TSTP Solution File: NUM980_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM980_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 : n017.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 : Sun May 5 08:44:03 EDT 2024
% Result : Theorem 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 300
% Syntax : Number of formulae : 773 ( 258 unt; 37 typ; 0 def)
% Number of atoms : 1664 ( 335 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1464 ( 536 ~; 512 |; 66 &)
% ( 191 <=>; 159 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 21 ( 11 >; 10 *; 0 +; 0 <<)
% Number of predicates : 166 ( 164 usr; 146 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-4 aty)
% Number of variables : 1117 (1082 !; 11 ?;1117 :)
% ( 24 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,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,
if:
!>[X0: $tType] : ( ( bool * X0 * X0 ) > X0 ) ).
tff(func_def_4,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_5,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_6,type,
fFalse: bool ).
tff(func_def_7,type,
fTrue: bool ).
tff(func_def_8,type,
n: nat ).
tff(func_def_9,type,
t: int ).
tff(func_def_10,type,
tn: nat ).
tff(func_def_11,type,
sK1: int > nat ).
tff(func_def_12,type,
sK2: ( nat * nat ) > nat ).
tff(func_def_13,type,
sK3: ( fun(int,bool) * int ) > int ).
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,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
ordere216010020id_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
ordere236663937imp_le:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
ordere223160158up_add:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_18,type,
pp: bool > $o ).
tff(pred_def_19,type,
sP0: ( nat * nat * fun(nat,fun(nat,bool)) ) > $o ).
tff(f2230,plain,
$false,
inference(avatar_sat_refutation,[],[f541,f546,f551,f556,f561,f566,f571,f576,f581,f586,f591,f596,f601,f606,f611,f616,f621,f626,f631,f636,f641,f646,f651,f656,f661,f666,f671,f676,f681,f686,f691,f696,f701,f705,f710,f715,f720,f724,f728,f735,f740,f745,f749,f753,f757,f761,f765,f769,f773,f777,f796,f800,f804,f808,f812,f820,f824,f829,f833,f837,f841,f845,f849,f853,f864,f892,f896,f900,f907,f920,f924,f928,f932,f936,f940,f944,f948,f952,f956,f960,f1013,f1017,f1021,f1025,f1029,f1033,f1037,f1041,f1045,f1049,f1053,f1090,f1121,f1125,f1129,f1133,f1173,f1181,f1185,f1189,f1193,f1197,f1201,f1205,f1209,f1214,f1218,f1222,f1359,f1363,f1367,f1371,f1375,f1379,f1383,f1387,f1392,f1396,f1400,f1649,f1653,f1657,f1661,f1665,f1669,f1673,f1915,f1919,f1923,f1927,f1932,f1936,f1972,f1976,f1980,f2010,f2056,f2060,f2064,f2141,f2184,f2191,f2199,f2207,f2229]) ).
tff(f2229,plain,
( ~ spl4_37
| ~ spl4_85
| spl4_137 ),
inference(avatar_split_clause,[],[f2177,f2007,f1023,f717]) ).
tff(f717,plain,
( spl4_37
<=> ord_less(nat,zero_zero(nat),n) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_37])]) ).
tff(f1023,plain,
( spl4_85
<=> ! [X0: nat] :
( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
| ~ ord_less(nat,zero_zero(nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_85])]) ).
tff(f2007,plain,
( spl4_137
<=> ord_less(int,zero_zero(int),semiring_1_of_nat(int,n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_137])]) ).
tff(f2177,plain,
( ~ ord_less(nat,zero_zero(nat),n)
| ~ spl4_85
| spl4_137 ),
inference(resolution,[],[f2009,f1024]) ).
tff(f1024,plain,
( ! [X0: nat] :
( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
| ~ ord_less(nat,zero_zero(nat),X0) )
| ~ spl4_85 ),
inference(avatar_component_clause,[],[f1023]) ).
tff(f2009,plain,
( ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,n))
| spl4_137 ),
inference(avatar_component_clause,[],[f2007]) ).
tff(f2207,plain,
spl4_145,
inference(avatar_split_clause,[],[f494,f2205]) ).
tff(f2205,plain,
( spl4_145
<=> ! [X2: int,X0: fun(int,bool),X1: int] :
( pp(aa(int,bool,X0,X1))
| ~ pp(aa(int,bool,X0,plus_plus(int,sK3(X0,X2),one_one(int))))
| ~ pp(aa(int,bool,X0,plus_plus(int,X2,one_one(int))))
| ~ ord_less(int,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_145])]) ).
tff(f494,plain,
! [X2: int,X0: fun(int,bool),X1: int] :
( pp(aa(int,bool,X0,X1))
| ~ pp(aa(int,bool,X0,plus_plus(int,sK3(X0,X2),one_one(int))))
| ~ pp(aa(int,bool,X0,plus_plus(int,X2,one_one(int))))
| ~ ord_less(int,X2,X1) ),
inference(cnf_transformation,[],[f330]) ).
tff(f330,plain,
! [X0: fun(int,bool),X1: int,X2: int] :
( pp(aa(int,bool,X0,X1))
| ( ~ pp(aa(int,bool,X0,plus_plus(int,sK3(X0,X2),one_one(int))))
& pp(aa(int,bool,X0,sK3(X0,X2)))
& ord_less(int,X2,sK3(X0,X2)) )
| ~ pp(aa(int,bool,X0,plus_plus(int,X2,one_one(int))))
| ~ ord_less(int,X2,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f282,f329]) ).
tff(f329,plain,
! [X0: fun(int,bool),X2: int] :
( ? [X3: int] :
( ~ pp(aa(int,bool,X0,plus_plus(int,X3,one_one(int))))
& pp(aa(int,bool,X0,X3))
& ord_less(int,X2,X3) )
=> ( ~ pp(aa(int,bool,X0,plus_plus(int,sK3(X0,X2),one_one(int))))
& pp(aa(int,bool,X0,sK3(X0,X2)))
& ord_less(int,X2,sK3(X0,X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f282,plain,
! [X0: fun(int,bool),X1: int,X2: int] :
( pp(aa(int,bool,X0,X1))
| ? [X3: int] :
( ~ pp(aa(int,bool,X0,plus_plus(int,X3,one_one(int))))
& pp(aa(int,bool,X0,X3))
& ord_less(int,X2,X3) )
| ~ pp(aa(int,bool,X0,plus_plus(int,X2,one_one(int))))
| ~ ord_less(int,X2,X1) ),
inference(flattening,[],[f281]) ).
tff(f281,plain,
! [X0: fun(int,bool),X1: int,X2: int] :
( pp(aa(int,bool,X0,X1))
| ? [X3: int] :
( ~ pp(aa(int,bool,X0,plus_plus(int,X3,one_one(int))))
& pp(aa(int,bool,X0,X3))
& ord_less(int,X2,X3) )
| ~ pp(aa(int,bool,X0,plus_plus(int,X2,one_one(int))))
| ~ ord_less(int,X2,X1) ),
inference(ennf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: fun(int,bool),X1: int,X2: int] :
( ord_less(int,X2,X1)
=> ( pp(aa(int,bool,X0,plus_plus(int,X2,one_one(int))))
=> ( ! [X3: int] :
( ord_less(int,X2,X3)
=> ( pp(aa(int,bool,X0,X3))
=> pp(aa(int,bool,X0,plus_plus(int,X3,one_one(int)))) ) )
=> pp(aa(int,bool,X0,X1)) ) ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X20: fun(int,bool),X28: int,X10: int] :
( ord_less(int,X10,X28)
=> ( pp(aa(int,bool,X20,plus_plus(int,X10,one_one(int))))
=> ( ! [X29: int] :
( ord_less(int,X10,X29)
=> ( pp(aa(int,bool,X20,X29))
=> pp(aa(int,bool,X20,plus_plus(int,X29,one_one(int)))) ) )
=> pp(aa(int,bool,X20,X28)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_int__gr__induct) ).
tff(f2199,plain,
spl4_144,
inference(avatar_split_clause,[],[f493,f2197]) ).
tff(f2197,plain,
( spl4_144
<=> ! [X2: int,X0: fun(int,bool),X1: int] :
( pp(aa(int,bool,X0,X1))
| pp(aa(int,bool,X0,sK3(X0,X2)))
| ~ pp(aa(int,bool,X0,plus_plus(int,X2,one_one(int))))
| ~ ord_less(int,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_144])]) ).
tff(f493,plain,
! [X2: int,X0: fun(int,bool),X1: int] :
( pp(aa(int,bool,X0,X1))
| pp(aa(int,bool,X0,sK3(X0,X2)))
| ~ pp(aa(int,bool,X0,plus_plus(int,X2,one_one(int))))
| ~ ord_less(int,X2,X1) ),
inference(cnf_transformation,[],[f330]) ).
tff(f2191,plain,
spl4_143,
inference(avatar_split_clause,[],[f492,f2189]) ).
tff(f2189,plain,
( spl4_143
<=> ! [X2: int,X0: fun(int,bool),X1: int] :
( pp(aa(int,bool,X0,X1))
| ord_less(int,X2,sK3(X0,X2))
| ~ pp(aa(int,bool,X0,plus_plus(int,X2,one_one(int))))
| ~ ord_less(int,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_143])]) ).
tff(f492,plain,
! [X2: int,X0: fun(int,bool),X1: int] :
( pp(aa(int,bool,X0,X1))
| ord_less(int,X2,sK3(X0,X2))
| ~ pp(aa(int,bool,X0,plus_plus(int,X2,one_one(int))))
| ~ ord_less(int,X2,X1) ),
inference(cnf_transformation,[],[f330]) ).
tff(f2184,plain,
spl4_142,
inference(avatar_split_clause,[],[f501,f2182]) ).
tff(f2182,plain,
( spl4_142
<=> ! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
| ord_less(nat,X1,X2)
| ( X1 = X2 )
| sP0(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_142])]) ).
tff(f501,plain,
! [X2: nat,X0: fun(nat,fun(nat,bool)),X1: nat] :
( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
| ord_less(nat,X1,X2)
| ( X1 = X2 )
| sP0(X2,X1,X0) ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X1,X2) )
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ( X1 = X2 ) )
| sP0(X2,X1,X0) ),
inference(definition_folding,[],[f288,f293]) ).
tff(f293,plain,
! [X2: nat,X1: nat,X0: fun(nat,fun(nat,bool))] :
( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X2,X1) )
| ~ sP0(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f288,plain,
! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X1,X2) )
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ( X1 = X2 ) )
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X2,X1) ) ),
inference(flattening,[],[f287]) ).
tff(f287,plain,
! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
( pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X1,X2) )
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ( X1 = X2 ) )
| ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X2,X1) ) ),
inference(ennf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: fun(nat,fun(nat,bool)),X1: nat,X2: nat] :
( ( ord_less(nat,X2,X1)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) )
=> ( ( ( X1 = X2 )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) )
=> ( ( ord_less(nat,X1,X2)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2)) ) ) ),
inference(rectify,[],[f50]) ).
tff(f50,axiom,
! [X20: fun(nat,fun(nat,bool)),X2: nat,X6: nat] :
( ( ord_less(nat,X6,X2)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X20,X2),X6)) )
=> ( ( ( X2 = X6 )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X20,X2),X6)) )
=> ( ( ord_less(nat,X2,X6)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X20,X2),X6)) )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X20,X2),X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_nat__less__cases) ).
tff(f2141,plain,
spl4_141,
inference(avatar_split_clause,[],[f489,f2139]) ).
tff(f2139,plain,
( spl4_141
<=> ! [X2: nat,X0: int,X1: nat] : ( plus_plus(int,semiring_1_of_nat(int,X2),plus_plus(int,semiring_1_of_nat(int,X1),X0)) = plus_plus(int,semiring_1_of_nat(int,plus_plus(nat,X2,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_141])]) ).
tff(f489,plain,
! [X2: nat,X0: int,X1: nat] : ( plus_plus(int,semiring_1_of_nat(int,X2),plus_plus(int,semiring_1_of_nat(int,X1),X0)) = plus_plus(int,semiring_1_of_nat(int,plus_plus(nat,X2,X1)),X0) ),
inference(cnf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: int,X1: nat,X2: nat] : ( plus_plus(int,semiring_1_of_nat(int,X2),plus_plus(int,semiring_1_of_nat(int,X1),X0)) = plus_plus(int,semiring_1_of_nat(int,plus_plus(nat,X2,X1)),X0) ),
inference(rectify,[],[f51]) ).
tff(f51,axiom,
! [X13: int,X4: nat,X5: nat] : ( plus_plus(int,semiring_1_of_nat(int,X5),plus_plus(int,semiring_1_of_nat(int,X4),X13)) = plus_plus(int,semiring_1_of_nat(int,plus_plus(nat,X5,X4)),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_zadd__int__left) ).
tff(f2064,plain,
spl4_140,
inference(avatar_split_clause,[],[f418,f2062]) ).
tff(f2062,plain,
( spl4_140
<=> ! [X0: $tType,X4: X0,X3: X0,X2: X0,X1: X0] :
( ord_less(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1))
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X4,X3)
| ~ ordere223160158up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_140])]) ).
tff(f418,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: X0] :
( ord_less(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1))
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X4,X3)
| ~ ordere223160158up_add(X0) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ord_less(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1))
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X4,X3) )
| ~ ordere223160158up_add(X0) ),
inference(flattening,[],[f251]) ).
tff(f251,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ord_less(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1))
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,X4,X3) )
| ~ ordere223160158up_add(X0) ),
inference(ennf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: $tType] :
( ordere223160158up_add(X0)
=> ! [X1: X0,X2: X0,X3: X0,X4: X0] :
( ord_less(X0,X4,X3)
=> ( ord_less(X0,X2,X1)
=> ord_less(X0,plus_plus(X0,X4,X2),plus_plus(X0,X3,X1)) ) ) ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X0: $tType] :
( ordere223160158up_add(X0)
=> ! [X25: X0,X22: X0,X24: X0,X23: X0] :
( ord_less(X0,X23,X24)
=> ( ord_less(X0,X22,X25)
=> ord_less(X0,plus_plus(X0,X23,X22),plus_plus(X0,X24,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_add__strict__mono) ).
tff(f2060,plain,
spl4_139,
inference(avatar_split_clause,[],[f412,f2058]) ).
tff(f2058,plain,
( spl4_139
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,X2,X1))
| ~ ord_less(X0,zero_zero(X0),X1)
| ~ ord_less(X0,zero_zero(X0),X2)
| ~ ordere216010020id_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_139])]) ).
tff(f412,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,X2,X1))
| ~ ord_less(X0,zero_zero(X0),X1)
| ~ ord_less(X0,zero_zero(X0),X2)
| ~ ordere216010020id_add(X0) ),
inference(cnf_transformation,[],[f245]) ).
tff(f245,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,X2,X1))
| ~ ord_less(X0,zero_zero(X0),X1)
| ~ ord_less(X0,zero_zero(X0),X2) )
| ~ ordere216010020id_add(X0) ),
inference(flattening,[],[f244]) ).
tff(f244,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,X2,X1))
| ~ ord_less(X0,zero_zero(X0),X1)
| ~ ord_less(X0,zero_zero(X0),X2) )
| ~ ordere216010020id_add(X0) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: $tType] :
( ordere216010020id_add(X0)
=> ! [X1: X0,X2: X0] :
( ord_less(X0,zero_zero(X0),X2)
=> ( ord_less(X0,zero_zero(X0),X1)
=> ord_less(X0,zero_zero(X0),plus_plus(X0,X2,X1)) ) ) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType] :
( ordere216010020id_add(X0)
=> ! [X24: X0,X23: X0] :
( ord_less(X0,zero_zero(X0),X23)
=> ( ord_less(X0,zero_zero(X0),X24)
=> ord_less(X0,zero_zero(X0),plus_plus(X0,X23,X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_add__pos__pos) ).
tff(f2056,plain,
spl4_138,
inference(avatar_split_clause,[],[f411,f2054]) ).
tff(f2054,plain,
( spl4_138
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,plus_plus(X0,X2,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,X2,zero_zero(X0))
| ~ ordere216010020id_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_138])]) ).
tff(f411,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,plus_plus(X0,X2,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,X2,zero_zero(X0))
| ~ ordere216010020id_add(X0) ),
inference(cnf_transformation,[],[f243]) ).
tff(f243,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,plus_plus(X0,X2,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,X2,zero_zero(X0)) )
| ~ ordere216010020id_add(X0) ),
inference(flattening,[],[f242]) ).
tff(f242,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,plus_plus(X0,X2,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,X2,zero_zero(X0)) )
| ~ ordere216010020id_add(X0) ),
inference(ennf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: $tType] :
( ordere216010020id_add(X0)
=> ! [X1: X0,X2: X0] :
( ord_less(X0,X2,zero_zero(X0))
=> ( ord_less(X0,X1,zero_zero(X0))
=> ord_less(X0,plus_plus(X0,X2,X1),zero_zero(X0)) ) ) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X0: $tType] :
( ordere216010020id_add(X0)
=> ! [X24: X0,X23: X0] :
( ord_less(X0,X23,zero_zero(X0))
=> ( ord_less(X0,X24,zero_zero(X0))
=> ord_less(X0,plus_plus(X0,X23,X24),zero_zero(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_add__neg__neg) ).
tff(f2010,plain,
( ~ spl4_30
| ~ spl4_132
| ~ spl4_137
| spl4_33
| ~ spl4_134 ),
inference(avatar_split_clause,[],[f1982,f1970,f698,f2007,f1929,f683]) ).
tff(f683,plain,
( spl4_30
<=> linordered_semidom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_30])]) ).
tff(f1929,plain,
( spl4_132
<=> ord_less(int,zero_zero(int),one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_132])]) ).
tff(f698,plain,
( spl4_33
<=> ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_33])]) ).
tff(f1970,plain,
( spl4_134
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ord_less(X0,X2,plus_plus(X0,X3,X1))
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,zero_zero(X0),X3)
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_134])]) ).
tff(f1982,plain,
( ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,n))
| ~ ord_less(int,zero_zero(int),one_one(int))
| ~ linordered_semidom(int)
| spl4_33
| ~ spl4_134 ),
inference(resolution,[],[f1971,f700]) ).
tff(f700,plain,
( ~ ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))
| spl4_33 ),
inference(avatar_component_clause,[],[f698]) ).
tff(f1971,plain,
( ! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less(X0,X2,plus_plus(X0,X3,X1))
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,zero_zero(X0),X3)
| ~ linordered_semidom(X0) )
| ~ spl4_134 ),
inference(avatar_component_clause,[],[f1970]) ).
tff(f1980,plain,
spl4_136,
inference(avatar_split_clause,[],[f511,f1978]) ).
tff(f1978,plain,
( spl4_136
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] :
( ord_less(nat,plus_plus(nat,X3,X1),plus_plus(nat,X2,X0))
| ~ ord_less(nat,X1,X0)
| ~ ord_less(nat,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_136])]) ).
tff(f511,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ord_less(nat,plus_plus(nat,X3,X1),plus_plus(nat,X2,X0))
| ~ ord_less(nat,X1,X0)
| ~ ord_less(nat,X3,X2) ),
inference(cnf_transformation,[],[f290]) ).
tff(f290,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ord_less(nat,plus_plus(nat,X3,X1),plus_plus(nat,X2,X0))
| ~ ord_less(nat,X1,X0)
| ~ ord_less(nat,X3,X2) ),
inference(flattening,[],[f289]) ).
tff(f289,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ord_less(nat,plus_plus(nat,X3,X1),plus_plus(nat,X2,X0))
| ~ ord_less(nat,X1,X0)
| ~ ord_less(nat,X3,X2) ),
inference(ennf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ord_less(nat,X3,X2)
=> ( ord_less(nat,X1,X0)
=> ord_less(nat,plus_plus(nat,X3,X1),plus_plus(nat,X2,X0)) ) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X19: nat,X16: nat,X11: nat,X12: nat] :
( ord_less(nat,X12,X11)
=> ( ord_less(nat,X16,X19)
=> ord_less(nat,plus_plus(nat,X12,X16),plus_plus(nat,X11,X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_add__less__mono) ).
tff(f1976,plain,
spl4_135,
inference(avatar_split_clause,[],[f482,f1974]) ).
tff(f1974,plain,
( spl4_135
<=> ! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ord_less(nat,zero_zero(nat),X1)
| ~ ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_135])]) ).
tff(f482,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ord_less(nat,zero_zero(nat),X1)
| ~ ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0)) ),
inference(cnf_transformation,[],[f328]) ).
tff(f328,plain,
! [X0: nat,X1: nat] :
( ( ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0))
| ( ~ ord_less(nat,zero_zero(nat),X0)
& ~ ord_less(nat,zero_zero(nat),X1) ) )
& ( ord_less(nat,zero_zero(nat),X0)
| ord_less(nat,zero_zero(nat),X1)
| ~ ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0)) ) ),
inference(flattening,[],[f327]) ).
tff(f327,plain,
! [X0: nat,X1: nat] :
( ( ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0))
| ( ~ ord_less(nat,zero_zero(nat),X0)
& ~ ord_less(nat,zero_zero(nat),X1) ) )
& ( ord_less(nat,zero_zero(nat),X0)
| ord_less(nat,zero_zero(nat),X1)
| ~ ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0)) ) ),
inference(nnf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0))
<=> ( ord_less(nat,zero_zero(nat),X0)
| ord_less(nat,zero_zero(nat),X1) ) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X2: nat,X6: nat] :
( ord_less(nat,zero_zero(nat),plus_plus(nat,X6,X2))
<=> ( ord_less(nat,zero_zero(nat),X2)
| ord_less(nat,zero_zero(nat),X6) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_add__gr__0) ).
tff(f1972,plain,
spl4_134,
inference(avatar_split_clause,[],[f441,f1970]) ).
tff(f441,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less(X0,X2,plus_plus(X0,X3,X1))
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,zero_zero(X0),X3)
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f270,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X2,plus_plus(X0,X3,X1))
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,zero_zero(X0),X3) )
| ~ linordered_semidom(X0) ),
inference(flattening,[],[f269]) ).
tff(f269,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X2,plus_plus(X0,X3,X1))
| ~ ord_less(X0,X2,X1)
| ~ ord_less(X0,zero_zero(X0),X3) )
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,zero_zero(X0),X3)
=> ( ord_less(X0,X2,X1)
=> ord_less(X0,X2,plus_plus(X0,X3,X1)) ) ) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X22: X0,X24: X0,X23: X0] :
( ord_less(X0,zero_zero(X0),X23)
=> ( ord_less(X0,X24,X22)
=> ord_less(X0,X24,plus_plus(X0,X23,X22)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_pos__add__strict) ).
tff(f1936,plain,
spl4_133,
inference(avatar_split_clause,[],[f512,f1934]) ).
tff(f1934,plain,
( spl4_133
<=> ! [X0: nat,X3: nat,X2: nat,X1: nat] :
( ord_less(nat,X1,X0)
| ( plus_plus(nat,X1,X2) != plus_plus(nat,X3,X0) )
| ~ ord_less(nat,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_133])]) ).
tff(f512,plain,
! [X2: nat,X3: nat,X0: nat,X1: nat] :
( ord_less(nat,X1,X0)
| ( plus_plus(nat,X1,X2) != plus_plus(nat,X3,X0) )
| ~ ord_less(nat,X3,X2) ),
inference(cnf_transformation,[],[f292]) ).
tff(f292,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ord_less(nat,X1,X0)
| ( plus_plus(nat,X1,X2) != plus_plus(nat,X3,X0) )
| ~ ord_less(nat,X3,X2) ),
inference(flattening,[],[f291]) ).
tff(f291,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ord_less(nat,X1,X0)
| ( plus_plus(nat,X1,X2) != plus_plus(nat,X3,X0) )
| ~ ord_less(nat,X3,X2) ),
inference(ennf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: nat,X1: nat,X2: nat,X3: nat] :
( ord_less(nat,X3,X2)
=> ( ( plus_plus(nat,X1,X2) = plus_plus(nat,X3,X0) )
=> ord_less(nat,X1,X0) ) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X4: nat,X5: nat,X19: nat,X16: nat] :
( ord_less(nat,X16,X19)
=> ( ( plus_plus(nat,X5,X19) = plus_plus(nat,X16,X4) )
=> ord_less(nat,X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_less__add__eq__less) ).
tff(f1932,plain,
( spl4_132
| ~ spl4_56
| ~ spl4_93 ),
inference(avatar_split_clause,[],[f1706,f1088,f810,f1929]) ).
tff(f810,plain,
( spl4_56
<=> ! [X1: int] : ord_less(int,X1,plus_plus(int,X1,one_one(int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_56])]) ).
tff(f1088,plain,
( spl4_93
<=> ! [X0: int] : ( plus_plus(int,zero_zero(int),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_93])]) ).
tff(f1706,plain,
( ord_less(int,zero_zero(int),one_one(int))
| ~ spl4_56
| ~ spl4_93 ),
inference(superposition,[],[f811,f1089]) ).
tff(f1089,plain,
( ! [X0: int] : ( plus_plus(int,zero_zero(int),X0) = X0 )
| ~ spl4_93 ),
inference(avatar_component_clause,[],[f1088]) ).
tff(f811,plain,
( ! [X1: int] : ord_less(int,X1,plus_plus(int,X1,one_one(int)))
| ~ spl4_56 ),
inference(avatar_component_clause,[],[f810]) ).
tff(f1927,plain,
spl4_131,
inference(avatar_split_clause,[],[f452,f1925]) ).
tff(f1925,plain,
( spl4_131
<=> ! [X0: int] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),zero_zero(int))
| ~ ord_less(int,X0,zero_zero(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_131])]) ).
tff(f452,plain,
! [X0: int] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),zero_zero(int))
| ~ ord_less(int,X0,zero_zero(int)) ),
inference(cnf_transformation,[],[f314]) ).
tff(f314,plain,
! [X0: int] :
( ( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),zero_zero(int))
| ~ ord_less(int,X0,zero_zero(int)) )
& ( ord_less(int,X0,zero_zero(int))
| ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),zero_zero(int)) ) ),
inference(nnf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: int] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),zero_zero(int))
<=> ord_less(int,X0,zero_zero(int)) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X9: int] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X9),X9),zero_zero(int))
<=> ord_less(int,X9,zero_zero(int)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_odd__less__0__iff) ).
tff(f1923,plain,
spl4_130,
inference(avatar_split_clause,[],[f451,f1921]) ).
tff(f1921,plain,
( spl4_130
<=> ! [X0: int] :
( ord_less(int,X0,zero_zero(int))
| ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),zero_zero(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_130])]) ).
tff(f451,plain,
! [X0: int] :
( ord_less(int,X0,zero_zero(int))
| ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),zero_zero(int)) ),
inference(cnf_transformation,[],[f314]) ).
tff(f1919,plain,
spl4_129,
inference(avatar_split_clause,[],[f415,f1917]) ).
tff(f1917,plain,
( spl4_129
<=> ! [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,[spl4_129])]) ).
tff(f415,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,[],[f248]) ).
tff(f248,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,[],[f164]) ).
tff(f164,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,[],[f8]) ).
tff(f8,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> ! [X4: nat,X5: nat] : ( semiring_1_of_nat(X0,plus_plus(nat,X5,X4)) = plus_plus(X0,semiring_1_of_nat(X0,X5),semiring_1_of_nat(X0,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_of__nat__add) ).
tff(f1915,plain,
spl4_128,
inference(avatar_split_clause,[],[f403,f1913]) ).
tff(f1913,plain,
( spl4_128
<=> ! [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,[spl4_128])]) ).
tff(f403,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,[],[f234]) ).
tff(f234,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,[],[f156]) ).
tff(f156,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,[],[f58]) ).
tff(f58,axiom,
! [X0: $tType] :
( ab_semigroup_add(X0)
=> ! [X22: X0,X24: X0,X23: X0] : ( plus_plus(X0,plus_plus(X0,X23,X24),X22) = plus_plus(X0,X23,plus_plus(X0,X24,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_ab__semigroup__add__class_Oadd__ac_I1_J) ).
tff(f1673,plain,
spl4_127,
inference(avatar_split_clause,[],[f500,f1671]) ).
tff(f1671,plain,
( spl4_127
<=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_127])]) ).
tff(f500,plain,
! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f332]) ).
tff(f332,plain,
! [X0: nat,X1: nat,X2: fun(nat,fun(nat,bool))] :
( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X2,X1),X0))
& ord_less(nat,X0,X1) )
| ~ sP0(X0,X1,X2) ),
inference(rectify,[],[f331]) ).
tff(f331,plain,
! [X2: nat,X1: nat,X0: fun(nat,fun(nat,bool))] :
( ( ~ pp(aa(nat,bool,aa(nat,fun(nat,bool),X0,X1),X2))
& ord_less(nat,X2,X1) )
| ~ sP0(X2,X1,X0) ),
inference(nnf_transformation,[],[f293]) ).
tff(f1669,plain,
spl4_126,
inference(avatar_split_clause,[],[f430,f1667]) ).
tff(f1667,plain,
( spl4_126
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
| ~ ord_less(X0,X2,X1)
| ~ ordere236663937imp_le(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_126])]) ).
tff(f430,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
| ~ ord_less(X0,X2,X1)
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f306]) ).
tff(f306,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
| ~ ord_less(X0,X2,X1) )
& ( ord_less(X0,X2,X1)
| ~ ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1)) ) )
| ~ ordere236663937imp_le(X0) ),
inference(nnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
<=> ord_less(X0,X2,X1) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f175]) ).
tff(f175,plain,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
<=> ord_less(X0,X2,X1) ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X7: X0,X3: X0,X8: X0] :
( ord_less(X0,plus_plus(X0,X8,X3),plus_plus(X0,X8,X7))
<=> ord_less(X0,X3,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_add__less__cancel__left) ).
tff(f1665,plain,
spl4_125,
inference(avatar_split_clause,[],[f428,f1663]) ).
tff(f1663,plain,
( spl4_125
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
| ~ ord_less(X0,X3,X1)
| ~ ordere236663937imp_le(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_125])]) ).
tff(f428,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
| ~ ord_less(X0,X3,X1)
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f305]) ).
tff(f305,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
| ~ ord_less(X0,X3,X1) )
& ( ord_less(X0,X3,X1)
| ~ ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2)) ) )
| ~ ordere236663937imp_le(X0) ),
inference(nnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
<=> ord_less(X0,X3,X1) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
<=> ord_less(X0,X3,X1) ) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X7: X0,X8: X0,X3: X0] :
( ord_less(X0,plus_plus(X0,X3,X8),plus_plus(X0,X7,X8))
<=> ord_less(X0,X3,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_add__less__cancel__right) ).
tff(f1661,plain,
spl4_124,
inference(avatar_split_clause,[],[f422,f1659]) ).
tff(f1659,plain,
( spl4_124
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
| ~ ordere236663937imp_le(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_124])]) ).
tff(f422,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f256]) ).
tff(f256,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X3,X1)
| ~ ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2)) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X1,X2))
=> ord_less(X0,X3,X1) ) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X24: X0,X22: X0,X23: X0] :
( ord_less(X0,plus_plus(X0,X23,X22),plus_plus(X0,X24,X22))
=> ord_less(X0,X23,X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_add__less__imp__less__right) ).
tff(f1657,plain,
spl4_123,
inference(avatar_split_clause,[],[f421,f1655]) ).
tff(f1655,plain,
( spl4_123
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ord_less(X0,X2,X1)
| ~ ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
| ~ ordere236663937imp_le(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_123])]) ).
tff(f421,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less(X0,X2,X1)
| ~ ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
| ~ ordere236663937imp_le(X0) ),
inference(cnf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X2,X1)
| ~ ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1)) )
| ~ ordere236663937imp_le(X0) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,plus_plus(X0,X3,X2),plus_plus(X0,X3,X1))
=> ord_less(X0,X2,X1) ) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X24: X0,X23: X0,X22: X0] :
( ord_less(X0,plus_plus(X0,X22,X23),plus_plus(X0,X22,X24))
=> ord_less(X0,X23,X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_add__less__imp__less__left) ).
tff(f1653,plain,
spl4_122,
inference(avatar_split_clause,[],[f417,f1651]) ).
tff(f1651,plain,
( spl4_122
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ord_less(X0,plus_plus(X0,X1,X3),plus_plus(X0,X1,X2))
| ~ ord_less(X0,X3,X2)
| ~ ordere223160158up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_122])]) ).
tff(f417,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less(X0,plus_plus(X0,X1,X3),plus_plus(X0,X1,X2))
| ~ ord_less(X0,X3,X2)
| ~ ordere223160158up_add(X0) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,plus_plus(X0,X1,X3),plus_plus(X0,X1,X2))
| ~ ord_less(X0,X3,X2) )
| ~ ordere223160158up_add(X0) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: $tType] :
( ordere223160158up_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X3,X2)
=> ord_less(X0,plus_plus(X0,X1,X3),plus_plus(X0,X1,X2)) ) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X0: $tType] :
( ordere223160158up_add(X0)
=> ! [X22: X0,X24: X0,X23: X0] :
( ord_less(X0,X23,X24)
=> ord_less(X0,plus_plus(X0,X22,X23),plus_plus(X0,X22,X24)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_add__strict__left__mono) ).
tff(f1649,plain,
spl4_121,
inference(avatar_split_clause,[],[f416,f1647]) ).
tff(f1647,plain,
( spl4_121
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ord_less(X0,plus_plus(X0,X3,X1),plus_plus(X0,X2,X1))
| ~ ord_less(X0,X3,X2)
| ~ ordere223160158up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_121])]) ).
tff(f416,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ord_less(X0,plus_plus(X0,X3,X1),plus_plus(X0,X2,X1))
| ~ ord_less(X0,X3,X2)
| ~ ordere223160158up_add(X0) ),
inference(cnf_transformation,[],[f249]) ).
tff(f249,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,plus_plus(X0,X3,X1),plus_plus(X0,X2,X1))
| ~ ord_less(X0,X3,X2) )
| ~ ordere223160158up_add(X0) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,plain,
! [X0: $tType] :
( ordere223160158up_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ord_less(X0,X3,X2)
=> ord_less(X0,plus_plus(X0,X3,X1),plus_plus(X0,X2,X1)) ) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X0: $tType] :
( ordere223160158up_add(X0)
=> ! [X22: X0,X24: X0,X23: X0] :
( ord_less(X0,X23,X24)
=> ord_less(X0,plus_plus(X0,X23,X22),plus_plus(X0,X24,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_add__strict__right__mono) ).
tff(f1400,plain,
spl4_120,
inference(avatar_split_clause,[],[f488,f1398]) ).
tff(f1398,plain,
( spl4_120
<=> ! [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,[spl4_120])]) ).
tff(f488,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,[],[f210]) ).
tff(f210,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,[],[f36]) ).
tff(f36,axiom,
! [X16: nat,X4: nat,X5: nat] : ( plus_plus(nat,plus_plus(nat,X5,X4),X16) = plus_plus(nat,X5,plus_plus(nat,X4,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_nat__add__assoc) ).
tff(f1396,plain,
spl4_119,
inference(avatar_split_clause,[],[f487,f1394]) ).
tff(f1394,plain,
( spl4_119
<=> ! [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,[spl4_119])]) ).
tff(f487,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,[],[f209]) ).
tff(f209,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,[],[f35]) ).
tff(f35,axiom,
! [X13: nat,X14: nat,X15: nat] : ( plus_plus(nat,X15,plus_plus(nat,X14,X13)) = plus_plus(nat,X14,plus_plus(nat,X15,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_nat__add__left__commute) ).
tff(f1392,plain,
( ~ spl4_118
| ~ spl4_71
| ~ spl4_88 ),
inference(avatar_split_clause,[],[f1321,f1035,f918,f1389]) ).
tff(f1389,plain,
( spl4_118
<=> ( one_one(int) = zero_zero(int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_118])]) ).
tff(f918,plain,
( spl4_71
<=> ! [X0: int] : ( zero_zero(int) != plus_plus(int,plus_plus(int,one_one(int),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_71])]) ).
tff(f1035,plain,
( spl4_88
<=> ! [X0: int] : ( plus_plus(int,X0,zero_zero(int)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_88])]) ).
tff(f1321,plain,
( ( one_one(int) != zero_zero(int) )
| ~ spl4_71
| ~ spl4_88 ),
inference(forward_demodulation,[],[f1312,f1036]) ).
tff(f1036,plain,
( ! [X0: int] : ( plus_plus(int,X0,zero_zero(int)) = X0 )
| ~ spl4_88 ),
inference(avatar_component_clause,[],[f1035]) ).
tff(f1312,plain,
( ( zero_zero(int) != plus_plus(int,one_one(int),zero_zero(int)) )
| ~ spl4_71
| ~ spl4_88 ),
inference(superposition,[],[f919,f1036]) ).
tff(f919,plain,
( ! [X0: int] : ( zero_zero(int) != plus_plus(int,plus_plus(int,one_one(int),X0),X0) )
| ~ spl4_71 ),
inference(avatar_component_clause,[],[f918]) ).
tff(f1387,plain,
spl4_117,
inference(avatar_split_clause,[],[f475,f1385]) ).
tff(f1385,plain,
( spl4_117
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ord_less(int,X1,X0)
| ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_117])]) ).
tff(f475,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ord_less(int,X1,X0)
| ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ),
inference(cnf_transformation,[],[f324]) ).
tff(f324,plain,
! [X0: int,X1: int] :
( ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ( ( X0 != X1 )
& ~ ord_less(int,X1,X0) ) )
& ( ( X0 = X1 )
| ord_less(int,X1,X0)
| ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ) ),
inference(flattening,[],[f323]) ).
tff(f323,plain,
! [X0: int,X1: int] :
( ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ( ( X0 != X1 )
& ~ ord_less(int,X1,X0) ) )
& ( ( X0 = X1 )
| ord_less(int,X1,X0)
| ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ) ),
inference(nnf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
<=> ( ( X0 = X1 )
| ord_less(int,X1,X0) ) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X9: int,X26: int] :
( ord_less(int,X26,plus_plus(int,X9,one_one(int)))
<=> ( ( X9 = X26 )
| ord_less(int,X26,X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_zless__add1__eq) ).
tff(f1383,plain,
spl4_116,
inference(avatar_split_clause,[],[f456,f1381]) ).
tff(f1381,plain,
( spl4_116
<=> ! [X0: nat,X1: nat] : ( semiring_1_of_nat(int,plus_plus(nat,X1,X0)) = plus_plus(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_116])]) ).
tff(f456,plain,
! [X0: nat,X1: nat] : ( semiring_1_of_nat(int,plus_plus(nat,X1,X0)) = plus_plus(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ),
inference(cnf_transformation,[],[f191]) ).
tff(f191,plain,
! [X0: nat,X1: nat] : ( semiring_1_of_nat(int,plus_plus(nat,X1,X0)) = plus_plus(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X4: nat,X5: nat] : ( semiring_1_of_nat(int,plus_plus(nat,X5,X4)) = plus_plus(int,semiring_1_of_nat(int,X5),semiring_1_of_nat(int,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_zadd__int) ).
tff(f1379,plain,
spl4_115,
inference(avatar_split_clause,[],[f396,f1377]) ).
tff(f1377,plain,
( spl4_115
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0))
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_115])]) ).
tff(f396,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0))
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f299]) ).
tff(f299,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0)) )
& ( ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0)) ) )
| ~ linord219039673up_add(X0) ),
inference(nnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
<=> ord_less(X0,X1,zero_zero(X0)) )
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X1: X0] :
( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
<=> ord_less(X0,X1,zero_zero(X0)) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X3: X0] :
( ord_less(X0,plus_plus(X0,X3,X3),zero_zero(X0))
<=> ord_less(X0,X3,zero_zero(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_double__add__less__zero__iff__single__add__less__zero) ).
tff(f1375,plain,
spl4_114,
inference(avatar_split_clause,[],[f395,f1373]) ).
tff(f1373,plain,
( spl4_114
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_114])]) ).
tff(f395,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f299]) ).
tff(f1371,plain,
spl4_113,
inference(avatar_split_clause,[],[f394,f1369]) ).
tff(f1369,plain,
( spl4_113
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,X1,X1))
| ~ ord_less(X0,zero_zero(X0),X1)
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_113])]) ).
tff(f394,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,X1,X1))
| ~ ord_less(X0,zero_zero(X0),X1)
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ord_less(X0,zero_zero(X0),plus_plus(X0,X1,X1))
| ~ ord_less(X0,zero_zero(X0),X1) )
& ( ord_less(X0,zero_zero(X0),X1)
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,X1,X1)) ) )
| ~ linord219039673up_add(X0) ),
inference(nnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,X1,X1))
<=> ord_less(X0,zero_zero(X0),X1) )
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,X1,X1))
<=> ord_less(X0,zero_zero(X0),X1) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X3: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,X3,X3))
<=> ord_less(X0,zero_zero(X0),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_zero__less__double__add__iff__zero__less__single__add) ).
tff(f1367,plain,
spl4_112,
inference(avatar_split_clause,[],[f393,f1365]) ).
tff(f1365,plain,
( spl4_112
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),X1)
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,X1,X1))
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_112])]) ).
tff(f393,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),X1)
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,X1,X1))
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f298]) ).
tff(f1363,plain,
spl4_111,
inference(avatar_split_clause,[],[f387,f1361]) ).
tff(f1361,plain,
( spl4_111
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_111])]) ).
tff(f387,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f295]) ).
tff(f295,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0)) )
& ( ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0)) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f224]) ).
tff(f224,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
<=> ord_less(X0,X1,zero_zero(X0)) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] :
( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
<=> ord_less(X0,X1,zero_zero(X0)) ) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X3: X0] :
( ord_less(X0,plus_plus(X0,X3,X3),zero_zero(X0))
<=> ord_less(X0,X3,zero_zero(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_even__less__0__iff) ).
tff(f1359,plain,
spl4_110,
inference(avatar_split_clause,[],[f386,f1357]) ).
tff(f1357,plain,
( spl4_110
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_110])]) ).
tff(f386,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f295]) ).
tff(f1222,plain,
spl4_109,
inference(avatar_split_clause,[],[f510,f1220]) ).
tff(f1220,plain,
( spl4_109
<=> ! [X2: nat,X0: nat,X1: nat] :
( ord_less(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0))
| ~ ord_less(nat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_109])]) ).
tff(f510,plain,
! [X2: nat,X0: nat,X1: nat] :
( ord_less(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0))
| ~ ord_less(nat,X1,X0) ),
inference(cnf_transformation,[],[f335]) ).
tff(f335,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ord_less(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0))
| ~ ord_less(nat,X1,X0) )
& ( ord_less(nat,X1,X0)
| ~ ord_less(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0)) ) ),
inference(nnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: nat,X1: nat,X2: nat] :
( ord_less(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0))
<=> ord_less(nat,X1,X0) ),
inference(rectify,[],[f25]) ).
tff(f25,axiom,
! [X2: nat,X6: nat,X10: nat] :
( ord_less(nat,plus_plus(nat,X10,X6),plus_plus(nat,X10,X2))
<=> ord_less(nat,X6,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_nat__add__left__cancel__less) ).
tff(f1218,plain,
spl4_108,
inference(avatar_split_clause,[],[f509,f1216]) ).
tff(f1216,plain,
( spl4_108
<=> ! [X2: nat,X0: nat,X1: nat] :
( ord_less(nat,X1,X0)
| ~ ord_less(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_108])]) ).
tff(f509,plain,
! [X2: nat,X0: nat,X1: nat] :
( ord_less(nat,X1,X0)
| ~ ord_less(nat,plus_plus(nat,X2,X1),plus_plus(nat,X2,X0)) ),
inference(cnf_transformation,[],[f335]) ).
tff(f1214,plain,
( spl4_107
| ~ spl4_25
| ~ spl4_62 ),
inference(avatar_split_clause,[],[f870,f839,f658,f1211]) ).
tff(f1211,plain,
( spl4_107
<=> ( one_one(nat) = semiring_1_of_nat(nat,one_one(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_107])]) ).
tff(f658,plain,
( spl4_25
<=> semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_25])]) ).
tff(f839,plain,
( spl4_62
<=> ! [X0: $tType] :
( ( semiring_1_of_nat(X0,one_one(nat)) = one_one(X0) )
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_62])]) ).
tff(f870,plain,
( ( one_one(nat) = semiring_1_of_nat(nat,one_one(nat)) )
| ~ spl4_25
| ~ spl4_62 ),
inference(resolution,[],[f840,f660]) ).
tff(f660,plain,
( semiring_1(nat)
| ~ spl4_25 ),
inference(avatar_component_clause,[],[f658]) ).
tff(f840,plain,
( ! [X0: $tType] :
( ~ semiring_1(X0)
| ( semiring_1_of_nat(X0,one_one(nat)) = one_one(X0) ) )
| ~ spl4_62 ),
inference(avatar_component_clause,[],[f839]) ).
tff(f1209,plain,
spl4_106,
inference(avatar_split_clause,[],[f497,f1207]) ).
tff(f1207,plain,
( spl4_106
<=> ! [X2: nat,X0: nat,X1: nat] :
( ord_less(nat,plus_plus(nat,X2,X0),plus_plus(nat,X1,X0))
| ~ ord_less(nat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_106])]) ).
tff(f497,plain,
! [X2: nat,X0: nat,X1: nat] :
( ord_less(nat,plus_plus(nat,X2,X0),plus_plus(nat,X1,X0))
| ~ ord_less(nat,X2,X1) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,plain,
! [X0: nat,X1: nat,X2: nat] :
( ord_less(nat,plus_plus(nat,X2,X0),plus_plus(nat,X1,X0))
| ~ ord_less(nat,X2,X1) ),
inference(ennf_transformation,[],[f216]) ).
tff(f216,plain,
! [X0: nat,X1: nat,X2: nat] :
( ord_less(nat,X2,X1)
=> ord_less(nat,plus_plus(nat,X2,X0),plus_plus(nat,X1,X0)) ),
inference(rectify,[],[f44]) ).
tff(f44,axiom,
! [X16: nat,X11: nat,X12: nat] :
( ord_less(nat,X12,X11)
=> ord_less(nat,plus_plus(nat,X12,X16),plus_plus(nat,X11,X16)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_add__less__mono1) ).
tff(f1205,plain,
spl4_105,
inference(avatar_split_clause,[],[f438,f1203]) ).
tff(f1203,plain,
( spl4_105
<=> ! [X0: $tType,X2: nat,X1: nat] :
( ord_less(nat,X2,X1)
| ~ ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_105])]) ).
tff(f438,plain,
! [X0: $tType,X2: nat,X1: nat] :
( ord_less(nat,X2,X1)
| ~ ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: $tType] :
( ! [X1: nat,X2: nat] :
( ord_less(nat,X2,X1)
| ~ ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1)) )
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X1: nat,X2: nat] :
( ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
=> ord_less(nat,X2,X1) ) ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X4: nat,X5: nat] :
( ord_less(X0,semiring_1_of_nat(X0,X5),semiring_1_of_nat(X0,X4))
=> ord_less(nat,X5,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_of__nat__less__imp__less) ).
tff(f1201,plain,
spl4_104,
inference(avatar_split_clause,[],[f437,f1199]) ).
tff(f1199,plain,
( spl4_104
<=> ! [X0: $tType,X2: nat,X1: nat] :
( ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
| ~ ord_less(nat,X2,X1)
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_104])]) ).
tff(f437,plain,
! [X0: $tType,X2: nat,X1: nat] :
( ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
| ~ ord_less(nat,X2,X1)
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: $tType] :
( ! [X1: nat,X2: nat] :
( ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1))
| ~ ord_less(nat,X2,X1) )
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X1: nat,X2: nat] :
( ord_less(nat,X2,X1)
=> ord_less(X0,semiring_1_of_nat(X0,X2),semiring_1_of_nat(X0,X1)) ) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X4: nat,X5: nat] :
( ord_less(nat,X5,X4)
=> ord_less(X0,semiring_1_of_nat(X0,X5),semiring_1_of_nat(X0,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_less__imp__of__nat__less) ).
tff(f1197,plain,
spl4_103,
inference(avatar_split_clause,[],[f436,f1195]) ).
tff(f1195,plain,
( spl4_103
<=> ! [X0: $tType,X1: nat] :
( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ ord_less(nat,zero_zero(nat),X1)
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_103])]) ).
tff(f436,plain,
! [X0: $tType,X1: nat] :
( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ ord_less(nat,zero_zero(nat),X1)
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f307]) ).
tff(f307,plain,
! [X0: $tType] :
( ! [X1: nat] :
( ( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ ord_less(nat,zero_zero(nat),X1) )
& ( ord_less(nat,zero_zero(nat),X1)
| ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1)) ) )
| ~ linordered_semidom(X0) ),
inference(nnf_transformation,[],[f265]) ).
tff(f265,plain,
! [X0: $tType] :
( ! [X1: nat] :
( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
<=> ord_less(nat,zero_zero(nat),X1) )
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X1: nat] :
( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
<=> ord_less(nat,zero_zero(nat),X1) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X2: nat] :
( ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X2))
<=> ord_less(nat,zero_zero(nat),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_of__nat__0__less__iff) ).
tff(f1193,plain,
spl4_102,
inference(avatar_split_clause,[],[f435,f1191]) ).
tff(f1191,plain,
( spl4_102
<=> ! [X0: $tType,X1: nat] :
( ord_less(nat,zero_zero(nat),X1)
| ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_102])]) ).
tff(f435,plain,
! [X0: $tType,X1: nat] :
( ord_less(nat,zero_zero(nat),X1)
| ~ ord_less(X0,zero_zero(X0),semiring_1_of_nat(X0,X1))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f307]) ).
tff(f1189,plain,
spl4_101,
inference(avatar_split_clause,[],[f420,f1187]) ).
tff(f1187,plain,
( spl4_101
<=> ! [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,[spl4_101])]) ).
tff(f420,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,[],[f254]) ).
tff(f254,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,[],[f169]) ).
tff(f169,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,[],[f55]) ).
tff(f55,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X22: X0,X23: X0,X24: X0] :
( ( plus_plus(X0,X24,X23) = plus_plus(X0,X22,X23) )
=> ( X22 = X24 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_add__right__imp__eq) ).
tff(f1185,plain,
spl4_100,
inference(avatar_split_clause,[],[f419,f1183]) ).
tff(f1183,plain,
( spl4_100
<=> ! [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,[spl4_100])]) ).
tff(f419,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,[],[f253]) ).
tff(f253,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,[],[f168]) ).
tff(f168,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,[],[f57]) ).
tff(f57,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X22: X0,X24: X0,X23: X0] :
( ( plus_plus(X0,X23,X24) = plus_plus(X0,X23,X22) )
=> ( X22 = X24 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_add__left__imp__eq) ).
tff(f1181,plain,
spl4_99,
inference(avatar_split_clause,[],[f404,f1179]) ).
tff(f1179,plain,
( spl4_99
<=> ! [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,[spl4_99])]) ).
tff(f404,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,[],[f235]) ).
tff(f235,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,[],[f157]) ).
tff(f157,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,[],[f56]) ).
tff(f56,axiom,
! [X0: $tType] :
( cancel146912293up_add(X0)
=> ! [X22: X0,X24: X0,X23: X0] :
( ( plus_plus(X0,X23,X24) = plus_plus(X0,X23,X22) )
=> ( X22 = X24 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_add__imp__eq) ).
tff(f1173,plain,
( spl4_98
| ~ spl4_25
| ~ spl4_61 ),
inference(avatar_split_clause,[],[f868,f835,f658,f1170]) ).
tff(f1170,plain,
( spl4_98
<=> ( zero_zero(nat) = semiring_1_of_nat(nat,zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_98])]) ).
tff(f835,plain,
( spl4_61
<=> ! [X0: $tType] :
( ( zero_zero(X0) = semiring_1_of_nat(X0,zero_zero(nat)) )
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_61])]) ).
tff(f868,plain,
( ( zero_zero(nat) = semiring_1_of_nat(nat,zero_zero(nat)) )
| ~ spl4_25
| ~ spl4_61 ),
inference(resolution,[],[f836,f660]) ).
tff(f836,plain,
( ! [X0: $tType] :
( ~ semiring_1(X0)
| ( zero_zero(X0) = semiring_1_of_nat(X0,zero_zero(nat)) ) )
| ~ spl4_61 ),
inference(avatar_component_clause,[],[f835]) ).
tff(f1133,plain,
spl4_97,
inference(avatar_split_clause,[],[f491,f1131]) ).
tff(f1131,plain,
( spl4_97
<=> ! [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,[spl4_97])]) ).
tff(f491,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,[],[f280]) ).
tff(f280,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,[],[f212]) ).
tff(f212,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,[],[f93]) ).
tff(f93,axiom,
! [X31: nat,X21: nat,X20: bool] :
( ( ~ pp(X20)
=> ( semiring_1_of_nat(int,X31) = semiring_1_of_nat(int,if(nat,X20,X21,X31)) ) )
& ( pp(X20)
=> ( semiring_1_of_nat(int,X21) = semiring_1_of_nat(int,if(nat,X20,X21,X31)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_int__if__cong) ).
tff(f1129,plain,
spl4_96,
inference(avatar_split_clause,[],[f490,f1127]) ).
tff(f1127,plain,
( spl4_96
<=> ! [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,[spl4_96])]) ).
tff(f490,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,[],[f280]) ).
tff(f1125,plain,
spl4_95,
inference(avatar_split_clause,[],[f389,f1123]) ).
tff(f1123,plain,
( spl4_95
<=> ! [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,[spl4_95])]) ).
tff(f389,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,X1,X1) )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f296]) ).
tff(f296,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,[],[f227]) ).
tff(f227,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
<=> ( zero_zero(X0) = X1 ) )
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X3: X0] :
( ( zero_zero(X0) = plus_plus(X0,X3,X3) )
<=> ( zero_zero(X0) = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_double__eq__0__iff) ).
tff(f1121,plain,
spl4_94,
inference(avatar_split_clause,[],[f388,f1119]) ).
tff(f1119,plain,
( spl4_94
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1)
| ( X1 = X2 )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_94])]) ).
tff(f388,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1)
| ( X1 = X2 )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f226]) ).
tff(f226,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1)
| ( X1 = X2 ) )
| ~ linordered_idom(X0) ),
inference(flattening,[],[f225]) ).
tff(f225,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,X1,X2)
| ord_less(X0,X2,X1)
| ( X1 = X2 ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0,X2: X0] :
( ( X1 != X2 )
=> ( ~ ord_less(X0,X2,X1)
=> ord_less(X0,X1,X2) ) ) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X14: X0,X15: X0] :
( ( X14 != X15 )
=> ( ~ ord_less(X0,X15,X14)
=> ord_less(X0,X14,X15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_linorder__neqE__linordered__idom) ).
tff(f1090,plain,
( spl4_93
| ~ spl4_15
| ~ spl4_59 ),
inference(avatar_split_clause,[],[f858,f827,f608,f1088]) ).
tff(f608,plain,
( spl4_15
<=> monoid_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_15])]) ).
tff(f827,plain,
( spl4_59
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_59])]) ).
tff(f858,plain,
( ! [X0: int] : ( plus_plus(int,zero_zero(int),X0) = X0 )
| ~ spl4_15
| ~ spl4_59 ),
inference(resolution,[],[f828,f610]) ).
tff(f610,plain,
( monoid_add(int)
| ~ spl4_15 ),
inference(avatar_component_clause,[],[f608]) ).
tff(f828,plain,
( ! [X0: $tType,X1: X0] :
( ~ monoid_add(X0)
| ( plus_plus(X0,zero_zero(X0),X1) = X1 ) )
| ~ spl4_59 ),
inference(avatar_component_clause,[],[f827]) ).
tff(f1053,plain,
spl4_92,
inference(avatar_split_clause,[],[f507,f1051]) ).
tff(f1051,plain,
( spl4_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,[spl4_92])]) ).
tff(f507,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X1 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X2,X0) ) ),
inference(cnf_transformation,[],[f334]) ).
tff(f334,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,[],[f220]) ).
tff(f220,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( plus_plus(nat,X2,X1) = plus_plus(nat,X2,X0) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X2: nat,X6: nat,X10: nat] :
( ( plus_plus(nat,X10,X6) = plus_plus(nat,X10,X2) )
<=> ( X2 = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_nat__add__left__cancel) ).
tff(f1049,plain,
spl4_91,
inference(avatar_split_clause,[],[f505,f1047]) ).
tff(f1047,plain,
( spl4_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,[spl4_91])]) ).
tff(f505,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( X0 = X2 )
| ( plus_plus(nat,X2,X1) != plus_plus(nat,X0,X1) ) ),
inference(cnf_transformation,[],[f333]) ).
tff(f333,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,[],[f219]) ).
tff(f219,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( plus_plus(nat,X2,X1) = plus_plus(nat,X0,X1) )
<=> ( X0 = X2 ) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X2: nat,X10: nat,X6: nat] :
( ( plus_plus(nat,X6,X10) = plus_plus(nat,X2,X10) )
<=> ( X2 = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_nat__add__right__cancel) ).
tff(f1045,plain,
spl4_90,
inference(avatar_split_clause,[],[f479,f1043]) ).
tff(f1043,plain,
( spl4_90
<=> ! [X0: nat,X1: nat] :
( ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
| ~ ord_less(nat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_90])]) ).
tff(f479,plain,
! [X0: nat,X1: nat] :
( ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
| ~ ord_less(nat,X1,X0) ),
inference(cnf_transformation,[],[f325]) ).
tff(f325,plain,
! [X0: nat,X1: nat] :
( ( ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
| ~ ord_less(nat,X1,X0) )
& ( ord_less(nat,X1,X0)
| ~ ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ) ),
inference(nnf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: nat,X1: nat] :
( ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0))
<=> ord_less(nat,X1,X0) ),
inference(rectify,[],[f89]) ).
tff(f89,axiom,
! [X31: nat,X21: nat] :
( ord_less(int,semiring_1_of_nat(int,X21),semiring_1_of_nat(int,X31))
<=> ord_less(nat,X21,X31) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).
tff(f1041,plain,
spl4_89,
inference(avatar_split_clause,[],[f478,f1039]) ).
tff(f1039,plain,
( spl4_89
<=> ! [X0: nat,X1: nat] :
( ord_less(nat,X1,X0)
| ~ ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_89])]) ).
tff(f478,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X1,X0)
| ~ ord_less(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ),
inference(cnf_transformation,[],[f325]) ).
tff(f1037,plain,
( spl4_88
| ~ spl4_14
| ~ spl4_57 ),
inference(avatar_split_clause,[],[f854,f818,f603,f1035]) ).
tff(f603,plain,
( spl4_14
<=> comm_monoid_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).
tff(f818,plain,
( spl4_57
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_57])]) ).
tff(f854,plain,
( ! [X0: int] : ( plus_plus(int,X0,zero_zero(int)) = X0 )
| ~ spl4_14
| ~ spl4_57 ),
inference(resolution,[],[f819,f605]) ).
tff(f605,plain,
( comm_monoid_add(int)
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f603]) ).
tff(f819,plain,
( ! [X0: $tType,X1: X0] :
( ~ comm_monoid_add(X0)
| ( plus_plus(X0,X1,zero_zero(X0)) = X1 ) )
| ~ spl4_57 ),
inference(avatar_component_clause,[],[f818]) ).
tff(f1033,plain,
spl4_87,
inference(avatar_split_clause,[],[f476,f1031]) ).
tff(f1031,plain,
( spl4_87
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ~ ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_87])]) ).
tff(f476,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f324]) ).
tff(f1029,plain,
spl4_86,
inference(avatar_split_clause,[],[f463,f1027]) ).
tff(f1027,plain,
( spl4_86
<=> ! [X0: nat,X1: nat] :
( ( plus_plus(nat,X1,sK2(X0,X1)) = X0 )
| ~ ord_less(nat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_86])]) ).
tff(f463,plain,
! [X0: nat,X1: nat] :
( ( plus_plus(nat,X1,sK2(X0,X1)) = X0 )
| ~ ord_less(nat,X1,X0) ),
inference(cnf_transformation,[],[f316]) ).
tff(f316,plain,
! [X0: nat,X1: nat] :
( ( ( plus_plus(nat,X1,sK2(X0,X1)) = X0 )
& ord_less(nat,zero_zero(nat),sK2(X0,X1)) )
| ~ ord_less(nat,X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f278,f315]) ).
tff(f315,plain,
! [X0: nat,X1: nat] :
( ? [X2: nat] :
( ( plus_plus(nat,X1,X2) = X0 )
& ord_less(nat,zero_zero(nat),X2) )
=> ( ( plus_plus(nat,X1,sK2(X0,X1)) = X0 )
& ord_less(nat,zero_zero(nat),sK2(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f278,plain,
! [X0: nat,X1: nat] :
( ? [X2: nat] :
( ( plus_plus(nat,X1,X2) = X0 )
& ord_less(nat,zero_zero(nat),X2) )
| ~ ord_less(nat,X1,X0) ),
inference(ennf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X1,X0)
=> ? [X2: nat] :
( ( plus_plus(nat,X1,X2) = X0 )
& ord_less(nat,zero_zero(nat),X2) ) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X11: nat,X12: nat] :
( ord_less(nat,X12,X11)
=> ? [X30: nat] :
( ( plus_plus(nat,X12,X30) = X11 )
& ord_less(nat,zero_zero(nat),X30) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_less__imp__add__positive) ).
tff(f1025,plain,
spl4_85,
inference(avatar_split_clause,[],[f450,f1023]) ).
tff(f450,plain,
! [X0: nat] :
( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
| ~ ord_less(nat,zero_zero(nat),X0) ),
inference(cnf_transformation,[],[f313]) ).
tff(f313,plain,
! [X0: nat] :
( ( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
| ~ ord_less(nat,zero_zero(nat),X0) )
& ( ord_less(nat,zero_zero(nat),X0)
| ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) ) ),
inference(nnf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: nat] :
( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0))
<=> ord_less(nat,zero_zero(nat),X0) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X2: nat] :
( ord_less(int,zero_zero(int),semiring_1_of_nat(int,X2))
<=> ord_less(nat,zero_zero(nat),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_zero__less__int__conv) ).
tff(f1021,plain,
spl4_84,
inference(avatar_split_clause,[],[f449,f1019]) ).
tff(f1019,plain,
( spl4_84
<=> ! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_84])]) ).
tff(f449,plain,
! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ~ ord_less(int,zero_zero(int),semiring_1_of_nat(int,X0)) ),
inference(cnf_transformation,[],[f313]) ).
tff(f1017,plain,
spl4_83,
inference(avatar_split_clause,[],[f433,f1015]) ).
tff(f1015,plain,
( spl4_83
<=> ! [X0: $tType] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,one_one(X0),one_one(X0)))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_83])]) ).
tff(f433,plain,
! [X0: $tType] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,one_one(X0),one_one(X0)))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: $tType] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,one_one(X0),one_one(X0)))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f84]) ).
tff(f84,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ord_less(X0,zero_zero(X0),plus_plus(X0,one_one(X0),one_one(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_zero__less__two) ).
tff(f1013,plain,
spl4_82,
inference(avatar_split_clause,[],[f401,f1011]) ).
tff(f1011,plain,
( spl4_82
<=> ! [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,[spl4_82])]) ).
tff(f401,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,[],[f302]) ).
tff(f302,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,[],[f233]) ).
tff(f233,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,[],[f155]) ).
tff(f155,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,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType] :
( semiring_char_0(X0)
=> ! [X2: nat,X6: nat] :
( ( semiring_1_of_nat(X0,X2) = semiring_1_of_nat(X0,X6) )
<=> ( X2 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_of__nat__eq__iff) ).
tff(f960,plain,
spl4_81,
inference(avatar_split_clause,[],[f513,f958]) ).
tff(f958,plain,
( spl4_81
<=> ! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_81])]) ).
tff(f513,plain,
! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ),
inference(equality_resolution,[],[f390]) ).
tff(f390,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
| ( zero_zero(X0) != X1 )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f296]) ).
tff(f956,plain,
spl4_80,
inference(avatar_split_clause,[],[f498,f954]) ).
tff(f954,plain,
( spl4_80
<=> ! [X2: nat,X0: nat,X1: nat] :
( ord_less(nat,X2,X0)
| ~ ord_less(nat,plus_plus(nat,X2,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_80])]) ).
tff(f498,plain,
! [X2: nat,X0: nat,X1: nat] :
( ord_less(nat,X2,X0)
| ~ ord_less(nat,plus_plus(nat,X2,X1),X0) ),
inference(cnf_transformation,[],[f286]) ).
tff(f286,plain,
! [X0: nat,X1: nat,X2: nat] :
( ord_less(nat,X2,X0)
| ~ ord_less(nat,plus_plus(nat,X2,X1),X0) ),
inference(ennf_transformation,[],[f217]) ).
tff(f217,plain,
! [X0: nat,X1: nat,X2: nat] :
( ord_less(nat,plus_plus(nat,X2,X1),X0)
=> ord_less(nat,X2,X0) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X16: nat,X11: nat,X12: nat] :
( ord_less(nat,plus_plus(nat,X12,X11),X16)
=> ord_less(nat,X12,X16) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_add__lessD1) ).
tff(f952,plain,
spl4_79,
inference(avatar_split_clause,[],[f496,f950]) ).
tff(f950,plain,
( spl4_79
<=> ! [X2: nat,X0: nat,X1: nat] :
( ord_less(nat,X2,plus_plus(nat,X1,X0))
| ~ ord_less(nat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_79])]) ).
tff(f496,plain,
! [X2: nat,X0: nat,X1: nat] :
( ord_less(nat,X2,plus_plus(nat,X1,X0))
| ~ ord_less(nat,X2,X1) ),
inference(cnf_transformation,[],[f284]) ).
tff(f284,plain,
! [X0: nat,X1: nat,X2: nat] :
( ord_less(nat,X2,plus_plus(nat,X1,X0))
| ~ ord_less(nat,X2,X1) ),
inference(ennf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: nat,X1: nat,X2: nat] :
( ord_less(nat,X2,X1)
=> ord_less(nat,X2,plus_plus(nat,X1,X0)) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X5: nat,X11: nat,X12: nat] :
( ord_less(nat,X12,X11)
=> ord_less(nat,X12,plus_plus(nat,X11,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_trans__less__add1) ).
tff(f948,plain,
spl4_78,
inference(avatar_split_clause,[],[f495,f946]) ).
tff(f946,plain,
( spl4_78
<=> ! [X2: nat,X0: nat,X1: nat] :
( ord_less(nat,X2,plus_plus(nat,X0,X1))
| ~ ord_less(nat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_78])]) ).
tff(f495,plain,
! [X2: nat,X0: nat,X1: nat] :
( ord_less(nat,X2,plus_plus(nat,X0,X1))
| ~ ord_less(nat,X2,X1) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: nat,X1: nat,X2: nat] :
( ord_less(nat,X2,plus_plus(nat,X0,X1))
| ~ ord_less(nat,X2,X1) ),
inference(ennf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: nat,X1: nat,X2: nat] :
( ord_less(nat,X2,X1)
=> ord_less(nat,X2,plus_plus(nat,X0,X1)) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X5: nat,X11: nat,X12: nat] :
( ord_less(nat,X12,X11)
=> ord_less(nat,X12,plus_plus(nat,X5,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_trans__less__add2) ).
tff(f944,plain,
spl4_77,
inference(avatar_split_clause,[],[f469,f942]) ).
tff(f942,plain,
( spl4_77
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_77])]) ).
tff(f469,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ),
inference(cnf_transformation,[],[f320]) ).
tff(f320,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,[],[f319]) ).
tff(f319,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,[],[f200]) ).
tff(f200,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = plus_plus(nat,X1,X0) )
<=> ( ( zero_zero(nat) = X0 )
& ( zero_zero(nat) = X1 ) ) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X2: nat,X6: nat] :
( ( zero_zero(nat) = plus_plus(nat,X6,X2) )
<=> ( ( zero_zero(nat) = X2 )
& ( zero_zero(nat) = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_add__is__0) ).
tff(f940,plain,
spl4_76,
inference(avatar_split_clause,[],[f468,f938]) ).
tff(f938,plain,
( spl4_76
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_76])]) ).
tff(f468,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ),
inference(cnf_transformation,[],[f320]) ).
tff(f936,plain,
spl4_75,
inference(avatar_split_clause,[],[f462,f934]) ).
tff(f934,plain,
( spl4_75
<=> ! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),sK2(X0,X1))
| ~ ord_less(nat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_75])]) ).
tff(f462,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),sK2(X0,X1))
| ~ ord_less(nat,X1,X0) ),
inference(cnf_transformation,[],[f316]) ).
tff(f932,plain,
spl4_74,
inference(avatar_split_clause,[],[f458,f930]) ).
tff(f930,plain,
( spl4_74
<=> ! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_74])]) ).
tff(f458,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f274]) ).
tff(f274,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ),
inference(flattening,[],[f273]) ).
tff(f273,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ ord_less(nat,X1,X0)
=> ord_less(nat,X0,X1) ) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X14: nat,X15: nat] :
( ( X14 != X15 )
=> ( ~ ord_less(nat,X15,X14)
=> ord_less(nat,X14,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_linorder__neqE__nat) ).
tff(f928,plain,
spl4_73,
inference(avatar_split_clause,[],[f444,f926]) ).
tff(f926,plain,
( spl4_73
<=> ! [X0: int] :
( ( semiring_1_of_nat(int,sK1(X0)) = X0 )
| ~ ord_less(int,zero_zero(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_73])]) ).
tff(f444,plain,
! [X0: int] :
( ( semiring_1_of_nat(int,sK1(X0)) = X0 )
| ~ ord_less(int,zero_zero(int),X0) ),
inference(cnf_transformation,[],[f310]) ).
tff(f310,plain,
! [X0: int] :
( ( ( semiring_1_of_nat(int,sK1(X0)) = X0 )
& ord_less(nat,zero_zero(nat),sK1(X0)) )
| ~ ord_less(int,zero_zero(int),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f272,f309]) ).
tff(f309,plain,
! [X0: int] :
( ? [X1: nat] :
( ( semiring_1_of_nat(int,X1) = X0 )
& ord_less(nat,zero_zero(nat),X1) )
=> ( ( semiring_1_of_nat(int,sK1(X0)) = X0 )
& ord_less(nat,zero_zero(nat),sK1(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f272,plain,
! [X0: int] :
( ? [X1: nat] :
( ( semiring_1_of_nat(int,X1) = X0 )
& ord_less(nat,zero_zero(nat),X1) )
| ~ ord_less(int,zero_zero(int),X0) ),
inference(ennf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: int] :
( ord_less(int,zero_zero(int),X0)
=> ? [X1: nat] :
( ( semiring_1_of_nat(int,X1) = X0 )
& ord_less(nat,zero_zero(nat),X1) ) ),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X16: int] :
( ord_less(int,zero_zero(int),X16)
=> ? [X27: nat] :
( ( semiring_1_of_nat(int,X27) = X16 )
& ord_less(nat,zero_zero(nat),X27) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_zero__less__imp__eq__int) ).
tff(f924,plain,
spl4_72,
inference(avatar_split_clause,[],[f443,f922]) ).
tff(f922,plain,
( spl4_72
<=> ! [X0: int] :
( ord_less(nat,zero_zero(nat),sK1(X0))
| ~ ord_less(int,zero_zero(int),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_72])]) ).
tff(f443,plain,
! [X0: int] :
( ord_less(nat,zero_zero(nat),sK1(X0))
| ~ ord_less(int,zero_zero(int),X0) ),
inference(cnf_transformation,[],[f310]) ).
tff(f920,plain,
spl4_71,
inference(avatar_split_clause,[],[f384,f918]) ).
tff(f384,plain,
! [X0: int] : ( zero_zero(int) != plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: int] : ( zero_zero(int) != plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X13: int] : ( zero_zero(int) != plus_plus(int,plus_plus(int,one_one(int),X13),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_odd__nonzero) ).
tff(f907,plain,
( ~ spl4_70
| ~ spl4_42
| ~ spl4_43 ),
inference(avatar_split_clause,[],[f780,f747,f742,f904]) ).
tff(f904,plain,
( spl4_70
<=> ord_less(int,zero_zero(int),zero_zero(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_70])]) ).
tff(f742,plain,
( spl4_42
<=> ( zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_42])]) ).
tff(f747,plain,
( spl4_43
<=> ! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_43])]) ).
tff(f780,plain,
( ~ ord_less(int,zero_zero(int),zero_zero(int))
| ~ spl4_42
| ~ spl4_43 ),
inference(superposition,[],[f748,f744]) ).
tff(f744,plain,
( ( zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)) )
| ~ spl4_42 ),
inference(avatar_component_clause,[],[f742]) ).
tff(f748,plain,
( ! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int))
| ~ spl4_43 ),
inference(avatar_component_clause,[],[f747]) ).
tff(f900,plain,
spl4_69,
inference(avatar_split_clause,[],[f471,f898]) ).
tff(f898,plain,
( spl4_69
<=> ! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_69])]) ).
tff(f471,plain,
! [X0: nat,X1: nat] :
( ( X0 = X1 )
| ( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ),
inference(cnf_transformation,[],[f321]) ).
tff(f321,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,[],[f201]) ).
tff(f201,plain,
! [X0: nat,X1: nat] :
( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X31: nat,X21: nat] :
( ( semiring_1_of_nat(int,X21) = semiring_1_of_nat(int,X31) )
<=> ( X21 = X31 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
tff(f896,plain,
spl4_68,
inference(avatar_split_clause,[],[f464,f894]) ).
tff(f894,plain,
( spl4_68
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( plus_plus(nat,X1,X0) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_68])]) ).
tff(f464,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( plus_plus(nat,X1,X0) != X1 ) ),
inference(cnf_transformation,[],[f279]) ).
tff(f279,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( plus_plus(nat,X1,X0) != X1 ) ),
inference(ennf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: nat,X1: nat] :
( ( plus_plus(nat,X1,X0) = X1 )
=> ( zero_zero(nat) = X0 ) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X4: nat,X5: nat] :
( ( plus_plus(nat,X5,X4) = X5 )
=> ( zero_zero(nat) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_add__eq__self__zero) ).
tff(f892,plain,
spl4_67,
inference(avatar_split_clause,[],[f447,f890]) ).
tff(f890,plain,
( spl4_67
<=> ! [X0: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_67])]) ).
tff(f447,plain,
! [X0: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(int) != semiring_1_of_nat(int,X0) ) ),
inference(cnf_transformation,[],[f312]) ).
tff(f312,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,[],[f185]) ).
tff(f185,plain,
! [X0: nat] :
( ( zero_zero(int) = semiring_1_of_nat(int,X0) )
<=> ( zero_zero(nat) = X0 ) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X2: nat] :
( ( zero_zero(int) = semiring_1_of_nat(int,X2) )
<=> ( zero_zero(nat) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_int__eq__0__conv) ).
tff(f864,plain,
( ~ spl4_66
| ~ spl4_41
| ~ spl4_43 ),
inference(avatar_split_clause,[],[f779,f747,f737,f861]) ).
tff(f861,plain,
( spl4_66
<=> ord_less(int,one_one(int),zero_zero(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_66])]) ).
tff(f737,plain,
( spl4_41
<=> ( one_one(int) = semiring_1_of_nat(int,one_one(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_41])]) ).
tff(f779,plain,
( ~ ord_less(int,one_one(int),zero_zero(int))
| ~ spl4_41
| ~ spl4_43 ),
inference(superposition,[],[f748,f739]) ).
tff(f739,plain,
( ( one_one(int) = semiring_1_of_nat(int,one_one(nat)) )
| ~ spl4_41 ),
inference(avatar_component_clause,[],[f737]) ).
tff(f853,plain,
spl4_65,
inference(avatar_split_clause,[],[f455,f851]) ).
tff(f851,plain,
( spl4_65
<=> ! [X0: nat,X1: nat] : ( plus_plus(nat,X1,X0) = plus_plus(nat,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_65])]) ).
tff(f455,plain,
! [X0: nat,X1: nat] : ( plus_plus(nat,X1,X0) = plus_plus(nat,X0,X1) ),
inference(cnf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: nat,X1: nat] : ( plus_plus(nat,X1,X0) = plus_plus(nat,X0,X1) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X4: nat,X5: nat] : ( plus_plus(nat,X5,X4) = plus_plus(nat,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_nat__add__commute) ).
tff(f849,plain,
spl4_64,
inference(avatar_split_clause,[],[f442,f847]) ).
tff(f847,plain,
( spl4_64
<=> ! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_64])]) ).
tff(f442,plain,
! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ),
inference(cnf_transformation,[],[f271]) ).
tff(f271,plain,
! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ),
inference(ennf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: nat] :
( ( zero_zero(nat) != X0 )
=> ord_less(nat,zero_zero(nat),X0) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X4: nat] :
( ( zero_zero(nat) != X4 )
=> ord_less(nat,zero_zero(nat),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_gr0I) ).
tff(f845,plain,
spl4_63,
inference(avatar_split_clause,[],[f434,f843]) ).
tff(f843,plain,
( spl4_63
<=> ! [X0: $tType,X1: nat] :
( ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_63])]) ).
tff(f434,plain,
! [X0: $tType,X1: nat] :
( ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f264]) ).
tff(f264,plain,
! [X0: $tType] :
( ! [X1: nat] : ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X1: nat] : ~ ord_less(X0,semiring_1_of_nat(X0,X1),zero_zero(X0)) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X5: nat] : ~ ord_less(X0,semiring_1_of_nat(X0,X5),zero_zero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_of__nat__less__0__iff) ).
tff(f841,plain,
spl4_62,
inference(avatar_split_clause,[],[f414,f839]) ).
tff(f414,plain,
! [X0: $tType] :
( ( semiring_1_of_nat(X0,one_one(nat)) = one_one(X0) )
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f247]) ).
tff(f247,plain,
! [X0: $tType] :
( ( semiring_1_of_nat(X0,one_one(nat)) = one_one(X0) )
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> ( semiring_1_of_nat(X0,one_one(nat)) = one_one(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_of__nat__1) ).
tff(f837,plain,
spl4_61,
inference(avatar_split_clause,[],[f413,f835]) ).
tff(f413,plain,
! [X0: $tType] :
( ( zero_zero(X0) = semiring_1_of_nat(X0,zero_zero(nat)) )
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: $tType] :
( ( zero_zero(X0) = semiring_1_of_nat(X0,zero_zero(nat)) )
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> ( zero_zero(X0) = semiring_1_of_nat(X0,zero_zero(nat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_of__nat__0) ).
tff(f833,plain,
spl4_60,
inference(avatar_split_clause,[],[f410,f831]) ).
tff(f831,plain,
( spl4_60
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ comm_monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_60])]) ).
tff(f410,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ comm_monoid_add(X0) ),
inference(cnf_transformation,[],[f241]) ).
tff(f241,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ comm_monoid_add(X0) ),
inference(ennf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X1: X0] : ( plus_plus(X0,zero_zero(X0),X1) = X1 ) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X23: X0] : ( plus_plus(X0,zero_zero(X0),X23) = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_add__0) ).
tff(f829,plain,
spl4_59,
inference(avatar_split_clause,[],[f409,f827]) ).
tff(f409,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,zero_zero(X0),X1) = X1 )
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X1: X0] : ( plus_plus(X0,zero_zero(X0),X1) = X1 ) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X23: X0] : ( plus_plus(X0,zero_zero(X0),X23) = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_add__0__left) ).
tff(f824,plain,
spl4_58,
inference(avatar_split_clause,[],[f408,f822]) ).
tff(f822,plain,
( spl4_58
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ monoid_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_58])]) ).
tff(f408,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ monoid_add(X0) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ monoid_add(X0) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X1: X0] : ( plus_plus(X0,X1,zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X0: $tType] :
( monoid_add(X0)
=> ! [X23: X0] : ( plus_plus(X0,X23,zero_zero(X0)) = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_add__0__right) ).
tff(f820,plain,
spl4_57,
inference(avatar_split_clause,[],[f407,f818]) ).
tff(f407,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,X1,zero_zero(X0)) = X1 )
| ~ comm_monoid_add(X0) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X1: X0] : ( plus_plus(X0,X1,zero_zero(X0)) = X1 ) ),
inference(rectify,[],[f65]) ).
tff(f65,axiom,
! [X0: $tType] :
( comm_monoid_add(X0)
=> ! [X23: X0] : ( plus_plus(X0,X23,zero_zero(X0)) = X23 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_add_Ocomm__neutral) ).
tff(f812,plain,
spl4_56,
inference(avatar_split_clause,[],[f533,f810]) ).
tff(f533,plain,
! [X1: int] : ord_less(int,X1,plus_plus(int,X1,one_one(int))),
inference(equality_resolution,[],[f477]) ).
tff(f477,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f324]) ).
tff(f808,plain,
spl4_55,
inference(avatar_split_clause,[],[f499,f806]) ).
tff(f806,plain,
( spl4_55
<=> ! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_55])]) ).
tff(f499,plain,
! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f332]) ).
tff(f804,plain,
spl4_54,
inference(avatar_split_clause,[],[f432,f802]) ).
tff(f802,plain,
( spl4_54
<=> ! [X0: $tType] :
( ord_less(X0,zero_zero(X0),one_one(X0))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_54])]) ).
tff(f432,plain,
! [X0: $tType] :
( ord_less(X0,zero_zero(X0),one_one(X0))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f262]) ).
tff(f262,plain,
! [X0: $tType] :
( ord_less(X0,zero_zero(X0),one_one(X0))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f98]) ).
tff(f98,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ord_less(X0,zero_zero(X0),one_one(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_zero__less__one) ).
tff(f800,plain,
spl4_53,
inference(avatar_split_clause,[],[f431,f798]) ).
tff(f798,plain,
( spl4_53
<=> ! [X0: $tType] :
( ~ ord_less(X0,one_one(X0),zero_zero(X0))
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_53])]) ).
tff(f431,plain,
! [X0: $tType] :
( ~ ord_less(X0,one_one(X0),zero_zero(X0))
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: $tType] :
( ~ ord_less(X0,one_one(X0),zero_zero(X0))
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f97]) ).
tff(f97,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ~ ord_less(X0,one_one(X0),zero_zero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_not__one__less__zero) ).
tff(f796,plain,
( spl4_51
| ~ spl4_52
| ~ spl4_39 ),
inference(avatar_split_clause,[],[f731,f726,f793,f790]) ).
tff(f790,plain,
( spl4_51
<=> ! [X0: bool] : ( fFalse = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_51])]) ).
tff(f793,plain,
( spl4_52
<=> ( fTrue = fFalse ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_52])]) ).
tff(f726,plain,
( spl4_39
<=> ! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_39])]) ).
tff(f731,plain,
( ! [X0: bool] :
( ( fTrue != fFalse )
| ( fFalse = X0 ) )
| ~ spl4_39 ),
inference(equality_factoring,[],[f727]) ).
tff(f727,plain,
( ! [X0: bool] :
( ( fTrue = X0 )
| ( fFalse = X0 ) )
| ~ spl4_39 ),
inference(avatar_component_clause,[],[f726]) ).
tff(f777,plain,
spl4_50,
inference(avatar_split_clause,[],[f486,f775]) ).
tff(f775,plain,
( spl4_50
<=> ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fTrue,X2,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_50])]) ).
tff(f486,plain,
! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fTrue,X2,X1) = X2 ),
inference(cnf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: $tType,X1: X0,X2: X0] : ( if(X0,fTrue,X2,X1) = X2 ),
inference(rectify,[],[f129]) ).
tff(f129,axiom,
! [X0: $tType,X14: X0,X15: X0] : ( if(X0,fTrue,X15,X14) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
tff(f773,plain,
spl4_49,
inference(avatar_split_clause,[],[f485,f771]) ).
tff(f771,plain,
( spl4_49
<=> ! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fFalse,X2,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_49])]) ).
tff(f485,plain,
! [X0: $tType,X2: X0,X1: X0] : ( if(X0,fFalse,X2,X1) = X1 ),
inference(cnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType,X1: X0,X2: X0] : ( if(X0,fFalse,X2,X1) = X1 ),
inference(rectify,[],[f130]) ).
tff(f130,axiom,
! [X0: $tType,X14: X0,X15: X0] : ( if(X0,fFalse,X15,X14) = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
tff(f769,plain,
spl4_48,
inference(avatar_split_clause,[],[f454,f767]) ).
tff(f767,plain,
( spl4_48
<=> ! [X0: nat,X1: nat] : ~ ord_less(nat,plus_plus(nat,X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_48])]) ).
tff(f454,plain,
! [X0: nat,X1: nat] : ~ ord_less(nat,plus_plus(nat,X1,X0),X0),
inference(cnf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: nat,X1: nat] : ~ ord_less(nat,plus_plus(nat,X1,X0),X0),
inference(rectify,[],[f30]) ).
tff(f30,axiom,
! [X12: nat,X11: nat] : ~ ord_less(nat,plus_plus(nat,X11,X12),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_not__add__less2) ).
tff(f765,plain,
spl4_47,
inference(avatar_split_clause,[],[f453,f763]) ).
tff(f763,plain,
( spl4_47
<=> ! [X0: nat,X1: nat] : ~ ord_less(nat,plus_plus(nat,X1,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_47])]) ).
tff(f453,plain,
! [X0: nat,X1: nat] : ~ ord_less(nat,plus_plus(nat,X1,X0),X1),
inference(cnf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: nat,X1: nat] : ~ ord_less(nat,plus_plus(nat,X1,X0),X1),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X11: nat,X12: nat] : ~ ord_less(nat,plus_plus(nat,X12,X11),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_not__add__less1) ).
tff(f761,plain,
spl4_46,
inference(avatar_split_clause,[],[f405,f759]) ).
tff(f759,plain,
( spl4_46
<=> ! [X0: $tType] :
( ( zero_zero(X0) != one_one(X0) )
| ~ zero_neq_one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_46])]) ).
tff(f405,plain,
! [X0: $tType] :
( ( zero_zero(X0) != one_one(X0) )
| ~ zero_neq_one(X0) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: $tType] :
( ( zero_zero(X0) != one_one(X0) )
| ~ zero_neq_one(X0) ),
inference(ennf_transformation,[],[f95]) ).
tff(f95,axiom,
! [X0: $tType] :
( zero_neq_one(X0)
=> ( zero_zero(X0) != one_one(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_zero__neq__one) ).
tff(f757,plain,
spl4_45,
inference(avatar_split_clause,[],[f383,f755]) ).
tff(f755,plain,
( spl4_45
<=> ! [X0: nat] : ( plus_plus(nat,zero_zero(nat),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_45])]) ).
tff(f383,plain,
! [X0: nat] : ( plus_plus(nat,zero_zero(nat),X0) = X0 ),
inference(cnf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: nat] : ( plus_plus(nat,zero_zero(nat),X0) = X0 ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X4: nat] : ( plus_plus(nat,zero_zero(nat),X4) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_plus__nat_Oadd__0) ).
tff(f753,plain,
spl4_44,
inference(avatar_split_clause,[],[f382,f751]) ).
tff(f751,plain,
( spl4_44
<=> ! [X0: nat] : ( plus_plus(nat,X0,zero_zero(nat)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_44])]) ).
tff(f382,plain,
! [X0: nat] : ( plus_plus(nat,X0,zero_zero(nat)) = X0 ),
inference(cnf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: nat] : ( plus_plus(nat,X0,zero_zero(nat)) = X0 ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X5: nat] : ( plus_plus(nat,X5,zero_zero(nat)) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_Nat_Oadd__0__right) ).
tff(f749,plain,
spl4_43,
inference(avatar_split_clause,[],[f381,f747]) ).
tff(f381,plain,
! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
inference(cnf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: nat] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X16: nat] : ~ ord_less(int,semiring_1_of_nat(int,X16),zero_zero(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_int__less__0__conv) ).
tff(f745,plain,
spl4_42,
inference(avatar_split_clause,[],[f374,f742]) ).
tff(f374,plain,
zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)),
inference(cnf_transformation,[],[f90]) ).
tff(f90,axiom,
zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_transfer__int__nat__numerals_I1_J) ).
tff(f740,plain,
spl4_41,
inference(avatar_split_clause,[],[f372,f737]) ).
tff(f372,plain,
one_one(int) = semiring_1_of_nat(int,one_one(nat)),
inference(cnf_transformation,[],[f87]) ).
tff(f87,axiom,
one_one(int) = semiring_1_of_nat(int,one_one(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_transfer__int__nat__numerals_I2_J) ).
tff(f735,plain,
( spl4_40
| ~ spl4_32
| ~ spl4_39 ),
inference(avatar_split_clause,[],[f730,f726,f693,f733]) ).
tff(f733,plain,
( spl4_40
<=> ! [X0: bool] :
( pp(X0)
| ( fFalse = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_40])]) ).
tff(f693,plain,
( spl4_32
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_32])]) ).
tff(f730,plain,
( ! [X0: bool] :
( pp(X0)
| ( fFalse = X0 ) )
| ~ spl4_32
| ~ spl4_39 ),
inference(superposition,[],[f695,f727]) ).
tff(f695,plain,
( pp(fTrue)
| ~ spl4_32 ),
inference(avatar_component_clause,[],[f693]) ).
tff(f728,plain,
spl4_39,
inference(avatar_split_clause,[],[f385,f726]) ).
tff(f385,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(cnf_transformation,[],[f146]) ).
tff(f146,plain,
! [X0: bool] :
( ( fFalse = X0 )
| ( fTrue = X0 ) ),
inference(rectify,[],[f131]) ).
tff(f131,axiom,
! [X32: bool] :
( ( fFalse = X32 )
| ( fTrue = X32 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
tff(f724,plain,
spl4_38,
inference(avatar_split_clause,[],[f378,f722]) ).
tff(f722,plain,
( spl4_38
<=> ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_38])]) ).
tff(f378,plain,
! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
inference(cnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X4: nat] : ~ ord_less(nat,X4,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_less__nat__zero__code) ).
tff(f720,plain,
spl4_37,
inference(avatar_split_clause,[],[f371,f717]) ).
tff(f371,plain,
ord_less(nat,zero_zero(nat),n),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
ord_less(nat,zero_zero(nat),n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_n0) ).
tff(f715,plain,
spl4_36,
inference(avatar_split_clause,[],[f370,f712]) ).
tff(f712,plain,
( spl4_36
<=> ord_less(nat,zero_zero(nat),tn) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_36])]) ).
tff(f370,plain,
ord_less(nat,zero_zero(nat),tn),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
ord_less(nat,zero_zero(nat),tn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tn0) ).
tff(f710,plain,
spl4_35,
inference(avatar_split_clause,[],[f369,f707]) ).
tff(f707,plain,
( spl4_35
<=> ord_less(int,one_one(int),t) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_35])]) ).
tff(f369,plain,
ord_less(int,one_one(int),t),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
ord_less(int,one_one(int),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_t1) ).
tff(f705,plain,
spl4_34,
inference(avatar_split_clause,[],[f376,f703]) ).
tff(f703,plain,
( spl4_34
<=> ! [X0: nat] : ~ ord_less(nat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_34])]) ).
tff(f376,plain,
! [X0: nat] : ~ ord_less(nat,X0,X0),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: nat] : ~ ord_less(nat,X0,X0),
inference(rectify,[],[f28]) ).
tff(f28,axiom,
! [X4: nat] : ~ ord_less(nat,X4,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_less__not__refl) ).
tff(f701,plain,
~ spl4_33,
inference(avatar_split_clause,[],[f336,f698]) ).
tff(f336,plain,
~ ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
~ ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(flattening,[],[f135]) ).
tff(f135,negated_conjecture,
~ ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(negated_conjecture,[],[f134]) ).
tff(f134,conjecture,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f696,plain,
spl4_32,
inference(avatar_split_clause,[],[f368,f693]) ).
tff(f368,plain,
pp(fTrue),
inference(cnf_transformation,[],[f133]) ).
tff(f133,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f691,plain,
spl4_31,
inference(avatar_split_clause,[],[f367,f688]) ).
tff(f688,plain,
( spl4_31
<=> linordered_semidom(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_31])]) ).
tff(f367,plain,
linordered_semidom(nat),
inference(cnf_transformation,[],[f120]) ).
tff(f120,axiom,
linordered_semidom(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
tff(f686,plain,
spl4_30,
inference(avatar_split_clause,[],[f366,f683]) ).
tff(f366,plain,
linordered_semidom(int),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
linordered_semidom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
tff(f681,plain,
spl4_29,
inference(avatar_split_clause,[],[f365,f678]) ).
tff(f678,plain,
( spl4_29
<=> ordere236663937imp_le(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_29])]) ).
tff(f365,plain,
ordere236663937imp_le(nat),
inference(cnf_transformation,[],[f116]) ).
tff(f116,axiom,
ordere236663937imp_le(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
tff(f676,plain,
spl4_28,
inference(avatar_split_clause,[],[f364,f673]) ).
tff(f673,plain,
( spl4_28
<=> cancel_semigroup_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_28])]) ).
tff(f364,plain,
cancel_semigroup_add(nat),
inference(cnf_transformation,[],[f119]) ).
tff(f119,axiom,
cancel_semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
tff(f671,plain,
spl4_27,
inference(avatar_split_clause,[],[f363,f668]) ).
tff(f668,plain,
( spl4_27
<=> ordere236663937imp_le(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_27])]) ).
tff(f363,plain,
ordere236663937imp_le(int),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
ordere236663937imp_le(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
tff(f666,plain,
spl4_26,
inference(avatar_split_clause,[],[f362,f663]) ).
tff(f663,plain,
( spl4_26
<=> cancel_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_26])]) ).
tff(f362,plain,
cancel_semigroup_add(int),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
cancel_semigroup_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
tff(f661,plain,
spl4_25,
inference(avatar_split_clause,[],[f361,f658]) ).
tff(f361,plain,
semiring_1(nat),
inference(cnf_transformation,[],[f126]) ).
tff(f126,axiom,
semiring_1(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
tff(f656,plain,
spl4_24,
inference(avatar_split_clause,[],[f360,f653]) ).
tff(f653,plain,
( spl4_24
<=> ordere223160158up_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_24])]) ).
tff(f360,plain,
ordere223160158up_add(nat),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
ordere223160158up_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
tff(f651,plain,
spl4_23,
inference(avatar_split_clause,[],[f359,f648]) ).
tff(f648,plain,
( spl4_23
<=> semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_23])]) ).
tff(f359,plain,
semiring_1(int),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
tff(f646,plain,
spl4_22,
inference(avatar_split_clause,[],[f358,f643]) ).
tff(f643,plain,
( spl4_22
<=> ordere223160158up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_22])]) ).
tff(f358,plain,
ordere223160158up_add(int),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
ordere223160158up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) ).
tff(f641,plain,
spl4_21,
inference(avatar_split_clause,[],[f357,f638]) ).
tff(f638,plain,
( spl4_21
<=> comm_monoid_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_21])]) ).
tff(f357,plain,
comm_monoid_add(nat),
inference(cnf_transformation,[],[f122]) ).
tff(f122,axiom,
comm_monoid_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
tff(f636,plain,
spl4_20,
inference(avatar_split_clause,[],[f356,f633]) ).
tff(f633,plain,
( spl4_20
<=> zero_neq_one(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).
tff(f356,plain,
zero_neq_one(nat),
inference(cnf_transformation,[],[f124]) ).
tff(f124,axiom,
zero_neq_one(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
tff(f631,plain,
spl4_19,
inference(avatar_split_clause,[],[f355,f628]) ).
tff(f628,plain,
( spl4_19
<=> monoid_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_19])]) ).
tff(f355,plain,
monoid_add(nat),
inference(cnf_transformation,[],[f125]) ).
tff(f125,axiom,
monoid_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
tff(f626,plain,
spl4_18,
inference(avatar_split_clause,[],[f354,f623]) ).
tff(f623,plain,
( spl4_18
<=> ordere216010020id_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).
tff(f354,plain,
ordere216010020id_add(nat),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
ordere216010020id_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
tff(f621,plain,
spl4_17,
inference(avatar_split_clause,[],[f353,f618]) ).
tff(f618,plain,
( spl4_17
<=> ordere216010020id_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).
tff(f353,plain,
ordere216010020id_add(int),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
ordere216010020id_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__comm__monoid__add) ).
tff(f616,plain,
spl4_16,
inference(avatar_split_clause,[],[f352,f613]) ).
tff(f613,plain,
( spl4_16
<=> zero_neq_one(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_16])]) ).
tff(f352,plain,
zero_neq_one(int),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
zero_neq_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
tff(f611,plain,
spl4_15,
inference(avatar_split_clause,[],[f351,f608]) ).
tff(f351,plain,
monoid_add(int),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
monoid_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
tff(f606,plain,
spl4_14,
inference(avatar_split_clause,[],[f350,f603]) ).
tff(f350,plain,
comm_monoid_add(int),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
comm_monoid_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
tff(f601,plain,
spl4_13,
inference(avatar_split_clause,[],[f349,f598]) ).
tff(f598,plain,
( spl4_13
<=> cancel146912293up_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).
tff(f349,plain,
cancel146912293up_add(nat),
inference(cnf_transformation,[],[f118]) ).
tff(f118,axiom,
cancel146912293up_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
tff(f596,plain,
spl4_12,
inference(avatar_split_clause,[],[f348,f593]) ).
tff(f593,plain,
( spl4_12
<=> zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).
tff(f348,plain,
zero(nat),
inference(cnf_transformation,[],[f127]) ).
tff(f127,axiom,
zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
tff(f591,plain,
spl4_11,
inference(avatar_split_clause,[],[f347,f588]) ).
tff(f588,plain,
( spl4_11
<=> one(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).
tff(f347,plain,
one(nat),
inference(cnf_transformation,[],[f128]) ).
tff(f128,axiom,
one(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
tff(f586,plain,
spl4_10,
inference(avatar_split_clause,[],[f346,f583]) ).
tff(f583,plain,
( spl4_10
<=> semiring_char_0(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).
tff(f346,plain,
semiring_char_0(nat),
inference(cnf_transformation,[],[f123]) ).
tff(f123,axiom,
semiring_char_0(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
tff(f581,plain,
spl4_9,
inference(avatar_split_clause,[],[f345,f578]) ).
tff(f578,plain,
( spl4_9
<=> ab_semigroup_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).
tff(f345,plain,
ab_semigroup_add(nat),
inference(cnf_transformation,[],[f121]) ).
tff(f121,axiom,
ab_semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
tff(f576,plain,
spl4_8,
inference(avatar_split_clause,[],[f344,f573]) ).
tff(f573,plain,
( spl4_8
<=> zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).
tff(f344,plain,
zero(int),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
tff(f571,plain,
spl4_7,
inference(avatar_split_clause,[],[f343,f568]) ).
tff(f568,plain,
( spl4_7
<=> ab_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).
tff(f343,plain,
ab_semigroup_add(int),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
ab_semigroup_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
tff(f566,plain,
spl4_6,
inference(avatar_split_clause,[],[f342,f563]) ).
tff(f563,plain,
( spl4_6
<=> one(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).
tff(f342,plain,
one(int),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
tff(f561,plain,
spl4_5,
inference(avatar_split_clause,[],[f341,f558]) ).
tff(f558,plain,
( spl4_5
<=> cancel146912293up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).
tff(f341,plain,
cancel146912293up_add(int),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
cancel146912293up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
tff(f556,plain,
spl4_4,
inference(avatar_split_clause,[],[f340,f553]) ).
tff(f553,plain,
( spl4_4
<=> semiring_char_0(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).
tff(f340,plain,
semiring_char_0(int),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
semiring_char_0(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
tff(f551,plain,
spl4_3,
inference(avatar_split_clause,[],[f339,f548]) ).
tff(f548,plain,
( spl4_3
<=> linord219039673up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).
tff(f339,plain,
linord219039673up_add(int),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
linord219039673up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
tff(f546,plain,
spl4_2,
inference(avatar_split_clause,[],[f338,f543]) ).
tff(f543,plain,
( spl4_2
<=> linordered_idom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).
tff(f338,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
linordered_idom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
tff(f541,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f337,f538]) ).
tff(f538,plain,
( spl4_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).
tff(f337,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f132]) ).
tff(f132,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : NUM980_5 : TPTP v8.1.2. Released v6.0.0.
% 0.08/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 14:15:23 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (14347)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (14350)WARNING: value z3 for option sas not known
% 0.14/0.38 % (14351)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (14348)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (14352)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)
% 0.14/0.38 % (14353)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)
% 0.14/0.38 % (14350)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)
% 0.14/0.38 % (14349)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (14354)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)
% 0.14/0.39 % (14354)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.39 % Exception at run slice level
% 0.14/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.39 % Exception at run slice level
% 0.14/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.39 % Exception at run slice level
% 0.14/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.40 % (14355)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.14/0.40 % (14356)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)
% 0.14/0.40 % (14357)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)
% 0.14/0.41 % (14355)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.41 % Exception at run slice level
% 0.14/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.41 % (14356)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.42 % (14358)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 % (14352)First to succeed.
% 0.22/0.45 % (14352)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-14347"
% 0.22/0.45 % (14352)Refutation found. Thanks to Tanya!
% 0.22/0.45 % SZS status Theorem for theBenchmark
% 0.22/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.45 % (14352)------------------------------
% 0.22/0.45 % (14352)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.45 % (14352)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (14352)Memory used [KB]: 1719
% 0.22/0.45 % (14352)Time elapsed: 0.065 s
% 0.22/0.45 % (14352)Instructions burned: 99 (million)
% 0.22/0.45 % (14347)Success in time 0.087 s
%------------------------------------------------------------------------------