TSTP Solution File: NUN015_5 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUN015_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 : n020.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 08:44:53 EDT 2024
% Result : Theorem 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 275
% Syntax : Number of formulae : 778 ( 251 unt; 37 typ; 0 def)
% Number of atoms : 1827 ( 450 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1805 ( 719 ~; 683 |; 92 &)
% ( 228 <=>; 83 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 17 ( 10 >; 7 *; 0 +; 0 <<)
% Number of predicates : 162 ( 160 usr; 142 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 988 ( 965 !; 0 ?; 988 :)
% ( 23 !>; 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,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
bit0: int > int ).
tff(func_def_3,type,
bit1: int > int ).
tff(func_def_4,type,
pls: int ).
tff(func_def_5,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_6,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_7,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_8,type,
fFalse: bool ).
tff(func_def_9,type,
fTrue: bool ).
tff(func_def_10,type,
n: nat ).
tff(func_def_11,type,
tn: nat ).
tff(func_def_12,type,
v: int ).
tff(func_def_13,type,
w: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
power:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
no_zero_divisors:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
ring_11004092258visors:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
ordere236663937imp_le:
!>[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(f1802,plain,
$false,
inference(avatar_sat_refutation,[],[f611,f616,f621,f626,f631,f636,f641,f646,f651,f656,f661,f666,f671,f676,f681,f686,f691,f696,f701,f706,f711,f716,f721,f726,f731,f736,f741,f746,f752,f757,f762,f767,f771,f775,f781,f786,f791,f795,f799,f804,f808,f812,f816,f822,f826,f830,f834,f844,f848,f852,f856,f861,f865,f874,f878,f882,f886,f895,f899,f903,f907,f911,f915,f919,f923,f927,f931,f960,f964,f969,f973,f977,f981,f1001,f1005,f1009,f1013,f1017,f1021,f1031,f1035,f1039,f1043,f1047,f1051,f1055,f1059,f1063,f1077,f1130,f1134,f1138,f1142,f1146,f1150,f1154,f1158,f1162,f1166,f1170,f1255,f1259,f1263,f1267,f1271,f1275,f1279,f1283,f1287,f1291,f1295,f1419,f1423,f1427,f1431,f1435,f1439,f1463,f1467,f1487,f1491,f1497,f1512,f1516,f1520,f1524,f1614,f1618,f1628,f1644,f1656,f1663,f1676,f1680,f1692,f1696,f1716,f1723,f1771,f1801]) ).
tff(f1801,plain,
( ~ spl1_5
| spl1_35
| ~ spl1_32
| ~ spl1_131
| ~ spl1_136 ),
inference(avatar_split_clause,[],[f1688,f1678,f1625,f764,f778,f628]) ).
tff(f628,plain,
( spl1_5
<=> linordered_idom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
tff(f778,plain,
( spl1_35
<=> ( v = pls ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_35])]) ).
tff(f764,plain,
( spl1_32
<=> ( zero_zero(int) = pls ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_32])]) ).
tff(f1625,plain,
( spl1_131
<=> ( pls = plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_131])]) ).
tff(f1678,plain,
( spl1_136
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X2 )
| ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_136])]) ).
tff(f1688,plain,
( ( v = pls )
| ~ linordered_idom(int)
| ~ spl1_32
| ~ spl1_131
| ~ spl1_136 ),
inference(forward_demodulation,[],[f1687,f766]) ).
tff(f766,plain,
( ( zero_zero(int) = pls )
| ~ spl1_32 ),
inference(avatar_component_clause,[],[f764]) ).
tff(f1687,plain,
( ( v = zero_zero(int) )
| ~ linordered_idom(int)
| ~ spl1_32
| ~ spl1_131
| ~ spl1_136 ),
inference(trivial_inequality_removal,[],[f1686]) ).
tff(f1686,plain,
( ( pls != pls )
| ( v = zero_zero(int) )
| ~ linordered_idom(int)
| ~ spl1_32
| ~ spl1_131
| ~ spl1_136 ),
inference(forward_demodulation,[],[f1685,f766]) ).
tff(f1685,plain,
( ( zero_zero(int) != pls )
| ( v = zero_zero(int) )
| ~ linordered_idom(int)
| ~ spl1_131
| ~ spl1_136 ),
inference(superposition,[],[f1679,f1627]) ).
tff(f1627,plain,
( ( pls = plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ spl1_131 ),
inference(avatar_component_clause,[],[f1625]) ).
tff(f1679,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ( zero_zero(X0) = X2 )
| ~ linordered_idom(X0) )
| ~ spl1_136 ),
inference(avatar_component_clause,[],[f1678]) ).
tff(f1771,plain,
( ~ spl1_5
| spl1_141
| ~ spl1_32
| ~ spl1_131
| ~ spl1_135 ),
inference(avatar_split_clause,[],[f1684,f1674,f1625,f764,f1768,f628]) ).
tff(f1768,plain,
( spl1_141
<=> ( pls = w ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_141])]) ).
tff(f1674,plain,
( spl1_135
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_135])]) ).
tff(f1684,plain,
( ( pls = w )
| ~ linordered_idom(int)
| ~ spl1_32
| ~ spl1_131
| ~ spl1_135 ),
inference(forward_demodulation,[],[f1683,f766]) ).
tff(f1683,plain,
( ( zero_zero(int) = w )
| ~ linordered_idom(int)
| ~ spl1_32
| ~ spl1_131
| ~ spl1_135 ),
inference(trivial_inequality_removal,[],[f1682]) ).
tff(f1682,plain,
( ( pls != pls )
| ( zero_zero(int) = w )
| ~ linordered_idom(int)
| ~ spl1_32
| ~ spl1_131
| ~ spl1_135 ),
inference(forward_demodulation,[],[f1681,f766]) ).
tff(f1681,plain,
( ( zero_zero(int) != pls )
| ( zero_zero(int) = w )
| ~ linordered_idom(int)
| ~ spl1_131
| ~ spl1_135 ),
inference(superposition,[],[f1675,f1627]) ).
tff(f1675,plain,
( ! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) )
| ~ spl1_135 ),
inference(avatar_component_clause,[],[f1674]) ).
tff(f1723,plain,
( spl1_140
| ~ spl1_6
| ~ spl1_39
| ~ spl1_42
| ~ spl1_85
| ~ spl1_129
| ~ spl1_139 ),
inference(avatar_split_clause,[],[f1719,f1714,f1612,f1049,f810,f797,f633,f1721]) ).
tff(f1721,plain,
( spl1_140
<=> ! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(bit1(pls))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_140])]) ).
tff(f633,plain,
( spl1_6
<=> number_ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
tff(f797,plain,
( spl1_39
<=> ! [X0: int] : ( number_number_of(int,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_39])]) ).
tff(f810,plain,
( spl1_42
<=> ! [X0: int] : ( plus_plus(int,pls,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_42])]) ).
tff(f1049,plain,
( spl1_85
<=> ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_85])]) ).
tff(f1612,plain,
( spl1_129
<=> ! [X0: $tType,X3: int,X2: int,X1: X0] :
( ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_129])]) ).
tff(f1714,plain,
( spl1_139
<=> ! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_139])]) ).
tff(f1719,plain,
( ! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(bit1(pls))))) )
| ~ spl1_6
| ~ spl1_39
| ~ spl1_42
| ~ spl1_85
| ~ spl1_129
| ~ spl1_139 ),
inference(forward_demodulation,[],[f1718,f811]) ).
tff(f811,plain,
( ! [X0: int] : ( plus_plus(int,pls,X0) = X0 )
| ~ spl1_42 ),
inference(avatar_component_clause,[],[f810]) ).
tff(f1718,plain,
( ! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(plus_plus(int,pls,bit1(pls)))))) )
| ~ spl1_6
| ~ spl1_39
| ~ spl1_85
| ~ spl1_129
| ~ spl1_139 ),
inference(forward_demodulation,[],[f1717,f1050]) ).
tff(f1050,plain,
( ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),plus_plus(int,X0,X0)) )
| ~ spl1_85 ),
inference(avatar_component_clause,[],[f1049]) ).
tff(f1717,plain,
( ! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),plus_plus(int,bit1(pls),plus_plus(int,bit1(pls),bit1(pls)))))) )
| ~ spl1_6
| ~ spl1_39
| ~ spl1_129
| ~ spl1_139 ),
inference(forward_demodulation,[],[f1715,f1622]) ).
tff(f1622,plain,
( ! [X2: int,X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,X0,plus_plus(int,X1,X2)) )
| ~ spl1_6
| ~ spl1_39
| ~ spl1_129 ),
inference(forward_demodulation,[],[f1621,f798]) ).
tff(f798,plain,
( ! [X0: int] : ( number_number_of(int,X0) = X0 )
| ~ spl1_39 ),
inference(avatar_component_clause,[],[f797]) ).
tff(f1621,plain,
( ! [X2: int,X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,number_number_of(int,X0),plus_plus(int,X1,X2)) )
| ~ spl1_6
| ~ spl1_39
| ~ spl1_129 ),
inference(forward_demodulation,[],[f1620,f798]) ).
tff(f1620,plain,
( ! [X2: int,X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X0,X1),X2) = plus_plus(int,number_number_of(int,X0),plus_plus(int,number_number_of(int,X1),X2)) )
| ~ spl1_6
| ~ spl1_39
| ~ spl1_129 ),
inference(forward_demodulation,[],[f1619,f798]) ).
tff(f1619,plain,
( ! [X2: int,X0: int,X1: int] : ( plus_plus(int,number_number_of(int,X0),plus_plus(int,number_number_of(int,X1),X2)) = plus_plus(int,number_number_of(int,plus_plus(int,X0,X1)),X2) )
| ~ spl1_6
| ~ spl1_129 ),
inference(resolution,[],[f1613,f635]) ).
tff(f635,plain,
( number_ring(int)
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f633]) ).
tff(f1613,plain,
( ! [X0: $tType,X2: int,X3: int,X1: X0] :
( ~ number_ring(X0)
| ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) ) )
| ~ spl1_129 ),
inference(avatar_component_clause,[],[f1612]) ).
tff(f1715,plain,
( ! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ spl1_139 ),
inference(avatar_component_clause,[],[f1714]) ).
tff(f1716,plain,
spl1_139,
inference(avatar_split_clause,[],[f517,f1714]) ).
tff(f517,plain,
! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))))) ),
inference(definition_unfolding,[],[f376,f375,f375,f375,f375]) ).
tff(f375,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X8: int] : ( bit0(X8) = plus_plus(int,X8,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Bit0__def) ).
tff(f376,plain,
! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))) = power_power(int,X0,number_number_of(nat,bit0(bit0(bit1(pls))))) ),
inference(cnf_transformation,[],[f141]) ).
tff(f141,plain,
! [X0: int] : ( power_power(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))) = power_power(int,X0,number_number_of(nat,bit0(bit0(bit1(pls))))) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X16: int] : ( power_power(int,power_power(int,X16,number_number_of(nat,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))) = power_power(int,X16,number_number_of(nat,bit0(bit0(bit1(pls))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_quartic__square__square) ).
tff(f1696,plain,
spl1_138,
inference(avatar_split_clause,[],[f528,f1694]) ).
tff(f1694,plain,
( spl1_138
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ( zero_zero(X0) = X2 )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_138])]) ).
tff(f528,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ( zero_zero(X0) = X2 )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f398,f375,f375]) ).
tff(f398,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
| ( zero_zero(X0) = X2 )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f276]) ).
tff(f276,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
| ( ( zero_zero(X0) = X1 )
& ( zero_zero(X0) = X2 ) ) )
& ( ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 )
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))) ) )
| ~ linordered_idom(X0) ),
inference(flattening,[],[f275]) ).
tff(f275,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
| ( ( zero_zero(X0) = X1 )
& ( zero_zero(X0) = X2 ) ) )
& ( ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 )
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f224]) ).
tff(f224,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
<=> ( ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 ) ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f153]) ).
tff(f153,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0,X2: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
<=> ( ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 ) ) ) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X3: X0,X4: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X3,number_number_of(nat,bit0(bit1(pls))))))
<=> ( ( zero_zero(X0) != X3 )
| ( zero_zero(X0) != X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_sum__power2__gt__zero__iff) ).
tff(f1692,plain,
spl1_137,
inference(avatar_split_clause,[],[f527,f1690]) ).
tff(f1690,plain,
( spl1_137
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_137])]) ).
tff(f527,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f399,f375,f375]) ).
tff(f399,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f276]) ).
tff(f1680,plain,
spl1_136,
inference(avatar_split_clause,[],[f526,f1678]) ).
tff(f526,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X2 )
| ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f394,f375,f375]) ).
tff(f394,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X2 )
| ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f274,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 ) )
& ( ( ( zero_zero(X0) = X1 )
& ( zero_zero(X0) = X2 ) )
| ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ) ) )
| ~ linordered_idom(X0) ),
inference(flattening,[],[f273]) ).
tff(f273,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 ) )
& ( ( ( zero_zero(X0) = X1 )
& ( zero_zero(X0) = X2 ) )
| ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f223]) ).
tff(f223,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
<=> ( ( zero_zero(X0) = X1 )
& ( zero_zero(X0) = X2 ) ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f152]) ).
tff(f152,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0,X2: X0] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
<=> ( ( zero_zero(X0) = X1 )
& ( zero_zero(X0) = X2 ) ) ) ),
inference(rectify,[],[f84]) ).
tff(f84,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X3: X0,X4: X0] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X4,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X3,number_number_of(nat,bit0(bit1(pls))))) )
<=> ( ( zero_zero(X0) = X3 )
& ( zero_zero(X0) = X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_sum__power2__eq__zero__iff) ).
tff(f1676,plain,
spl1_135,
inference(avatar_split_clause,[],[f525,f1674]) ).
tff(f525,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f395,f375,f375]) ).
tff(f395,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f1663,plain,
spl1_134,
inference(avatar_split_clause,[],[f564,f1661]) ).
tff(f1661,plain,
( spl1_134
<=> ! [X0: $tType] :
( ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_134])]) ).
tff(f564,plain,
! [X0: $tType] :
( ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f563]) ).
tff(f563,plain,
! [X0: $tType,X2: X0] :
( ( zero_zero(X0) != X2 )
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f529]) ).
tff(f529,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 )
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f397,f375,f375]) ).
tff(f397,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 )
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f276]) ).
tff(f1656,plain,
spl1_133,
inference(avatar_split_clause,[],[f562,f1654]) ).
tff(f1654,plain,
( spl1_133
<=> ! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_133])]) ).
tff(f562,plain,
! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f561]) ).
tff(f561,plain,
! [X0: $tType,X2: X0] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ( zero_zero(X0) != X2 )
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f524]) ).
tff(f524,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f396,f375,f375]) ).
tff(f396,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) )
| ( zero_zero(X0) != X1 )
| ( zero_zero(X0) != X2 )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f274]) ).
tff(f1644,plain,
spl1_132,
inference(avatar_split_clause,[],[f523,f1642]) ).
tff(f1642,plain,
( spl1_132
<=> ! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_132])]) ).
tff(f523,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f393,f375,f375]) ).
tff(f393,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0] : ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0,X2: X0] : ~ ord_less(X0,plus_plus(X0,power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0)) ),
inference(rectify,[],[f86]) ).
tff(f86,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X22: X0,X16: X0] : ~ ord_less(X0,plus_plus(X0,power_power(X0,X16,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X22,number_number_of(nat,bit0(bit1(pls))))),zero_zero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_not__sum__power2__lt__zero) ).
tff(f1628,plain,
spl1_131,
inference(avatar_split_clause,[],[f590,f1625]) ).
tff(f590,plain,
pls = plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
inference(forward_demodulation,[],[f516,f356]) ).
tff(f356,plain,
zero_zero(int) = pls,
inference(cnf_transformation,[],[f38]) ).
tff(f38,axiom,
zero_zero(int) = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Pls__def) ).
tff(f516,plain,
zero_zero(int) = plus_plus(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),power_power(int,w,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
inference(definition_unfolding,[],[f364,f375,f375]) ).
tff(f364,plain,
zero_zero(int) = plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f51]) ).
tff(f51,axiom,
zero_zero(int) = plus_plus(int,power_power(int,v,number_number_of(nat,bit0(bit1(pls)))),power_power(int,w,number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_calculation) ).
tff(f1618,plain,
spl1_130,
inference(avatar_split_clause,[],[f507,f1616]) ).
tff(f1616,plain,
( spl1_130
<=> ! [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,[spl1_130])]) ).
tff(f507,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,[],[f265]) ).
tff(f265,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,[],[f263,f264]) ).
tff(f264,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(f263,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,[],[f262]) ).
tff(f262,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,[],[f209]) ).
tff(f209,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,[],[f72]) ).
tff(f72,axiom,
! [X26: fun(nat,fun(nat,bool)),X12: nat,X21: nat] :
( ( ord_less(nat,X21,X12)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X26,X12),X21)) )
=> ( ( ( X12 = X21 )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X26,X12),X21)) )
=> ( ( ord_less(nat,X12,X21)
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X26,X12),X21)) )
=> pp(aa(nat,bool,aa(nat,fun(nat,bool),X26,X12),X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_nat__less__cases) ).
tff(f1614,plain,
spl1_129,
inference(avatar_split_clause,[],[f407,f1612]) ).
tff(f407,plain,
! [X0: $tType,X2: int,X3: int,X1: X0] :
( ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: $tType] :
( ! [X1: X0,X2: int,X3: int] : ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0,X2: int,X3: int] : ( plus_plus(X0,number_number_of(X0,X3),plus_plus(X0,number_number_of(X0,X2),X1)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) ) ),
inference(rectify,[],[f60]) ).
tff(f60,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X20: X0,X18: int,X19: int] : ( plus_plus(X0,number_number_of(X0,X19),plus_plus(X0,number_number_of(X0,X18),X20)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X19,X18)),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_add__number__of__left) ).
tff(f1524,plain,
spl1_128,
inference(avatar_split_clause,[],[f546,f1522]) ).
tff(f1522,plain,
( spl1_128
<=> ! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) = plus_plus(int,plus_plus(int,X1,X0),plus_plus(int,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_128])]) ).
tff(f546,plain,
! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) = plus_plus(int,plus_plus(int,X1,X0),plus_plus(int,X1,X0)) ),
inference(definition_unfolding,[],[f458,f375,f375,f375]) ).
tff(f458,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f186]) ).
tff(f186,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
inference(rectify,[],[f58]) ).
tff(f58,axiom,
! [X9: int,X8: int] : ( plus_plus(int,bit0(X8),bit0(X9)) = bit0(plus_plus(int,X8,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_add__Bit0__Bit0) ).
tff(f1520,plain,
spl1_127,
inference(avatar_split_clause,[],[f530,f1518]) ).
tff(f1518,plain,
( spl1_127
<=> ! [X0: $tType,X1: int] :
( ( plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X1,X1)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_127])]) ).
tff(f530,plain,
! [X0: $tType,X1: int] :
( ( plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X1,X1)) )
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f404,f375]) ).
tff(f404,plain,
! [X0: $tType,X1: int] :
( ( number_number_of(X0,bit0(X1)) = plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f229]) ).
tff(f229,plain,
! [X0: $tType] :
( ! [X1: int] : ( number_number_of(X0,bit0(X1)) = plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int] : ( number_number_of(X0,bit0(X1)) = plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) ) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X18: int] : ( number_number_of(X0,bit0(X18)) = plus_plus(X0,plus_plus(X0,zero_zero(X0),number_number_of(X0,X18)),number_number_of(X0,X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_number__of__Bit0) ).
tff(f1516,plain,
spl1_126,
inference(avatar_split_clause,[],[f521,f1514]) ).
tff(f1514,plain,
( spl1_126
<=> ! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_126])]) ).
tff(f521,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f392,f375]) ).
tff(f392,plain,
! [X0: $tType,X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ( zero_zero(X0) = X1 )
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ( zero_zero(X0) = X1 ) )
& ( ( zero_zero(X0) != X1 )
| ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
<=> ( zero_zero(X0) != X1 ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f150]) ).
tff(f150,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
<=> ( zero_zero(X0) != X1 ) ) ),
inference(rectify,[],[f2]) ).
tff(f2,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X2: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
<=> ( zero_zero(X0) != X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_zero__less__power2) ).
tff(f1512,plain,
( ~ spl1_123
| ~ spl1_124
| spl1_125
| ~ spl1_82
| ~ spl1_101 ),
inference(avatar_split_clause,[],[f1304,f1252,f1037,f1510,f1506,f1502]) ).
tff(f1502,plain,
( spl1_123
<=> number_ring(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_123])]) ).
tff(f1506,plain,
( spl1_124
<=> ring_char_0(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_124])]) ).
tff(f1510,plain,
( spl1_125
<=> ! [X0: int] :
( ( zero_zero(nat) != number_number_of(nat,X0) )
| ( power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_125])]) ).
tff(f1037,plain,
( spl1_82
<=> ! [X0: $tType,X2: int,X1: int] :
( ( X1 = X2 )
| ( number_number_of(X0,X1) != number_number_of(X0,X2) )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_82])]) ).
tff(f1252,plain,
( spl1_101
<=> ( zero_zero(nat) = number_number_of(nat,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_101])]) ).
tff(f1304,plain,
( ! [X0: int] :
( ( zero_zero(nat) != number_number_of(nat,X0) )
| ( power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) = X0 )
| ~ ring_char_0(nat)
| ~ number_ring(nat) )
| ~ spl1_82
| ~ spl1_101 ),
inference(superposition,[],[f1038,f1254]) ).
tff(f1254,plain,
( ( zero_zero(nat) = number_number_of(nat,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| ~ spl1_101 ),
inference(avatar_component_clause,[],[f1252]) ).
tff(f1038,plain,
( ! [X0: $tType,X2: int,X1: int] :
( ( number_number_of(X0,X1) != number_number_of(X0,X2) )
| ( X1 = X2 )
| ~ ring_char_0(X0)
| ~ number_ring(X0) )
| ~ spl1_82 ),
inference(avatar_component_clause,[],[f1037]) ).
tff(f1497,plain,
spl1_122,
inference(avatar_split_clause,[],[f570,f1495]) ).
tff(f1495,plain,
( spl1_122
<=> ! [X0: $tType,X1: nat] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),X1) )
| ( zero_zero(nat) = X1 )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_122])]) ).
tff(f570,plain,
! [X0: $tType,X1: nat] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),X1) )
| ( zero_zero(nat) = X1 )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(equality_resolution,[],[f432]) ).
tff(f432,plain,
! [X0: $tType,X2: X0,X1: nat] :
( ( zero_zero(X0) = power_power(X0,X2,X1) )
| ( zero_zero(nat) = X1 )
| ( zero_zero(X0) != X2 )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ( ( zero_zero(X0) = power_power(X0,X2,X1) )
| ( zero_zero(nat) = X1 )
| ( zero_zero(X0) != X2 ) )
& ( ( ( zero_zero(nat) != X1 )
& ( zero_zero(X0) = X2 ) )
| ( zero_zero(X0) != power_power(X0,X2,X1) ) ) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(flattening,[],[f286]) ).
tff(f286,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ( ( zero_zero(X0) = power_power(X0,X2,X1) )
| ( zero_zero(nat) = X1 )
| ( zero_zero(X0) != X2 ) )
& ( ( ( zero_zero(nat) != X1 )
& ( zero_zero(X0) = X2 ) )
| ( zero_zero(X0) != power_power(X0,X2,X1) ) ) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(nnf_transformation,[],[f251]) ).
tff(f251,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ( zero_zero(X0) = power_power(X0,X2,X1) )
<=> ( ( zero_zero(nat) != X1 )
& ( zero_zero(X0) = X2 ) ) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(flattening,[],[f250]) ).
tff(f250,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ( zero_zero(X0) = power_power(X0,X2,X1) )
<=> ( ( zero_zero(nat) != X1 )
& ( zero_zero(X0) = X2 ) ) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(ennf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: $tType] :
( ( zero_neq_one(X0)
& no_zero_divisors(X0)
& mult_zero(X0)
& power(X0) )
=> ! [X1: nat,X2: X0] :
( ( zero_zero(X0) = power_power(X0,X2,X1) )
<=> ( ( zero_zero(nat) != X1 )
& ( zero_zero(X0) = X2 ) ) ) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X0: $tType] :
( ( zero_neq_one(X0)
& no_zero_divisors(X0)
& mult_zero(X0)
& power(X0) )
=> ! [X12: nat,X2: X0] :
( ( zero_zero(X0) = power_power(X0,X2,X12) )
<=> ( ( zero_zero(nat) != X12 )
& ( zero_zero(X0) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_power__eq__0__iff) ).
tff(f1491,plain,
spl1_121,
inference(avatar_split_clause,[],[f504,f1489]) ).
tff(f1489,plain,
( spl1_121
<=> ! [X2: nat,X0: nat,X1: nat] :
( ord_less(nat,X1,X0)
| ~ ord_less(nat,power_power(nat,X2,X1),power_power(nat,X2,X0))
| ~ ord_less(nat,zero_zero(nat),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_121])]) ).
tff(f504,plain,
! [X2: nat,X0: nat,X1: nat] :
( ord_less(nat,X1,X0)
| ~ ord_less(nat,power_power(nat,X2,X1),power_power(nat,X2,X0))
| ~ ord_less(nat,zero_zero(nat),X2) ),
inference(cnf_transformation,[],[f261]) ).
tff(f261,plain,
! [X0: nat,X1: nat,X2: nat] :
( ord_less(nat,X1,X0)
| ~ ord_less(nat,power_power(nat,X2,X1),power_power(nat,X2,X0))
| ~ ord_less(nat,zero_zero(nat),X2) ),
inference(flattening,[],[f260]) ).
tff(f260,plain,
! [X0: nat,X1: nat,X2: nat] :
( ord_less(nat,X1,X0)
| ~ ord_less(nat,power_power(nat,X2,X1),power_power(nat,X2,X0))
| ~ ord_less(nat,zero_zero(nat),X2) ),
inference(ennf_transformation,[],[f208]) ).
tff(f208,plain,
! [X0: nat,X1: nat,X2: nat] :
( ord_less(nat,zero_zero(nat),X2)
=> ( ord_less(nat,power_power(nat,X2,X1),power_power(nat,X2,X0))
=> ord_less(nat,X1,X0) ) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X17: nat,X23: nat,X27: nat] :
( ord_less(nat,zero_zero(nat),X27)
=> ( ord_less(nat,power_power(nat,X27,X23),power_power(nat,X27,X17))
=> ord_less(nat,X23,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_nat__power__less__imp__less) ).
tff(f1487,plain,
spl1_120,
inference(avatar_split_clause,[],[f430,f1485]) ).
tff(f1485,plain,
( spl1_120
<=> ! [X0: $tType,X2: X0,X1: nat] :
( ( zero_zero(X0) = X2 )
| ( zero_zero(X0) != power_power(X0,X2,X1) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_120])]) ).
tff(f430,plain,
! [X0: $tType,X2: X0,X1: nat] :
( ( zero_zero(X0) = X2 )
| ( zero_zero(X0) != power_power(X0,X2,X1) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f287]) ).
tff(f1467,plain,
spl1_119,
inference(avatar_split_clause,[],[f560,f1465]) ).
tff(f1465,plain,
( spl1_119
<=> ! [X0: $tType] :
( ~ ord_less(X0,zero_zero(X0),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_119])]) ).
tff(f560,plain,
! [X0: $tType] :
( ~ ord_less(X0,zero_zero(X0),power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ~ linordered_idom(X0) ),
inference(equality_resolution,[],[f522]) ).
tff(f522,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) != X1 )
| ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f391,f375]) ).
tff(f391,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) != X1 )
| ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f272]) ).
tff(f1463,plain,
spl1_118,
inference(avatar_split_clause,[],[f494,f1461]) ).
tff(f1461,plain,
( spl1_118
<=> ! [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,[spl1_118])]) ).
tff(f494,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,[],[f317]) ).
tff(f317,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,[],[f316]) ).
tff(f316,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,[],[f205]) ).
tff(f205,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,[],[f97]) ).
tff(f97,axiom,
! [X12: nat,X21: nat] :
( ord_less(nat,zero_zero(nat),plus_plus(nat,X21,X12))
<=> ( ord_less(nat,zero_zero(nat),X12)
| ord_less(nat,zero_zero(nat),X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_add__gr__0) ).
tff(f1439,plain,
spl1_117,
inference(avatar_split_clause,[],[f557,f1437]) ).
tff(f1437,plain,
( spl1_117
<=> ! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ ring_11004092258visors(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_117])]) ).
tff(f557,plain,
! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ ring_11004092258visors(X0) ),
inference(equality_resolution,[],[f518]) ).
tff(f518,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
| ( zero_zero(X0) != X1 )
| ~ ring_11004092258visors(X0) ),
inference(definition_unfolding,[],[f378,f375]) ).
tff(f378,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
| ( zero_zero(X0) != X1 )
| ~ ring_11004092258visors(X0) ),
inference(cnf_transformation,[],[f266]) ).
tff(f266,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
| ( zero_zero(X0) != X1 ) )
& ( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) ) ) )
| ~ ring_11004092258visors(X0) ),
inference(nnf_transformation,[],[f213]) ).
tff(f213,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
<=> ( zero_zero(X0) = X1 ) )
| ~ ring_11004092258visors(X0) ),
inference(ennf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: $tType] :
( ring_11004092258visors(X0)
=> ! [X1: X0] :
( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) )
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f4]) ).
tff(f4,axiom,
! [X0: $tType] :
( ring_11004092258visors(X0)
=> ! [X2: X0] :
( ( zero_zero(X0) = power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))) )
<=> ( zero_zero(X0) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_zero__eq__power2) ).
tff(f1435,plain,
spl1_116,
inference(avatar_split_clause,[],[f531,f1433]) ).
tff(f1433,plain,
( spl1_116
<=> ! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_116])]) ).
tff(f531,plain,
! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ semiring_1(X0) ),
inference(definition_unfolding,[],[f409,f375]) ).
tff(f409,plain,
! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls)))) )
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f234]) ).
tff(f234,plain,
! [X0: $tType] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls)))) )
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f3]) ).
tff(f3,axiom,
! [X0: $tType] :
( semiring_1(X0)
=> ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_zero__power2) ).
tff(f1431,plain,
spl1_115,
inference(avatar_split_clause,[],[f520,f1429]) ).
tff(f1429,plain,
( spl1_115
<=> ! [X0: $tType,X1: X0] :
( ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_115])]) ).
tff(f520,plain,
! [X0: $tType,X1: X0] :
( ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f388,f375]) ).
tff(f388,plain,
! [X0: $tType,X1: X0] :
( ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: $tType] :
( ! [X1: X0] : ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f148]) ).
tff(f148,plain,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] : ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0)) ),
inference(rectify,[],[f47]) ).
tff(f47,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X15: X0] : ~ ord_less(X0,power_power(X0,X15,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_power2__less__0) ).
tff(f1427,plain,
spl1_114,
inference(avatar_split_clause,[],[f488,f1425]) ).
tff(f1425,plain,
( spl1_114
<=> ! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),X1)
| ( zero_zero(nat) = X0 )
| ~ ord_less(nat,zero_zero(nat),power_power(nat,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_114])]) ).
tff(f488,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),X1)
| ( zero_zero(nat) = X0 )
| ~ ord_less(nat,zero_zero(nat),power_power(nat,X1,X0)) ),
inference(cnf_transformation,[],[f313]) ).
tff(f313,plain,
! [X0: nat,X1: nat] :
( ( ord_less(nat,zero_zero(nat),power_power(nat,X1,X0))
| ( ~ ord_less(nat,zero_zero(nat),X1)
& ( zero_zero(nat) != X0 ) ) )
& ( ord_less(nat,zero_zero(nat),X1)
| ( zero_zero(nat) = X0 )
| ~ ord_less(nat,zero_zero(nat),power_power(nat,X1,X0)) ) ),
inference(flattening,[],[f312]) ).
tff(f312,plain,
! [X0: nat,X1: nat] :
( ( ord_less(nat,zero_zero(nat),power_power(nat,X1,X0))
| ( ~ ord_less(nat,zero_zero(nat),X1)
& ( zero_zero(nat) != X0 ) ) )
& ( ord_less(nat,zero_zero(nat),X1)
| ( zero_zero(nat) = X0 )
| ~ ord_less(nat,zero_zero(nat),power_power(nat,X1,X0)) ) ),
inference(nnf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),power_power(nat,X1,X0))
<=> ( ord_less(nat,zero_zero(nat),X1)
| ( zero_zero(nat) = X0 ) ) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X12: nat,X4: nat] :
( ord_less(nat,zero_zero(nat),power_power(nat,X4,X12))
<=> ( ord_less(nat,zero_zero(nat),X4)
| ( zero_zero(nat) = X12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_zero__less__power__nat__eq) ).
tff(f1423,plain,
spl1_113,
inference(avatar_split_clause,[],[f405,f1421]) ).
tff(f1421,plain,
( spl1_113
<=> ! [X0: $tType,X2: int,X1: int] :
( ( plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_113])]) ).
tff(f405,plain,
! [X0: $tType,X2: int,X1: int] :
( ( plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] : ( plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int,X2: int] : ( plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X2,X1)) ) ),
inference(rectify,[],[f59]) ).
tff(f59,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X18: int,X19: int] : ( plus_plus(X0,number_number_of(X0,X19),number_number_of(X0,X18)) = number_number_of(X0,plus_plus(int,X19,X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_add__number__of__eq) ).
tff(f1419,plain,
( spl1_112
| ~ spl1_69
| ~ spl1_101 ),
inference(avatar_split_clause,[],[f1297,f1252,f962,f1417]) ).
tff(f1417,plain,
( spl1_112
<=> ! [X0: int] :
( ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
| ord_less(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_112])]) ).
tff(f962,plain,
( spl1_69
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_69])]) ).
tff(f1297,plain,
( ! [X0: int] :
( ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
| ord_less(int,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),X0) )
| ~ spl1_69
| ~ spl1_101 ),
inference(superposition,[],[f963,f1254]) ).
tff(f963,plain,
( ! [X0: int,X1: int] :
( ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ord_less(int,X1,X0) )
| ~ spl1_69 ),
inference(avatar_component_clause,[],[f962]) ).
tff(f1295,plain,
spl1_111,
inference(avatar_split_clause,[],[f571,f1293]) ).
tff(f1293,plain,
( spl1_111
<=> ! [X0: $tType,X2: X0] :
( ( zero_zero(X0) != power_power(X0,X2,zero_zero(nat)) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_111])]) ).
tff(f571,plain,
! [X0: $tType,X2: X0] :
( ( zero_zero(X0) != power_power(X0,X2,zero_zero(nat)) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(equality_resolution,[],[f431]) ).
tff(f431,plain,
! [X0: $tType,X2: X0,X1: nat] :
( ( zero_zero(nat) != X1 )
| ( zero_zero(X0) != power_power(X0,X2,X1) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f287]) ).
tff(f1291,plain,
spl1_110,
inference(avatar_split_clause,[],[f506,f1289]) ).
tff(f1289,plain,
( spl1_110
<=> ! [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,[spl1_110])]) ).
tff(f506,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,[],[f323]) ).
tff(f323,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,[],[f322]) ).
tff(f322,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,[],[f264]) ).
tff(f1287,plain,
spl1_109,
inference(avatar_split_clause,[],[f500,f1285]) ).
tff(f1285,plain,
( spl1_109
<=> ! [X0: int,X1: int] :
( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less(int,X1,X0)
| ~ ord_less(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_109])]) ).
tff(f500,plain,
! [X0: int,X1: int] :
( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less(int,X1,X0)
| ~ ord_less(int,pls,X0) ),
inference(cnf_transformation,[],[f319]) ).
tff(f319,plain,
! [X0: int,X1: int] :
( ( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less(int,X1,X0)
| ( ~ ord_less(int,pls,X0)
& ord_less(int,X1,X0) ) )
& ( ( ord_less(int,X1,X0)
& ( ord_less(int,pls,X0)
| ~ ord_less(int,X1,X0) ) )
| ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ),
inference(flattening,[],[f318]) ).
tff(f318,plain,
! [X0: int,X1: int] :
( ( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less(int,X1,X0)
| ( ~ ord_less(int,pls,X0)
& ord_less(int,X1,X0) ) )
& ( ( ord_less(int,X1,X0)
& ( ord_less(int,pls,X0)
| ~ ord_less(int,X1,X0) ) )
| ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ),
inference(nnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X0: int,X1: int] :
( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
<=> ( ord_less(int,X1,X0)
& ( ord_less(int,pls,X0)
| ~ ord_less(int,X1,X0) ) ) ),
inference(ennf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: int,X1: int] :
( ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0))
<=> ( ord_less(int,X1,X0)
& ( ord_less(int,X1,X0)
=> ord_less(int,pls,X0) ) ) ),
inference(rectify,[],[f31]) ).
tff(f31,axiom,
! [X10: int,X11: int] :
( ord_less(nat,number_number_of(nat,X11),number_number_of(nat,X10))
<=> ( ord_less(int,X11,X10)
& ( ord_less(int,X11,X10)
=> ord_less(int,pls,X10) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_less__nat__number__of) ).
tff(f1283,plain,
spl1_108,
inference(avatar_split_clause,[],[f497,f1281]) ).
tff(f1281,plain,
( spl1_108
<=> ! [X0: int,X1: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,X1,X0)
| ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_108])]) ).
tff(f497,plain,
! [X0: int,X1: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,X1,X0)
| ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ),
inference(cnf_transformation,[],[f319]) ).
tff(f1279,plain,
spl1_107,
inference(avatar_split_clause,[],[f429,f1277]) ).
tff(f1277,plain,
( spl1_107
<=> ! [X0: $tType,X2: int,X1: int] :
( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ ord_less(int,X2,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_107])]) ).
tff(f429,plain,
! [X0: $tType,X2: int,X1: int] :
( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ ord_less(int,X2,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ ord_less(int,X2,X1) )
& ( ord_less(int,X2,X1)
| ~ ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f249]) ).
tff(f249,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less(int,X2,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f248]) ).
tff(f248,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less(int,X2,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int,X2: int] :
( ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less(int,X2,X1) ) ),
inference(rectify,[],[f12]) ).
tff(f12,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X3: int,X4: int] :
( ord_less(X0,number_number_of(X0,X4),number_number_of(X0,X3))
<=> ord_less(int,X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_less__number__of) ).
tff(f1275,plain,
spl1_106,
inference(avatar_split_clause,[],[f428,f1273]) ).
tff(f1273,plain,
( spl1_106
<=> ! [X0: $tType,X2: int,X1: int] :
( ord_less(int,X2,X1)
| ~ ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_106])]) ).
tff(f428,plain,
! [X0: $tType,X2: int,X1: int] :
( ord_less(int,X2,X1)
| ~ ord_less(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f285]) ).
tff(f1271,plain,
spl1_105,
inference(avatar_split_clause,[],[f420,f1269]) ).
tff(f1269,plain,
( spl1_105
<=> ! [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,[spl1_105])]) ).
tff(f420,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,[],[f281]) ).
tff(f281,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,[],[f240]) ).
tff(f240,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,[],[f165]) ).
tff(f165,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,[],[f90]) ).
tff(f90,axiom,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X28: X0,X29: X0,X2: X0] :
( ord_less(X0,plus_plus(X0,X2,X29),plus_plus(X0,X28,X29))
<=> ord_less(X0,X2,X28) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_add__less__cancel__right) ).
tff(f1267,plain,
spl1_104,
inference(avatar_split_clause,[],[f419,f1265]) ).
tff(f1265,plain,
( spl1_104
<=> ! [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,[spl1_104])]) ).
tff(f419,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,[],[f281]) ).
tff(f1263,plain,
spl1_103,
inference(avatar_split_clause,[],[f418,f1261]) ).
tff(f1261,plain,
( spl1_103
<=> ! [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,[spl1_103])]) ).
tff(f418,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,[],[f280]) ).
tff(f280,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,[],[f239]) ).
tff(f239,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,[],[f164]) ).
tff(f164,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,[],[f96]) ).
tff(f96,axiom,
! [X0: $tType] :
( ordere236663937imp_le(X0)
=> ! [X28: X0,X2: X0,X29: X0] :
( ord_less(X0,plus_plus(X0,X29,X2),plus_plus(X0,X29,X28))
<=> ord_less(X0,X2,X28) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_add__less__cancel__left) ).
tff(f1259,plain,
spl1_102,
inference(avatar_split_clause,[],[f417,f1257]) ).
tff(f1257,plain,
( spl1_102
<=> ! [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,[spl1_102])]) ).
tff(f417,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,[],[f280]) ).
tff(f1255,plain,
( spl1_101
| spl1_29
| ~ spl1_68 ),
inference(avatar_split_clause,[],[f1180,f958,f749,f1252]) ).
tff(f749,plain,
( spl1_29
<=> ord_less(int,pls,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).
tff(f958,plain,
( spl1_68
<=> ! [X0: int] :
( ord_less(int,pls,X0)
| ( zero_zero(nat) = number_number_of(nat,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_68])]) ).
tff(f1180,plain,
( ( zero_zero(nat) = number_number_of(nat,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) )
| spl1_29
| ~ spl1_68 ),
inference(resolution,[],[f959,f751]) ).
tff(f751,plain,
( ~ ord_less(int,pls,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| spl1_29 ),
inference(avatar_component_clause,[],[f749]) ).
tff(f959,plain,
( ! [X0: int] :
( ord_less(int,pls,X0)
| ( zero_zero(nat) = number_number_of(nat,X0) ) )
| ~ spl1_68 ),
inference(avatar_component_clause,[],[f958]) ).
tff(f1170,plain,
spl1_100,
inference(avatar_split_clause,[],[f427,f1168]) ).
tff(f1168,plain,
( spl1_100
<=> ! [X0: $tType,X1: int] :
( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ ord_less(int,X1,pls)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_100])]) ).
tff(f427,plain,
! [X0: $tType,X1: int] :
( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ ord_less(int,X1,pls)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f284]) ).
tff(f284,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ ord_less(int,X1,pls) )
& ( ord_less(int,X1,pls)
| ~ ord_less(X0,number_number_of(X0,X1),zero_zero(X0)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f247]) ).
tff(f247,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less(int,X1,pls) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f246]) ).
tff(f246,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less(int,X1,pls) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int] :
( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less(int,X1,pls) ) ),
inference(rectify,[],[f6]) ).
tff(f6,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X4: int] :
( ord_less(X0,number_number_of(X0,X4),zero_zero(X0))
<=> ord_less(int,X4,pls) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_less__special_I3_J) ).
tff(f1166,plain,
spl1_99,
inference(avatar_split_clause,[],[f426,f1164]) ).
tff(f1164,plain,
( spl1_99
<=> ! [X0: $tType,X1: int] :
( ord_less(int,X1,pls)
| ~ ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_99])]) ).
tff(f426,plain,
! [X0: $tType,X1: int] :
( ord_less(int,X1,pls)
| ~ ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f284]) ).
tff(f1162,plain,
spl1_98,
inference(avatar_split_clause,[],[f425,f1160]) ).
tff(f1160,plain,
( spl1_98
<=> ! [X0: $tType,X1: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ ord_less(int,pls,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_98])]) ).
tff(f425,plain,
! [X0: $tType,X1: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ ord_less(int,pls,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ ord_less(int,pls,X1) )
& ( ord_less(int,pls,X1)
| ~ ord_less(X0,zero_zero(X0),number_number_of(X0,X1)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f245]) ).
tff(f245,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less(int,pls,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f244]) ).
tff(f244,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less(int,pls,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less(int,pls,X1) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X3: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X3))
<=> ord_less(int,pls,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_less__special_I1_J) ).
tff(f1158,plain,
spl1_97,
inference(avatar_split_clause,[],[f424,f1156]) ).
tff(f1156,plain,
( spl1_97
<=> ! [X0: $tType,X1: int] :
( ord_less(int,pls,X1)
| ~ ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_97])]) ).
tff(f424,plain,
! [X0: $tType,X1: int] :
( ord_less(int,pls,X1)
| ~ ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f283]) ).
tff(f1154,plain,
spl1_96,
inference(avatar_split_clause,[],[f410,f1152]) ).
tff(f1152,plain,
( spl1_96
<=> ! [X0: $tType,X2: X0,X1: nat] :
( ord_less(X0,zero_zero(X0),power_power(X0,X2,X1))
| ~ ord_less(X0,zero_zero(X0),X2)
| ~ linordered_semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_96])]) ).
tff(f410,plain,
! [X0: $tType,X2: X0,X1: nat] :
( ord_less(X0,zero_zero(X0),power_power(X0,X2,X1))
| ~ ord_less(X0,zero_zero(X0),X2)
| ~ linordered_semidom(X0) ),
inference(cnf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X2,X1))
| ~ ord_less(X0,zero_zero(X0),X2) )
| ~ linordered_semidom(X0) ),
inference(ennf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X1: nat,X2: X0] :
( ord_less(X0,zero_zero(X0),X2)
=> ord_less(X0,zero_zero(X0),power_power(X0,X2,X1)) ) ),
inference(rectify,[],[f52]) ).
tff(f52,axiom,
! [X0: $tType] :
( linordered_semidom(X0)
=> ! [X17: nat,X15: X0] :
( ord_less(X0,zero_zero(X0),X15)
=> ord_less(X0,zero_zero(X0),power_power(X0,X15,X17)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_zero__less__power) ).
tff(f1150,plain,
spl1_95,
inference(avatar_split_clause,[],[f390,f1148]) ).
tff(f1148,plain,
( spl1_95
<=> ! [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,[spl1_95])]) ).
tff(f390,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,[],[f271]) ).
tff(f271,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,[],[f220]) ).
tff(f220,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,[],[f149]) ).
tff(f149,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,[],[f76]) ).
tff(f76,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X2: X0] :
( ord_less(X0,plus_plus(X0,X2,X2),zero_zero(X0))
<=> ord_less(X0,X2,zero_zero(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_even__less__0__iff) ).
tff(f1146,plain,
spl1_94,
inference(avatar_split_clause,[],[f389,f1144]) ).
tff(f1144,plain,
( spl1_94
<=> ! [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,[spl1_94])]) ).
tff(f389,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,[],[f271]) ).
tff(f1142,plain,
spl1_93,
inference(avatar_split_clause,[],[f387,f1140]) ).
tff(f1140,plain,
( spl1_93
<=> ! [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,[spl1_93])]) ).
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))
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f270,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,[],[f218]) ).
tff(f218,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,[],[f147]) ).
tff(f147,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,[],[f89]) ).
tff(f89,axiom,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X2: X0] :
( ord_less(X0,plus_plus(X0,X2,X2),zero_zero(X0))
<=> ord_less(X0,X2,zero_zero(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_double__add__less__zero__iff__single__add__less__zero) ).
tff(f1138,plain,
spl1_92,
inference(avatar_split_clause,[],[f386,f1136]) ).
tff(f1136,plain,
( spl1_92
<=> ! [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,[spl1_92])]) ).
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))
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f270]) ).
tff(f1134,plain,
spl1_91,
inference(avatar_split_clause,[],[f385,f1132]) ).
tff(f1132,plain,
( spl1_91
<=> ! [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,[spl1_91])]) ).
tff(f385,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,[],[f269]) ).
tff(f269,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,[],[f217]) ).
tff(f217,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,[],[f146]) ).
tff(f146,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,[],[f88]) ).
tff(f88,axiom,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X2: X0] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,X2,X2))
<=> ord_less(X0,zero_zero(X0),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_zero__less__double__add__iff__zero__less__single__add) ).
tff(f1130,plain,
spl1_90,
inference(avatar_split_clause,[],[f384,f1128]) ).
tff(f1128,plain,
( spl1_90
<=> ! [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,[spl1_90])]) ).
tff(f384,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,[],[f269]) ).
tff(f1077,plain,
( spl1_89
| ~ spl1_64
| ~ spl1_74 ),
inference(avatar_split_clause,[],[f1027,f998,f917,f1074]) ).
tff(f1074,plain,
( spl1_89
<=> ord_less(int,pls,bit1(pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_89])]) ).
tff(f917,plain,
( spl1_64
<=> ! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,pls,plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_64])]) ).
tff(f998,plain,
( spl1_74
<=> ord_less(int,pls,plus_plus(int,bit1(pls),bit1(pls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_74])]) ).
tff(f1027,plain,
( ord_less(int,pls,bit1(pls))
| ~ spl1_64
| ~ spl1_74 ),
inference(resolution,[],[f1000,f918]) ).
tff(f918,plain,
( ! [X0: int] :
( ~ ord_less(int,pls,plus_plus(int,X0,X0))
| ord_less(int,pls,X0) )
| ~ spl1_64 ),
inference(avatar_component_clause,[],[f917]) ).
tff(f1000,plain,
( ord_less(int,pls,plus_plus(int,bit1(pls),bit1(pls)))
| ~ spl1_74 ),
inference(avatar_component_clause,[],[f998]) ).
tff(f1063,plain,
spl1_88,
inference(avatar_split_clause,[],[f554,f1061]) ).
tff(f1061,plain,
( spl1_88
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_88])]) ).
tff(f554,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f479,f375,f375]) ).
tff(f479,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit0(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f307]) ).
tff(f307,plain,
! [X0: int,X1: int] :
( ( ord_less(int,bit0(X1),bit0(X0))
| ~ ord_less(int,X1,X0) )
& ( ord_less(int,X1,X0)
| ~ ord_less(int,bit0(X1),bit0(X0)) ) ),
inference(nnf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: int,X1: int] :
( ord_less(int,bit0(X1),bit0(X0))
<=> ord_less(int,X1,X0) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X13: int,X14: int] :
( ord_less(int,bit0(X14),bit0(X13))
<=> ord_less(int,X14,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_less__int__code_I13_J) ).
tff(f1059,plain,
spl1_87,
inference(avatar_split_clause,[],[f553,f1057]) ).
tff(f1057,plain,
( spl1_87
<=> ! [X0: int,X1: int] :
( ord_less(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0))
| ~ ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_87])]) ).
tff(f553,plain,
! [X0: int,X1: int] :
( ord_less(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0))
| ~ ord_less(int,X1,X0) ),
inference(definition_unfolding,[],[f480,f375,f375]) ).
tff(f480,plain,
! [X0: int,X1: int] :
( ord_less(int,bit0(X1),bit0(X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f307]) ).
tff(f1055,plain,
spl1_86,
inference(avatar_split_clause,[],[f545,f1053]) ).
tff(f1053,plain,
( spl1_86
<=> ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,plus_plus(int,X1,X1),bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_86])]) ).
tff(f545,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,plus_plus(int,X1,X1),bit1(X0)) ),
inference(definition_unfolding,[],[f457,f375]) ).
tff(f457,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f185]) ).
tff(f185,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
inference(rectify,[],[f61]) ).
tff(f61,axiom,
! [X9: int,X8: int] : ( plus_plus(int,bit0(X8),bit1(X9)) = bit1(plus_plus(int,X8,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_add__Bit0__Bit1) ).
tff(f1051,plain,
spl1_85,
inference(avatar_split_clause,[],[f544,f1049]) ).
tff(f544,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f456,f375]) ).
tff(f456,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),bit0(X0)) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X9: int,X8: int] : ( bit1(plus_plus(int,X8,X9)) = plus_plus(int,bit1(X8),bit0(X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_add__Bit1__Bit0) ).
tff(f1047,plain,
spl1_84,
inference(avatar_split_clause,[],[f512,f1045]) ).
tff(f1045,plain,
( spl1_84
<=> ! [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,[spl1_84])]) ).
tff(f512,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,[],[f324]) ).
tff(f324,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,[],[f210]) ).
tff(f210,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,[],[f94]) ).
tff(f94,axiom,
! [X12: nat,X21: nat,X5: nat] :
( ord_less(nat,plus_plus(nat,X5,X21),plus_plus(nat,X5,X12))
<=> ord_less(nat,X21,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_nat__add__left__cancel__less) ).
tff(f1043,plain,
spl1_83,
inference(avatar_split_clause,[],[f511,f1041]) ).
tff(f1041,plain,
( spl1_83
<=> ! [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,[spl1_83])]) ).
tff(f511,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,[],[f324]) ).
tff(f1039,plain,
spl1_82,
inference(avatar_split_clause,[],[f422,f1037]) ).
tff(f422,plain,
! [X0: $tType,X2: int,X1: int] :
( ( X1 = X2 )
| ( number_number_of(X0,X1) != number_number_of(X0,X2) )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f282]) ).
tff(f282,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( ( number_number_of(X0,X1) = number_number_of(X0,X2) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( number_number_of(X0,X1) != number_number_of(X0,X2) ) ) )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f243]) ).
tff(f243,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( number_number_of(X0,X1) = number_number_of(X0,X2) )
<=> ( X1 = X2 ) )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f242]) ).
tff(f242,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( number_number_of(X0,X1) = number_number_of(X0,X2) )
<=> ( X1 = X2 ) )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: $tType] :
( ( ring_char_0(X0)
& number_ring(X0) )
=> ! [X1: int,X2: int] :
( ( number_number_of(X0,X1) = number_number_of(X0,X2) )
<=> ( X1 = X2 ) ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType] :
( ( ring_char_0(X0)
& number_ring(X0) )
=> ! [X3: int,X4: int] :
( ( number_number_of(X0,X3) = number_number_of(X0,X4) )
<=> ( X3 = X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_eq__number__of) ).
tff(f1035,plain,
spl1_81,
inference(avatar_split_clause,[],[f415,f1033]) ).
tff(f1033,plain,
( spl1_81
<=> ! [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,[spl1_81])]) ).
tff(f415,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,[],[f279]) ).
tff(f279,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( ( plus_plus(X0,X3,X2) = plus_plus(X0,X1,X2) )
| ( X1 != X3 ) )
& ( ( X1 = X3 )
| ( plus_plus(X0,X3,X2) != plus_plus(X0,X1,X2) ) ) )
| ~ cancel_semigroup_add(X0) ),
inference(nnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( plus_plus(X0,X3,X2) = plus_plus(X0,X1,X2) )
<=> ( X1 = X3 ) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,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,[],[f92]) ).
tff(f92,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X29: X0,X2: X0,X28: X0] :
( ( plus_plus(X0,X28,X2) = plus_plus(X0,X29,X2) )
<=> ( X28 = X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_add__right__cancel) ).
tff(f1031,plain,
spl1_80,
inference(avatar_split_clause,[],[f413,f1029]) ).
tff(f1029,plain,
( spl1_80
<=> ! [X0: $tType,X3: X0,X2: X0,X1: X0] :
( ( X1 = X2 )
| ( plus_plus(X0,X3,X1) != plus_plus(X0,X3,X2) )
| ~ cancel_semigroup_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_80])]) ).
tff(f413,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0] :
( ( X1 = X2 )
| ( plus_plus(X0,X3,X1) != plus_plus(X0,X3,X2) )
| ~ cancel_semigroup_add(X0) ),
inference(cnf_transformation,[],[f278]) ).
tff(f278,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( ( plus_plus(X0,X3,X1) = plus_plus(X0,X3,X2) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( plus_plus(X0,X3,X1) != plus_plus(X0,X3,X2) ) ) )
| ~ cancel_semigroup_add(X0) ),
inference(nnf_transformation,[],[f237]) ).
tff(f237,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: X0] :
( ( plus_plus(X0,X3,X1) = plus_plus(X0,X3,X2) )
<=> ( X1 = X2 ) )
| ~ cancel_semigroup_add(X0) ),
inference(ennf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X1: X0,X2: X0,X3: X0] :
( ( plus_plus(X0,X3,X1) = plus_plus(X0,X3,X2) )
<=> ( X1 = X2 ) ) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X0: $tType] :
( cancel_semigroup_add(X0)
=> ! [X29: X0,X28: X0,X2: X0] :
( ( plus_plus(X0,X2,X29) = plus_plus(X0,X2,X28) )
<=> ( X28 = X29 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_add__left__cancel) ).
tff(f1021,plain,
spl1_79,
inference(avatar_split_clause,[],[f496,f1019]) ).
tff(f1019,plain,
( spl1_79
<=> ! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0))
| ~ ord_less(nat,zero_zero(nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_79])]) ).
tff(f496,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0))
| ~ ord_less(nat,zero_zero(nat),X0) ),
inference(cnf_transformation,[],[f317]) ).
tff(f1017,plain,
spl1_78,
inference(avatar_split_clause,[],[f495,f1015]) ).
tff(f1015,plain,
( spl1_78
<=> ! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0))
| ~ ord_less(nat,zero_zero(nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_78])]) ).
tff(f495,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),plus_plus(nat,X1,X0))
| ~ ord_less(nat,zero_zero(nat),X1) ),
inference(cnf_transformation,[],[f317]) ).
tff(f1013,plain,
spl1_77,
inference(avatar_split_clause,[],[f490,f1011]) ).
tff(f1011,plain,
( spl1_77
<=> ! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),power_power(nat,X1,X0))
| ~ ord_less(nat,zero_zero(nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_77])]) ).
tff(f490,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),power_power(nat,X1,X0))
| ~ ord_less(nat,zero_zero(nat),X1) ),
inference(cnf_transformation,[],[f313]) ).
tff(f1009,plain,
spl1_76,
inference(avatar_split_clause,[],[f380,f1007]) ).
tff(f1007,plain,
( spl1_76
<=> ! [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,[spl1_76])]) ).
tff(f380,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,X1,X1) )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,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,[],[f215]) ).
tff(f215,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
<=> ( zero_zero(X0) = X1 ) )
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f144]) ).
tff(f144,plain,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f57]) ).
tff(f57,axiom,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X2: X0] :
( ( zero_zero(X0) = plus_plus(X0,X2,X2) )
<=> ( zero_zero(X0) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_double__eq__0__iff) ).
tff(f1005,plain,
spl1_75,
inference(avatar_split_clause,[],[f379,f1003]) ).
tff(f1003,plain,
( spl1_75
<=> ! [X0: $tType,X2: X0,X1: nat] :
( ( zero_zero(X0) != power_power(X0,X2,X1) )
| ( zero_zero(X0) = X2 )
| ~ ring_11004092258visors(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_75])]) ).
tff(f379,plain,
! [X0: $tType,X2: X0,X1: nat] :
( ( zero_zero(X0) != power_power(X0,X2,X1) )
| ( zero_zero(X0) = X2 )
| ~ ring_11004092258visors(X0) ),
inference(cnf_transformation,[],[f214]) ).
tff(f214,plain,
! [X0: $tType] :
( ! [X1: nat,X2: X0] :
( ( zero_zero(X0) != power_power(X0,X2,X1) )
| ( zero_zero(X0) = X2 ) )
| ~ ring_11004092258visors(X0) ),
inference(ennf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: $tType] :
( ring_11004092258visors(X0)
=> ! [X1: nat,X2: X0] :
( ( zero_zero(X0) != X2 )
=> ( zero_zero(X0) != power_power(X0,X2,X1) ) ) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X0: $tType] :
( ring_11004092258visors(X0)
=> ! [X17: nat,X15: X0] :
( ( zero_zero(X0) != X15 )
=> ( zero_zero(X0) != power_power(X0,X15,X17) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_field__power__not__zero) ).
tff(f1001,plain,
( spl1_74
| ~ spl1_58
| ~ spl1_70 ),
inference(avatar_split_clause,[],[f986,f966,f893,f998]) ).
tff(f893,plain,
( spl1_58
<=> ! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_58])]) ).
tff(f966,plain,
( spl1_70
<=> ord_less(nat,zero_zero(nat),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_70])]) ).
tff(f986,plain,
( ord_less(int,pls,plus_plus(int,bit1(pls),bit1(pls)))
| ~ spl1_58
| ~ spl1_70 ),
inference(resolution,[],[f968,f894]) ).
tff(f894,plain,
( ! [X0: int] :
( ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
| ord_less(int,pls,X0) )
| ~ spl1_58 ),
inference(avatar_component_clause,[],[f893]) ).
tff(f968,plain,
( ord_less(nat,zero_zero(nat),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))
| ~ spl1_70 ),
inference(avatar_component_clause,[],[f966]) ).
tff(f981,plain,
spl1_73,
inference(avatar_split_clause,[],[f550,f979]) ).
tff(f979,plain,
( spl1_73
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_73])]) ).
tff(f550,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f475,f375]) ).
tff(f475,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f305]) ).
tff(f305,plain,
! [X0: int,X1: int] :
( ( ord_less(int,bit1(X1),bit0(X0))
| ~ ord_less(int,X1,X0) )
& ( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),bit0(X0)) ) ),
inference(nnf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit0(X0))
<=> ord_less(int,X1,X0) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X6: int,X5: int] :
( ord_less(int,bit1(X5),bit0(X6))
<=> ord_less(int,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_rel__simps_I16_J) ).
tff(f977,plain,
spl1_72,
inference(avatar_split_clause,[],[f549,f975]) ).
tff(f975,plain,
( spl1_72
<=> ! [X0: int,X1: int] :
( ord_less(int,bit1(X1),plus_plus(int,X0,X0))
| ~ ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_72])]) ).
tff(f549,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),plus_plus(int,X0,X0))
| ~ ord_less(int,X1,X0) ),
inference(definition_unfolding,[],[f476,f375]) ).
tff(f476,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit0(X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f305]) ).
tff(f973,plain,
spl1_71,
inference(avatar_split_clause,[],[f548,f971]) ).
tff(f971,plain,
( spl1_71
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( plus_plus(int,X0,X0) != plus_plus(int,X1,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_71])]) ).
tff(f548,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( plus_plus(int,X0,X0) != plus_plus(int,X1,X1) ) ),
inference(definition_unfolding,[],[f469,f375,f375]) ).
tff(f469,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit0(X0) != bit0(X1) ) ),
inference(cnf_transformation,[],[f302]) ).
tff(f302,plain,
! [X0: int,X1: int] :
( ( ( bit0(X0) = bit0(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( bit0(X0) != bit0(X1) ) ) ),
inference(nnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: int,X1: int] :
( ( bit0(X0) = bit0(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X6: int,X5: int] :
( ( bit0(X5) = bit0(X6) )
<=> ( X5 = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_rel__simps_I48_J) ).
tff(f969,plain,
spl1_70,
inference(avatar_split_clause,[],[f515,f966]) ).
tff(f515,plain,
ord_less(nat,zero_zero(nat),number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))),
inference(definition_unfolding,[],[f363,f375]) ).
tff(f363,plain,
ord_less(nat,zero_zero(nat),number_number_of(nat,bit0(bit1(pls)))),
inference(cnf_transformation,[],[f50]) ).
tff(f50,axiom,
ord_less(nat,zero_zero(nat),number_number_of(nat,bit0(bit1(pls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_pos2) ).
tff(f964,plain,
spl1_69,
inference(avatar_split_clause,[],[f498,f962]) ).
tff(f498,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ),
inference(cnf_transformation,[],[f319]) ).
tff(f960,plain,
( spl1_68
| ~ spl1_48
| ~ spl1_58 ),
inference(avatar_split_clause,[],[f932,f893,f842,f958]) ).
tff(f842,plain,
( spl1_48
<=> ! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_48])]) ).
tff(f932,plain,
( ! [X0: int] :
( ord_less(int,pls,X0)
| ( zero_zero(nat) = number_number_of(nat,X0) ) )
| ~ spl1_48
| ~ spl1_58 ),
inference(resolution,[],[f894,f843]) ).
tff(f843,plain,
( ! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) )
| ~ spl1_48 ),
inference(avatar_component_clause,[],[f842]) ).
tff(f931,plain,
spl1_67,
inference(avatar_split_clause,[],[f558,f929]) ).
tff(f929,plain,
( spl1_67
<=> ! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_67])]) ).
tff(f558,plain,
! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ),
inference(equality_resolution,[],[f381]) ).
tff(f381,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
| ( zero_zero(X0) != X1 )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f267]) ).
tff(f927,plain,
spl1_66,
inference(avatar_split_clause,[],[f539,f925]) ).
tff(f925,plain,
( spl1_66
<=> ! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,plus_plus(int,X0,X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_66])]) ).
tff(f539,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,plus_plus(int,X0,X0),pls) ),
inference(definition_unfolding,[],[f446,f375]) ).
tff(f446,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,bit0(X0),pls) ),
inference(cnf_transformation,[],[f295]) ).
tff(f295,plain,
! [X0: int] :
( ( ord_less(int,bit0(X0),pls)
| ~ ord_less(int,X0,pls) )
& ( ord_less(int,X0,pls)
| ~ ord_less(int,bit0(X0),pls) ) ),
inference(nnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: int] :
( ord_less(int,bit0(X0),pls)
<=> ord_less(int,X0,pls) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X5: int] :
( ord_less(int,bit0(X5),pls)
<=> ord_less(int,X5,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_rel__simps_I10_J) ).
tff(f923,plain,
spl1_65,
inference(avatar_split_clause,[],[f538,f921]) ).
tff(f921,plain,
( spl1_65
<=> ! [X0: int] :
( ord_less(int,plus_plus(int,X0,X0),pls)
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_65])]) ).
tff(f538,plain,
! [X0: int] :
( ord_less(int,plus_plus(int,X0,X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(definition_unfolding,[],[f447,f375]) ).
tff(f447,plain,
! [X0: int] :
( ord_less(int,bit0(X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(cnf_transformation,[],[f295]) ).
tff(f919,plain,
spl1_64,
inference(avatar_split_clause,[],[f537,f917]) ).
tff(f537,plain,
! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,pls,plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f442,f375]) ).
tff(f442,plain,
! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,pls,bit0(X0)) ),
inference(cnf_transformation,[],[f293]) ).
tff(f293,plain,
! [X0: int] :
( ( ord_less(int,pls,bit0(X0))
| ~ ord_less(int,pls,X0) )
& ( ord_less(int,pls,X0)
| ~ ord_less(int,pls,bit0(X0)) ) ),
inference(nnf_transformation,[],[f176]) ).
tff(f176,plain,
! [X0: int] :
( ord_less(int,pls,bit0(X0))
<=> ord_less(int,pls,X0) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X5: int] :
( ord_less(int,pls,bit0(X5))
<=> ord_less(int,pls,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_rel__simps_I4_J) ).
tff(f915,plain,
spl1_63,
inference(avatar_split_clause,[],[f536,f913]) ).
tff(f913,plain,
( spl1_63
<=> ! [X0: int] :
( ord_less(int,pls,plus_plus(int,X0,X0))
| ~ ord_less(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_63])]) ).
tff(f536,plain,
! [X0: int] :
( ord_less(int,pls,plus_plus(int,X0,X0))
| ~ ord_less(int,pls,X0) ),
inference(definition_unfolding,[],[f443,f375]) ).
tff(f443,plain,
! [X0: int] :
( ord_less(int,pls,bit0(X0))
| ~ ord_less(int,pls,X0) ),
inference(cnf_transformation,[],[f293]) ).
tff(f911,plain,
spl1_62,
inference(avatar_split_clause,[],[f484,f909]) ).
tff(f909,plain,
( spl1_62
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_62])]) ).
tff(f484,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X0 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ),
inference(cnf_transformation,[],[f310]) ).
tff(f310,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,[],[f309]) ).
tff(f309,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,[],[f201]) ).
tff(f201,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = plus_plus(nat,X1,X0) )
<=> ( ( zero_zero(nat) = X0 )
& ( zero_zero(nat) = X1 ) ) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X12: nat,X21: nat] :
( ( zero_zero(nat) = plus_plus(nat,X21,X12) )
<=> ( ( zero_zero(nat) = X12 )
& ( zero_zero(nat) = X21 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add__is__0) ).
tff(f907,plain,
spl1_61,
inference(avatar_split_clause,[],[f483,f905]) ).
tff(f905,plain,
( spl1_61
<=> ! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_61])]) ).
tff(f483,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = X1 )
| ( zero_zero(nat) != plus_plus(nat,X1,X0) ) ),
inference(cnf_transformation,[],[f310]) ).
tff(f903,plain,
spl1_60,
inference(avatar_split_clause,[],[f460,f901]) ).
tff(f901,plain,
( spl1_60
<=> ! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_60])]) ).
tff(f460,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f255]) ).
tff(f255,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ),
inference(flattening,[],[f254]) ).
tff(f254,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ord_less(nat,X1,X0)
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: nat,X1: nat] :
( ( X0 != X1 )
=> ( ~ ord_less(nat,X1,X0)
=> ord_less(nat,X0,X1) ) ),
inference(rectify,[],[f68]) ).
tff(f68,axiom,
! [X22: nat,X16: nat] :
( ( X16 != X22 )
=> ( ~ ord_less(nat,X16,X22)
=> ord_less(nat,X22,X16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_linorder__neqE__nat) ).
tff(f899,plain,
spl1_59,
inference(avatar_split_clause,[],[f453,f897]) ).
tff(f897,plain,
( spl1_59
<=> ! [X0: int] :
( ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
| ~ ord_less(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_59])]) ).
tff(f453,plain,
! [X0: int] :
( ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
| ~ ord_less(int,pls,X0) ),
inference(cnf_transformation,[],[f298]) ).
tff(f298,plain,
! [X0: int] :
( ( ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
| ~ ord_less(int,pls,X0) )
& ( ord_less(int,pls,X0)
| ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0)) ) ),
inference(nnf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: int] :
( ord_less(nat,zero_zero(nat),number_number_of(nat,X0))
<=> ord_less(int,pls,X0) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X11: int] :
( ord_less(nat,zero_zero(nat),number_number_of(nat,X11))
<=> ord_less(int,pls,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_less__0__number__of) ).
tff(f895,plain,
spl1_58,
inference(avatar_split_clause,[],[f452,f893]) ).
tff(f452,plain,
! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(nat,zero_zero(nat),number_number_of(nat,X0)) ),
inference(cnf_transformation,[],[f298]) ).
tff(f886,plain,
spl1_57,
inference(avatar_split_clause,[],[f472,f884]) ).
tff(f884,plain,
( spl1_57
<=> ! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit1(X0))
| ~ ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_57])]) ).
tff(f472,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit1(X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f303]) ).
tff(f303,plain,
! [X0: int,X1: int] :
( ( ord_less(int,bit1(X1),bit1(X0))
| ~ ord_less(int,X1,X0) )
& ( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),bit1(X0)) ) ),
inference(nnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit1(X0))
<=> ord_less(int,X1,X0) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X13: int,X14: int] :
( ord_less(int,bit1(X14),bit1(X13))
<=> ord_less(int,X14,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_less__int__code_I16_J) ).
tff(f882,plain,
spl1_56,
inference(avatar_split_clause,[],[f471,f880]) ).
tff(f880,plain,
( spl1_56
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_56])]) ).
tff(f471,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f303]) ).
tff(f878,plain,
spl1_55,
inference(avatar_split_clause,[],[f403,f876]) ).
tff(f876,plain,
( spl1_55
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_55])]) ).
tff(f403,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 ) ),
inference(rectify,[],[f78]) ).
tff(f78,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X15: X0] : ( plus_plus(X0,number_number_of(X0,pls),X15) = X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_add__numeral__0) ).
tff(f874,plain,
spl1_54,
inference(avatar_split_clause,[],[f402,f872]) ).
tff(f872,plain,
( spl1_54
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_54])]) ).
tff(f402,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 ) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X15: X0] : ( plus_plus(X0,X15,number_number_of(X0,pls)) = X15 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_add__numeral__0__right) ).
tff(f865,plain,
spl1_53,
inference(avatar_split_clause,[],[f585,f863]) ).
tff(f863,plain,
( spl1_53
<=> ! [X1: nat] : ord_less(nat,zero_zero(nat),power_power(nat,X1,zero_zero(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_53])]) ).
tff(f585,plain,
! [X1: nat] : ord_less(nat,zero_zero(nat),power_power(nat,X1,zero_zero(nat))),
inference(equality_resolution,[],[f489]) ).
tff(f489,plain,
! [X0: nat,X1: nat] :
( ord_less(nat,zero_zero(nat),power_power(nat,X1,X0))
| ( zero_zero(nat) != X0 ) ),
inference(cnf_transformation,[],[f313]) ).
tff(f861,plain,
spl1_52,
inference(avatar_split_clause,[],[f584,f858]) ).
tff(f858,plain,
( spl1_52
<=> ( zero_zero(nat) = plus_plus(nat,zero_zero(nat),zero_zero(nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_52])]) ).
tff(f584,plain,
zero_zero(nat) = plus_plus(nat,zero_zero(nat),zero_zero(nat)),
inference(equality_resolution,[],[f583]) ).
tff(f583,plain,
! [X1: nat] :
( ( zero_zero(nat) = plus_plus(nat,X1,zero_zero(nat)) )
| ( zero_zero(nat) != X1 ) ),
inference(equality_resolution,[],[f485]) ).
tff(f485,plain,
! [X0: nat,X1: nat] :
( ( zero_zero(nat) = plus_plus(nat,X1,X0) )
| ( zero_zero(nat) != X0 )
| ( zero_zero(nat) != X1 ) ),
inference(cnf_transformation,[],[f310]) ).
tff(f856,plain,
spl1_51,
inference(avatar_split_clause,[],[f533,f854]) ).
tff(f854,plain,
( spl1_51
<=> ! [X0: int] :
( ( pls = X0 )
| ( pls != plus_plus(int,X0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_51])]) ).
tff(f533,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls != plus_plus(int,X0,X0) ) ),
inference(definition_unfolding,[],[f438,f375]) ).
tff(f438,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls != bit0(X0) ) ),
inference(cnf_transformation,[],[f291]) ).
tff(f291,plain,
! [X0: int] :
( ( ( pls = bit0(X0) )
| ( pls != X0 ) )
& ( ( pls = X0 )
| ( pls != bit0(X0) ) ) ),
inference(nnf_transformation,[],[f174]) ).
tff(f174,plain,
! [X0: int] :
( ( pls = bit0(X0) )
<=> ( pls = X0 ) ),
inference(rectify,[],[f23]) ).
tff(f23,axiom,
! [X5: int] :
( ( pls = bit0(X5) )
<=> ( pls = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_rel__simps_I44_J) ).
tff(f852,plain,
spl1_50,
inference(avatar_split_clause,[],[f445,f850]) ).
tff(f850,plain,
( spl1_50
<=> ! [X0: int] :
( ord_less(int,bit1(X0),pls)
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_50])]) ).
tff(f445,plain,
! [X0: int] :
( ord_less(int,bit1(X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(cnf_transformation,[],[f294]) ).
tff(f294,plain,
! [X0: int] :
( ( ord_less(int,bit1(X0),pls)
| ~ ord_less(int,X0,pls) )
& ( ord_less(int,X0,pls)
| ~ ord_less(int,bit1(X0),pls) ) ),
inference(nnf_transformation,[],[f177]) ).
tff(f177,plain,
! [X0: int] :
( ord_less(int,bit1(X0),pls)
<=> ord_less(int,X0,pls) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X5: int] :
( ord_less(int,bit1(X5),pls)
<=> ord_less(int,X5,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_rel__simps_I12_J) ).
tff(f848,plain,
spl1_49,
inference(avatar_split_clause,[],[f444,f846]) ).
tff(f846,plain,
( spl1_49
<=> ! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,bit1(X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_49])]) ).
tff(f444,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,bit1(X0),pls) ),
inference(cnf_transformation,[],[f294]) ).
tff(f844,plain,
spl1_48,
inference(avatar_split_clause,[],[f421,f842]) ).
tff(f421,plain,
! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ),
inference(cnf_transformation,[],[f241]) ).
tff(f241,plain,
! [X0: nat] :
( ord_less(nat,zero_zero(nat),X0)
| ( zero_zero(nat) = X0 ) ),
inference(ennf_transformation,[],[f166]) ).
tff(f166,plain,
! [X0: nat] :
( ( zero_zero(nat) != X0 )
=> ord_less(nat,zero_zero(nat),X0) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X17: nat] :
( ( zero_zero(nat) != X17 )
=> ord_less(nat,zero_zero(nat),X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_gr0I) ).
tff(f834,plain,
spl1_47,
inference(avatar_split_clause,[],[f505,f832]) ).
tff(f832,plain,
( spl1_47
<=> ! [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,[spl1_47])]) ).
tff(f505,plain,
! [X2: fun(nat,fun(nat,bool)),X0: nat,X1: nat] :
( ord_less(nat,X0,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f323]) ).
tff(f830,plain,
spl1_46,
inference(avatar_split_clause,[],[f467,f828]) ).
tff(f828,plain,
( spl1_46
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit1(X0) != bit1(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_46])]) ).
tff(f467,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit1(X0) != bit1(X1) ) ),
inference(cnf_transformation,[],[f301]) ).
tff(f301,plain,
! [X0: int,X1: int] :
( ( ( bit1(X0) = bit1(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( bit1(X0) != bit1(X1) ) ) ),
inference(nnf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: int,X1: int] :
( ( bit1(X0) = bit1(X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X6: int,X5: int] :
( ( bit1(X5) = bit1(X6) )
<=> ( X5 = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_rel__simps_I51_J) ).
tff(f826,plain,
spl1_45,
inference(avatar_split_clause,[],[f408,f824]) ).
tff(f824,plain,
( spl1_45
<=> ! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_45])]) ).
tff(f408,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f233]) ).
tff(f233,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f41]) ).
tff(f41,axiom,
! [X0: $tType] :
( number_semiring(X0)
=> ( zero_zero(X0) = number_number_of(X0,pls) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_semiring__numeral__0__eq__0) ).
tff(f822,plain,
spl1_44,
inference(avatar_split_clause,[],[f400,f820]) ).
tff(f820,plain,
( spl1_44
<=> ! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_44])]) ).
tff(f400,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f225]) ).
tff(f225,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( zero_zero(X0) = number_number_of(X0,pls) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_semiring__norm_I112_J) ).
tff(f816,plain,
spl1_43,
inference(avatar_split_clause,[],[f542,f814]) ).
tff(f814,plain,
( spl1_43
<=> ! [X0: int,X1: int] : ( bit1(X0) != plus_plus(int,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_43])]) ).
tff(f542,plain,
! [X0: int,X1: int] : ( bit1(X0) != plus_plus(int,X1,X1) ),
inference(definition_unfolding,[],[f454,f375]) ).
tff(f454,plain,
! [X0: int,X1: int] : ( bit1(X0) != bit0(X1) ),
inference(cnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: int,X1: int] : ( bit1(X0) != bit0(X1) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X9: int,X8: int] : ( bit1(X9) != bit0(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_rel__simps_I49_J) ).
tff(f812,plain,
spl1_42,
inference(avatar_split_clause,[],[f374,f810]) ).
tff(f374,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(cnf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X8: int] : ( plus_plus(int,pls,X8) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_add__Pls) ).
tff(f808,plain,
spl1_41,
inference(avatar_split_clause,[],[f373,f806]) ).
tff(f806,plain,
( spl1_41
<=> ! [X0: int] : ( plus_plus(int,X0,pls) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_41])]) ).
tff(f373,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(rectify,[],[f74]) ).
tff(f74,axiom,
! [X8: int] : ( plus_plus(int,X8,pls) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_add__Pls__right) ).
tff(f804,plain,
spl1_40,
inference(avatar_split_clause,[],[f361,f801]) ).
tff(f801,plain,
( spl1_40
<=> ( zero_zero(nat) = number_number_of(nat,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_40])]) ).
tff(f361,plain,
zero_zero(nat) = number_number_of(nat,pls),
inference(cnf_transformation,[],[f36]) ).
tff(f36,axiom,
zero_zero(nat) = number_number_of(nat,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_semiring__norm_I113_J) ).
tff(f799,plain,
spl1_39,
inference(avatar_split_clause,[],[f372,f797]) ).
tff(f372,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X8: int] : ( number_number_of(int,X8) = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_number__of__is__id) ).
tff(f795,plain,
spl1_38,
inference(avatar_split_clause,[],[f369,f793]) ).
tff(f793,plain,
( spl1_38
<=> ! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_38])]) ).
tff(f369,plain,
! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
inference(cnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: nat] : ~ ord_less(nat,X0,zero_zero(nat)),
inference(rectify,[],[f83]) ).
tff(f83,axiom,
! [X17: nat] : ~ ord_less(nat,X17,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_not__less0) ).
tff(f791,plain,
spl1_37,
inference(avatar_split_clause,[],[f359,f788]) ).
tff(f788,plain,
( spl1_37
<=> ord_less(nat,zero_zero(nat),n) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_37])]) ).
tff(f359,plain,
ord_less(nat,zero_zero(nat),n),
inference(cnf_transformation,[],[f18]) ).
tff(f18,axiom,
ord_less(nat,zero_zero(nat),n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_n0) ).
tff(f786,plain,
spl1_36,
inference(avatar_split_clause,[],[f358,f783]) ).
tff(f783,plain,
( spl1_36
<=> ord_less(nat,zero_zero(nat),tn) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_36])]) ).
tff(f358,plain,
ord_less(nat,zero_zero(nat),tn),
inference(cnf_transformation,[],[f14]) ).
tff(f14,axiom,
ord_less(nat,zero_zero(nat),tn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_tn0) ).
tff(f781,plain,
( ~ spl1_35
| spl1_30
| ~ spl1_32 ),
inference(avatar_split_clause,[],[f776,f764,f754,f778]) ).
tff(f754,plain,
( spl1_30
<=> ( v = zero_zero(int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_30])]) ).
tff(f776,plain,
( ( v != pls )
| spl1_30
| ~ spl1_32 ),
inference(superposition,[],[f756,f766]) ).
tff(f756,plain,
( ( v != zero_zero(int) )
| spl1_30 ),
inference(avatar_component_clause,[],[f754]) ).
tff(f775,plain,
spl1_34,
inference(avatar_split_clause,[],[f367,f773]) ).
tff(f773,plain,
( spl1_34
<=> ! [X0: nat] : ~ ord_less(nat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_34])]) ).
tff(f367,plain,
! [X0: nat] : ~ ord_less(nat,X0,X0),
inference(cnf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: nat] : ~ ord_less(nat,X0,X0),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X17: nat] : ~ ord_less(nat,X17,X17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_less__irrefl__nat) ).
tff(f771,plain,
spl1_33,
inference(avatar_split_clause,[],[f365,f769]) ).
tff(f769,plain,
( spl1_33
<=> ! [X0: int] : ( pls != bit1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_33])]) ).
tff(f365,plain,
! [X0: int] : ( pls != bit1(X0) ),
inference(cnf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: int] : ( pls != bit1(X0) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X8: int] : ( pls != bit1(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_rel__simps_I46_J) ).
tff(f767,plain,
spl1_32,
inference(avatar_split_clause,[],[f356,f764]) ).
tff(f762,plain,
~ spl1_31,
inference(avatar_split_clause,[],[f354,f759]) ).
tff(f759,plain,
( spl1_31
<=> ord_less(int,pls,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_31])]) ).
tff(f354,plain,
~ ord_less(int,pls,pls),
inference(cnf_transformation,[],[f28]) ).
tff(f28,axiom,
~ ord_less(int,pls,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_rel__simps_I2_J) ).
tff(f757,plain,
~ spl1_30,
inference(avatar_split_clause,[],[f353,f754]) ).
tff(f353,plain,
v != zero_zero(int),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
v != zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096v_A_126_061_A0_096) ).
tff(f752,plain,
( ~ spl1_29
| spl1_28 ),
inference(avatar_split_clause,[],[f747,f743,f749]) ).
tff(f743,plain,
( spl1_28
<=> ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).
tff(f747,plain,
( ~ ord_less(int,pls,power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| spl1_28 ),
inference(forward_demodulation,[],[f745,f356]) ).
tff(f745,plain,
( ~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls)))))
| spl1_28 ),
inference(avatar_component_clause,[],[f743]) ).
tff(f746,plain,
~ spl1_28,
inference(avatar_split_clause,[],[f513,f743]) ).
tff(f513,plain,
~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,plus_plus(int,bit1(pls),bit1(pls))))),
inference(definition_unfolding,[],[f325,f375]) ).
tff(f325,plain,
~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f129]) ).
tff(f129,plain,
~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
inference(flattening,[],[f128]) ).
tff(f128,negated_conjecture,
~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
inference(negated_conjecture,[],[f127]) ).
tff(f127,conjecture,
ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f741,plain,
spl1_27,
inference(avatar_split_clause,[],[f352,f738]) ).
tff(f738,plain,
( spl1_27
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_27])]) ).
tff(f352,plain,
pp(fTrue),
inference(cnf_transformation,[],[f126]) ).
tff(f126,axiom,
pp(fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f736,plain,
spl1_26,
inference(avatar_split_clause,[],[f351,f733]) ).
tff(f733,plain,
( spl1_26
<=> ordere236663937imp_le(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_26])]) ).
tff(f351,plain,
ordere236663937imp_le(nat),
inference(cnf_transformation,[],[f114]) ).
tff(f114,axiom,
ordere236663937imp_le(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
tff(f731,plain,
spl1_25,
inference(avatar_split_clause,[],[f350,f728]) ).
tff(f728,plain,
( spl1_25
<=> power(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_25])]) ).
tff(f350,plain,
power(nat),
inference(cnf_transformation,[],[f122]) ).
tff(f122,axiom,
power(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
tff(f726,plain,
spl1_24,
inference(avatar_split_clause,[],[f349,f723]) ).
tff(f723,plain,
( spl1_24
<=> mult_zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_24])]) ).
tff(f349,plain,
mult_zero(nat),
inference(cnf_transformation,[],[f121]) ).
tff(f121,axiom,
mult_zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
tff(f721,plain,
spl1_23,
inference(avatar_split_clause,[],[f348,f718]) ).
tff(f718,plain,
( spl1_23
<=> zero_neq_one(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_23])]) ).
tff(f348,plain,
zero_neq_one(nat),
inference(cnf_transformation,[],[f119]) ).
tff(f119,axiom,
zero_neq_one(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
tff(f716,plain,
spl1_22,
inference(avatar_split_clause,[],[f347,f713]) ).
tff(f713,plain,
( spl1_22
<=> no_zero_divisors(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_22])]) ).
tff(f347,plain,
no_zero_divisors(nat),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
no_zero_divisors(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
tff(f711,plain,
spl1_21,
inference(avatar_split_clause,[],[f346,f708]) ).
tff(f708,plain,
( spl1_21
<=> cancel_semigroup_add(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_21])]) ).
tff(f346,plain,
cancel_semigroup_add(nat),
inference(cnf_transformation,[],[f115]) ).
tff(f115,axiom,
cancel_semigroup_add(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
tff(f706,plain,
spl1_20,
inference(avatar_split_clause,[],[f345,f703]) ).
tff(f703,plain,
( spl1_20
<=> no_zero_divisors(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_20])]) ).
tff(f345,plain,
no_zero_divisors(int),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
no_zero_divisors(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
tff(f701,plain,
spl1_19,
inference(avatar_split_clause,[],[f344,f698]) ).
tff(f698,plain,
( spl1_19
<=> power(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).
tff(f344,plain,
power(int),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
power(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
tff(f696,plain,
spl1_18,
inference(avatar_split_clause,[],[f343,f693]) ).
tff(f693,plain,
( spl1_18
<=> cancel_semigroup_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
tff(f343,plain,
cancel_semigroup_add(int),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
cancel_semigroup_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
tff(f691,plain,
spl1_17,
inference(avatar_split_clause,[],[f342,f688]) ).
tff(f688,plain,
( spl1_17
<=> ordere236663937imp_le(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
tff(f342,plain,
ordere236663937imp_le(int),
inference(cnf_transformation,[],[f98]) ).
tff(f98,axiom,
ordere236663937imp_le(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
tff(f686,plain,
spl1_16,
inference(avatar_split_clause,[],[f341,f683]) ).
tff(f683,plain,
( spl1_16
<=> mult_zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
tff(f341,plain,
mult_zero(int),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
mult_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
tff(f681,plain,
spl1_15,
inference(avatar_split_clause,[],[f340,f678]) ).
tff(f678,plain,
( spl1_15
<=> zero_neq_one(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
tff(f340,plain,
zero_neq_one(int),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
zero_neq_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
tff(f676,plain,
spl1_14,
inference(avatar_split_clause,[],[f339,f673]) ).
tff(f673,plain,
( spl1_14
<=> number_semiring(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
tff(f339,plain,
number_semiring(nat),
inference(cnf_transformation,[],[f118]) ).
tff(f118,axiom,
number_semiring(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
tff(f671,plain,
spl1_13,
inference(avatar_split_clause,[],[f338,f668]) ).
tff(f668,plain,
( spl1_13
<=> linordered_semidom(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
tff(f338,plain,
linordered_semidom(nat),
inference(cnf_transformation,[],[f116]) ).
tff(f116,axiom,
linordered_semidom(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
tff(f666,plain,
spl1_12,
inference(avatar_split_clause,[],[f337,f663]) ).
tff(f663,plain,
( spl1_12
<=> semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
tff(f337,plain,
semiring_1(nat),
inference(cnf_transformation,[],[f120]) ).
tff(f120,axiom,
semiring_1(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
tff(f661,plain,
spl1_11,
inference(avatar_split_clause,[],[f336,f658]) ).
tff(f658,plain,
( spl1_11
<=> number(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
tff(f336,plain,
number(nat),
inference(cnf_transformation,[],[f124]) ).
tff(f124,axiom,
number(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
tff(f656,plain,
spl1_10,
inference(avatar_split_clause,[],[f335,f653]) ).
tff(f653,plain,
( spl1_10
<=> semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
tff(f335,plain,
semiring_1(int),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
tff(f651,plain,
spl1_9,
inference(avatar_split_clause,[],[f334,f648]) ).
tff(f648,plain,
( spl1_9
<=> number_semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
tff(f334,plain,
number_semiring(int),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
number_semiring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
tff(f646,plain,
spl1_8,
inference(avatar_split_clause,[],[f333,f643]) ).
tff(f643,plain,
( spl1_8
<=> number(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
tff(f333,plain,
number(int),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
number(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
tff(f641,plain,
spl1_7,
inference(avatar_split_clause,[],[f332,f638]) ).
tff(f638,plain,
( spl1_7
<=> linordered_semidom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
tff(f332,plain,
linordered_semidom(int),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
linordered_semidom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
tff(f636,plain,
spl1_6,
inference(avatar_split_clause,[],[f331,f633]) ).
tff(f331,plain,
number_ring(int),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
number_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f631,plain,
spl1_5,
inference(avatar_split_clause,[],[f330,f628]) ).
tff(f330,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
linordered_idom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
tff(f626,plain,
spl1_4,
inference(avatar_split_clause,[],[f329,f623]) ).
tff(f623,plain,
( spl1_4
<=> linord219039673up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
tff(f329,plain,
linord219039673up_add(int),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
linord219039673up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
tff(f621,plain,
spl1_3,
inference(avatar_split_clause,[],[f328,f618]) ).
tff(f618,plain,
( spl1_3
<=> ring_11004092258visors(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
tff(f328,plain,
ring_11004092258visors(int),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
tff(f616,plain,
spl1_2,
inference(avatar_split_clause,[],[f327,f613]) ).
tff(f613,plain,
( spl1_2
<=> ring_char_0(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
tff(f327,plain,
ring_char_0(int),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
ring_char_0(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
tff(f611,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f326,f608]) ).
tff(f608,plain,
( spl1_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
tff(f326,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f125]) ).
tff(f125,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUN015_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n020.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 18:54:53 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (10330)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (10333)WARNING: value z3 for option sas not known
% 0.14/0.39 % (10334)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 % (10331)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39 % (10336)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)
% 0.14/0.39 % (10332)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39 % (10333)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)
% 0.14/0.39 % (10337)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 % (10335)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)
% 0.14/0.39 % (10337)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.14/0.39 % Exception at run slice level% Exception at run slice level
% 0.14/0.39
% 0.14/0.39 User error: User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructsFinite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.14/0.39
% 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
% 0.21/0.41 % (10338)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.41 % (10339)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)
% 0.21/0.41 % (10340)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)
% 0.21/0.41 % (10338)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.41 % Exception at run slice level
% 0.21/0.41 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.41 % (10339)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.42 % (10335)First to succeed.
% 0.21/0.43 % (10341)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)
% 0.21/0.43 % (10335)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-10330"
% 0.21/0.43 % (10335)Refutation found. Thanks to Tanya!
% 0.21/0.43 % SZS status Theorem for theBenchmark
% 0.21/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.44 % (10335)------------------------------
% 0.21/0.44 % (10335)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.44 % (10335)Termination reason: Refutation
% 0.21/0.44
% 0.21/0.44 % (10335)Memory used [KB]: 1514
% 0.21/0.44 % (10335)Time elapsed: 0.047 s
% 0.21/0.44 % (10335)Instructions burned: 74 (million)
% 0.21/0.44 % (10330)Success in time 0.069 s
%------------------------------------------------------------------------------