1,X0)),vAPP(X0,sum_sum(X1,X0),sum_Inr(X0,X1),X2)) ),
inference(rectify,[],[f208]) ).
thf(f208,axiom,
! [X2: $tType,X0: $tType,X5: X2] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(sum_sum(X0,X2),nat,size_size(sum_sum(X0,X2)),vAPP(X2,sum_sum(X0,X2),sum_Inr(X2,X0),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_sum_Osize_I4_J) ).
thf(f2366,plain,
spl151_84,
inference(avatar_split_clause,[],[f1228,f2364]) ).
thf(f2364,plain,
( spl151_84
<=> ! [X1: $tType,X0: $tType,X2: X0] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(sum_sum(X0,X1),nat,size_size(sum_sum(X0,X1)),vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_84])]) ).
thf(f1228,plain,
! [X1: $tType,X0: $tType,X2: X0] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(sum_sum(X0,X1),nat,size_size(sum_sum(X0,X1)),vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X2)) ),
inference(cnf_transformation,[],[f726]) ).
thf(f726,plain,
! [X0: $tType,X1: $tType,X2: X0] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(sum_sum(X0,X1),nat,size_size(sum_sum(X0,X1)),vAPP(X0,sum_sum(X0,X1),sum_Inl(X0,X1),X2)) ),
inference(rectify,[],[f206]) ).
thf(f206,axiom,
! [X0: $tType,X2: $tType,X9: X0] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(sum_sum(X0,X2),nat,size_size(sum_sum(X0,X2)),vAPP(X0,sum_sum(X0,X2),sum_Inl(X0,X2),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_sum_Osize_I3_J) ).
thf(f2361,plain,
spl151_83,
inference(avatar_split_clause,[],[f1283,f2359]) ).
thf(f2359,plain,
( spl151_83
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: X1] :
( ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X2) != vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X3) )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_83])]) ).
thf(f1283,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: X1] :
( ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X2) != vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X3) )
| ( X2 = X3 ) ),
inference(cnf_transformation,[],[f855]) ).
thf(f855,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X1] :
( ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X2) != vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X3) )
| ( X2 = X3 ) ),
inference(ennf_transformation,[],[f758]) ).
thf(f758,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: X1] :
( ( X2 != X3 )
=> ( vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X2) != vAPP(X1,sum_sum(X0,X1),sum_Inr(X1,X0),X3) ) ),
inference(rectify,[],[f211]) ).
thf(f211,axiom,
! [X2: $tType,X0: $tType,X55: X0,X51: X0] :
( ( X51 != X55 )
=> ( vAPP(X0,sum_sum(X2,X0),sum_Inr(X0,X2),X55) != vAPP(X0,sum_sum(X2,X0),sum_Inr(X0,X2),X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_not__arg__cong__Inr) ).
thf(f2357,plain,
spl151_82,
inference(avatar_split_clause,[],[f1269,f2355]) ).
thf(f2355,plain,
( spl151_82
<=> ! [X2: com,X0: list(char),X1: aexp,X3: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X2),X3) != vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_82])]) ).
thf(f1269,plain,
! [X2: com,X3: com,X0: list(char),X1: aexp] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X2),X3) != vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1) ),
inference(cnf_transformation,[],[f750]) ).
thf(f750,plain,
! [X0: list(char),X1: aexp,X2: com,X3: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X2),X3) != vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1) ),
inference(rectify,[],[f166]) ).
thf(f166,axiom,
! [X132: list(char),X133: aexp,X82: com,X83: com] : ( vAPP(com,com,vAPP(com,sTfun(com,com),seq,X82),X83) != vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X132),X133) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_com_Odistinct_I9_J) ).
thf(f2353,plain,
spl151_81,
inference(avatar_split_clause,[],[f1268,f2351]) ).
thf(f2351,plain,
( spl151_81
<=> ! [X2: bexp,X0: list(char),X1: aexp,X3: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X3) != vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_81])]) ).
thf(f1268,plain,
! [X2: bexp,X3: com,X0: list(char),X1: aexp] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X3) != vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1) ),
inference(cnf_transformation,[],[f749]) ).
thf(f749,plain,
! [X0: list(char),X1: aexp,X2: bexp,X3: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X3) != vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1) ),
inference(rectify,[],[f164]) ).
thf(f164,axiom,
! [X132: list(char),X133: aexp,X71: bexp,X72: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X71),X72) != vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X132),X133) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_com_Odistinct_I13_J) ).
thf(f2349,plain,
spl151_80,
inference(avatar_split_clause,[],[f1180,f2347]) ).
thf(f2347,plain,
( spl151_80
<=> ! [X0: $tType,X1: X0 > nat] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(option(X0),nat,vAPP(sTfun(X0,nat),sTfun(option(X0),nat),size_option(X0),X1),none(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_80])]) ).
thf(f1180,plain,
! [X0: $tType,X1: X0 > nat] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(option(X0),nat,vAPP(sTfun(X0,nat),sTfun(option(X0),nat),size_option(X0),X1),none(X0)) ),
inference(cnf_transformation,[],[f709]) ).
thf(f709,plain,
! [X0: $tType,X1: X0 > nat] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(option(X0),nat,vAPP(sTfun(X0,nat),sTfun(option(X0),nat),size_option(X0),X1),none(X0)) ),
inference(rectify,[],[f199]) ).
thf(f199,axiom,
! [X0: $tType,X55: X0 > nat] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(option(X0),nat,vAPP(sTfun(X0,nat),sTfun(option(X0),nat),size_option(X0),X55),none(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_option_Osize__gen_I1_J) ).
thf(f2345,plain,
spl151_79,
inference(avatar_split_clause,[],[f1800,f2343]) ).
thf(f2343,plain,
( spl151_79
<=> ! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1) )
| ( X0 != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_79])]) ).
thf(f1800,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1) )
| ( X0 != X1 ) ),
inference(equality_proxy_clausification,[],[f1799]) ).
thf(f1799,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f1795]) ).
thf(f1795,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1192]) ).
thf(f1192,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ),
inference(cnf_transformation,[],[f382]) ).
thf(f382,plain,
! [X0: nat,X1: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ),
inference(fool_elimination,[],[f381]) ).
thf(f381,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1) )
= ( X0 = X1 ) ),
inference(rectify,[],[f14]) ).
thf(f14,axiom,
! [X7: nat,X8: nat] :
( ( vAPP(nat,nat,suc,X7) = vAPP(nat,nat,suc,X8) )
= ( X7 = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_old_Onat_Oinject) ).
thf(f2341,plain,
spl151_78,
inference(avatar_split_clause,[],[f1267,f2339]) ).
thf(f2339,plain,
( spl151_78
<=> ! [X2: bexp,X0: com,X1: com,X3: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X3) != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_78])]) ).
thf(f1267,plain,
! [X2: bexp,X3: com,X0: com,X1: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X3) != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) ),
inference(cnf_transformation,[],[f748]) ).
thf(f748,plain,
! [X0: com,X1: com,X2: bexp,X3: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X2),X3) != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) ),
inference(rectify,[],[f71]) ).
thf(f71,axiom,
! [X82: com,X83: com,X71: bexp,X72: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X71),X72) != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X82),X83) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_com_Odistinct_I17_J) ).
thf(f2329,plain,
spl151_77,
inference(avatar_split_clause,[],[f1453,f2326]) ).
thf(f2326,plain,
( spl151_77
<=> ( vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),q,ua),t_a) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_77])]) ).
thf(f1453,plain,
vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),q,ua),t_a) = $true,
inference(cnf_transformation,[],[f668]) ).
thf(f668,plain,
vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),q,ua),t_a) = $true,
inference(fool_elimination,[],[f667]) ).
thf(f667,plain,
vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),q,ua),t_a),
inference(rectify,[],[f8]) ).
thf(f8,axiom,
vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),q,ua),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_Suc_Oprems_I5_J) ).
thf(f2324,plain,
spl151_76,
inference(avatar_split_clause,[],[f1452,f2321]) ).
thf(f2321,plain,
( spl151_76
<=> ( vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),q,u),t) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_76])]) ).
thf(f1452,plain,
vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),q,u),t) = $true,
inference(cnf_transformation,[],[f666]) ).
thf(f666,plain,
vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),q,u),t) = $true,
inference(fool_elimination,[],[f665]) ).
thf(f665,plain,
vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),q,u),t),
inference(rectify,[],[f20]) ).
thf(f20,axiom,
vAPP(sTfun(list(char),int),$o,vAPP(sTfun(list(char),int),sTfun(sTfun(list(char),int),$o),q,u),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19__092_060open_062Q_Au_____At_H_____092_060close_062) ).
thf(f2319,plain,
spl151_75,
inference(avatar_split_clause,[],[f1211,f2317]) ).
thf(f2317,plain,
( spl151_75
<=> ! [X0: com > $o] :
( ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK19,X0)) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_75])]) ).
thf(f1211,plain,
! [X0: com > $o] :
( ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK19,X0)) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ),
inference(cnf_transformation,[],[f984]) ).
thf(f2315,plain,
spl151_74,
inference(avatar_split_clause,[],[f1210,f2313]) ).
thf(f2313,plain,
( spl151_74
<=> ! [X0: com > $o] :
( ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK18,X0)) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_74])]) ).
thf(f1210,plain,
! [X0: com > $o] :
( ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK18,X0)) )
| ( $true != vAPP(sTfun(com,$o),$o,sP0,X0) ) ),
inference(cnf_transformation,[],[f984]) ).
thf(f2311,plain,
spl151_73,
inference(avatar_split_clause,[],[f1208,f2309]) ).
thf(f2309,plain,
( spl151_73
<=> ! [X0: com > $o] :
( ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK17,X0)) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_73])]) ).
thf(f1208,plain,
! [X0: com > $o] :
( ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK17,X0)) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f980]) ).
thf(f2307,plain,
spl151_72,
inference(avatar_split_clause,[],[f1207,f2305]) ).
thf(f2305,plain,
( spl151_72
<=> ! [X0: com > $o] :
( ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK16,X0)) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_72])]) ).
thf(f1207,plain,
! [X0: com > $o] :
( ( $true = vAPP(com,$o,X0,vAPP(sTfun(com,$o),com,sK16,X0)) )
| ( $true != vAPP(sTfun(com,$o),$o,sP1,X0) ) ),
inference(cnf_transformation,[],[f980]) ).
thf(f2302,plain,
spl151_71,
inference(avatar_split_clause,[],[f1227,f2300]) ).
thf(f2300,plain,
( spl151_71
<=> ! [X2: com,X0: bexp,X1: com] : ( skip != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_71])]) ).
thf(f1227,plain,
! [X2: com,X0: bexp,X1: com] : ( skip != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2) ),
inference(cnf_transformation,[],[f725]) ).
thf(f725,plain,
! [X0: bexp,X1: com,X2: com] : ( skip != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X0),X1),X2) ),
inference(rectify,[],[f104]) ).
thf(f104,axiom,
! [X99: bexp,X100: com,X101: com] : ( skip != vAPP(com,com,vAPP(com,sTfun(com,com),vAPP(bexp,sTfun(com,sTfun(com,com)),if,X99),X100),X101) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_com_Odistinct_I5_J) ).
thf(f2298,plain,
spl151_70,
inference(avatar_split_clause,[],[f1179,f2296]) ).
thf(f2296,plain,
( spl151_70
<=> ! [X0: $tType,X1: X0] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(option(X0),nat,size_size(option(X0)),vAPP(X0,option(X0),some(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_70])]) ).
thf(f1179,plain,
! [X0: $tType,X1: X0] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(option(X0),nat,size_size(option(X0)),vAPP(X0,option(X0),some(X0),X1)) ),
inference(cnf_transformation,[],[f708]) ).
thf(f708,plain,
! [X0: $tType,X1: X0] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(option(X0),nat,size_size(option(X0)),vAPP(X0,option(X0),some(X0),X1)) ),
inference(rectify,[],[f197]) ).
thf(f197,axiom,
! [X0: $tType,X5: X0] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(option(X0),nat,size_size(option(X0)),vAPP(X0,option(X0),some(X0),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_option_Osize_I4_J) ).
thf(f2294,plain,
spl151_69,
inference(avatar_split_clause,[],[f1178,f2292]) ).
thf(f2292,plain,
( spl151_69
<=> ! [X0: list(char),X1: aexp] : ( zero_zero(nat) = vAPP(com,nat,size_size(com),vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_69])]) ).
thf(f1178,plain,
! [X0: list(char),X1: aexp] : ( zero_zero(nat) = vAPP(com,nat,size_size(com),vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1)) ),
inference(cnf_transformation,[],[f707]) ).
thf(f707,plain,
! [X0: list(char),X1: aexp] : ( zero_zero(nat) = vAPP(com,nat,size_size(com),vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1)) ),
inference(rectify,[],[f178]) ).
thf(f178,axiom,
! [X132: list(char),X133: aexp] : ( zero_zero(nat) = vAPP(com,nat,size_size(com),vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X132),X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_com_Osize_I7_J) ).
thf(f2256,plain,
spl151_68,
inference(avatar_split_clause,[],[f1451,f2253]) ).
thf(f1451,plain,
vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),sa) = $true,
inference(cnf_transformation,[],[f664]) ).
thf(f664,plain,
vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),sa) = $true,
inference(fool_elimination,[],[f663]) ).
thf(f663,plain,
vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),sa),
inference(rectify,[],[f1]) ).
thf(f1,axiom,
vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),sa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Suc_Oprems_I6_J) ).
thf(f2251,plain,
( spl151_67
| ~ spl151_37
| ~ spl151_52 ),
inference(avatar_split_clause,[],[f2195,f2181,f2119,f2249]) ).
thf(f2249,plain,
( spl151_67
<=> ! [X0: nat] :
( ( vAPP(nat,nat,sK14,X0) != X0 )
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_67])]) ).
thf(f2119,plain,
( spl151_37
<=> ! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_37])]) ).
thf(f2195,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,sK14,X0) != X0 )
| ( zero_zero(nat) = X0 ) )
| ~ spl151_37
| ~ spl151_52 ),
inference(superposition,[],[f2120,f2182]) ).
thf(f2120,plain,
( ! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 )
| ~ spl151_37 ),
inference(avatar_component_clause,[],[f2119]) ).
thf(f2247,plain,
spl151_66,
inference(avatar_split_clause,[],[f1450,f2244]) ).
thf(f2244,plain,
( spl151_66
<=> ( vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),s2) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_66])]) ).
thf(f1450,plain,
vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),s2) = $true,
inference(cnf_transformation,[],[f662]) ).
thf(f662,plain,
vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),s2) = $true,
inference(fool_elimination,[],[f661]) ).
thf(f661,plain,
vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),s2),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
vAPP(sTfun(list(char),int),$o,vAPP(bexp,sTfun(sTfun(list(char),int),$o),bval,b),s2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062bval_Ab_As_____092_060close_062) ).
thf(f2242,plain,
spl151_65,
inference(avatar_split_clause,[],[f1177,f2240]) ).
thf(f2240,plain,
( spl151_65
<=> ! [X0: list(char),X1: aexp] : ( zero_zero(nat) = vAPP(com,nat,size_com,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_65])]) ).
thf(f1177,plain,
! [X0: list(char),X1: aexp] : ( zero_zero(nat) = vAPP(com,nat,size_com,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1)) ),
inference(cnf_transformation,[],[f706]) ).
thf(f706,plain,
! [X0: list(char),X1: aexp] : ( zero_zero(nat) = vAPP(com,nat,size_com,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1)) ),
inference(rectify,[],[f180]) ).
thf(f180,axiom,
! [X132: list(char),X133: aexp] : ( zero_zero(nat) = vAPP(com,nat,size_com,vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X132),X133)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_com_Osize__gen_I2_J) ).
thf(f2238,plain,
spl151_64,
inference(avatar_split_clause,[],[f1163,f2236]) ).
thf(f1163,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( cancel1352612707id_add(X0) != $true ) ),
inference(cnf_transformation,[],[f818]) ).
thf(f818,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( cancel1352612707id_add(X0) != $true ) ),
inference(ennf_transformation,[],[f358]) ).
thf(f358,plain,
! [X0: $tType] :
( ( cancel1352612707id_add(X0) = $true )
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 ) ),
inference(fool_elimination,[],[f357]) ).
thf(f357,plain,
! [X0: $tType] :
( cancel1352612707id_add(X0)
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f185]) ).
thf(f185,axiom,
! [X0: $tType] :
( cancel1352612707id_add(X0)
=> ! [X11: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X11),zero_zero(X0)) = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_verit__sum__simplify) ).
thf(f2234,plain,
spl151_63,
inference(avatar_split_clause,[],[f1156,f2232]) ).
thf(f1156,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( comm_monoid_add(X0) != $true ) ),
inference(cnf_transformation,[],[f811]) ).
thf(f811,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( comm_monoid_add(X0) != $true ) ),
inference(ennf_transformation,[],[f344]) ).
thf(f344,plain,
! [X0: $tType] :
( ( comm_monoid_add(X0) = $true )
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 ) ),
inference(fool_elimination,[],[f343]) ).
thf(f343,plain,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 ) ),
inference(rectify,[],[f145]) ).
thf(f145,axiom,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X11: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X11) = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_comm__monoid__add__class_Oadd__0) ).
thf(f2230,plain,
spl151_62,
inference(avatar_split_clause,[],[f1155,f2228]) ).
thf(f1155,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( comm_monoid_add(X0) != $true ) ),
inference(cnf_transformation,[],[f810]) ).
thf(f810,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( comm_monoid_add(X0) != $true ) ),
inference(ennf_transformation,[],[f342]) ).
thf(f342,plain,
! [X0: $tType] :
( ( comm_monoid_add(X0) = $true )
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 ) ),
inference(fool_elimination,[],[f341]) ).
thf(f341,plain,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f146]) ).
thf(f146,axiom,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X11: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X11),zero_zero(X0)) = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_add_Ocomm__neutral) ).
thf(f2226,plain,
spl151_61,
inference(avatar_split_clause,[],[f1148,f2224]) ).
thf(f1148,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( monoid_add(X0) != $true ) ),
inference(cnf_transformation,[],[f803]) ).
thf(f803,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( monoid_add(X0) != $true ) ),
inference(ennf_transformation,[],[f328]) ).
thf(f328,plain,
! [X0: $tType] :
( ( monoid_add(X0) = $true )
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 ) ),
inference(fool_elimination,[],[f327]) ).
thf(f327,plain,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 ) ),
inference(rectify,[],[f132]) ).
thf(f132,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X11: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X11) = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_add_Oleft__neutral) ).
thf(f2222,plain,
spl151_60,
inference(avatar_split_clause,[],[f1147,f2220]) ).
thf(f1147,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( group_add(X0) != $true ) ),
inference(cnf_transformation,[],[f802]) ).
thf(f802,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 )
| ( group_add(X0) != $true ) ),
inference(ennf_transformation,[],[f326]) ).
thf(f326,plain,
! [X0: $tType] :
( ( group_add(X0) = $true )
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 ) ),
inference(fool_elimination,[],[f325]) ).
thf(f325,plain,
! [X0: $tType] :
( group_add(X0)
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X1) = X1 ) ),
inference(rectify,[],[f147]) ).
thf(f147,axiom,
! [X0: $tType] :
( group_add(X0)
=> ! [X11: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),zero_zero(X0)),X11) = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_add_Ogroup__left__neutral) ).
thf(f2218,plain,
spl151_59,
inference(avatar_split_clause,[],[f1146,f2216]) ).
thf(f1146,plain,
! [X0: $tType,X1: X0] :
( ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( monoid_add(X0) != $true ) ),
inference(cnf_transformation,[],[f801]) ).
thf(f801,plain,
! [X0: $tType] :
( ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 )
| ( monoid_add(X0) != $true ) ),
inference(ennf_transformation,[],[f324]) ).
thf(f324,plain,
! [X0: $tType] :
( ( monoid_add(X0) = $true )
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 ) ),
inference(fool_elimination,[],[f323]) ).
thf(f323,plain,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X1: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f133]) ).
thf(f133,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X11: X0] : ( vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X11),zero_zero(X0)) = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_add_Oright__neutral) ).
thf(f2212,plain,
spl151_58,
inference(avatar_split_clause,[],[f1206,f2210]) ).
thf(f2210,plain,
( spl151_58
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_58])]) ).
thf(f1206,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) != X0 ) ),
inference(cnf_transformation,[],[f826]) ).
thf(f826,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) != X0 ) ),
inference(ennf_transformation,[],[f721]) ).
thf(f721,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = X0 )
=> ( zero_zero(nat) = X1 ) ),
inference(rectify,[],[f162]) ).
thf(f162,axiom,
! [X86: nat,X68: nat] :
( ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X86),X68) = X86 )
=> ( zero_zero(nat) = X68 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_add__eq__self__zero) ).
thf(f2208,plain,
( spl151_57
| ~ spl151_37
| ~ spl151_51 ),
inference(avatar_split_clause,[],[f2193,f2177,f2119,f2206]) ).
thf(f2206,plain,
( spl151_57
<=> ! [X0: nat] :
( ( vAPP(nat,nat,sK13,X0) != X0 )
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_57])]) ).
thf(f2193,plain,
( ! [X0: nat] :
( ( vAPP(nat,nat,sK13,X0) != X0 )
| ( zero_zero(nat) = X0 ) )
| ~ spl151_37
| ~ spl151_51 ),
inference(superposition,[],[f2120,f2178]) ).
thf(f2203,plain,
spl151_56,
inference(avatar_split_clause,[],[f1222,f2201]) ).
thf(f1222,plain,
! [X0: $tType,X1: nat] : ( vAPP(list(X0),nat,size_size(list(X0)),vAPP(nat,list(X0),sK27(X0),X1)) = X1 ),
inference(cnf_transformation,[],[f996]) ).
thf(f996,plain,
! [X0: $tType,X1: nat] : ( vAPP(list(X0),nat,size_size(list(X0)),vAPP(nat,list(X0),sK27(X0),X1)) = X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f722,f995]) ).
thf(f995,plain,
! [X0: $tType,X1: nat] :
( ? [X2: list(X0)] : ( vAPP(list(X0),nat,size_size(list(X0)),X2) = X1 )
=> ( vAPP(list(X0),nat,size_size(list(X0)),vAPP(nat,list(X0),sK27(X0),X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
thf(f722,plain,
! [X0: $tType,X1: nat] :
? [X2: list(X0)] : ( vAPP(list(X0),nat,size_size(list(X0)),X2) = X1 ),
inference(rectify,[],[f228]) ).
thf(f228,axiom,
! [X0: $tType,X68: nat] :
? [X165: list(X0)] : ( vAPP(list(X0),nat,size_size(list(X0)),X165) = X68 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_Ex__list__of__length) ).
thf(f2199,plain,
spl151_55,
inference(avatar_split_clause,[],[f1129,f2197]) ).
thf(f2197,plain,
( spl151_55
<=> ! [X0: $tType] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(option(X0),nat,size_size(option(X0)),none(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_55])]) ).
thf(f1129,plain,
! [X0: $tType] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(option(X0),nat,size_size(option(X0)),none(X0)) ),
inference(cnf_transformation,[],[f196]) ).
thf(f196,axiom,
! [X0: $tType] : ( vAPP(nat,nat,suc,zero_zero(nat)) = vAPP(option(X0),nat,size_size(option(X0)),none(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_option_Osize_I3_J) ).
thf(f2191,plain,
spl151_54,
inference(avatar_split_clause,[],[f1266,f2189]) ).
thf(f2189,plain,
( spl151_54
<=> ! [X1: $tType,X2: $tType,X0: $tType,X3: tuple_isomorphism(X0,X1,X2)] : ( zero_zero(nat) != vAPP(tuple_isomorphism(X0,X1,X2),nat,size_size(tuple_isomorphism(X0,X1,X2)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_54])]) ).
thf(f1266,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: tuple_isomorphism(X0,X1,X2)] : ( zero_zero(nat) != vAPP(tuple_isomorphism(X0,X1,X2),nat,size_size(tuple_isomorphism(X0,X1,X2)),X3) ),
inference(cnf_transformation,[],[f747]) ).
thf(f747,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: tuple_isomorphism(X0,X1,X2)] : ( zero_zero(nat) != vAPP(tuple_isomorphism(X0,X1,X2),nat,size_size(tuple_isomorphism(X0,X1,X2)),X3) ),
inference(rectify,[],[f200]) ).
thf(f200,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X55: tuple_isomorphism(X0,X2,X1)] : ( zero_zero(nat) != vAPP(tuple_isomorphism(X0,X2,X1),nat,size_size(tuple_isomorphism(X0,X2,X1)),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_tuple__isomorphism_Osize__neq) ).
thf(f2187,plain,
spl151_53,
inference(avatar_split_clause,[],[f1798,f2185]) ).
thf(f1798,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) != vAPP(nat,nat,suc,X1) )
| ( X0 = X1 ) ),
inference(equality_proxy_clausification,[],[f1797]) ).
thf(f1797,plain,
! [X0: nat,X1: nat] :
( ( vAPP(nat,nat,suc,X0) != vAPP(nat,nat,suc,X1) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
inference(equality_proxy_clausification,[],[f1796]) ).
thf(f1796,plain,
! [X0: nat,X1: nat] :
( ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1) ) ),
inference(binary_proxy_clausification,[],[f1192]) ).
thf(f2183,plain,
spl151_52,
inference(avatar_split_clause,[],[f1136,f2181]) ).
thf(f1136,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK14,X0)) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(cnf_transformation,[],[f976]) ).
thf(f976,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK14,X0)) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f790,f975]) ).
thf(f975,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
=> ( vAPP(nat,nat,suc,vAPP(nat,nat,sK14,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f790,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(ennf_transformation,[],[f701]) ).
thf(f701,plain,
! [X0: nat] :
( ( zero_zero(nat) != X0 )
=> ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 ) ),
inference(rectify,[],[f160]) ).
thf(f160,axiom,
! [X68: nat] :
( ( zero_zero(nat) != X68 )
=> ? [X138: nat] : ( vAPP(nat,nat,suc,X138) = X68 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_not0__implies__Suc) ).
thf(f2179,plain,
spl151_51,
inference(avatar_split_clause,[],[f1135,f2177]) ).
thf(f1135,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK13,X0)) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(cnf_transformation,[],[f974]) ).
thf(f974,plain,
! [X0: nat] :
( ( vAPP(nat,nat,suc,vAPP(nat,nat,sK13,X0)) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f789,f973]) ).
thf(f973,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
=> ( vAPP(nat,nat,suc,vAPP(nat,nat,sK13,X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
thf(f789,plain,
! [X0: nat] :
( ? [X1: nat] : ( vAPP(nat,nat,suc,X1) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(ennf_transformation,[],[f700]) ).
thf(f700,plain,
! [X0: nat] :
( ( zero_zero(nat) != X0 )
=> ~ ! [X1: nat] : ( vAPP(nat,nat,suc,X1) != X0 ) ),
inference(rectify,[],[f158]) ).
thf(f158,axiom,
! [X51: nat] :
( ( zero_zero(nat) != X51 )
=> ~ ! [X137: nat] : ( vAPP(nat,nat,suc,X137) != X51 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_old_Onat_Oexhaust) ).
thf(f2175,plain,
spl151_50,
inference(avatar_split_clause,[],[f1128,f2173]) ).
thf(f2173,plain,
( spl151_50
<=> ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),zero_zero(nat)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_50])]) ).
thf(f1128,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),zero_zero(nat)),X0) = X0 ),
inference(cnf_transformation,[],[f698]) ).
thf(f698,plain,
! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),zero_zero(nat)),X0) = X0 ),
inference(rectify,[],[f161]) ).
thf(f161,axiom,
! [X68: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),zero_zero(nat)),X68) = X68 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_plus__nat_Oadd__0) ).
thf(f2171,plain,
spl151_49,
inference(avatar_split_clause,[],[f1127,f2169]) ).
thf(f2169,plain,
( spl151_49
<=> ! [X0: nat] : ( vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),zero_zero(nat)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_49])]) ).
thf(f2167,plain,
spl151_48,
inference(avatar_split_clause,[],[f1176,f2165]) ).
thf(f2165,plain,
( spl151_48
<=> ! [X0: list(char),X1: aexp] : ( skip != vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_48])]) ).
thf(f1176,plain,
! [X0: list(char),X1: aexp] : ( skip != vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1) ),
inference(cnf_transformation,[],[f705]) ).
thf(f705,plain,
! [X0: list(char),X1: aexp] : ( skip != vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X0),X1) ),
inference(rectify,[],[f165]) ).
thf(f165,axiom,
! [X132: list(char),X133: aexp] : ( skip != vAPP(aexp,com,vAPP(list(char),sTfun(aexp,com),assign,X132),X133) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_com_Odistinct_I1_J) ).
thf(f2163,plain,
spl151_47,
inference(avatar_split_clause,[],[f1226,f2161]) ).
thf(f2161,plain,
( spl151_47
<=> ! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( zero_zero(nat) != vAPP(product_prod(X0,X1),nat,size_size(product_prod(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_47])]) ).
thf(f1226,plain,
! [X1: $tType,X0: $tType,X2: product_prod(X0,X1)] : ( zero_zero(nat) != vAPP(product_prod(X0,X1),nat,size_size(product_prod(X0,X1)),X2) ),
inference(cnf_transformation,[],[f724]) ).
thf(f724,plain,
! [X0: $tType,X1: $tType,X2: product_prod(X0,X1)] : ( zero_zero(nat) != vAPP(product_prod(X0,X1),nat,size_size(product_prod(X0,X1)),X2) ),
inference(rectify,[],[f201]) ).
thf(f201,axiom,
! [X0: $tType,X2: $tType,X55: product_prod(X0,X2)] : ( zero_zero(nat) != vAPP(product_prod(X0,X2),nat,size_size(product_prod(X0,X2)),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_prod_Osize__neq) ).
thf(f2159,plain,
spl151_46,
inference(avatar_split_clause,[],[f1225,f2157]) ).
thf(f2157,plain,
( spl151_46
<=> ! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] : ( zero_zero(nat) != vAPP(sum_sum(X0,X1),nat,size_size(sum_sum(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_46])]) ).
thf(f1225,plain,
! [X1: $tType,X0: $tType,X2: sum_sum(X0,X1)] : ( zero_zero(nat) != vAPP(sum_sum(X0,X1),nat,size_size(sum_sum(X0,X1)),X2) ),
inference(cnf_transformation,[],[f723]) ).
thf(f723,plain,
! [X0: $tType,X1: $tType,X2: sum_sum(X0,X1)] : ( zero_zero(nat) != vAPP(sum_sum(X0,X1),nat,size_size(sum_sum(X0,X1)),X2) ),
inference(rectify,[],[f202]) ).
thf(f202,axiom,
! [X0: $tType,X2: $tType,X55: sum_sum(X0,X2)] : ( zero_zero(nat) != vAPP(sum_sum(X0,X2),nat,size_size(sum_sum(X0,X2)),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_sum_Osize__neq) ).
thf(f2155,plain,
spl151_45,
inference(avatar_split_clause,[],[f1175,f2153]) ).
thf(f2153,plain,
( spl151_45
<=> ! [X0: bexp,X1: com] : ( skip != vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_45])]) ).
thf(f1175,plain,
! [X0: bexp,X1: com] : ( skip != vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1) ),
inference(cnf_transformation,[],[f704]) ).
thf(f704,plain,
! [X0: bexp,X1: com] : ( skip != vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X0),X1) ),
inference(rectify,[],[f72]) ).
thf(f72,axiom,
! [X71: bexp,X72: com] : ( vAPP(com,com,vAPP(bexp,sTfun(com,com),while,X71),X72) != skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_com_Odistinct_I7_J) ).
thf(f2151,plain,
spl151_44,
inference(avatar_split_clause,[],[f1174,f2149]) ).
thf(f2149,plain,
( spl151_44
<=> ! [X0: com,X1: com] : ( skip != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_44])]) ).
thf(f1174,plain,
! [X0: com,X1: com] : ( skip != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) ),
inference(cnf_transformation,[],[f703]) ).
thf(f703,plain,
! [X0: com,X1: com] : ( skip != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X0),X1) ),
inference(rectify,[],[f70]) ).
thf(f70,axiom,
! [X82: com,X83: com] : ( skip != vAPP(com,com,vAPP(com,sTfun(com,com),seq,X82),X83) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_com_Odistinct_I3_J) ).
thf(f2147,plain,
spl151_43,
inference(avatar_split_clause,[],[f1173,f2145]) ).
thf(f2145,plain,
( spl151_43
<=> ! [X0: $tType,X1: option(X0)] : ( zero_zero(nat) != vAPP(option(X0),nat,size_size(option(X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_43])]) ).
thf(f1173,plain,
! [X0: $tType,X1: option(X0)] : ( zero_zero(nat) != vAPP(option(X0),nat,size_size(option(X0)),X1) ),
inference(cnf_transformation,[],[f702]) ).
thf(f702,plain,
! [X0: $tType,X1: option(X0)] : ( zero_zero(nat) != vAPP(option(X0),nat,size_size(option(X0)),X1) ),
inference(rectify,[],[f195]) ).
thf(f195,axiom,
! [X0: $tType,X55: option(X0)] : ( zero_zero(nat) != vAPP(option(X0),nat,size_size(option(X0)),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_option_Osize__neq) ).
thf(f2143,plain,
spl151_42,
inference(avatar_split_clause,[],[f1126,f2141]) ).
thf(f2141,plain,
( spl151_42
<=> ! [X0: typerep] : ( zero_zero(nat) != vAPP(typerep,nat,size_size(typerep),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_42])]) ).
thf(f1126,plain,
! [X0: typerep] : ( zero_zero(nat) != vAPP(typerep,nat,size_size(typerep),X0) ),
inference(cnf_transformation,[],[f696]) ).
thf(f696,plain,
! [X0: typerep] : ( zero_zero(nat) != vAPP(typerep,nat,size_size(typerep),X0) ),
inference(rectify,[],[f204]) ).
thf(f204,axiom,
! [X55: typerep] : ( zero_zero(nat) != vAPP(typerep,nat,size_size(typerep),X55) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_typerep_Osize__neq) ).
thf(f2139,plain,
spl151_41,
inference(avatar_split_clause,[],[f1116,f2136]) ).
thf(f2136,plain,
( spl151_41
<=> ( zero_zero(nat) = vAPP(com,nat,size_size(com),skip) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_41])]) ).
thf(f1116,plain,
zero_zero(nat) = vAPP(com,nat,size_size(com),skip),
inference(cnf_transformation,[],[f177]) ).
thf(f177,axiom,
zero_zero(nat) = vAPP(com,nat,size_size(com),skip),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_com_Osize_I6_J) ).
thf(f2134,plain,
spl151_40,
inference(avatar_split_clause,[],[f1120,f2132]) ).
thf(f2132,plain,
( spl151_40
<=> ! [X0: nat] : ( zero_zero(nat) != vAPP(nat,nat,suc,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_40])]) ).
thf(f1120,plain,
! [X0: nat] : ( zero_zero(nat) != vAPP(nat,nat,suc,X0) ),
inference(cnf_transformation,[],[f690]) ).
thf(f690,plain,
! [X0: nat] : ( zero_zero(nat) != vAPP(nat,nat,suc,X0) ),
inference(rectify,[],[f149]) ).
thf(f149,axiom,
! [X136: nat] : ( zero_zero(nat) != vAPP(nat,nat,suc,X136) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_old_Onat_Odistinct_I2_J) ).
thf(f2130,plain,
spl151_39,
inference(avatar_split_clause,[],[f1115,f2127]) ).
thf(f2127,plain,
( spl151_39
<=> ( zero_zero(nat) = vAPP(com,nat,size_com,skip) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_39])]) ).
thf(f1115,plain,
zero_zero(nat) = vAPP(com,nat,size_com,skip),
inference(cnf_transformation,[],[f179]) ).
thf(f179,axiom,
zero_zero(nat) = vAPP(com,nat,size_com,skip),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_com_Osize__gen_I1_J) ).
thf(f2125,plain,
spl151_38,
inference(avatar_split_clause,[],[f1265,f2123]) ).
thf(f2123,plain,
( spl151_38
<=> ! [X1: $tType,X0: $tType,X2: $tType] : ( $true = size(tuple_isomorphism(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_38])]) ).
thf(f1265,plain,
! [X1: $tType,X0: $tType,X2: $tType] : ( $true = size(tuple_isomorphism(X0,X1,X2)) ),
inference(cnf_transformation,[],[f442]) ).
thf(f442,plain,
! [X0: $tType,X1: $tType,X2: $tType] : ( $true = size(tuple_isomorphism(X0,X1,X2)) ),
inference(fool_elimination,[],[f441]) ).
thf(f441,plain,
! [X0: $tType,X1: $tType,X2: $tType] : size(tuple_isomorphism(X0,X1,X2)),
inference(rectify,[],[f288]) ).
thf(f288,axiom,
! [X174: $tType,X175: $tType,X176: $tType] : size(tuple_isomorphism(X174,X175,X176)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Record_Otuple__isomorphism___Nat_Osize_20) ).
thf(f2121,plain,
spl151_37,
inference(avatar_split_clause,[],[f1119,f2119]) ).
thf(f1119,plain,
! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ),
inference(cnf_transformation,[],[f689]) ).
thf(f689,plain,
! [X0: nat] : ( vAPP(nat,nat,suc,X0) != X0 ),
inference(rectify,[],[f50]) ).
thf(f50,axiom,
! [X68: nat] : ( vAPP(nat,nat,suc,X68) != X68 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_n__not__Suc__n) ).
thf(f2089,plain,
spl151_36,
inference(avatar_split_clause,[],[f1224,f2087]) ).
thf(f2087,plain,
( spl151_36
<=> ! [X1: $tType,X0: $tType] : ( $true = size(product_prod(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_36])]) ).
thf(f1224,plain,
! [X1: $tType,X0: $tType] : ( $true = size(product_prod(X0,X1)) ),
inference(cnf_transformation,[],[f418]) ).
thf(f418,plain,
! [X0: $tType,X1: $tType] : ( $true = size(product_prod(X0,X1)) ),
inference(fool_elimination,[],[f417]) ).
thf(f417,plain,
! [X0: $tType,X1: $tType] : size(product_prod(X0,X1)),
inference(rectify,[],[f287]) ).
thf(f287,axiom,
! [X174: $tType,X175: $tType] : size(product_prod(X174,X175)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Nat_Osize_19) ).
thf(f2085,plain,
spl151_35,
inference(avatar_split_clause,[],[f1223,f2083]) ).
thf(f2083,plain,
( spl151_35
<=> ! [X1: $tType,X0: $tType] : ( $true = size(sum_sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_35])]) ).
thf(f1223,plain,
! [X1: $tType,X0: $tType] : ( $true = size(sum_sum(X0,X1)) ),
inference(cnf_transformation,[],[f416]) ).
thf(f416,plain,
! [X0: $tType,X1: $tType] : ( $true = size(sum_sum(X0,X1)) ),
inference(fool_elimination,[],[f415]) ).
thf(f415,plain,
! [X0: $tType,X1: $tType] : size(sum_sum(X0,X1)),
inference(rectify,[],[f284]) ).
thf(f284,axiom,
! [X174: $tType,X175: $tType] : size(sum_sum(X174,X175)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Sum__Type_Osum___Nat_Osize_16) ).
thf(f2081,plain,
spl151_34,
inference(avatar_split_clause,[],[f292,f2079]) ).
thf(f292,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f2077,plain,
spl151_33,
inference(avatar_split_clause,[],[f1170,f2075]) ).
thf(f2075,plain,
( spl151_33
<=> ! [X0: $tType] : ( $true = size(list(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_33])]) ).
thf(f1170,plain,
! [X0: $tType] : ( $true = size(list(X0)) ),
inference(cnf_transformation,[],[f372]) ).
thf(f372,plain,
! [X0: $tType] : ( $true = size(list(X0)) ),
inference(fool_elimination,[],[f371]) ).
thf(f371,plain,
! [X0: $tType] : size(list(X0)),
inference(rectify,[],[f282]) ).
thf(f282,axiom,
! [X174: $tType] : size(list(X174)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Nat_Osize_14) ).
thf(f2073,plain,
spl151_32,
inference(avatar_split_clause,[],[f1169,f2071]) ).
thf(f2071,plain,
( spl151_32
<=> ! [X0: $tType] : ( $true = size(option(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_32])]) ).
thf(f1169,plain,
! [X0: $tType] : ( $true = size(option(X0)) ),
inference(cnf_transformation,[],[f370]) ).
thf(f370,plain,
! [X0: $tType] : ( $true = size(option(X0)) ),
inference(fool_elimination,[],[f369]) ).
thf(f369,plain,
! [X0: $tType] : size(option(X0)),
inference(rectify,[],[f285]) ).
thf(f285,axiom,
! [X174: $tType] : size(option(X174)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Option_Ooption___Nat_Osize_17) ).
thf(f2069,plain,
spl151_31,
inference(avatar_split_clause,[],[f1449,f2066]) ).
thf(f2066,plain,
( spl151_31
<=> ( size(char) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_31])]) ).
thf(f1449,plain,
size(char) = $true,
inference(cnf_transformation,[],[f660]) ).
thf(f660,plain,
size(char) = $true,
inference(fool_elimination,[],[f659]) ).
thf(f659,plain,
size(char),
inference(rectify,[],[f283]) ).
thf(f283,axiom,
size(char),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_String_Ochar___Nat_Osize_15) ).
thf(f2064,plain,
spl151_30,
inference(avatar_split_clause,[],[f1448,f2061]) ).
thf(f2061,plain,
( spl151_30
<=> ( size(com) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_30])]) ).
thf(f1448,plain,
size(com) = $true,
inference(cnf_transformation,[],[f658]) ).
thf(f658,plain,
size(com) = $true,
inference(fool_elimination,[],[f657]) ).
thf(f657,plain,
size(com),
inference(rectify,[],[f254]) ).
thf(f254,axiom,
size(com),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Com_Ocom___Nat_Osize) ).
thf(f2059,plain,
spl151_29,
inference(avatar_split_clause,[],[f1447,f2056]) ).
thf(f2056,plain,
( spl151_29
<=> ( size(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_29])]) ).
thf(f1447,plain,
size(nat) = $true,
inference(cnf_transformation,[],[f656]) ).
thf(f656,plain,
size(nat) = $true,
inference(fool_elimination,[],[f655]) ).
thf(f655,plain,
size(nat),
inference(rectify,[],[f279]) ).
thf(f279,axiom,
size(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osize_11) ).
thf(f2054,plain,
spl151_28,
inference(avatar_split_clause,[],[f1446,f2051]) ).
thf(f2051,plain,
( spl151_28
<=> ( size(bexp) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_28])]) ).
thf(f1446,plain,
size(bexp) = $true,
inference(cnf_transformation,[],[f654]) ).
thf(f654,plain,
size(bexp) = $true,
inference(fool_elimination,[],[f653]) ).
thf(f653,plain,
size(bexp),
inference(rectify,[],[f281]) ).
thf(f281,axiom,
size(bexp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_BExp_Obexp___Nat_Osize_13) ).
thf(f2049,plain,
spl151_27,
inference(avatar_split_clause,[],[f1445,f2046]) ).
thf(f2046,plain,
( spl151_27
<=> ( size(typerep) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_27])]) ).
thf(f1445,plain,
size(typerep) = $true,
inference(cnf_transformation,[],[f652]) ).
thf(f652,plain,
size(typerep) = $true,
inference(fool_elimination,[],[f651]) ).
thf(f651,plain,
size(typerep),
inference(rectify,[],[f286]) ).
thf(f286,axiom,
size(typerep),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Typerep_Otyperep___Nat_Osize_18) ).
thf(f2044,plain,
spl151_26,
inference(avatar_split_clause,[],[f1444,f2041]) ).
thf(f2041,plain,
( spl151_26
<=> ( size(aexp) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_26])]) ).
thf(f1444,plain,
size(aexp) = $true,
inference(cnf_transformation,[],[f650]) ).
thf(f650,plain,
size(aexp) = $true,
inference(fool_elimination,[],[f649]) ).
thf(f649,plain,
size(aexp),
inference(rectify,[],[f280]) ).
thf(f280,axiom,
size(aexp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_AExp_Oaexp___Nat_Osize_12) ).
thf(f2039,plain,
spl151_25,
inference(avatar_split_clause,[],[f1443,f2036]) ).
thf(f2036,plain,
( spl151_25
<=> ( cancel1352612707id_add(int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_25])]) ).
thf(f1443,plain,
cancel1352612707id_add(int) = $true,
inference(cnf_transformation,[],[f648]) ).
thf(f648,plain,
cancel1352612707id_add(int) = $true,
inference(fool_elimination,[],[f647]) ).
thf(f647,plain,
cancel1352612707id_add(int),
inference(rectify,[],[f259]) ).
thf(f259,axiom,
cancel1352612707id_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__comm__monoid__add) ).
thf(f2034,plain,
spl151_24,
inference(avatar_split_clause,[],[f1442,f2031]) ).
thf(f2031,plain,
( spl151_24
<=> ( cancel1352612707id_add(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_24])]) ).
thf(f1442,plain,
cancel1352612707id_add(nat) = $true,
inference(cnf_transformation,[],[f646]) ).
thf(f646,plain,
cancel1352612707id_add(nat) = $true,
inference(fool_elimination,[],[f645]) ).
thf(f645,plain,
cancel1352612707id_add(nat),
inference(rectify,[],[f272]) ).
thf(f272,axiom,
cancel1352612707id_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_4) ).
thf(f2029,plain,
spl151_23,
inference(avatar_split_clause,[],[f1441,f2026]) ).
thf(f2026,plain,
( spl151_23
<=> ( comm_monoid_add(int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_23])]) ).
thf(f1441,plain,
comm_monoid_add(int) = $true,
inference(cnf_transformation,[],[f644]) ).
thf(f644,plain,
comm_monoid_add(int) = $true,
inference(fool_elimination,[],[f643]) ).
thf(f643,plain,
comm_monoid_add(int),
inference(rectify,[],[f262]) ).
thf(f262,axiom,
comm_monoid_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(f2024,plain,
spl151_22,
inference(avatar_split_clause,[],[f1440,f2021]) ).
thf(f2021,plain,
( spl151_22
<=> ( cancel_semigroup_add(int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_22])]) ).
thf(f1440,plain,
cancel_semigroup_add(int) = $true,
inference(cnf_transformation,[],[f642]) ).
thf(f642,plain,
cancel_semigroup_add(int) = $true,
inference(fool_elimination,[],[f641]) ).
thf(f641,plain,
cancel_semigroup_add(int),
inference(rectify,[],[f260]) ).
thf(f260,axiom,
cancel_semigroup_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(f2019,plain,
spl151_21,
inference(avatar_split_clause,[],[f1439,f2016]) ).
thf(f2016,plain,
( spl151_21
<=> ( comm_monoid_add(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_21])]) ).
thf(f1439,plain,
comm_monoid_add(nat) = $true,
inference(cnf_transformation,[],[f640]) ).
thf(f640,plain,
comm_monoid_add(nat) = $true,
inference(fool_elimination,[],[f639]) ).
thf(f639,plain,
comm_monoid_add(nat),
inference(rectify,[],[f275]) ).
thf(f275,axiom,
comm_monoid_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__add_7) ).
thf(f2014,plain,
spl151_20,
inference(avatar_split_clause,[],[f1438,f2011]) ).
thf(f2011,plain,
( spl151_20
<=> ( cancel_semigroup_add(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_20])]) ).
thf(f1438,plain,
cancel_semigroup_add(nat) = $true,
inference(cnf_transformation,[],[f638]) ).
thf(f638,plain,
cancel_semigroup_add(nat) = $true,
inference(fool_elimination,[],[f637]) ).
thf(f637,plain,
cancel_semigroup_add(nat),
inference(rectify,[],[f273]) ).
thf(f273,axiom,
cancel_semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add_5) ).
thf(f2009,plain,
spl151_19,
inference(avatar_split_clause,[],[f1437,f2006]) ).
thf(f2006,plain,
( spl151_19
<=> ( ab_semigroup_add(int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_19])]) ).
thf(f1437,plain,
ab_semigroup_add(int) = $true,
inference(cnf_transformation,[],[f636]) ).
thf(f636,plain,
ab_semigroup_add(int) = $true,
inference(fool_elimination,[],[f635]) ).
thf(f635,plain,
ab_semigroup_add(int),
inference(rectify,[],[f261]) ).
thf(f261,axiom,
ab_semigroup_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oab__semigroup__add) ).
thf(f2004,plain,
spl151_18,
inference(avatar_split_clause,[],[f1436,f2001]) ).
thf(f2001,plain,
( spl151_18
<=> ( ab_semigroup_add(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_18])]) ).
thf(f1436,plain,
ab_semigroup_add(nat) = $true,
inference(cnf_transformation,[],[f634]) ).
thf(f634,plain,
ab_semigroup_add(nat) = $true,
inference(fool_elimination,[],[f633]) ).
thf(f633,plain,
ab_semigroup_add(nat),
inference(rectify,[],[f274]) ).
thf(f274,axiom,
ab_semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add_6) ).
thf(f1999,plain,
spl151_17,
inference(avatar_split_clause,[],[f1435,f1996]) ).
thf(f1996,plain,
( spl151_17
<=> ( zero(int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_17])]) ).
thf(f1435,plain,
zero(int) = $true,
inference(cnf_transformation,[],[f632]) ).
thf(f632,plain,
zero(int) = $true,
inference(fool_elimination,[],[f631]) ).
thf(f631,plain,
zero(int),
inference(rectify,[],[f267]) ).
thf(f267,axiom,
zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero) ).
thf(f1994,plain,
spl151_16,
inference(avatar_split_clause,[],[f1434,f1991]) ).
thf(f1434,plain,
group_add(int) = $true,
inference(cnf_transformation,[],[f630]) ).
thf(f630,plain,
group_add(int) = $true,
inference(fool_elimination,[],[f629]) ).
thf(f629,plain,
group_add(int),
inference(rectify,[],[f265]) ).
thf(f265,axiom,
group_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ogroup__add) ).
thf(f1989,plain,
spl151_15,
inference(avatar_split_clause,[],[f1433,f1986]) ).
thf(f1433,plain,
monoid_add(int) = $true,
inference(cnf_transformation,[],[f628]) ).
thf(f628,plain,
monoid_add(int) = $true,
inference(fool_elimination,[],[f627]) ).
thf(f627,plain,
monoid_add(int),
inference(rectify,[],[f264]) ).
thf(f264,axiom,
monoid_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Omonoid__add) ).
thf(f1984,plain,
spl151_14,
inference(avatar_split_clause,[],[f1432,f1981]) ).
thf(f1981,plain,
( spl151_14
<=> ( monoid_add(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_14])]) ).
thf(f1432,plain,
monoid_add(nat) = $true,
inference(cnf_transformation,[],[f626]) ).
thf(f626,plain,
monoid_add(nat) = $true,
inference(fool_elimination,[],[f625]) ).
thf(f625,plain,
monoid_add(nat),
inference(rectify,[],[f277]) ).
thf(f277,axiom,
monoid_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__add_9) ).
thf(f1979,plain,
spl151_13,
inference(avatar_split_clause,[],[f1431,f1976]) ).
thf(f1976,plain,
( spl151_13
<=> ( zero(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_13])]) ).
thf(f1431,plain,
zero(nat) = $true,
inference(cnf_transformation,[],[f624]) ).
thf(f624,plain,
zero(nat) = $true,
inference(fool_elimination,[],[f623]) ).
thf(f623,plain,
zero(nat),
inference(rectify,[],[f278]) ).
thf(f278,axiom,
zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_10) ).
thf(f1974,plain,
spl151_12,
inference(avatar_split_clause,[],[f1430,f1971]) ).
thf(f1971,plain,
( spl151_12
<=> ( linord219039673up_add(int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_12])]) ).
thf(f1430,plain,
linord219039673up_add(int) = $true,
inference(cnf_transformation,[],[f622]) ).
thf(f622,plain,
linord219039673up_add(int) = $true,
inference(fool_elimination,[],[f621]) ).
thf(f621,plain,
linord219039673up_add(int),
inference(rectify,[],[f258]) ).
thf(f258,axiom,
linord219039673up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(f1969,plain,
spl151_11,
inference(avatar_split_clause,[],[f1429,f1966]) ).
thf(f1966,plain,
( spl151_11
<=> ( ordere779506340up_add(int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_11])]) ).
thf(f1429,plain,
ordere779506340up_add(int) = $true,
inference(cnf_transformation,[],[f620]) ).
thf(f620,plain,
ordere779506340up_add(int) = $true,
inference(fool_elimination,[],[f619]) ).
thf(f619,plain,
ordere779506340up_add(int),
inference(rectify,[],[f257]) ).
thf(f257,axiom,
ordere779506340up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__add) ).
thf(f1964,plain,
spl151_10,
inference(avatar_split_clause,[],[f1428,f1961]) ).
thf(f1961,plain,
( spl151_10
<=> ( unique1598680935umeral(int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_10])]) ).
thf(f1428,plain,
unique1598680935umeral(int) = $true,
inference(cnf_transformation,[],[f618]) ).
thf(f618,plain,
unique1598680935umeral(int) = $true,
inference(fool_elimination,[],[f617]) ).
thf(f617,plain,
unique1598680935umeral(int),
inference(rectify,[],[f256]) ).
thf(f256,axiom,
unique1598680935umeral(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Divides_Ounique__euclidean__semiring__numeral) ).
thf(f1959,plain,
spl151_9,
inference(avatar_split_clause,[],[f1427,f1956]) ).
thf(f1956,plain,
( spl151_9
<=> ( semigroup_add(int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_9])]) ).
thf(f1427,plain,
semigroup_add(int) = $true,
inference(cnf_transformation,[],[f616]) ).
thf(f616,plain,
semigroup_add(int) = $true,
inference(fool_elimination,[],[f615]) ).
thf(f615,plain,
semigroup_add(int),
inference(rectify,[],[f263]) ).
thf(f263,axiom,
semigroup_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Osemigroup__add) ).
thf(f1954,plain,
spl151_8,
inference(avatar_split_clause,[],[f1426,f1951]) ).
thf(f1951,plain,
( spl151_8
<=> ( semiri456707255roduct(int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_8])]) ).
thf(f1426,plain,
semiri456707255roduct(int) = $true,
inference(cnf_transformation,[],[f614]) ).
thf(f614,plain,
semiri456707255roduct(int) = $true,
inference(fool_elimination,[],[f613]) ).
thf(f613,plain,
semiri456707255roduct(int),
inference(rectify,[],[f255]) ).
thf(f255,axiom,
semiri456707255roduct(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(f1949,plain,
spl151_7,
inference(avatar_split_clause,[],[f1425,f1946]) ).
thf(f1946,plain,
( spl151_7
<=> ( unique1598680935umeral(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_7])]) ).
thf(f1425,plain,
unique1598680935umeral(nat) = $true,
inference(cnf_transformation,[],[f612]) ).
thf(f612,plain,
unique1598680935umeral(nat) = $true,
inference(fool_elimination,[],[f611]) ).
thf(f611,plain,
unique1598680935umeral(nat),
inference(rectify,[],[f269]) ).
thf(f269,axiom,
unique1598680935umeral(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Divides_Ounique__euclidean__semiring__numeral_2) ).
thf(f1944,plain,
spl151_6,
inference(avatar_split_clause,[],[f1424,f1941]) ).
thf(f1941,plain,
( spl151_6
<=> ( canoni770627133id_add(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_6])]) ).
thf(f1424,plain,
canoni770627133id_add(nat) = $true,
inference(cnf_transformation,[],[f610]) ).
thf(f610,plain,
canoni770627133id_add(nat) = $true,
inference(fool_elimination,[],[f609]) ).
thf(f609,plain,
canoni770627133id_add(nat),
inference(rectify,[],[f270]) ).
thf(f270,axiom,
canoni770627133id_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(f1939,plain,
spl151_5,
inference(avatar_split_clause,[],[f1423,f1936]) ).
thf(f1936,plain,
( spl151_5
<=> ( semiri456707255roduct(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_5])]) ).
thf(f1423,plain,
semiri456707255roduct(nat) = $true,
inference(cnf_transformation,[],[f608]) ).
thf(f608,plain,
semiri456707255roduct(nat) = $true,
inference(fool_elimination,[],[f607]) ).
thf(f607,plain,
semiri456707255roduct(nat),
inference(rectify,[],[f268]) ).
thf(f268,axiom,
semiri456707255roduct(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_1) ).
thf(f1934,plain,
spl151_4,
inference(avatar_split_clause,[],[f1422,f1931]) ).
thf(f1931,plain,
( spl151_4
<=> ( ordere779506340up_add(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_4])]) ).
thf(f1422,plain,
ordere779506340up_add(nat) = $true,
inference(cnf_transformation,[],[f606]) ).
thf(f606,plain,
ordere779506340up_add(nat) = $true,
inference(fool_elimination,[],[f605]) ).
thf(f605,plain,
ordere779506340up_add(nat),
inference(rectify,[],[f271]) ).
thf(f271,axiom,
ordere779506340up_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_3) ).
thf(f1929,plain,
spl151_3,
inference(avatar_split_clause,[],[f1421,f1926]) ).
thf(f1926,plain,
( spl151_3
<=> ( semigroup_add(nat) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_3])]) ).
thf(f1421,plain,
semigroup_add(nat) = $true,
inference(cnf_transformation,[],[f604]) ).
thf(f604,plain,
semigroup_add(nat) = $true,
inference(fool_elimination,[],[f603]) ).
thf(f603,plain,
semigroup_add(nat),
inference(rectify,[],[f276]) ).
thf(f276,axiom,
semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add_8) ).
thf(f1924,plain,
spl151_2,
inference(avatar_split_clause,[],[f1420,f1921]) ).
thf(f1921,plain,
( spl151_2
<=> ( neg_numeral(int) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_2])]) ).
thf(f1420,plain,
neg_numeral(int) = $true,
inference(cnf_transformation,[],[f602]) ).
thf(f602,plain,
neg_numeral(int) = $true,
inference(fool_elimination,[],[f601]) ).
thf(f601,plain,
neg_numeral(int),
inference(rectify,[],[f266]) ).
thf(f266,axiom,
neg_numeral(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Num_Oneg__numeral) ).
thf(f1919,plain,
~ spl151_1,
inference(avatar_split_clause,[],[f291,f1916]) ).
thf(f1916,plain,
( spl151_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl151_1])]) ).
thf(f291,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP166^2 : TPTP v8.2.0. Released v7.5.0.
% 0.12/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat May 18 18:29:38 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (15727)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.38 % (15733)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.39 % (15730)WARNING: value z3 for option sas not known
% 0.20/0.39 % (15728)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.39 % (15729)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.39 % (15730)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.39 % (15731)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.39 % (15732)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.39 % (15734)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.46 % (15734)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.47 % Exception at run slice level
% 0.20/0.47 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.47 % Exception at run slice level
% 0.20/0.47 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.48 % (15767)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.49 % (15768)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.20/0.50 % Exception at run slice level
% 0.20/0.50 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.52 % (15792)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.20/0.53 % (15767)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.54 % (15768)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.38/0.56 % Exception at run slice level
% 1.38/0.56 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 1.38/0.57 % (15816)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 2.70/0.78 % (15732)First to succeed.
% 2.70/0.80 % (15732)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-15727"
% 2.70/0.80 % (15732)Refutation found. Thanks to Tanya!
% 2.70/0.80 % SZS status Theorem for theBenchmark
% 2.70/0.80 % SZS output start Proof for theBenchmark
% See solution above
% 2.70/0.81 % (15732)------------------------------
% 2.70/0.81 % (15732)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.70/0.81 % (15732)Termination reason: Refutation
% 2.70/0.81
% 2.70/0.81 % (15732)Memory used [KB]: 5835
% 2.70/0.81 % (15732)Time elapsed: 0.411 s
% 2.70/0.81 % (15732)Instructions burned: 1520 (million)
% 2.70/0.81 % (15727)Success in time 0.456 s
%------------------------------------------------------------------------------