TSTP Solution File: SCT179_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT179_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n022.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 : Tue Apr 30 14:57:13 EDT 2024
% Result : Theorem 0.22s 0.44s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 309
% Syntax : Number of formulae : 817 ( 238 unt; 56 typ; 0 def)
% Number of atoms : 1658 ( 321 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1508 ( 611 ~; 601 |; 49 &)
% ( 180 <=>; 67 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 55 ( 36 >; 19 *; 0 +; 0 <<)
% Number of predicates : 173 ( 171 usr; 153 prp; 0-6 aty)
% Number of functors : 34 ( 34 usr; 6 con; 0-5 aty)
% Number of variables : 1382 (1299 !; 26 ?;1382 :)
% ( 57 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
arrow_411405190le_alt: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_9,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
arrow_1985332922le_Lin: fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool) ).
tff(func_def_1,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_2,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_3,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_4,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_5,type,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_6,type,
order_215145569der_on:
!>[X0: $tType] : ( fun(X0,bool) > fun(fun(product_prod(X0,X0),bool),bool) ) ).
tff(func_def_7,type,
bot_bot:
!>[X0: $tType] : X0 ).
tff(func_def_8,type,
top_top:
!>[X0: $tType] : X0 ).
tff(func_def_9,type,
domain:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > fun(X0,bool) ) ).
tff(func_def_10,type,
id:
!>[X0: $tType] : fun(product_prod(X0,X0),bool) ).
tff(func_def_11,type,
id_on:
!>[X0: $tType] : ( fun(X0,bool) > fun(product_prod(X0,X0),bool) ) ).
tff(func_def_12,type,
range:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > fun(X1,bool) ) ).
tff(func_def_13,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_14,type,
lex_prod:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(product_prod(X1,X1),bool) ) > fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),bool) ) ).
tff(func_def_15,type,
measure:
!>[X0: $tType] : ( fun(X0,nat) > fun(product_prod(X0,X0),bool) ) ).
tff(func_def_16,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_17,type,
fFalse: bool ).
tff(func_def_18,type,
fNot: fun(bool,bool) ).
tff(func_def_19,type,
fTrue: bool ).
tff(func_def_20,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_21,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_22,type,
r: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_23,type,
sK0:
!>[X0: $tType] : X0 ).
tff(func_def_24,type,
sK1:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_25,type,
sK2:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_26,type,
sK3:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_27,type,
sK4:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_28,type,
sK5:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_29,type,
sK6:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_30,type,
sK7:
!>[X0: $tType] : ( fun(X0,bool) > fun(product_prod(X0,X0),bool) ) ).
tff(func_def_31,type,
sK8:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
cl_Groups_Ominus:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
bot:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
top:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
group_add:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
ordered_ab_group_add:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
order_1409979114der_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_8,type,
order_915043626der_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_9,type,
order_preorder_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_10,type,
order_well_order_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_11,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_12,type,
inv_imagep:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X0,bool)) * fun(X1,X0) * X1 * X1 ) > $o ) ).
tff(pred_def_13,type,
antisym:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_14,type,
irrefl:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_15,type,
refl_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_16,type,
total_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_17,type,
trans:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_18,type,
wf:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_19,type,
pp: bool > $o ).
tff(f1562,plain,
$false,
inference(avatar_sat_refutation,[],[f501,f506,f511,f516,f521,f526,f530,f534,f538,f542,f546,f550,f554,f558,f562,f566,f570,f574,f578,f586,f591,f595,f599,f603,f607,f613,f617,f623,f628,f633,f637,f641,f645,f649,f653,f657,f661,f665,f669,f673,f690,f694,f698,f702,f707,f711,f718,f722,f726,f730,f734,f738,f742,f746,f750,f768,f772,f776,f781,f788,f793,f798,f803,f807,f811,f815,f819,f823,f827,f841,f846,f860,f864,f869,f885,f890,f895,f899,f903,f907,f916,f927,f932,f938,f943,f949,f956,f962,f966,f970,f974,f978,f992,f996,f1001,f1007,f1013,f1019,f1024,f1031,f1038,f1042,f1046,f1051,f1056,f1060,f1064,f1068,f1085,f1089,f1127,f1133,f1137,f1141,f1147,f1151,f1157,f1179,f1204,f1209,f1215,f1225,f1231,f1238,f1242,f1247,f1251,f1256,f1317,f1321,f1356,f1360,f1365,f1370,f1375,f1386,f1391,f1401,f1405,f1418,f1422,f1470,f1476,f1507,f1511,f1517,f1526,f1532,f1541,f1547,f1556,f1561]) ).
tff(f1561,plain,
( ~ spl9_56
| ~ spl9_145 ),
inference(avatar_contradiction_clause,[],[f1559]) ).
tff(f1559,plain,
( $false
| ~ spl9_56
| ~ spl9_145 ),
inference(resolution,[],[f1506,f749]) ).
tff(f749,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : order_1409979114der_on(X0,X1,sK7(X0,X1))
| ~ spl9_56 ),
inference(avatar_component_clause,[],[f748]) ).
tff(f748,plain,
( spl9_56
<=> ! [X0: $tType,X1: fun(X0,bool)] : order_1409979114der_on(X0,X1,sK7(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_56])]) ).
tff(f1506,plain,
( ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ order_1409979114der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue),X0)
| ~ spl9_145 ),
inference(avatar_component_clause,[],[f1505]) ).
tff(f1505,plain,
( spl9_145
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ order_1409979114der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_145])]) ).
tff(f1556,plain,
spl9_152,
inference(avatar_split_clause,[],[f419,f1554]) ).
tff(f1554,plain,
( spl9_152
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK6(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_152])]) ).
tff(f419,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK6(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 ) ),
inference(cnf_transformation,[],[f310]) ).
tff(f310,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK6(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 ) )
& ( ( bot_bot(fun(X0,bool)) != X1 )
| ! [X3: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f308,f309]) ).
tff(f309,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X2: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
=> pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK6(X0,X1)),X1)) ),
introduced(choice_axiom,[]) ).
tff(f308,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ? [X2: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ( bot_bot(fun(X0,bool)) = X1 ) )
& ( ( bot_bot(fun(X0,bool)) != X1 )
| ! [X3: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) ) ),
inference(rectify,[],[f307]) ).
tff(f307,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ? [X2: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ( bot_bot(fun(X0,bool)) = X1 ) )
& ( ( bot_bot(fun(X0,bool)) != X1 )
| ! [X2: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
inference(nnf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X2: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
<=> ( bot_bot(fun(X0,bool)) != X1 ) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X0: $tType,X4: fun(X0,bool)] :
( ? [X16: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X16),X4))
<=> ( bot_bot(fun(X0,bool)) != X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_ex__in__conv) ).
tff(f1547,plain,
( spl9_151
| ~ spl9_75
| ~ spl9_131
| ~ spl9_150 ),
inference(avatar_split_clause,[],[f1543,f1539,f1319,f867,f1545]) ).
tff(f1545,plain,
( spl9_151
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK5(X0,X1)))
| ( combk(bool,X0,fFalse) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_151])]) ).
tff(f867,plain,
( spl9_75
<=> ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_75])]) ).
tff(f1319,plain,
( spl9_131
<=> ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_131])]) ).
tff(f1539,plain,
( spl9_150
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK5(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_150])]) ).
tff(f1543,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK5(X0,X1)))
| ( combk(bool,X0,fFalse) = X1 ) )
| ~ spl9_75
| ~ spl9_131
| ~ spl9_150 ),
inference(forward_demodulation,[],[f1542,f1320]) ).
tff(f1320,plain,
( ! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) )
| ~ spl9_131 ),
inference(avatar_component_clause,[],[f1319]) ).
tff(f1542,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK5(X0,X1)),X1)) )
| ~ spl9_75
| ~ spl9_150 ),
inference(forward_demodulation,[],[f1540,f868]) ).
tff(f868,plain,
( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse) )
| ~ spl9_75 ),
inference(avatar_component_clause,[],[f867]) ).
tff(f1540,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK5(X0,X1)),X1)) )
| ~ spl9_150 ),
inference(avatar_component_clause,[],[f1539]) ).
tff(f1541,plain,
spl9_150,
inference(avatar_split_clause,[],[f416,f1539]) ).
tff(f416,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK5(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f306]) ).
tff(f306,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ! [X2: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ( bot_bot(fun(X0,bool)) != X1 ) )
& ( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK5(X0,X1)),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f304,f305]) ).
tff(f305,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X3: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1))
=> pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK5(X0,X1)),X1)) ),
introduced(choice_axiom,[]) ).
tff(f304,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ! [X2: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ( bot_bot(fun(X0,bool)) != X1 ) )
& ( ( bot_bot(fun(X0,bool)) = X1 )
| ? [X3: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X1)) ) ),
inference(rectify,[],[f303]) ).
tff(f303,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ! [X2: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ( bot_bot(fun(X0,bool)) != X1 ) )
& ( ( bot_bot(fun(X0,bool)) = X1 )
| ? [X2: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
inference(nnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ! [X2: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
<=> ( bot_bot(fun(X0,bool)) = X1 ) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X0: $tType,X4: fun(X0,bool)] :
( ! [X16: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X16),X4))
<=> ( bot_bot(fun(X0,bool)) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_all__not__in__conv) ).
tff(f1532,plain,
( spl9_149
| ~ spl9_72
| ~ spl9_131
| ~ spl9_148 ),
inference(avatar_split_clause,[],[f1528,f1524,f1319,f844,f1530]) ).
tff(f1530,plain,
( spl9_149
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK2(X0,X1)))
| ( combk(bool,X0,fTrue) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_149])]) ).
tff(f844,plain,
( spl9_72
<=> ! [X0: $tType] : ( top_top(fun(X0,bool)) = combk(bool,X0,fTrue) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_72])]) ).
tff(f1524,plain,
( spl9_148
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( top_top(fun(X0,bool)) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_148])]) ).
tff(f1528,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK2(X0,X1)))
| ( combk(bool,X0,fTrue) = X1 ) )
| ~ spl9_72
| ~ spl9_131
| ~ spl9_148 ),
inference(forward_demodulation,[],[f1527,f1320]) ).
tff(f1527,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fTrue) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1)),X1)) )
| ~ spl9_72
| ~ spl9_148 ),
inference(forward_demodulation,[],[f1525,f845]) ).
tff(f845,plain,
( ! [X0: $tType] : ( top_top(fun(X0,bool)) = combk(bool,X0,fTrue) )
| ~ spl9_72 ),
inference(avatar_component_clause,[],[f844]) ).
tff(f1525,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( top_top(fun(X0,bool)) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1)),X1)) )
| ~ spl9_148 ),
inference(avatar_component_clause,[],[f1524]) ).
tff(f1526,plain,
spl9_148,
inference(avatar_split_clause,[],[f407,f1524]) ).
tff(f407,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( top_top(fun(X0,bool)) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f292]) ).
tff(f292,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( top_top(fun(X0,bool)) = X1 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1)),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f250,f291]) ).
tff(f291,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X2: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
=> ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK2(X0,X1)),X1)) ),
introduced(choice_axiom,[]) ).
tff(f250,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( top_top(fun(X0,bool)) = X1 )
| ? [X2: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ),
inference(ennf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ! [X2: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
=> ( top_top(fun(X0,bool)) = X1 ) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType,X4: fun(X0,bool)] :
( ! [X9: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X9),X4))
=> ( top_top(fun(X0,bool)) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_UNIV__eq__I) ).
tff(f1517,plain,
( spl9_147
| ~ spl9_75
| ~ spl9_131
| ~ spl9_146 ),
inference(avatar_split_clause,[],[f1513,f1509,f1319,f867,f1515]) ).
tff(f1515,plain,
( spl9_147
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK1(X0,X1)))
| ( combk(bool,X0,fFalse) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_147])]) ).
tff(f1509,plain,
( spl9_146
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK1(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_146])]) ).
tff(f1513,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK1(X0,X1)))
| ( combk(bool,X0,fFalse) = X1 ) )
| ~ spl9_75
| ~ spl9_131
| ~ spl9_146 ),
inference(forward_demodulation,[],[f1512,f1320]) ).
tff(f1512,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK1(X0,X1)),X1)) )
| ~ spl9_75
| ~ spl9_146 ),
inference(forward_demodulation,[],[f1510,f868]) ).
tff(f1510,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK1(X0,X1)),X1)) )
| ~ spl9_146 ),
inference(avatar_component_clause,[],[f1509]) ).
tff(f1511,plain,
spl9_146,
inference(avatar_split_clause,[],[f406,f1509]) ).
tff(f406,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK1(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK1(X0,X1)),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f249,f289]) ).
tff(f289,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X2: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
=> pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK1(X0,X1)),X1)) ),
introduced(choice_axiom,[]) ).
tff(f249,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| ? [X2: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ),
inference(ennf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ! [X2: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
=> ( bot_bot(fun(X0,bool)) = X1 ) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X0: $tType,X4: fun(X0,bool)] :
( ! [X18: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X18),X4))
=> ( bot_bot(fun(X0,bool)) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_equals0I) ).
tff(f1507,plain,
( spl9_145
| ~ spl9_7
| ~ spl9_72
| ~ spl9_141 ),
inference(avatar_split_clause,[],[f1435,f1416,f844,f528,f1505]) ).
tff(f528,plain,
( spl9_7
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).
tff(f1416,plain,
( spl9_141
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0))))
| ~ order_1409979114der_on(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_141])]) ).
tff(f1435,plain,
( ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ order_1409979114der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue),X0)
| ~ spl9_7
| ~ spl9_72
| ~ spl9_141 ),
inference(forward_demodulation,[],[f1423,f845]) ).
tff(f1423,plain,
( ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ order_1409979114der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),X0)
| ~ spl9_7
| ~ spl9_141 ),
inference(resolution,[],[f1417,f529]) ).
tff(f529,plain,
( ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),X0))
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f528]) ).
tff(f1417,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0))))
| ~ order_1409979114der_on(X0,X2,X1) )
| ~ spl9_141 ),
inference(avatar_component_clause,[],[f1416]) ).
tff(f1476,plain,
spl9_144,
inference(avatar_split_clause,[],[f480,f1474]) ).
tff(f1474,plain,
( spl9_144
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X2,fun(X1,X0)),X4: fun(X2,X1),X3: X2] : ( aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_144])]) ).
tff(f480,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ),
inference(cnf_transformation,[],[f225]) ).
tff(f225,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X2,fun(X1,X0))] : ( aa(X2,X0,combs(X2,X1,X0,X5,X4),X3) = aa(X1,X0,aa(X2,fun(X1,X0),X5,X3),aa(X2,X1,X4,X3)) ),
inference(rectify,[],[f116]) ).
tff(f116,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X33: X0,X34: fun(X0,X1),X32: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combs(X0,X1,X2,X32,X34),X33) = aa(X1,X2,aa(X0,fun(X1,X2),X32,X33),aa(X0,X1,X34,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
tff(f1470,plain,
spl9_143,
inference(avatar_split_clause,[],[f398,f1468]) ).
tff(f1468,plain,
( spl9_143
<=> ! [X1: $tType,X0: $tType,X4: X1,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( aa(X1,X0,minus_minus(fun(X1,X0),X3,X2),X4) = minus_minus(X0,aa(X1,X0,X3,X4),aa(X1,X0,X2,X4)) )
| ~ cl_Groups_Ominus(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_143])]) ).
tff(f398,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0),X4: X1] :
( ( aa(X1,X0,minus_minus(fun(X1,X0),X3,X2),X4) = minus_minus(X0,aa(X1,X0,X3,X4),aa(X1,X0,X2,X4)) )
| ~ cl_Groups_Ominus(X0) ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: fun(X1,X0),X3: fun(X1,X0),X4: X1] : ( aa(X1,X0,minus_minus(fun(X1,X0),X3,X2),X4) = minus_minus(X0,aa(X1,X0,X3,X4),aa(X1,X0,X2,X4)) )
| ~ cl_Groups_Ominus(X0) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $tType,X1: $tType] :
( cl_Groups_Ominus(X0)
=> ! [X2: fun(X1,X0),X3: fun(X1,X0),X4: X1] : ( aa(X1,X0,minus_minus(fun(X1,X0),X3,X2),X4) = minus_minus(X0,aa(X1,X0,X3,X4),aa(X1,X0,X2,X4)) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X1: $tType,X0: $tType] :
( cl_Groups_Ominus(X1)
=> ! [X5: fun(X0,X1),X4: fun(X0,X1),X8: X0] : ( aa(X0,X1,minus_minus(fun(X0,X1),X4,X5),X8) = minus_minus(X1,aa(X0,X1,X4,X8),aa(X0,X1,X5,X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_fun__diff__def) ).
tff(f1422,plain,
spl9_142,
inference(avatar_split_clause,[],[f473,f1420]) ).
tff(f1420,plain,
( spl9_142
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK8(X0,X1,X2,X3)) != aa(X1,X0,X2,sK8(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_142])]) ).
tff(f473,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK8(X0,X1,X2,X3)) != aa(X1,X0,X2,sK8(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f328]) ).
tff(f328,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK8(X0,X1,X2,X3)) != aa(X1,X0,X2,sK8(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f282,f327]) ).
tff(f327,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) )
=> ( aa(X1,X0,X3,sK8(X0,X1,X2,X3)) != aa(X1,X0,X2,sK8(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f282,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ? [X4: X1] : ( aa(X1,X0,X3,X4) != aa(X1,X0,X2,X4) ) ),
inference(ennf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ! [X4: X1] : ( aa(X1,X0,X3,X4) = aa(X1,X0,X2,X4) )
=> ( X2 = X3 ) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X1: $tType,X0: $tType,X24: fun(X0,X1),X14: fun(X0,X1)] :
( ! [X9: X0] : ( aa(X0,X1,X14,X9) = aa(X0,X1,X24,X9) )
=> ( X14 = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
tff(f1418,plain,
spl9_141,
inference(avatar_split_clause,[],[f424,f1416]) ).
tff(f424,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0))))
| ~ order_1409979114der_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f251]) ).
tff(f251,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0))))
| ~ order_1409979114der_on(X0,X2,X1) ),
inference(ennf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( order_1409979114der_on(X0,X2,X1)
=> pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0)))) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X0: $tType,X3: fun(product_prod(X0,X0),bool),X4: fun(X0,bool)] :
( order_1409979114der_on(X0,X4,X3)
=> pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X4),minus_minus(fun(product_prod(X0,X0),bool),X3,id(X0)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_strict__linear__order__on__diff__Id) ).
tff(f1405,plain,
( spl9_140
| ~ spl9_75
| ~ spl9_134 ),
inference(avatar_split_clause,[],[f1366,f1363,f867,f1403]) ).
tff(f1403,plain,
( spl9_140
<=> ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool)] :
( ( domain(X1,X0,X2) != combk(bool,X1,fFalse) )
| ( bot_bot(fun(product_prod(X1,X0),bool)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_140])]) ).
tff(f1363,plain,
( spl9_134
<=> ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool)] :
( ( bot_bot(fun(product_prod(X1,X0),bool)) = X2 )
| ( bot_bot(fun(X1,bool)) != domain(X1,X0,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_134])]) ).
tff(f1366,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool)] :
( ( domain(X1,X0,X2) != combk(bool,X1,fFalse) )
| ( bot_bot(fun(product_prod(X1,X0),bool)) = X2 ) )
| ~ spl9_75
| ~ spl9_134 ),
inference(forward_demodulation,[],[f1364,f868]) ).
tff(f1364,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool)] :
( ( bot_bot(fun(product_prod(X1,X0),bool)) = X2 )
| ( bot_bot(fun(X1,bool)) != domain(X1,X0,X2) ) )
| ~ spl9_134 ),
inference(avatar_component_clause,[],[f1363]) ).
tff(f1401,plain,
( spl9_139
| ~ spl9_75
| ~ spl9_133 ),
inference(avatar_split_clause,[],[f1361,f1358,f867,f1399]) ).
tff(f1399,plain,
( spl9_139
<=> ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool)] :
( ( combk(bool,X0,fFalse) != range(X1,X0,X2) )
| ( bot_bot(fun(product_prod(X1,X0),bool)) = X2 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_139])]) ).
tff(f1358,plain,
( spl9_133
<=> ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool)] :
( ( bot_bot(fun(product_prod(X1,X0),bool)) = X2 )
| ( bot_bot(fun(X0,bool)) != range(X1,X0,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_133])]) ).
tff(f1361,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool)] :
( ( combk(bool,X0,fFalse) != range(X1,X0,X2) )
| ( bot_bot(fun(product_prod(X1,X0),bool)) = X2 ) )
| ~ spl9_75
| ~ spl9_133 ),
inference(forward_demodulation,[],[f1359,f868]) ).
tff(f1359,plain,
( ! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool)] :
( ( bot_bot(fun(product_prod(X1,X0),bool)) = X2 )
| ( bot_bot(fun(X0,bool)) != range(X1,X0,X2) ) )
| ~ spl9_133 ),
inference(avatar_component_clause,[],[f1358]) ).
tff(f1391,plain,
( spl9_138
| ~ spl9_131
| ~ spl9_137 ),
inference(avatar_split_clause,[],[f1387,f1384,f1319,f1389]) ).
tff(f1389,plain,
( spl9_138
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_138])]) ).
tff(f1384,plain,
( spl9_137
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_137])]) ).
tff(f1387,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl9_131
| ~ spl9_137 ),
inference(forward_demodulation,[],[f1385,f1320]) ).
tff(f1385,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) )
| ~ spl9_137 ),
inference(avatar_component_clause,[],[f1384]) ).
tff(f1386,plain,
spl9_137,
inference(avatar_split_clause,[],[f454,f1384]) ).
tff(f454,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f326]) ).
tff(f326,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa(X0,bool,X1,X2)) )
& ( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
inference(nnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
<=> pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType,X4: fun(X0,bool),X7: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X7),X4))
<=> pp(aa(X0,bool,X4,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
tff(f1375,plain,
( spl9_136
| ~ spl9_131
| ~ spl9_135 ),
inference(avatar_split_clause,[],[f1371,f1368,f1319,f1373]) ).
tff(f1373,plain,
( spl9_136
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_136])]) ).
tff(f1368,plain,
( spl9_135
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_135])]) ).
tff(f1371,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),X2))
| pp(aa(X0,bool,X1,X2)) )
| ~ spl9_131
| ~ spl9_135 ),
inference(forward_demodulation,[],[f1369,f1320]) ).
tff(f1369,plain,
( ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) )
| ~ spl9_135 ),
inference(avatar_component_clause,[],[f1368]) ).
tff(f1370,plain,
spl9_135,
inference(avatar_split_clause,[],[f453,f1368]) ).
tff(f453,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ),
inference(cnf_transformation,[],[f326]) ).
tff(f1365,plain,
spl9_134,
inference(avatar_split_clause,[],[f445,f1363]) ).
tff(f445,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool)] :
( ( bot_bot(fun(product_prod(X1,X0),bool)) = X2 )
| ( bot_bot(fun(X1,bool)) != domain(X1,X0,X2) ) ),
inference(cnf_transformation,[],[f322]) ).
tff(f322,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool)] :
( ( ( bot_bot(fun(X1,bool)) = domain(X1,X0,X2) )
| ( bot_bot(fun(product_prod(X1,X0),bool)) != X2 ) )
& ( ( bot_bot(fun(product_prod(X1,X0),bool)) = X2 )
| ( bot_bot(fun(X1,bool)) != domain(X1,X0,X2) ) ) ),
inference(nnf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool)] :
( ( bot_bot(fun(X1,bool)) = domain(X1,X0,X2) )
<=> ( bot_bot(fun(product_prod(X1,X0),bool)) = X2 ) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X1: $tType,X0: $tType,X3: fun(product_prod(X0,X1),bool)] :
( ( bot_bot(fun(X0,bool)) = domain(X0,X1,X3) )
<=> ( bot_bot(fun(product_prod(X0,X1),bool)) = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Domain__empty__iff) ).
tff(f1360,plain,
spl9_133,
inference(avatar_split_clause,[],[f443,f1358]) ).
tff(f443,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool)] :
( ( bot_bot(fun(product_prod(X1,X0),bool)) = X2 )
| ( bot_bot(fun(X0,bool)) != range(X1,X0,X2) ) ),
inference(cnf_transformation,[],[f321]) ).
tff(f321,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool)] :
( ( ( bot_bot(fun(X0,bool)) = range(X1,X0,X2) )
| ( bot_bot(fun(product_prod(X1,X0),bool)) != X2 ) )
& ( ( bot_bot(fun(product_prod(X1,X0),bool)) = X2 )
| ( bot_bot(fun(X0,bool)) != range(X1,X0,X2) ) ) ),
inference(nnf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool)] :
( ( bot_bot(fun(X0,bool)) = range(X1,X0,X2) )
<=> ( bot_bot(fun(product_prod(X1,X0),bool)) = X2 ) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X0: $tType,X1: $tType,X3: fun(product_prod(X1,X0),bool)] :
( ( bot_bot(fun(X0,bool)) = range(X1,X0,X3) )
<=> ( bot_bot(fun(product_prod(X1,X0),bool)) = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_Range__empty__iff) ).
tff(f1356,plain,
( spl9_132
| ~ spl9_7
| ~ spl9_72
| ~ spl9_130 ),
inference(avatar_split_clause,[],[f1332,f1315,f844,f528,f1354]) ).
tff(f1354,plain,
( spl9_132
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ~ total_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue),X0)
| ~ irrefl(arrow_411405190le_alt,X0)
| ~ trans(arrow_411405190le_alt,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_132])]) ).
tff(f1315,plain,
( spl9_130
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
| ~ total_on(X0,X2,X1)
| ~ irrefl(X0,X1)
| ~ trans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_130])]) ).
tff(f1332,plain,
( ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ~ total_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue),X0)
| ~ irrefl(arrow_411405190le_alt,X0)
| ~ trans(arrow_411405190le_alt,X0) )
| ~ spl9_7
| ~ spl9_72
| ~ spl9_130 ),
inference(forward_demodulation,[],[f1322,f845]) ).
tff(f1322,plain,
( ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),X0)
| ~ irrefl(arrow_411405190le_alt,X0)
| ~ trans(arrow_411405190le_alt,X0) )
| ~ spl9_7
| ~ spl9_130 ),
inference(resolution,[],[f1316,f529]) ).
tff(f1316,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
| ~ total_on(X0,X2,X1)
| ~ irrefl(X0,X1)
| ~ trans(X0,X1) )
| ~ spl9_130 ),
inference(avatar_component_clause,[],[f1315]) ).
tff(f1321,plain,
spl9_131,
inference(avatar_split_clause,[],[f479,f1319]) ).
tff(f479,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(cnf_transformation,[],[f224]) ).
tff(f224,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X0,X4: X2,X5: fun(X0,fun(X2,X1))] : ( aa(X0,X1,combc(X0,X2,X1,X5,X4),X3) = aa(X2,X1,aa(X0,fun(X2,X1),X5,X3),X4) ),
inference(rectify,[],[f114]) ).
tff(f114,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X33: X0,X34: X1,X32: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combc(X0,X1,X2,X32,X34),X33) = aa(X1,X2,aa(X0,fun(X1,X2),X32,X33),X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
tff(f1317,plain,
spl9_130,
inference(avatar_split_clause,[],[f450,f1315]) ).
tff(f450,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
| ~ total_on(X0,X2,X1)
| ~ irrefl(X0,X1)
| ~ trans(X0,X1) ),
inference(cnf_transformation,[],[f324]) ).
tff(f324,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
| ~ total_on(X0,X2,X1)
| ~ irrefl(X0,X1)
| ~ trans(X0,X1) )
& ( ( total_on(X0,X2,X1)
& irrefl(X0,X1)
& trans(X0,X1) )
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ) ),
inference(flattening,[],[f323]) ).
tff(f323,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
| ~ total_on(X0,X2,X1)
| ~ irrefl(X0,X1)
| ~ trans(X0,X1) )
& ( ( total_on(X0,X2,X1)
& irrefl(X0,X1)
& trans(X0,X1) )
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ) ),
inference(nnf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1))
<=> ( total_on(X0,X2,X1)
& irrefl(X0,X1)
& trans(X0,X1) ) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X0: $tType,X3: fun(product_prod(X0,X0),bool),X4: fun(X0,bool)] :
( pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X4),X3))
<=> ( total_on(X0,X4,X3)
& irrefl(X0,X3)
& trans(X0,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_strict__linear__order__on__def) ).
tff(f1256,plain,
( spl9_129
| ~ spl9_72
| ~ spl9_120 ),
inference(avatar_split_clause,[],[f1205,f1201,f844,f1253]) ).
tff(f1253,plain,
( spl9_129
<=> ( arrow_1985332922le_Lin = collect(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),order_215145569der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_129])]) ).
tff(f1201,plain,
( spl9_120
<=> ( arrow_1985332922le_Lin = collect(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_120])]) ).
tff(f1205,plain,
( ( arrow_1985332922le_Lin = collect(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),order_215145569der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue))) )
| ~ spl9_72
| ~ spl9_120 ),
inference(forward_demodulation,[],[f1203,f845]) ).
tff(f1203,plain,
( ( arrow_1985332922le_Lin = collect(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)))) )
| ~ spl9_120 ),
inference(avatar_component_clause,[],[f1201]) ).
tff(f1251,plain,
spl9_128,
inference(avatar_split_clause,[],[f478,f1249]) ).
tff(f1249,plain,
( spl9_128
<=> ! [X1: $tType,X2: $tType,X0: $tType,X5: fun(X1,X0),X4: fun(X2,X1),X3: X2] : ( aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_128])]) ).
tff(f478,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(cnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2,X4: fun(X2,X1),X5: fun(X1,X0)] : ( aa(X2,X0,combb(X1,X0,X2,X5,X4),X3) = aa(X1,X0,X5,aa(X2,X1,X4,X3)) ),
inference(rectify,[],[f113]) ).
tff(f113,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X33: X0,X34: fun(X0,X1),X32: fun(X1,X2)] : ( aa(X0,X2,combb(X1,X2,X0,X32,X34),X33) = aa(X1,X2,X32,aa(X0,X1,X34,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
tff(f1247,plain,
( spl9_127
| ~ spl9_7
| ~ spl9_72
| ~ spl9_110 ),
inference(avatar_split_clause,[],[f1108,f1083,f844,f528,f1244]) ).
tff(f1244,plain,
( spl9_127
<=> ( order_215145569der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue)) = combk(bool,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_127])]) ).
tff(f1083,plain,
( spl9_110
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK3(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_110])]) ).
tff(f1108,plain,
( ( order_215145569der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue)) = combk(bool,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fFalse) )
| ~ spl9_7
| ~ spl9_72
| ~ spl9_110 ),
inference(forward_demodulation,[],[f1096,f845]) ).
tff(f1096,plain,
( ( order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))) = combk(bool,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fFalse) )
| ~ spl9_7
| ~ spl9_110 ),
inference(resolution,[],[f1084,f529]) ).
tff(f1084,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,sK3(X0,X1)))
| ( combk(bool,X0,fFalse) = X1 ) )
| ~ spl9_110 ),
inference(avatar_component_clause,[],[f1083]) ).
tff(f1242,plain,
spl9_126,
inference(avatar_split_clause,[],[f466,f1240]) ).
tff(f1240,plain,
( spl9_126
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X1,X0),bool),X2: fun(product_prod(X1,X0),bool)] :
( ord_less_eq(fun(X1,bool),domain(X1,X0,X3),domain(X1,X0,X2))
| ~ ord_less_eq(fun(product_prod(X1,X0),bool),X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_126])]) ).
tff(f466,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( ord_less_eq(fun(X1,bool),domain(X1,X0,X3),domain(X1,X0,X2))
| ~ ord_less_eq(fun(product_prod(X1,X0),bool),X3,X2) ),
inference(cnf_transformation,[],[f274]) ).
tff(f274,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( ord_less_eq(fun(X1,bool),domain(X1,X0,X3),domain(X1,X0,X2))
| ~ ord_less_eq(fun(product_prod(X1,X0),bool),X3,X2) ),
inference(ennf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X0),bool),X3: fun(product_prod(X1,X0),bool)] :
( ord_less_eq(fun(product_prod(X1,X0),bool),X3,X2)
=> ord_less_eq(fun(X1,bool),domain(X1,X0,X3),domain(X1,X0,X2)) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X1: $tType,X0: $tType,X25: fun(product_prod(X0,X1),bool),X3: fun(product_prod(X0,X1),bool)] :
( ord_less_eq(fun(product_prod(X0,X1),bool),X3,X25)
=> ord_less_eq(fun(X0,bool),domain(X0,X1,X3),domain(X0,X1,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Domain__mono) ).
tff(f1238,plain,
spl9_125,
inference(avatar_split_clause,[],[f422,f1236]) ).
tff(f1236,plain,
( spl9_125
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( minus_minus(fun(X0,bool),X2,X1) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_125])]) ).
tff(f422,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( minus_minus(fun(X0,bool),X2,X1) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X2,X1),X1) ),
inference(cnf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] : ( minus_minus(fun(X0,bool),X2,X1) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X2,X1),X1) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: $tType,X5: fun(X0,bool),X4: fun(X0,bool)] : ( minus_minus(fun(X0,bool),X4,X5) = minus_minus(fun(X0,bool),minus_minus(fun(X0,bool),X4,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_Diff__idemp) ).
tff(f1231,plain,
( spl9_124
| ~ spl9_72
| ~ spl9_123 ),
inference(avatar_split_clause,[],[f1227,f1223,f844,f1229]) ).
tff(f1229,plain,
( spl9_124
<=> ! [X0: $tType,X1: X0] : pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fTrue)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_124])]) ).
tff(f1223,plain,
( spl9_123
<=> ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),top_top(fun(X0,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_123])]) ).
tff(f1227,plain,
( ! [X0: $tType,X1: X0] : pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fTrue)),X1))
| ~ spl9_72
| ~ spl9_123 ),
inference(forward_demodulation,[],[f1226,f845]) ).
tff(f1226,plain,
( ! [X0: $tType,X1: X0] : pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),top_top(fun(X0,bool))),X1))
| ~ spl9_123 ),
inference(forward_demodulation,[],[f1224,f479]) ).
tff(f1224,plain,
( ! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),top_top(fun(X0,bool))))
| ~ spl9_123 ),
inference(avatar_component_clause,[],[f1223]) ).
tff(f1225,plain,
spl9_123,
inference(avatar_split_clause,[],[f391,f1223]) ).
tff(f391,plain,
! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),top_top(fun(X0,bool)))),
inference(cnf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: $tType,X1: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),top_top(fun(X0,bool)))),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X0: $tType,X7: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X7),top_top(fun(X0,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_UNIV__I) ).
tff(f1215,plain,
( spl9_122
| ~ spl9_75
| ~ spl9_121 ),
inference(avatar_split_clause,[],[f1211,f1207,f867,f1213]) ).
tff(f1213,plain,
( spl9_122
<=> ! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_122])]) ).
tff(f1207,plain,
( spl9_121
<=> ! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_121])]) ).
tff(f1211,plain,
( ! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)),X1))
| ~ spl9_75
| ~ spl9_121 ),
inference(forward_demodulation,[],[f1210,f868]) ).
tff(f1210,plain,
( ! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))),X1))
| ~ spl9_121 ),
inference(forward_demodulation,[],[f1208,f479]) ).
tff(f1208,plain,
( ! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool))))
| ~ spl9_121 ),
inference(avatar_component_clause,[],[f1207]) ).
tff(f1209,plain,
spl9_121,
inference(avatar_split_clause,[],[f389,f1207]) ).
tff(f389,plain,
! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))),
inference(cnf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: $tType,X1: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X1),bot_bot(fun(X0,bool)))),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X0: $tType,X12: X0] : ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X12),bot_bot(fun(X0,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_emptyE) ).
tff(f1204,plain,
spl9_120,
inference(avatar_split_clause,[],[f342,f1201]) ).
tff(f342,plain,
arrow_1985332922le_Lin = collect(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)))),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
arrow_1985332922le_Lin = collect(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_Lin__def) ).
tff(f1179,plain,
spl9_119,
inference(avatar_split_clause,[],[f460,f1177]) ).
tff(f1177,plain,
( spl9_119
<=> ! [X0: $tType,X3: fun(X0,bool),X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ ord_less_eq(fun(X0,bool),X3,X1)
| ~ pp(aa(X0,bool,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_119])]) ).
tff(f460,plain,
! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ ord_less_eq(fun(X0,bool),X3,X1)
| ~ pp(aa(X0,bool,X3,X2)) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0,X3: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ ord_less_eq(fun(X0,bool),X3,X1)
| ~ pp(aa(X0,bool,X3,X2)) ),
inference(flattening,[],[f262]) ).
tff(f262,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0,X3: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ ord_less_eq(fun(X0,bool),X3,X1)
| ~ pp(aa(X0,bool,X3,X2)) ),
inference(ennf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0,X3: fun(X0,bool)] :
( pp(aa(X0,bool,X3,X2))
=> ( ord_less_eq(fun(X0,bool),X3,X1)
=> pp(aa(X0,bool,X1,X2)) ) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X0: $tType,X29: fun(X0,bool),X7: X0,X17: fun(X0,bool)] :
( pp(aa(X0,bool,X17,X7))
=> ( ord_less_eq(fun(X0,bool),X17,X29)
=> pp(aa(X0,bool,X29,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_rev__predicate1D) ).
tff(f1157,plain,
( spl9_118
| ~ spl9_75
| ~ spl9_115 ),
inference(avatar_split_clause,[],[f1143,f1139,f867,f1155]) ).
tff(f1155,plain,
( spl9_118
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ~ ord_less_eq(fun(X0,bool),X1,combk(bool,X0,fFalse))
| ( combk(bool,X0,fFalse) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_118])]) ).
tff(f1139,plain,
( spl9_115
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| ~ ord_less_eq(fun(X0,bool),X1,bot_bot(fun(X0,bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_115])]) ).
tff(f1143,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ~ ord_less_eq(fun(X0,bool),X1,combk(bool,X0,fFalse))
| ( combk(bool,X0,fFalse) = X1 ) )
| ~ spl9_75
| ~ spl9_115 ),
inference(forward_demodulation,[],[f1142,f868]) ).
tff(f1142,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| ~ ord_less_eq(fun(X0,bool),X1,bot_bot(fun(X0,bool))) )
| ~ spl9_75
| ~ spl9_115 ),
inference(forward_demodulation,[],[f1140,f868]) ).
tff(f1140,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| ~ ord_less_eq(fun(X0,bool),X1,bot_bot(fun(X0,bool))) )
| ~ spl9_115 ),
inference(avatar_component_clause,[],[f1139]) ).
tff(f1151,plain,
( spl9_117
| ~ spl9_75
| ~ spl9_112 ),
inference(avatar_split_clause,[],[f1129,f1125,f867,f1149]) ).
tff(f1149,plain,
( spl9_117
<=> ! [X0: $tType] : ( id_on(X0,combk(bool,X0,fFalse)) = combk(bool,product_prod(X0,X0),fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_117])]) ).
tff(f1125,plain,
( spl9_112
<=> ! [X0: $tType] : ( bot_bot(fun(product_prod(X0,X0),bool)) = id_on(X0,bot_bot(fun(X0,bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_112])]) ).
tff(f1129,plain,
( ! [X0: $tType] : ( id_on(X0,combk(bool,X0,fFalse)) = combk(bool,product_prod(X0,X0),fFalse) )
| ~ spl9_75
| ~ spl9_112 ),
inference(forward_demodulation,[],[f1128,f868]) ).
tff(f1128,plain,
( ! [X0: $tType] : ( bot_bot(fun(product_prod(X0,X0),bool)) = id_on(X0,combk(bool,X0,fFalse)) )
| ~ spl9_75
| ~ spl9_112 ),
inference(forward_demodulation,[],[f1126,f868]) ).
tff(f1126,plain,
( ! [X0: $tType] : ( bot_bot(fun(product_prod(X0,X0),bool)) = id_on(X0,bot_bot(fun(X0,bool))) )
| ~ spl9_112 ),
inference(avatar_component_clause,[],[f1125]) ).
tff(f1147,plain,
spl9_116,
inference(avatar_split_clause,[],[f427,f1145]) ).
tff(f1145,plain,
( spl9_116
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( X1 = X2 )
| ~ ord_less_eq(fun(X0,bool),X1,X2)
| ~ ord_less_eq(fun(X0,bool),X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_116])]) ).
tff(f427,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( X1 = X2 )
| ~ ord_less_eq(fun(X0,bool),X1,X2)
| ~ ord_less_eq(fun(X0,bool),X2,X1) ),
inference(cnf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( X1 = X2 )
| ~ ord_less_eq(fun(X0,bool),X1,X2)
| ~ ord_less_eq(fun(X0,bool),X2,X1) ),
inference(flattening,[],[f254]) ).
tff(f254,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( X1 = X2 )
| ~ ord_less_eq(fun(X0,bool),X1,X2)
| ~ ord_less_eq(fun(X0,bool),X2,X1) ),
inference(ennf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ord_less_eq(fun(X0,bool),X2,X1)
=> ( ord_less_eq(fun(X0,bool),X1,X2)
=> ( X1 = X2 ) ) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X0: $tType,X5: fun(X0,bool),X4: fun(X0,bool)] :
( ord_less_eq(fun(X0,bool),X4,X5)
=> ( ord_less_eq(fun(X0,bool),X5,X4)
=> ( X4 = X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_equalityI) ).
tff(f1141,plain,
spl9_115,
inference(avatar_split_clause,[],[f410,f1139]) ).
tff(f410,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| ~ ord_less_eq(fun(X0,bool),X1,bot_bot(fun(X0,bool))) ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ord_less_eq(fun(X0,bool),X1,bot_bot(fun(X0,bool)))
| ( bot_bot(fun(X0,bool)) != X1 ) )
& ( ( bot_bot(fun(X0,bool)) = X1 )
| ~ ord_less_eq(fun(X0,bool),X1,bot_bot(fun(X0,bool))) ) ),
inference(nnf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ord_less_eq(fun(X0,bool),X1,bot_bot(fun(X0,bool)))
<=> ( bot_bot(fun(X0,bool)) = X1 ) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X0: $tType,X4: fun(X0,bool)] :
( ord_less_eq(fun(X0,bool),X4,bot_bot(fun(X0,bool)))
<=> ( bot_bot(fun(X0,bool)) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_subset__empty) ).
tff(f1137,plain,
spl9_114,
inference(avatar_split_clause,[],[f405,f1135]) ).
tff(f1135,plain,
( spl9_114
<=> ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0)))
| ~ antisym(X0,X1)
| ~ trans(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_114])]) ).
tff(f405,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0)))
| ~ antisym(X0,X1)
| ~ trans(X0,X1) ),
inference(cnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0)))
| ~ antisym(X0,X1)
| ~ trans(X0,X1) ),
inference(flattening,[],[f247]) ).
tff(f247,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0)))
| ~ antisym(X0,X1)
| ~ trans(X0,X1) ),
inference(ennf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
=> ( antisym(X0,X1)
=> trans(X0,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0))) ) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X0: $tType,X3: fun(product_prod(X0,X0),bool)] :
( trans(X0,X3)
=> ( antisym(X0,X3)
=> trans(X0,minus_minus(fun(product_prod(X0,X0),bool),X3,id(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_trans__diff__Id) ).
tff(f1133,plain,
( spl9_113
| ~ spl9_12
| ~ spl9_73 ),
inference(avatar_split_clause,[],[f1074,f858,f548,f1131]) ).
tff(f1131,plain,
( spl9_113
<=> ! [X0: bool,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( fFalse = aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,X0)),X1) )
| ( fFalse = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_113])]) ).
tff(f548,plain,
( spl9_12
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).
tff(f858,plain,
( spl9_73
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ( fFalse = aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_73])]) ).
tff(f1074,plain,
( ! [X0: bool,X1: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ( fFalse = aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,X0)),X1) )
| ( fFalse = X0 ) )
| ~ spl9_12
| ~ spl9_73 ),
inference(superposition,[],[f859,f549]) ).
tff(f549,plain,
( ! [X0: bool] :
( ( fTrue = X0 )
| ( fFalse = X0 ) )
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f548]) ).
tff(f859,plain,
( ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ( fFalse = aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue)),X0) )
| ~ spl9_73 ),
inference(avatar_component_clause,[],[f858]) ).
tff(f1127,plain,
spl9_112,
inference(avatar_split_clause,[],[f358,f1125]) ).
tff(f358,plain,
! [X0: $tType] : ( bot_bot(fun(product_prod(X0,X0),bool)) = id_on(X0,bot_bot(fun(X0,bool))) ),
inference(cnf_transformation,[],[f67]) ).
tff(f67,axiom,
! [X0: $tType] : ( bot_bot(fun(product_prod(X0,X0),bool)) = id_on(X0,bot_bot(fun(X0,bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Id__on__empty) ).
tff(f1089,plain,
( spl9_111
| ~ spl9_75
| ~ spl9_105 ),
inference(avatar_split_clause,[],[f1052,f1049,f867,f1087]) ).
tff(f1087,plain,
( spl9_111
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK4(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_111])]) ).
tff(f1049,plain,
( spl9_105
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK4(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_105])]) ).
tff(f1052,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK4(X0,X1))) )
| ~ spl9_75
| ~ spl9_105 ),
inference(forward_demodulation,[],[f1050,f868]) ).
tff(f1050,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK4(X0,X1))) )
| ~ spl9_105 ),
inference(avatar_component_clause,[],[f1049]) ).
tff(f1085,plain,
( spl9_110
| ~ spl9_75
| ~ spl9_104 ),
inference(avatar_split_clause,[],[f1047,f1044,f867,f1083]) ).
tff(f1044,plain,
( spl9_104
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK3(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_104])]) ).
tff(f1047,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK3(X0,X1))) )
| ~ spl9_75
| ~ spl9_104 ),
inference(forward_demodulation,[],[f1045,f868]) ).
tff(f1045,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK3(X0,X1))) )
| ~ spl9_104 ),
inference(avatar_component_clause,[],[f1044]) ).
tff(f1068,plain,
( spl9_109
| ~ spl9_72
| ~ spl9_75
| ~ spl9_98 ),
inference(avatar_split_clause,[],[f1015,f1011,f867,f844,f1066]) ).
tff(f1066,plain,
( spl9_109
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = minus_minus(fun(X0,bool),X1,combk(bool,X0,fTrue)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_109])]) ).
tff(f1011,plain,
( spl9_98
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),X1,top_top(fun(X0,bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_98])]) ).
tff(f1015,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = minus_minus(fun(X0,bool),X1,combk(bool,X0,fTrue)) )
| ~ spl9_72
| ~ spl9_75
| ~ spl9_98 ),
inference(forward_demodulation,[],[f1014,f868]) ).
tff(f1014,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),X1,combk(bool,X0,fTrue)) )
| ~ spl9_72
| ~ spl9_98 ),
inference(forward_demodulation,[],[f1012,f845]) ).
tff(f1012,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),X1,top_top(fun(X0,bool))) )
| ~ spl9_98 ),
inference(avatar_component_clause,[],[f1011]) ).
tff(f1064,plain,
( spl9_108
| ~ spl9_75
| ~ spl9_97 ),
inference(avatar_split_clause,[],[f1009,f1005,f867,f1062]) ).
tff(f1062,plain,
( spl9_108
<=> ! [X1: $tType,X0: $tType] : ( combk(bool,X1,fFalse) = domain(X1,X0,combk(bool,product_prod(X1,X0),fFalse)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_108])]) ).
tff(f1005,plain,
( spl9_97
<=> ! [X1: $tType,X0: $tType] : ( bot_bot(fun(X1,bool)) = domain(X1,X0,bot_bot(fun(product_prod(X1,X0),bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_97])]) ).
tff(f1009,plain,
( ! [X1: $tType,X0: $tType] : ( combk(bool,X1,fFalse) = domain(X1,X0,combk(bool,product_prod(X1,X0),fFalse)) )
| ~ spl9_75
| ~ spl9_97 ),
inference(forward_demodulation,[],[f1008,f868]) ).
tff(f1008,plain,
( ! [X1: $tType,X0: $tType] : ( bot_bot(fun(X1,bool)) = domain(X1,X0,combk(bool,product_prod(X1,X0),fFalse)) )
| ~ spl9_75
| ~ spl9_97 ),
inference(forward_demodulation,[],[f1006,f868]) ).
tff(f1006,plain,
( ! [X1: $tType,X0: $tType] : ( bot_bot(fun(X1,bool)) = domain(X1,X0,bot_bot(fun(product_prod(X1,X0),bool))) )
| ~ spl9_97 ),
inference(avatar_component_clause,[],[f1005]) ).
tff(f1060,plain,
( spl9_107
| ~ spl9_75
| ~ spl9_96 ),
inference(avatar_split_clause,[],[f1003,f999,f867,f1058]) ).
tff(f1058,plain,
( spl9_107
<=> ! [X1: $tType,X0: $tType] : ( range(X0,X1,combk(bool,product_prod(X0,X1),fFalse)) = combk(bool,X1,fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_107])]) ).
tff(f999,plain,
( spl9_96
<=> ! [X1: $tType,X0: $tType] : ( bot_bot(fun(X1,bool)) = range(X0,X1,bot_bot(fun(product_prod(X0,X1),bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_96])]) ).
tff(f1003,plain,
( ! [X1: $tType,X0: $tType] : ( range(X0,X1,combk(bool,product_prod(X0,X1),fFalse)) = combk(bool,X1,fFalse) )
| ~ spl9_75
| ~ spl9_96 ),
inference(forward_demodulation,[],[f1002,f868]) ).
tff(f1002,plain,
( ! [X1: $tType,X0: $tType] : ( bot_bot(fun(X1,bool)) = range(X0,X1,combk(bool,product_prod(X0,X1),fFalse)) )
| ~ spl9_75
| ~ spl9_96 ),
inference(forward_demodulation,[],[f1000,f868]) ).
tff(f1000,plain,
( ! [X1: $tType,X0: $tType] : ( bot_bot(fun(X1,bool)) = range(X0,X1,bot_bot(fun(product_prod(X0,X1),bool))) )
| ~ spl9_96 ),
inference(avatar_component_clause,[],[f999]) ).
tff(f1056,plain,
( spl9_106
| ~ spl9_75
| ~ spl9_95 ),
inference(avatar_split_clause,[],[f997,f994,f867,f1054]) ).
tff(f1054,plain,
( spl9_106
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = minus_minus(fun(X0,bool),combk(bool,X0,fFalse),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_106])]) ).
tff(f994,plain,
( spl9_95
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),bot_bot(fun(X0,bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_95])]) ).
tff(f997,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = minus_minus(fun(X0,bool),combk(bool,X0,fFalse),X1) )
| ~ spl9_75
| ~ spl9_95 ),
inference(forward_demodulation,[],[f995,f868]) ).
tff(f995,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),bot_bot(fun(X0,bool)),X1) )
| ~ spl9_95 ),
inference(avatar_component_clause,[],[f994]) ).
tff(f1051,plain,
spl9_105,
inference(avatar_split_clause,[],[f495,f1049]) ).
tff(f495,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK4(X0,X1))) ),
inference(forward_demodulation,[],[f415,f376]) ).
tff(f376,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(cnf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X0: $tType,X17: fun(X0,bool)] : ( collect(X0,X17) = X17 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
tff(f415,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| pp(aa(X0,bool,X1,sK4(X0,X1))) ),
inference(cnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| pp(aa(X0,bool,X1,sK4(X0,X1))) )
& ( ! [X3: X0] : ~ pp(aa(X0,bool,X1,X3))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f300,f301]) ).
tff(f301,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X2: X0] : pp(aa(X0,bool,X1,X2))
=> pp(aa(X0,bool,X1,sK4(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f300,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| ? [X2: X0] : pp(aa(X0,bool,X1,X2)) )
& ( ! [X3: X0] : ~ pp(aa(X0,bool,X1,X3))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(rectify,[],[f299]) ).
tff(f299,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| ? [X2: X0] : pp(aa(X0,bool,X1,X2)) )
& ( ! [X2: X0] : ~ pp(aa(X0,bool,X1,X2))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(nnf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
<=> ! [X2: X0] : ~ pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X0: $tType,X17: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X17) )
<=> ! [X16: X0] : ~ pp(aa(X0,bool,X17,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_Collect__empty__eq) ).
tff(f1046,plain,
spl9_104,
inference(avatar_split_clause,[],[f493,f1044]) ).
tff(f493,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK3(X0,X1))) ),
inference(forward_demodulation,[],[f413,f376]) ).
tff(f413,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| pp(aa(X0,bool,X1,sK3(X0,X1))) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| pp(aa(X0,bool,X1,sK3(X0,X1))) )
& ( ! [X3: X0] : ~ pp(aa(X0,bool,X1,X3))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f296,f297]) ).
tff(f297,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X2: X0] : pp(aa(X0,bool,X1,X2))
=> pp(aa(X0,bool,X1,sK3(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f296,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| ? [X2: X0] : pp(aa(X0,bool,X1,X2)) )
& ( ! [X3: X0] : ~ pp(aa(X0,bool,X1,X3))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(rectify,[],[f295]) ).
tff(f295,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| ? [X2: X0] : pp(aa(X0,bool,X1,X2)) )
& ( ! [X2: X0] : ~ pp(aa(X0,bool,X1,X2))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ) ),
inference(nnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
<=> ! [X2: X0] : ~ pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X0: $tType,X17: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X17) )
<=> ! [X16: X0] : ~ pp(aa(X0,bool,X17,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_empty__Collect__eq) ).
tff(f1042,plain,
spl9_103,
inference(avatar_split_clause,[],[f452,f1040]) ).
tff(f1040,plain,
( spl9_103
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0)))
| ~ total_on(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_103])]) ).
tff(f452,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0)))
| ~ total_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f325]) ).
tff(f325,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( total_on(X0,X2,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0)))
| ~ total_on(X0,X2,X1) )
& ( total_on(X0,X2,X1)
| ~ total_on(X0,X2,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0))) ) ),
inference(nnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( total_on(X0,X2,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0)))
<=> total_on(X0,X2,X1) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X0: $tType,X3: fun(product_prod(X0,X0),bool),X4: fun(X0,bool)] :
( total_on(X0,X4,minus_minus(fun(product_prod(X0,X0),bool),X3,id(X0)))
<=> total_on(X0,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_total__on__diff__Id) ).
tff(f1038,plain,
spl9_102,
inference(avatar_split_clause,[],[f451,f1036]) ).
tff(f1036,plain,
( spl9_102
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| ~ total_on(X0,X2,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_102])]) ).
tff(f451,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| ~ total_on(X0,X2,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0))) ),
inference(cnf_transformation,[],[f325]) ).
tff(f1031,plain,
spl9_101,
inference(avatar_split_clause,[],[f449,f1029]) ).
tff(f1029,plain,
( spl9_101
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_101])]) ).
tff(f449,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ),
inference(cnf_transformation,[],[f324]) ).
tff(f1024,plain,
( spl9_100
| ~ spl9_99 ),
inference(avatar_split_clause,[],[f1020,f1017,f1022]) ).
tff(f1022,plain,
( spl9_100
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_100])]) ).
tff(f1017,plain,
( spl9_99
<=> ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_99])]) ).
tff(f1020,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl9_99 ),
inference(forward_demodulation,[],[f1018,f479]) ).
tff(f1018,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl9_99 ),
inference(avatar_component_clause,[],[f1017]) ).
tff(f1019,plain,
spl9_99,
inference(avatar_split_clause,[],[f393,f1017]) ).
tff(f393,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(cnf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(rectify,[],[f119]) ).
tff(f119,axiom,
! [X34: bool,X32: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X32),X34))
| ~ pp(X34)
| ~ pp(X32) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
tff(f1013,plain,
spl9_98,
inference(avatar_split_clause,[],[f388,f1011]) ).
tff(f388,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),X1,top_top(fun(X0,bool))) ),
inference(cnf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),X1,top_top(fun(X0,bool))) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X0: $tType,X4: fun(X0,bool)] : ( minus_minus(fun(X0,bool),X4,top_top(fun(X0,bool))) = bot_bot(fun(X0,bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_Diff__UNIV) ).
tff(f1007,plain,
spl9_97,
inference(avatar_split_clause,[],[f387,f1005]) ).
tff(f387,plain,
! [X1: $tType,X0: $tType] : ( bot_bot(fun(X1,bool)) = domain(X1,X0,bot_bot(fun(product_prod(X1,X0),bool))) ),
inference(cnf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType,X1: $tType] : ( bot_bot(fun(X1,bool)) = domain(X1,X0,bot_bot(fun(product_prod(X1,X0),bool))) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X1: $tType,X0: $tType] : ( bot_bot(fun(X0,bool)) = domain(X0,X1,bot_bot(fun(product_prod(X0,X1),bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_Domain__empty) ).
tff(f1001,plain,
spl9_96,
inference(avatar_split_clause,[],[f386,f999]) ).
tff(f386,plain,
! [X1: $tType,X0: $tType] : ( bot_bot(fun(X1,bool)) = range(X0,X1,bot_bot(fun(product_prod(X0,X1),bool))) ),
inference(cnf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: $tType,X1: $tType] : ( bot_bot(fun(X1,bool)) = range(X0,X1,bot_bot(fun(product_prod(X0,X1),bool))) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X1: $tType,X0: $tType] : ( bot_bot(fun(X0,bool)) = range(X1,X0,bot_bot(fun(product_prod(X1,X0),bool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_Range__empty) ).
tff(f996,plain,
spl9_95,
inference(avatar_split_clause,[],[f385,f994]) ).
tff(f385,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),bot_bot(fun(X0,bool)),X1) ),
inference(cnf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),bot_bot(fun(X0,bool)),X1) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X0: $tType,X4: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),bot_bot(fun(X0,bool)),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_empty__Diff) ).
tff(f992,plain,
( spl9_94
| ~ spl9_5
| ~ spl9_47
| ~ spl9_75
| ~ spl9_79 ),
inference(avatar_split_clause,[],[f920,f897,f867,f709,f518,f989]) ).
tff(f989,plain,
( spl9_94
<=> ( fFalse = bot_bot(bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_94])]) ).
tff(f518,plain,
( spl9_5
<=> bot(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).
tff(f709,plain,
( spl9_47
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_47])]) ).
tff(f897,plain,
( spl9_79
<=> ! [X1: $tType,X0: $tType,X2: X0] :
( ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) )
| ~ bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_79])]) ).
tff(f920,plain,
( ( fFalse = bot_bot(bool) )
| ~ spl9_5
| ~ spl9_47
| ~ spl9_75
| ~ spl9_79 ),
inference(forward_demodulation,[],[f919,f710]) ).
tff(f710,plain,
( ! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 )
| ~ spl9_47 ),
inference(avatar_component_clause,[],[f709]) ).
tff(f919,plain,
( ! [X0: $tType,X1: X0] : ( bot_bot(bool) = aa(X0,bool,combk(bool,X0,fFalse),X1) )
| ~ spl9_5
| ~ spl9_75
| ~ spl9_79 ),
inference(forward_demodulation,[],[f917,f868]) ).
tff(f917,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,bool,bot_bot(fun(X0,bool)),X1) = bot_bot(bool) )
| ~ spl9_5
| ~ spl9_79 ),
inference(resolution,[],[f898,f520]) ).
tff(f520,plain,
( bot(bool)
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f518]) ).
tff(f898,plain,
( ! [X1: $tType,X0: $tType,X2: X0] :
( ~ bot(X1)
| ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) ) )
| ~ spl9_79 ),
inference(avatar_component_clause,[],[f897]) ).
tff(f978,plain,
spl9_93,
inference(avatar_split_clause,[],[f459,f976]) ).
tff(f976,plain,
( spl9_93
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X0,X0),bool),X2: fun(product_prod(X1,X1),bool)] :
( trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
| ~ trans(X1,X2)
| ~ trans(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_93])]) ).
tff(f459,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
( trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
| ~ trans(X1,X2)
| ~ trans(X0,X3) ),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
( trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
| ~ trans(X1,X2)
| ~ trans(X0,X3) ),
inference(flattening,[],[f260]) ).
tff(f260,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
( trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
| ~ trans(X1,X2)
| ~ trans(X0,X3) ),
inference(ennf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
( trans(X0,X3)
=> ( trans(X1,X2)
=> trans(product_prod(X0,X1),lex_prod(X0,X1,X3,X2)) ) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X0: $tType,X1: $tType,X19: fun(product_prod(X1,X1),bool),X20: fun(product_prod(X0,X0),bool)] :
( trans(X0,X20)
=> ( trans(X1,X19)
=> trans(product_prod(X0,X1),lex_prod(X0,X1,X20,X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_trans__lex__prod) ).
tff(f974,plain,
spl9_92,
inference(avatar_split_clause,[],[f458,f972]) ).
tff(f972,plain,
( spl9_92
<=> ! [X1: $tType,X0: $tType,X3: fun(product_prod(X0,X0),bool),X2: fun(product_prod(X1,X1),bool)] :
( wf(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
| ~ wf(X1,X2)
| ~ wf(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_92])]) ).
tff(f458,plain,
! [X1: $tType,X0: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
( wf(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
| ~ wf(X1,X2)
| ~ wf(X0,X3) ),
inference(cnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
( wf(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
| ~ wf(X1,X2)
| ~ wf(X0,X3) ),
inference(flattening,[],[f258]) ).
tff(f258,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
( wf(product_prod(X0,X1),lex_prod(X0,X1,X3,X2))
| ~ wf(X1,X2)
| ~ wf(X0,X3) ),
inference(ennf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: $tType,X1: $tType,X2: fun(product_prod(X1,X1),bool),X3: fun(product_prod(X0,X0),bool)] :
( wf(X0,X3)
=> ( wf(X1,X2)
=> wf(product_prod(X0,X1),lex_prod(X0,X1,X3,X2)) ) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X0: $tType,X1: $tType,X21: fun(product_prod(X1,X1),bool),X22: fun(product_prod(X0,X0),bool)] :
( wf(X0,X22)
=> ( wf(X1,X21)
=> wf(product_prod(X0,X1),lex_prod(X0,X1,X22,X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_wf__lex__prod) ).
tff(f970,plain,
spl9_91,
inference(avatar_split_clause,[],[f448,f968]) ).
tff(f968,plain,
( spl9_91
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( irrefl(X0,X1)
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_91])]) ).
tff(f448,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( irrefl(X0,X1)
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ),
inference(cnf_transformation,[],[f324]) ).
tff(f966,plain,
spl9_90,
inference(avatar_split_clause,[],[f447,f964]) ).
tff(f964,plain,
( spl9_90
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_90])]) ).
tff(f447,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ~ pp(aa(fun(product_prod(X0,X0),bool),bool,order_215145569der_on(X0,X2),X1)) ),
inference(cnf_transformation,[],[f324]) ).
tff(f962,plain,
spl9_89,
inference(avatar_split_clause,[],[f436,f960]) ).
tff(f960,plain,
( spl9_89
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( wf(X0,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0)))
| ~ order_well_order_on(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_89])]) ).
tff(f436,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( wf(X0,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0)))
| ~ order_well_order_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f257]) ).
tff(f257,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( wf(X0,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0)))
& order_1409979114der_on(X0,X2,X1) )
| ~ order_well_order_on(X0,X2,X1) ),
inference(ennf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( order_well_order_on(X0,X2,X1)
=> ( wf(X0,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0)))
& order_1409979114der_on(X0,X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f195]) ).
tff(f195,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( order_well_order_on(X0,X2,X1)
<=> ( wf(X0,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0)))
& order_1409979114der_on(X0,X2,X1) ) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType,X3: fun(product_prod(X0,X0),bool),X4: fun(X0,bool)] :
( order_well_order_on(X0,X4,X3)
<=> ( wf(X0,minus_minus(fun(product_prod(X0,X0),bool),X3,id(X0)))
& order_1409979114der_on(X0,X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_well__order__on__def) ).
tff(f956,plain,
( spl9_88
| ~ spl9_75
| ~ spl9_87 ),
inference(avatar_split_clause,[],[f950,f947,f867,f954]) ).
tff(f954,plain,
( spl9_88
<=> ! [X0: $tType,X1: fun(X0,bool),X3: X0] :
( ( combk(bool,X0,fFalse) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_88])]) ).
tff(f947,plain,
( spl9_87
<=> ! [X0: $tType,X1: fun(X0,bool),X3: X0] :
( ( bot_bot(fun(X0,bool)) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_87])]) ).
tff(f950,plain,
( ! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) )
| ~ spl9_75
| ~ spl9_87 ),
inference(forward_demodulation,[],[f948,f868]) ).
tff(f948,plain,
( ! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) )
| ~ spl9_87 ),
inference(avatar_component_clause,[],[f947]) ).
tff(f949,plain,
spl9_87,
inference(avatar_split_clause,[],[f494,f947]) ).
tff(f494,plain,
! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) ),
inference(forward_demodulation,[],[f412,f376]) ).
tff(f412,plain,
! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
( ~ pp(aa(X0,bool,X1,X3))
| ( bot_bot(fun(X0,bool)) != collect(X0,X1) ) ),
inference(cnf_transformation,[],[f298]) ).
tff(f943,plain,
( spl9_86
| ~ spl9_85 ),
inference(avatar_split_clause,[],[f939,f936,f941]) ).
tff(f941,plain,
( spl9_86
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_86])]) ).
tff(f936,plain,
( spl9_85
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_85])]) ).
tff(f939,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) )
| ~ spl9_85 ),
inference(forward_demodulation,[],[f937,f479]) ).
tff(f937,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl9_85 ),
inference(avatar_component_clause,[],[f936]) ).
tff(f938,plain,
spl9_85,
inference(avatar_split_clause,[],[f395,f936]) ).
tff(f395,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f121]) ).
tff(f121,axiom,
! [X34: bool,X32: bool] :
( pp(X34)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X32),X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
tff(f932,plain,
( spl9_84
| ~ spl9_83 ),
inference(avatar_split_clause,[],[f928,f925,f930]) ).
tff(f930,plain,
( spl9_84
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_84])]) ).
tff(f925,plain,
( spl9_83
<=> ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_83])]) ).
tff(f928,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) )
| ~ spl9_83 ),
inference(forward_demodulation,[],[f926,f479]) ).
tff(f926,plain,
( ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl9_83 ),
inference(avatar_component_clause,[],[f925]) ).
tff(f927,plain,
spl9_83,
inference(avatar_split_clause,[],[f394,f925]) ).
tff(f394,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f120]) ).
tff(f120,axiom,
! [X34: bool,X32: bool] :
( pp(X32)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X32),X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
tff(f916,plain,
( spl9_82
| ~ spl9_4
| ~ spl9_47
| ~ spl9_72
| ~ spl9_78 ),
inference(avatar_split_clause,[],[f911,f893,f844,f709,f513,f913]) ).
tff(f913,plain,
( spl9_82
<=> ( fTrue = top_top(bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_82])]) ).
tff(f513,plain,
( spl9_4
<=> top(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
tff(f893,plain,
( spl9_78
<=> ! [X1: $tType,X0: $tType,X2: X0] :
( ( aa(X0,X1,top_top(fun(X0,X1)),X2) = top_top(X1) )
| ~ top(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_78])]) ).
tff(f911,plain,
( ( fTrue = top_top(bool) )
| ~ spl9_4
| ~ spl9_47
| ~ spl9_72
| ~ spl9_78 ),
inference(forward_demodulation,[],[f910,f710]) ).
tff(f910,plain,
( ! [X0: $tType,X1: X0] : ( top_top(bool) = aa(X0,bool,combk(bool,X0,fTrue),X1) )
| ~ spl9_4
| ~ spl9_72
| ~ spl9_78 ),
inference(forward_demodulation,[],[f908,f845]) ).
tff(f908,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,bool,top_top(fun(X0,bool)),X1) = top_top(bool) )
| ~ spl9_4
| ~ spl9_78 ),
inference(resolution,[],[f894,f515]) ).
tff(f515,plain,
( top(bool)
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f513]) ).
tff(f894,plain,
( ! [X1: $tType,X0: $tType,X2: X0] :
( ~ top(X1)
| ( aa(X0,X1,top_top(fun(X0,X1)),X2) = top_top(X1) ) )
| ~ spl9_78 ),
inference(avatar_component_clause,[],[f893]) ).
tff(f907,plain,
( spl9_81
| ~ spl9_75
| ~ spl9_77 ),
inference(avatar_split_clause,[],[f891,f888,f867,f905]) ).
tff(f905,plain,
( spl9_81
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( minus_minus(fun(X0,bool),X1,combk(bool,X0,fFalse)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_81])]) ).
tff(f888,plain,
( spl9_77
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( minus_minus(fun(X0,bool),X1,bot_bot(fun(X0,bool))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_77])]) ).
tff(f891,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( minus_minus(fun(X0,bool),X1,combk(bool,X0,fFalse)) = X1 )
| ~ spl9_75
| ~ spl9_77 ),
inference(forward_demodulation,[],[f889,f868]) ).
tff(f889,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( minus_minus(fun(X0,bool),X1,bot_bot(fun(X0,bool))) = X1 )
| ~ spl9_77 ),
inference(avatar_component_clause,[],[f888]) ).
tff(f903,plain,
( spl9_80
| ~ spl9_75
| ~ spl9_76 ),
inference(avatar_split_clause,[],[f886,f883,f867,f901]) ).
tff(f901,plain,
( spl9_80
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = minus_minus(fun(X0,bool),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_80])]) ).
tff(f883,plain,
( spl9_76
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_76])]) ).
tff(f886,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = minus_minus(fun(X0,bool),X1,X1) )
| ~ spl9_75
| ~ spl9_76 ),
inference(forward_demodulation,[],[f884,f868]) ).
tff(f884,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),X1,X1) )
| ~ spl9_76 ),
inference(avatar_component_clause,[],[f883]) ).
tff(f899,plain,
spl9_79,
inference(avatar_split_clause,[],[f403,f897]) ).
tff(f403,plain,
! [X1: $tType,X0: $tType,X2: X0] :
( ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) )
| ~ bot(X1) ),
inference(cnf_transformation,[],[f245]) ).
tff(f245,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: X0] : ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) )
| ~ bot(X1) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType,X1: $tType] :
( bot(X1)
=> ! [X2: X0] : ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) ) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X1: $tType,X0: $tType] :
( bot(X0)
=> ! [X7: X1] : ( aa(X1,X0,bot_bot(fun(X1,X0)),X7) = bot_bot(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_bot__apply) ).
tff(f895,plain,
spl9_78,
inference(avatar_split_clause,[],[f401,f893]) ).
tff(f401,plain,
! [X1: $tType,X0: $tType,X2: X0] :
( ( aa(X0,X1,top_top(fun(X0,X1)),X2) = top_top(X1) )
| ~ top(X1) ),
inference(cnf_transformation,[],[f243]) ).
tff(f243,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: X0] : ( aa(X0,X1,top_top(fun(X0,X1)),X2) = top_top(X1) )
| ~ top(X1) ),
inference(ennf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: $tType,X1: $tType] :
( top(X1)
=> ! [X2: X0] : ( aa(X0,X1,top_top(fun(X0,X1)),X2) = top_top(X1) ) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X1: $tType,X0: $tType] :
( top(X0)
=> ! [X7: X1] : ( aa(X1,X0,top_top(fun(X1,X0)),X7) = top_top(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_top__apply) ).
tff(f890,plain,
spl9_77,
inference(avatar_split_clause,[],[f384,f888]) ).
tff(f384,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( minus_minus(fun(X0,bool),X1,bot_bot(fun(X0,bool))) = X1 ),
inference(cnf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( minus_minus(fun(X0,bool),X1,bot_bot(fun(X0,bool))) = X1 ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X0: $tType,X4: fun(X0,bool)] : ( minus_minus(fun(X0,bool),X4,bot_bot(fun(X0,bool))) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_Diff__empty) ).
tff(f885,plain,
spl9_76,
inference(avatar_split_clause,[],[f383,f883]) ).
tff(f383,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),X1,X1) ),
inference(cnf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),X1,X1) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X0: $tType,X4: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = minus_minus(fun(X0,bool),X4,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Diff__cancel) ).
tff(f869,plain,
( spl9_75
| ~ spl9_24
| ~ spl9_74 ),
inference(avatar_split_clause,[],[f865,f862,f601,f867]) ).
tff(f601,plain,
( spl9_24
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_24])]) ).
tff(f862,plain,
( spl9_74
<=> ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_74])]) ).
tff(f865,plain,
( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse) )
| ~ spl9_24
| ~ spl9_74 ),
inference(forward_demodulation,[],[f863,f602]) ).
tff(f602,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 )
| ~ spl9_24 ),
inference(avatar_component_clause,[],[f601]) ).
tff(f863,plain,
( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) )
| ~ spl9_74 ),
inference(avatar_component_clause,[],[f862]) ).
tff(f864,plain,
spl9_74,
inference(avatar_split_clause,[],[f357,f862]) ).
tff(f357,plain,
! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ),
inference(cnf_transformation,[],[f34]) ).
tff(f34,axiom,
! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_empty__def) ).
tff(f860,plain,
( spl9_73
| ~ spl9_20
| ~ spl9_72 ),
inference(avatar_split_clause,[],[f847,f844,f584,f858]) ).
tff(f584,plain,
( spl9_20
<=> ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ( fFalse = aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_20])]) ).
tff(f847,plain,
( ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ( fFalse = aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,combk(bool,arrow_411405190le_alt,fTrue)),X0) )
| ~ spl9_20
| ~ spl9_72 ),
inference(superposition,[],[f585,f845]) ).
tff(f585,plain,
( ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ( fFalse = aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),X0) )
| ~ spl9_20 ),
inference(avatar_component_clause,[],[f584]) ).
tff(f846,plain,
( spl9_72
| ~ spl9_24
| ~ spl9_71 ),
inference(avatar_split_clause,[],[f842,f839,f601,f844]) ).
tff(f839,plain,
( spl9_71
<=> ! [X0: $tType] : ( top_top(fun(X0,bool)) = collect(X0,combk(bool,X0,fTrue)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_71])]) ).
tff(f842,plain,
( ! [X0: $tType] : ( top_top(fun(X0,bool)) = combk(bool,X0,fTrue) )
| ~ spl9_24
| ~ spl9_71 ),
inference(forward_demodulation,[],[f840,f602]) ).
tff(f840,plain,
( ! [X0: $tType] : ( top_top(fun(X0,bool)) = collect(X0,combk(bool,X0,fTrue)) )
| ~ spl9_71 ),
inference(avatar_component_clause,[],[f839]) ).
tff(f841,plain,
spl9_71,
inference(avatar_split_clause,[],[f356,f839]) ).
tff(f356,plain,
! [X0: $tType] : ( top_top(fun(X0,bool)) = collect(X0,combk(bool,X0,fTrue)) ),
inference(cnf_transformation,[],[f13]) ).
tff(f13,axiom,
! [X0: $tType] : ( top_top(fun(X0,bool)) = collect(X0,combk(bool,X0,fTrue)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_UNIV__def) ).
tff(f827,plain,
( spl9_70
| ~ spl9_63 ),
inference(avatar_split_clause,[],[f799,f796,f825]) ).
tff(f825,plain,
( spl9_70
<=> ! [X0: $tType] : order_1409979114der_on(X0,bot_bot(fun(X0,bool)),id_on(X0,bot_bot(fun(X0,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_70])]) ).
tff(f796,plain,
( spl9_63
<=> ! [X0: $tType] : order_1409979114der_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_63])]) ).
tff(f799,plain,
( ! [X0: $tType] : order_1409979114der_on(X0,bot_bot(fun(X0,bool)),id_on(X0,bot_bot(fun(X0,bool))))
| ~ spl9_63 ),
inference(forward_demodulation,[],[f797,f358]) ).
tff(f797,plain,
( ! [X0: $tType] : order_1409979114der_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool)))
| ~ spl9_63 ),
inference(avatar_component_clause,[],[f796]) ).
tff(f823,plain,
( spl9_69
| ~ spl9_38
| ~ spl9_56 ),
inference(avatar_split_clause,[],[f783,f748,f663,f821]) ).
tff(f821,plain,
( spl9_69
<=> ! [X0: $tType,X1: fun(X0,bool)] : total_on(X0,X1,sK7(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_69])]) ).
tff(f663,plain,
( spl9_38
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| ~ order_1409979114der_on(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_38])]) ).
tff(f783,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : total_on(X0,X1,sK7(X0,X1))
| ~ spl9_38
| ~ spl9_56 ),
inference(resolution,[],[f749,f664]) ).
tff(f664,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( ~ order_1409979114der_on(X0,X2,X1)
| total_on(X0,X2,X1) )
| ~ spl9_38 ),
inference(avatar_component_clause,[],[f663]) ).
tff(f819,plain,
( spl9_68
| ~ spl9_62 ),
inference(avatar_split_clause,[],[f794,f791,f817]) ).
tff(f817,plain,
( spl9_68
<=> ! [X0: $tType] : order_well_order_on(X0,bot_bot(fun(X0,bool)),id_on(X0,bot_bot(fun(X0,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_68])]) ).
tff(f791,plain,
( spl9_62
<=> ! [X0: $tType] : order_well_order_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_62])]) ).
tff(f794,plain,
( ! [X0: $tType] : order_well_order_on(X0,bot_bot(fun(X0,bool)),id_on(X0,bot_bot(fun(X0,bool))))
| ~ spl9_62 ),
inference(forward_demodulation,[],[f792,f358]) ).
tff(f792,plain,
( ! [X0: $tType] : order_well_order_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool)))
| ~ spl9_62 ),
inference(avatar_component_clause,[],[f791]) ).
tff(f815,plain,
( spl9_67
| ~ spl9_61 ),
inference(avatar_split_clause,[],[f789,f786,f813]) ).
tff(f813,plain,
( spl9_67
<=> ! [X0: $tType] : refl_on(X0,bot_bot(fun(X0,bool)),id_on(X0,bot_bot(fun(X0,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_67])]) ).
tff(f786,plain,
( spl9_61
<=> ! [X0: $tType] : refl_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_61])]) ).
tff(f789,plain,
( ! [X0: $tType] : refl_on(X0,bot_bot(fun(X0,bool)),id_on(X0,bot_bot(fun(X0,bool))))
| ~ spl9_61 ),
inference(forward_demodulation,[],[f787,f358]) ).
tff(f787,plain,
( ! [X0: $tType] : refl_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool)))
| ~ spl9_61 ),
inference(avatar_component_clause,[],[f786]) ).
tff(f811,plain,
( spl9_66
| ~ spl9_60 ),
inference(avatar_split_clause,[],[f782,f779,f809]) ).
tff(f809,plain,
( spl9_66
<=> ! [X0: $tType] : order_915043626der_on(X0,bot_bot(fun(X0,bool)),id_on(X0,bot_bot(fun(X0,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_66])]) ).
tff(f779,plain,
( spl9_60
<=> ! [X0: $tType] : order_915043626der_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_60])]) ).
tff(f782,plain,
( ! [X0: $tType] : order_915043626der_on(X0,bot_bot(fun(X0,bool)),id_on(X0,bot_bot(fun(X0,bool))))
| ~ spl9_60 ),
inference(forward_demodulation,[],[f780,f358]) ).
tff(f780,plain,
( ! [X0: $tType] : order_915043626der_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool)))
| ~ spl9_60 ),
inference(avatar_component_clause,[],[f779]) ).
tff(f807,plain,
( spl9_65
| ~ spl9_59 ),
inference(avatar_split_clause,[],[f777,f774,f805]) ).
tff(f805,plain,
( spl9_65
<=> ! [X0: $tType] : order_preorder_on(X0,bot_bot(fun(X0,bool)),id_on(X0,bot_bot(fun(X0,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_65])]) ).
tff(f774,plain,
( spl9_59
<=> ! [X0: $tType] : order_preorder_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_59])]) ).
tff(f777,plain,
( ! [X0: $tType] : order_preorder_on(X0,bot_bot(fun(X0,bool)),id_on(X0,bot_bot(fun(X0,bool))))
| ~ spl9_59 ),
inference(forward_demodulation,[],[f775,f358]) ).
tff(f775,plain,
( ! [X0: $tType] : order_preorder_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool)))
| ~ spl9_59 ),
inference(avatar_component_clause,[],[f774]) ).
tff(f803,plain,
spl9_64,
inference(avatar_split_clause,[],[f439,f801]) ).
tff(f801,plain,
( spl9_64
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( order_1409979114der_on(X0,X2,X1)
| ~ total_on(X0,X2,X1)
| ~ order_915043626der_on(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_64])]) ).
tff(f439,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( order_1409979114der_on(X0,X2,X1)
| ~ total_on(X0,X2,X1)
| ~ order_915043626der_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f318]) ).
tff(f318,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( order_1409979114der_on(X0,X2,X1)
| ~ total_on(X0,X2,X1)
| ~ order_915043626der_on(X0,X2,X1) )
& ( ( total_on(X0,X2,X1)
& order_915043626der_on(X0,X2,X1) )
| ~ order_1409979114der_on(X0,X2,X1) ) ),
inference(flattening,[],[f317]) ).
tff(f317,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( order_1409979114der_on(X0,X2,X1)
| ~ total_on(X0,X2,X1)
| ~ order_915043626der_on(X0,X2,X1) )
& ( ( total_on(X0,X2,X1)
& order_915043626der_on(X0,X2,X1) )
| ~ order_1409979114der_on(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( order_1409979114der_on(X0,X2,X1)
<=> ( total_on(X0,X2,X1)
& order_915043626der_on(X0,X2,X1) ) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X0: $tType,X3: fun(product_prod(X0,X0),bool),X4: fun(X0,bool)] :
( order_1409979114der_on(X0,X4,X3)
<=> ( total_on(X0,X4,X3)
& order_915043626der_on(X0,X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_linear__order__on__def) ).
tff(f798,plain,
spl9_63,
inference(avatar_split_clause,[],[f355,f796]) ).
tff(f355,plain,
! [X0: $tType] : order_1409979114der_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool))),
inference(cnf_transformation,[],[f40]) ).
tff(f40,axiom,
! [X0: $tType] : order_1409979114der_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_lnear__order__on__empty) ).
tff(f793,plain,
spl9_62,
inference(avatar_split_clause,[],[f354,f791]) ).
tff(f354,plain,
! [X0: $tType] : order_well_order_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool))),
inference(cnf_transformation,[],[f41]) ).
tff(f41,axiom,
! [X0: $tType] : order_well_order_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_well__order__on__empty) ).
tff(f788,plain,
spl9_61,
inference(avatar_split_clause,[],[f353,f786]) ).
tff(f353,plain,
! [X0: $tType] : refl_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool))),
inference(cnf_transformation,[],[f55]) ).
tff(f55,axiom,
! [X0: $tType] : refl_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_refl__on__empty) ).
tff(f781,plain,
spl9_60,
inference(avatar_split_clause,[],[f352,f779]) ).
tff(f352,plain,
! [X0: $tType] : order_915043626der_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool))),
inference(cnf_transformation,[],[f57]) ).
tff(f57,axiom,
! [X0: $tType] : order_915043626der_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_partial__order__on__empty) ).
tff(f776,plain,
spl9_59,
inference(avatar_split_clause,[],[f351,f774]) ).
tff(f351,plain,
! [X0: $tType] : order_preorder_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool))),
inference(cnf_transformation,[],[f66]) ).
tff(f66,axiom,
! [X0: $tType] : order_preorder_on(X0,bot_bot(fun(X0,bool)),bot_bot(fun(product_prod(X0,X0),bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_preorder__on__empty) ).
tff(f772,plain,
spl9_58,
inference(avatar_split_clause,[],[f350,f770]) ).
tff(f770,plain,
( spl9_58
<=> ! [X0: $tType] : ( top_top(fun(X0,bool)) = domain(X0,X0,id(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_58])]) ).
tff(f350,plain,
! [X0: $tType] : ( top_top(fun(X0,bool)) = domain(X0,X0,id(X0)) ),
inference(cnf_transformation,[],[f49]) ).
tff(f49,axiom,
! [X0: $tType] : ( top_top(fun(X0,bool)) = domain(X0,X0,id(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_Domain__Id) ).
tff(f768,plain,
spl9_57,
inference(avatar_split_clause,[],[f349,f766]) ).
tff(f766,plain,
( spl9_57
<=> ! [X0: $tType] : ( top_top(fun(X0,bool)) = range(X0,X0,id(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_57])]) ).
tff(f349,plain,
! [X0: $tType] : ( top_top(fun(X0,bool)) = range(X0,X0,id(X0)) ),
inference(cnf_transformation,[],[f48]) ).
tff(f48,axiom,
! [X0: $tType] : ( top_top(fun(X0,bool)) = range(X0,X0,id(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Range__Id) ).
tff(f750,plain,
( spl9_56
| ~ spl9_19
| ~ spl9_36 ),
inference(avatar_split_clause,[],[f680,f655,f576,f748]) ).
tff(f576,plain,
( spl9_19
<=> ! [X0: $tType,X1: fun(X0,bool)] : order_well_order_on(X0,X1,sK7(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_19])]) ).
tff(f655,plain,
( spl9_36
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( order_1409979114der_on(X0,X2,X1)
| ~ order_well_order_on(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_36])]) ).
tff(f680,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : order_1409979114der_on(X0,X1,sK7(X0,X1))
| ~ spl9_19
| ~ spl9_36 ),
inference(resolution,[],[f656,f577]) ).
tff(f577,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : order_well_order_on(X0,X1,sK7(X0,X1))
| ~ spl9_19 ),
inference(avatar_component_clause,[],[f576]) ).
tff(f656,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( ~ order_well_order_on(X0,X2,X1)
| order_1409979114der_on(X0,X2,X1) )
| ~ spl9_36 ),
inference(avatar_component_clause,[],[f655]) ).
tff(f746,plain,
spl9_55,
inference(avatar_split_clause,[],[f434,f744]) ).
tff(f744,plain,
( spl9_55
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( order_preorder_on(X0,X2,X1)
| ~ trans(X0,X1)
| ~ refl_on(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_55])]) ).
tff(f434,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( order_preorder_on(X0,X2,X1)
| ~ trans(X0,X1)
| ~ refl_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f316]) ).
tff(f316,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( order_preorder_on(X0,X2,X1)
| ~ trans(X0,X1)
| ~ refl_on(X0,X2,X1) )
& ( ( trans(X0,X1)
& refl_on(X0,X2,X1) )
| ~ order_preorder_on(X0,X2,X1) ) ),
inference(flattening,[],[f315]) ).
tff(f315,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( order_preorder_on(X0,X2,X1)
| ~ trans(X0,X1)
| ~ refl_on(X0,X2,X1) )
& ( ( trans(X0,X1)
& refl_on(X0,X2,X1) )
| ~ order_preorder_on(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( order_preorder_on(X0,X2,X1)
<=> ( trans(X0,X1)
& refl_on(X0,X2,X1) ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X0: $tType,X3: fun(product_prod(X0,X0),bool),X4: fun(X0,bool)] :
( order_preorder_on(X0,X4,X3)
<=> ( trans(X0,X3)
& refl_on(X0,X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_preorder__on__def) ).
tff(f742,plain,
spl9_54,
inference(avatar_split_clause,[],[f431,f740]) ).
tff(f740,plain,
( spl9_54
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( order_915043626der_on(X0,X2,X1)
| ~ antisym(X0,X1)
| ~ order_preorder_on(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_54])]) ).
tff(f431,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( order_915043626der_on(X0,X2,X1)
| ~ antisym(X0,X1)
| ~ order_preorder_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f314]) ).
tff(f314,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( order_915043626der_on(X0,X2,X1)
| ~ antisym(X0,X1)
| ~ order_preorder_on(X0,X2,X1) )
& ( ( antisym(X0,X1)
& order_preorder_on(X0,X2,X1) )
| ~ order_915043626der_on(X0,X2,X1) ) ),
inference(flattening,[],[f313]) ).
tff(f313,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( order_915043626der_on(X0,X2,X1)
| ~ antisym(X0,X1)
| ~ order_preorder_on(X0,X2,X1) )
& ( ( antisym(X0,X1)
& order_preorder_on(X0,X2,X1) )
| ~ order_915043626der_on(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( order_915043626der_on(X0,X2,X1)
<=> ( antisym(X0,X1)
& order_preorder_on(X0,X2,X1) ) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X0: $tType,X3: fun(product_prod(X0,X0),bool),X4: fun(X0,bool)] :
( order_915043626der_on(X0,X4,X3)
<=> ( antisym(X0,X3)
& order_preorder_on(X0,X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_partial__order__on__def) ).
tff(f738,plain,
spl9_53,
inference(avatar_split_clause,[],[f421,f736]) ).
tff(f736,plain,
( spl9_53
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ord_less_eq(fun(X0,bool),minus_minus(fun(X0,bool),X2,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_53])]) ).
tff(f421,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ord_less_eq(fun(X0,bool),minus_minus(fun(X0,bool),X2,X1),X2),
inference(cnf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] : ord_less_eq(fun(X0,bool),minus_minus(fun(X0,bool),X2,X1),X2),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X0: $tType,X5: fun(X0,bool),X4: fun(X0,bool)] : ord_less_eq(fun(X0,bool),minus_minus(fun(X0,bool),X4,X5),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_Diff__subset) ).
tff(f734,plain,
spl9_52,
inference(avatar_split_clause,[],[f382,f732]) ).
tff(f732,plain,
( spl9_52
<=> ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] : irrefl(X0,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_52])]) ).
tff(f382,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] : irrefl(X0,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0))),
inference(cnf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] : irrefl(X0,minus_minus(fun(product_prod(X0,X0),bool),X1,id(X0))),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType,X3: fun(product_prod(X0,X0),bool)] : irrefl(X0,minus_minus(fun(product_prod(X0,X0),bool),X3,id(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_irrefl__diff__Id) ).
tff(f730,plain,
spl9_51,
inference(avatar_split_clause,[],[f369,f728]) ).
tff(f728,plain,
( spl9_51
<=> ! [X0: $tType,X1: X0] :
( ( bot_bot(X0) = X1 )
| ~ ord_less_eq(X0,X1,bot_bot(X0))
| ~ bot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_51])]) ).
tff(f369,plain,
! [X0: $tType,X1: X0] :
( ( bot_bot(X0) = X1 )
| ~ ord_less_eq(X0,X1,bot_bot(X0))
| ~ bot(X0) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( bot_bot(X0) = X1 )
| ~ ord_less_eq(X0,X1,bot_bot(X0)) )
| ~ bot(X0) ),
inference(ennf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: $tType] :
( bot(X0)
=> ! [X1: X0] :
( ord_less_eq(X0,X1,bot_bot(X0))
=> ( bot_bot(X0) = X1 ) ) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X0: $tType] :
( bot(X0)
=> ! [X26: X0] :
( ord_less_eq(X0,X26,bot_bot(X0))
=> ( bot_bot(X0) = X26 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_le__bot) ).
tff(f726,plain,
spl9_50,
inference(avatar_split_clause,[],[f365,f724]) ).
tff(f724,plain,
( spl9_50
<=> ! [X0: $tType,X1: X0] :
( ( top_top(X0) = X1 )
| ~ ord_less_eq(X0,top_top(X0),X1)
| ~ top(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_50])]) ).
tff(f365,plain,
! [X0: $tType,X1: X0] :
( ( top_top(X0) = X1 )
| ~ ord_less_eq(X0,top_top(X0),X1)
| ~ top(X0) ),
inference(cnf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( top_top(X0) = X1 )
| ~ ord_less_eq(X0,top_top(X0),X1) )
| ~ top(X0) ),
inference(ennf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: $tType] :
( top(X0)
=> ! [X1: X0] :
( ord_less_eq(X0,top_top(X0),X1)
=> ( top_top(X0) = X1 ) ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X0: $tType] :
( top(X0)
=> ! [X26: X0] :
( ord_less_eq(X0,top_top(X0),X26)
=> ( top_top(X0) = X26 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_top__le) ).
tff(f722,plain,
spl9_49,
inference(avatar_split_clause,[],[f348,f720]) ).
tff(f720,plain,
( spl9_49
<=> ! [X0: $tType] : ( top_top(fun(X0,bool)) != bot_bot(fun(X0,bool)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_49])]) ).
tff(f348,plain,
! [X0: $tType] : ( top_top(fun(X0,bool)) != bot_bot(fun(X0,bool)) ),
inference(cnf_transformation,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType] : ( top_top(fun(X0,bool)) != bot_bot(fun(X0,bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_UNIV__not__empty) ).
tff(f718,plain,
spl9_48,
inference(avatar_split_clause,[],[f333,f715]) ).
tff(f715,plain,
( spl9_48
<=> wf(arrow_411405190le_alt,minus_minus(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),r,id(arrow_411405190le_alt))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_48])]) ).
tff(f333,plain,
wf(arrow_411405190le_alt,minus_minus(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),r,id(arrow_411405190le_alt))),
inference(cnf_transformation,[],[f125]) ).
tff(f125,axiom,
wf(arrow_411405190le_alt,minus_minus(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),r,id(arrow_411405190le_alt))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f711,plain,
spl9_47,
inference(avatar_split_clause,[],[f455,f709]) ).
tff(f455,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(cnf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(rectify,[],[f115]) ).
tff(f115,axiom,
! [X1: $tType,X0: $tType,X34: X1,X32: X0] : ( aa(X1,X0,combk(X0,X1,X32),X34) = X32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
tff(f707,plain,
spl9_46,
inference(avatar_split_clause,[],[f381,f705]) ).
tff(f705,plain,
( spl9_46
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( domain(X0,X0,id_on(X0,X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_46])]) ).
tff(f381,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( domain(X0,X0,id_on(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( domain(X0,X0,id_on(X0,X1)) = X1 ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X0: $tType,X4: fun(X0,bool)] : ( domain(X0,X0,id_on(X0,X4)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Domain__Id__on) ).
tff(f702,plain,
spl9_45,
inference(avatar_split_clause,[],[f380,f700]) ).
tff(f700,plain,
( spl9_45
<=> ! [X0: $tType,X1: fun(X0,bool)] : ord_less_eq(fun(X0,bool),bot_bot(fun(X0,bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_45])]) ).
tff(f380,plain,
! [X0: $tType,X1: fun(X0,bool)] : ord_less_eq(fun(X0,bool),bot_bot(fun(X0,bool)),X1),
inference(cnf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: $tType,X1: fun(X0,bool)] : ord_less_eq(fun(X0,bool),bot_bot(fun(X0,bool)),X1),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X0: $tType,X4: fun(X0,bool)] : ord_less_eq(fun(X0,bool),bot_bot(fun(X0,bool)),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_empty__subsetI) ).
tff(f698,plain,
spl9_44,
inference(avatar_split_clause,[],[f379,f696]) ).
tff(f696,plain,
( spl9_44
<=> ! [X0: $tType,X1: fun(X0,bool)] : ord_less_eq(fun(X0,bool),X1,top_top(fun(X0,bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_44])]) ).
tff(f379,plain,
! [X0: $tType,X1: fun(X0,bool)] : ord_less_eq(fun(X0,bool),X1,top_top(fun(X0,bool))),
inference(cnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: $tType,X1: fun(X0,bool)] : ord_less_eq(fun(X0,bool),X1,top_top(fun(X0,bool))),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X0: $tType,X4: fun(X0,bool)] : ord_less_eq(fun(X0,bool),X4,top_top(fun(X0,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_subset__UNIV) ).
tff(f694,plain,
spl9_43,
inference(avatar_split_clause,[],[f378,f692]) ).
tff(f692,plain,
( spl9_43
<=> ! [X0: $tType,X1: X0] : pp(aa(X0,bool,top_top(fun(X0,bool)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_43])]) ).
tff(f378,plain,
! [X0: $tType,X1: X0] : pp(aa(X0,bool,top_top(fun(X0,bool)),X1)),
inference(cnf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: $tType,X1: X0] : pp(aa(X0,bool,top_top(fun(X0,bool)),X1)),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType,X7: X0] : pp(aa(X0,bool,top_top(fun(X0,bool)),X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_top1I) ).
tff(f690,plain,
( spl9_41
| ~ spl9_42
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f582,f548,f687,f684]) ).
tff(f684,plain,
( spl9_41
<=> ! [X0: bool] : ( fFalse = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_41])]) ).
tff(f687,plain,
( spl9_42
<=> ( fTrue = fFalse ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_42])]) ).
tff(f582,plain,
( ! [X0: bool] :
( ( fTrue != fFalse )
| ( fFalse = X0 ) )
| ~ spl9_12 ),
inference(equality_factoring,[],[f549]) ).
tff(f673,plain,
( spl9_40
| ~ spl9_29 ),
inference(avatar_split_clause,[],[f629,f626,f671]) ).
tff(f671,plain,
( spl9_40
<=> ! [X0: $tType] : wf(X0,id_on(X0,bot_bot(fun(X0,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_40])]) ).
tff(f626,plain,
( spl9_29
<=> ! [X0: $tType] : wf(X0,bot_bot(fun(product_prod(X0,X0),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_29])]) ).
tff(f629,plain,
( ! [X0: $tType] : wf(X0,id_on(X0,bot_bot(fun(X0,bool))))
| ~ spl9_29 ),
inference(forward_demodulation,[],[f627,f358]) ).
tff(f627,plain,
( ! [X0: $tType] : wf(X0,bot_bot(fun(product_prod(X0,X0),bool)))
| ~ spl9_29 ),
inference(avatar_component_clause,[],[f626]) ).
tff(f669,plain,
( spl9_39
| ~ spl9_28 ),
inference(avatar_split_clause,[],[f624,f621,f667]) ).
tff(f667,plain,
( spl9_39
<=> ! [X0: $tType] : antisym(X0,id_on(X0,bot_bot(fun(X0,bool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_39])]) ).
tff(f621,plain,
( spl9_28
<=> ! [X0: $tType] : antisym(X0,bot_bot(fun(product_prod(X0,X0),bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_28])]) ).
tff(f624,plain,
( ! [X0: $tType] : antisym(X0,id_on(X0,bot_bot(fun(X0,bool))))
| ~ spl9_28 ),
inference(forward_demodulation,[],[f622,f358]) ).
tff(f622,plain,
( ! [X0: $tType] : antisym(X0,bot_bot(fun(product_prod(X0,X0),bool)))
| ~ spl9_28 ),
inference(avatar_component_clause,[],[f621]) ).
tff(f665,plain,
spl9_38,
inference(avatar_split_clause,[],[f438,f663]) ).
tff(f438,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( total_on(X0,X2,X1)
| ~ order_1409979114der_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f318]) ).
tff(f661,plain,
spl9_37,
inference(avatar_split_clause,[],[f437,f659]) ).
tff(f659,plain,
( spl9_37
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( order_915043626der_on(X0,X2,X1)
| ~ order_1409979114der_on(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_37])]) ).
tff(f437,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( order_915043626der_on(X0,X2,X1)
| ~ order_1409979114der_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f318]) ).
tff(f657,plain,
spl9_36,
inference(avatar_split_clause,[],[f435,f655]) ).
tff(f435,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( order_1409979114der_on(X0,X2,X1)
| ~ order_well_order_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f257]) ).
tff(f653,plain,
spl9_35,
inference(avatar_split_clause,[],[f432,f651]) ).
tff(f651,plain,
( spl9_35
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( refl_on(X0,X2,X1)
| ~ order_preorder_on(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_35])]) ).
tff(f432,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( refl_on(X0,X2,X1)
| ~ order_preorder_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f316]) ).
tff(f649,plain,
spl9_34,
inference(avatar_split_clause,[],[f429,f647]) ).
tff(f647,plain,
( spl9_34
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( order_preorder_on(X0,X2,X1)
| ~ order_915043626der_on(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_34])]) ).
tff(f429,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( order_preorder_on(X0,X2,X1)
| ~ order_915043626der_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f314]) ).
tff(f645,plain,
spl9_33,
inference(avatar_split_clause,[],[f362,f643]) ).
tff(f643,plain,
( spl9_33
<=> ! [X0: bool] :
( ~ pp(X0)
| ~ pp(aa(bool,bool,fNot,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_33])]) ).
tff(f362,plain,
! [X0: bool] :
( ~ pp(X0)
| ~ pp(aa(bool,bool,fNot,X0)) ),
inference(cnf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: bool] :
( ~ pp(X0)
| ~ pp(aa(bool,bool,fNot,X0)) ),
inference(rectify,[],[f111]) ).
tff(f111,axiom,
! [X32: bool] :
( ~ pp(X32)
| ~ pp(aa(bool,bool,fNot,X32)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
tff(f641,plain,
spl9_32,
inference(avatar_split_clause,[],[f359,f639]) ).
tff(f639,plain,
( spl9_32
<=> ! [X0: bool] :
( pp(aa(bool,bool,fNot,X0))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_32])]) ).
tff(f359,plain,
! [X0: bool] :
( pp(aa(bool,bool,fNot,X0))
| pp(X0) ),
inference(cnf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: bool] :
( pp(aa(bool,bool,fNot,X0))
| pp(X0) ),
inference(rectify,[],[f112]) ).
tff(f112,axiom,
! [X32: bool] :
( pp(aa(bool,bool,fNot,X32))
| pp(X32) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
tff(f637,plain,
spl9_31,
inference(avatar_split_clause,[],[f347,f635]) ).
tff(f635,plain,
( spl9_31
<=> ! [X0: $tType] : refl_on(X0,top_top(fun(X0,bool)),id(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_31])]) ).
tff(f347,plain,
! [X0: $tType] : refl_on(X0,top_top(fun(X0,bool)),id(X0)),
inference(cnf_transformation,[],[f50]) ).
tff(f50,axiom,
! [X0: $tType] : refl_on(X0,top_top(fun(X0,bool)),id(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_refl__Id) ).
tff(f633,plain,
( spl9_30
| ~ spl9_6
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f580,f548,f523,f631]) ).
tff(f631,plain,
( spl9_30
<=> ! [X0: bool] :
( pp(X0)
| ( fFalse = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_30])]) ).
tff(f523,plain,
( spl9_6
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
tff(f580,plain,
( ! [X0: bool] :
( pp(X0)
| ( fFalse = X0 ) )
| ~ spl9_6
| ~ spl9_12 ),
inference(superposition,[],[f525,f549]) ).
tff(f525,plain,
( pp(fTrue)
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f523]) ).
tff(f628,plain,
spl9_29,
inference(avatar_split_clause,[],[f346,f626]) ).
tff(f346,plain,
! [X0: $tType] : wf(X0,bot_bot(fun(product_prod(X0,X0),bool))),
inference(cnf_transformation,[],[f44]) ).
tff(f44,axiom,
! [X0: $tType] : wf(X0,bot_bot(fun(product_prod(X0,X0),bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_wf__empty) ).
tff(f623,plain,
spl9_28,
inference(avatar_split_clause,[],[f345,f621]) ).
tff(f345,plain,
! [X0: $tType] : antisym(X0,bot_bot(fun(product_prod(X0,X0),bool))),
inference(cnf_transformation,[],[f62]) ).
tff(f62,axiom,
! [X0: $tType] : antisym(X0,bot_bot(fun(product_prod(X0,X0),bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_antisym__empty) ).
tff(f617,plain,
spl9_27,
inference(avatar_split_clause,[],[f433,f615]) ).
tff(f615,plain,
( spl9_27
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ~ order_preorder_on(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_27])]) ).
tff(f433,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( trans(X0,X1)
| ~ order_preorder_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f316]) ).
tff(f613,plain,
spl9_26,
inference(avatar_split_clause,[],[f430,f611]) ).
tff(f611,plain,
( spl9_26
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( antisym(X0,X1)
| ~ order_915043626der_on(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_26])]) ).
tff(f430,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool)] :
( antisym(X0,X1)
| ~ order_915043626der_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f314]) ).
tff(f607,plain,
spl9_25,
inference(avatar_split_clause,[],[f377,f605]) ).
tff(f605,plain,
( spl9_25
<=> ! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] : total_on(X0,bot_bot(fun(X0,bool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_25])]) ).
tff(f377,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] : total_on(X0,bot_bot(fun(X0,bool)),X1),
inference(cnf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] : total_on(X0,bot_bot(fun(X0,bool)),X1),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X0: $tType,X3: fun(product_prod(X0,X0),bool)] : total_on(X0,bot_bot(fun(X0,bool)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_total__on__empty) ).
tff(f603,plain,
spl9_24,
inference(avatar_split_clause,[],[f376,f601]) ).
tff(f599,plain,
spl9_23,
inference(avatar_split_clause,[],[f368,f597]) ).
tff(f597,plain,
( spl9_23
<=> ! [X0: $tType,X1: X0] :
( ord_less_eq(X0,bot_bot(X0),X1)
| ~ bot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_23])]) ).
tff(f368,plain,
! [X0: $tType,X1: X0] :
( ord_less_eq(X0,bot_bot(X0),X1)
| ~ bot(X0) ),
inference(cnf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: $tType] :
( ! [X1: X0] : ord_less_eq(X0,bot_bot(X0),X1)
| ~ bot(X0) ),
inference(ennf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: $tType] :
( bot(X0)
=> ! [X1: X0] : ord_less_eq(X0,bot_bot(X0),X1) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X0: $tType] :
( bot(X0)
=> ! [X26: X0] : ord_less_eq(X0,bot_bot(X0),X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_bot__least) ).
tff(f595,plain,
spl9_22,
inference(avatar_split_clause,[],[f364,f593]) ).
tff(f593,plain,
( spl9_22
<=> ! [X0: $tType,X1: X0] :
( ord_less_eq(X0,X1,top_top(X0))
| ~ top(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_22])]) ).
tff(f364,plain,
! [X0: $tType,X1: X0] :
( ord_less_eq(X0,X1,top_top(X0))
| ~ top(X0) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: $tType] :
( ! [X1: X0] : ord_less_eq(X0,X1,top_top(X0))
| ~ top(X0) ),
inference(ennf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: $tType] :
( top(X0)
=> ! [X1: X0] : ord_less_eq(X0,X1,top_top(X0)) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X0: $tType] :
( top(X0)
=> ! [X26: X0] : ord_less_eq(X0,X26,top_top(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_top__greatest) ).
tff(f591,plain,
spl9_21,
inference(avatar_split_clause,[],[f332,f588]) ).
tff(f588,plain,
( spl9_21
<=> order_1409979114der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),r) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_21])]) ).
tff(f332,plain,
order_1409979114der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),r),
inference(cnf_transformation,[],[f124]) ).
tff(f124,axiom,
order_1409979114der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f586,plain,
( spl9_20
| ~ spl9_6
| ~ spl9_7
| ~ spl9_12 ),
inference(avatar_split_clause,[],[f581,f548,f528,f523,f584]) ).
tff(f581,plain,
( ! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( ~ pp(fTrue)
| ( fFalse = aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),X0) ) )
| ~ spl9_7
| ~ spl9_12 ),
inference(superposition,[],[f529,f549]) ).
tff(f578,plain,
spl9_19,
inference(avatar_split_clause,[],[f420,f576]) ).
tff(f420,plain,
! [X0: $tType,X1: fun(X0,bool)] : order_well_order_on(X0,X1,sK7(X0,X1)),
inference(cnf_transformation,[],[f312]) ).
tff(f312,plain,
! [X0: $tType,X1: fun(X0,bool)] : order_well_order_on(X0,X1,sK7(X0,X1)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f184,f311]) ).
tff(f311,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X2: fun(product_prod(X0,X0),bool)] : order_well_order_on(X0,X1,X2)
=> order_well_order_on(X0,X1,sK7(X0,X1)) ),
introduced(choice_axiom,[]) ).
tff(f184,plain,
! [X0: $tType,X1: fun(X0,bool)] :
? [X2: fun(product_prod(X0,X0),bool)] : order_well_order_on(X0,X1,X2),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X0: $tType,X4: fun(X0,bool)] :
? [X15: fun(product_prod(X0,X0),bool)] : order_well_order_on(X0,X4,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_well__order__on) ).
tff(f574,plain,
spl9_18,
inference(avatar_split_clause,[],[f402,f572]) ).
tff(f572,plain,
( spl9_18
<=> ! [X1: $tType,X0: $tType] :
( bot(fun(X0,X1))
| ~ bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_18])]) ).
tff(f402,plain,
! [X1: $tType,X0: $tType] :
( bot(fun(X0,X1))
| ~ bot(X1) ),
inference(cnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: $tType,X1: $tType] :
( bot(fun(X0,X1))
| ~ bot(X1) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: $tType,X1: $tType] :
( bot(X1)
=> bot(fun(X0,X1)) ),
inference(rectify,[],[f103]) ).
tff(f103,axiom,
! [X30: $tType,X31: $tType] :
( bot(X31)
=> bot(fun(X30,X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
tff(f570,plain,
spl9_17,
inference(avatar_split_clause,[],[f400,f568]) ).
tff(f568,plain,
( spl9_17
<=> ! [X1: $tType,X0: $tType] :
( top(fun(X0,X1))
| ~ top(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_17])]) ).
tff(f400,plain,
! [X1: $tType,X0: $tType] :
( top(fun(X0,X1))
| ~ top(X1) ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: $tType,X1: $tType] :
( top(fun(X0,X1))
| ~ top(X1) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: $tType,X1: $tType] :
( top(X1)
=> top(fun(X0,X1)) ),
inference(rectify,[],[f102]) ).
tff(f102,axiom,
! [X30: $tType,X31: $tType] :
( top(X31)
=> top(fun(X30,X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Otop) ).
tff(f566,plain,
spl9_16,
inference(avatar_split_clause,[],[f397,f564]) ).
tff(f564,plain,
( spl9_16
<=> ! [X1: $tType,X0: $tType] :
( cl_Groups_Ominus(fun(X0,X1))
| ~ cl_Groups_Ominus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_16])]) ).
tff(f397,plain,
! [X1: $tType,X0: $tType] :
( cl_Groups_Ominus(fun(X0,X1))
| ~ cl_Groups_Ominus(X1) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: $tType,X1: $tType] :
( cl_Groups_Ominus(fun(X0,X1))
| ~ cl_Groups_Ominus(X1) ),
inference(ennf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: $tType,X1: $tType] :
( cl_Groups_Ominus(X1)
=> cl_Groups_Ominus(fun(X0,X1)) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X30: $tType,X31: $tType] :
( cl_Groups_Ominus(X31)
=> cl_Groups_Ominus(fun(X30,X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
tff(f562,plain,
spl9_15,
inference(avatar_split_clause,[],[f396,f560]) ).
tff(f560,plain,
( spl9_15
<=> ! [X1: $tType,X0: $tType] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_15])]) ).
tff(f396,plain,
! [X1: $tType,X0: $tType] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: $tType,X1: $tType] :
( preorder(fun(X0,X1))
| ~ preorder(X1) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $tType,X1: $tType] :
( preorder(X1)
=> preorder(fun(X0,X1)) ),
inference(rectify,[],[f101]) ).
tff(f101,axiom,
! [X30: $tType,X31: $tType] :
( preorder(X31)
=> preorder(fun(X30,X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
tff(f558,plain,
spl9_14,
inference(avatar_split_clause,[],[f375,f556]) ).
tff(f556,plain,
( spl9_14
<=> ! [X0: $tType,X1: fun(X0,bool)] : ord_less_eq(fun(X0,bool),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_14])]) ).
tff(f375,plain,
! [X0: $tType,X1: fun(X0,bool)] : ord_less_eq(fun(X0,bool),X1,X1),
inference(cnf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: $tType,X1: fun(X0,bool)] : ord_less_eq(fun(X0,bool),X1,X1),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X0: $tType,X4: fun(X0,bool)] : ord_less_eq(fun(X0,bool),X4,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_subset__refl) ).
tff(f554,plain,
spl9_13,
inference(avatar_split_clause,[],[f363,f552]) ).
tff(f552,plain,
( spl9_13
<=> ! [X0: $tType,X1: X0] :
( ord_less_eq(X0,X1,X1)
| ~ preorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_13])]) ).
tff(f363,plain,
! [X0: $tType,X1: X0] :
( ord_less_eq(X0,X1,X1)
| ~ preorder(X0) ),
inference(cnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: $tType] :
( ! [X1: X0] : ord_less_eq(X0,X1,X1)
| ~ preorder(X0) ),
inference(ennf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: $tType] :
( preorder(X0)
=> ! [X1: X0] : ord_less_eq(X0,X1,X1) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X0: $tType] :
( preorder(X0)
=> ! [X23: X0] : ord_less_eq(X0,X23,X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_order__refl) ).
tff(f550,plain,
spl9_12,
inference(avatar_split_clause,[],[f360,f548]) ).
tff(f360,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f118]) ).
tff(f118,axiom,
! [X32: bool] :
( ( fFalse = X32 )
| ( fTrue = X32 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
tff(f546,plain,
spl9_11,
inference(avatar_split_clause,[],[f374,f544]) ).
tff(f544,plain,
( spl9_11
<=> ! [X0: $tType,X1: fun(X0,bool)] : trans(X0,id_on(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).
tff(f374,plain,
! [X0: $tType,X1: fun(X0,bool)] : trans(X0,id_on(X0,X1)),
inference(cnf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: $tType,X1: fun(X0,bool)] : trans(X0,id_on(X0,X1)),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X0: $tType,X4: fun(X0,bool)] : trans(X0,id_on(X0,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_trans__Id__on) ).
tff(f542,plain,
spl9_10,
inference(avatar_split_clause,[],[f373,f540]) ).
tff(f540,plain,
( spl9_10
<=> ! [X0: $tType,X1: fun(X0,nat)] : wf(X0,measure(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_10])]) ).
tff(f373,plain,
! [X0: $tType,X1: fun(X0,nat)] : wf(X0,measure(X0,X1)),
inference(cnf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: $tType,X1: fun(X0,nat)] : wf(X0,measure(X0,X1)),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X0: $tType,X14: fun(X0,nat)] : wf(X0,measure(X0,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_wf__measure) ).
tff(f538,plain,
spl9_9,
inference(avatar_split_clause,[],[f344,f536]) ).
tff(f536,plain,
( spl9_9
<=> ! [X0: $tType] : trans(X0,id(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_9])]) ).
tff(f344,plain,
! [X0: $tType] : trans(X0,id(X0)),
inference(cnf_transformation,[],[f56]) ).
tff(f56,axiom,
! [X0: $tType] : trans(X0,id(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_trans__Id) ).
tff(f534,plain,
spl9_8,
inference(avatar_split_clause,[],[f343,f532]) ).
tff(f532,plain,
( spl9_8
<=> ! [X0: $tType] : antisym(X0,id(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).
tff(f343,plain,
! [X0: $tType] : antisym(X0,id(X0)),
inference(cnf_transformation,[],[f63]) ).
tff(f63,axiom,
! [X0: $tType] : antisym(X0,id(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_antisym__Id) ).
tff(f530,plain,
spl9_7,
inference(avatar_split_clause,[],[f331,f528]) ).
tff(f331,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),X0)),
inference(cnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : ~ pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),X0)),
inference(ennf_transformation,[],[f128]) ).
tff(f128,plain,
~ ? [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),X0)),
inference(rectify,[],[f127]) ).
tff(f127,negated_conjecture,
~ ? [X35: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),X35)),
inference(negated_conjecture,[],[f126]) ).
tff(f126,conjecture,
? [X35: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] : pp(aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool,order_215145569der_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),X35)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
tff(f526,plain,
spl9_6,
inference(avatar_split_clause,[],[f340,f523]) ).
tff(f340,plain,
pp(fTrue),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
tff(f521,plain,
spl9_5,
inference(avatar_split_clause,[],[f339,f518]) ).
tff(f339,plain,
bot(bool),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
bot(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
tff(f516,plain,
spl9_4,
inference(avatar_split_clause,[],[f338,f513]) ).
tff(f338,plain,
top(bool),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
top(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Otop) ).
tff(f511,plain,
spl9_3,
inference(avatar_split_clause,[],[f337,f508]) ).
tff(f508,plain,
( spl9_3
<=> cl_Groups_Ominus(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
tff(f337,plain,
cl_Groups_Ominus(bool),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
cl_Groups_Ominus(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
tff(f506,plain,
spl9_2,
inference(avatar_split_clause,[],[f336,f503]) ).
tff(f503,plain,
( spl9_2
<=> preorder(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
tff(f336,plain,
preorder(bool),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
preorder(bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
tff(f501,plain,
~ spl9_1,
inference(avatar_split_clause,[],[f334,f498]) ).
tff(f498,plain,
( spl9_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
tff(f334,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SCT179_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n022.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon Apr 29 22:18:43 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.16/0.36 % (8950)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (8953)WARNING: value z3 for option sas not known
% 0.22/0.38 % (8954)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (8951)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (8952)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (8955)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)
% 0.22/0.39 % (8957)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)
% 0.22/0.39 % (8953)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)
% 0.22/0.39 % (8956)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)
% 0.22/0.39 % (8957)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.39 % Exception at run slice level% Exception at run slice level
% 0.22/0.39 User error:
% 0.22/0.39 Finite model buillding is currently not compatible with polymorphism or higher-order constructsUser error:
% 0.22/0.39 Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.39 % Exception at run slice level
% 0.22/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.41 % (8958)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.41 % (8959)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)
% 0.22/0.41 % (8960)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)
% 0.22/0.41 % (8958)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.41 % (8959)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.41 % Exception at run slice level
% 0.22/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.43 % (8961)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)
% 0.22/0.43 % (8955)First to succeed.
% 0.22/0.44 % (8955)Refutation found. Thanks to Tanya!
% 0.22/0.44 % SZS status Theorem for theBenchmark
% 0.22/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.45 % (8955)------------------------------
% 0.22/0.45 % (8955)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.45 % (8955)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (8955)Memory used [KB]: 1606
% 0.22/0.45 % (8955)Time elapsed: 0.055 s
% 0.22/0.45 % (8955)Instructions burned: 87 (million)
% 0.22/0.45 % (8955)------------------------------
% 0.22/0.45 % (8955)------------------------------
% 0.22/0.45 % (8950)Success in time 0.08 s
%------------------------------------------------------------------------------