TSTP Solution File: SWW535_5 by Vampire-SAT---4.9
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.9
% Problem : SWW535_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d SAT
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:53:34 EDT 2024
% Result : Theorem 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 263
% Syntax : Number of formulae : 780 ( 255 unt; 0 typ; 0 def)
% Number of atoms : 1677 ( 621 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1446 ( 549 ~; 552 |; 67 &)
% ( 182 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 171 ( 169 usr; 152 prp; 0-2 aty)
% Number of functors : 38 ( 38 usr; 6 con; 0-5 aty)
% Number of variables : 1710 (1683 !; 27 ?;1710 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
huffma1450048681e_tree: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_4,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_6,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_7,type,
huffma675207370phabet:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > fun(X0,bool) ) ).
tff(func_def_8,type,
huffma1134658180e_cost:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_9,type,
huffma410068972_depth:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).
tff(func_def_10,type,
huffma1352802255e_freq:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).
tff(func_def_11,type,
huffma1146269203erNode:
!>[X0: $tType] : ( ( nat * huffma1450048681e_tree(X0) * huffma1450048681e_tree(X0) ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_12,type,
huffma2021818691e_Leaf:
!>[X0: $tType] : ( ( nat * X0 ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_13,type,
huffma107959123e_case:
!>[X0: $tType,X1: $tType] : ( ( fun(nat,fun(X0,X1)) * fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))) * huffma1450048681e_tree(X0) ) > X1 ) ).
tff(func_def_14,type,
huffma1280178957ee_rec:
!>[X0: $tType,X1: $tType] : ( ( fun(nat,fun(X0,X1)) * fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))) * huffma1450048681e_tree(X0) ) > X1 ) ).
tff(func_def_15,type,
huffma83463279weight:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_16,type,
inf_inf:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_17,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_18,type,
bot_bot:
!>[X0: $tType] : X0 ).
tff(func_def_19,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_20,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_21,type,
fFalse: bool ).
tff(func_def_22,type,
fTrue: bool ).
tff(func_def_23,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_24,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_25,type,
t_1: huffma1450048681e_tree(a) ).
tff(func_def_26,type,
t_2: huffma1450048681e_tree(a) ).
tff(func_def_27,type,
w: nat ).
tff(func_def_28,type,
sK0:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_29,type,
sK1:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_30,type,
sK2:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_31,type,
sK3:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_32,type,
sK4:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).
tff(func_def_33,type,
sK5:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_34,type,
sK6:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_35,type,
sK7:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
bounded_lattice:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
bot:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
lattice:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
semilattice_inf:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
bounded_lattice_bot:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
huffma1518433673istent:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > $o ) ).
tff(pred_def_18,type,
pp: bool > $o ).
tff(f1867,plain,
$false,
inference(avatar_sat_refutation,[],[f548,f553,f558,f563,f568,f573,f578,f583,f588,f593,f598,f603,f608,f613,f618,f623,f628,f633,f638,f643,f647,f651,f655,f659,f663,f667,f671,f679,f688,f692,f697,f701,f705,f709,f716,f721,f725,f729,f733,f737,f742,f746,f757,f764,f768,f772,f776,f780,f784,f789,f800,f804,f809,f813,f817,f821,f825,f841,f845,f849,f853,f857,f877,f882,f886,f890,f894,f898,f910,f914,f918,f922,f926,f930,f935,f940,f945,f951,f955,f987,f994,f998,f1002,f1006,f1090,f1095,f1100,f1105,f1109,f1117,f1121,f1125,f1129,f1134,f1139,f1143,f1174,f1179,f1183,f1209,f1213,f1217,f1221,f1225,f1229,f1233,f1237,f1241,f1245,f1249,f1290,f1294,f1326,f1332,f1340,f1344,f1374,f1379,f1391,f1395,f1425,f1430,f1434,f1476,f1480,f1484,f1489,f1498,f1503,f1513,f1533,f1537,f1541,f1562,f1567,f1571,f1575,f1700,f1704,f1788,f1794,f1803,f1809,f1813,f1822,f1827,f1837,f1843,f1852,f1858,f1866]) ).
tff(f1866,plain,
~ spl8_145,
inference(avatar_contradiction_clause,[],[f1865]) ).
tff(f1865,plain,
( $false
| ~ spl8_145 ),
inference(equality_resolution,[],[f1812]) ).
tff(f1812,plain,
( ! [X0: nat] : ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != huffma1134658180e_cost(a,huffma1146269203erNode(a,X0,t_1,t_2)) )
| ~ spl8_145 ),
inference(avatar_component_clause,[],[f1811]) ).
tff(f1811,plain,
( spl8_145
<=> ! [X0: nat] : ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != huffma1134658180e_cost(a,huffma1146269203erNode(a,X0,t_1,t_2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_145])]) ).
tff(f1858,plain,
( spl8_151
| ~ spl8_65
| ~ spl8_123
| ~ spl8_150 ),
inference(avatar_split_clause,[],[f1854,f1850,f1428,f880,f1856]) ).
tff(f1856,plain,
( spl8_151
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK6(X0,X1,X2)))
| ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),X2,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_151])]) ).
tff(f880,plain,
( spl8_65
<=> ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_65])]) ).
tff(f1428,plain,
( spl8_123
<=> ! [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,[spl8_123])]) ).
tff(f1850,plain,
( spl8_150
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X2,X1) )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK6(X0,X1,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_150])]) ).
tff(f1854,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK6(X0,X1,X2)))
| ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),X2,X1) ) )
| ~ spl8_65
| ~ spl8_123
| ~ spl8_150 ),
inference(forward_demodulation,[],[f1853,f1429]) ).
tff(f1429,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) )
| ~ spl8_123 ),
inference(avatar_component_clause,[],[f1428]) ).
tff(f1853,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),X2,X1) )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK6(X0,X1,X2)),X1)) )
| ~ spl8_65
| ~ spl8_150 ),
inference(forward_demodulation,[],[f1851,f881]) ).
tff(f881,plain,
( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse) )
| ~ spl8_65 ),
inference(avatar_component_clause,[],[f880]) ).
tff(f1851,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X2,X1) )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK6(X0,X1,X2)),X1)) )
| ~ spl8_150 ),
inference(avatar_component_clause,[],[f1850]) ).
tff(f1852,plain,
spl8_150,
inference(avatar_split_clause,[],[f464,f1850]) ).
tff(f464,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X2,X1) )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK6(X0,X1,X2)),X1)) ),
inference(cnf_transformation,[],[f338]) ).
tff(f338,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X2,X1) )
| ( ( sK5(X0,X1,X2) = sK6(X0,X1,X2) )
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK6(X0,X1,X2)),X1))
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK5(X0,X1,X2)),X2)) ) )
& ( ! [X5: X0] :
( ! [X6: X0] :
( ( X5 != X6 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X6),X1)) )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X5),X2)) )
| ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),X2,X1) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f335,f337,f336]) ).
tff(f336,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ? [X3: X0] :
( ? [X4: X0] :
( ( X3 = X4 )
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X1)) )
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) )
=> ( ? [X4: X0] :
( ( sK5(X0,X1,X2) = X4 )
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X1)) )
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK5(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f337,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ? [X4: X0] :
( ( sK5(X0,X1,X2) = X4 )
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X1)) )
=> ( ( sK5(X0,X1,X2) = sK6(X0,X1,X2) )
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK6(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f335,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X2,X1) )
| ? [X3: X0] :
( ? [X4: X0] :
( ( X3 = X4 )
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X1)) )
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) ) )
& ( ! [X5: X0] :
( ! [X6: X0] :
( ( X5 != X6 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X6),X1)) )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X5),X2)) )
| ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),X2,X1) ) ) ),
inference(rectify,[],[f334]) ).
tff(f334,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X2,X1) )
| ? [X3: X0] :
( ? [X4: X0] :
( ( X3 = X4 )
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X1)) )
& pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) ) )
& ( ! [X3: X0] :
( ! [X4: X0] :
( ( X3 != X4 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X1)) )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) )
| ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),X2,X1) ) ) ),
inference(nnf_transformation,[],[f292]) ).
tff(f292,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X2,X1) )
<=> ! [X3: X0] :
( ! [X4: X0] :
( ( X3 != X4 )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X1)) )
| ~ pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) ) ),
inference(ennf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X2,X1) )
<=> ! [X3: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))
=> ! [X4: X0] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X4),X1))
=> ( X3 != X4 ) ) ) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X1: $tType,X41: fun(X1,bool),X42: fun(X1,bool)] :
( ( bot_bot(fun(X1,bool)) = inf_inf(fun(X1,bool),X42,X41) )
<=> ! [X43: X1] :
( pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X43),X42))
=> ! [X49: X1] :
( pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X49),X41))
=> ( X43 != X49 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1843,plain,
( spl8_149
| ~ spl8_65
| ~ spl8_123
| ~ spl8_148 ),
inference(avatar_split_clause,[],[f1839,f1835,f1428,f880,f1841]) ).
tff(f1841,plain,
( spl8_149
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X2),sK5(X0,X1,X2)))
| ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),X2,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_149])]) ).
tff(f1835,plain,
( spl8_148
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X2,X1) )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK5(X0,X1,X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_148])]) ).
tff(f1839,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X2),sK5(X0,X1,X2)))
| ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),X2,X1) ) )
| ~ spl8_65
| ~ spl8_123
| ~ spl8_148 ),
inference(forward_demodulation,[],[f1838,f1429]) ).
tff(f1838,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),X2,X1) )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK5(X0,X1,X2)),X2)) )
| ~ spl8_65
| ~ spl8_148 ),
inference(forward_demodulation,[],[f1836,f881]) ).
tff(f1836,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X2,X1) )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK5(X0,X1,X2)),X2)) )
| ~ spl8_148 ),
inference(avatar_component_clause,[],[f1835]) ).
tff(f1837,plain,
spl8_148,
inference(avatar_split_clause,[],[f463,f1835]) ).
tff(f463,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X2,X1) )
| pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK5(X0,X1,X2)),X2)) ),
inference(cnf_transformation,[],[f338]) ).
tff(f1827,plain,
( spl8_147
| ~ spl8_65
| ~ spl8_146 ),
inference(avatar_split_clause,[],[f1823,f1820,f880,f1825]) ).
tff(f1825,plain,
( spl8_147
<=> ! [X0: $tType,X3: nat,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
( ( combk(bool,X0,fFalse) != inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
| huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
| ~ huffma1518433673istent(X0,X1)
| ~ huffma1518433673istent(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_147])]) ).
tff(f1820,plain,
( spl8_146
<=> ! [X0: $tType,X3: nat,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
( huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
| ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
| ~ huffma1518433673istent(X0,X1)
| ~ huffma1518433673istent(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_146])]) ).
tff(f1823,plain,
( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
( ( combk(bool,X0,fFalse) != inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
| huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
| ~ huffma1518433673istent(X0,X1)
| ~ huffma1518433673istent(X0,X2) )
| ~ spl8_65
| ~ spl8_146 ),
inference(forward_demodulation,[],[f1821,f881]) ).
tff(f1821,plain,
( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
( huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
| ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
| ~ huffma1518433673istent(X0,X1)
| ~ huffma1518433673istent(X0,X2) )
| ~ spl8_146 ),
inference(avatar_component_clause,[],[f1820]) ).
tff(f1822,plain,
spl8_146,
inference(avatar_split_clause,[],[f490,f1820]) ).
tff(f490,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
( huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
| ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
| ~ huffma1518433673istent(X0,X1)
| ~ huffma1518433673istent(X0,X2) ),
inference(cnf_transformation,[],[f343]) ).
tff(f343,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] :
( ( huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
| ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
| ~ huffma1518433673istent(X0,X1)
| ~ huffma1518433673istent(X0,X2) )
& ( ( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
& huffma1518433673istent(X0,X1)
& huffma1518433673istent(X0,X2) )
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ) ),
inference(flattening,[],[f342]) ).
tff(f342,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] :
( ( huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
| ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
| ~ huffma1518433673istent(X0,X1)
| ~ huffma1518433673istent(X0,X2) )
& ( ( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
& huffma1518433673istent(X0,X1)
& huffma1518433673istent(X0,X2) )
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ) ),
inference(nnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] :
( huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
<=> ( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
& huffma1518433673istent(X0,X1)
& huffma1518433673istent(X0,X2) ) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X1: $tType,X37: huffma1450048681e_tree(X1),X38: huffma1450048681e_tree(X1),X39: nat] :
( huffma1518433673istent(X1,huffma1146269203erNode(X1,X39,X38,X37))
<=> ( ( inf_inf(fun(X1,bool),huffma675207370phabet(X1,X38),huffma675207370phabet(X1,X37)) = bot_bot(fun(X1,bool)) )
& huffma1518433673istent(X1,X37)
& huffma1518433673istent(X1,X38) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1813,plain,
( spl8_145
| spl8_29
| ~ spl8_140 ),
inference(avatar_split_clause,[],[f1750,f1702,f685,f1811]) ).
tff(f685,plain,
( spl8_29
<=> ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) = plus_plus(nat,plus_plus(nat,huffma1134658180e_cost(a,t_1),plus_plus(nat,huffma83463279weight(a,t_1),huffma83463279weight(a,t_2))),huffma1134658180e_cost(a,t_2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_29])]) ).
tff(f1702,plain,
( spl8_140
<=> ! [X0: $tType,X3: nat,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] : ( huffma1134658180e_cost(X0,huffma1146269203erNode(X0,X3,X2,X1)) = plus_plus(nat,plus_plus(nat,huffma1134658180e_cost(X0,X2),plus_plus(nat,huffma83463279weight(X0,X2),huffma83463279weight(X0,X1))),huffma1134658180e_cost(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_140])]) ).
tff(f1750,plain,
( ! [X0: nat] : ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != huffma1134658180e_cost(a,huffma1146269203erNode(a,X0,t_1,t_2)) )
| spl8_29
| ~ spl8_140 ),
inference(superposition,[],[f687,f1703]) ).
tff(f1703,plain,
( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] : ( huffma1134658180e_cost(X0,huffma1146269203erNode(X0,X3,X2,X1)) = plus_plus(nat,plus_plus(nat,huffma1134658180e_cost(X0,X2),plus_plus(nat,huffma83463279weight(X0,X2),huffma83463279weight(X0,X1))),huffma1134658180e_cost(X0,X1)) )
| ~ spl8_140 ),
inference(avatar_component_clause,[],[f1702]) ).
tff(f687,plain,
( ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,plus_plus(nat,huffma1134658180e_cost(a,t_1),plus_plus(nat,huffma83463279weight(a,t_1),huffma83463279weight(a,t_2))),huffma1134658180e_cost(a,t_2)) )
| spl8_29 ),
inference(avatar_component_clause,[],[f685]) ).
tff(f1809,plain,
( spl8_144
| ~ spl8_65
| ~ spl8_123
| ~ spl8_143 ),
inference(avatar_split_clause,[],[f1805,f1801,f1428,f880,f1807]) ).
tff(f1807,plain,
( spl8_144
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK3(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_144])]) ).
tff(f1801,plain,
( spl8_143
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK3(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_143])]) ).
tff(f1805,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK3(X0,X1))) )
| ~ spl8_65
| ~ spl8_123
| ~ spl8_143 ),
inference(forward_demodulation,[],[f1804,f881]) ).
tff(f1804,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),X1),sK3(X0,X1)))
| ( bot_bot(fun(X0,bool)) = X1 ) )
| ~ spl8_123
| ~ spl8_143 ),
inference(forward_demodulation,[],[f1802,f1429]) ).
tff(f1802,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK3(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 ) )
| ~ spl8_143 ),
inference(avatar_component_clause,[],[f1801]) ).
tff(f1803,plain,
spl8_143,
inference(avatar_split_clause,[],[f447,f1801]) ).
tff(f447,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK3(X0,X1)),X1))
| ( bot_bot(fun(X0,bool)) = X1 ) ),
inference(cnf_transformation,[],[f329]) ).
tff(f329,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK3(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,[sK3])],[f327,f328]) ).
tff(f328,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),sK3(X0,X1)),X1)) ),
introduced(choice_axiom,[]) ).
tff(f327,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,[],[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))
| ( 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,[],[f197]) ).
tff(f197,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,[],[f54]) ).
tff(f54,axiom,
! [X1: $tType,X42: fun(X1,bool)] :
( ? [X43: X1] : pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X43),X42))
<=> ( bot_bot(fun(X1,bool)) != X42 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1794,plain,
( spl8_142
| ~ spl8_65
| ~ spl8_123
| ~ spl8_141 ),
inference(avatar_split_clause,[],[f1790,f1786,f1428,f880,f1792]) ).
tff(f1792,plain,
( spl8_142
<=> ! [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,fFalse) = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_142])]) ).
tff(f1786,plain,
( spl8_141
<=> ! [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),sK2(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_141])]) ).
tff(f1790,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,fFalse) = X1 ) )
| ~ spl8_65
| ~ spl8_123
| ~ spl8_141 ),
inference(forward_demodulation,[],[f1789,f1429]) ).
tff(f1789,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),sK2(X0,X1)),X1)) )
| ~ spl8_65
| ~ spl8_141 ),
inference(forward_demodulation,[],[f1787,f881]) ).
tff(f1787,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),sK2(X0,X1)),X1)) )
| ~ spl8_141 ),
inference(avatar_component_clause,[],[f1786]) ).
tff(f1788,plain,
spl8_141,
inference(avatar_split_clause,[],[f444,f1786]) ).
tff(f444,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),sK2(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f325]) ).
tff(f325,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),sK2(X0,X1)),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f323,f324]) ).
tff(f324,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),sK2(X0,X1)),X1)) ),
introduced(choice_axiom,[]) ).
tff(f323,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,[],[f322]) ).
tff(f322,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,[],[f196]) ).
tff(f196,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,[],[f44]) ).
tff(f44,axiom,
! [X1: $tType,X42: fun(X1,bool)] :
( ! [X43: X1] : ~ pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X43),X42))
<=> ( bot_bot(fun(X1,bool)) = X42 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1704,plain,
spl8_140,
inference(avatar_split_clause,[],[f539,f1702]) ).
tff(f539,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] : ( huffma1134658180e_cost(X0,huffma1146269203erNode(X0,X3,X2,X1)) = plus_plus(nat,plus_plus(nat,huffma1134658180e_cost(X0,X2),plus_plus(nat,huffma83463279weight(X0,X2),huffma83463279weight(X0,X1))),huffma1134658180e_cost(X0,X1)) ),
inference(forward_demodulation,[],[f538,f453]) ).
tff(f453,plain,
! [X2: nat,X0: nat,X1: nat] : ( plus_plus(nat,X2,plus_plus(nat,X1,X0)) = plus_plus(nat,X1,plus_plus(nat,X2,X0)) ),
inference(cnf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: nat,X1: nat,X2: nat] : ( plus_plus(nat,X2,plus_plus(nat,X1,X0)) = plus_plus(nat,X1,plus_plus(nat,X2,X0)) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X24: nat,X25: nat,X26: nat] : ( plus_plus(nat,X26,plus_plus(nat,X25,X24)) = plus_plus(nat,X25,plus_plus(nat,X26,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f538,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] : ( huffma1134658180e_cost(X0,huffma1146269203erNode(X0,X3,X2,X1)) = plus_plus(nat,plus_plus(nat,huffma83463279weight(X0,X2),plus_plus(nat,huffma1134658180e_cost(X0,X2),huffma83463279weight(X0,X1))),huffma1134658180e_cost(X0,X1)) ),
inference(forward_demodulation,[],[f473,f454]) ).
tff(f454,plain,
! [X2: nat,X0: nat,X1: nat] : ( plus_plus(nat,X2,plus_plus(nat,X1,X0)) = plus_plus(nat,plus_plus(nat,X2,X1),X0) ),
inference(cnf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: nat,X1: nat,X2: nat] : ( plus_plus(nat,X2,plus_plus(nat,X1,X0)) = plus_plus(nat,plus_plus(nat,X2,X1),X0) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X27: nat,X22: nat,X23: nat] : ( plus_plus(nat,plus_plus(nat,X23,X22),X27) = plus_plus(nat,X23,plus_plus(nat,X22,X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f473,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] : ( huffma1134658180e_cost(X0,huffma1146269203erNode(X0,X3,X2,X1)) = plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(X0,X2),huffma1134658180e_cost(X0,X2)),huffma83463279weight(X0,X1)),huffma1134658180e_cost(X0,X1)) ),
inference(cnf_transformation,[],[f217]) ).
tff(f217,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] : ( huffma1134658180e_cost(X0,huffma1146269203erNode(X0,X3,X2,X1)) = plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(X0,X2),huffma1134658180e_cost(X0,X2)),huffma83463279weight(X0,X1)),huffma1134658180e_cost(X0,X1)) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: $tType,X10: huffma1450048681e_tree(X0),X11: huffma1450048681e_tree(X0),X12: nat] : ( huffma1134658180e_cost(X0,huffma1146269203erNode(X0,X12,X11,X10)) = plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(X0,X11),huffma1134658180e_cost(X0,X11)),huffma83463279weight(X0,X10)),huffma1134658180e_cost(X0,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1700,plain,
spl8_139,
inference(avatar_split_clause,[],[f507,f1698]) ).
tff(f1698,plain,
( spl8_139
<=> ! [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,[spl8_139])]) ).
tff(f507,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,[],[f239]) ).
tff(f239,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,[],[f127]) ).
tff(f127,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X54: X0,X55: fun(X0,X1),X56: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combs(X0,X1,X2,X56,X55),X54) = aa(X1,X2,aa(X0,fun(X1,X2),X56,X54),aa(X0,X1,X55,X54)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1575,plain,
spl8_138,
inference(avatar_split_clause,[],[f472,f1573]) ).
tff(f1573,plain,
( spl8_138
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X3,inf_inf(fun(X0,bool),X2,X1)) = inf_inf(fun(X0,bool),inf_inf(fun(X0,bool),X3,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_138])]) ).
tff(f472,plain,
! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X3,inf_inf(fun(X0,bool),X2,X1)) = inf_inf(fun(X0,bool),inf_inf(fun(X0,bool),X3,X2),X1) ),
inference(cnf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X3,inf_inf(fun(X0,bool),X2,X1)) = inf_inf(fun(X0,bool),inf_inf(fun(X0,bool),X3,X2),X1) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X1: $tType,X45: fun(X1,bool),X41: fun(X1,bool),X42: fun(X1,bool)] : ( inf_inf(fun(X1,bool),X42,inf_inf(fun(X1,bool),X41,X45)) = inf_inf(fun(X1,bool),inf_inf(fun(X1,bool),X42,X41),X45) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1571,plain,
spl8_137,
inference(avatar_split_clause,[],[f471,f1569]) ).
tff(f1569,plain,
( spl8_137
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X3,inf_inf(fun(X0,bool),X2,X1)) = inf_inf(fun(X0,bool),X2,inf_inf(fun(X0,bool),X3,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_137])]) ).
tff(f471,plain,
! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X3,inf_inf(fun(X0,bool),X2,X1)) = inf_inf(fun(X0,bool),X2,inf_inf(fun(X0,bool),X3,X1)) ),
inference(cnf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool),X3: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X3,inf_inf(fun(X0,bool),X2,X1)) = inf_inf(fun(X0,bool),X2,inf_inf(fun(X0,bool),X3,X1)) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X1: $tType,X45: fun(X1,bool),X41: fun(X1,bool),X42: fun(X1,bool)] : ( inf_inf(fun(X1,bool),X42,inf_inf(fun(X1,bool),X41,X45)) = inf_inf(fun(X1,bool),X41,inf_inf(fun(X1,bool),X42,X45)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1567,plain,
spl8_136,
inference(avatar_split_clause,[],[f433,f1565]) ).
tff(f1565,plain,
( spl8_136
<=> ! [X1: $tType,X0: $tType,X4: fun(X1,X0),X3: fun(X1,X0),X2: X1] :
( ( aa(X1,X0,inf_inf(fun(X1,X0),X4,X3),X2) = inf_inf(X0,aa(X1,X0,X4,X2),aa(X1,X0,X3,X2)) )
| ~ lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_136])]) ).
tff(f433,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: fun(X1,X0),X4: fun(X1,X0)] :
( ( aa(X1,X0,inf_inf(fun(X1,X0),X4,X3),X2) = inf_inf(X0,aa(X1,X0,X4,X2),aa(X1,X0,X3,X2)) )
| ~ lattice(X0) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: X1,X3: fun(X1,X0),X4: fun(X1,X0)] : ( aa(X1,X0,inf_inf(fun(X1,X0),X4,X3),X2) = inf_inf(X0,aa(X1,X0,X4,X2),aa(X1,X0,X3,X2)) )
| ~ lattice(X0) ),
inference(ennf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: $tType,X1: $tType] :
( lattice(X0)
=> ! [X2: X1,X3: fun(X1,X0),X4: fun(X1,X0)] : ( aa(X1,X0,inf_inf(fun(X1,X0),X4,X3),X2) = inf_inf(X0,aa(X1,X0,X4,X2),aa(X1,X0,X3,X2)) ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X1: $tType,X2: $tType] :
( lattice(X1)
=> ! [X40: X2,X46: fun(X2,X1),X47: fun(X2,X1)] : ( aa(X2,X1,inf_inf(fun(X2,X1),X47,X46),X40) = inf_inf(X1,aa(X2,X1,X47,X40),aa(X2,X1,X46,X40)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1562,plain,
( spl8_135
| ~ spl8_65
| ~ spl8_134 ),
inference(avatar_split_clause,[],[f1542,f1539,f880,f1560]) ).
tff(f1560,plain,
( spl8_135
<=> ! [X0: $tType,X3: nat,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
( ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_135])]) ).
tff(f1539,plain,
( spl8_134
<=> ! [X0: $tType,X3: nat,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_134])]) ).
tff(f1542,plain,
( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
( ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) )
| ~ spl8_65
| ~ spl8_134 ),
inference(forward_demodulation,[],[f1540,f881]) ).
tff(f1540,plain,
( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) )
| ~ spl8_134 ),
inference(avatar_component_clause,[],[f1539]) ).
tff(f1541,plain,
spl8_134,
inference(avatar_split_clause,[],[f489,f1539]) ).
tff(f489,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) )
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ),
inference(cnf_transformation,[],[f343]) ).
tff(f1537,plain,
spl8_133,
inference(avatar_split_clause,[],[f486,f1535]) ).
tff(f1535,plain,
( spl8_133
<=> ! [X1: $tType,X0: $tType,X3: fun(X1,X0),X2: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK7(X0,X1,X2,X3)) != aa(X1,X0,X2,sK7(X0,X1,X2,X3)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_133])]) ).
tff(f486,plain,
! [X1: $tType,X0: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK7(X0,X1,X2,X3)) != aa(X1,X0,X2,sK7(X0,X1,X2,X3)) ) ),
inference(cnf_transformation,[],[f341]) ).
tff(f341,plain,
! [X0: $tType,X1: $tType,X2: fun(X1,X0),X3: fun(X1,X0)] :
( ( X2 = X3 )
| ( aa(X1,X0,X3,sK7(X0,X1,X2,X3)) != aa(X1,X0,X2,sK7(X0,X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f304,f340]) ).
tff(f340,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,sK7(X0,X1,X2,X3)) != aa(X1,X0,X2,sK7(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
tff(f304,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,[],[f227]) ).
tff(f227,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,[],[f75]) ).
tff(f75,axiom,
! [X2: $tType,X1: $tType,X46: fun(X1,X2),X47: fun(X1,X2)] :
( ! [X48: X1] : ( aa(X1,X2,X47,X48) = aa(X1,X2,X46,X48) )
=> ( X46 = X47 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1533,plain,
( spl8_132
| ~ spl8_38
| ~ spl8_84
| ~ spl8_113 ),
inference(avatar_split_clause,[],[f1384,f1292,f1000,f727,f1531]) ).
tff(f1531,plain,
( spl8_132
<=> ! [X0: nat] : ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,huffma1134658180e_cost(a,t_1),plus_plus(nat,huffma1134658180e_cost(a,t_2),huffma83463279weight(a,huffma1146269203erNode(a,X0,t_1,t_2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_132])]) ).
tff(f727,plain,
( spl8_38
<=> ! [X0: nat,X1: nat] : ( plus_plus(nat,X1,X0) = plus_plus(nat,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_38])]) ).
tff(f1000,plain,
( spl8_84
<=> ! [X2: nat,X0: nat,X1: nat] : ( plus_plus(nat,X2,plus_plus(nat,X1,X0)) = plus_plus(nat,plus_plus(nat,X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_84])]) ).
tff(f1292,plain,
( spl8_113
<=> ! [X0: nat] : ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,plus_plus(nat,huffma1134658180e_cost(a,t_1),huffma83463279weight(a,huffma1146269203erNode(a,X0,t_1,t_2))),huffma1134658180e_cost(a,t_2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_113])]) ).
tff(f1384,plain,
( ! [X0: nat] : ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,huffma1134658180e_cost(a,t_1),plus_plus(nat,huffma1134658180e_cost(a,t_2),huffma83463279weight(a,huffma1146269203erNode(a,X0,t_1,t_2)))) )
| ~ spl8_38
| ~ spl8_84
| ~ spl8_113 ),
inference(forward_demodulation,[],[f1381,f728]) ).
tff(f728,plain,
( ! [X0: nat,X1: nat] : ( plus_plus(nat,X1,X0) = plus_plus(nat,X0,X1) )
| ~ spl8_38 ),
inference(avatar_component_clause,[],[f727]) ).
tff(f1381,plain,
( ! [X0: nat] : ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,huffma1134658180e_cost(a,t_1),plus_plus(nat,huffma83463279weight(a,huffma1146269203erNode(a,X0,t_1,t_2)),huffma1134658180e_cost(a,t_2))) )
| ~ spl8_84
| ~ spl8_113 ),
inference(superposition,[],[f1293,f1001]) ).
tff(f1001,plain,
( ! [X2: nat,X0: nat,X1: nat] : ( plus_plus(nat,X2,plus_plus(nat,X1,X0)) = plus_plus(nat,plus_plus(nat,X2,X1),X0) )
| ~ spl8_84 ),
inference(avatar_component_clause,[],[f1000]) ).
tff(f1293,plain,
( ! [X0: nat] : ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,plus_plus(nat,huffma1134658180e_cost(a,t_1),huffma83463279weight(a,huffma1146269203erNode(a,X0,t_1,t_2))),huffma1134658180e_cost(a,t_2)) )
| ~ spl8_113 ),
inference(avatar_component_clause,[],[f1292]) ).
tff(f1513,plain,
spl8_131,
inference(avatar_split_clause,[],[f476,f1511]) ).
tff(f1511,plain,
( spl8_131
<=> ! [X0: $tType,X3: fun(X0,bool),X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,inf_inf(fun(X0,bool),X3,X1),X2))
| ~ pp(aa(X0,bool,X1,X2))
| ~ pp(aa(X0,bool,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_131])]) ).
tff(f476,plain,
! [X0: $tType,X2: X0,X3: fun(X0,bool),X1: fun(X0,bool)] :
( pp(aa(X0,bool,inf_inf(fun(X0,bool),X3,X1),X2))
| ~ pp(aa(X0,bool,X1,X2))
| ~ pp(aa(X0,bool,X3,X2)) ),
inference(cnf_transformation,[],[f295]) ).
tff(f295,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0,X3: fun(X0,bool)] :
( pp(aa(X0,bool,inf_inf(fun(X0,bool),X3,X1),X2))
| ~ pp(aa(X0,bool,X1,X2))
| ~ pp(aa(X0,bool,X3,X2)) ),
inference(flattening,[],[f294]) ).
tff(f294,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0,X3: fun(X0,bool)] :
( pp(aa(X0,bool,inf_inf(fun(X0,bool),X3,X1),X2))
| ~ pp(aa(X0,bool,X1,X2))
| ~ pp(aa(X0,bool,X3,X2)) ),
inference(ennf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0,X3: fun(X0,bool)] :
( pp(aa(X0,bool,X3,X2))
=> ( pp(aa(X0,bool,X1,X2))
=> pp(aa(X0,bool,inf_inf(fun(X0,bool),X3,X1),X2)) ) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X1: $tType,X41: fun(X1,bool),X40: X1,X42: fun(X1,bool)] :
( pp(aa(X1,bool,X42,X40))
=> ( pp(aa(X1,bool,X41,X40))
=> pp(aa(X1,bool,inf_inf(fun(X1,bool),X42,X41),X40)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1503,plain,
( spl8_130
| ~ spl8_123
| ~ spl8_129 ),
inference(avatar_split_clause,[],[f1499,f1496,f1428,f1501]) ).
tff(f1501,plain,
( spl8_130
<=> ! [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,[spl8_130])]) ).
tff(f1496,plain,
( spl8_129
<=> ! [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,[spl8_129])]) ).
tff(f1499,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)) )
| ~ spl8_123
| ~ spl8_129 ),
inference(forward_demodulation,[],[f1497,f1429]) ).
tff(f1497,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)) )
| ~ spl8_129 ),
inference(avatar_component_clause,[],[f1496]) ).
tff(f1498,plain,
spl8_129,
inference(avatar_split_clause,[],[f467,f1496]) ).
tff(f467,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,[],[f339]) ).
tff(f339,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,[],[f211]) ).
tff(f211,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,[],[f76]) ).
tff(f76,axiom,
! [X1: $tType,X42: fun(X1,bool),X40: X1] :
( pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X40),X42))
<=> pp(aa(X1,bool,X42,X40)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1489,plain,
( spl8_128
| ~ spl8_123
| ~ spl8_127 ),
inference(avatar_split_clause,[],[f1485,f1482,f1428,f1487]) ).
tff(f1487,plain,
( spl8_128
<=> ! [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,[spl8_128])]) ).
tff(f1482,plain,
( spl8_127
<=> ! [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,[spl8_127])]) ).
tff(f1485,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)) )
| ~ spl8_123
| ~ spl8_127 ),
inference(forward_demodulation,[],[f1483,f1429]) ).
tff(f1483,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)) )
| ~ spl8_127 ),
inference(avatar_component_clause,[],[f1482]) ).
tff(f1484,plain,
spl8_127,
inference(avatar_split_clause,[],[f466,f1482]) ).
tff(f466,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,[],[f339]) ).
tff(f1480,plain,
spl8_126,
inference(avatar_split_clause,[],[f398,f1478]) ).
tff(f1478,plain,
( spl8_126
<=> ! [X0: $tType,X4: X0,X3: X0,X2: X0,X1: X0] :
( ( plus_plus(X0,plus_plus(X0,X4,X3),plus_plus(X0,X2,X1)) = plus_plus(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_126])]) ).
tff(f398,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ( plus_plus(X0,plus_plus(X0,X4,X3),plus_plus(X0,X2,X1)) = plus_plus(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] : ( plus_plus(X0,plus_plus(X0,X4,X3),plus_plus(X0,X2,X1)) = plus_plus(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] : ( plus_plus(X0,plus_plus(X0,X4,X3),plus_plus(X0,X2,X1)) = plus_plus(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1)) ) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X30: X0,X28: X0,X31: X0,X29: X0] : ( plus_plus(X0,plus_plus(X0,X29,X31),plus_plus(X0,X28,X30)) = plus_plus(X0,plus_plus(X0,X29,X28),plus_plus(X0,X31,X30)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1476,plain,
( spl8_125
| ~ spl8_38
| ~ spl8_113 ),
inference(avatar_split_clause,[],[f1382,f1292,f727,f1474]) ).
tff(f1474,plain,
( spl8_125
<=> ! [X0: nat] : ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,huffma1134658180e_cost(a,t_2),plus_plus(nat,huffma1134658180e_cost(a,t_1),huffma83463279weight(a,huffma1146269203erNode(a,X0,t_1,t_2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_125])]) ).
tff(f1382,plain,
( ! [X0: nat] : ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,huffma1134658180e_cost(a,t_2),plus_plus(nat,huffma1134658180e_cost(a,t_1),huffma83463279weight(a,huffma1146269203erNode(a,X0,t_1,t_2)))) )
| ~ spl8_38
| ~ spl8_113 ),
inference(superposition,[],[f1293,f728]) ).
tff(f1434,plain,
( spl8_124
| ~ spl8_65
| ~ spl8_122 ),
inference(avatar_split_clause,[],[f1426,f1423,f880,f1432]) ).
tff(f1432,plain,
( spl8_124
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),X2,X1) )
| ( sK5(X0,X1,X2) = sK6(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_124])]) ).
tff(f1423,plain,
( spl8_122
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X2,X1) )
| ( sK5(X0,X1,X2) = sK6(X0,X1,X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_122])]) ).
tff(f1426,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),X2,X1) )
| ( sK5(X0,X1,X2) = sK6(X0,X1,X2) ) )
| ~ spl8_65
| ~ spl8_122 ),
inference(forward_demodulation,[],[f1424,f881]) ).
tff(f1424,plain,
( ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X2,X1) )
| ( sK5(X0,X1,X2) = sK6(X0,X1,X2) ) )
| ~ spl8_122 ),
inference(avatar_component_clause,[],[f1423]) ).
tff(f1430,plain,
spl8_123,
inference(avatar_split_clause,[],[f506,f1428]) ).
tff(f506,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,[],[f238]) ).
tff(f238,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,[],[f125]) ).
tff(f125,axiom,
! [X0: $tType,X2: $tType,X1: $tType,X54: X0,X55: X1,X56: fun(X0,fun(X1,X2))] : ( aa(X0,X2,combc(X0,X1,X2,X56,X55),X54) = aa(X1,X2,aa(X0,fun(X1,X2),X56,X54),X55) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1425,plain,
spl8_122,
inference(avatar_split_clause,[],[f465,f1423]) ).
tff(f465,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X2,X1) )
| ( sK5(X0,X1,X2) = sK6(X0,X1,X2) ) ),
inference(cnf_transformation,[],[f338]) ).
tff(f1395,plain,
spl8_121,
inference(avatar_split_clause,[],[f505,f1393]) ).
tff(f1393,plain,
( spl8_121
<=> ! [X1: $tType,X0: $tType,X5: fun(nat,fun(X1,X0)),X4: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))))),X3: nat,X2: X1] : ( aa(X1,X0,aa(nat,fun(X1,X0),X5,X3),X2) = huffma1280178957ee_rec(X1,X0,X5,X4,huffma2021818691e_Leaf(X1,X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_121])]) ).
tff(f505,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: nat,X4: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))))),X5: fun(nat,fun(X1,X0))] : ( aa(X1,X0,aa(nat,fun(X1,X0),X5,X3),X2) = huffma1280178957ee_rec(X1,X0,X5,X4,huffma2021818691e_Leaf(X1,X3,X2)) ),
inference(cnf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: nat,X4: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),fun(X0,fun(X0,X0))))),X5: fun(nat,fun(X1,X0))] : ( aa(X1,X0,aa(nat,fun(X1,X0),X5,X3),X2) = huffma1280178957ee_rec(X1,X0,X5,X4,huffma2021818691e_Leaf(X1,X3,X2)) ),
inference(rectify,[],[f27]) ).
tff(f27,axiom,
! [X1: $tType,X2: $tType,X18: X2,X9: nat,X20: fun(nat,fun(huffma1450048681e_tree(X2),fun(huffma1450048681e_tree(X2),fun(X1,fun(X1,X1))))),X21: fun(nat,fun(X2,X1))] : ( aa(X2,X1,aa(nat,fun(X2,X1),X21,X9),X18) = huffma1280178957ee_rec(X2,X1,X21,X20,huffma2021818691e_Leaf(X2,X9,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1391,plain,
spl8_120,
inference(avatar_split_clause,[],[f504,f1389]) ).
tff(f1389,plain,
( spl8_120
<=> ! [X1: $tType,X0: $tType,X3: nat,X4: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0))),X5: fun(nat,fun(X1,X0)),X2: X1] : ( huffma107959123e_case(X1,X0,X5,X4,huffma2021818691e_Leaf(X1,X3,X2)) = aa(X1,X0,aa(nat,fun(X1,X0),X5,X3),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_120])]) ).
tff(f504,plain,
! [X1: $tType,X0: $tType,X2: X1,X3: nat,X4: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0))),X5: fun(nat,fun(X1,X0))] : ( huffma107959123e_case(X1,X0,X5,X4,huffma2021818691e_Leaf(X1,X3,X2)) = aa(X1,X0,aa(nat,fun(X1,X0),X5,X3),X2) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: $tType,X1: $tType,X2: X1,X3: nat,X4: fun(nat,fun(huffma1450048681e_tree(X1),fun(huffma1450048681e_tree(X1),X0))),X5: fun(nat,fun(X1,X0))] : ( huffma107959123e_case(X1,X0,X5,X4,huffma2021818691e_Leaf(X1,X3,X2)) = aa(X1,X0,aa(nat,fun(X1,X0),X5,X3),X2) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X1: $tType,X2: $tType,X18: X2,X9: nat,X20: fun(nat,fun(huffma1450048681e_tree(X2),fun(huffma1450048681e_tree(X2),X1))),X21: fun(nat,fun(X2,X1))] : ( huffma107959123e_case(X2,X1,X21,X20,huffma2021818691e_Leaf(X2,X9,X18)) = aa(X2,X1,aa(nat,fun(X2,X1),X21,X9),X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1379,plain,
( spl8_119
| ~ spl8_118 ),
inference(avatar_split_clause,[],[f1375,f1372,f1377]) ).
tff(f1377,plain,
( spl8_119
<=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] : pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),huffma675207370phabet(X0,X1)),sK4(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_119])]) ).
tff(f1372,plain,
( spl8_118
<=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1)),huffma675207370phabet(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_118])]) ).
tff(f1375,plain,
( ! [X0: $tType,X1: huffma1450048681e_tree(X0)] : pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),huffma675207370phabet(X0,X1)),sK4(X0,X1)))
| ~ spl8_118 ),
inference(forward_demodulation,[],[f1373,f506]) ).
tff(f1373,plain,
( ! [X0: $tType,X1: huffma1450048681e_tree(X0)] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1)),huffma675207370phabet(X0,X1)))
| ~ spl8_118 ),
inference(avatar_component_clause,[],[f1372]) ).
tff(f1374,plain,
spl8_118,
inference(avatar_split_clause,[],[f448,f1372]) ).
tff(f448,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1)),huffma675207370phabet(X0,X1))),
inference(cnf_transformation,[],[f331]) ).
tff(f331,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1)),huffma675207370phabet(X0,X1))),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f198,f330]) ).
tff(f330,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ? [X2: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),huffma675207370phabet(X0,X1)))
=> pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),sK4(X0,X1)),huffma675207370phabet(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f198,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
? [X2: X0] : pp(aa(fun(X0,bool),bool,aa(X0,fun(fun(X0,bool),bool),member(X0),X2),huffma675207370phabet(X0,X1))),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X1: $tType,X50: huffma1450048681e_tree(X1)] :
? [X51: X1] : pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X51),huffma675207370phabet(X1,X50))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1344,plain,
spl8_117,
inference(avatar_split_clause,[],[f503,f1342]) ).
tff(f1342,plain,
( spl8_117
<=> ! [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,[spl8_117])]) ).
tff(f503,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,[],[f235]) ).
tff(f235,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,[],[f124]) ).
tff(f124,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X54: X0,X55: fun(X0,X1),X56: fun(X1,X2)] : ( aa(X0,X2,combb(X1,X2,X0,X56,X55),X54) = aa(X1,X2,X56,aa(X0,X1,X55,X54)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1340,plain,
spl8_116,
inference(avatar_split_clause,[],[f455,f1338]) ).
tff(f1338,plain,
( spl8_116
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X2,inf_inf(fun(X0,bool),X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_116])]) ).
tff(f455,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X2,inf_inf(fun(X0,bool),X2,X1)) ),
inference(cnf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X2,inf_inf(fun(X0,bool),X2,X1)) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X1: $tType,X41: fun(X1,bool),X42: fun(X1,bool)] : ( inf_inf(fun(X1,bool),X42,X41) = inf_inf(fun(X1,bool),X42,inf_inf(fun(X1,bool),X42,X41)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1332,plain,
( spl8_115
| ~ spl8_65
| ~ spl8_114 ),
inference(avatar_split_clause,[],[f1328,f1324,f880,f1330]) ).
tff(f1330,plain,
( spl8_115
<=> ! [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,[spl8_115])]) ).
tff(f1324,plain,
( spl8_114
<=> ! [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,[spl8_114])]) ).
tff(f1328,plain,
( ! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),combk(bool,X0,fFalse)),X1))
| ~ spl8_65
| ~ spl8_114 ),
inference(forward_demodulation,[],[f1327,f881]) ).
tff(f1327,plain,
( ! [X0: $tType,X1: X0] : ~ pp(aa(X0,bool,combc(X0,fun(X0,bool),bool,member(X0),bot_bot(fun(X0,bool))),X1))
| ~ spl8_114 ),
inference(forward_demodulation,[],[f1325,f506]) ).
tff(f1325,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))))
| ~ spl8_114 ),
inference(avatar_component_clause,[],[f1324]) ).
tff(f1326,plain,
spl8_114,
inference(avatar_split_clause,[],[f421,f1324]) ).
tff(f421,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,[],[f178]) ).
tff(f178,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,[],[f46]) ).
tff(f46,axiom,
! [X1: $tType,X16: X1] : ~ pp(aa(fun(X1,bool),bool,aa(X1,fun(fun(X1,bool),bool),member(X1),X16),bot_bot(fun(X1,bool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1294,plain,
( spl8_113
| spl8_29
| ~ spl8_91 ),
inference(avatar_split_clause,[],[f1151,f1115,f685,f1292]) ).
tff(f1115,plain,
( spl8_91
<=> ! [X0: $tType,X3: nat,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] : ( huffma83463279weight(X0,huffma1146269203erNode(X0,X3,X2,X1)) = plus_plus(nat,huffma83463279weight(X0,X2),huffma83463279weight(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_91])]) ).
tff(f1151,plain,
( ! [X0: nat] : ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,plus_plus(nat,huffma1134658180e_cost(a,t_1),huffma83463279weight(a,huffma1146269203erNode(a,X0,t_1,t_2))),huffma1134658180e_cost(a,t_2)) )
| spl8_29
| ~ spl8_91 ),
inference(superposition,[],[f687,f1116]) ).
tff(f1116,plain,
( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] : ( huffma83463279weight(X0,huffma1146269203erNode(X0,X3,X2,X1)) = plus_plus(nat,huffma83463279weight(X0,X2),huffma83463279weight(X0,X1)) )
| ~ spl8_91 ),
inference(avatar_component_clause,[],[f1115]) ).
tff(f1290,plain,
spl8_112,
inference(avatar_split_clause,[],[f494,f1288]) ).
tff(f1288,plain,
( spl8_112
<=> ! [X0: $tType,X2: huffma1450048681e_tree(X0),X4: X0,X3: nat,X1: huffma1450048681e_tree(X0)] : ( huffma1352802255e_freq(X0,huffma1146269203erNode(X0,X3,X2,X1),X4) = plus_plus(nat,huffma1352802255e_freq(X0,X2,X4),huffma1352802255e_freq(X0,X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_112])]) ).
tff(f494,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X4: X0] : ( huffma1352802255e_freq(X0,huffma1146269203erNode(X0,X3,X2,X1),X4) = plus_plus(nat,huffma1352802255e_freq(X0,X2,X4),huffma1352802255e_freq(X0,X1,X4)) ),
inference(cnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat,X4: X0] : ( huffma1352802255e_freq(X0,huffma1146269203erNode(X0,X3,X2,X1),X4) = plus_plus(nat,huffma1352802255e_freq(X0,X2,X4),huffma1352802255e_freq(X0,X1,X4)) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X0: $tType,X10: huffma1450048681e_tree(X0),X11: huffma1450048681e_tree(X0),X12: nat,X19: X0] : ( huffma1352802255e_freq(X0,huffma1146269203erNode(X0,X12,X11,X10),X19) = plus_plus(nat,huffma1352802255e_freq(X0,X11,X19),huffma1352802255e_freq(X0,X10,X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1249,plain,
spl8_111,
inference(avatar_split_clause,[],[f478,f1247]) ).
tff(f1247,plain,
( spl8_111
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: X0] :
( pp(aa(X0,bool,X2,X1))
| ~ pp(aa(X0,bool,inf_inf(fun(X0,bool),X3,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_111])]) ).
tff(f478,plain,
! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: X0] :
( pp(aa(X0,bool,X2,X1))
| ~ pp(aa(X0,bool,inf_inf(fun(X0,bool),X3,X2),X1)) ),
inference(cnf_transformation,[],[f297]) ).
tff(f297,plain,
! [X0: $tType,X1: X0,X2: fun(X0,bool),X3: fun(X0,bool)] :
( pp(aa(X0,bool,X2,X1))
| ~ pp(aa(X0,bool,inf_inf(fun(X0,bool),X3,X2),X1)) ),
inference(ennf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: $tType,X1: X0,X2: fun(X0,bool),X3: fun(X0,bool)] :
( pp(aa(X0,bool,inf_inf(fun(X0,bool),X3,X2),X1))
=> pp(aa(X0,bool,X2,X1)) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X1: $tType,X40: X1,X41: fun(X1,bool),X42: fun(X1,bool)] :
( pp(aa(X1,bool,inf_inf(fun(X1,bool),X42,X41),X40))
=> pp(aa(X1,bool,X41,X40)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1245,plain,
spl8_110,
inference(avatar_split_clause,[],[f477,f1243]) ).
tff(f1243,plain,
( spl8_110
<=> ! [X0: $tType,X3: fun(X0,bool),X2: fun(X0,bool),X1: X0] :
( pp(aa(X0,bool,X3,X1))
| ~ pp(aa(X0,bool,inf_inf(fun(X0,bool),X3,X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_110])]) ).
tff(f477,plain,
! [X0: $tType,X2: fun(X0,bool),X3: fun(X0,bool),X1: X0] :
( pp(aa(X0,bool,X3,X1))
| ~ pp(aa(X0,bool,inf_inf(fun(X0,bool),X3,X2),X1)) ),
inference(cnf_transformation,[],[f296]) ).
tff(f296,plain,
! [X0: $tType,X1: X0,X2: fun(X0,bool),X3: fun(X0,bool)] :
( pp(aa(X0,bool,X3,X1))
| ~ pp(aa(X0,bool,inf_inf(fun(X0,bool),X3,X2),X1)) ),
inference(ennf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: $tType,X1: X0,X2: fun(X0,bool),X3: fun(X0,bool)] :
( pp(aa(X0,bool,inf_inf(fun(X0,bool),X3,X2),X1))
=> pp(aa(X0,bool,X3,X1)) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X1: $tType,X40: X1,X41: fun(X1,bool),X42: fun(X1,bool)] :
( pp(aa(X1,bool,inf_inf(fun(X1,bool),X42,X41),X40))
=> pp(aa(X1,bool,X42,X40)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1241,plain,
spl8_109,
inference(avatar_split_clause,[],[f413,f1239]) ).
tff(f1239,plain,
( spl8_109
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( inf_inf(X0,X3,inf_inf(X0,X2,X1)) = inf_inf(X0,inf_inf(X0,X3,X2),X1) )
| ~ semilattice_inf(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_109])]) ).
tff(f413,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( inf_inf(X0,X3,inf_inf(X0,X2,X1)) = inf_inf(X0,inf_inf(X0,X3,X2),X1) )
| ~ semilattice_inf(X0) ),
inference(cnf_transformation,[],[f278]) ).
tff(f278,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( inf_inf(X0,X3,inf_inf(X0,X2,X1)) = inf_inf(X0,inf_inf(X0,X3,X2),X1) )
| ~ semilattice_inf(X0) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: $tType] :
( semilattice_inf(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( inf_inf(X0,X3,inf_inf(X0,X2,X1)) = inf_inf(X0,inf_inf(X0,X3,X2),X1) ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X0: $tType] :
( semilattice_inf(X0)
=> ! [X28: X0,X31: X0,X29: X0] : ( inf_inf(X0,X29,inf_inf(X0,X31,X28)) = inf_inf(X0,inf_inf(X0,X29,X31),X28) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1237,plain,
spl8_108,
inference(avatar_split_clause,[],[f411,f1235]) ).
tff(f1235,plain,
( spl8_108
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( inf_inf(X0,X3,inf_inf(X0,X2,X1)) = inf_inf(X0,X2,inf_inf(X0,X3,X1)) )
| ~ semilattice_inf(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_108])]) ).
tff(f411,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( inf_inf(X0,X3,inf_inf(X0,X2,X1)) = inf_inf(X0,X2,inf_inf(X0,X3,X1)) )
| ~ semilattice_inf(X0) ),
inference(cnf_transformation,[],[f276]) ).
tff(f276,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( inf_inf(X0,X3,inf_inf(X0,X2,X1)) = inf_inf(X0,X2,inf_inf(X0,X3,X1)) )
| ~ semilattice_inf(X0) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $tType] :
( semilattice_inf(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( inf_inf(X0,X3,inf_inf(X0,X2,X1)) = inf_inf(X0,X2,inf_inf(X0,X3,X1)) ) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X0: $tType] :
( semilattice_inf(X0)
=> ! [X28: X0,X29: X0,X31: X0] : ( inf_inf(X0,X31,inf_inf(X0,X29,X28)) = inf_inf(X0,X29,inf_inf(X0,X31,X28)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1233,plain,
spl8_107,
inference(avatar_split_clause,[],[f404,f1231]) ).
tff(f1231,plain,
( spl8_107
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( inf_inf(X0,X3,inf_inf(X0,X2,X1)) = inf_inf(X0,inf_inf(X0,X3,X2),X1) )
| ~ lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_107])]) ).
tff(f404,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( inf_inf(X0,X3,inf_inf(X0,X2,X1)) = inf_inf(X0,inf_inf(X0,X3,X2),X1) )
| ~ lattice(X0) ),
inference(cnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( inf_inf(X0,X3,inf_inf(X0,X2,X1)) = inf_inf(X0,inf_inf(X0,X3,X2),X1) )
| ~ lattice(X0) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: $tType] :
( lattice(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( inf_inf(X0,X3,inf_inf(X0,X2,X1)) = inf_inf(X0,inf_inf(X0,X3,X2),X1) ) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X0: $tType] :
( lattice(X0)
=> ! [X24: X0,X25: X0,X26: X0] : ( inf_inf(X0,X26,inf_inf(X0,X25,X24)) = inf_inf(X0,inf_inf(X0,X26,X25),X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1229,plain,
spl8_106,
inference(avatar_split_clause,[],[f403,f1227]) ).
tff(f1227,plain,
( spl8_106
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( inf_inf(X0,X3,inf_inf(X0,X2,X1)) = inf_inf(X0,X2,inf_inf(X0,X3,X1)) )
| ~ lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_106])]) ).
tff(f403,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( inf_inf(X0,X3,inf_inf(X0,X2,X1)) = inf_inf(X0,X2,inf_inf(X0,X3,X1)) )
| ~ lattice(X0) ),
inference(cnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( inf_inf(X0,X3,inf_inf(X0,X2,X1)) = inf_inf(X0,X2,inf_inf(X0,X3,X1)) )
| ~ lattice(X0) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType] :
( lattice(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( inf_inf(X0,X3,inf_inf(X0,X2,X1)) = inf_inf(X0,X2,inf_inf(X0,X3,X1)) ) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X0: $tType] :
( lattice(X0)
=> ! [X24: X0,X25: X0,X26: X0] : ( inf_inf(X0,X26,inf_inf(X0,X25,X24)) = inf_inf(X0,X25,inf_inf(X0,X26,X24)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1225,plain,
spl8_105,
inference(avatar_split_clause,[],[f397,f1223]) ).
tff(f1223,plain,
( spl8_105
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,plus_plus(X0,X3,X1),X2) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_105])]) ).
tff(f397,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,plus_plus(X0,X3,X1),X2) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,plus_plus(X0,X3,X1),X2) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,plus_plus(X0,X3,X1),X2) ) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X28: X0,X31: X0,X29: X0] : ( plus_plus(X0,plus_plus(X0,X29,X31),X28) = plus_plus(X0,plus_plus(X0,X29,X28),X31) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1221,plain,
spl8_104,
inference(avatar_split_clause,[],[f395,f1219]) ).
tff(f1219,plain,
( spl8_104
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_104])]) ).
tff(f395,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) ) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X30: X0,X28: X0,X29: X0] : ( plus_plus(X0,X29,plus_plus(X0,X28,X30)) = plus_plus(X0,plus_plus(X0,X29,X28),X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1217,plain,
spl8_103,
inference(avatar_split_clause,[],[f394,f1215]) ).
tff(f1215,plain,
( spl8_103
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( plus_plus(X0,X3,plus_plus(X0,X2,X1)) = plus_plus(X0,X2,plus_plus(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_103])]) ).
tff(f394,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( plus_plus(X0,X3,plus_plus(X0,X2,X1)) = plus_plus(X0,X2,plus_plus(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( plus_plus(X0,X3,plus_plus(X0,X2,X1)) = plus_plus(X0,X2,plus_plus(X0,X3,X1)) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( plus_plus(X0,X3,plus_plus(X0,X2,X1)) = plus_plus(X0,X2,plus_plus(X0,X3,X1)) ) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X30: X0,X28: X0,X29: X0] : ( plus_plus(X0,X29,plus_plus(X0,X28,X30)) = plus_plus(X0,X28,plus_plus(X0,X29,X30)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1213,plain,
spl8_102,
inference(avatar_split_clause,[],[f386,f1211]) ).
tff(f1211,plain,
( spl8_102
<=> ! [X0: $tType,X2: nat,X1: nat] :
( ( semiring_1_of_nat(X0,plus_plus(nat,X2,X1)) = plus_plus(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1)) )
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_102])]) ).
tff(f386,plain,
! [X0: $tType,X2: nat,X1: nat] :
( ( semiring_1_of_nat(X0,plus_plus(nat,X2,X1)) = plus_plus(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1)) )
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f253]) ).
tff(f253,plain,
! [X0: $tType] :
( ! [X1: nat,X2: nat] : ( semiring_1_of_nat(X0,plus_plus(nat,X2,X1)) = plus_plus(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1)) )
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: $tType] :
( semiring_1(X0)
=> ! [X1: nat,X2: nat] : ( semiring_1_of_nat(X0,plus_plus(nat,X2,X1)) = plus_plus(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1)) ) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> ! [X22: nat,X23: nat] : ( semiring_1_of_nat(X0,plus_plus(nat,X23,X22)) = plus_plus(X0,semiring_1_of_nat(X0,X23),semiring_1_of_nat(X0,X22)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1209,plain,
spl8_101,
inference(avatar_split_clause,[],[f382,f1207]) ).
tff(f1207,plain,
( spl8_101
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) )
| ~ ab_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_101])]) ).
tff(f382,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) )
| ~ ab_semigroup_add(X0) ),
inference(cnf_transformation,[],[f249]) ).
tff(f249,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] : ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) )
| ~ ab_semigroup_add(X0) ),
inference(ennf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] : ( plus_plus(X0,plus_plus(X0,X3,X2),X1) = plus_plus(X0,X3,plus_plus(X0,X2,X1)) ) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X28: X0,X31: X0,X29: X0] : ( plus_plus(X0,plus_plus(X0,X29,X31),X28) = plus_plus(X0,X29,plus_plus(X0,X31,X28)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1183,plain,
( spl8_100
| ~ spl8_65
| ~ spl8_95 ),
inference(avatar_split_clause,[],[f1135,f1132,f880,f1181]) ).
tff(f1181,plain,
( spl8_100
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK1(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_100])]) ).
tff(f1132,plain,
( spl8_95
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK1(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_95])]) ).
tff(f1135,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK1(X0,X1))) )
| ~ spl8_65
| ~ spl8_95 ),
inference(forward_demodulation,[],[f1133,f881]) ).
tff(f1133,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK1(X0,X1))) )
| ~ spl8_95 ),
inference(avatar_component_clause,[],[f1132]) ).
tff(f1179,plain,
( spl8_99
| ~ spl8_65
| ~ spl8_94 ),
inference(avatar_split_clause,[],[f1130,f1127,f880,f1177]) ).
tff(f1177,plain,
( spl8_99
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK0(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_99])]) ).
tff(f1127,plain,
( spl8_94
<=> ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK0(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_94])]) ).
tff(f1130,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) = X1 )
| pp(aa(X0,bool,X1,sK0(X0,X1))) )
| ~ spl8_65
| ~ spl8_94 ),
inference(forward_demodulation,[],[f1128,f881]) ).
tff(f1128,plain,
( ! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK0(X0,X1))) )
| ~ spl8_94 ),
inference(avatar_component_clause,[],[f1127]) ).
tff(f1174,plain,
( spl8_98
| ~ spl8_18
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f711,f703,f630,f1172]) ).
tff(f1172,plain,
( spl8_98
<=> ! [X0: bool] : ( inf_inf(bool,X0,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_98])]) ).
tff(f630,plain,
( spl8_18
<=> semilattice_inf(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).
tff(f703,plain,
( spl8_33
<=> ! [X0: $tType,X1: X0] :
( ( inf_inf(X0,X1,X1) = X1 )
| ~ semilattice_inf(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_33])]) ).
tff(f711,plain,
( ! [X0: bool] : ( inf_inf(bool,X0,X0) = X0 )
| ~ spl8_18
| ~ spl8_33 ),
inference(resolution,[],[f704,f632]) ).
tff(f632,plain,
( semilattice_inf(bool)
| ~ spl8_18 ),
inference(avatar_component_clause,[],[f630]) ).
tff(f704,plain,
( ! [X0: $tType,X1: X0] :
( ~ semilattice_inf(X0)
| ( inf_inf(X0,X1,X1) = X1 ) )
| ~ spl8_33 ),
inference(avatar_component_clause,[],[f703]) ).
tff(f1143,plain,
( spl8_97
| ~ spl8_65
| ~ spl8_87 ),
inference(avatar_split_clause,[],[f1096,f1093,f880,f1141]) ).
tff(f1141,plain,
( spl8_97
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),combk(bool,X0,fFalse),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_97])]) ).
tff(f1093,plain,
( spl8_87
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),bot_bot(fun(X0,bool)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_87])]) ).
tff(f1096,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),combk(bool,X0,fFalse),X1) )
| ~ spl8_65
| ~ spl8_87 ),
inference(forward_demodulation,[],[f1094,f881]) ).
tff(f1094,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),bot_bot(fun(X0,bool)),X1) )
| ~ spl8_87 ),
inference(avatar_component_clause,[],[f1093]) ).
tff(f1139,plain,
( spl8_96
| ~ spl8_65
| ~ spl8_86 ),
inference(avatar_split_clause,[],[f1091,f1088,f880,f1137]) ).
tff(f1137,plain,
( spl8_96
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),X1,combk(bool,X0,fFalse)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_96])]) ).
tff(f1088,plain,
( spl8_86
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X1,bot_bot(fun(X0,bool))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_86])]) ).
tff(f1091,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( combk(bool,X0,fFalse) = inf_inf(fun(X0,bool),X1,combk(bool,X0,fFalse)) )
| ~ spl8_65
| ~ spl8_86 ),
inference(forward_demodulation,[],[f1089,f881]) ).
tff(f1089,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X1,bot_bot(fun(X0,bool))) )
| ~ spl8_86 ),
inference(avatar_component_clause,[],[f1088]) ).
tff(f1134,plain,
spl8_95,
inference(avatar_split_clause,[],[f536,f1132]) ).
tff(f536,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK1(X0,X1))) ),
inference(forward_demodulation,[],[f443,f416]) ).
tff(f416,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(cnf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X1: $tType,X44: fun(X1,bool)] : ( collect(X1,X44) = X44 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f443,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| pp(aa(X0,bool,X1,sK1(X0,X1))) ),
inference(cnf_transformation,[],[f321]) ).
tff(f321,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| pp(aa(X0,bool,X1,sK1(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,[sK1])],[f319,f320]) ).
tff(f320,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X2: X0] : pp(aa(X0,bool,X1,X2))
=> pp(aa(X0,bool,X1,sK1(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f319,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,[],[f318]) ).
tff(f318,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,[],[f195]) ).
tff(f195,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,[],[f45]) ).
tff(f45,axiom,
! [X1: $tType,X44: fun(X1,bool)] :
( ( bot_bot(fun(X1,bool)) = collect(X1,X44) )
<=> ! [X43: X1] : ~ pp(aa(X1,bool,X44,X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1129,plain,
spl8_94,
inference(avatar_split_clause,[],[f534,f1127]) ).
tff(f534,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = X1 )
| pp(aa(X0,bool,X1,sK0(X0,X1))) ),
inference(forward_demodulation,[],[f441,f416]) ).
tff(f441,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| pp(aa(X0,bool,X1,sK0(X0,X1))) ),
inference(cnf_transformation,[],[f317]) ).
tff(f317,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( ( bot_bot(fun(X0,bool)) = collect(X0,X1) )
| pp(aa(X0,bool,X1,sK0(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,[sK0])],[f315,f316]) ).
tff(f316,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ? [X2: X0] : pp(aa(X0,bool,X1,X2))
=> pp(aa(X0,bool,X1,sK0(X0,X1))) ),
introduced(choice_axiom,[]) ).
tff(f315,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,[],[f314]) ).
tff(f314,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,[],[f194]) ).
tff(f194,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,[],[f47]) ).
tff(f47,axiom,
! [X1: $tType,X44: fun(X1,bool)] :
( ( bot_bot(fun(X1,bool)) = collect(X1,X44) )
<=> ! [X43: X1] : ~ pp(aa(X1,bool,X44,X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1125,plain,
spl8_93,
inference(avatar_split_clause,[],[f512,f1123]) ).
tff(f1123,plain,
( spl8_93
<=> ! [X0: $tType,X2: huffma1450048681e_tree(X0),X6: nat,X4: huffma1450048681e_tree(X0),X3: nat,X5: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
( ( X1 = X4 )
| ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_93])]) ).
tff(f512,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
( ( X1 = X4 )
| ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ),
inference(cnf_transformation,[],[f349]) ).
tff(f349,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X6: nat] :
( ( ( huffma1146269203erNode(X0,X3,X2,X1) = huffma1146269203erNode(X0,X6,X5,X4) )
| ( X1 != X4 )
| ( X2 != X5 )
| ( X3 != X6 ) )
& ( ( ( X1 = X4 )
& ( X2 = X5 )
& ( X3 = X6 ) )
| ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
inference(flattening,[],[f348]) ).
tff(f348,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X6: nat] :
( ( ( huffma1146269203erNode(X0,X3,X2,X1) = huffma1146269203erNode(X0,X6,X5,X4) )
| ( X1 != X4 )
| ( X2 != X5 )
| ( X3 != X6 ) )
& ( ( ( X1 = X4 )
& ( X2 = X5 )
& ( X3 = X6 ) )
| ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
inference(nnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0),X6: nat] :
( ( huffma1146269203erNode(X0,X3,X2,X1) = huffma1146269203erNode(X0,X6,X5,X4) )
<=> ( ( X1 = X4 )
& ( X2 = X5 )
& ( X3 = X6 ) ) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X1: $tType,X4: huffma1450048681e_tree(X1),X5: huffma1450048681e_tree(X1),X6: nat,X7: huffma1450048681e_tree(X1),X8: huffma1450048681e_tree(X1),X9: nat] :
( ( huffma1146269203erNode(X1,X9,X8,X7) = huffma1146269203erNode(X1,X6,X5,X4) )
<=> ( ( X4 = X7 )
& ( X5 = X8 )
& ( X6 = X9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1121,plain,
spl8_92,
inference(avatar_split_clause,[],[f511,f1119]) ).
tff(f1119,plain,
( spl8_92
<=> ! [X0: $tType,X6: nat,X4: huffma1450048681e_tree(X0),X3: nat,X5: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
( ( X2 = X5 )
| ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_92])]) ).
tff(f511,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
( ( X2 = X5 )
| ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ),
inference(cnf_transformation,[],[f349]) ).
tff(f1117,plain,
spl8_91,
inference(avatar_split_clause,[],[f470,f1115]) ).
tff(f470,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] : ( huffma83463279weight(X0,huffma1146269203erNode(X0,X3,X2,X1)) = plus_plus(nat,huffma83463279weight(X0,X2),huffma83463279weight(X0,X1)) ),
inference(cnf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] : ( huffma83463279weight(X0,huffma1146269203erNode(X0,X3,X2,X1)) = plus_plus(nat,huffma83463279weight(X0,X2),huffma83463279weight(X0,X1)) ),
inference(rectify,[],[f3]) ).
tff(f3,axiom,
! [X0: $tType,X10: huffma1450048681e_tree(X0),X11: huffma1450048681e_tree(X0),X12: nat] : ( huffma83463279weight(X0,huffma1146269203erNode(X0,X12,X11,X10)) = plus_plus(nat,huffma83463279weight(X0,X11),huffma83463279weight(X0,X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1109,plain,
( spl8_90
| ~ spl8_17
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f710,f703,f625,f1107]) ).
tff(f1107,plain,
( spl8_90
<=> ! [X0: nat] : ( inf_inf(nat,X0,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_90])]) ).
tff(f625,plain,
( spl8_17
<=> semilattice_inf(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_17])]) ).
tff(f710,plain,
( ! [X0: nat] : ( inf_inf(nat,X0,X0) = X0 )
| ~ spl8_17
| ~ spl8_33 ),
inference(resolution,[],[f704,f627]) ).
tff(f627,plain,
( semilattice_inf(nat)
| ~ spl8_17 ),
inference(avatar_component_clause,[],[f625]) ).
tff(f1105,plain,
( spl8_89
| ~ spl8_88 ),
inference(avatar_split_clause,[],[f1101,f1098,f1103]) ).
tff(f1103,plain,
( spl8_89
<=> ! [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,[spl8_89])]) ).
tff(f1098,plain,
( spl8_88
<=> ! [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,[spl8_88])]) ).
tff(f1101,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl8_88 ),
inference(forward_demodulation,[],[f1099,f506]) ).
tff(f1099,plain,
( ! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) )
| ~ spl8_88 ),
inference(avatar_component_clause,[],[f1098]) ).
tff(f1100,plain,
spl8_88,
inference(avatar_split_clause,[],[f423,f1098]) ).
tff(f423,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(cnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: bool,X1: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0))
| ~ pp(X0)
| ~ pp(X1) ),
inference(rectify,[],[f128]) ).
tff(f128,axiom,
! [X55: bool,X56: bool] :
( pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X56),X55))
| ~ pp(X55)
| ~ pp(X56) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1095,plain,
spl8_87,
inference(avatar_split_clause,[],[f420,f1093]) ).
tff(f420,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),bot_bot(fun(X0,bool)),X1) ),
inference(cnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),bot_bot(fun(X0,bool)),X1) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X1: $tType,X41: fun(X1,bool)] : ( bot_bot(fun(X1,bool)) = inf_inf(fun(X1,bool),bot_bot(fun(X1,bool)),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1090,plain,
spl8_86,
inference(avatar_split_clause,[],[f419,f1088]) ).
tff(f419,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X1,bot_bot(fun(X0,bool))) ),
inference(cnf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( bot_bot(fun(X0,bool)) = inf_inf(fun(X0,bool),X1,bot_bot(fun(X0,bool))) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X1: $tType,X42: fun(X1,bool)] : ( bot_bot(fun(X1,bool)) = inf_inf(fun(X1,bool),X42,bot_bot(fun(X1,bool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1006,plain,
spl8_85,
inference(avatar_split_clause,[],[f510,f1004]) ).
tff(f1004,plain,
( spl8_85
<=> ! [X0: $tType,X5: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X6: nat,X3: nat,X1: huffma1450048681e_tree(X0)] :
( ( X3 = X6 )
| ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_85])]) ).
tff(f510,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X6: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] :
( ( X3 = X6 )
| ( huffma1146269203erNode(X0,X3,X2,X1) != huffma1146269203erNode(X0,X6,X5,X4) ) ),
inference(cnf_transformation,[],[f349]) ).
tff(f1002,plain,
spl8_84,
inference(avatar_split_clause,[],[f454,f1000]) ).
tff(f998,plain,
spl8_83,
inference(avatar_split_clause,[],[f453,f996]) ).
tff(f996,plain,
( spl8_83
<=> ! [X2: nat,X0: nat,X1: nat] : ( plus_plus(nat,X2,plus_plus(nat,X1,X0)) = plus_plus(nat,X1,plus_plus(nat,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_83])]) ).
tff(f994,plain,
spl8_82,
inference(avatar_split_clause,[],[f452,f992]) ).
tff(f992,plain,
( spl8_82
<=> ! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_82])]) ).
tff(f452,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X1,X2) ),
inference(cnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X1,X2) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X1: $tType,X41: fun(X1,bool),X42: fun(X1,bool)] : ( inf_inf(fun(X1,bool),X42,X41) = inf_inf(fun(X1,bool),X41,X42) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f987,plain,
( spl8_81
| ~ spl8_65
| ~ spl8_80 ),
inference(avatar_split_clause,[],[f956,f953,f880,f985]) ).
tff(f985,plain,
( spl8_81
<=> ! [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,[spl8_81])]) ).
tff(f953,plain,
( spl8_80
<=> ! [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,[spl8_80])]) ).
tff(f956,plain,
( ! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
( ( combk(bool,X0,fFalse) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) )
| ~ spl8_65
| ~ spl8_80 ),
inference(forward_demodulation,[],[f954,f881]) ).
tff(f954,plain,
( ! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) )
| ~ spl8_80 ),
inference(avatar_component_clause,[],[f953]) ).
tff(f955,plain,
spl8_80,
inference(avatar_split_clause,[],[f535,f953]) ).
tff(f535,plain,
! [X0: $tType,X3: X0,X1: fun(X0,bool)] :
( ( bot_bot(fun(X0,bool)) != X1 )
| ~ pp(aa(X0,bool,X1,X3)) ),
inference(forward_demodulation,[],[f440,f416]) ).
tff(f440,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,[],[f317]) ).
tff(f951,plain,
( spl8_79
| ~ spl8_14
| ~ spl8_49
| ~ spl8_65
| ~ spl8_66 ),
inference(avatar_split_clause,[],[f904,f884,f880,f778,f610,f948]) ).
tff(f948,plain,
( spl8_79
<=> ( fFalse = bot_bot(bool) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_79])]) ).
tff(f610,plain,
( spl8_14
<=> bot(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).
tff(f778,plain,
( spl8_49
<=> ! [X1: $tType,X0: $tType,X3: X1,X2: X0] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_49])]) ).
tff(f884,plain,
( spl8_66
<=> ! [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,[spl8_66])]) ).
tff(f904,plain,
( ( fFalse = bot_bot(bool) )
| ~ spl8_14
| ~ spl8_49
| ~ spl8_65
| ~ spl8_66 ),
inference(forward_demodulation,[],[f903,f779]) ).
tff(f779,plain,
( ! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 )
| ~ spl8_49 ),
inference(avatar_component_clause,[],[f778]) ).
tff(f903,plain,
( ! [X0: $tType,X1: X0] : ( bot_bot(bool) = aa(X0,bool,combk(bool,X0,fFalse),X1) )
| ~ spl8_14
| ~ spl8_65
| ~ spl8_66 ),
inference(forward_demodulation,[],[f900,f881]) ).
tff(f900,plain,
( ! [X0: $tType,X1: X0] : ( aa(X0,bool,bot_bot(fun(X0,bool)),X1) = bot_bot(bool) )
| ~ spl8_14
| ~ spl8_66 ),
inference(resolution,[],[f885,f612]) ).
tff(f612,plain,
( bot(bool)
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f610]) ).
tff(f885,plain,
( ! [X1: $tType,X0: $tType,X2: X0] :
( ~ bot(X1)
| ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) ) )
| ~ spl8_66 ),
inference(avatar_component_clause,[],[f884]) ).
tff(f945,plain,
( spl8_78
| ~ spl8_77 ),
inference(avatar_split_clause,[],[f941,f938,f943]) ).
tff(f943,plain,
( spl8_78
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_78])]) ).
tff(f938,plain,
( spl8_77
<=> ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_77])]) ).
tff(f941,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X1) )
| ~ spl8_77 ),
inference(forward_demodulation,[],[f939,f506]) ).
tff(f939,plain,
( ! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl8_77 ),
inference(avatar_component_clause,[],[f938]) ).
tff(f940,plain,
spl8_77,
inference(avatar_split_clause,[],[f425,f938]) ).
tff(f425,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: bool,X1: bool] :
( pp(X1)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f129]) ).
tff(f129,axiom,
! [X55: bool,X56: bool] :
( pp(X56)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X56),X55)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f935,plain,
( spl8_76
| ~ spl8_75 ),
inference(avatar_split_clause,[],[f931,f928,f933]) ).
tff(f933,plain,
( spl8_76
<=> ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_76])]) ).
tff(f928,plain,
( spl8_75
<=> ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_75])]) ).
tff(f931,plain,
( ! [X0: bool,X1: bool] :
( ~ pp(aa(bool,bool,combc(bool,bool,bool,fconj,X0),X1))
| pp(X0) )
| ~ spl8_75 ),
inference(forward_demodulation,[],[f929,f506]) ).
tff(f929,plain,
( ! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) )
| ~ spl8_75 ),
inference(avatar_component_clause,[],[f928]) ).
tff(f930,plain,
spl8_75,
inference(avatar_split_clause,[],[f424,f928]) ).
tff(f424,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(cnf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: bool,X1: bool] :
( pp(X0)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X1),X0)) ),
inference(rectify,[],[f130]) ).
tff(f130,axiom,
! [X55: bool,X56: bool] :
( pp(X55)
| ~ pp(aa(bool,bool,aa(bool,fun(bool,bool),fconj,X56),X55)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f926,plain,
spl8_74,
inference(avatar_split_clause,[],[f409,f924]) ).
tff(f924,plain,
( spl8_74
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( inf_inf(X0,X2,X1) = inf_inf(X0,X2,inf_inf(X0,X2,X1)) )
| ~ semilattice_inf(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_74])]) ).
tff(f409,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( inf_inf(X0,X2,X1) = inf_inf(X0,X2,inf_inf(X0,X2,X1)) )
| ~ semilattice_inf(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f274,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( inf_inf(X0,X2,X1) = inf_inf(X0,X2,inf_inf(X0,X2,X1)) )
| ~ semilattice_inf(X0) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $tType] :
( semilattice_inf(X0)
=> ! [X1: X0,X2: X0] : ( inf_inf(X0,X2,X1) = inf_inf(X0,X2,inf_inf(X0,X2,X1)) ) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X0: $tType] :
( semilattice_inf(X0)
=> ! [X31: X0,X29: X0] : ( inf_inf(X0,X29,X31) = inf_inf(X0,X29,inf_inf(X0,X29,X31)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f922,plain,
spl8_73,
inference(avatar_split_clause,[],[f402,f920]) ).
tff(f920,plain,
( spl8_73
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( inf_inf(X0,X2,X1) = inf_inf(X0,X2,inf_inf(X0,X2,X1)) )
| ~ lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_73])]) ).
tff(f402,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( inf_inf(X0,X2,X1) = inf_inf(X0,X2,inf_inf(X0,X2,X1)) )
| ~ lattice(X0) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( inf_inf(X0,X2,X1) = inf_inf(X0,X2,inf_inf(X0,X2,X1)) )
| ~ lattice(X0) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: $tType] :
( lattice(X0)
=> ! [X1: X0,X2: X0] : ( inf_inf(X0,X2,X1) = inf_inf(X0,X2,inf_inf(X0,X2,X1)) ) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X0: $tType] :
( lattice(X0)
=> ! [X25: X0,X26: X0] : ( inf_inf(X0,X26,X25) = inf_inf(X0,X26,inf_inf(X0,X26,X25)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f918,plain,
spl8_72,
inference(avatar_split_clause,[],[f388,f916]) ).
tff(f916,plain,
( spl8_72
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( X1 = X3 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X1,X2) )
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_72])]) ).
tff(f388,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( X1 = X3 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X1,X2) )
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( X1 = X3 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X1,X2) ) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( plus_plus(X0,X3,X2) = plus_plus(X0,X1,X2) )
=> ( X1 = X3 ) ) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X28: X0,X29: X0,X31: X0] :
( ( plus_plus(X0,X28,X29) = plus_plus(X0,X31,X29) )
=> ( X28 = X31 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f914,plain,
spl8_71,
inference(avatar_split_clause,[],[f387,f912]) ).
tff(f912,plain,
( spl8_71
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( X1 = X2 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) )
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_71])]) ).
tff(f387,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( X1 = X2 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) )
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f254]) ).
tff(f254,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( X1 = X2 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) ) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( plus_plus(X0,X3,X2) = plus_plus(X0,X3,X1) )
=> ( X1 = X2 ) ) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X28: X0,X31: X0,X29: X0] :
( ( plus_plus(X0,X29,X28) = plus_plus(X0,X29,X31) )
=> ( X28 = X31 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f910,plain,
spl8_70,
inference(avatar_split_clause,[],[f383,f908]) ).
tff(f908,plain,
( spl8_70
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( X1 = X2 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) )
| ~ cancel146912293up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_70])]) ).
tff(f383,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( X1 = X2 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) )
| ~ cancel146912293up_add(X0) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( X1 = X2 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X3,X1) ) )
| ~ cancel146912293up_add(X0) ),
inference(ennf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: $tType] :
( cancel146912293up_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( plus_plus(X0,X3,X2) = plus_plus(X0,X3,X1) )
=> ( X1 = X2 ) ) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType] :
( cancel146912293up_add(X0)
=> ! [X28: X0,X31: X0,X29: X0] :
( ( plus_plus(X0,X29,X28) = plus_plus(X0,X29,X31) )
=> ( X28 = X31 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f898,plain,
spl8_69,
inference(avatar_split_clause,[],[f499,f896]) ).
tff(f896,plain,
( spl8_69
<=> ! [X0: $tType,X2: nat,X4: nat,X3: X0,X1: X0] :
( ( X1 = X3 )
| ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_69])]) ).
tff(f499,plain,
! [X0: $tType,X2: nat,X3: X0,X1: X0,X4: nat] :
( ( X1 = X3 )
| ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ),
inference(cnf_transformation,[],[f347]) ).
tff(f347,plain,
! [X0: $tType,X1: X0,X2: nat,X3: X0,X4: nat] :
( ( ( huffma2021818691e_Leaf(X0,X2,X1) = huffma2021818691e_Leaf(X0,X4,X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ) ),
inference(flattening,[],[f346]) ).
tff(f346,plain,
! [X0: $tType,X1: X0,X2: nat,X3: X0,X4: nat] :
( ( ( huffma2021818691e_Leaf(X0,X2,X1) = huffma2021818691e_Leaf(X0,X4,X3) )
| ( X1 != X3 )
| ( X2 != X4 ) )
& ( ( ( X1 = X3 )
& ( X2 = X4 ) )
| ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ) ),
inference(nnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: $tType,X1: X0,X2: nat,X3: X0,X4: nat] :
( ( huffma2021818691e_Leaf(X0,X2,X1) = huffma2021818691e_Leaf(X0,X4,X3) )
<=> ( ( X1 = X3 )
& ( X2 = X4 ) ) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X1: $tType,X36: X1,X6: nat,X18: X1,X9: nat] :
( ( huffma2021818691e_Leaf(X1,X9,X18) = huffma2021818691e_Leaf(X1,X6,X36) )
<=> ( ( X18 = X36 )
& ( X6 = X9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f894,plain,
spl8_68,
inference(avatar_split_clause,[],[f498,f892]) ).
tff(f892,plain,
( spl8_68
<=> ! [X0: $tType,X4: nat,X3: X0,X2: nat,X1: X0] :
( ( X2 = X4 )
| ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_68])]) ).
tff(f498,plain,
! [X0: $tType,X2: nat,X3: X0,X1: X0,X4: nat] :
( ( X2 = X4 )
| ( huffma2021818691e_Leaf(X0,X2,X1) != huffma2021818691e_Leaf(X0,X4,X3) ) ),
inference(cnf_transformation,[],[f347]) ).
tff(f890,plain,
spl8_67,
inference(avatar_split_clause,[],[f475,f888]) ).
tff(f888,plain,
( spl8_67
<=> ! [X0: $tType,X3: X0,X2: X0,X1: nat] :
( ( zero_zero(nat) = huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_67])]) ).
tff(f475,plain,
! [X0: $tType,X2: X0,X3: X0,X1: nat] :
( ( zero_zero(nat) = huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) )
| ( X2 = X3 ) ),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
! [X0: $tType,X1: nat,X2: X0,X3: X0] :
( ( ( zero_zero(nat) = huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) )
| ( X2 = X3 ) )
& ( ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) = X1 )
| ( X2 != X3 ) ) ),
inference(ennf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: $tType,X1: nat,X2: X0,X3: X0] :
( ( ( X2 != X3 )
=> ( zero_zero(nat) = huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) ) )
& ( ( X2 = X3 )
=> ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) = X1 ) ) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X0: $tType,X12: nat,X29: X0,X19: X0] :
( ( ( X19 != X29 )
=> ( zero_zero(nat) = huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X12,X29),X19) ) )
& ( ( X19 = X29 )
=> ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X12,X29),X19) = X12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f886,plain,
spl8_66,
inference(avatar_split_clause,[],[f429,f884]) ).
tff(f429,plain,
! [X1: $tType,X0: $tType,X2: X0] :
( ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) )
| ~ bot(X1) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,plain,
! [X0: $tType,X1: $tType] :
( ! [X2: X0] : ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) )
| ~ bot(X1) ),
inference(ennf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: $tType,X1: $tType] :
( bot(X1)
=> ! [X2: X0] : ( bot_bot(X1) = aa(X0,X1,bot_bot(fun(X0,X1)),X2) ) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X2: $tType,X1: $tType] :
( bot(X1)
=> ! [X40: X2] : ( aa(X2,X1,bot_bot(fun(X2,X1)),X40) = bot_bot(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f882,plain,
( spl8_65
| ~ spl8_32
| ~ spl8_64 ),
inference(avatar_split_clause,[],[f878,f875,f699,f880]) ).
tff(f699,plain,
( spl8_32
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_32])]) ).
tff(f875,plain,
( spl8_64
<=> ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_64])]) ).
tff(f878,plain,
( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = combk(bool,X0,fFalse) )
| ~ spl8_32
| ~ spl8_64 ),
inference(forward_demodulation,[],[f876,f700]) ).
tff(f700,plain,
( ! [X0: $tType,X1: fun(X0,bool)] : ( collect(X0,X1) = X1 )
| ~ spl8_32 ),
inference(avatar_component_clause,[],[f699]) ).
tff(f876,plain,
( ! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) )
| ~ spl8_64 ),
inference(avatar_component_clause,[],[f875]) ).
tff(f877,plain,
spl8_64,
inference(avatar_split_clause,[],[f373,f875]) ).
tff(f373,plain,
! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: $tType] : ( bot_bot(fun(X0,bool)) = collect(X0,combk(bool,X0,fFalse)) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X1: $tType] : ( bot_bot(fun(X1,bool)) = collect(X1,combk(bool,X1,fFalse)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f857,plain,
spl8_63,
inference(avatar_split_clause,[],[f460,f855]) ).
tff(f855,plain,
( spl8_63
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_63])]) ).
tff(f460,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X2,X0) ) ),
inference(cnf_transformation,[],[f333]) ).
tff(f333,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( plus_plus(nat,X2,X1) = plus_plus(nat,X2,X0) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X2,X0) ) ) ),
inference(nnf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( plus_plus(nat,X2,X1) = plus_plus(nat,X2,X0) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X13: nat,X14: nat,X15: nat] :
( ( plus_plus(nat,X15,X14) = plus_plus(nat,X15,X13) )
<=> ( X13 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f853,plain,
spl8_62,
inference(avatar_split_clause,[],[f458,f851]) ).
tff(f851,plain,
( spl8_62
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_62])]) ).
tff(f458,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X0,X1) ) ),
inference(cnf_transformation,[],[f332]) ).
tff(f332,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( plus_plus(nat,X2,X1) = plus_plus(nat,X0,X1) )
| ( X0 != X2 ) )
& ( ( X0 = X2 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X0,X1) ) ) ),
inference(nnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( plus_plus(nat,X2,X1) = plus_plus(nat,X0,X1) )
<=> ( X0 = X2 ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X13: nat,X15: nat,X14: nat] :
( ( plus_plus(nat,X14,X15) = plus_plus(nat,X13,X15) )
<=> ( X13 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f849,plain,
spl8_61,
inference(avatar_split_clause,[],[f380,f847]) ).
tff(f847,plain,
( spl8_61
<=> ! [X0: $tType,X2: nat,X1: nat] :
( ( X1 = X2 )
| ( semiring_1_of_nat(X0,X2) != semiring_1_of_nat(X0,X1) )
| ~ semiring_char_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_61])]) ).
tff(f380,plain,
! [X0: $tType,X2: nat,X1: nat] :
( ( X1 = X2 )
| ( semiring_1_of_nat(X0,X2) != semiring_1_of_nat(X0,X1) )
| ~ semiring_char_0(X0) ),
inference(cnf_transformation,[],[f308]) ).
tff(f308,plain,
! [X0: $tType] :
( ! [X1: nat,X2: nat] :
( ( ( semiring_1_of_nat(X0,X2) = semiring_1_of_nat(X0,X1) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( semiring_1_of_nat(X0,X2) != semiring_1_of_nat(X0,X1) ) ) )
| ~ semiring_char_0(X0) ),
inference(nnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: $tType] :
( ! [X1: nat,X2: nat] :
( ( semiring_1_of_nat(X0,X2) = semiring_1_of_nat(X0,X1) )
<=> ( X1 = X2 ) )
| ~ semiring_char_0(X0) ),
inference(ennf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: $tType] :
( semiring_char_0(X0)
=> ! [X1: nat,X2: nat] :
( ( semiring_1_of_nat(X0,X2) = semiring_1_of_nat(X0,X1) )
<=> ( X1 = X2 ) ) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X1: $tType] :
( semiring_char_0(X1)
=> ! [X13: nat,X14: nat] :
( ( semiring_1_of_nat(X1,X14) = semiring_1_of_nat(X1,X13) )
<=> ( X13 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f845,plain,
spl8_60,
inference(avatar_split_clause,[],[f378,f843]) ).
tff(f843,plain,
( spl8_60
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( plus_plus(X0,X2,X1) != X2 )
| ~ semiri456707255roduct(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_60])]) ).
tff(f378,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( plus_plus(X0,X2,X1) != X2 )
| ~ semiri456707255roduct(X0) ),
inference(cnf_transformation,[],[f307]) ).
tff(f307,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ( plus_plus(X0,X2,X1) = X2 )
| ( zero_zero(X0) != X1 ) )
& ( ( zero_zero(X0) = X1 )
| ( plus_plus(X0,X2,X1) != X2 ) ) )
| ~ semiri456707255roduct(X0) ),
inference(nnf_transformation,[],[f247]) ).
tff(f247,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( plus_plus(X0,X2,X1) = X2 )
<=> ( zero_zero(X0) = X1 ) )
| ~ semiri456707255roduct(X0) ),
inference(ennf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: $tType] :
( semiri456707255roduct(X0)
=> ! [X1: X0,X2: X0] :
( ( plus_plus(X0,X2,X1) = X2 )
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X1: $tType] :
( semiri456707255roduct(X1)
=> ! [X18: X1,X17: X1] :
( ( plus_plus(X1,X17,X18) = X17 )
<=> ( zero_zero(X1) = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f841,plain,
( spl8_59
| ~ spl8_31
| ~ spl8_51 ),
inference(avatar_split_clause,[],[f796,f787,f694,f838]) ).
tff(f838,plain,
( spl8_59
<=> huffma1518433673istent(a,t_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_59])]) ).
tff(f694,plain,
( spl8_31
<=> huffma1518433673istent(a,huffma1146269203erNode(a,w,t_1,t_2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_31])]) ).
tff(f787,plain,
( spl8_51
<=> ! [X0: $tType,X3: nat,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
( huffma1518433673istent(X0,X1)
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_51])]) ).
tff(f796,plain,
( huffma1518433673istent(a,t_2)
| ~ spl8_31
| ~ spl8_51 ),
inference(resolution,[],[f788,f696]) ).
tff(f696,plain,
( huffma1518433673istent(a,huffma1146269203erNode(a,w,t_1,t_2))
| ~ spl8_31 ),
inference(avatar_component_clause,[],[f694]) ).
tff(f788,plain,
( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
( ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
| huffma1518433673istent(X0,X1) )
| ~ spl8_51 ),
inference(avatar_component_clause,[],[f787]) ).
tff(f825,plain,
spl8_58,
inference(avatar_split_clause,[],[f501,f823]) ).
tff(f823,plain,
( spl8_58
<=> ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X4: X0,X5: nat,X1: huffma1450048681e_tree(X0)] : ( huffma1146269203erNode(X0,X3,X2,X1) != huffma2021818691e_Leaf(X0,X5,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_58])]) ).
tff(f501,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X4: X0,X5: nat] : ( huffma1146269203erNode(X0,X3,X2,X1) != huffma2021818691e_Leaf(X0,X5,X4) ),
inference(cnf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat,X4: X0,X5: nat] : ( huffma1146269203erNode(X0,X3,X2,X1) != huffma2021818691e_Leaf(X0,X5,X4) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X0: $tType,X33: huffma1450048681e_tree(X0),X34: huffma1450048681e_tree(X0),X35: nat,X29: X0,X32: nat] : ( huffma1146269203erNode(X0,X35,X34,X33) != huffma2021818691e_Leaf(X0,X32,X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f821,plain,
spl8_57,
inference(avatar_split_clause,[],[f436,f819]) ).
tff(f819,plain,
( spl8_57
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_57])]) ).
tff(f436,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ),
inference(cnf_transformation,[],[f312]) ).
tff(f312,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero(nat) = plus_plus(nat,X1,X0) )
| ( zero_zero(nat) != X0 )
| ( zero_zero(nat) != X1 ) )
& ( ( ( zero_zero(nat) = X0 )
& ( zero_zero(nat) = X1 ) )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ) ),
inference(flattening,[],[f311]) ).
tff(f311,plain,
! [X0: nat,X1: nat] :
( ( ( zero_zero(nat) = plus_plus(nat,X1,X0) )
| ( zero_zero(nat) != X0 )
| ( zero_zero(nat) != X1 ) )
& ( ( ( zero_zero(nat) = X0 )
& ( zero_zero(nat) = X1 ) )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ) ),
inference(nnf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = plus_plus(nat,X1,X0) )
<=> ( ( zero_zero(nat) = X0 )
& ( zero_zero(nat) = X1 ) ) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X13: nat,X14: nat] :
( ( zero_zero(nat) = plus_plus(nat,X14,X13) )
<=> ( ( zero_zero(nat) = X13 )
& ( zero_zero(nat) = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f817,plain,
spl8_56,
inference(avatar_split_clause,[],[f435,f815]) ).
tff(f815,plain,
( spl8_56
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_56])]) ).
tff(f435,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ),
inference(cnf_transformation,[],[f312]) ).
tff(f813,plain,
spl8_55,
inference(avatar_split_clause,[],[f407,f811]) ).
tff(f811,plain,
( spl8_55
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( inf_inf(X0,X2,X1) = inf_inf(X0,X1,X2) )
| ~ semilattice_inf(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_55])]) ).
tff(f407,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( inf_inf(X0,X2,X1) = inf_inf(X0,X1,X2) )
| ~ semilattice_inf(X0) ),
inference(cnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( inf_inf(X0,X2,X1) = inf_inf(X0,X1,X2) )
| ~ semilattice_inf(X0) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: $tType] :
( semilattice_inf(X0)
=> ! [X1: X0,X2: X0] : ( inf_inf(X0,X2,X1) = inf_inf(X0,X1,X2) ) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X0: $tType] :
( semilattice_inf(X0)
=> ! [X31: X0,X29: X0] : ( inf_inf(X0,X29,X31) = inf_inf(X0,X31,X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f809,plain,
( spl8_54
| ~ spl8_31
| ~ spl8_50 ),
inference(avatar_split_clause,[],[f795,f782,f694,f806]) ).
tff(f806,plain,
( spl8_54
<=> huffma1518433673istent(a,t_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_54])]) ).
tff(f782,plain,
( spl8_50
<=> ! [X0: $tType,X3: nat,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] :
( huffma1518433673istent(X0,X2)
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_50])]) ).
tff(f795,plain,
( huffma1518433673istent(a,t_1)
| ~ spl8_31
| ~ spl8_50 ),
inference(resolution,[],[f783,f696]) ).
tff(f783,plain,
( ! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
( ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
| huffma1518433673istent(X0,X2) )
| ~ spl8_50 ),
inference(avatar_component_clause,[],[f782]) ).
tff(f804,plain,
spl8_53,
inference(avatar_split_clause,[],[f401,f802]) ).
tff(f802,plain,
( spl8_53
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( inf_inf(X0,X2,X1) = inf_inf(X0,X1,X2) )
| ~ lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_53])]) ).
tff(f401,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( inf_inf(X0,X2,X1) = inf_inf(X0,X1,X2) )
| ~ lattice(X0) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( inf_inf(X0,X2,X1) = inf_inf(X0,X1,X2) )
| ~ lattice(X0) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: $tType] :
( lattice(X0)
=> ! [X1: X0,X2: X0] : ( inf_inf(X0,X2,X1) = inf_inf(X0,X1,X2) ) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X0: $tType] :
( lattice(X0)
=> ! [X25: X0,X26: X0] : ( inf_inf(X0,X26,X25) = inf_inf(X0,X25,X26) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f800,plain,
spl8_52,
inference(avatar_split_clause,[],[f393,f798]) ).
tff(f798,plain,
( spl8_52
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( plus_plus(X0,X2,X1) = plus_plus(X0,X1,X2) )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_52])]) ).
tff(f393,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( plus_plus(X0,X2,X1) = plus_plus(X0,X1,X2) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( plus_plus(X0,X2,X1) = plus_plus(X0,X1,X2) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0] : ( plus_plus(X0,X2,X1) = plus_plus(X0,X1,X2) ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X28: X0,X29: X0] : ( plus_plus(X0,X29,X28) = plus_plus(X0,X28,X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f789,plain,
spl8_51,
inference(avatar_split_clause,[],[f488,f787]) ).
tff(f488,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
( huffma1518433673istent(X0,X1)
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ),
inference(cnf_transformation,[],[f343]) ).
tff(f784,plain,
spl8_50,
inference(avatar_split_clause,[],[f487,f782]) ).
tff(f487,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
( huffma1518433673istent(X0,X2)
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ),
inference(cnf_transformation,[],[f343]) ).
tff(f780,plain,
spl8_49,
inference(avatar_split_clause,[],[f469,f778]) ).
tff(f469,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(cnf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: X1] : ( aa(X0,X1,combk(X1,X0,X3),X2) = X3 ),
inference(rectify,[],[f126]) ).
tff(f126,axiom,
! [X1: $tType,X0: $tType,X55: X1,X56: X0] : ( aa(X1,X0,combk(X0,X1,X56),X55) = X56 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f776,plain,
spl8_48,
inference(avatar_split_clause,[],[f468,f774]) ).
tff(f774,plain,
( spl8_48
<=> ! [X0: $tType,X3: nat,X2: X0,X1: X0] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_48])]) ).
tff(f468,plain,
! [X0: $tType,X2: X0,X3: nat,X1: X0] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) ),
inference(cnf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: $tType,X1: X0,X2: X0,X3: nat] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X0: $tType,X29: X0,X31: X0,X12: nat] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X12,X31),X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f772,plain,
spl8_47,
inference(avatar_split_clause,[],[f418,f770]) ).
tff(f770,plain,
( spl8_47
<=> ! [X0: $tType,X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X1,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_47])]) ).
tff(f418,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X1,X1) = X1 ),
inference(cnf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: $tType,X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X1,X1) = X1 ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X1: $tType,X42: fun(X1,bool)] : ( inf_inf(fun(X1,bool),X42,X42) = X42 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f768,plain,
spl8_46,
inference(avatar_split_clause,[],[f400,f766]) ).
tff(f766,plain,
( spl8_46
<=> ! [X0: $tType,X1: X0] :
( ( bot_bot(X0) = inf_inf(X0,bot_bot(X0),X1) )
| ~ bounded_lattice_bot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_46])]) ).
tff(f400,plain,
! [X0: $tType,X1: X0] :
( ( bot_bot(X0) = inf_inf(X0,bot_bot(X0),X1) )
| ~ bounded_lattice_bot(X0) ),
inference(cnf_transformation,[],[f265]) ).
tff(f265,plain,
! [X0: $tType] :
( ! [X1: X0] : ( bot_bot(X0) = inf_inf(X0,bot_bot(X0),X1) )
| ~ bounded_lattice_bot(X0) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType] :
( bounded_lattice_bot(X0)
=> ! [X1: X0] : ( bot_bot(X0) = inf_inf(X0,bot_bot(X0),X1) ) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X0: $tType] :
( bounded_lattice_bot(X0)
=> ! [X26: X0] : ( bot_bot(X0) = inf_inf(X0,bot_bot(X0),X26) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f764,plain,
spl8_45,
inference(avatar_split_clause,[],[f399,f762]) ).
tff(f762,plain,
( spl8_45
<=> ! [X0: $tType,X1: X0] :
( ( bot_bot(X0) = inf_inf(X0,X1,bot_bot(X0)) )
| ~ bounded_lattice_bot(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_45])]) ).
tff(f399,plain,
! [X0: $tType,X1: X0] :
( ( bot_bot(X0) = inf_inf(X0,X1,bot_bot(X0)) )
| ~ bounded_lattice_bot(X0) ),
inference(cnf_transformation,[],[f264]) ).
tff(f264,plain,
! [X0: $tType] :
( ! [X1: X0] : ( bot_bot(X0) = inf_inf(X0,X1,bot_bot(X0)) )
| ~ bounded_lattice_bot(X0) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: $tType] :
( bounded_lattice_bot(X0)
=> ! [X1: X0] : ( bot_bot(X0) = inf_inf(X0,X1,bot_bot(X0)) ) ),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X0: $tType] :
( bounded_lattice_bot(X0)
=> ! [X26: X0] : ( bot_bot(X0) = inf_inf(X0,X26,bot_bot(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f757,plain,
( spl8_43
| ~ spl8_44
| ~ spl8_21 ),
inference(avatar_split_clause,[],[f674,f645,f754,f751]) ).
tff(f751,plain,
( spl8_43
<=> ! [X0: bool] : ( fTrue = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_43])]) ).
tff(f754,plain,
( spl8_44
<=> ( fFalse = fTrue ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_44])]) ).
tff(f645,plain,
( spl8_21
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_21])]) ).
tff(f674,plain,
( ! [X0: bool] :
( ( fFalse != fTrue )
| ( fTrue = X0 ) )
| ~ spl8_21 ),
inference(equality_factoring,[],[f646]) ).
tff(f646,plain,
( ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) )
| ~ spl8_21 ),
inference(avatar_component_clause,[],[f645]) ).
tff(f746,plain,
spl8_42,
inference(avatar_split_clause,[],[f528,f744]) ).
tff(f744,plain,
( spl8_42
<=> ! [X0: $tType,X1: nat,X3: X0] : ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X3),X3) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_42])]) ).
tff(f528,plain,
! [X0: $tType,X3: X0,X1: nat] : ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X3),X3) = X1 ),
inference(equality_resolution,[],[f474]) ).
tff(f474,plain,
! [X0: $tType,X2: X0,X3: X0,X1: nat] :
( ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) = X1 )
| ( X2 != X3 ) ),
inference(cnf_transformation,[],[f293]) ).
tff(f742,plain,
spl8_41,
inference(avatar_split_clause,[],[f521,f739]) ).
tff(f739,plain,
( spl8_41
<=> ( zero_zero(nat) = plus_plus(nat,zero_zero(nat),zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_41])]) ).
tff(f521,plain,
zero_zero(nat) = plus_plus(nat,zero_zero(nat),zero_zero(nat)),
inference(equality_resolution,[],[f520]) ).
tff(f520,plain,
! [X1: nat] :
( ( zero_zero(nat) = plus_plus(nat,X1,zero_zero(nat)) )
| ( zero_zero(nat) != X1 ) ),
inference(equality_resolution,[],[f437]) ).
tff(f437,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = plus_plus(nat,X1,X0) )
| ( zero_zero(nat) != X0 )
| ( zero_zero(nat) != X1 ) ),
inference(cnf_transformation,[],[f312]) ).
tff(f737,plain,
spl8_40,
inference(avatar_split_clause,[],[f516,f735]) ).
tff(f735,plain,
( spl8_40
<=> ! [X0: $tType,X2: X0] :
( ( plus_plus(X0,X2,zero_zero(X0)) = X2 )
| ~ semiri456707255roduct(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_40])]) ).
tff(f516,plain,
! [X0: $tType,X2: X0] :
( ( plus_plus(X0,X2,zero_zero(X0)) = X2 )
| ~ semiri456707255roduct(X0) ),
inference(equality_resolution,[],[f379]) ).
tff(f379,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( plus_plus(X0,X2,X1) = X2 )
| ( zero_zero(X0) != X1 )
| ~ semiri456707255roduct(X0) ),
inference(cnf_transformation,[],[f307]) ).
tff(f733,plain,
spl8_39,
inference(avatar_split_clause,[],[f451,f731]) ).
tff(f731,plain,
( spl8_39
<=> ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_39])]) ).
tff(f451,plain,
! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
inference(cnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: $tType,X1: X0,X2: nat] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
inference(rectify,[],[f95]) ).
tff(f95,axiom,
! [X0: $tType,X29: X0,X12: nat] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X12,X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f729,plain,
spl8_38,
inference(avatar_split_clause,[],[f417,f727]) ).
tff(f417,plain,
! [X0: nat,X1: nat] : ( plus_plus(nat,X1,X0) = plus_plus(nat,X0,X1) ),
inference(cnf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: nat,X1: nat] : ( plus_plus(nat,X1,X0) = plus_plus(nat,X0,X1) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X22: nat,X23: nat] : ( plus_plus(nat,X23,X22) = plus_plus(nat,X22,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f725,plain,
spl8_37,
inference(avatar_split_clause,[],[f385,f723]) ).
tff(f723,plain,
( spl8_37
<=> ! [X0: $tType] :
( ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) )
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_37])]) ).
tff(f385,plain,
! [X0: $tType] :
( ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) )
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: $tType] :
( ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) )
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f92]) ).
tff(f92,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f721,plain,
spl8_36,
inference(avatar_split_clause,[],[f384,f719]) ).
tff(f719,plain,
( spl8_36
<=> ! [X0: $tType] :
( ( semiring_1_of_nat(X0,one_one(nat)) = one_one(X0) )
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_36])]) ).
tff(f384,plain,
! [X0: $tType] :
( ( semiring_1_of_nat(X0,one_one(nat)) = one_one(X0) )
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f251]) ).
tff(f251,plain,
! [X0: $tType] :
( ( semiring_1_of_nat(X0,one_one(nat)) = one_one(X0) )
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f35]) ).
tff(f35,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> ( semiring_1_of_nat(X0,one_one(nat)) = one_one(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f716,plain,
spl8_35,
inference(avatar_split_clause,[],[f375,f714]) ).
tff(f714,plain,
( spl8_35
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_35])]) ).
tff(f375,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ),
inference(cnf_transformation,[],[f245]) ).
tff(f245,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ),
inference(ennf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X1: X0] : ( plus_plus(X0,X1,zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X29: X0] : ( plus_plus(X0,X29,zero_zero(X0)) = X29 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f709,plain,
spl8_34,
inference(avatar_split_clause,[],[f450,f707]) ).
tff(f707,plain,
( spl8_34
<=> ! [X0: $tType,X2: nat,X1: X0] : ( huffma83463279weight(X0,huffma2021818691e_Leaf(X0,X2,X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_34])]) ).
tff(f450,plain,
! [X0: $tType,X2: nat,X1: X0] : ( huffma83463279weight(X0,huffma2021818691e_Leaf(X0,X2,X1)) = X2 ),
inference(cnf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: $tType,X1: X0,X2: nat] : ( huffma83463279weight(X0,huffma2021818691e_Leaf(X0,X2,X1)) = X2 ),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X0: $tType,X29: X0,X12: nat] : ( huffma83463279weight(X0,huffma2021818691e_Leaf(X0,X12,X29)) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f705,plain,
spl8_33,
inference(avatar_split_clause,[],[f405,f703]) ).
tff(f405,plain,
! [X0: $tType,X1: X0] :
( ( inf_inf(X0,X1,X1) = X1 )
| ~ semilattice_inf(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f270,plain,
! [X0: $tType] :
( ! [X1: X0] : ( inf_inf(X0,X1,X1) = X1 )
| ~ semilattice_inf(X0) ),
inference(ennf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: $tType] :
( semilattice_inf(X0)
=> ! [X1: X0] : ( inf_inf(X0,X1,X1) = X1 ) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X0: $tType] :
( semilattice_inf(X0)
=> ! [X29: X0] : ( inf_inf(X0,X29,X29) = X29 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f701,plain,
spl8_32,
inference(avatar_split_clause,[],[f416,f699]) ).
tff(f697,plain,
spl8_31,
inference(avatar_split_clause,[],[f372,f694]) ).
tff(f372,plain,
huffma1518433673istent(a,huffma1146269203erNode(a,w,t_1,t_2)),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
huffma1518433673istent(a,huffma1146269203erNode(a,w,t_1,t_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f692,plain,
( spl8_30
| spl8_1
| ~ spl8_21 ),
inference(avatar_split_clause,[],[f673,f645,f545,f690]) ).
tff(f690,plain,
( spl8_30
<=> ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_30])]) ).
tff(f545,plain,
( spl8_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
tff(f673,plain,
( ! [X0: bool] :
( ~ pp(X0)
| ( fTrue = X0 ) )
| spl8_1
| ~ spl8_21 ),
inference(superposition,[],[f547,f646]) ).
tff(f547,plain,
( ~ pp(fFalse)
| spl8_1 ),
inference(avatar_component_clause,[],[f545]) ).
tff(f688,plain,
( ~ spl8_29
| spl8_28 ),
inference(avatar_split_clause,[],[f683,f676,f685]) ).
tff(f676,plain,
( spl8_28
<=> ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) = plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),huffma83463279weight(a,t_2)),huffma1134658180e_cost(a,t_2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_28])]) ).
tff(f683,plain,
( ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,plus_plus(nat,huffma1134658180e_cost(a,t_1),plus_plus(nat,huffma83463279weight(a,t_1),huffma83463279weight(a,t_2))),huffma1134658180e_cost(a,t_2)) )
| spl8_28 ),
inference(forward_demodulation,[],[f682,f453]) ).
tff(f682,plain,
( ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),plus_plus(nat,huffma1134658180e_cost(a,t_1),huffma83463279weight(a,t_2))),huffma1134658180e_cost(a,t_2)) )
| spl8_28 ),
inference(forward_demodulation,[],[f681,f417]) ).
tff(f681,plain,
( ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),plus_plus(nat,huffma83463279weight(a,t_2),huffma1134658180e_cost(a,t_1))),huffma1134658180e_cost(a,t_2)) )
| spl8_28 ),
inference(forward_demodulation,[],[f680,f453]) ).
tff(f680,plain,
( ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_2),plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1))),huffma1134658180e_cost(a,t_2)) )
| spl8_28 ),
inference(forward_demodulation,[],[f678,f417]) ).
tff(f678,plain,
( ( huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),huffma83463279weight(a,t_2)),huffma1134658180e_cost(a,t_2)) )
| spl8_28 ),
inference(avatar_component_clause,[],[f676]) ).
tff(f679,plain,
~ spl8_28,
inference(avatar_split_clause,[],[f350,f676]) ).
tff(f350,plain,
huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),huffma83463279weight(a,t_2)),huffma1134658180e_cost(a,t_2)),
inference(cnf_transformation,[],[f135]) ).
tff(f135,plain,
huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),huffma83463279weight(a,t_2)),huffma1134658180e_cost(a,t_2)),
inference(flattening,[],[f134]) ).
tff(f134,negated_conjecture,
( ~ huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) = plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),huffma83463279weight(a,t_2)),huffma1134658180e_cost(a,t_2)) ),
inference(negated_conjecture,[],[f133]) ).
tff(f133,conjecture,
huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) = plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),huffma83463279weight(a,t_2)),huffma1134658180e_cost(a,t_2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f671,plain,
spl8_27,
inference(avatar_split_clause,[],[f449,f669]) ).
tff(f669,plain,
( spl8_27
<=> ! [X0: $tType,X2: nat,X1: X0] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_27])]) ).
tff(f449,plain,
! [X0: $tType,X2: nat,X1: X0] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)),
inference(cnf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: $tType,X1: X0,X2: nat] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X0: $tType,X29: X0,X12: nat] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X12,X29)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f667,plain,
spl8_26,
inference(avatar_split_clause,[],[f432,f665]) ).
tff(f665,plain,
( spl8_26
<=> ! [X1: $tType,X0: $tType] :
( semilattice_inf(fun(X0,X1))
| ~ lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_26])]) ).
tff(f432,plain,
! [X1: $tType,X0: $tType] :
( semilattice_inf(fun(X0,X1))
| ~ lattice(X1) ),
inference(cnf_transformation,[],[f288]) ).
tff(f288,plain,
! [X0: $tType,X1: $tType] :
( semilattice_inf(fun(X0,X1))
| ~ lattice(X1) ),
inference(ennf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: $tType,X1: $tType] :
( lattice(X1)
=> semilattice_inf(fun(X0,X1)) ),
inference(rectify,[],[f102]) ).
tff(f102,axiom,
! [X52: $tType,X53: $tType] :
( lattice(X53)
=> semilattice_inf(fun(X52,X53)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f663,plain,
spl8_25,
inference(avatar_split_clause,[],[f431,f661]) ).
tff(f661,plain,
( spl8_25
<=> ! [X1: $tType,X0: $tType] :
( lattice(fun(X0,X1))
| ~ lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).
tff(f431,plain,
! [X1: $tType,X0: $tType] :
( lattice(fun(X0,X1))
| ~ lattice(X1) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,plain,
! [X0: $tType,X1: $tType] :
( lattice(fun(X0,X1))
| ~ lattice(X1) ),
inference(ennf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: $tType,X1: $tType] :
( lattice(X1)
=> lattice(fun(X0,X1)) ),
inference(rectify,[],[f103]) ).
tff(f103,axiom,
! [X52: $tType,X53: $tType] :
( lattice(X53)
=> lattice(fun(X52,X53)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f659,plain,
spl8_24,
inference(avatar_split_clause,[],[f428,f657]) ).
tff(f657,plain,
( spl8_24
<=> ! [X1: $tType,X0: $tType] :
( bot(fun(X0,X1))
| ~ bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_24])]) ).
tff(f428,plain,
! [X1: $tType,X0: $tType] :
( bot(fun(X0,X1))
| ~ bot(X1) ),
inference(cnf_transformation,[],[f284]) ).
tff(f284,plain,
! [X0: $tType,X1: $tType] :
( bot(fun(X0,X1))
| ~ bot(X1) ),
inference(ennf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: $tType,X1: $tType] :
( bot(X1)
=> bot(fun(X0,X1)) ),
inference(rectify,[],[f104]) ).
tff(f104,axiom,
! [X52: $tType,X53: $tType] :
( bot(X53)
=> bot(fun(X52,X53)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f655,plain,
spl8_23,
inference(avatar_split_clause,[],[f427,f653]) ).
tff(f653,plain,
( spl8_23
<=> ! [X1: $tType,X0: $tType] :
( bounded_lattice(fun(X0,X1))
| ~ bounded_lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_23])]) ).
tff(f427,plain,
! [X1: $tType,X0: $tType] :
( bounded_lattice(fun(X0,X1))
| ~ bounded_lattice(X1) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: $tType,X1: $tType] :
( bounded_lattice(fun(X0,X1))
| ~ bounded_lattice(X1) ),
inference(ennf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: $tType,X1: $tType] :
( bounded_lattice(X1)
=> bounded_lattice(fun(X0,X1)) ),
inference(rectify,[],[f100]) ).
tff(f100,axiom,
! [X52: $tType,X53: $tType] :
( bounded_lattice(X53)
=> bounded_lattice(fun(X52,X53)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f651,plain,
spl8_22,
inference(avatar_split_clause,[],[f426,f649]) ).
tff(f649,plain,
( spl8_22
<=> ! [X1: $tType,X0: $tType] :
( bounded_lattice_bot(fun(X0,X1))
| ~ bounded_lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_22])]) ).
tff(f426,plain,
! [X1: $tType,X0: $tType] :
( bounded_lattice_bot(fun(X0,X1))
| ~ bounded_lattice(X1) ),
inference(cnf_transformation,[],[f282]) ).
tff(f282,plain,
! [X0: $tType,X1: $tType] :
( bounded_lattice_bot(fun(X0,X1))
| ~ bounded_lattice(X1) ),
inference(ennf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: $tType,X1: $tType] :
( bounded_lattice(X1)
=> bounded_lattice_bot(fun(X0,X1)) ),
inference(rectify,[],[f101]) ).
tff(f101,axiom,
! [X52: $tType,X53: $tType] :
( bounded_lattice(X53)
=> bounded_lattice_bot(fun(X52,X53)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f647,plain,
spl8_21,
inference(avatar_split_clause,[],[f374,f645]) ).
tff(f374,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f132]) ).
tff(f132,axiom,
! [X56: bool] :
( ( fFalse = X56 )
| ( fTrue = X56 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f643,plain,
spl8_20,
inference(avatar_split_clause,[],[f371,f640]) ).
tff(f640,plain,
( spl8_20
<=> ( zero_zero(nat) = bot_bot(nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_20])]) ).
tff(f371,plain,
zero_zero(nat) = bot_bot(nat),
inference(cnf_transformation,[],[f96]) ).
tff(f96,axiom,
zero_zero(nat) = bot_bot(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f638,plain,
spl8_19,
inference(avatar_split_clause,[],[f370,f635]) ).
tff(f635,plain,
( spl8_19
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).
tff(f370,plain,
pp(fTrue),
inference(cnf_transformation,[],[f123]) ).
tff(f123,axiom,
pp(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f633,plain,
spl8_18,
inference(avatar_split_clause,[],[f369,f630]) ).
tff(f369,plain,
semilattice_inf(bool),
inference(cnf_transformation,[],[f119]) ).
tff(f119,axiom,
semilattice_inf(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f628,plain,
spl8_17,
inference(avatar_split_clause,[],[f368,f625]) ).
tff(f368,plain,
semilattice_inf(nat),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
semilattice_inf(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f623,plain,
spl8_16,
inference(avatar_split_clause,[],[f367,f620]) ).
tff(f620,plain,
( spl8_16
<=> lattice(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_16])]) ).
tff(f367,plain,
lattice(bool),
inference(cnf_transformation,[],[f120]) ).
tff(f120,axiom,
lattice(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f618,plain,
spl8_15,
inference(avatar_split_clause,[],[f366,f615]) ).
tff(f615,plain,
( spl8_15
<=> lattice(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).
tff(f366,plain,
lattice(nat),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
lattice(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f613,plain,
spl8_14,
inference(avatar_split_clause,[],[f365,f610]) ).
tff(f365,plain,
bot(bool),
inference(cnf_transformation,[],[f121]) ).
tff(f121,axiom,
bot(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f608,plain,
spl8_13,
inference(avatar_split_clause,[],[f364,f605]) ).
tff(f605,plain,
( spl8_13
<=> bot(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).
tff(f364,plain,
bot(nat),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
bot(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f603,plain,
spl8_12,
inference(avatar_split_clause,[],[f363,f600]) ).
tff(f600,plain,
( spl8_12
<=> bounded_lattice(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).
tff(f363,plain,
bounded_lattice(bool),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
bounded_lattice(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f598,plain,
spl8_11,
inference(avatar_split_clause,[],[f362,f595]) ).
tff(f595,plain,
( spl8_11
<=> bounded_lattice_bot(bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
tff(f362,plain,
bounded_lattice_bot(bool),
inference(cnf_transformation,[],[f118]) ).
tff(f118,axiom,
bounded_lattice_bot(bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f593,plain,
spl8_10,
inference(avatar_split_clause,[],[f361,f590]) ).
tff(f590,plain,
( spl8_10
<=> comm_semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
tff(f361,plain,
comm_semiring_1(nat),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
comm_semiring_1(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f588,plain,
spl8_9,
inference(avatar_split_clause,[],[f360,f585]) ).
tff(f585,plain,
( spl8_9
<=> cancel_semigroup_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
tff(f360,plain,
cancel_semigroup_add(nat),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
cancel_semigroup_add(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f583,plain,
spl8_8,
inference(avatar_split_clause,[],[f359,f580]) ).
tff(f580,plain,
( spl8_8
<=> semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
tff(f359,plain,
semiring_1(nat),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
semiring_1(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f578,plain,
spl8_7,
inference(avatar_split_clause,[],[f358,f575]) ).
tff(f575,plain,
( spl8_7
<=> comm_monoid_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
tff(f358,plain,
comm_monoid_add(nat),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
comm_monoid_add(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f573,plain,
spl8_6,
inference(avatar_split_clause,[],[f357,f570]) ).
tff(f570,plain,
( spl8_6
<=> one(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
tff(f357,plain,
one(nat),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
one(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f568,plain,
spl8_5,
inference(avatar_split_clause,[],[f356,f565]) ).
tff(f565,plain,
( spl8_5
<=> semiring_char_0(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
tff(f356,plain,
semiring_char_0(nat),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
semiring_char_0(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f563,plain,
spl8_4,
inference(avatar_split_clause,[],[f355,f560]) ).
tff(f560,plain,
( spl8_4
<=> ab_semigroup_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
tff(f355,plain,
ab_semigroup_add(nat),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
ab_semigroup_add(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f558,plain,
spl8_3,
inference(avatar_split_clause,[],[f354,f555]) ).
tff(f555,plain,
( spl8_3
<=> cancel146912293up_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
tff(f354,plain,
cancel146912293up_add(nat),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
cancel146912293up_add(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f553,plain,
spl8_2,
inference(avatar_split_clause,[],[f353,f550]) ).
tff(f550,plain,
( spl8_2
<=> semiri456707255roduct(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
tff(f353,plain,
semiri456707255roduct(nat),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
semiri456707255roduct(nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f548,plain,
~ spl8_1,
inference(avatar_split_clause,[],[f351,f545]) ).
tff(f351,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f131]) ).
tff(f131,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW535_5 : TPTP v8.2.0. Released v6.0.0.
% 0.03/0.12 % Command : run_vampire %s %d SAT
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 08:43:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TF1_THM_EQU_NAR problem
% 0.12/0.35 Running first-order model finding
% 0.12/0.35 Running /export/starexec/sandbox2/solver/bin/vampire --mode casc_sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.40 % (31366)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.40 % (31373)fmb+10_1:1_sil=256000:fmbes=contour:i=214858:bce=on_0 on theBenchmark for (2999ds/214858Mi)
% 0.20/0.40 % Exception at run slice level
% 0.20/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.42 % (31366)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (31371)fmb+10_1:1_sil=256000:i=98885:tgt=full:fmbsr=1.3:fmbss=10_0 on theBenchmark for (2999ds/98885Mi)
% 0.20/0.42 % (31366)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (31372)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:i=99418_0 on theBenchmark for (2999ds/99418Mi)
% 0.20/0.42 % (31366)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (31374)fmb+10_1:1_sil=256000:fmbss=23:fmbes=contour:newcnf=on:fmbsr=1.14:i=152523:nm=2:gsp=on:rp=on_0 on theBenchmark for (2999ds/152523Mi)
% 0.20/0.42 % (31366)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (31376)ott+11_8:59_sil=16000:sp=occurrence:lsd=20:abs=on:i=146:aac=none:nm=16:fdi=10:rawr=on:nicw=on_0 on theBenchmark for (2999ds/146Mi)
% 0.20/0.42 % (31366)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (31375)ott+21_1:1_sil=4000:i=104:fsd=on:fd=off:newcnf=on_0 on theBenchmark for (2999ds/104Mi)
% 0.20/0.42 % (31366)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (31377)ott-4_1:1_sil=4000:sp=reverse_arity:lcm=predicate:newcnf=on:i=115:bce=on:fd=off:fs=off:fsr=off_0 on theBenchmark for (2999ds/115Mi)
% 0.20/0.42 % (31374)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.42 % (31377)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.42 % (31375)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.43 % (31374)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.43 % Exception at run slice level
% 0.20/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.43 % Exception at run slice level
% 0.20/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.43 % Exception at run slice level
% 0.20/0.43 User error: Immediate (shared) subterms of term/literal plus_plus(huffma1134658180e_cost,X0,X1) have different types/not well-typed!
% 0.20/0.43 % (31366)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43 % (31393)dis+11_1:3_bsr=unit_only:sil=2000:rp=on:newcnf=on:i=404:kws=precedence:lsd=100_0 on theBenchmark for (2999ds/404Mi)
% 0.20/0.43 % (31393)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.48 % (31377)Instruction limit reached!
% 0.20/0.48 % (31377)------------------------------
% 0.20/0.48 % (31377)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.48 % (31377)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.48 % (31377)Termination reason: Time limit
% 0.20/0.48 % (31377)Termination phase: Saturation
% 0.20/0.48
% 0.20/0.48 % (31377)Memory used [KB]: 1630
% 0.20/0.48 % (31377)Time elapsed: 0.058 s
% 0.20/0.48 % (31377)Instructions burned: 117 (million)
% 0.20/0.48 % (31366)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.48 % (31410)ott+4_1:1_sil=2000:i=900:bd=off:fsr=off_0 on theBenchmark for (2999ds/900Mi)
% 0.20/0.48 % (31372)First to succeed.
% 0.20/0.48 % (31375)Instruction limit reached!
% 0.20/0.48 % (31375)------------------------------
% 0.20/0.48 % (31375)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.48 % (31375)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.48 % (31375)Termination reason: Time limit
% 0.20/0.48 % (31375)Termination phase: Saturation
% 0.20/0.48
% 0.20/0.48 % (31375)Memory used [KB]: 1450
% 0.20/0.48 % (31375)Time elapsed: 0.063 s
% 0.20/0.48 % (31375)Instructions burned: 105 (million)
% 0.20/0.49 % (31366)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.49 % (31407)ott-21_1:1_sil=4000:sp=const_frequency:i=175:fsr=off:fs=off:av=off_0 on theBenchmark for (2999ds/175Mi)
% 0.20/0.49 % (31366)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.49 % (31408)ott+33_1:1_to=lpo:sil=8000:sp=weighted_frequency:rp=on:i=270:nm=3:fsr=off:sac=on_0 on theBenchmark for (2999ds/270Mi)
% 0.20/0.50 % (31372)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-31366"
% 0.20/0.50 % (31366)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.50 % (31372)Refutation found. Thanks to Tanya!
% 0.20/0.50 % SZS status Theorem for theBenchmark
% 0.20/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50 % (31372)------------------------------
% 0.20/0.50 % (31372)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.50 % (31372)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.50 % (31372)Termination reason: Refutation
% 0.20/0.50
% 0.20/0.50 % (31372)Memory used [KB]: 1895
% 0.20/0.50 % (31372)Time elapsed: 0.074 s
% 0.20/0.50 % (31372)Instructions burned: 116 (million)
% 0.20/0.50 % (31372)------------------------------
% 0.20/0.50 % (31372)------------------------------
% 0.20/0.50 % (31366)Success in time 0.133 s
%------------------------------------------------------------------------------