TSTP Solution File: SWW538_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW538_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 17:35:29 EDT 2024
% Result : Theorem 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 283
% Syntax : Number of formulae : 687 ( 253 unt; 62 typ; 0 def)
% Number of atoms : 1264 ( 665 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 978 ( 339 ~; 339 |; 72 &)
% ( 157 <=>; 71 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 60 ( 39 >; 21 *; 0 +; 0 <<)
% Number of predicates : 144 ( 142 usr; 125 prp; 0-4 aty)
% Number of functors : 40 ( 40 usr; 5 con; 0-5 aty)
% Number of variables : 1104 (1045 !; 12 ?;1104 :)
% ( 47 !>; 0 ?*; 0 @-; 0 @+)
% 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,
int: $tType ).
tff(type_def_9,type,
nat: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
huffma675207370phabet:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > fun(X0,bool) ) ).
tff(func_def_4,type,
huffma854194513Weight:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_5,type,
huffma1134658180e_cost:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_6,type,
huffma410068972_depth:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).
tff(func_def_7,type,
huffma1352802255e_freq:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).
tff(func_def_8,type,
huffma945805758height:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_9,type,
huffma1146269203erNode:
!>[X0: $tType] : ( ( nat * huffma1450048681e_tree(X0) * huffma1450048681e_tree(X0) ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_10,type,
huffma2021818691e_Leaf:
!>[X0: $tType] : ( ( nat * X0 ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_11,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_12,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_13,type,
huffma1926487300e_size:
!>[X0: $tType] : ( ( fun(X0,nat) * huffma1450048681e_tree(X0) ) > nat ) ).
tff(func_def_14,type,
huffma921447403eTrees:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * huffma1450048681e_tree(X0) ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_15,type,
huffma83463279weight:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_16,type,
if:
!>[X0: $tType] : ( ( bool * X0 * X0 ) > X0 ) ).
tff(func_def_17,type,
suc: nat > nat ).
tff(func_def_18,type,
nat_size: nat > nat ).
tff(func_def_19,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_20,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_21,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_22,type,
fFalse: bool ).
tff(func_def_23,type,
fTrue: bool ).
tff(func_def_24,type,
t_1: huffma1450048681e_tree(a) ).
tff(func_def_25,type,
t_2: huffma1450048681e_tree(a) ).
tff(func_def_26,type,
sK2: a ).
tff(func_def_27,type,
sK3: nat > nat ).
tff(func_def_28,type,
sK4: nat > nat ).
tff(func_def_29,type,
sK5:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).
tff(func_def_30,type,
sK6: fun(nat,bool) > nat ).
tff(func_def_31,type,
sK7: fun(nat,bool) > nat ).
tff(func_def_32,type,
sK8:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_33,type,
sK9:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > huffma1450048681e_tree(X0) ) ).
tff(func_def_34,type,
sK10:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > huffma1450048681e_tree(X0) ) ).
tff(func_def_35,type,
sK11:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_36,type,
sK12:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).
tff(func_def_37,type,
sK13:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
semiring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
huffma1518433673istent:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > $o ) ).
tff(pred_def_14,type,
nat_tr1645093318rphism:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * fun(X0,bool) ) > $o ) ).
tff(pred_def_15,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_16,type,
pp: bool > $o ).
tff(pred_def_17,type,
sP0: ( nat * nat ) > $o ).
tff(pred_def_18,type,
sP1: ( nat * nat ) > $o ).
tff(f1625,plain,
$false,
inference(avatar_sat_refutation,[],[f525,f530,f535,f540,f545,f550,f555,f560,f565,f570,f575,f580,f585,f590,f595,f600,f605,f610,f615,f620,f625,f630,f635,f639,f643,f647,f651,f656,f661,f666,f671,f679,f684,f688,f692,f696,f700,f704,f711,f715,f719,f725,f729,f733,f737,f741,f745,f749,f757,f761,f765,f769,f773,f777,f781,f785,f789,f825,f831,f835,f839,f843,f847,f851,f855,f859,f875,f879,f883,f887,f891,f895,f899,f903,f907,f911,f915,f919,f923,f927,f931,f935,f1010,f1014,f1018,f1022,f1026,f1030,f1034,f1038,f1042,f1067,f1107,f1111,f1115,f1119,f1123,f1133,f1137,f1141,f1145,f1149,f1153,f1172,f1188,f1192,f1196,f1200,f1273,f1277,f1281,f1285,f1450,f1454,f1458,f1493,f1497,f1501,f1508,f1512,f1528,f1584,f1588,f1622]) ).
tff(f1622,plain,
( spl14_32
| ~ spl14_123 ),
inference(avatar_contradiction_clause,[],[f1621]) ).
tff(f1621,plain,
( $false
| spl14_32
| ~ spl14_123 ),
inference(trivial_inequality_removal,[],[f1598]) ).
tff(f1598,plain,
( ( plus_plus(nat,huffma1352802255e_freq(a,t_1,sK2),huffma1352802255e_freq(a,t_2,sK2)) != plus_plus(nat,huffma1352802255e_freq(a,t_1,sK2),huffma1352802255e_freq(a,t_2,sK2)) )
| spl14_32
| ~ spl14_123 ),
inference(superposition,[],[f678,f1583]) ).
tff(f1583,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)) )
| ~ spl14_123 ),
inference(avatar_component_clause,[],[f1582]) ).
tff(f1582,plain,
( spl14_123
<=> ! [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,[spl14_123])]) ).
tff(f678,plain,
( ( plus_plus(nat,huffma1352802255e_freq(a,t_1,sK2),huffma1352802255e_freq(a,t_2,sK2)) != huffma1352802255e_freq(a,huffma1146269203erNode(a,plus_plus(nat,huffma854194513Weight(a,t_1),huffma854194513Weight(a,t_2)),t_1,t_2),sK2) )
| spl14_32 ),
inference(avatar_component_clause,[],[f676]) ).
tff(f676,plain,
( spl14_32
<=> ( plus_plus(nat,huffma1352802255e_freq(a,t_1,sK2),huffma1352802255e_freq(a,t_2,sK2)) = huffma1352802255e_freq(a,huffma1146269203erNode(a,plus_plus(nat,huffma854194513Weight(a,t_1),huffma854194513Weight(a,t_2)),t_1,t_2),sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_32])]) ).
tff(f1588,plain,
( spl14_124
| ~ spl14_93
| ~ spl14_105 ),
inference(avatar_split_clause,[],[f1445,f1170,f1065,f1586]) ).
tff(f1586,plain,
( spl14_124
<=> ! [X0: nat] : ( zero_zero(nat) != nat_size(nat_size(suc(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_124])]) ).
tff(f1065,plain,
( spl14_93
<=> ! [X0: nat] : ( nat_size(suc(X0)) = suc(nat_size(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_93])]) ).
tff(f1170,plain,
( spl14_105
<=> ! [X0: nat] : ( zero_zero(nat) != nat_size(suc(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_105])]) ).
tff(f1445,plain,
( ! [X0: nat] : ( zero_zero(nat) != nat_size(nat_size(suc(X0))) )
| ~ spl14_93
| ~ spl14_105 ),
inference(superposition,[],[f1171,f1066]) ).
tff(f1066,plain,
( ! [X0: nat] : ( nat_size(suc(X0)) = suc(nat_size(X0)) )
| ~ spl14_93 ),
inference(avatar_component_clause,[],[f1065]) ).
tff(f1171,plain,
( ! [X0: nat] : ( zero_zero(nat) != nat_size(suc(X0)) )
| ~ spl14_105 ),
inference(avatar_component_clause,[],[f1170]) ).
tff(f1584,plain,
spl14_123,
inference(avatar_split_clause,[],[f467,f1582]) ).
tff(f467,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,[],[f215]) ).
tff(f215,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,[],[f5]) ).
tff(f5,axiom,
! [X0: $tType,X9: huffma1450048681e_tree(X0),X10: huffma1450048681e_tree(X0),X11: nat,X12: X0] : ( huffma1352802255e_freq(X0,huffma1146269203erNode(X0,X11,X10,X9),X12) = plus_plus(nat,huffma1352802255e_freq(X0,X10,X12),huffma1352802255e_freq(X0,X9,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_freq_Osimps_I2_J) ).
tff(f1528,plain,
spl14_122,
inference(avatar_split_clause,[],[f461,f1526]) ).
tff(f1526,plain,
( spl14_122
<=> ! [X0: $tType,X3: fun(X0,nat),X2: nat,X1: X0] : ( huffma1926487300e_size(X0,X3,huffma2021818691e_Leaf(X0,X2,X1)) = plus_plus(nat,aa(X0,nat,X3,X1),suc(zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_122])]) ).
tff(f461,plain,
! [X0: $tType,X2: nat,X3: fun(X0,nat),X1: X0] : ( huffma1926487300e_size(X0,X3,huffma2021818691e_Leaf(X0,X2,X1)) = plus_plus(nat,aa(X0,nat,X3,X1),suc(zero_zero(nat))) ),
inference(cnf_transformation,[],[f210]) ).
tff(f210,plain,
! [X0: $tType,X1: X0,X2: nat,X3: fun(X0,nat)] : ( huffma1926487300e_size(X0,X3,huffma2021818691e_Leaf(X0,X2,X1)) = plus_plus(nat,aa(X0,nat,X3,X1),suc(zero_zero(nat))) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X2: $tType,X8: X2,X28: nat,X53: fun(X2,nat)] : ( huffma1926487300e_size(X2,X53,huffma2021818691e_Leaf(X2,X28,X8)) = plus_plus(nat,aa(X2,nat,X53,X8),suc(zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_tree_Osize_I1_J) ).
tff(f1512,plain,
spl14_121,
inference(avatar_split_clause,[],[f389,f1510]) ).
tff(f1510,plain,
( spl14_121
<=> ! [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,[spl14_121])]) ).
tff(f389,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,[],[f254]) ).
tff(f254,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,[],[f163]) ).
tff(f163,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,[],[f18]) ).
tff(f18,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X19: X0,X22: X0,X20: X0] : ( plus_plus(X0,plus_plus(X0,X20,X22),X19) = plus_plus(X0,plus_plus(X0,X20,X19),X22) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
tff(f1508,plain,
spl14_120,
inference(avatar_split_clause,[],[f387,f1506]) ).
tff(f1506,plain,
( spl14_120
<=> ! [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,[spl14_120])]) ).
tff(f387,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,[],[f252]) ).
tff(f252,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,[],[f161]) ).
tff(f161,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,[],[f11]) ).
tff(f11,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X21: X0,X19: X0,X20: X0] : ( plus_plus(X0,X20,plus_plus(X0,X19,X21)) = plus_plus(X0,plus_plus(X0,X20,X19),X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
tff(f1501,plain,
spl14_119,
inference(avatar_split_clause,[],[f386,f1499]) ).
tff(f1499,plain,
( spl14_119
<=> ! [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,[spl14_119])]) ).
tff(f386,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,[],[f251]) ).
tff(f251,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,[],[f160]) ).
tff(f160,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,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X21: X0,X19: X0,X20: X0] : ( plus_plus(X0,X20,plus_plus(X0,X19,X21)) = plus_plus(X0,X19,plus_plus(X0,X20,X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
tff(f1497,plain,
spl14_118,
inference(avatar_split_clause,[],[f376,f1495]) ).
tff(f1495,plain,
( spl14_118
<=> ! [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,[spl14_118])]) ).
tff(f376,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,[],[f243]) ).
tff(f243,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,[],[f152]) ).
tff(f152,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,[],[f26]) ).
tff(f26,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> ! [X13: nat,X14: nat] : ( semiring_1_of_nat(X0,plus_plus(nat,X14,X13)) = plus_plus(X0,semiring_1_of_nat(X0,X14),semiring_1_of_nat(X0,X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_of__nat__add) ).
tff(f1493,plain,
spl14_117,
inference(avatar_split_clause,[],[f369,f1491]) ).
tff(f1491,plain,
( spl14_117
<=> ! [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,[spl14_117])]) ).
tff(f369,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,[],[f236]) ).
tff(f236,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,[],[f146]) ).
tff(f146,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,[],[f19]) ).
tff(f19,axiom,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X19: X0,X22: X0,X20: X0] : ( plus_plus(X0,plus_plus(X0,X20,X22),X19) = plus_plus(X0,X20,plus_plus(X0,X22,X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_ab__semigroup__add__class_Oadd__ac_I1_J) ).
tff(f1458,plain,
spl14_116,
inference(avatar_split_clause,[],[f483,f1456]) ).
tff(f1456,plain,
( spl14_116
<=> ! [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,[spl14_116])]) ).
tff(f483,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,[],[f320]) ).
tff(f320,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,[],[f319]) ).
tff(f319,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,[],[f225]) ).
tff(f225,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,[],[f13]) ).
tff(f13,axiom,
! [X2: $tType,X23: huffma1450048681e_tree(X2),X24: huffma1450048681e_tree(X2),X25: nat,X26: huffma1450048681e_tree(X2),X27: huffma1450048681e_tree(X2),X28: nat] :
( ( huffma1146269203erNode(X2,X28,X27,X26) = huffma1146269203erNode(X2,X25,X24,X23) )
<=> ( ( X23 = X26 )
& ( X24 = X27 )
& ( X25 = X28 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_tree_Osimps_I2_J) ).
tff(f1454,plain,
spl14_115,
inference(avatar_split_clause,[],[f482,f1452]) ).
tff(f1452,plain,
( spl14_115
<=> ! [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,[spl14_115])]) ).
tff(f482,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,[],[f320]) ).
tff(f1450,plain,
spl14_114,
inference(avatar_split_clause,[],[f460,f1448]) ).
tff(f1448,plain,
( spl14_114
<=> ! [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,[spl14_114])]) ).
tff(f460,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,[],[f209]) ).
tff(f209,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,[],[f21]) ).
tff(f21,axiom,
! [X0: $tType,X9: huffma1450048681e_tree(X0),X10: huffma1450048681e_tree(X0),X11: nat] : ( huffma83463279weight(X0,huffma1146269203erNode(X0,X11,X10,X9)) = plus_plus(nat,huffma83463279weight(X0,X10),huffma83463279weight(X0,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_weight_Osimps_I2_J) ).
tff(f1285,plain,
spl14_113,
inference(avatar_split_clause,[],[f481,f1283]) ).
tff(f1283,plain,
( spl14_113
<=> ! [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,[spl14_113])]) ).
tff(f481,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,[],[f320]) ).
tff(f1281,plain,
spl14_112,
inference(avatar_split_clause,[],[f446,f1279]) ).
tff(f1279,plain,
( spl14_112
<=> ! [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,[spl14_112])]) ).
tff(f446,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,[],[f197]) ).
tff(f197,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,[],[f8]) ).
tff(f8,axiom,
! [X18: nat,X13: nat,X14: nat] : ( plus_plus(nat,plus_plus(nat,X14,X13),X18) = plus_plus(nat,X14,plus_plus(nat,X13,X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_nat__add__assoc) ).
tff(f1277,plain,
spl14_111,
inference(avatar_split_clause,[],[f445,f1275]) ).
tff(f1275,plain,
( spl14_111
<=> ! [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,[spl14_111])]) ).
tff(f445,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,[],[f196]) ).
tff(f196,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,[],[f7]) ).
tff(f7,axiom,
! [X15: nat,X16: nat,X17: nat] : ( plus_plus(nat,X17,plus_plus(nat,X16,X15)) = plus_plus(nat,X16,plus_plus(nat,X17,X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_nat__add__left__commute) ).
tff(f1273,plain,
spl14_110,
inference(avatar_split_clause,[],[f399,f1271]) ).
tff(f1271,plain,
( spl14_110
<=> ! [X0: nat,X1: nat] : ( plus_plus(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) = semiring_1_of_nat(int,plus_plus(nat,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_110])]) ).
tff(f399,plain,
! [X0: nat,X1: nat] : ( plus_plus(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) = semiring_1_of_nat(int,plus_plus(nat,X1,X0)) ),
inference(cnf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: nat,X1: nat] : ( plus_plus(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) = semiring_1_of_nat(int,plus_plus(nat,X1,X0)) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X16: nat,X17: nat] : ( plus_plus(int,semiring_1_of_nat(int,X17),semiring_1_of_nat(int,X16)) = semiring_1_of_nat(int,plus_plus(nat,X17,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
tff(f1200,plain,
( spl14_109
| ~ spl14_24
| ~ spl14_93 ),
inference(avatar_split_clause,[],[f1129,f1065,f637,f1198]) ).
tff(f1198,plain,
( spl14_109
<=> ! [X0: nat] : ( nat_size(suc(X0)) != nat_size(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_109])]) ).
tff(f637,plain,
( spl14_24
<=> ! [X0: nat] : ( suc(X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_24])]) ).
tff(f1129,plain,
( ! [X0: nat] : ( nat_size(suc(X0)) != nat_size(X0) )
| ~ spl14_24
| ~ spl14_93 ),
inference(superposition,[],[f638,f1066]) ).
tff(f638,plain,
( ! [X0: nat] : ( suc(X0) != X0 )
| ~ spl14_24 ),
inference(avatar_component_clause,[],[f637]) ).
tff(f1196,plain,
spl14_108,
inference(avatar_split_clause,[],[f378,f1194]) ).
tff(f1194,plain,
( spl14_108
<=> ! [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,[spl14_108])]) ).
tff(f378,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,[],[f245]) ).
tff(f245,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,[],[f154]) ).
tff(f154,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,[],[f14]) ).
tff(f14,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X19: X0,X20: X0,X22: X0] :
( ( plus_plus(X0,X19,X20) = plus_plus(X0,X22,X20) )
=> ( X19 = X22 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_add__right__imp__eq) ).
tff(f1192,plain,
spl14_107,
inference(avatar_split_clause,[],[f377,f1190]) ).
tff(f1190,plain,
( spl14_107
<=> ! [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,[spl14_107])]) ).
tff(f377,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,[],[f244]) ).
tff(f244,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,[],[f153]) ).
tff(f153,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,[],[f16]) ).
tff(f16,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X19: X0,X22: X0,X20: X0] :
( ( plus_plus(X0,X20,X19) = plus_plus(X0,X20,X22) )
=> ( X19 = X22 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_add__left__imp__eq) ).
tff(f1188,plain,
spl14_106,
inference(avatar_split_clause,[],[f370,f1186]) ).
tff(f1186,plain,
( spl14_106
<=> ! [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,[spl14_106])]) ).
tff(f370,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,[],[f237]) ).
tff(f237,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,[],[f147]) ).
tff(f147,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,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType] :
( cancel146912293up_add(X0)
=> ! [X19: X0,X22: X0,X20: X0] :
( ( plus_plus(X0,X20,X19) = plus_plus(X0,X20,X22) )
=> ( X19 = X22 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_add__imp__eq) ).
tff(f1172,plain,
( spl14_105
| ~ spl14_25
| ~ spl14_93 ),
inference(avatar_split_clause,[],[f1128,f1065,f641,f1170]) ).
tff(f641,plain,
( spl14_25
<=> ! [X0: nat] : ( zero_zero(nat) != suc(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_25])]) ).
tff(f1128,plain,
( ! [X0: nat] : ( zero_zero(nat) != nat_size(suc(X0)) )
| ~ spl14_25
| ~ spl14_93 ),
inference(superposition,[],[f642,f1066]) ).
tff(f642,plain,
( ! [X0: nat] : ( zero_zero(nat) != suc(X0) )
| ~ spl14_25 ),
inference(avatar_component_clause,[],[f641]) ).
tff(f1153,plain,
spl14_104,
inference(avatar_split_clause,[],[f473,f1151]) ).
tff(f1151,plain,
( spl14_104
<=> ! [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,[spl14_104])]) ).
tff(f473,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,[],[f318]) ).
tff(f318,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,[],[f317]) ).
tff(f317,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,[],[f218]) ).
tff(f218,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,[],[f30]) ).
tff(f30,axiom,
! [X2: $tType,X36: X2,X25: nat,X8: X2,X28: nat] :
( ( huffma2021818691e_Leaf(X2,X28,X8) = huffma2021818691e_Leaf(X2,X25,X36) )
<=> ( ( X8 = X36 )
& ( X25 = X28 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_tree_Osimps_I1_J) ).
tff(f1149,plain,
spl14_103,
inference(avatar_split_clause,[],[f472,f1147]) ).
tff(f1147,plain,
( spl14_103
<=> ! [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,[spl14_103])]) ).
tff(f472,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,[],[f318]) ).
tff(f1145,plain,
spl14_102,
inference(avatar_split_clause,[],[f465,f1143]) ).
tff(f1143,plain,
( spl14_102
<=> ! [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,[spl14_102])]) ).
tff(f465,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,[],[f270]) ).
tff(f270,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,[],[f213]) ).
tff(f213,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,[],[f37]) ).
tff(f37,axiom,
! [X0: $tType,X11: nat,X20: X0,X12: X0] :
( ( ( X12 != X20 )
=> ( zero_zero(nat) = huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X11,X20),X12) ) )
& ( ( X12 = X20 )
=> ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X11,X20),X12) = X11 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_freq_Osimps_I1_J) ).
tff(f1141,plain,
spl14_101,
inference(avatar_split_clause,[],[f451,f1139]) ).
tff(f1139,plain,
( spl14_101
<=> ! [X0: $tType,X2: X0,X1: huffma1450048681e_tree(X0)] :
( ( zero_zero(nat) = huffma1352802255e_freq(X0,X1,X2) )
| member(X0,X2,huffma675207370phabet(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_101])]) ).
tff(f451,plain,
! [X0: $tType,X2: X0,X1: huffma1450048681e_tree(X0)] :
( ( zero_zero(nat) = huffma1352802255e_freq(X0,X1,X2) )
| member(X0,X2,huffma675207370phabet(X0,X1)) ),
inference(cnf_transformation,[],[f269]) ).
tff(f269,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: X0] :
( ( zero_zero(nat) = huffma1352802255e_freq(X0,X1,X2) )
| member(X0,X2,huffma675207370phabet(X0,X1)) ),
inference(ennf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: X0] :
( ~ member(X0,X2,huffma675207370phabet(X0,X1))
=> ( zero_zero(nat) = huffma1352802255e_freq(X0,X1,X2) ) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X2: $tType,X47: huffma1450048681e_tree(X2),X8: X2] :
( ~ member(X2,X8,huffma675207370phabet(X2,X47))
=> ( zero_zero(nat) = huffma1352802255e_freq(X2,X47,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_notin__alphabet__imp__freq__0) ).
tff(f1137,plain,
spl14_100,
inference(avatar_split_clause,[],[f450,f1135]) ).
tff(f1135,plain,
( spl14_100
<=> ! [X2: bool,X0: nat,X1: nat] :
( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
| pp(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_100])]) ).
tff(f450,plain,
! [X2: bool,X0: nat,X1: nat] :
( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
| pp(X2) ),
inference(cnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X0: nat,X1: nat,X2: bool] :
( ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
| pp(X2) )
& ( ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
| ~ pp(X2) ) ),
inference(ennf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: nat,X1: nat,X2: bool] :
( ( ~ pp(X2)
=> ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) ) )
& ( pp(X2)
=> ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) ) ) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X41: nat,X42: nat,X43: bool] :
( ( ~ pp(X43)
=> ( semiring_1_of_nat(int,if(nat,X43,X42,X41)) = semiring_1_of_nat(int,X41) ) )
& ( pp(X43)
=> ( semiring_1_of_nat(int,X42) = semiring_1_of_nat(int,if(nat,X43,X42,X41)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_int__if__cong) ).
tff(f1133,plain,
spl14_99,
inference(avatar_split_clause,[],[f449,f1131]) ).
tff(f1131,plain,
( spl14_99
<=> ! [X2: bool,X0: nat,X1: nat] :
( ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
| ~ pp(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_99])]) ).
tff(f449,plain,
! [X2: bool,X0: nat,X1: nat] :
( ( semiring_1_of_nat(int,X1) = semiring_1_of_nat(int,if(nat,X2,X1,X0)) )
| ~ pp(X2) ),
inference(cnf_transformation,[],[f268]) ).
tff(f1123,plain,
spl14_98,
inference(avatar_split_clause,[],[f431,f1121]) ).
tff(f1121,plain,
( spl14_98
<=> ! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = X0 )
| ( suc(zero_zero(nat)) = X1 )
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_98])]) ).
tff(f431,plain,
! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = X0 )
| ( suc(zero_zero(nat)) = X1 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f310]) ).
tff(f310,plain,
! [X0: nat,X1: nat] :
( ( sP1(X0,X1)
| ( ( ( suc(zero_zero(nat)) != X0 )
| ( zero_zero(nat) != X1 ) )
& ( ( zero_zero(nat) != X0 )
| ( suc(zero_zero(nat)) != X1 ) ) ) )
& ( ( ( suc(zero_zero(nat)) = X0 )
& ( zero_zero(nat) = X1 ) )
| ( ( zero_zero(nat) = X0 )
& ( suc(zero_zero(nat)) = X1 ) )
| ~ sP1(X0,X1) ) ),
inference(flattening,[],[f309]) ).
tff(f309,plain,
! [X0: nat,X1: nat] :
( ( sP1(X0,X1)
| ( ( ( suc(zero_zero(nat)) != X0 )
| ( zero_zero(nat) != X1 ) )
& ( ( zero_zero(nat) != X0 )
| ( suc(zero_zero(nat)) != X1 ) ) ) )
& ( ( ( suc(zero_zero(nat)) = X0 )
& ( zero_zero(nat) = X1 ) )
| ( ( zero_zero(nat) = X0 )
& ( suc(zero_zero(nat)) = X1 ) )
| ~ sP1(X0,X1) ) ),
inference(nnf_transformation,[],[f275]) ).
tff(f275,plain,
! [X0: nat,X1: nat] :
( sP1(X0,X1)
<=> ( ( ( suc(zero_zero(nat)) = X0 )
& ( zero_zero(nat) = X1 ) )
| ( ( zero_zero(nat) = X0 )
& ( suc(zero_zero(nat)) = X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f1119,plain,
spl14_97,
inference(avatar_split_clause,[],[f423,f1117]) ).
tff(f1117,plain,
( spl14_97
<=> ! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = X0 )
| ( suc(zero_zero(nat)) = X1 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_97])]) ).
tff(f423,plain,
! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = X0 )
| ( suc(zero_zero(nat)) = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f307]) ).
tff(f307,plain,
! [X0: nat,X1: nat] :
( ( sP0(X0,X1)
| ( ( ( suc(zero_zero(nat)) != X0 )
| ( zero_zero(nat) != X1 ) )
& ( ( zero_zero(nat) != X0 )
| ( suc(zero_zero(nat)) != X1 ) ) ) )
& ( ( ( suc(zero_zero(nat)) = X0 )
& ( zero_zero(nat) = X1 ) )
| ( ( zero_zero(nat) = X0 )
& ( suc(zero_zero(nat)) = X1 ) )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f306]) ).
tff(f306,plain,
! [X0: nat,X1: nat] :
( ( sP0(X0,X1)
| ( ( ( suc(zero_zero(nat)) != X0 )
| ( zero_zero(nat) != X1 ) )
& ( ( zero_zero(nat) != X0 )
| ( suc(zero_zero(nat)) != X1 ) ) ) )
& ( ( ( suc(zero_zero(nat)) = X0 )
& ( zero_zero(nat) = X1 ) )
| ( ( zero_zero(nat) = X0 )
& ( suc(zero_zero(nat)) = X1 ) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f273]) ).
tff(f273,plain,
! [X0: nat,X1: nat] :
( sP0(X0,X1)
<=> ( ( ( suc(zero_zero(nat)) = X0 )
& ( zero_zero(nat) = X1 ) )
| ( ( zero_zero(nat) = X0 )
& ( suc(zero_zero(nat)) = X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f1115,plain,
spl14_96,
inference(avatar_split_clause,[],[f405,f1113]) ).
tff(f1113,plain,
( spl14_96
<=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ( huffma854194513Weight(X0,X1) = huffma83463279weight(X0,X1) )
| ( zero_zero(nat) != huffma945805758height(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_96])]) ).
tff(f405,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ( huffma854194513Weight(X0,X1) = huffma83463279weight(X0,X1) )
| ( zero_zero(nat) != huffma945805758height(X0,X1) ) ),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ( huffma854194513Weight(X0,X1) = huffma83463279weight(X0,X1) )
| ( zero_zero(nat) != huffma945805758height(X0,X1) ) ),
inference(ennf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ( zero_zero(nat) = huffma945805758height(X0,X1) )
=> ( huffma854194513Weight(X0,X1) = huffma83463279weight(X0,X1) ) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X0: $tType,X44: huffma1450048681e_tree(X0)] :
( ( zero_zero(nat) = huffma945805758height(X0,X44) )
=> ( huffma854194513Weight(X0,X44) = huffma83463279weight(X0,X44) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_height__0__imp__cachedWeight__eq__weight) ).
tff(f1111,plain,
spl14_95,
inference(avatar_split_clause,[],[f402,f1109]) ).
tff(f1109,plain,
( spl14_95
<=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK5(X0,X1)) )
| ~ huffma1518433673istent(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_95])]) ).
tff(f402,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK5(X0,X1)) )
| ~ huffma1518433673istent(X0,X1) ),
inference(cnf_transformation,[],[f292]) ).
tff(f292,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK5(X0,X1)) )
& member(X0,sK5(X0,X1),huffma675207370phabet(X0,X1)) )
| ~ huffma1518433673istent(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f258,f291]) ).
tff(f291,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ? [X2: X0] :
( ( huffma410068972_depth(X0,X1,X2) = huffma945805758height(X0,X1) )
& member(X0,X2,huffma675207370phabet(X0,X1)) )
=> ( ( huffma945805758height(X0,X1) = huffma410068972_depth(X0,X1,sK5(X0,X1)) )
& member(X0,sK5(X0,X1),huffma675207370phabet(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f258,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ? [X2: X0] :
( ( huffma410068972_depth(X0,X1,X2) = huffma945805758height(X0,X1) )
& member(X0,X2,huffma675207370phabet(X0,X1)) )
| ~ huffma1518433673istent(X0,X1) ),
inference(ennf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( huffma1518433673istent(X0,X1)
=> ? [X2: X0] :
( ( huffma410068972_depth(X0,X1,X2) = huffma945805758height(X0,X1) )
& member(X0,X2,huffma675207370phabet(X0,X1)) ) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X2: $tType,X47: huffma1450048681e_tree(X2)] :
( huffma1518433673istent(X2,X47)
=> ? [X48: X2] :
( ( huffma410068972_depth(X2,X47,X48) = huffma945805758height(X2,X47) )
& member(X2,X48,huffma675207370phabet(X2,X47)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_exists__at__height) ).
tff(f1107,plain,
spl14_94,
inference(avatar_split_clause,[],[f359,f1105]) ).
tff(f1105,plain,
( spl14_94
<=> ! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,X1,X1) )
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_94])]) ).
tff(f359,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,X1,X1) )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f279]) ).
tff(f279,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
| ( zero_zero(X0) != X1 ) )
& ( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,X1,X1) ) ) )
| ~ linord219039673up_add(X0) ),
inference(nnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
<=> ( zero_zero(X0) = X1 ) )
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f41]) ).
tff(f41,axiom,
! [X2: $tType] :
( linord219039673up_add(X2)
=> ! [X8: X2] :
( ( plus_plus(X2,X8,X8) = zero_zero(X2) )
<=> ( zero_zero(X2) = X8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_double__eq__0__iff) ).
tff(f1067,plain,
( spl14_93
| ~ spl14_34
| ~ spl14_68
| ~ spl14_72 ),
inference(avatar_split_clause,[],[f966,f889,f873,f686,f1065]) ).
tff(f686,plain,
( spl14_34
<=> ! [X0: nat] : ( plus_plus(nat,X0,zero_zero(nat)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_34])]) ).
tff(f873,plain,
( spl14_68
<=> ! [X0: nat] : ( nat_size(suc(X0)) = plus_plus(nat,nat_size(X0),suc(zero_zero(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_68])]) ).
tff(f889,plain,
( spl14_72
<=> ! [X0: nat,X1: nat] : ( suc(plus_plus(nat,X1,X0)) = plus_plus(nat,X1,suc(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_72])]) ).
tff(f966,plain,
( ! [X0: nat] : ( nat_size(suc(X0)) = suc(nat_size(X0)) )
| ~ spl14_34
| ~ spl14_68
| ~ spl14_72 ),
inference(forward_demodulation,[],[f958,f687]) ).
tff(f687,plain,
( ! [X0: nat] : ( plus_plus(nat,X0,zero_zero(nat)) = X0 )
| ~ spl14_34 ),
inference(avatar_component_clause,[],[f686]) ).
tff(f958,plain,
( ! [X0: nat] : ( nat_size(suc(X0)) = suc(plus_plus(nat,nat_size(X0),zero_zero(nat))) )
| ~ spl14_68
| ~ spl14_72 ),
inference(superposition,[],[f890,f874]) ).
tff(f874,plain,
( ! [X0: nat] : ( nat_size(suc(X0)) = plus_plus(nat,nat_size(X0),suc(zero_zero(nat))) )
| ~ spl14_68 ),
inference(avatar_component_clause,[],[f873]) ).
tff(f890,plain,
( ! [X0: nat,X1: nat] : ( suc(plus_plus(nat,X1,X0)) = plus_plus(nat,X1,suc(X0)) )
| ~ spl14_72 ),
inference(avatar_component_clause,[],[f889]) ).
tff(f1042,plain,
spl14_92,
inference(avatar_split_clause,[],[f456,f1040]) ).
tff(f1040,plain,
( spl14_92
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X2,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_92])]) ).
tff(f456,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X2,X0) ) ),
inference(cnf_transformation,[],[f314]) ).
tff(f314,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,[],[f204]) ).
tff(f204,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( plus_plus(nat,X2,X1) = plus_plus(nat,X2,X0) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f1]) ).
tff(f1,axiom,
! [X3: nat,X4: nat,X5: nat] :
( ( plus_plus(nat,X5,X4) = plus_plus(nat,X5,X3) )
<=> ( X3 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_nat__add__left__cancel) ).
tff(f1038,plain,
spl14_91,
inference(avatar_split_clause,[],[f454,f1036]) ).
tff(f1036,plain,
( spl14_91
<=> ! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_91])]) ).
tff(f454,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X0,X1) ) ),
inference(cnf_transformation,[],[f313]) ).
tff(f313,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,[],[f203]) ).
tff(f203,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( plus_plus(nat,X2,X1) = plus_plus(nat,X0,X1) )
<=> ( X0 = X2 ) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X3: nat,X5: nat,X4: nat] :
( ( plus_plus(nat,X4,X5) = plus_plus(nat,X3,X5) )
<=> ( X3 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_nat__add__right__cancel) ).
tff(f1034,plain,
spl14_90,
inference(avatar_split_clause,[],[f432,f1032]) ).
tff(f1032,plain,
( spl14_90
<=> ! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = X0 )
| ( zero_zero(nat) = X0 )
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_90])]) ).
tff(f432,plain,
! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = X0 )
| ( zero_zero(nat) = X0 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f310]) ).
tff(f1030,plain,
spl14_89,
inference(avatar_split_clause,[],[f429,f1028]) ).
tff(f1028,plain,
( spl14_89
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( suc(zero_zero(nat)) = X1 )
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_89])]) ).
tff(f429,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( suc(zero_zero(nat)) = X1 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f310]) ).
tff(f1026,plain,
spl14_88,
inference(avatar_split_clause,[],[f424,f1024]) ).
tff(f1024,plain,
( spl14_88
<=> ! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = X0 )
| ( zero_zero(nat) = X0 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_88])]) ).
tff(f424,plain,
! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = X0 )
| ( zero_zero(nat) = X0 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f307]) ).
tff(f1022,plain,
spl14_87,
inference(avatar_split_clause,[],[f421,f1020]) ).
tff(f1020,plain,
( spl14_87
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( suc(zero_zero(nat)) = X1 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_87])]) ).
tff(f421,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( suc(zero_zero(nat)) = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f307]) ).
tff(f1018,plain,
spl14_86,
inference(avatar_split_clause,[],[f404,f1016]) ).
tff(f1016,plain,
( spl14_86
<=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ( zero_zero(nat) = huffma1134658180e_cost(X0,X1) )
| ( zero_zero(nat) != huffma945805758height(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_86])]) ).
tff(f404,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ( zero_zero(nat) = huffma1134658180e_cost(X0,X1) )
| ( zero_zero(nat) != huffma945805758height(X0,X1) ) ),
inference(cnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ( zero_zero(nat) = huffma1134658180e_cost(X0,X1) )
| ( zero_zero(nat) != huffma945805758height(X0,X1) ) ),
inference(ennf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ( zero_zero(nat) = huffma945805758height(X0,X1) )
=> ( zero_zero(nat) = huffma1134658180e_cost(X0,X1) ) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X0: $tType,X44: huffma1450048681e_tree(X0)] :
( ( zero_zero(nat) = huffma945805758height(X0,X44) )
=> ( zero_zero(nat) = huffma1134658180e_cost(X0,X44) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_height__0__imp__cost__0) ).
tff(f1014,plain,
spl14_85,
inference(avatar_split_clause,[],[f367,f1012]) ).
tff(f1012,plain,
( spl14_85
<=> ! [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,[spl14_85])]) ).
tff(f367,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,[],[f283]) ).
tff(f283,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,[],[f235]) ).
tff(f235,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,[],[f145]) ).
tff(f145,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,[],[f29]) ).
tff(f29,axiom,
! [X2: $tType] :
( semiring_char_0(X2)
=> ! [X3: nat,X4: nat] :
( ( semiring_1_of_nat(X2,X4) = semiring_1_of_nat(X2,X3) )
<=> ( X3 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_of__nat__eq__iff) ).
tff(f1010,plain,
spl14_84,
inference(avatar_split_clause,[],[f365,f1008]) ).
tff(f1008,plain,
( spl14_84
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( plus_plus(X0,X2,X1) != X2 )
| ~ semiri456707255roduct(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_84])]) ).
tff(f365,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( plus_plus(X0,X2,X1) != X2 )
| ~ semiri456707255roduct(X0) ),
inference(cnf_transformation,[],[f282]) ).
tff(f282,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,[],[f234]) ).
tff(f234,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( plus_plus(X0,X2,X1) = X2 )
<=> ( zero_zero(X0) = X1 ) )
| ~ semiri456707255roduct(X0) ),
inference(ennf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: $tType] :
( semiri456707255roduct(X0)
=> ! [X1: X0,X2: X0] :
( ( plus_plus(X0,X2,X1) = X2 )
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X2: $tType] :
( semiri456707255roduct(X2)
=> ! [X8: X2,X7: X2] :
( ( plus_plus(X2,X7,X8) = X7 )
<=> ( zero_zero(X2) = X8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_add__0__iff) ).
tff(f935,plain,
spl14_83,
inference(avatar_split_clause,[],[f486,f933]) ).
tff(f933,plain,
( spl14_83
<=> ! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_83])]) ).
tff(f486,plain,
! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ),
inference(equality_resolution,[],[f360]) ).
tff(f360,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
| ( zero_zero(X0) != X1 )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f279]) ).
tff(f931,plain,
spl14_82,
inference(avatar_split_clause,[],[f475,f929]) ).
tff(f929,plain,
( spl14_82
<=> ! [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,[spl14_82])]) ).
tff(f475,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,[],[f219]) ).
tff(f219,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,[],[f27]) ).
tff(f27,axiom,
! [X0: $tType,X32: huffma1450048681e_tree(X0),X33: huffma1450048681e_tree(X0),X34: nat,X20: X0,X35: nat] : ( huffma2021818691e_Leaf(X0,X35,X20) != huffma1146269203erNode(X0,X34,X33,X32) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_tree_Osimps_I3_J) ).
tff(f927,plain,
spl14_81,
inference(avatar_split_clause,[],[f436,f925]) ).
tff(f925,plain,
( spl14_81
<=> ! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = plus_plus(nat,X1,X0) )
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_81])]) ).
tff(f436,plain,
! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = plus_plus(nat,X1,X0) )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f311]) ).
tff(f311,plain,
! [X0: nat,X1: nat] :
( ( ( suc(zero_zero(nat)) = plus_plus(nat,X1,X0) )
| ~ sP1(X0,X1) )
& ( sP1(X0,X1)
| ( suc(zero_zero(nat)) != plus_plus(nat,X1,X0) ) ) ),
inference(nnf_transformation,[],[f276]) ).
tff(f276,plain,
! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = plus_plus(nat,X1,X0) )
<=> sP1(X0,X1) ),
inference(definition_folding,[],[f187,f275]) ).
tff(f187,plain,
! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = plus_plus(nat,X1,X0) )
<=> ( ( ( suc(zero_zero(nat)) = X0 )
& ( zero_zero(nat) = X1 ) )
| ( ( zero_zero(nat) = X0 )
& ( suc(zero_zero(nat)) = X1 ) ) ) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X3: nat,X4: nat] :
( ( plus_plus(nat,X4,X3) = suc(zero_zero(nat)) )
<=> ( ( ( suc(zero_zero(nat)) = X3 )
& ( zero_zero(nat) = X4 ) )
| ( ( zero_zero(nat) = X3 )
& ( suc(zero_zero(nat)) = X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_one__is__add) ).
tff(f923,plain,
spl14_80,
inference(avatar_split_clause,[],[f435,f921]) ).
tff(f921,plain,
( spl14_80
<=> ! [X0: nat,X1: nat] :
( sP1(X0,X1)
| ( suc(zero_zero(nat)) != plus_plus(nat,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_80])]) ).
tff(f435,plain,
! [X0: nat,X1: nat] :
( sP1(X0,X1)
| ( suc(zero_zero(nat)) != plus_plus(nat,X1,X0) ) ),
inference(cnf_transformation,[],[f311]) ).
tff(f919,plain,
spl14_79,
inference(avatar_split_clause,[],[f430,f917]) ).
tff(f917,plain,
( spl14_79
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( zero_zero(nat) = X0 )
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_79])]) ).
tff(f430,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( zero_zero(nat) = X0 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f310]) ).
tff(f915,plain,
spl14_78,
inference(avatar_split_clause,[],[f428,f913]) ).
tff(f913,plain,
( spl14_78
<=> ! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = plus_plus(nat,X1,X0) )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_78])]) ).
tff(f428,plain,
! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = plus_plus(nat,X1,X0) )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f308]) ).
tff(f308,plain,
! [X0: nat,X1: nat] :
( ( ( suc(zero_zero(nat)) = plus_plus(nat,X1,X0) )
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| ( suc(zero_zero(nat)) != plus_plus(nat,X1,X0) ) ) ),
inference(nnf_transformation,[],[f274]) ).
tff(f274,plain,
! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = plus_plus(nat,X1,X0) )
<=> sP0(X0,X1) ),
inference(definition_folding,[],[f186,f273]) ).
tff(f186,plain,
! [X0: nat,X1: nat] :
( ( suc(zero_zero(nat)) = plus_plus(nat,X1,X0) )
<=> ( ( ( suc(zero_zero(nat)) = X0 )
& ( zero_zero(nat) = X1 ) )
| ( ( zero_zero(nat) = X0 )
& ( suc(zero_zero(nat)) = X1 ) ) ) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X3: nat,X4: nat] :
( ( plus_plus(nat,X4,X3) = suc(zero_zero(nat)) )
<=> ( ( ( suc(zero_zero(nat)) = X3 )
& ( zero_zero(nat) = X4 ) )
| ( ( zero_zero(nat) = X3 )
& ( suc(zero_zero(nat)) = X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_add__is__1) ).
tff(f911,plain,
spl14_77,
inference(avatar_split_clause,[],[f427,f909]) ).
tff(f909,plain,
( spl14_77
<=> ! [X0: nat,X1: nat] :
( sP0(X0,X1)
| ( suc(zero_zero(nat)) != plus_plus(nat,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_77])]) ).
tff(f427,plain,
! [X0: nat,X1: nat] :
( sP0(X0,X1)
| ( suc(zero_zero(nat)) != plus_plus(nat,X1,X0) ) ),
inference(cnf_transformation,[],[f308]) ).
tff(f907,plain,
spl14_76,
inference(avatar_split_clause,[],[f422,f905]) ).
tff(f905,plain,
( spl14_76
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( zero_zero(nat) = X0 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_76])]) ).
tff(f422,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( zero_zero(nat) = X0 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f307]) ).
tff(f903,plain,
spl14_75,
inference(avatar_split_clause,[],[f415,f901]) ).
tff(f901,plain,
( spl14_75
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_75])]) ).
tff(f415,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ),
inference(cnf_transformation,[],[f303]) ).
tff(f303,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,[],[f302]) ).
tff(f302,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,[],[f183]) ).
tff(f183,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = plus_plus(nat,X1,X0) )
<=> ( ( zero_zero(nat) = X0 )
& ( zero_zero(nat) = X1 ) ) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X3: nat,X4: nat] :
( ( zero_zero(nat) = plus_plus(nat,X4,X3) )
<=> ( ( zero_zero(nat) = X3 )
& ( zero_zero(nat) = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_add__is__0) ).
tff(f899,plain,
spl14_74,
inference(avatar_split_clause,[],[f414,f897]) ).
tff(f897,plain,
( spl14_74
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_74])]) ).
tff(f414,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ),
inference(cnf_transformation,[],[f303]) ).
tff(f895,plain,
spl14_73,
inference(avatar_split_clause,[],[f401,f893]) ).
tff(f893,plain,
( spl14_73
<=> ! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( member(X0,sK5(X0,X1),huffma675207370phabet(X0,X1))
| ~ huffma1518433673istent(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_73])]) ).
tff(f401,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( member(X0,sK5(X0,X1),huffma675207370phabet(X0,X1))
| ~ huffma1518433673istent(X0,X1) ),
inference(cnf_transformation,[],[f292]) ).
tff(f891,plain,
spl14_72,
inference(avatar_split_clause,[],[f397,f889]) ).
tff(f397,plain,
! [X0: nat,X1: nat] : ( suc(plus_plus(nat,X1,X0)) = plus_plus(nat,X1,suc(X0)) ),
inference(cnf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: nat,X1: nat] : ( suc(plus_plus(nat,X1,X0)) = plus_plus(nat,X1,suc(X0)) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X13: nat,X14: nat] : ( plus_plus(nat,X14,suc(X13)) = suc(plus_plus(nat,X14,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_add__Suc__right) ).
tff(f887,plain,
( spl14_71
| ~ spl14_15
| ~ spl14_45 ),
inference(avatar_split_clause,[],[f797,f735,f592,f885]) ).
tff(f885,plain,
( spl14_71
<=> ! [X0: int] : ( plus_plus(int,zero_zero(int),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_71])]) ).
tff(f592,plain,
( spl14_15
<=> monoid_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_15])]) ).
tff(f735,plain,
( spl14_45
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_45])]) ).
tff(f797,plain,
( ! [X0: int] : ( plus_plus(int,zero_zero(int),X0) = X0 )
| ~ spl14_15
| ~ spl14_45 ),
inference(resolution,[],[f736,f594]) ).
tff(f594,plain,
( monoid_add(int)
| ~ spl14_15 ),
inference(avatar_component_clause,[],[f592]) ).
tff(f736,plain,
( ! [X0: $tType,X1: X0] :
( ~ monoid_add(X0)
| ( plus_plus(X0,zero_zero(X0),X1) = X1 ) )
| ~ spl14_45 ),
inference(avatar_component_clause,[],[f735]) ).
tff(f883,plain,
spl14_70,
inference(avatar_split_clause,[],[f396,f881]) ).
tff(f881,plain,
( spl14_70
<=> ! [X0: nat,X1: nat] : ( suc(plus_plus(nat,X1,X0)) = plus_plus(nat,suc(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_70])]) ).
tff(f396,plain,
! [X0: nat,X1: nat] : ( suc(plus_plus(nat,X1,X0)) = plus_plus(nat,suc(X1),X0) ),
inference(cnf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: nat,X1: nat] : ( suc(plus_plus(nat,X1,X0)) = plus_plus(nat,suc(X1),X0) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X13: nat,X14: nat] : ( suc(plus_plus(nat,X14,X13)) = plus_plus(nat,suc(X14),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_add__Suc) ).
tff(f879,plain,
spl14_69,
inference(avatar_split_clause,[],[f385,f877]) ).
tff(f877,plain,
( spl14_69
<=> ! [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,[spl14_69])]) ).
tff(f385,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( plus_plus(X0,X2,X1) = plus_plus(X0,X1,X2) )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ( plus_plus(X0,X2,X1) = plus_plus(X0,X1,X2) )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0,X2: X0] : ( plus_plus(X0,X2,X1) = plus_plus(X0,X1,X2) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X19: X0,X20: X0] : ( plus_plus(X0,X20,X19) = plus_plus(X0,X19,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
tff(f875,plain,
spl14_68,
inference(avatar_split_clause,[],[f357,f873]) ).
tff(f357,plain,
! [X0: nat] : ( nat_size(suc(X0)) = plus_plus(nat,nat_size(X0),suc(zero_zero(nat))) ),
inference(cnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: nat] : ( nat_size(suc(X0)) = plus_plus(nat,nat_size(X0),suc(zero_zero(nat))) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X35: nat] : ( nat_size(suc(X35)) = plus_plus(nat,nat_size(X35),suc(zero_zero(nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_nat_Osize_I2_J) ).
tff(f859,plain,
( spl14_67
| ~ spl14_14
| ~ spl14_43 ),
inference(avatar_split_clause,[],[f792,f727,f587,f857]) ).
tff(f857,plain,
( spl14_67
<=> ! [X0: int] : ( plus_plus(int,X0,zero_zero(int)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_67])]) ).
tff(f587,plain,
( spl14_14
<=> comm_monoid_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_14])]) ).
tff(f727,plain,
( spl14_43
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_43])]) ).
tff(f792,plain,
( ! [X0: int] : ( plus_plus(int,X0,zero_zero(int)) = X0 )
| ~ spl14_14
| ~ spl14_43 ),
inference(resolution,[],[f728,f589]) ).
tff(f589,plain,
( comm_monoid_add(int)
| ~ spl14_14 ),
inference(avatar_component_clause,[],[f587]) ).
tff(f728,plain,
( ! [X0: $tType,X1: X0] :
( ~ comm_monoid_add(X0)
| ( plus_plus(X0,X1,zero_zero(X0)) = X1 ) )
| ~ spl14_43 ),
inference(avatar_component_clause,[],[f727]) ).
tff(f855,plain,
spl14_66,
inference(avatar_split_clause,[],[f459,f853]) ).
tff(f853,plain,
( spl14_66
<=> ! [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,[spl14_66])]) ).
tff(f459,plain,
! [X0: $tType,X2: X0,X3: nat,X1: X0] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) ),
inference(cnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: $tType,X1: X0,X2: X0,X3: nat] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X3,X2),X1) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X0: $tType,X20: X0,X22: X0,X11: nat] : ( zero_zero(nat) = huffma410068972_depth(X0,huffma2021818691e_Leaf(X0,X11,X22),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_depth_Osimps_I1_J) ).
tff(f851,plain,
spl14_65,
inference(avatar_split_clause,[],[f453,f849]) ).
tff(f849,plain,
( spl14_65
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_65])]) ).
tff(f453,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f312]) ).
tff(f312,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( ( member(X0,X2,X1)
| ~ pp(aa(X0,bool,X1,X2)) )
& ( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( member(X0,X2,X1)
<=> pp(aa(X0,bool,X1,X2)) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X2: $tType,X49: fun(X2,bool),X42: X2] :
( member(X2,X42,X49)
<=> pp(aa(X2,bool,X49,X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).
tff(f847,plain,
spl14_64,
inference(avatar_split_clause,[],[f452,f845]) ).
tff(f845,plain,
( spl14_64
<=> ! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_64])]) ).
tff(f452,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa(X0,bool,X1,X2))
| ~ member(X0,X2,X1) ),
inference(cnf_transformation,[],[f312]) ).
tff(f843,plain,
spl14_63,
inference(avatar_split_clause,[],[f444,f841]) ).
tff(f841,plain,
( spl14_63
<=> ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_63])]) ).
tff(f444,plain,
! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X2,X1)) ),
inference(cnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: $tType,X1: X0,X2: nat] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X2,X1)) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X0: $tType,X20: X0,X35: nat] : ( zero_zero(nat) = size_size(huffma1450048681e_tree(X0),huffma2021818691e_Leaf(X0,X35,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_tree_Osize_I3_J) ).
tff(f839,plain,
spl14_62,
inference(avatar_split_clause,[],[f417,f837]) ).
tff(f837,plain,
( spl14_62
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_62])]) ).
tff(f417,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ),
inference(cnf_transformation,[],[f304]) ).
tff(f304,plain,
! [X0: nat,X1: nat] :
( ( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ) ),
inference(nnf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: nat,X1: nat] :
( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X41: nat,X42: nat] :
( ( semiring_1_of_nat(int,X42) = semiring_1_of_nat(int,X41) )
<=> ( X41 = X42 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_transfer__int__nat__relations_I1_J) ).
tff(f835,plain,
spl14_61,
inference(avatar_split_clause,[],[f406,f833]) ).
tff(f833,plain,
( spl14_61
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( plus_plus(nat,X1,X0) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_61])]) ).
tff(f406,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( plus_plus(nat,X1,X0) != X1 ) ),
inference(cnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( plus_plus(nat,X1,X0) != X1 ) ),
inference(ennf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: nat,X1: nat] :
( ( plus_plus(nat,X1,X0) = X1 )
=> ( zero_zero(nat) = X0 ) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X13: nat,X14: nat] :
( ( plus_plus(nat,X14,X13) = X14 )
=> ( zero_zero(nat) = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_add__eq__self__zero) ).
tff(f831,plain,
spl14_60,
inference(avatar_split_clause,[],[f393,f829]) ).
tff(f829,plain,
( spl14_60
<=> ! [X0: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_60])]) ).
tff(f393,plain,
! [X0: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,plain,
! [X0: nat] :
( ( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
| ( zero_zero(nat) != X0 ) )
& ( ( zero_zero(nat) = X0 )
| ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ) ),
inference(nnf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: nat] :
( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
<=> ( zero_zero(nat) = X0 ) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X3: nat] :
( ( semiring_1_of_nat(int,X3) = zero_zero(int) )
<=> ( zero_zero(nat) = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_int__eq__0__conv) ).
tff(f825,plain,
( spl14_59
| ~ spl14_17
| ~ spl14_42 ),
inference(avatar_split_clause,[],[f791,f723,f602,f822]) ).
tff(f822,plain,
( spl14_59
<=> ( zero_zero(nat) = semiring_1_of_nat(nat,zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_59])]) ).
tff(f602,plain,
( spl14_17
<=> semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_17])]) ).
tff(f723,plain,
( spl14_42
<=> ! [X0: $tType] :
( ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) )
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_42])]) ).
tff(f791,plain,
( ( zero_zero(nat) = semiring_1_of_nat(nat,zero_zero(nat)) )
| ~ spl14_17
| ~ spl14_42 ),
inference(resolution,[],[f724,f604]) ).
tff(f604,plain,
( semiring_1(nat)
| ~ spl14_17 ),
inference(avatar_component_clause,[],[f602]) ).
tff(f724,plain,
( ! [X0: $tType] :
( ~ semiring_1(X0)
| ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) ) )
| ~ spl14_42 ),
inference(avatar_component_clause,[],[f723]) ).
tff(f789,plain,
spl14_58,
inference(avatar_split_clause,[],[f510,f787]) ).
tff(f787,plain,
( spl14_58
<=> ! [X0: $tType,X1: nat,X3: X0] : ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X3),X3) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_58])]) ).
tff(f510,plain,
! [X0: $tType,X3: X0,X1: nat] : ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X3),X3) = X1 ),
inference(equality_resolution,[],[f464]) ).
tff(f464,plain,
! [X0: $tType,X2: X0,X3: X0,X1: nat] :
( ( huffma1352802255e_freq(X0,huffma2021818691e_Leaf(X0,X1,X2),X3) = X1 )
| ( X2 != X3 ) ),
inference(cnf_transformation,[],[f270]) ).
tff(f785,plain,
spl14_57,
inference(avatar_split_clause,[],[f490,f783]) ).
tff(f783,plain,
( spl14_57
<=> ! [X0: $tType,X2: X0] :
( ( plus_plus(X0,X2,zero_zero(X0)) = X2 )
| ~ semiri456707255roduct(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_57])]) ).
tff(f490,plain,
! [X0: $tType,X2: X0] :
( ( plus_plus(X0,X2,zero_zero(X0)) = X2 )
| ~ semiri456707255roduct(X0) ),
inference(equality_resolution,[],[f366]) ).
tff(f366,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( plus_plus(X0,X2,X1) = X2 )
| ( zero_zero(X0) != X1 )
| ~ semiri456707255roduct(X0) ),
inference(cnf_transformation,[],[f282]) ).
tff(f781,plain,
spl14_56,
inference(avatar_split_clause,[],[f458,f779]) ).
tff(f779,plain,
( spl14_56
<=> ! [X0: $tType,X3: nat,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] : ( huffma854194513Weight(X0,huffma1146269203erNode(X0,X3,X2,X1)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_56])]) ).
tff(f458,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] : ( huffma854194513Weight(X0,huffma1146269203erNode(X0,X3,X2,X1)) = X3 ),
inference(cnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] : ( huffma854194513Weight(X0,huffma1146269203erNode(X0,X3,X2,X1)) = X3 ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X0: $tType,X9: huffma1450048681e_tree(X0),X10: huffma1450048681e_tree(X0),X11: nat] : ( huffma854194513Weight(X0,huffma1146269203erNode(X0,X11,X10,X9)) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_cachedWeight_Osimps_I2_J) ).
tff(f777,plain,
spl14_55,
inference(avatar_split_clause,[],[f443,f775]) ).
tff(f775,plain,
( spl14_55
<=> ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_55])]) ).
tff(f443,plain,
! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
inference(cnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: $tType,X1: X0,X2: nat] : ( zero_zero(nat) = huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X0: $tType,X20: X0,X11: nat] : ( huffma1134658180e_cost(X0,huffma2021818691e_Leaf(X0,X11,X20)) = zero_zero(nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_cost_Osimps_I1_J) ).
tff(f773,plain,
spl14_54,
inference(avatar_split_clause,[],[f442,f771]) ).
tff(f771,plain,
( spl14_54
<=> ! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_54])]) ).
tff(f442,plain,
! [X0: $tType,X2: nat,X1: X0] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
inference(cnf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: $tType,X1: X0,X2: nat] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X0: $tType,X20: X0,X11: nat] : ( zero_zero(nat) = huffma945805758height(X0,huffma2021818691e_Leaf(X0,X11,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_height_Osimps_I1_J) ).
tff(f769,plain,
spl14_53,
inference(avatar_split_clause,[],[f395,f767]) ).
tff(f767,plain,
( spl14_53
<=> ! [X0: nat,X1: nat] : ( plus_plus(nat,X1,X0) = plus_plus(nat,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_53])]) ).
tff(f395,plain,
! [X0: nat,X1: nat] : ( plus_plus(nat,X1,X0) = plus_plus(nat,X0,X1) ),
inference(cnf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: nat,X1: nat] : ( plus_plus(nat,X1,X0) = plus_plus(nat,X0,X1) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X13: nat,X14: nat] : ( plus_plus(nat,X14,X13) = plus_plus(nat,X13,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_nat__add__commute) ).
tff(f765,plain,
spl14_52,
inference(avatar_split_clause,[],[f392,f763]) ).
tff(f763,plain,
( spl14_52
<=> ! [X0: nat] :
( ( suc(sK4(X0)) = X0 )
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_52])]) ).
tff(f392,plain,
! [X0: nat] :
( ( suc(sK4(X0)) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(cnf_transformation,[],[f289]) ).
tff(f289,plain,
! [X0: nat] :
( ( suc(sK4(X0)) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f257,f288]) ).
tff(f288,plain,
! [X0: nat] :
( ? [X1: nat] : ( suc(X1) = X0 )
=> ( suc(sK4(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f257,plain,
! [X0: nat] :
( ? [X1: nat] : ( suc(X1) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: nat] :
( ( zero_zero(nat) != X0 )
=> ? [X1: nat] : ( suc(X1) = X0 ) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X13: nat] :
( ( zero_zero(nat) != X13 )
=> ? [X54: nat] : ( suc(X54) = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_not0__implies__Suc) ).
tff(f761,plain,
spl14_51,
inference(avatar_split_clause,[],[f391,f759]) ).
tff(f759,plain,
( spl14_51
<=> ! [X0: nat] :
( ( suc(sK3(X0)) = X0 )
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_51])]) ).
tff(f391,plain,
! [X0: nat] :
( ( suc(sK3(X0)) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,plain,
! [X0: nat] :
( ( suc(sK3(X0)) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f256,f286]) ).
tff(f286,plain,
! [X0: nat] :
( ? [X1: nat] : ( suc(X1) = X0 )
=> ( suc(sK3(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f256,plain,
! [X0: nat] :
( ? [X1: nat] : ( suc(X1) = X0 )
| ( zero_zero(nat) = X0 ) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: nat] :
( ( zero_zero(nat) != X0 )
=> ~ ! [X1: nat] : ( suc(X1) != X0 ) ),
inference(rectify,[],[f94]) ).
tff(f94,axiom,
! [X16: nat] :
( ( zero_zero(nat) != X16 )
=> ~ ! [X37: nat] : ( suc(X37) != X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_nat_Oexhaust) ).
tff(f757,plain,
( spl14_49
| ~ spl14_50
| ~ spl14_26 ),
inference(avatar_split_clause,[],[f674,f645,f754,f751]) ).
tff(f751,plain,
( spl14_49
<=> ! [X0: bool] : ( fFalse = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_49])]) ).
tff(f754,plain,
( spl14_50
<=> ( fTrue = fFalse ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_50])]) ).
tff(f645,plain,
( spl14_26
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_26])]) ).
tff(f674,plain,
( ! [X0: bool] :
( ( fTrue != fFalse )
| ( fFalse = X0 ) )
| ~ spl14_26 ),
inference(equality_factoring,[],[f646]) ).
tff(f646,plain,
( ! [X0: bool] :
( ( fTrue = X0 )
| ( fFalse = X0 ) )
| ~ spl14_26 ),
inference(avatar_component_clause,[],[f645]) ).
tff(f749,plain,
spl14_48,
inference(avatar_split_clause,[],[f384,f747]) ).
tff(f747,plain,
( spl14_48
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_48])]) ).
tff(f384,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f249]) ).
tff(f249,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( plus_plus(X0,zero_zero(X0),X1) = X1 ) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X20: X0] : ( plus_plus(X0,zero_zero(X0),X20) = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
tff(f745,plain,
spl14_47,
inference(avatar_split_clause,[],[f383,f743]) ).
tff(f743,plain,
( spl14_47
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ comm_semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_47])]) ).
tff(f383,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ comm_semiring_1(X0) ),
inference(cnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ comm_semiring_1(X0) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X1: X0] : ( plus_plus(X0,X1,zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X0: $tType] :
( comm_semiring_1(X0)
=> ! [X20: X0] : ( plus_plus(X0,X20,zero_zero(X0)) = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
tff(f741,plain,
spl14_46,
inference(avatar_split_clause,[],[f375,f739]) ).
tff(f739,plain,
( spl14_46
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ comm_monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_46])]) ).
tff(f375,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ comm_monoid_add(X0) ),
inference(cnf_transformation,[],[f242]) ).
tff(f242,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ comm_monoid_add(X0) ),
inference(ennf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X1: X0] : ( plus_plus(X0,zero_zero(X0),X1) = X1 ) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X20: X0] : ( plus_plus(X0,zero_zero(X0),X20) = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_add__0) ).
tff(f737,plain,
spl14_45,
inference(avatar_split_clause,[],[f374,f735]) ).
tff(f374,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f241]) ).
tff(f241,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X1: X0] : ( plus_plus(X0,zero_zero(X0),X1) = X1 ) ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X20: X0] : ( plus_plus(X0,zero_zero(X0),X20) = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_add__0__left) ).
tff(f733,plain,
spl14_44,
inference(avatar_split_clause,[],[f373,f731]) ).
tff(f731,plain,
( spl14_44
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_44])]) ).
tff(f373,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X1: X0] : ( plus_plus(X0,X1,zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X20: X0] : ( plus_plus(X0,X20,zero_zero(X0)) = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_add__0__right) ).
tff(f729,plain,
spl14_43,
inference(avatar_split_clause,[],[f372,f727]) ).
tff(f372,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ),
inference(ennf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X1: X0] : ( plus_plus(X0,X1,zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X20: X0] : ( plus_plus(X0,X20,zero_zero(X0)) = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_add_Ocomm__neutral) ).
tff(f725,plain,
spl14_42,
inference(avatar_split_clause,[],[f371,f723]) ).
tff(f371,plain,
! [X0: $tType] :
( ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) )
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: $tType] :
( ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) )
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f44]) ).
tff(f44,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> ( semiring_1_of_nat(X0,zero_zero(nat)) = zero_zero(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_of__nat__0) ).
tff(f719,plain,
spl14_41,
inference(avatar_split_clause,[],[f441,f717]) ).
tff(f717,plain,
( spl14_41
<=> ! [X0: $tType,X2: nat,X1: X0] : ( huffma83463279weight(X0,huffma2021818691e_Leaf(X0,X2,X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_41])]) ).
tff(f441,plain,
! [X0: $tType,X2: nat,X1: X0] : ( huffma83463279weight(X0,huffma2021818691e_Leaf(X0,X2,X1)) = X2 ),
inference(cnf_transformation,[],[f192]) ).
tff(f192,plain,
! [X0: $tType,X1: X0,X2: nat] : ( huffma83463279weight(X0,huffma2021818691e_Leaf(X0,X2,X1)) = X2 ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X0: $tType,X20: X0,X11: nat] : ( huffma83463279weight(X0,huffma2021818691e_Leaf(X0,X11,X20)) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_weight_Osimps_I1_J) ).
tff(f715,plain,
spl14_40,
inference(avatar_split_clause,[],[f440,f713]) ).
tff(f713,plain,
( spl14_40
<=> ! [X0: $tType,X2: nat,X1: X0] : ( huffma854194513Weight(X0,huffma2021818691e_Leaf(X0,X2,X1)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_40])]) ).
tff(f440,plain,
! [X0: $tType,X2: nat,X1: X0] : ( huffma854194513Weight(X0,huffma2021818691e_Leaf(X0,X2,X1)) = X2 ),
inference(cnf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: $tType,X1: X0,X2: nat] : ( huffma854194513Weight(X0,huffma2021818691e_Leaf(X0,X2,X1)) = X2 ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X0: $tType,X20: X0,X11: nat] : ( huffma854194513Weight(X0,huffma2021818691e_Leaf(X0,X11,X20)) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_cachedWeight_Osimps_I1_J) ).
tff(f711,plain,
spl14_39,
inference(avatar_split_clause,[],[f403,f709]) ).
tff(f709,plain,
( spl14_39
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( suc(X0) != suc(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_39])]) ).
tff(f403,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( suc(X0) != suc(X1) ) ),
inference(cnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( suc(X0) != suc(X1) ) ),
inference(ennf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: nat,X1: nat] :
( ( suc(X0) = suc(X1) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X16: nat,X17: nat] :
( ( suc(X17) = suc(X16) )
=> ( X16 = X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Suc__inject) ).
tff(f704,plain,
spl14_38,
inference(avatar_split_clause,[],[f439,f702]) ).
tff(f702,plain,
( spl14_38
<=> ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fTrue,X2,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_38])]) ).
tff(f439,plain,
! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fTrue,X2,X1) = X2 ),
inference(cnf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: $tType,X1: X0,X2: X0] : ( if(X0,fTrue,X2,X1) = X2 ),
inference(rectify,[],[f121]) ).
tff(f121,axiom,
! [X0: $tType,X16: X0,X17: X0] : ( if(X0,fTrue,X17,X16) = X17 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
tff(f700,plain,
spl14_37,
inference(avatar_split_clause,[],[f438,f698]) ).
tff(f698,plain,
( spl14_37
<=> ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fFalse,X2,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_37])]) ).
tff(f438,plain,
! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fFalse,X2,X1) = X1 ),
inference(cnf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: $tType,X1: X0,X2: X0] : ( if(X0,fFalse,X2,X1) = X1 ),
inference(rectify,[],[f122]) ).
tff(f122,axiom,
! [X0: $tType,X16: X0,X17: X0] : ( if(X0,fFalse,X17,X16) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
tff(f696,plain,
( spl14_36
| ~ spl14_23
| ~ spl14_26 ),
inference(avatar_split_clause,[],[f673,f645,f632,f694]) ).
tff(f694,plain,
( spl14_36
<=> ! [X0: bool] :
( pp(X0)
| ( fFalse = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_36])]) ).
tff(f632,plain,
( spl14_23
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_23])]) ).
tff(f673,plain,
( ! [X0: bool] :
( pp(X0)
| ( fFalse = X0 ) )
| ~ spl14_23
| ~ spl14_26 ),
inference(superposition,[],[f634,f646]) ).
tff(f634,plain,
( pp(fTrue)
| ~ spl14_23 ),
inference(avatar_component_clause,[],[f632]) ).
tff(f692,plain,
spl14_35,
inference(avatar_split_clause,[],[f356,f690]) ).
tff(f690,plain,
( spl14_35
<=> ! [X0: nat] : ( plus_plus(nat,zero_zero(nat),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_35])]) ).
tff(f356,plain,
! [X0: nat] : ( plus_plus(nat,zero_zero(nat),X0) = X0 ),
inference(cnf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: nat] : ( plus_plus(nat,zero_zero(nat),X0) = X0 ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X13: nat] : ( plus_plus(nat,zero_zero(nat),X13) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_plus__nat_Oadd__0) ).
tff(f688,plain,
spl14_34,
inference(avatar_split_clause,[],[f355,f686]) ).
tff(f355,plain,
! [X0: nat] : ( plus_plus(nat,X0,zero_zero(nat)) = X0 ),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: nat] : ( plus_plus(nat,X0,zero_zero(nat)) = X0 ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X14: nat] : ( plus_plus(nat,X14,zero_zero(nat)) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Nat_Oadd__0__right) ).
tff(f684,plain,
spl14_33,
inference(avatar_split_clause,[],[f345,f681]) ).
tff(f681,plain,
( spl14_33
<=> ( zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_33])]) ).
tff(f345,plain,
zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)),
inference(cnf_transformation,[],[f65]) ).
tff(f65,axiom,
zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_transfer__int__nat__numerals_I1_J) ).
tff(f679,plain,
~ spl14_32,
inference(avatar_split_clause,[],[f485,f676]) ).
tff(f485,plain,
plus_plus(nat,huffma1352802255e_freq(a,t_1,sK2),huffma1352802255e_freq(a,t_2,sK2)) != huffma1352802255e_freq(a,huffma1146269203erNode(a,plus_plus(nat,huffma854194513Weight(a,t_1),huffma854194513Weight(a,t_2)),t_1,t_2),sK2),
inference(definition_unfolding,[],[f321,f447]) ).
tff(f447,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] : ( huffma921447403eTrees(X0,X2,X1) = huffma1146269203erNode(X0,plus_plus(nat,huffma854194513Weight(X0,X2),huffma854194513Weight(X0,X1)),X2,X1) ),
inference(cnf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0)] : ( huffma921447403eTrees(X0,X2,X1) = huffma1146269203erNode(X0,plus_plus(nat,huffma854194513Weight(X0,X2),huffma854194513Weight(X0,X1)),X2,X1) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType,X9: huffma1450048681e_tree(X0),X10: huffma1450048681e_tree(X0)] : ( huffma921447403eTrees(X0,X10,X9) = huffma1146269203erNode(X0,plus_plus(nat,huffma854194513Weight(X0,X10),huffma854194513Weight(X0,X9)),X10,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_uniteTrees__def) ).
tff(f321,plain,
huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),sK2) != plus_plus(nat,huffma1352802255e_freq(a,t_1,sK2),huffma1352802255e_freq(a,t_2,sK2)),
inference(cnf_transformation,[],[f278]) ).
tff(f278,plain,
huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),sK2) != plus_plus(nat,huffma1352802255e_freq(a,t_1,sK2),huffma1352802255e_freq(a,t_2,sK2)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f230,f277]) ).
tff(f277,plain,
( ? [X0: a] : ( huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),X0) != plus_plus(nat,huffma1352802255e_freq(a,t_1,X0),huffma1352802255e_freq(a,t_2,X0)) )
=> ( huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),sK2) != plus_plus(nat,huffma1352802255e_freq(a,t_1,sK2),huffma1352802255e_freq(a,t_2,sK2)) ) ),
introduced(choice_axiom,[]) ).
tff(f230,plain,
? [X0: a] : ( huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),X0) != plus_plus(nat,huffma1352802255e_freq(a,t_1,X0),huffma1352802255e_freq(a,t_2,X0)) ),
inference(ennf_transformation,[],[f128]) ).
tff(f128,plain,
~ ! [X0: a] : ( huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),X0) = plus_plus(nat,huffma1352802255e_freq(a,t_1,X0),huffma1352802255e_freq(a,t_2,X0)) ),
inference(rectify,[],[f127]) ).
tff(f127,negated_conjecture,
~ ! [X48: a] : ( huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),X48) = plus_plus(nat,huffma1352802255e_freq(a,t_1,X48),huffma1352802255e_freq(a,t_2,X48)) ),
inference(negated_conjecture,[],[f126]) ).
tff(f126,conjecture,
! [X48: a] : ( huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),X48) = plus_plus(nat,huffma1352802255e_freq(a,t_1,X48),huffma1352802255e_freq(a,t_2,X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f671,plain,
spl14_31,
inference(avatar_split_clause,[],[f507,f668]) ).
tff(f668,plain,
( spl14_31
<=> sP1(zero_zero(nat),suc(zero_zero(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_31])]) ).
tff(f507,plain,
sP1(zero_zero(nat),suc(zero_zero(nat))),
inference(equality_resolution,[],[f506]) ).
tff(f506,plain,
! [X1: nat] :
( sP1(zero_zero(nat),X1)
| ( suc(zero_zero(nat)) != X1 ) ),
inference(equality_resolution,[],[f433]) ).
tff(f433,plain,
! [X0: nat,X1: nat] :
( sP1(X0,X1)
| ( zero_zero(nat) != X0 )
| ( suc(zero_zero(nat)) != X1 ) ),
inference(cnf_transformation,[],[f310]) ).
tff(f666,plain,
spl14_30,
inference(avatar_split_clause,[],[f505,f663]) ).
tff(f663,plain,
( spl14_30
<=> sP1(suc(zero_zero(nat)),zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_30])]) ).
tff(f505,plain,
sP1(suc(zero_zero(nat)),zero_zero(nat)),
inference(equality_resolution,[],[f504]) ).
tff(f504,plain,
! [X1: nat] :
( sP1(suc(zero_zero(nat)),X1)
| ( zero_zero(nat) != X1 ) ),
inference(equality_resolution,[],[f434]) ).
tff(f434,plain,
! [X0: nat,X1: nat] :
( sP1(X0,X1)
| ( suc(zero_zero(nat)) != X0 )
| ( zero_zero(nat) != X1 ) ),
inference(cnf_transformation,[],[f310]) ).
tff(f661,plain,
spl14_29,
inference(avatar_split_clause,[],[f503,f658]) ).
tff(f658,plain,
( spl14_29
<=> sP0(zero_zero(nat),suc(zero_zero(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_29])]) ).
tff(f503,plain,
sP0(zero_zero(nat),suc(zero_zero(nat))),
inference(equality_resolution,[],[f502]) ).
tff(f502,plain,
! [X1: nat] :
( sP0(zero_zero(nat),X1)
| ( suc(zero_zero(nat)) != X1 ) ),
inference(equality_resolution,[],[f425]) ).
tff(f425,plain,
! [X0: nat,X1: nat] :
( sP0(X0,X1)
| ( zero_zero(nat) != X0 )
| ( suc(zero_zero(nat)) != X1 ) ),
inference(cnf_transformation,[],[f307]) ).
tff(f656,plain,
spl14_28,
inference(avatar_split_clause,[],[f501,f653]) ).
tff(f653,plain,
( spl14_28
<=> sP0(suc(zero_zero(nat)),zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_28])]) ).
tff(f501,plain,
sP0(suc(zero_zero(nat)),zero_zero(nat)),
inference(equality_resolution,[],[f500]) ).
tff(f500,plain,
! [X1: nat] :
( sP0(suc(zero_zero(nat)),X1)
| ( zero_zero(nat) != X1 ) ),
inference(equality_resolution,[],[f426]) ).
tff(f426,plain,
! [X0: nat,X1: nat] :
( sP0(X0,X1)
| ( suc(zero_zero(nat)) != X0 )
| ( zero_zero(nat) != X1 ) ),
inference(cnf_transformation,[],[f307]) ).
tff(f651,plain,
spl14_27,
inference(avatar_split_clause,[],[f437,f649]) ).
tff(f649,plain,
( spl14_27
<=> ! [X0: $tType,X2: nat,X1: X0] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_27])]) ).
tff(f437,plain,
! [X0: $tType,X2: nat,X1: X0] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)),
inference(cnf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: $tType,X1: X0,X2: nat] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X2,X1)),
inference(rectify,[],[f38]) ).
tff(f38,axiom,
! [X0: $tType,X20: X0,X11: nat] : huffma1518433673istent(X0,huffma2021818691e_Leaf(X0,X11,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_consistent_Osimps_I1_J) ).
tff(f647,plain,
spl14_26,
inference(avatar_split_clause,[],[f358,f645]) ).
tff(f358,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f123]) ).
tff(f123,axiom,
! [X59: bool] :
( ( fFalse = X59 )
| ( fTrue = X59 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
tff(f643,plain,
spl14_25,
inference(avatar_split_clause,[],[f349,f641]) ).
tff(f349,plain,
! [X0: nat] : ( zero_zero(nat) != suc(X0) ),
inference(cnf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: nat] : ( zero_zero(nat) != suc(X0) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X52: nat] : ( zero_zero(nat) != suc(X52) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_nat_Osimps_I3_J) ).
tff(f639,plain,
spl14_24,
inference(avatar_split_clause,[],[f347,f637]) ).
tff(f347,plain,
! [X0: nat] : ( suc(X0) != X0 ),
inference(cnf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: nat] : ( suc(X0) != X0 ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X13: nat] : ( suc(X13) != X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_n__not__Suc__n) ).
tff(f635,plain,
spl14_23,
inference(avatar_split_clause,[],[f344,f632]) ).
tff(f344,plain,
pp(fTrue),
inference(cnf_transformation,[],[f125]) ).
tff(f125,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f630,plain,
spl14_22,
inference(avatar_split_clause,[],[f343,f627]) ).
tff(f627,plain,
( spl14_22
<=> comm_semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_22])]) ).
tff(f343,plain,
comm_semiring_1(nat),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
comm_semiring_1(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
tff(f625,plain,
spl14_21,
inference(avatar_split_clause,[],[f342,f622]) ).
tff(f622,plain,
( spl14_21
<=> comm_semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_21])]) ).
tff(f342,plain,
comm_semiring_1(int),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
comm_semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
tff(f620,plain,
spl14_20,
inference(avatar_split_clause,[],[f341,f617]) ).
tff(f617,plain,
( spl14_20
<=> cancel_semigroup_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_20])]) ).
tff(f341,plain,
cancel_semigroup_add(nat),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
cancel_semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
tff(f615,plain,
spl14_19,
inference(avatar_split_clause,[],[f340,f612]) ).
tff(f612,plain,
( spl14_19
<=> cancel_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_19])]) ).
tff(f340,plain,
cancel_semigroup_add(int),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
cancel_semigroup_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
tff(f610,plain,
spl14_18,
inference(avatar_split_clause,[],[f339,f607]) ).
tff(f607,plain,
( spl14_18
<=> comm_monoid_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_18])]) ).
tff(f339,plain,
comm_monoid_add(nat),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
comm_monoid_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
tff(f605,plain,
spl14_17,
inference(avatar_split_clause,[],[f338,f602]) ).
tff(f338,plain,
semiring_1(nat),
inference(cnf_transformation,[],[f118]) ).
tff(f118,axiom,
semiring_1(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
tff(f600,plain,
spl14_16,
inference(avatar_split_clause,[],[f337,f597]) ).
tff(f597,plain,
( spl14_16
<=> monoid_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_16])]) ).
tff(f337,plain,
monoid_add(nat),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
monoid_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
tff(f595,plain,
spl14_15,
inference(avatar_split_clause,[],[f336,f592]) ).
tff(f336,plain,
monoid_add(int),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
monoid_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
tff(f590,plain,
spl14_14,
inference(avatar_split_clause,[],[f335,f587]) ).
tff(f335,plain,
comm_monoid_add(int),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
comm_monoid_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
tff(f585,plain,
spl14_13,
inference(avatar_split_clause,[],[f334,f582]) ).
tff(f582,plain,
( spl14_13
<=> semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_13])]) ).
tff(f334,plain,
semiring_1(int),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
tff(f580,plain,
spl14_12,
inference(avatar_split_clause,[],[f333,f577]) ).
tff(f577,plain,
( spl14_12
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_12])]) ).
tff(f333,plain,
zero(nat),
inference(cnf_transformation,[],[f119]) ).
tff(f119,axiom,
zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f575,plain,
spl14_11,
inference(avatar_split_clause,[],[f332,f572]) ).
tff(f572,plain,
( spl14_11
<=> ab_semigroup_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_11])]) ).
tff(f332,plain,
ab_semigroup_add(nat),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
ab_semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
tff(f570,plain,
spl14_10,
inference(avatar_split_clause,[],[f331,f567]) ).
tff(f567,plain,
( spl14_10
<=> semiring_char_0(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_10])]) ).
tff(f331,plain,
semiring_char_0(nat),
inference(cnf_transformation,[],[f116]) ).
tff(f116,axiom,
semiring_char_0(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
tff(f565,plain,
spl14_9,
inference(avatar_split_clause,[],[f330,f562]) ).
tff(f562,plain,
( spl14_9
<=> cancel146912293up_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_9])]) ).
tff(f330,plain,
cancel146912293up_add(nat),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
cancel146912293up_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
tff(f560,plain,
spl14_8,
inference(avatar_split_clause,[],[f329,f557]) ).
tff(f557,plain,
( spl14_8
<=> semiri456707255roduct(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_8])]) ).
tff(f329,plain,
semiri456707255roduct(nat),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
semiri456707255roduct(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
tff(f555,plain,
spl14_7,
inference(avatar_split_clause,[],[f328,f552]) ).
tff(f552,plain,
( spl14_7
<=> zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_7])]) ).
tff(f328,plain,
zero(int),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
tff(f550,plain,
spl14_6,
inference(avatar_split_clause,[],[f327,f547]) ).
tff(f547,plain,
( spl14_6
<=> cancel146912293up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_6])]) ).
tff(f327,plain,
cancel146912293up_add(int),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
cancel146912293up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
tff(f545,plain,
spl14_5,
inference(avatar_split_clause,[],[f326,f542]) ).
tff(f542,plain,
( spl14_5
<=> semiring_char_0(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_5])]) ).
tff(f326,plain,
semiring_char_0(int),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
semiring_char_0(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
tff(f540,plain,
spl14_4,
inference(avatar_split_clause,[],[f325,f537]) ).
tff(f537,plain,
( spl14_4
<=> ab_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_4])]) ).
tff(f325,plain,
ab_semigroup_add(int),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
ab_semigroup_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
tff(f535,plain,
spl14_3,
inference(avatar_split_clause,[],[f324,f532]) ).
tff(f532,plain,
( spl14_3
<=> semiri456707255roduct(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_3])]) ).
tff(f324,plain,
semiri456707255roduct(int),
inference(cnf_transformation,[],[f98]) ).
tff(f98,axiom,
semiri456707255roduct(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
tff(f530,plain,
spl14_2,
inference(avatar_split_clause,[],[f323,f527]) ).
tff(f527,plain,
( spl14_2
<=> linord219039673up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_2])]) ).
tff(f323,plain,
linord219039673up_add(int),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
linord219039673up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
tff(f525,plain,
~ spl14_1,
inference(avatar_split_clause,[],[f322,f522]) ).
tff(f522,plain,
( spl14_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_1])]) ).
tff(f322,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f124]) ).
tff(f124,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW538_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 03:02:03 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (2431)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (2434)WARNING: value z3 for option sas not known
% 0.15/0.39 % (2432)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 % (2433)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (2435)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (2434)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.39 % (2436)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.39 % (2437)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.39 % (2438)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.39 % (2438)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.15/0.39 % Exception at run slice level
% 0.15/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.41 % (2439)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.41 % (2441)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.22/0.41 % (2440)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.22/0.41 % (2439)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.41 % Exception at run slice level
% 0.22/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.41 % (2440)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.42 % (2436)First to succeed.
% 0.22/0.43 % (2442)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 0.22/0.43 % (2436)Refutation found. Thanks to Tanya!
% 0.22/0.43 % SZS status Theorem for theBenchmark
% 0.22/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.44 % (2436)------------------------------
% 0.22/0.44 % (2436)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.44 % (2436)Termination reason: Refutation
% 0.22/0.44
% 0.22/0.44 % (2436)Memory used [KB]: 1479
% 0.22/0.44 % (2436)Time elapsed: 0.049 s
% 0.22/0.44 % (2436)Instructions burned: 80 (million)
% 0.22/0.44 % (2436)------------------------------
% 0.22/0.44 % (2436)------------------------------
% 0.22/0.44 % (2431)Success in time 0.071 s
%------------------------------------------------------------------------------