TSTP Solution File: NUM957_5 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM957_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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 14:39:16 EDT 2024
% Result : Theorem 0.19s 0.42s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 252
% Syntax : Number of formulae : 794 ( 232 unt; 27 typ; 0 def)
% Number of atoms : 1951 ( 446 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 2092 ( 908 ~; 877 |; 49 &)
% ( 190 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 14 ( 10 >; 4 *; 0 +; 0 <<)
% Number of predicates : 149 ( 147 usr; 136 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-3 aty)
% Number of variables : 1038 (1023 !; 0 ?;1038 :)
% ( 15 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(func_def_0,type,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
bit0: int > int ).
tff(func_def_6,type,
bit1: int > int ).
tff(func_def_7,type,
pls: int ).
tff(func_def_8,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_9,type,
fFalse: bool ).
tff(func_def_10,type,
fTrue: bool ).
tff(func_def_11,type,
m: int ).
tff(func_def_12,type,
t: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semiring:
!>[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,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
zprime: int > $o ).
tff(pred_def_10,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_11,type,
twoSqu1567020053sum2sq: int > $o ).
tff(pred_def_12,type,
pp: bool > $o ).
tff(f1632,plain,
$false,
inference(avatar_sat_refutation,[],[f500,f505,f510,f515,f520,f525,f530,f535,f540,f545,f550,f555,f559,f563,f567,f571,f575,f579,f584,f588,f596,f600,f604,f608,f615,f623,f628,f633,f637,f641,f645,f649,f657,f669,f673,f677,f682,f686,f690,f705,f709,f714,f719,f723,f727,f731,f735,f739,f743,f755,f759,f764,f787,f791,f795,f799,f819,f825,f830,f834,f838,f842,f846,f850,f888,f898,f902,f906,f910,f914,f918,f922,f926,f930,f934,f986,f992,f997,f1002,f1007,f1011,f1015,f1019,f1023,f1027,f1031,f1098,f1103,f1108,f1115,f1119,f1123,f1128,f1132,f1136,f1149,f1153,f1192,f1196,f1200,f1204,f1208,f1214,f1237,f1242,f1247,f1252,f1373,f1378,f1382,f1386,f1404,f1412,f1426,f1431,f1437,f1441,f1446,f1468,f1473,f1534,f1538,f1542,f1546,f1563,f1573,f1578,f1584,f1589,f1600,f1604,f1608,f1612,f1616,f1625,f1631]) ).
tff(f1631,plain,
( spl0_121
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| ~ spl0_62
| ~ spl0_99
| ~ spl0_101
| ~ spl0_110
| ~ spl0_135 ),
inference(avatar_split_clause,[],[f1630,f1622,f1380,f1202,f1194,f840,f612,f573,f561,f527,f1527]) ).
tff(f1527,plain,
( spl0_121
<=> ord_less(int,minus_minus(int,bit1(plus_plus(int,m,m)),one_one(int)),t) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
tff(f527,plain,
( spl0_7
<=> number_semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
tff(f561,plain,
( spl0_14
<=> ! [X0: int] : ( number_number_of(int,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
tff(f573,plain,
( spl0_17
<=> ! [X0: int] : ( plus_plus(int,X0,pls) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
tff(f612,plain,
( spl0_25
<=> ( bit1(pls) = one_one(int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
tff(f840,plain,
( spl0_62
<=> ! [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,[spl0_62])]) ).
tff(f1194,plain,
( spl0_99
<=> ! [X2: int,X0: int,X1: int] : ( times_times(int,X2,plus_plus(int,X1,X0)) = plus_plus(int,times_times(int,X2,X1),times_times(int,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
tff(f1202,plain,
( spl0_101
<=> ! [X2: int,X0: int,X1: int] : ( times_times(int,plus_plus(int,X2,X1),X0) = plus_plus(int,times_times(int,X2,X0),times_times(int,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
tff(f1380,plain,
( spl0_110
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,plus_plus(int,one_one(int),one_one(int))),X1) )
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
tff(f1622,plain,
( spl0_135
<=> ord_less(int,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),one_one(int)),t) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
tff(f1630,plain,
( ord_less(int,minus_minus(int,bit1(plus_plus(int,m,m)),one_one(int)),t)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| ~ spl0_62
| ~ spl0_99
| ~ spl0_101
| ~ spl0_110
| ~ spl0_135 ),
inference(forward_demodulation,[],[f1629,f880]) ).
tff(f880,plain,
( ! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,X0,X0),one_one(int)) )
| ~ spl0_17
| ~ spl0_25
| ~ spl0_62 ),
inference(forward_demodulation,[],[f877,f574]) ).
tff(f574,plain,
( ! [X0: int] : ( plus_plus(int,X0,pls) = X0 )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f573]) ).
tff(f877,plain,
( ! [X0: int] : ( bit1(plus_plus(int,X0,pls)) = plus_plus(int,plus_plus(int,X0,X0),one_one(int)) )
| ~ spl0_25
| ~ spl0_62 ),
inference(superposition,[],[f841,f614]) ).
tff(f614,plain,
( ( bit1(pls) = one_one(int) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f612]) ).
tff(f841,plain,
( ! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,plus_plus(int,X1,X1),bit1(X0)) )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f840]) ).
tff(f1629,plain,
( ord_less(int,minus_minus(int,plus_plus(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),one_one(int)),one_one(int)),t)
| ~ spl0_7
| ~ spl0_14
| ~ spl0_25
| ~ spl0_99
| ~ spl0_101
| ~ spl0_110
| ~ spl0_135 ),
inference(forward_demodulation,[],[f1628,f1398]) ).
tff(f1398,plain,
( ! [X0: int] : ( plus_plus(int,X0,X0) = times_times(int,plus_plus(int,one_one(int),one_one(int)),X0) )
| ~ spl0_7
| ~ spl0_14
| ~ spl0_110 ),
inference(forward_demodulation,[],[f1397,f562]) ).
tff(f562,plain,
( ! [X0: int] : ( number_number_of(int,X0) = X0 )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f561]) ).
tff(f1397,plain,
( ! [X0: int] : ( plus_plus(int,X0,X0) = times_times(int,number_number_of(int,plus_plus(int,one_one(int),one_one(int))),X0) )
| ~ spl0_7
| ~ spl0_110 ),
inference(resolution,[],[f1381,f529]) ).
tff(f529,plain,
( number_semiring(int)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f527]) ).
tff(f1381,plain,
( ! [X0: $tType,X1: X0] :
( ~ number_semiring(X0)
| ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,plus_plus(int,one_one(int),one_one(int))),X1) ) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1380]) ).
tff(f1628,plain,
( ord_less(int,minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,m,m)),one_one(int)),one_one(int)),t)
| ~ spl0_14
| ~ spl0_25
| ~ spl0_99
| ~ spl0_101
| ~ spl0_135 ),
inference(forward_demodulation,[],[f1627,f614]) ).
tff(f1627,plain,
( ord_less(int,minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,m,m)),one_one(int)),one_one(int)),t)
| ~ spl0_14
| ~ spl0_99
| ~ spl0_101
| ~ spl0_135 ),
inference(forward_demodulation,[],[f1626,f1335]) ).
tff(f1335,plain,
( ! [X0: int,X1: int] : ( times_times(int,plus_plus(int,X0,X0),X1) = times_times(int,X0,plus_plus(int,X1,X1)) )
| ~ spl0_99
| ~ spl0_101 ),
inference(superposition,[],[f1203,f1195]) ).
tff(f1195,plain,
( ! [X2: int,X0: int,X1: int] : ( times_times(int,X2,plus_plus(int,X1,X0)) = plus_plus(int,times_times(int,X2,X1),times_times(int,X2,X0)) )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f1194]) ).
tff(f1203,plain,
( ! [X2: int,X0: int,X1: int] : ( times_times(int,plus_plus(int,X2,X1),X0) = plus_plus(int,times_times(int,X2,X0),times_times(int,X1,X0)) )
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f1202]) ).
tff(f1626,plain,
( ord_less(int,minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))),m),one_one(int)),one_one(int)),t)
| ~ spl0_14
| ~ spl0_135 ),
inference(forward_demodulation,[],[f1624,f562]) ).
tff(f1624,plain,
( ord_less(int,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),one_one(int)),t)
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1622]) ).
tff(f1625,plain,
spl0_135,
inference(avatar_split_clause,[],[f414,f1622]) ).
tff(f414,plain,
ord_less(int,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),one_one(int)),t),
inference(definition_unfolding,[],[f290,f298,f298]) ).
tff(f298,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(cnf_transformation,[],[f119]) ).
tff(f119,plain,
! [X0: int] : ( bit0(X0) = plus_plus(int,X0,X0) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X6: int] : ( bit0(X6) = plus_plus(int,X6,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Bit0__def) ).
tff(f290,plain,
ord_less(int,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),t),
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
ord_less(int,minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int)),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__0964_A_K_Am_A_L_A1_A_N_A1_A_060_At_096) ).
tff(f1616,plain,
spl0_134,
inference(avatar_split_clause,[],[f336,f1614]) ).
tff(f1614,plain,
( spl0_134
<=> ! [X0: $tType,X3: X0,X2: X0,X1: int] :
( ( times_times(X0,plus_plus(X0,X3,X2),number_number_of(X0,X1)) = plus_plus(X0,times_times(X0,X3,number_number_of(X0,X1)),times_times(X0,X2,number_number_of(X0,X1))) )
| ~ semiring(X0)
| ~ number(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
tff(f336,plain,
! [X0: $tType,X2: X0,X3: X0,X1: int] :
( ( times_times(X0,plus_plus(X0,X3,X2),number_number_of(X0,X1)) = plus_plus(X0,times_times(X0,X3,number_number_of(X0,X1)),times_times(X0,X2,number_number_of(X0,X1))) )
| ~ semiring(X0)
| ~ number(X0) ),
inference(cnf_transformation,[],[f221]) ).
tff(f221,plain,
! [X0: $tType] :
( ! [X1: int,X2: X0,X3: X0] : ( times_times(X0,plus_plus(X0,X3,X2),number_number_of(X0,X1)) = plus_plus(X0,times_times(X0,X3,number_number_of(X0,X1)),times_times(X0,X2,number_number_of(X0,X1))) )
| ~ semiring(X0)
| ~ number(X0) ),
inference(flattening,[],[f220]) ).
tff(f220,plain,
! [X0: $tType] :
( ! [X1: int,X2: X0,X3: X0] : ( times_times(X0,plus_plus(X0,X3,X2),number_number_of(X0,X1)) = plus_plus(X0,times_times(X0,X3,number_number_of(X0,X1)),times_times(X0,X2,number_number_of(X0,X1))) )
| ~ semiring(X0)
| ~ number(X0) ),
inference(ennf_transformation,[],[f140]) ).
tff(f140,plain,
! [X0: $tType] :
( ( semiring(X0)
& number(X0) )
=> ! [X1: int,X2: X0,X3: X0] : ( times_times(X0,plus_plus(X0,X3,X2),number_number_of(X0,X1)) = plus_plus(X0,times_times(X0,X3,number_number_of(X0,X1)),times_times(X0,X2,number_number_of(X0,X1))) ) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X10: $tType] :
( ( semiring(X10)
& number(X10) )
=> ! [X2: int,X11: X10,X12: X10] : ( times_times(X10,plus_plus(X10,X12,X11),number_number_of(X10,X2)) = plus_plus(X10,times_times(X10,X12,number_number_of(X10,X2)),times_times(X10,X11,number_number_of(X10,X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_left__distrib__number__of) ).
tff(f1612,plain,
spl0_133,
inference(avatar_split_clause,[],[f335,f1610]) ).
tff(f1610,plain,
( spl0_133
<=> ! [X0: $tType,X3: X0,X2: X0,X1: int] :
( ( times_times(X0,minus_minus(X0,X3,X2),number_number_of(X0,X1)) = minus_minus(X0,times_times(X0,X3,number_number_of(X0,X1)),times_times(X0,X2,number_number_of(X0,X1))) )
| ~ ring(X0)
| ~ number(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
tff(f335,plain,
! [X0: $tType,X2: X0,X3: X0,X1: int] :
( ( times_times(X0,minus_minus(X0,X3,X2),number_number_of(X0,X1)) = minus_minus(X0,times_times(X0,X3,number_number_of(X0,X1)),times_times(X0,X2,number_number_of(X0,X1))) )
| ~ ring(X0)
| ~ number(X0) ),
inference(cnf_transformation,[],[f219]) ).
tff(f219,plain,
! [X0: $tType] :
( ! [X1: int,X2: X0,X3: X0] : ( times_times(X0,minus_minus(X0,X3,X2),number_number_of(X0,X1)) = minus_minus(X0,times_times(X0,X3,number_number_of(X0,X1)),times_times(X0,X2,number_number_of(X0,X1))) )
| ~ ring(X0)
| ~ number(X0) ),
inference(flattening,[],[f218]) ).
tff(f218,plain,
! [X0: $tType] :
( ! [X1: int,X2: X0,X3: X0] : ( times_times(X0,minus_minus(X0,X3,X2),number_number_of(X0,X1)) = minus_minus(X0,times_times(X0,X3,number_number_of(X0,X1)),times_times(X0,X2,number_number_of(X0,X1))) )
| ~ ring(X0)
| ~ number(X0) ),
inference(ennf_transformation,[],[f139]) ).
tff(f139,plain,
! [X0: $tType] :
( ( ring(X0)
& number(X0) )
=> ! [X1: int,X2: X0,X3: X0] : ( times_times(X0,minus_minus(X0,X3,X2),number_number_of(X0,X1)) = minus_minus(X0,times_times(X0,X3,number_number_of(X0,X1)),times_times(X0,X2,number_number_of(X0,X1))) ) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X10: $tType] :
( ( ring(X10)
& number(X10) )
=> ! [X2: int,X11: X10,X12: X10] : ( times_times(X10,minus_minus(X10,X12,X11),number_number_of(X10,X2)) = minus_minus(X10,times_times(X10,X12,number_number_of(X10,X2)),times_times(X10,X11,number_number_of(X10,X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_left__diff__distrib__number__of) ).
tff(f1608,plain,
spl0_132,
inference(avatar_split_clause,[],[f334,f1606]) ).
tff(f1606,plain,
( spl0_132
<=> ! [X0: $tType,X3: int,X2: X0,X1: X0] :
( ( times_times(X0,number_number_of(X0,X3),plus_plus(X0,X2,X1)) = plus_plus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) )
| ~ semiring(X0)
| ~ number(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
tff(f334,plain,
! [X0: $tType,X2: X0,X3: int,X1: X0] :
( ( times_times(X0,number_number_of(X0,X3),plus_plus(X0,X2,X1)) = plus_plus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) )
| ~ semiring(X0)
| ~ number(X0) ),
inference(cnf_transformation,[],[f217]) ).
tff(f217,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: int] : ( times_times(X0,number_number_of(X0,X3),plus_plus(X0,X2,X1)) = plus_plus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) )
| ~ semiring(X0)
| ~ number(X0) ),
inference(flattening,[],[f216]) ).
tff(f216,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: int] : ( times_times(X0,number_number_of(X0,X3),plus_plus(X0,X2,X1)) = plus_plus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) )
| ~ semiring(X0)
| ~ number(X0) ),
inference(ennf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: $tType] :
( ( semiring(X0)
& number(X0) )
=> ! [X1: X0,X2: X0,X3: int] : ( times_times(X0,number_number_of(X0,X3),plus_plus(X0,X2,X1)) = plus_plus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) ) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X10: $tType] :
( ( semiring(X10)
& number(X10) )
=> ! [X13: X10,X11: X10,X2: int] : ( times_times(X10,number_number_of(X10,X2),plus_plus(X10,X11,X13)) = plus_plus(X10,times_times(X10,number_number_of(X10,X2),X11),times_times(X10,number_number_of(X10,X2),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_right__distrib__number__of) ).
tff(f1604,plain,
spl0_131,
inference(avatar_split_clause,[],[f333,f1602]) ).
tff(f1602,plain,
( spl0_131
<=> ! [X0: $tType,X3: int,X2: X0,X1: X0] :
( ( times_times(X0,number_number_of(X0,X3),minus_minus(X0,X2,X1)) = minus_minus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) )
| ~ ring(X0)
| ~ number(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
tff(f333,plain,
! [X0: $tType,X2: X0,X3: int,X1: X0] :
( ( times_times(X0,number_number_of(X0,X3),minus_minus(X0,X2,X1)) = minus_minus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) )
| ~ ring(X0)
| ~ number(X0) ),
inference(cnf_transformation,[],[f215]) ).
tff(f215,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: int] : ( times_times(X0,number_number_of(X0,X3),minus_minus(X0,X2,X1)) = minus_minus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) )
| ~ ring(X0)
| ~ number(X0) ),
inference(flattening,[],[f214]) ).
tff(f214,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: int] : ( times_times(X0,number_number_of(X0,X3),minus_minus(X0,X2,X1)) = minus_minus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) )
| ~ ring(X0)
| ~ number(X0) ),
inference(ennf_transformation,[],[f137]) ).
tff(f137,plain,
! [X0: $tType] :
( ( ring(X0)
& number(X0) )
=> ! [X1: X0,X2: X0,X3: int] : ( times_times(X0,number_number_of(X0,X3),minus_minus(X0,X2,X1)) = minus_minus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) ) ),
inference(rectify,[],[f40]) ).
tff(f40,axiom,
! [X10: $tType] :
( ( ring(X10)
& number(X10) )
=> ! [X13: X10,X11: X10,X2: int] : ( times_times(X10,number_number_of(X10,X2),minus_minus(X10,X11,X13)) = minus_minus(X10,times_times(X10,number_number_of(X10,X2),X11),times_times(X10,number_number_of(X10,X2),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_right__diff__distrib__number__of) ).
tff(f1600,plain,
( spl0_130
| ~ spl0_10
| ~ spl0_14
| ~ spl0_25
| ~ spl0_75
| ~ spl0_99
| ~ spl0_101
| ~ spl0_123
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1595,f1586,f1536,f1202,f1194,f932,f612,f561,f542,f1597]) ).
tff(f1597,plain,
( spl0_130
<=> twoSqu1567020053sum2sq(plus_plus(int,times_times(int,plus_plus(int,one_one(int),one_one(int)),times_times(int,m,plus_plus(int,t,t))),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
tff(f542,plain,
( spl0_10
<=> number_ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
tff(f932,plain,
( spl0_75
<=> ! [X0: int] : ( times_times(int,one_one(int),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
tff(f1536,plain,
( spl0_123
<=> ! [X0: $tType,X3: int,X2: int,X1: X0] :
( ( times_times(X0,number_number_of(X0,X3),times_times(X0,number_number_of(X0,X2),X1)) = times_times(X0,number_number_of(X0,times_times(int,X3,X2)),X1) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
tff(f1586,plain,
( spl0_129
<=> twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
tff(f1595,plain,
( twoSqu1567020053sum2sq(plus_plus(int,times_times(int,plus_plus(int,one_one(int),one_one(int)),times_times(int,m,plus_plus(int,t,t))),t))
| ~ spl0_10
| ~ spl0_14
| ~ spl0_25
| ~ spl0_75
| ~ spl0_99
| ~ spl0_101
| ~ spl0_123
| ~ spl0_129 ),
inference(forward_demodulation,[],[f1594,f614]) ).
tff(f1594,plain,
( twoSqu1567020053sum2sq(plus_plus(int,times_times(int,plus_plus(int,bit1(pls),bit1(pls)),times_times(int,m,plus_plus(int,t,t))),t))
| ~ spl0_10
| ~ spl0_14
| ~ spl0_75
| ~ spl0_99
| ~ spl0_101
| ~ spl0_123
| ~ spl0_129 ),
inference(forward_demodulation,[],[f1593,f1195]) ).
tff(f1593,plain,
( twoSqu1567020053sum2sq(plus_plus(int,times_times(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,times_times(int,m,t),times_times(int,m,t))),t))
| ~ spl0_10
| ~ spl0_14
| ~ spl0_75
| ~ spl0_99
| ~ spl0_101
| ~ spl0_123
| ~ spl0_129 ),
inference(forward_demodulation,[],[f1592,f1335]) ).
tff(f1592,plain,
( twoSqu1567020053sum2sq(plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))),times_times(int,m,t)),t))
| ~ spl0_10
| ~ spl0_14
| ~ spl0_75
| ~ spl0_101
| ~ spl0_123
| ~ spl0_129 ),
inference(forward_demodulation,[],[f1591,f562]) ).
tff(f1591,plain,
( twoSqu1567020053sum2sq(plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),times_times(int,m,t)),t))
| ~ spl0_10
| ~ spl0_14
| ~ spl0_75
| ~ spl0_101
| ~ spl0_123
| ~ spl0_129 ),
inference(forward_demodulation,[],[f1590,f1550]) ).
tff(f1550,plain,
( ! [X2: int,X0: int,X1: int] : ( times_times(int,times_times(int,X0,X1),X2) = times_times(int,X0,times_times(int,X1,X2)) )
| ~ spl0_10
| ~ spl0_14
| ~ spl0_123 ),
inference(forward_demodulation,[],[f1549,f562]) ).
tff(f1549,plain,
( ! [X2: int,X0: int,X1: int] : ( times_times(int,times_times(int,X0,X1),X2) = times_times(int,number_number_of(int,X0),times_times(int,X1,X2)) )
| ~ spl0_10
| ~ spl0_14
| ~ spl0_123 ),
inference(forward_demodulation,[],[f1548,f562]) ).
tff(f1548,plain,
( ! [X2: int,X0: int,X1: int] : ( times_times(int,number_number_of(int,X0),times_times(int,number_number_of(int,X1),X2)) = times_times(int,times_times(int,X0,X1),X2) )
| ~ spl0_10
| ~ spl0_14
| ~ spl0_123 ),
inference(forward_demodulation,[],[f1547,f562]) ).
tff(f1547,plain,
( ! [X2: int,X0: int,X1: int] : ( times_times(int,number_number_of(int,X0),times_times(int,number_number_of(int,X1),X2)) = times_times(int,number_number_of(int,times_times(int,X0,X1)),X2) )
| ~ spl0_10
| ~ spl0_123 ),
inference(resolution,[],[f1537,f544]) ).
tff(f544,plain,
( number_ring(int)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f542]) ).
tff(f1537,plain,
( ! [X0: $tType,X2: int,X3: int,X1: X0] :
( ~ number_ring(X0)
| ( times_times(X0,number_number_of(X0,X3),times_times(X0,number_number_of(X0,X2),X1)) = times_times(X0,number_number_of(X0,times_times(int,X3,X2)),X1) ) )
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1536]) ).
tff(f1590,plain,
( twoSqu1567020053sum2sq(plus_plus(int,times_times(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),t),t))
| ~ spl0_75
| ~ spl0_101
| ~ spl0_129 ),
inference(forward_demodulation,[],[f1588,f1334]) ).
tff(f1334,plain,
( ! [X0: int,X1: int] : ( times_times(int,plus_plus(int,X1,one_one(int)),X0) = plus_plus(int,times_times(int,X1,X0),X0) )
| ~ spl0_75
| ~ spl0_101 ),
inference(superposition,[],[f1203,f933]) ).
tff(f933,plain,
( ! [X0: int] : ( times_times(int,one_one(int),X0) = X0 )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f932]) ).
tff(f1588,plain,
( twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),t))
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1586]) ).
tff(f1589,plain,
spl0_129,
inference(avatar_split_clause,[],[f412,f1586]) ).
tff(f412,plain,
twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),t)),
inference(definition_unfolding,[],[f288,f298,f298]) ).
tff(f288,plain,
twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
twoSqu1567020053sum2sq(times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_qf1pt) ).
tff(f1584,plain,
( spl0_122
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| ~ spl0_62
| ~ spl0_99
| ~ spl0_101
| ~ spl0_110
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1583,f1575,f1380,f1202,f1194,f840,f612,f573,f561,f527,f1531]) ).
tff(f1531,plain,
( spl0_122
<=> ord_less(int,pls,bit1(plus_plus(int,m,m))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
tff(f1575,plain,
( spl0_128
<=> ord_less(int,pls,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
tff(f1583,plain,
( ord_less(int,pls,bit1(plus_plus(int,m,m)))
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| ~ spl0_62
| ~ spl0_99
| ~ spl0_101
| ~ spl0_110
| ~ spl0_128 ),
inference(forward_demodulation,[],[f1582,f880]) ).
tff(f1582,plain,
( ord_less(int,pls,plus_plus(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),one_one(int)))
| ~ spl0_7
| ~ spl0_14
| ~ spl0_25
| ~ spl0_99
| ~ spl0_101
| ~ spl0_110
| ~ spl0_128 ),
inference(forward_demodulation,[],[f1581,f1398]) ).
tff(f1581,plain,
( ord_less(int,pls,plus_plus(int,times_times(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,m,m)),one_one(int)))
| ~ spl0_14
| ~ spl0_25
| ~ spl0_99
| ~ spl0_101
| ~ spl0_128 ),
inference(forward_demodulation,[],[f1580,f614]) ).
tff(f1580,plain,
( ord_less(int,pls,plus_plus(int,times_times(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,m,m)),one_one(int)))
| ~ spl0_14
| ~ spl0_99
| ~ spl0_101
| ~ spl0_128 ),
inference(forward_demodulation,[],[f1579,f1335]) ).
tff(f1579,plain,
( ord_less(int,pls,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))),m),one_one(int)))
| ~ spl0_14
| ~ spl0_128 ),
inference(forward_demodulation,[],[f1577,f562]) ).
tff(f1577,plain,
( ord_less(int,pls,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)))
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1575]) ).
tff(f1578,plain,
spl0_128,
inference(avatar_split_clause,[],[f465,f1575]) ).
tff(f465,plain,
ord_less(int,pls,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int))),
inference(forward_demodulation,[],[f413,f283]) ).
tff(f283,plain,
zero_zero(int) = pls,
inference(cnf_transformation,[],[f52]) ).
tff(f52,axiom,
zero_zero(int) = pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_Pls__def) ).
tff(f413,plain,
ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int))),
inference(definition_unfolding,[],[f289,f298,f298]) ).
tff(f289,plain,
ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
ord_less(int,zero_zero(int),plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_p0) ).
tff(f1573,plain,
( ~ spl0_127
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| ~ spl0_62
| ~ spl0_99
| ~ spl0_101
| ~ spl0_110
| spl0_126 ),
inference(avatar_split_clause,[],[f1568,f1560,f1380,f1202,f1194,f840,f612,f573,f561,f527,f1570]) ).
tff(f1570,plain,
( spl0_127
<=> ord_less(int,t,bit1(plus_plus(int,m,m))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
tff(f1560,plain,
( spl0_126
<=> ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
tff(f1568,plain,
( ~ ord_less(int,t,bit1(plus_plus(int,m,m)))
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| ~ spl0_62
| ~ spl0_99
| ~ spl0_101
| ~ spl0_110
| spl0_126 ),
inference(forward_demodulation,[],[f1567,f880]) ).
tff(f1567,plain,
( ~ ord_less(int,t,plus_plus(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),one_one(int)))
| ~ spl0_7
| ~ spl0_14
| ~ spl0_25
| ~ spl0_99
| ~ spl0_101
| ~ spl0_110
| spl0_126 ),
inference(forward_demodulation,[],[f1566,f1398]) ).
tff(f1566,plain,
( ~ ord_less(int,t,plus_plus(int,times_times(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,m,m)),one_one(int)))
| ~ spl0_14
| ~ spl0_25
| ~ spl0_99
| ~ spl0_101
| spl0_126 ),
inference(forward_demodulation,[],[f1565,f614]) ).
tff(f1565,plain,
( ~ ord_less(int,t,plus_plus(int,times_times(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,m,m)),one_one(int)))
| ~ spl0_14
| ~ spl0_99
| ~ spl0_101
| spl0_126 ),
inference(forward_demodulation,[],[f1564,f1335]) ).
tff(f1564,plain,
( ~ ord_less(int,t,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))),m),one_one(int)))
| ~ spl0_14
| spl0_126 ),
inference(forward_demodulation,[],[f1562,f562]) ).
tff(f1562,plain,
( ~ ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)))
| spl0_126 ),
inference(avatar_component_clause,[],[f1560]) ).
tff(f1563,plain,
~ spl0_126,
inference(avatar_split_clause,[],[f411,f1560]) ).
tff(f411,plain,
~ ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int))),
inference(definition_unfolding,[],[f287,f298,f298]) ).
tff(f287,plain,
~ ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
~ ord_less(int,t,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096_126_At_A_060_A4_A_K_Am_A_L_A1_096) ).
tff(f1546,plain,
spl0_125,
inference(avatar_split_clause,[],[f332,f1544]) ).
tff(f1544,plain,
( spl0_125
<=> ! [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,[spl0_125])]) ).
tff(f332,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,[],[f213]) ).
tff(f213,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,[],[f136]) ).
tff(f136,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,[],[f44]) ).
tff(f44,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X14: X0,X1: int,X2: int] : ( plus_plus(X0,number_number_of(X0,X2),plus_plus(X0,number_number_of(X0,X1),X14)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X2,X1)),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_add__number__of__left) ).
tff(f1542,plain,
spl0_124,
inference(avatar_split_clause,[],[f331,f1540]) ).
tff(f1540,plain,
( spl0_124
<=> ! [X0: $tType,X3: int,X2: int,X1: X0] :
( ( plus_plus(X0,number_number_of(X0,X3),minus_minus(X0,number_number_of(X0,X2),X1)) = minus_minus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
tff(f331,plain,
! [X0: $tType,X2: int,X3: int,X1: X0] :
( ( plus_plus(X0,number_number_of(X0,X3),minus_minus(X0,number_number_of(X0,X2),X1)) = minus_minus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: $tType] :
( ! [X1: X0,X2: int,X3: int] : ( plus_plus(X0,number_number_of(X0,X3),minus_minus(X0,number_number_of(X0,X2),X1)) = minus_minus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f135]) ).
tff(f135,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0,X2: int,X3: int] : ( plus_plus(X0,number_number_of(X0,X3),minus_minus(X0,number_number_of(X0,X2),X1)) = minus_minus(X0,number_number_of(X0,plus_plus(int,X3,X2)),X1) ) ),
inference(rectify,[],[f93]) ).
tff(f93,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X13: X0,X1: int,X2: int] : ( plus_plus(X0,number_number_of(X0,X2),minus_minus(X0,number_number_of(X0,X1),X13)) = minus_minus(X0,number_number_of(X0,plus_plus(int,X2,X1)),X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_add__number__of__diff1) ).
tff(f1538,plain,
spl0_123,
inference(avatar_split_clause,[],[f330,f1536]) ).
tff(f330,plain,
! [X0: $tType,X2: int,X3: int,X1: X0] :
( ( times_times(X0,number_number_of(X0,X3),times_times(X0,number_number_of(X0,X2),X1)) = times_times(X0,number_number_of(X0,times_times(int,X3,X2)),X1) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f211]) ).
tff(f211,plain,
! [X0: $tType] :
( ! [X1: X0,X2: int,X3: int] : ( times_times(X0,number_number_of(X0,X3),times_times(X0,number_number_of(X0,X2),X1)) = times_times(X0,number_number_of(X0,times_times(int,X3,X2)),X1) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0,X2: int,X3: int] : ( times_times(X0,number_number_of(X0,X3),times_times(X0,number_number_of(X0,X2),X1)) = times_times(X0,number_number_of(X0,times_times(int,X3,X2)),X1) ) ),
inference(rectify,[],[f42]) ).
tff(f42,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X14: X0,X1: int,X2: int] : ( times_times(X0,number_number_of(X0,X2),times_times(X0,number_number_of(X0,X1),X14)) = times_times(X0,number_number_of(X0,times_times(int,X2,X1)),X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_mult__number__of__left) ).
tff(f1534,plain,
( ~ spl0_121
| ~ spl0_122
| ~ spl0_107
| spl0_114 ),
inference(avatar_split_clause,[],[f1427,f1423,f1250,f1531,f1527]) ).
tff(f1250,plain,
( spl0_107
<=> ! [X2: int,X0: int,X1: int] :
( ~ ord_less(int,pls,X0)
| ord_less(int,times_times(int,X0,X2),times_times(int,X0,X1))
| ~ ord_less(int,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
tff(f1423,plain,
( spl0_114
<=> ord_less(int,times_times(int,bit1(plus_plus(int,m,m)),minus_minus(int,bit1(plus_plus(int,m,m)),one_one(int))),times_times(int,bit1(plus_plus(int,m,m)),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
tff(f1427,plain,
( ~ ord_less(int,pls,bit1(plus_plus(int,m,m)))
| ~ ord_less(int,minus_minus(int,bit1(plus_plus(int,m,m)),one_one(int)),t)
| ~ spl0_107
| spl0_114 ),
inference(resolution,[],[f1425,f1251]) ).
tff(f1251,plain,
( ! [X2: int,X0: int,X1: int] :
( ord_less(int,times_times(int,X0,X2),times_times(int,X0,X1))
| ~ ord_less(int,pls,X0)
| ~ ord_less(int,X2,X1) )
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1250]) ).
tff(f1425,plain,
( ~ ord_less(int,times_times(int,bit1(plus_plus(int,m,m)),minus_minus(int,bit1(plus_plus(int,m,m)),one_one(int))),times_times(int,bit1(plus_plus(int,m,m)),t))
| spl0_114 ),
inference(avatar_component_clause,[],[f1423]) ).
tff(f1473,plain,
( spl0_120
| ~ spl0_16
| ~ spl0_25
| ~ spl0_93
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1469,f1466,f1126,f612,f569,f1471]) ).
tff(f1471,plain,
( spl0_120
<=> ! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) = minus_minus(int,bit1(plus_plus(int,X1,X0)),one_one(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
tff(f569,plain,
( spl0_16
<=> ! [X0: int] : ( minus_minus(int,X0,pls) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
tff(f1126,plain,
( spl0_93
<=> ! [X0: int,X1: int] : ( minus_minus(int,bit1(X1),bit1(X0)) = plus_plus(int,minus_minus(int,X1,X0),minus_minus(int,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
tff(f1466,plain,
( spl0_119
<=> ! [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,[spl0_119])]) ).
tff(f1469,plain,
( ! [X0: int,X1: int] : ( plus_plus(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) = minus_minus(int,bit1(plus_plus(int,X1,X0)),one_one(int)) )
| ~ spl0_16
| ~ spl0_25
| ~ spl0_93
| ~ spl0_119 ),
inference(forward_demodulation,[],[f1467,f1177]) ).
tff(f1177,plain,
( ! [X0: int] : ( plus_plus(int,X0,X0) = minus_minus(int,bit1(X0),one_one(int)) )
| ~ spl0_16
| ~ spl0_25
| ~ spl0_93 ),
inference(forward_demodulation,[],[f1154,f614]) ).
tff(f1154,plain,
( ! [X0: int] : ( plus_plus(int,X0,X0) = minus_minus(int,bit1(X0),bit1(pls)) )
| ~ spl0_16
| ~ spl0_93 ),
inference(superposition,[],[f1127,f570]) ).
tff(f570,plain,
( ! [X0: int] : ( minus_minus(int,X0,pls) = X0 )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f569]) ).
tff(f1127,plain,
( ! [X0: int,X1: int] : ( minus_minus(int,bit1(X1),bit1(X0)) = plus_plus(int,minus_minus(int,X1,X0),minus_minus(int,X1,X0)) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1126]) ).
tff(f1467,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)) )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1466]) ).
tff(f1468,plain,
spl0_119,
inference(avatar_split_clause,[],[f440,f1466]) ).
tff(f440,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,[],[f373,f298,f298,f298]) ).
tff(f373,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f163]) ).
tff(f163,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
inference(rectify,[],[f34]) ).
tff(f34,axiom,
! [X5: int,X6: int] : ( plus_plus(int,bit0(X6),bit0(X5)) = bit0(plus_plus(int,X6,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_add__Bit0__Bit0) ).
tff(f1446,plain,
( spl0_118
| ~ spl0_93
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1442,f1439,f1126,f1444]) ).
tff(f1444,plain,
( spl0_118
<=> ! [X0: int,X1: int] : ( minus_minus(int,bit1(X1),bit1(X0)) = minus_minus(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
tff(f1439,plain,
( spl0_117
<=> ! [X0: int,X1: int] : ( plus_plus(int,minus_minus(int,X1,X0),minus_minus(int,X1,X0)) = minus_minus(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
tff(f1442,plain,
( ! [X0: int,X1: int] : ( minus_minus(int,bit1(X1),bit1(X0)) = minus_minus(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) )
| ~ spl0_93
| ~ spl0_117 ),
inference(forward_demodulation,[],[f1440,f1127]) ).
tff(f1440,plain,
( ! [X0: int,X1: int] : ( plus_plus(int,minus_minus(int,X1,X0),minus_minus(int,X1,X0)) = minus_minus(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f1439]) ).
tff(f1441,plain,
spl0_117,
inference(avatar_split_clause,[],[f436,f1439]) ).
tff(f436,plain,
! [X0: int,X1: int] : ( plus_plus(int,minus_minus(int,X1,X0),minus_minus(int,X1,X0)) = minus_minus(int,plus_plus(int,X1,X1),plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f369,f298,f298,f298]) ).
tff(f369,plain,
! [X0: int,X1: int] : ( bit0(minus_minus(int,X1,X0)) = minus_minus(int,bit0(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f159]) ).
tff(f159,plain,
! [X0: int,X1: int] : ( bit0(minus_minus(int,X1,X0)) = minus_minus(int,bit0(X1),bit0(X0)) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X5: int,X6: int] : ( bit0(minus_minus(int,X6,X5)) = minus_minus(int,bit0(X6),bit0(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_diff__bin__simps_I7_J) ).
tff(f1437,plain,
spl0_116,
inference(avatar_split_clause,[],[f421,f1435]) ).
tff(f1435,plain,
( spl0_116
<=> ! [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,[spl0_116])]) ).
tff(f421,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,[],[f324,f298]) ).
tff(f324,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,[],[f205]) ).
tff(f205,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,[],[f65]) ).
tff(f65,axiom,
! [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)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_number__of__Bit0) ).
tff(f1431,plain,
spl0_115,
inference(avatar_split_clause,[],[f420,f1429]) ).
tff(f1429,plain,
( spl0_115
<=> ! [X0: $tType,X1: int] :
( ( times_times(X0,plus_plus(X0,one_one(X0),one_one(X0)),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X1,X1)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
tff(f420,plain,
! [X0: $tType,X1: int] :
( ( times_times(X0,plus_plus(X0,one_one(X0),one_one(X0)),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,X1,X1)) )
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f322,f298]) ).
tff(f322,plain,
! [X0: $tType,X1: int] :
( ( number_number_of(X0,bit0(X1)) = times_times(X0,plus_plus(X0,one_one(X0),one_one(X0)),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f203]) ).
tff(f203,plain,
! [X0: $tType] :
( ! [X1: int] : ( number_number_of(X0,bit0(X1)) = times_times(X0,plus_plus(X0,one_one(X0),one_one(X0)),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f95]) ).
tff(f95,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int] : ( number_number_of(X0,bit0(X1)) = times_times(X0,plus_plus(X0,one_one(X0),one_one(X0)),number_number_of(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_double__number__of__Bit0) ).
tff(f1426,plain,
( ~ spl0_114
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| ~ spl0_62
| ~ spl0_75
| ~ spl0_82
| ~ spl0_99
| ~ spl0_101
| ~ spl0_110
| spl0_113 ),
inference(avatar_split_clause,[],[f1421,f1409,f1380,f1202,f1194,f1013,f932,f840,f612,f573,f561,f527,f1423]) ).
tff(f1013,plain,
( spl0_82
<=> ! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,times_times(int,plus_plus(int,X1,X1),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
tff(f1409,plain,
( spl0_113
<=> ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),one_one(int))),times_times(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
tff(f1421,plain,
( ~ ord_less(int,times_times(int,bit1(plus_plus(int,m,m)),minus_minus(int,bit1(plus_plus(int,m,m)),one_one(int))),times_times(int,bit1(plus_plus(int,m,m)),t))
| ~ spl0_7
| ~ spl0_14
| ~ spl0_17
| ~ spl0_25
| ~ spl0_62
| ~ spl0_75
| ~ spl0_82
| ~ spl0_99
| ~ spl0_101
| ~ spl0_110
| spl0_113 ),
inference(forward_demodulation,[],[f1420,f880]) ).
tff(f1420,plain,
( ~ ord_less(int,times_times(int,plus_plus(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),one_one(int)),minus_minus(int,plus_plus(int,plus_plus(int,plus_plus(int,m,m),plus_plus(int,m,m)),one_one(int)),one_one(int))),times_times(int,bit1(plus_plus(int,m,m)),t))
| ~ spl0_7
| ~ spl0_14
| ~ spl0_25
| ~ spl0_75
| ~ spl0_82
| ~ spl0_99
| ~ spl0_101
| ~ spl0_110
| spl0_113 ),
inference(forward_demodulation,[],[f1419,f1398]) ).
tff(f1419,plain,
( ~ ord_less(int,times_times(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,m,m)),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,m,m)),one_one(int)),one_one(int))),times_times(int,bit1(plus_plus(int,m,m)),t))
| ~ spl0_14
| ~ spl0_25
| ~ spl0_75
| ~ spl0_82
| ~ spl0_99
| ~ spl0_101
| spl0_113 ),
inference(forward_demodulation,[],[f1418,f1335]) ).
tff(f1418,plain,
( ~ ord_less(int,times_times(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),one_one(int)),one_one(int))),times_times(int,bit1(plus_plus(int,m,m)),t))
| ~ spl0_14
| ~ spl0_25
| ~ spl0_75
| ~ spl0_82
| ~ spl0_99
| ~ spl0_101
| spl0_113 ),
inference(forward_demodulation,[],[f1417,f933]) ).
tff(f1417,plain,
( ~ ord_less(int,times_times(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))),m),one_one(int)),one_one(int))),times_times(int,bit1(times_times(int,one_one(int),plus_plus(int,m,m))),t))
| ~ spl0_14
| ~ spl0_25
| ~ spl0_75
| ~ spl0_82
| ~ spl0_99
| ~ spl0_101
| spl0_113 ),
inference(forward_demodulation,[],[f1416,f614]) ).
tff(f1416,plain,
( ~ ord_less(int,times_times(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))),m),one_one(int)),one_one(int))),times_times(int,bit1(times_times(int,bit1(pls),plus_plus(int,m,m))),t))
| ~ spl0_14
| ~ spl0_75
| ~ spl0_82
| ~ spl0_99
| ~ spl0_101
| spl0_113 ),
inference(forward_demodulation,[],[f1415,f1335]) ).
tff(f1415,plain,
( ~ ord_less(int,times_times(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))),m),one_one(int)),one_one(int))),times_times(int,bit1(times_times(int,plus_plus(int,bit1(pls),bit1(pls)),m)),t))
| ~ spl0_14
| ~ spl0_75
| ~ spl0_82
| ~ spl0_101
| spl0_113 ),
inference(forward_demodulation,[],[f1414,f1354]) ).
tff(f1354,plain,
( ! [X2: int,X0: int,X1: int] : ( times_times(int,bit1(times_times(int,X0,X1)),X2) = plus_plus(int,times_times(int,times_times(int,plus_plus(int,X0,X0),X1),X2),X2) )
| ~ spl0_82
| ~ spl0_101 ),
inference(superposition,[],[f1014,f1203]) ).
tff(f1014,plain,
( ! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,times_times(int,plus_plus(int,X1,X1),X0),X0) )
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f1013]) ).
tff(f1414,plain,
( ~ ord_less(int,times_times(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))),m),one_one(int)),one_one(int))),plus_plus(int,times_times(int,times_times(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls))),m),t),t))
| ~ spl0_14
| ~ spl0_75
| ~ spl0_101
| spl0_113 ),
inference(forward_demodulation,[],[f1413,f562]) ).
tff(f1413,plain,
( ~ ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),one_one(int))),plus_plus(int,times_times(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),t),t))
| ~ spl0_75
| ~ spl0_101
| spl0_113 ),
inference(forward_demodulation,[],[f1411,f1334]) ).
tff(f1411,plain,
( ~ ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),one_one(int))),times_times(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),t))
| spl0_113 ),
inference(avatar_component_clause,[],[f1409]) ).
tff(f1412,plain,
~ spl0_113,
inference(avatar_split_clause,[],[f409,f1409]) ).
tff(f409,plain,
~ ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),one_one(int))),times_times(int,plus_plus(int,times_times(int,number_number_of(int,plus_plus(int,plus_plus(int,bit1(pls),bit1(pls)),plus_plus(int,bit1(pls),bit1(pls)))),m),one_one(int)),t)),
inference(definition_unfolding,[],[f270,f298,f298,f298,f298,f298,f298]) ).
tff(f270,plain,
~ ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
inference(cnf_transformation,[],[f111]) ).
tff(f111,plain,
~ ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
inference(flattening,[],[f110]) ).
tff(f110,negated_conjecture,
~ ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
inference(negated_conjecture,[],[f109]) ).
tff(f109,conjecture,
ord_less(int,times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),minus_minus(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),one_one(int))),times_times(int,plus_plus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m),one_one(int)),t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f1404,plain,
spl0_112,
inference(avatar_split_clause,[],[f323,f1402]) ).
tff(f1402,plain,
( spl0_112
<=> ! [X0: $tType,X1: int] :
( ( number_number_of(X0,bit1(X1)) = plus_plus(X0,plus_plus(X0,one_one(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
tff(f323,plain,
! [X0: $tType,X1: int] :
( ( number_number_of(X0,bit1(X1)) = plus_plus(X0,plus_plus(X0,one_one(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: $tType] :
( ! [X1: int] : ( number_number_of(X0,bit1(X1)) = plus_plus(X0,plus_plus(X0,one_one(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f89]) ).
tff(f89,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int] : ( number_number_of(X0,bit1(X1)) = plus_plus(X0,plus_plus(X0,one_one(X0),number_number_of(X0,X1)),number_number_of(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_number__of__Bit1) ).
tff(f1386,plain,
( spl0_111
| ~ spl0_25
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f1248,f1245,f612,f1384]) ).
tff(f1384,plain,
( spl0_111
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,plus_plus(int,one_one(int),one_one(int))),X1) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
tff(f1245,plain,
( spl0_106
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,plus_plus(int,bit1(pls),bit1(pls))),X1) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
tff(f1248,plain,
( ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,plus_plus(int,one_one(int),one_one(int))),X1) )
| ~ number_ring(X0) )
| ~ spl0_25
| ~ spl0_106 ),
inference(forward_demodulation,[],[f1246,f614]) ).
tff(f1246,plain,
( ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,plus_plus(int,bit1(pls),bit1(pls))),X1) )
| ~ number_ring(X0) )
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1245]) ).
tff(f1382,plain,
( spl0_110
| ~ spl0_25
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f1243,f1240,f612,f1380]) ).
tff(f1240,plain,
( spl0_105
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,plus_plus(int,bit1(pls),bit1(pls))),X1) )
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
tff(f1243,plain,
( ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,plus_plus(int,one_one(int),one_one(int))),X1) )
| ~ number_semiring(X0) )
| ~ spl0_25
| ~ spl0_105 ),
inference(forward_demodulation,[],[f1241,f614]) ).
tff(f1241,plain,
( ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,plus_plus(int,bit1(pls),bit1(pls))),X1) )
| ~ number_semiring(X0) )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1240]) ).
tff(f1378,plain,
( spl0_109
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1229,f1212,f612,f573,f569,f1375]) ).
tff(f1375,plain,
( spl0_109
<=> ( pls = minus_minus(int,one_one(int),one_one(int)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
tff(f1212,plain,
( spl0_103
<=> ! [X0: int] : ( minus_minus(int,pls,plus_plus(int,X0,X0)) = minus_minus(int,one_one(int),bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
tff(f1229,plain,
( ( pls = minus_minus(int,one_one(int),one_one(int)) )
| ~ spl0_16
| ~ spl0_17
| ~ spl0_25
| ~ spl0_103 ),
inference(forward_demodulation,[],[f1228,f614]) ).
tff(f1228,plain,
( ( pls = minus_minus(int,one_one(int),bit1(pls)) )
| ~ spl0_16
| ~ spl0_17
| ~ spl0_103 ),
inference(forward_demodulation,[],[f1222,f570]) ).
tff(f1222,plain,
( ( minus_minus(int,one_one(int),bit1(pls)) = minus_minus(int,pls,pls) )
| ~ spl0_17
| ~ spl0_103 ),
inference(superposition,[],[f1213,f574]) ).
tff(f1213,plain,
( ! [X0: int] : ( minus_minus(int,pls,plus_plus(int,X0,X0)) = minus_minus(int,one_one(int),bit1(X0)) )
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1212]) ).
tff(f1373,plain,
( spl0_108
| ~ spl0_25
| ~ spl0_104 ),
inference(avatar_split_clause,[],[f1238,f1235,f612,f1371]) ).
tff(f1371,plain,
( spl0_108
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,X1,number_number_of(X0,plus_plus(int,one_one(int),one_one(int)))) )
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
tff(f1235,plain,
( spl0_104
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,X1,number_number_of(X0,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
tff(f1238,plain,
( ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,X1,number_number_of(X0,plus_plus(int,one_one(int),one_one(int)))) )
| ~ number_semiring(X0) )
| ~ spl0_25
| ~ spl0_104 ),
inference(forward_demodulation,[],[f1236,f614]) ).
tff(f1236,plain,
( ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,X1,number_number_of(X0,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ number_semiring(X0) )
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f1235]) ).
tff(f1252,plain,
spl0_107,
inference(avatar_split_clause,[],[f495,f1250]) ).
tff(f495,plain,
! [X2: int,X0: int,X1: int] :
( ~ ord_less(int,pls,X0)
| ord_less(int,times_times(int,X0,X2),times_times(int,X0,X1))
| ~ ord_less(int,X2,X1) ),
inference(forward_demodulation,[],[f408,f283]) ).
tff(f408,plain,
! [X2: int,X0: int,X1: int] :
( ord_less(int,times_times(int,X0,X2),times_times(int,X0,X1))
| ~ ord_less(int,zero_zero(int),X0)
| ~ ord_less(int,X2,X1) ),
inference(cnf_transformation,[],[f238]) ).
tff(f238,plain,
! [X0: int,X1: int,X2: int] :
( ord_less(int,times_times(int,X0,X2),times_times(int,X0,X1))
| ~ ord_less(int,zero_zero(int),X0)
| ~ ord_less(int,X2,X1) ),
inference(flattening,[],[f237]) ).
tff(f237,plain,
! [X0: int,X1: int,X2: int] :
( ord_less(int,times_times(int,X0,X2),times_times(int,X0,X1))
| ~ ord_less(int,zero_zero(int),X0)
| ~ ord_less(int,X2,X1) ),
inference(ennf_transformation,[],[f184]) ).
tff(f184,plain,
! [X0: int,X1: int,X2: int] :
( ord_less(int,X2,X1)
=> ( ord_less(int,zero_zero(int),X0)
=> ord_less(int,times_times(int,X0,X2),times_times(int,X0,X1)) ) ),
inference(rectify,[],[f62]) ).
tff(f62,axiom,
! [X6: int,X18: int,X19: int] :
( ord_less(int,X19,X18)
=> ( ord_less(int,zero_zero(int),X6)
=> ord_less(int,times_times(int,X6,X19),times_times(int,X6,X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_zmult__zless__mono2) ).
tff(f1247,plain,
spl0_106,
inference(avatar_split_clause,[],[f419,f1245]) ).
tff(f419,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,plus_plus(int,bit1(pls),bit1(pls))),X1) )
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f319,f298]) ).
tff(f319,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,bit0(bit1(pls))),X1) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f200]) ).
tff(f200,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,bit0(bit1(pls))),X1) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,bit0(bit1(pls))),X1) ) ),
inference(rectify,[],[f97]) ).
tff(f97,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X14: X0] : ( times_times(X0,number_number_of(X0,bit0(bit1(pls))),X14) = plus_plus(X0,X14,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_mult__2) ).
tff(f1242,plain,
spl0_105,
inference(avatar_split_clause,[],[f417,f1240]) ).
tff(f417,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,plus_plus(int,bit1(pls),bit1(pls))),X1) )
| ~ number_semiring(X0) ),
inference(definition_unfolding,[],[f307,f298]) ).
tff(f307,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,bit0(bit1(pls))),X1) )
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f190]) ).
tff(f190,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,bit0(bit1(pls))),X1) )
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f125]) ).
tff(f125,plain,
! [X0: $tType] :
( number_semiring(X0)
=> ! [X1: X0] : ( plus_plus(X0,X1,X1) = times_times(X0,number_number_of(X0,bit0(bit1(pls))),X1) ) ),
inference(rectify,[],[f96]) ).
tff(f96,axiom,
! [X0: $tType] :
( number_semiring(X0)
=> ! [X14: X0] : ( times_times(X0,number_number_of(X0,bit0(bit1(pls))),X14) = plus_plus(X0,X14,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_semiring__mult__2) ).
tff(f1237,plain,
spl0_104,
inference(avatar_split_clause,[],[f416,f1235]) ).
tff(f416,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,X1,number_number_of(X0,plus_plus(int,bit1(pls),bit1(pls)))) )
| ~ number_semiring(X0) ),
inference(definition_unfolding,[],[f306,f298]) ).
tff(f306,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,X1) = times_times(X0,X1,number_number_of(X0,bit0(bit1(pls)))) )
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f189]) ).
tff(f189,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,X1,X1) = times_times(X0,X1,number_number_of(X0,bit0(bit1(pls)))) )
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f124]) ).
tff(f124,plain,
! [X0: $tType] :
( number_semiring(X0)
=> ! [X1: X0] : ( plus_plus(X0,X1,X1) = times_times(X0,X1,number_number_of(X0,bit0(bit1(pls)))) ) ),
inference(rectify,[],[f98]) ).
tff(f98,axiom,
! [X0: $tType] :
( number_semiring(X0)
=> ! [X14: X0] : ( plus_plus(X0,X14,X14) = times_times(X0,X14,number_number_of(X0,bit0(bit1(pls)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_semiring__mult__2__right) ).
tff(f1214,plain,
( spl0_103
| ~ spl0_25
| ~ spl0_93
| ~ spl0_102 ),
inference(avatar_split_clause,[],[f1210,f1206,f1126,f612,f1212]) ).
tff(f1206,plain,
( spl0_102
<=> ! [X0: int] : ( minus_minus(int,pls,plus_plus(int,X0,X0)) = plus_plus(int,minus_minus(int,pls,X0),minus_minus(int,pls,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
tff(f1210,plain,
( ! [X0: int] : ( minus_minus(int,pls,plus_plus(int,X0,X0)) = minus_minus(int,one_one(int),bit1(X0)) )
| ~ spl0_25
| ~ spl0_93
| ~ spl0_102 ),
inference(forward_demodulation,[],[f1209,f614]) ).
tff(f1209,plain,
( ! [X0: int] : ( minus_minus(int,pls,plus_plus(int,X0,X0)) = minus_minus(int,bit1(pls),bit1(X0)) )
| ~ spl0_93
| ~ spl0_102 ),
inference(forward_demodulation,[],[f1207,f1127]) ).
tff(f1207,plain,
( ! [X0: int] : ( minus_minus(int,pls,plus_plus(int,X0,X0)) = plus_plus(int,minus_minus(int,pls,X0),minus_minus(int,pls,X0)) )
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f1206]) ).
tff(f1208,plain,
spl0_102,
inference(avatar_split_clause,[],[f415,f1206]) ).
tff(f415,plain,
! [X0: int] : ( minus_minus(int,pls,plus_plus(int,X0,X0)) = plus_plus(int,minus_minus(int,pls,X0),minus_minus(int,pls,X0)) ),
inference(definition_unfolding,[],[f301,f298,f298]) ).
tff(f301,plain,
! [X0: int] : ( minus_minus(int,pls,bit0(X0)) = bit0(minus_minus(int,pls,X0)) ),
inference(cnf_transformation,[],[f122]) ).
tff(f122,plain,
! [X0: int] : ( minus_minus(int,pls,bit0(X0)) = bit0(minus_minus(int,pls,X0)) ),
inference(rectify,[],[f13]) ).
tff(f13,axiom,
! [X5: int] : ( minus_minus(int,pls,bit0(X5)) = bit0(minus_minus(int,pls,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_diff__bin__simps_I3_J) ).
tff(f1204,plain,
spl0_101,
inference(avatar_split_clause,[],[f407,f1202]) ).
tff(f407,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,plus_plus(int,X2,X1),X0) = plus_plus(int,times_times(int,X2,X0),times_times(int,X1,X0)) ),
inference(cnf_transformation,[],[f183]) ).
tff(f183,plain,
! [X0: int,X1: int,X2: int] : ( times_times(int,plus_plus(int,X2,X1),X0) = plus_plus(int,times_times(int,X2,X0),times_times(int,X1,X0)) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X1: int,X25: int,X26: int] : ( times_times(int,plus_plus(int,X26,X25),X1) = plus_plus(int,times_times(int,X26,X1),times_times(int,X25,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_int__distrib_I1_J) ).
tff(f1200,plain,
spl0_100,
inference(avatar_split_clause,[],[f406,f1198]) ).
tff(f1198,plain,
( spl0_100
<=> ! [X2: int,X0: int,X1: int] : ( times_times(int,minus_minus(int,X2,X1),X0) = minus_minus(int,times_times(int,X2,X0),times_times(int,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
tff(f406,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,minus_minus(int,X2,X1),X0) = minus_minus(int,times_times(int,X2,X0),times_times(int,X1,X0)) ),
inference(cnf_transformation,[],[f182]) ).
tff(f182,plain,
! [X0: int,X1: int,X2: int] : ( times_times(int,minus_minus(int,X2,X1),X0) = minus_minus(int,times_times(int,X2,X0),times_times(int,X1,X0)) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X1: int,X25: int,X26: int] : ( times_times(int,minus_minus(int,X26,X25),X1) = minus_minus(int,times_times(int,X26,X1),times_times(int,X25,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_int__distrib_I3_J) ).
tff(f1196,plain,
spl0_99,
inference(avatar_split_clause,[],[f405,f1194]) ).
tff(f405,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,X2,plus_plus(int,X1,X0)) = plus_plus(int,times_times(int,X2,X1),times_times(int,X2,X0)) ),
inference(cnf_transformation,[],[f181]) ).
tff(f181,plain,
! [X0: int,X1: int,X2: int] : ( times_times(int,X2,plus_plus(int,X1,X0)) = plus_plus(int,times_times(int,X2,X1),times_times(int,X2,X0)) ),
inference(rectify,[],[f77]) ).
tff(f77,axiom,
! [X25: int,X26: int,X1: int] : ( times_times(int,X1,plus_plus(int,X26,X25)) = plus_plus(int,times_times(int,X1,X26),times_times(int,X1,X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_int__distrib_I2_J) ).
tff(f1192,plain,
spl0_98,
inference(avatar_split_clause,[],[f404,f1190]) ).
tff(f1190,plain,
( spl0_98
<=> ! [X2: int,X0: int,X1: int] : ( times_times(int,X2,minus_minus(int,X1,X0)) = minus_minus(int,times_times(int,X2,X1),times_times(int,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
tff(f404,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,X2,minus_minus(int,X1,X0)) = minus_minus(int,times_times(int,X2,X1),times_times(int,X2,X0)) ),
inference(cnf_transformation,[],[f180]) ).
tff(f180,plain,
! [X0: int,X1: int,X2: int] : ( times_times(int,X2,minus_minus(int,X1,X0)) = minus_minus(int,times_times(int,X2,X1),times_times(int,X2,X0)) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X25: int,X26: int,X1: int] : ( times_times(int,X1,minus_minus(int,X26,X25)) = minus_minus(int,times_times(int,X1,X26),times_times(int,X1,X25)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_int__distrib_I4_J) ).
tff(f1153,plain,
( spl0_97
| ~ spl0_24
| ~ spl0_65
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f1078,f1013,f886,f606,f1151]) ).
tff(f1151,plain,
( spl0_97
<=> ! [X0: int] : ord_less(int,plus_plus(int,X0,X0),bit1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
tff(f606,plain,
( spl0_24
<=> ! [X1: int] : ord_less(int,X1,plus_plus(int,X1,one_one(int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
tff(f886,plain,
( spl0_65
<=> ! [X0: int] : ( times_times(int,X0,one_one(int)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
tff(f1078,plain,
( ! [X0: int] : ord_less(int,plus_plus(int,X0,X0),bit1(X0))
| ~ spl0_24
| ~ spl0_65
| ~ spl0_82 ),
inference(forward_demodulation,[],[f1077,f887]) ).
tff(f887,plain,
( ! [X0: int] : ( times_times(int,X0,one_one(int)) = X0 )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f886]) ).
tff(f1077,plain,
( ! [X0: int] : ord_less(int,times_times(int,plus_plus(int,X0,X0),one_one(int)),bit1(X0))
| ~ spl0_24
| ~ spl0_65
| ~ spl0_82 ),
inference(forward_demodulation,[],[f1064,f887]) ).
tff(f1064,plain,
( ! [X0: int] : ord_less(int,times_times(int,plus_plus(int,X0,X0),one_one(int)),times_times(int,bit1(X0),one_one(int)))
| ~ spl0_24
| ~ spl0_82 ),
inference(superposition,[],[f607,f1014]) ).
tff(f607,plain,
( ! [X1: int] : ord_less(int,X1,plus_plus(int,X1,one_one(int)))
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f606]) ).
tff(f1149,plain,
( spl0_96
| ~ spl0_25
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f1124,f1121,f612,f1147]) ).
tff(f1147,plain,
( spl0_96
<=> ! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,one_one(int),one_one(int))) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
tff(f1121,plain,
( spl0_92
<=> ! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,bit1(pls),bit1(pls))) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
tff(f1124,plain,
( ! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,one_one(int),one_one(int))) )
| ~ number_ring(X0) )
| ~ spl0_25
| ~ spl0_92 ),
inference(forward_demodulation,[],[f1122,f614]) ).
tff(f1122,plain,
( ! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,bit1(pls),bit1(pls))) )
| ~ number_ring(X0) )
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f1121]) ).
tff(f1136,plain,
( spl0_95
| ~ spl0_25
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f1104,f1101,f612,f1134]) ).
tff(f1134,plain,
( spl0_95
<=> ! [X0: $tType,X1: int] :
( ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,one_one(int))) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
tff(f1101,plain,
( spl0_88
<=> ! [X0: $tType,X1: int] :
( ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls))) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
tff(f1104,plain,
( ! [X0: $tType,X1: int] :
( ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,one_one(int))) )
| ~ number_ring(X0) )
| ~ spl0_25
| ~ spl0_88 ),
inference(forward_demodulation,[],[f1102,f614]) ).
tff(f1102,plain,
( ! [X0: $tType,X1: int] :
( ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls))) )
| ~ number_ring(X0) )
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f1101]) ).
tff(f1132,plain,
( spl0_94
| ~ spl0_25
| ~ spl0_87 ),
inference(avatar_split_clause,[],[f1099,f1096,f612,f1130]) ).
tff(f1130,plain,
( spl0_94
<=> ! [X0: $tType,X1: int] :
( ( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,one_one(int),X1)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
tff(f1096,plain,
( spl0_87
<=> ! [X0: $tType,X1: int] :
( ( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,bit1(pls),X1)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
tff(f1099,plain,
( ! [X0: $tType,X1: int] :
( ( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,one_one(int),X1)) )
| ~ number_ring(X0) )
| ~ spl0_25
| ~ spl0_87 ),
inference(forward_demodulation,[],[f1097,f614]) ).
tff(f1097,plain,
( ! [X0: $tType,X1: int] :
( ( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,bit1(pls),X1)) )
| ~ number_ring(X0) )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f1096]) ).
tff(f1128,plain,
spl0_93,
inference(avatar_split_clause,[],[f437,f1126]) ).
tff(f437,plain,
! [X0: int,X1: int] : ( minus_minus(int,bit1(X1),bit1(X0)) = plus_plus(int,minus_minus(int,X1,X0),minus_minus(int,X1,X0)) ),
inference(definition_unfolding,[],[f370,f298]) ).
tff(f370,plain,
! [X0: int,X1: int] : ( bit0(minus_minus(int,X1,X0)) = minus_minus(int,bit1(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f160]) ).
tff(f160,plain,
! [X0: int,X1: int] : ( bit0(minus_minus(int,X1,X0)) = minus_minus(int,bit1(X1),bit1(X0)) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X5: int,X6: int] : ( minus_minus(int,bit1(X6),bit1(X5)) = bit0(minus_minus(int,X6,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_diff__bin__simps_I10_J) ).
tff(f1123,plain,
spl0_92,
inference(avatar_split_clause,[],[f418,f1121]) ).
tff(f418,plain,
! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,bit1(pls),bit1(pls))) )
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f314,f298]) ).
tff(f314,plain,
! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f195]) ).
tff(f195,plain,
! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f10]) ).
tff(f10,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_one__add__one__is__two) ).
tff(f1119,plain,
spl0_91,
inference(avatar_split_clause,[],[f328,f1117]) ).
tff(f1117,plain,
( spl0_91
<=> ! [X0: $tType,X2: int,X1: int] :
( ( number_number_of(X0,plus_plus(int,X2,X1)) = plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
tff(f328,plain,
! [X0: $tType,X2: int,X1: int] :
( ( number_number_of(X0,plus_plus(int,X2,X1)) = plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f209]) ).
tff(f209,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] : ( number_number_of(X0,plus_plus(int,X2,X1)) = plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f84]) ).
tff(f84,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int,X2: int] : ( number_number_of(X0,plus_plus(int,X2,X1)) = plus_plus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_number__of__add) ).
tff(f1115,plain,
spl0_90,
inference(avatar_split_clause,[],[f326,f1113]) ).
tff(f1113,plain,
( spl0_90
<=> ! [X0: $tType,X2: int,X1: int] :
( ( number_number_of(X0,times_times(int,X2,X1)) = times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
tff(f326,plain,
! [X0: $tType,X2: int,X1: int] :
( ( number_number_of(X0,times_times(int,X2,X1)) = times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f207]) ).
tff(f207,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] : ( number_number_of(X0,times_times(int,X2,X1)) = times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f83]) ).
tff(f83,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int,X2: int] : ( number_number_of(X0,times_times(int,X2,X1)) = times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_number__of__mult) ).
tff(f1108,plain,
spl0_89,
inference(avatar_split_clause,[],[f325,f1106]) ).
tff(f1106,plain,
( spl0_89
<=> ! [X0: $tType,X2: int,X1: int] :
( ( number_number_of(X0,minus_minus(int,X2,X1)) = minus_minus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
tff(f325,plain,
! [X0: $tType,X2: int,X1: int] :
( ( number_number_of(X0,minus_minus(int,X2,X1)) = minus_minus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f206]) ).
tff(f206,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] : ( number_number_of(X0,minus_minus(int,X2,X1)) = minus_minus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f86]) ).
tff(f86,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int,X2: int] : ( number_number_of(X0,minus_minus(int,X2,X1)) = minus_minus(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_number__of__diff) ).
tff(f1103,plain,
spl0_88,
inference(avatar_split_clause,[],[f321,f1101]) ).
tff(f321,plain,
! [X0: $tType,X1: int] :
( ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls))) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $tType] :
( ! [X1: int] : ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls))) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int] : ( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls))) ) ),
inference(rectify,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X2: int] : ( plus_plus(X0,number_number_of(X0,X2),one_one(X0)) = number_number_of(X0,plus_plus(int,X2,bit1(pls))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_add__special_I3_J) ).
tff(f1098,plain,
spl0_87,
inference(avatar_split_clause,[],[f320,f1096]) ).
tff(f320,plain,
! [X0: $tType,X1: int] :
( ( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,bit1(pls),X1)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: $tType] :
( ! [X1: int] : ( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,bit1(pls),X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f6]) ).
tff(f6,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int] : ( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,bit1(pls),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_add__special_I2_J) ).
tff(f1031,plain,
( spl0_86
| ~ spl0_25
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f1003,f1000,f612,f1029]) ).
tff(f1029,plain,
( spl0_86
<=> ! [X0: $tType,X1: int] :
( ~ ord_less(int,X1,one_one(int))
| ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
tff(f1000,plain,
( spl0_79
<=> ! [X0: $tType,X1: int] :
( ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ ord_less(int,X1,bit1(pls))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
tff(f1003,plain,
( ! [X0: $tType,X1: int] :
( ~ ord_less(int,X1,one_one(int))
| ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) )
| ~ spl0_25
| ~ spl0_79 ),
inference(forward_demodulation,[],[f1001,f614]) ).
tff(f1001,plain,
( ! [X0: $tType,X1: int] :
( ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ ord_less(int,X1,bit1(pls))
| ~ linordered_idom(X0)
| ~ number_ring(X0) )
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f1000]) ).
tff(f1027,plain,
( spl0_85
| ~ spl0_25
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f998,f995,f612,f1025]) ).
tff(f1025,plain,
( spl0_85
<=> ! [X0: $tType,X1: int] :
( ord_less(int,X1,one_one(int))
| ~ ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
tff(f995,plain,
( spl0_78
<=> ! [X0: $tType,X1: int] :
( ord_less(int,X1,bit1(pls))
| ~ ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
tff(f998,plain,
( ! [X0: $tType,X1: int] :
( ord_less(int,X1,one_one(int))
| ~ ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) )
| ~ spl0_25
| ~ spl0_78 ),
inference(forward_demodulation,[],[f996,f614]) ).
tff(f996,plain,
( ! [X0: $tType,X1: int] :
( ord_less(int,X1,bit1(pls))
| ~ ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f995]) ).
tff(f1023,plain,
( spl0_84
| ~ spl0_25
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f993,f990,f612,f1021]) ).
tff(f1021,plain,
( spl0_84
<=> ! [X0: $tType,X1: int] :
( ~ ord_less(int,one_one(int),X1)
| ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
tff(f990,plain,
( spl0_77
<=> ! [X0: $tType,X1: int] :
( ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less(int,bit1(pls),X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
tff(f993,plain,
( ! [X0: $tType,X1: int] :
( ~ ord_less(int,one_one(int),X1)
| ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) )
| ~ spl0_25
| ~ spl0_77 ),
inference(forward_demodulation,[],[f991,f614]) ).
tff(f991,plain,
( ! [X0: $tType,X1: int] :
( ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less(int,bit1(pls),X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f990]) ).
tff(f1019,plain,
( spl0_83
| ~ spl0_25
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f987,f984,f612,f1017]) ).
tff(f1017,plain,
( spl0_83
<=> ! [X0: $tType,X1: int] :
( ord_less(int,one_one(int),X1)
| ~ ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
tff(f984,plain,
( spl0_76
<=> ! [X0: $tType,X1: int] :
( ord_less(int,bit1(pls),X1)
| ~ ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
tff(f987,plain,
( ! [X0: $tType,X1: int] :
( ord_less(int,one_one(int),X1)
| ~ ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) )
| ~ spl0_25
| ~ spl0_76 ),
inference(forward_demodulation,[],[f985,f614]) ).
tff(f985,plain,
( ! [X0: $tType,X1: int] :
( ord_less(int,bit1(pls),X1)
| ~ ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f984]) ).
tff(f1015,plain,
spl0_82,
inference(avatar_split_clause,[],[f481,f1013]) ).
tff(f481,plain,
! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,times_times(int,plus_plus(int,X1,X1),X0),X0) ),
inference(forward_demodulation,[],[f441,f434]) ).
tff(f434,plain,
! [X0: int,X1: int] : ( plus_plus(int,times_times(int,X1,X0),times_times(int,X1,X0)) = times_times(int,plus_plus(int,X1,X1),X0) ),
inference(definition_unfolding,[],[f367,f298,f298]) ).
tff(f367,plain,
! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
inference(cnf_transformation,[],[f157]) ).
tff(f157,plain,
! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X5: int,X6: int] : ( bit0(times_times(int,X6,X5)) = times_times(int,bit0(X6),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_mult__Bit0) ).
tff(f441,plain,
! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,plus_plus(int,times_times(int,X1,X0),times_times(int,X1,X0)),X0) ),
inference(definition_unfolding,[],[f374,f298]) ).
tff(f374,plain,
! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,bit0(times_times(int,X1,X0)),X0) ),
inference(cnf_transformation,[],[f164]) ).
tff(f164,plain,
! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,bit0(times_times(int,X1,X0)),X0) ),
inference(rectify,[],[f11]) ).
tff(f11,axiom,
! [X5: int,X6: int] : ( times_times(int,bit1(X6),X5) = plus_plus(int,bit0(times_times(int,X6,X5)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_mult__Bit1) ).
tff(f1011,plain,
spl0_81,
inference(avatar_split_clause,[],[f348,f1009]) ).
tff(f1009,plain,
( spl0_81
<=> ! [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,[spl0_81])]) ).
tff(f348,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,[],[f247]) ).
tff(f247,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,[],[f233]) ).
tff(f233,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,[],[f232]) ).
tff(f232,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,[],[f146]) ).
tff(f146,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,[],[f41]) ).
tff(f41,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/sandbox2/benchmark/theBenchmark.p',fact_40_less__number__of) ).
tff(f1007,plain,
spl0_80,
inference(avatar_split_clause,[],[f347,f1005]) ).
tff(f1005,plain,
( spl0_80
<=> ! [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,[spl0_80])]) ).
tff(f347,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,[],[f247]) ).
tff(f1002,plain,
spl0_79,
inference(avatar_split_clause,[],[f346,f1000]) ).
tff(f346,plain,
! [X0: $tType,X1: int] :
( ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ ord_less(int,X1,bit1(pls))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f246]) ).
tff(f246,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ ord_less(int,X1,bit1(pls)) )
& ( ord_less(int,X1,bit1(pls))
| ~ ord_less(X0,number_number_of(X0,X1),one_one(X0)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f231]) ).
tff(f231,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,number_number_of(X0,X1),one_one(X0))
<=> ord_less(int,X1,bit1(pls)) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f230]) ).
tff(f230,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,number_number_of(X0,X1),one_one(X0))
<=> ord_less(int,X1,bit1(pls)) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f145]) ).
tff(f145,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int] :
( ord_less(X0,number_number_of(X0,X1),one_one(X0))
<=> ord_less(int,X1,bit1(pls)) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X4: int] :
( ord_less(X0,number_number_of(X0,X4),one_one(X0))
<=> ord_less(int,X4,bit1(pls)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_less__special_I4_J) ).
tff(f997,plain,
spl0_78,
inference(avatar_split_clause,[],[f345,f995]) ).
tff(f345,plain,
! [X0: $tType,X1: int] :
( ord_less(int,X1,bit1(pls))
| ~ ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f246]) ).
tff(f992,plain,
spl0_77,
inference(avatar_split_clause,[],[f342,f990]) ).
tff(f342,plain,
! [X0: $tType,X1: int] :
( ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less(int,bit1(pls),X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less(int,bit1(pls),X1) )
& ( ord_less(int,bit1(pls),X1)
| ~ ord_less(X0,one_one(X0),number_number_of(X0,X1)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f227]) ).
tff(f227,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less(int,bit1(pls),X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f226]) ).
tff(f226,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less(int,bit1(pls),X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f143]) ).
tff(f143,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int] :
( ord_less(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less(int,bit1(pls),X1) ) ),
inference(rectify,[],[f8]) ).
tff(f8,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X3: int] :
( ord_less(X0,one_one(X0),number_number_of(X0,X3))
<=> ord_less(int,bit1(pls),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_less__special_I2_J) ).
tff(f986,plain,
spl0_76,
inference(avatar_split_clause,[],[f341,f984]) ).
tff(f341,plain,
! [X0: $tType,X1: int] :
( ord_less(int,bit1(pls),X1)
| ~ ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f244]) ).
tff(f934,plain,
( spl0_75
| ~ spl0_10
| ~ spl0_14
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f783,f757,f561,f542,f932]) ).
tff(f757,plain,
( spl0_51
<=> ! [X0: $tType,X1: X0] :
( ( times_times(X0,number_number_of(X0,one_one(int)),X1) = X1 )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
tff(f783,plain,
( ! [X0: int] : ( times_times(int,one_one(int),X0) = X0 )
| ~ spl0_10
| ~ spl0_14
| ~ spl0_51 ),
inference(forward_demodulation,[],[f782,f562]) ).
tff(f782,plain,
( ! [X0: int] : ( times_times(int,number_number_of(int,one_one(int)),X0) = X0 )
| ~ spl0_10
| ~ spl0_51 ),
inference(resolution,[],[f758,f544]) ).
tff(f758,plain,
( ! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( times_times(X0,number_number_of(X0,one_one(int)),X1) = X1 ) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f757]) ).
tff(f930,plain,
spl0_74,
inference(avatar_split_clause,[],[f488,f928]) ).
tff(f928,plain,
( spl0_74
<=> ! [X0: int,X1: int] :
( ~ ord_less(int,pls,X1)
| ( one_one(int) = X1 )
| ( one_one(int) != times_times(int,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
tff(f488,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,pls,X1)
| ( one_one(int) = X1 )
| ( one_one(int) != times_times(int,X1,X0) ) ),
inference(forward_demodulation,[],[f378,f283]) ).
tff(f378,plain,
! [X0: int,X1: int] :
( ( one_one(int) = X1 )
| ( one_one(int) != times_times(int,X1,X0) )
| ~ ord_less(int,zero_zero(int),X1) ),
inference(cnf_transformation,[],[f257]) ).
tff(f257,plain,
! [X0: int,X1: int] :
( ( ( ( one_one(int) = times_times(int,X1,X0) )
| ( one_one(int) != X0 )
| ( one_one(int) != X1 ) )
& ( ( ( one_one(int) = X0 )
& ( one_one(int) = X1 ) )
| ( one_one(int) != times_times(int,X1,X0) ) ) )
| ~ ord_less(int,zero_zero(int),X1) ),
inference(flattening,[],[f256]) ).
tff(f256,plain,
! [X0: int,X1: int] :
( ( ( ( one_one(int) = times_times(int,X1,X0) )
| ( one_one(int) != X0 )
| ( one_one(int) != X1 ) )
& ( ( ( one_one(int) = X0 )
& ( one_one(int) = X1 ) )
| ( one_one(int) != times_times(int,X1,X0) ) ) )
| ~ ord_less(int,zero_zero(int),X1) ),
inference(nnf_transformation,[],[f236]) ).
tff(f236,plain,
! [X0: int,X1: int] :
( ( ( one_one(int) = times_times(int,X1,X0) )
<=> ( ( one_one(int) = X0 )
& ( one_one(int) = X1 ) ) )
| ~ ord_less(int,zero_zero(int),X1) ),
inference(ennf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: int,X1: int] :
( ord_less(int,zero_zero(int),X1)
=> ( ( one_one(int) = times_times(int,X1,X0) )
<=> ( ( one_one(int) = X0 )
& ( one_one(int) = X1 ) ) ) ),
inference(rectify,[],[f66]) ).
tff(f66,axiom,
! [X20: int,X21: int] :
( ord_less(int,zero_zero(int),X21)
=> ( ( one_one(int) = times_times(int,X21,X20) )
<=> ( ( one_one(int) = X20 )
& ( one_one(int) = X21 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_pos__zmult__eq__1__iff) ).
tff(f926,plain,
spl0_73,
inference(avatar_split_clause,[],[f487,f924]) ).
tff(f924,plain,
( spl0_73
<=> ! [X0: int,X1: int] :
( ~ ord_less(int,pls,X1)
| ( one_one(int) = X0 )
| ( one_one(int) != times_times(int,X1,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
tff(f487,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,pls,X1)
| ( one_one(int) = X0 )
| ( one_one(int) != times_times(int,X1,X0) ) ),
inference(forward_demodulation,[],[f379,f283]) ).
tff(f379,plain,
! [X0: int,X1: int] :
( ( one_one(int) = X0 )
| ( one_one(int) != times_times(int,X1,X0) )
| ~ ord_less(int,zero_zero(int),X1) ),
inference(cnf_transformation,[],[f257]) ).
tff(f922,plain,
spl0_72,
inference(avatar_split_clause,[],[f399,f920]) ).
tff(f920,plain,
( spl0_72
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ord_less(int,X1,X0)
| ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
tff(f399,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ord_less(int,X1,X0)
| ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ),
inference(cnf_transformation,[],[f268]) ).
tff(f268,plain,
! [X0: int,X1: int] :
( ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ( ( X0 != X1 )
& ~ ord_less(int,X1,X0) ) )
& ( ( X0 = X1 )
| ord_less(int,X1,X0)
| ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ) ),
inference(flattening,[],[f267]) ).
tff(f267,plain,
! [X0: int,X1: int] :
( ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ( ( X0 != X1 )
& ~ ord_less(int,X1,X0) ) )
& ( ( X0 = X1 )
| ord_less(int,X1,X0)
| ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ) ),
inference(nnf_transformation,[],[f178]) ).
tff(f178,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
<=> ( ( X0 = X1 )
| ord_less(int,X1,X0) ) ),
inference(rectify,[],[f88]) ).
tff(f88,axiom,
! [X22: int,X17: int] :
( ord_less(int,X17,plus_plus(int,X22,one_one(int)))
<=> ( ( X17 = X22 )
| ord_less(int,X17,X22) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_zless__add1__eq) ).
tff(f918,plain,
spl0_71,
inference(avatar_split_clause,[],[f344,f916]) ).
tff(f916,plain,
( spl0_71
<=> ! [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,[spl0_71])]) ).
tff(f344,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,[],[f245]) ).
tff(f245,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,[],[f229]) ).
tff(f229,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,[],[f228]) ).
tff(f228,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,[],[f144]) ).
tff(f144,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,[],[f50]) ).
tff(f50,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/sandbox2/benchmark/theBenchmark.p',fact_49_less__special_I3_J) ).
tff(f914,plain,
spl0_70,
inference(avatar_split_clause,[],[f343,f912]) ).
tff(f912,plain,
( spl0_70
<=> ! [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,[spl0_70])]) ).
tff(f343,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,[],[f245]) ).
tff(f910,plain,
spl0_69,
inference(avatar_split_clause,[],[f340,f908]) ).
tff(f908,plain,
( spl0_69
<=> ! [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,[spl0_69])]) ).
tff(f340,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,[],[f243]) ).
tff(f243,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,[],[f225]) ).
tff(f225,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,[],[f224]) ).
tff(f224,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,[],[f142]) ).
tff(f142,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,[],[f51]) ).
tff(f51,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/sandbox2/benchmark/theBenchmark.p',fact_50_less__special_I1_J) ).
tff(f906,plain,
spl0_68,
inference(avatar_split_clause,[],[f339,f904]) ).
tff(f904,plain,
( spl0_68
<=> ! [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,[spl0_68])]) ).
tff(f339,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,[],[f243]) ).
tff(f902,plain,
spl0_67,
inference(avatar_split_clause,[],[f311,f900]) ).
tff(f900,plain,
( spl0_67
<=> ! [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,[spl0_67])]) ).
tff(f311,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,[],[f241]) ).
tff(f241,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,[],[f192]) ).
tff(f192,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,[],[f127]) ).
tff(f127,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,[],[f56]) ).
tff(f56,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X9: X0] :
( ord_less(X0,plus_plus(X0,X9,X9),zero_zero(X0))
<=> ord_less(X0,X9,zero_zero(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_even__less__0__iff) ).
tff(f898,plain,
spl0_66,
inference(avatar_split_clause,[],[f310,f896]) ).
tff(f896,plain,
( spl0_66
<=> ! [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,[spl0_66])]) ).
tff(f310,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,[],[f241]) ).
tff(f888,plain,
( spl0_65
| ~ spl0_10
| ~ spl0_14
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f781,f753,f561,f542,f886]) ).
tff(f753,plain,
( spl0_50
<=> ! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,number_number_of(X0,one_one(int))) = X1 )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
tff(f781,plain,
( ! [X0: int] : ( times_times(int,X0,one_one(int)) = X0 )
| ~ spl0_10
| ~ spl0_14
| ~ spl0_50 ),
inference(forward_demodulation,[],[f780,f562]) ).
tff(f780,plain,
( ! [X0: int] : ( times_times(int,X0,number_number_of(int,one_one(int))) = X0 )
| ~ spl0_10
| ~ spl0_50 ),
inference(resolution,[],[f754,f544]) ).
tff(f754,plain,
( ! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( times_times(X0,X1,number_number_of(X0,one_one(int))) = X1 ) )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f753]) ).
tff(f850,plain,
spl0_64,
inference(avatar_split_clause,[],[f449,f848]) ).
tff(f848,plain,
( spl0_64
<=> ! [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,[spl0_64])]) ).
tff(f449,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,[],[f395,f298,f298]) ).
tff(f395,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit0(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f265]) ).
tff(f265,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,[],[f176]) ).
tff(f176,plain,
! [X0: int,X1: int] :
( ord_less(int,bit0(X1),bit0(X0))
<=> ord_less(int,X1,X0) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X23: int,X24: int] :
( ord_less(int,bit0(X24),bit0(X23))
<=> ord_less(int,X24,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_less__int__code_I13_J) ).
tff(f846,plain,
spl0_63,
inference(avatar_split_clause,[],[f448,f844]) ).
tff(f844,plain,
( spl0_63
<=> ! [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,[spl0_63])]) ).
tff(f448,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,[],[f396,f298,f298]) ).
tff(f396,plain,
! [X0: int,X1: int] :
( ord_less(int,bit0(X1),bit0(X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f265]) ).
tff(f842,plain,
spl0_62,
inference(avatar_split_clause,[],[f439,f840]) ).
tff(f439,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,plus_plus(int,X1,X1),bit1(X0)) ),
inference(definition_unfolding,[],[f372,f298]) ).
tff(f372,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f162]) ).
tff(f162,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit0(X1),bit1(X0)) ),
inference(rectify,[],[f16]) ).
tff(f16,axiom,
! [X5: int,X6: int] : ( plus_plus(int,bit0(X6),bit1(X5)) = bit1(plus_plus(int,X6,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_add__Bit0__Bit1) ).
tff(f838,plain,
spl0_61,
inference(avatar_split_clause,[],[f438,f836]) ).
tff(f836,plain,
( spl0_61
<=> ! [X0: int,X1: int] : ( bit1(minus_minus(int,X1,X0)) = minus_minus(int,bit1(X1),plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
tff(f438,plain,
! [X0: int,X1: int] : ( bit1(minus_minus(int,X1,X0)) = minus_minus(int,bit1(X1),plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f371,f298]) ).
tff(f371,plain,
! [X0: int,X1: int] : ( minus_minus(int,bit1(X1),bit0(X0)) = bit1(minus_minus(int,X1,X0)) ),
inference(cnf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: int,X1: int] : ( minus_minus(int,bit1(X1),bit0(X0)) = bit1(minus_minus(int,X1,X0)) ),
inference(rectify,[],[f14]) ).
tff(f14,axiom,
! [X5: int,X6: int] : ( minus_minus(int,bit1(X6),bit0(X5)) = bit1(minus_minus(int,X6,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_diff__bin__simps_I9_J) ).
tff(f834,plain,
spl0_60,
inference(avatar_split_clause,[],[f435,f832]) ).
tff(f832,plain,
( spl0_60
<=> ! [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,[spl0_60])]) ).
tff(f435,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f368,f298]) ).
tff(f368,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: int,X1: int] : ( bit1(plus_plus(int,X1,X0)) = plus_plus(int,bit1(X1),bit0(X0)) ),
inference(rectify,[],[f17]) ).
tff(f17,axiom,
! [X5: int,X6: int] : ( bit1(plus_plus(int,X6,X5)) = plus_plus(int,bit1(X6),bit0(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_add__Bit1__Bit0) ).
tff(f830,plain,
( ~ spl0_59
| ~ spl0_17
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f700,f688,f573,f827]) ).
tff(f827,plain,
( spl0_59
<=> ( pls = plus_plus(int,one_one(int),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
tff(f688,plain,
( spl0_39
<=> ! [X0: int] : ( pls != plus_plus(int,plus_plus(int,one_one(int),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
tff(f700,plain,
( ( pls != plus_plus(int,one_one(int),pls) )
| ~ spl0_17
| ~ spl0_39 ),
inference(superposition,[],[f689,f574]) ).
tff(f689,plain,
( ! [X0: int] : ( pls != plus_plus(int,plus_plus(int,one_one(int),X0),X0) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f688]) ).
tff(f825,plain,
spl0_58,
inference(avatar_split_clause,[],[f337,f823]) ).
tff(f823,plain,
( spl0_58
<=> ! [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,[spl0_58])]) ).
tff(f337,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,[],[f242]) ).
tff(f242,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,[],[f223]) ).
tff(f223,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,[],[f222]) ).
tff(f222,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,[],[f141]) ).
tff(f141,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,[],[f18]) ).
tff(f18,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/sandbox2/benchmark/theBenchmark.p',fact_17_eq__number__of) ).
tff(f819,plain,
spl0_57,
inference(avatar_split_clause,[],[f302,f817]) ).
tff(f817,plain,
( spl0_57
<=> ! [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,[spl0_57])]) ).
tff(f302,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,X1,X1) )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,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,[],[f186]) ).
tff(f186,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
<=> ( zero_zero(X0) = X1 ) )
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f123]) ).
tff(f123,plain,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X9: X0] :
( ( plus_plus(X0,X9,X9) = zero_zero(X0) )
<=> ( zero_zero(X0) = X9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_double__eq__0__iff) ).
tff(f799,plain,
spl0_56,
inference(avatar_split_clause,[],[f445,f797]) ).
tff(f797,plain,
( spl0_56
<=> ! [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,[spl0_56])]) ).
tff(f445,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f391,f298]) ).
tff(f391,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),bit0(X0)) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,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,[],[f174]) ).
tff(f174,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit0(X0))
<=> ord_less(int,X1,X0) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X23: int,X24: int] :
( ord_less(int,bit1(X24),bit0(X23))
<=> ord_less(int,X24,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_less__int__code_I15_J) ).
tff(f795,plain,
spl0_55,
inference(avatar_split_clause,[],[f444,f793]) ).
tff(f793,plain,
( spl0_55
<=> ! [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,[spl0_55])]) ).
tff(f444,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),plus_plus(int,X0,X0))
| ~ ord_less(int,X1,X0) ),
inference(definition_unfolding,[],[f392,f298]) ).
tff(f392,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit0(X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f263]) ).
tff(f791,plain,
spl0_54,
inference(avatar_split_clause,[],[f443,f789]) ).
tff(f789,plain,
( spl0_54
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( plus_plus(int,X0,X0) != plus_plus(int,X1,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
tff(f443,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( plus_plus(int,X0,X0) != plus_plus(int,X1,X1) ) ),
inference(definition_unfolding,[],[f385,f298,f298]) ).
tff(f385,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit0(X1) != bit0(X0) ) ),
inference(cnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: int,X1: int] :
( ( ( bit0(X1) = bit0(X0) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( bit0(X1) != bit0(X0) ) ) ),
inference(nnf_transformation,[],[f171]) ).
tff(f171,plain,
! [X0: int,X1: int] :
( ( bit0(X1) = bit0(X0) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X7: int,X8: int] :
( ( bit0(X8) = bit0(X7) )
<=> ( X7 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_rel__simps_I48_J) ).
tff(f787,plain,
spl0_53,
inference(avatar_split_clause,[],[f400,f785]) ).
tff(f785,plain,
( spl0_53
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ~ ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
tff(f400,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f268]) ).
tff(f764,plain,
( spl0_52
| ~ spl0_18
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f619,f606,f577,f761]) ).
tff(f761,plain,
( spl0_52
<=> ord_less(int,pls,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
tff(f577,plain,
( spl0_18
<=> ! [X0: int] : ( plus_plus(int,pls,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
tff(f619,plain,
( ord_less(int,pls,one_one(int))
| ~ spl0_18
| ~ spl0_24 ),
inference(superposition,[],[f607,f578]) ).
tff(f578,plain,
( ! [X0: int] : ( plus_plus(int,pls,X0) = X0 )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f577]) ).
tff(f759,plain,
( spl0_51
| ~ spl0_25
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f715,f712,f612,f757]) ).
tff(f712,plain,
( spl0_42
<=> ! [X0: $tType,X1: X0] :
( ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
tff(f715,plain,
( ! [X0: $tType,X1: X0] :
( ( times_times(X0,number_number_of(X0,one_one(int)),X1) = X1 )
| ~ number_ring(X0) )
| ~ spl0_25
| ~ spl0_42 ),
inference(forward_demodulation,[],[f713,f614]) ).
tff(f713,plain,
( ! [X0: $tType,X1: X0] :
( ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 )
| ~ number_ring(X0) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f712]) ).
tff(f755,plain,
( spl0_50
| ~ spl0_25
| ~ spl0_41 ),
inference(avatar_split_clause,[],[f710,f707,f612,f753]) ).
tff(f707,plain,
( spl0_41
<=> ! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
tff(f710,plain,
( ! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,number_number_of(X0,one_one(int))) = X1 )
| ~ number_ring(X0) )
| ~ spl0_25
| ~ spl0_41 ),
inference(forward_demodulation,[],[f708,f614]) ).
tff(f708,plain,
( ! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 )
| ~ number_ring(X0) )
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f707]) ).
tff(f743,plain,
spl0_49,
inference(avatar_split_clause,[],[f490,f741]) ).
tff(f741,plain,
( spl0_49
<=> ! [X0: int,X1: int] :
( ord_less(int,minus_minus(int,X1,X0),pls)
| ~ ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
tff(f490,plain,
! [X0: int,X1: int] :
( ord_less(int,minus_minus(int,X1,X0),pls)
| ~ ord_less(int,X1,X0) ),
inference(forward_demodulation,[],[f381,f283]) ).
tff(f381,plain,
! [X0: int,X1: int] :
( ord_less(int,minus_minus(int,X1,X0),zero_zero(int))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: int,X1: int] :
( ( ord_less(int,X1,X0)
| ~ ord_less(int,minus_minus(int,X1,X0),zero_zero(int)) )
& ( ord_less(int,minus_minus(int,X1,X0),zero_zero(int))
| ~ ord_less(int,X1,X0) ) ),
inference(nnf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
<=> ord_less(int,minus_minus(int,X1,X0),zero_zero(int)) ),
inference(rectify,[],[f64]) ).
tff(f64,axiom,
! [X7: int,X8: int] :
( ord_less(int,X8,X7)
<=> ord_less(int,minus_minus(int,X8,X7),zero_zero(int)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_less__bin__lemma) ).
tff(f739,plain,
spl0_48,
inference(avatar_split_clause,[],[f489,f737]) ).
tff(f737,plain,
( spl0_48
<=> ! [X0: int,X1: int] :
( ~ ord_less(int,minus_minus(int,X1,X0),pls)
| ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
tff(f489,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,minus_minus(int,X1,X0),pls)
| ord_less(int,X1,X0) ),
inference(forward_demodulation,[],[f382,f283]) ).
tff(f382,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,minus_minus(int,X1,X0),zero_zero(int)) ),
inference(cnf_transformation,[],[f258]) ).
tff(f735,plain,
spl0_47,
inference(avatar_split_clause,[],[f452,f733]) ).
tff(f733,plain,
( spl0_47
<=> ! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
tff(f452,plain,
! [X0: $tType] :
( ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) )
| ~ linord219039673up_add(X0) ),
inference(equality_resolution,[],[f303]) ).
tff(f303,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
| ( zero_zero(X0) != X1 )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f239]) ).
tff(f731,plain,
spl0_46,
inference(avatar_split_clause,[],[f429,f729]) ).
tff(f729,plain,
( spl0_46
<=> ! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,plus_plus(int,X0,X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
tff(f429,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,plus_plus(int,X0,X0),pls) ),
inference(definition_unfolding,[],[f357,f298]) ).
tff(f357,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,bit0(X0),pls) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,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,[],[f151]) ).
tff(f151,plain,
! [X0: int] :
( ord_less(int,bit0(X0),pls)
<=> ord_less(int,X0,pls) ),
inference(rectify,[],[f48]) ).
tff(f48,axiom,
! [X8: int] :
( ord_less(int,bit0(X8),pls)
<=> ord_less(int,X8,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_rel__simps_I10_J) ).
tff(f727,plain,
spl0_45,
inference(avatar_split_clause,[],[f428,f725]) ).
tff(f725,plain,
( spl0_45
<=> ! [X0: int] :
( ord_less(int,plus_plus(int,X0,X0),pls)
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
tff(f428,plain,
! [X0: int] :
( ord_less(int,plus_plus(int,X0,X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(definition_unfolding,[],[f358,f298]) ).
tff(f358,plain,
! [X0: int] :
( ord_less(int,bit0(X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(cnf_transformation,[],[f252]) ).
tff(f723,plain,
spl0_44,
inference(avatar_split_clause,[],[f427,f721]) ).
tff(f721,plain,
( spl0_44
<=> ! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,pls,plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
tff(f427,plain,
! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,pls,plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f353,f298]) ).
tff(f353,plain,
! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less(int,pls,bit0(X0)) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,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,[],[f149]) ).
tff(f149,plain,
! [X0: int] :
( ord_less(int,pls,bit0(X0))
<=> ord_less(int,pls,X0) ),
inference(rectify,[],[f49]) ).
tff(f49,axiom,
! [X8: int] :
( ord_less(int,pls,bit0(X8))
<=> ord_less(int,pls,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_rel__simps_I4_J) ).
tff(f719,plain,
spl0_43,
inference(avatar_split_clause,[],[f426,f717]) ).
tff(f717,plain,
( spl0_43
<=> ! [X0: int] :
( ord_less(int,pls,plus_plus(int,X0,X0))
| ~ ord_less(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
tff(f426,plain,
! [X0: int] :
( ord_less(int,pls,plus_plus(int,X0,X0))
| ~ ord_less(int,pls,X0) ),
inference(definition_unfolding,[],[f354,f298]) ).
tff(f354,plain,
! [X0: int] :
( ord_less(int,pls,bit0(X0))
| ~ ord_less(int,pls,X0) ),
inference(cnf_transformation,[],[f250]) ).
tff(f714,plain,
spl0_42,
inference(avatar_split_clause,[],[f318,f712]) ).
tff(f318,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 ) ),
inference(rectify,[],[f90]) ).
tff(f90,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X12: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X12) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_mult__numeral__1) ).
tff(f709,plain,
spl0_41,
inference(avatar_split_clause,[],[f317,f707]) ).
tff(f317,plain,
! [X0: $tType,X1: X0] :
( ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f198]) ).
tff(f198,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f130]) ).
tff(f130,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( times_times(X0,X1,number_number_of(X0,bit1(pls))) = X1 ) ),
inference(rectify,[],[f91]) ).
tff(f91,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X12: X0] : ( times_times(X0,X12,number_number_of(X0,bit1(pls))) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_mult__numeral__1__right) ).
tff(f705,plain,
spl0_40,
inference(avatar_split_clause,[],[f300,f703]) ).
tff(f703,plain,
( spl0_40
<=> ! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
tff(f300,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f121]) ).
tff(f121,plain,
! [X0: int] : ( bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(rectify,[],[f87]) ).
tff(f87,axiom,
! [X6: int] : ( bit1(X6) = plus_plus(int,plus_plus(int,one_one(int),X6),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_Bit1__def) ).
tff(f690,plain,
spl0_39,
inference(avatar_split_clause,[],[f466,f688]) ).
tff(f466,plain,
! [X0: int] : ( pls != plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(forward_demodulation,[],[f299,f283]) ).
tff(f299,plain,
! [X0: int] : ( zero_zero(int) != plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(cnf_transformation,[],[f120]) ).
tff(f120,plain,
! [X0: int] : ( zero_zero(int) != plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X14: int] : ( zero_zero(int) != plus_plus(int,plus_plus(int,one_one(int),X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_odd__nonzero) ).
tff(f686,plain,
spl0_38,
inference(avatar_split_clause,[],[f388,f684]) ).
tff(f684,plain,
( spl0_38
<=> ! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit1(X0))
| ~ ord_less(int,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
tff(f388,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit1(X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f261]) ).
tff(f261,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,[],[f172]) ).
tff(f172,plain,
! [X0: int,X1: int] :
( ord_less(int,bit1(X1),bit1(X0))
<=> ord_less(int,X1,X0) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X7: int,X8: int] :
( ord_less(int,bit1(X8),bit1(X7))
<=> ord_less(int,X8,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_rel__simps_I17_J) ).
tff(f682,plain,
( ~ spl0_37
| ~ spl0_13
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f653,f612,f557,f679]) ).
tff(f679,plain,
( spl0_37
<=> ( pls = one_one(int) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
tff(f557,plain,
( spl0_13
<=> ! [X0: int] : ( pls != bit1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
tff(f653,plain,
( ( pls != one_one(int) )
| ~ spl0_13
| ~ spl0_25 ),
inference(superposition,[],[f558,f614]) ).
tff(f558,plain,
( ! [X0: int] : ( pls != bit1(X0) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f557]) ).
tff(f677,plain,
spl0_36,
inference(avatar_split_clause,[],[f387,f675]) ).
tff(f675,plain,
( spl0_36
<=> ! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),bit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
tff(f387,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ~ ord_less(int,bit1(X1),bit1(X0)) ),
inference(cnf_transformation,[],[f261]) ).
tff(f673,plain,
spl0_35,
inference(avatar_split_clause,[],[f316,f671]) ).
tff(f671,plain,
( spl0_35
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
tff(f316,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f129]) ).
tff(f129,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( plus_plus(X0,number_number_of(X0,pls),X1) = X1 ) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X12: X0] : ( plus_plus(X0,number_number_of(X0,pls),X12) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_add__numeral__0) ).
tff(f669,plain,
spl0_34,
inference(avatar_split_clause,[],[f315,f667]) ).
tff(f667,plain,
( spl0_34
<=> ! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
tff(f315,plain,
! [X0: $tType,X1: X0] :
( ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: $tType] :
( ! [X1: X0] : ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( plus_plus(X0,X1,number_number_of(X0,pls)) = X1 ) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X12: X0] : ( plus_plus(X0,X12,number_number_of(X0,pls)) = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add__numeral__0__right) ).
tff(f657,plain,
( spl0_33
| ~ spl0_25
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f629,f626,f612,f655]) ).
tff(f655,plain,
( spl0_33
<=> ! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,one_one(int)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
tff(f626,plain,
( spl0_27
<=> ! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
tff(f629,plain,
( ! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,one_one(int)) )
| ~ number_ring(X0) )
| ~ spl0_25
| ~ spl0_27 ),
inference(forward_demodulation,[],[f627,f614]) ).
tff(f627,plain,
( ! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_ring(X0) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f626]) ).
tff(f649,plain,
( spl0_32
| ~ spl0_25
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f624,f621,f612,f647]) ).
tff(f647,plain,
( spl0_32
<=> ! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,one_one(int)) )
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
tff(f621,plain,
( spl0_26
<=> ! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
tff(f624,plain,
( ! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,one_one(int)) )
| ~ number_semiring(X0) )
| ~ spl0_25
| ~ spl0_26 ),
inference(forward_demodulation,[],[f622,f614]) ).
tff(f622,plain,
( ! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_semiring(X0) )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f621]) ).
tff(f645,plain,
spl0_31,
inference(avatar_split_clause,[],[f423,f643]) ).
tff(f643,plain,
( spl0_31
<=> ! [X0: int] :
( ( pls = X0 )
| ( pls != plus_plus(int,X0,X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
tff(f423,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls != plus_plus(int,X0,X0) ) ),
inference(definition_unfolding,[],[f349,f298]) ).
tff(f349,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls != bit0(X0) ) ),
inference(cnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: int] :
( ( ( pls = bit0(X0) )
| ( pls != X0 ) )
& ( ( pls = X0 )
| ( pls != bit0(X0) ) ) ),
inference(nnf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: int] :
( ( pls = bit0(X0) )
<=> ( pls = X0 ) ),
inference(rectify,[],[f26]) ).
tff(f26,axiom,
! [X8: int] :
( ( pls = bit0(X8) )
<=> ( pls = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_rel__simps_I44_J) ).
tff(f641,plain,
spl0_30,
inference(avatar_split_clause,[],[f377,f639]) ).
tff(f639,plain,
( spl0_30
<=> ! [X0: int,X1: int] :
( twoSqu1567020053sum2sq(times_times(int,X1,X0))
| ~ twoSqu1567020053sum2sq(X0)
| ~ twoSqu1567020053sum2sq(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
tff(f377,plain,
! [X0: int,X1: int] :
( twoSqu1567020053sum2sq(times_times(int,X1,X0))
| ~ twoSqu1567020053sum2sq(X0)
| ~ twoSqu1567020053sum2sq(X1) ),
inference(cnf_transformation,[],[f235]) ).
tff(f235,plain,
! [X0: int,X1: int] :
( twoSqu1567020053sum2sq(times_times(int,X1,X0))
| ~ twoSqu1567020053sum2sq(X0)
| ~ twoSqu1567020053sum2sq(X1) ),
inference(flattening,[],[f234]) ).
tff(f234,plain,
! [X0: int,X1: int] :
( twoSqu1567020053sum2sq(times_times(int,X1,X0))
| ~ twoSqu1567020053sum2sq(X0)
| ~ twoSqu1567020053sum2sq(X1) ),
inference(ennf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: int,X1: int] :
( twoSqu1567020053sum2sq(X1)
=> ( twoSqu1567020053sum2sq(X0)
=> twoSqu1567020053sum2sq(times_times(int,X1,X0)) ) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X15: int,X16: int] :
( twoSqu1567020053sum2sq(X16)
=> ( twoSqu1567020053sum2sq(X15)
=> twoSqu1567020053sum2sq(times_times(int,X16,X15)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_is__mult__sum2sq) ).
tff(f637,plain,
spl0_29,
inference(avatar_split_clause,[],[f356,f635]) ).
tff(f635,plain,
( spl0_29
<=> ! [X0: int] :
( ord_less(int,bit1(X0),pls)
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
tff(f356,plain,
! [X0: int] :
( ord_less(int,bit1(X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(cnf_transformation,[],[f251]) ).
tff(f251,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,[],[f150]) ).
tff(f150,plain,
! [X0: int] :
( ord_less(int,bit1(X0),pls)
<=> ord_less(int,X0,pls) ),
inference(rectify,[],[f46]) ).
tff(f46,axiom,
! [X8: int] :
( ord_less(int,bit1(X8),pls)
<=> ord_less(int,X8,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_rel__simps_I12_J) ).
tff(f633,plain,
spl0_28,
inference(avatar_split_clause,[],[f355,f631]) ).
tff(f631,plain,
( spl0_28
<=> ! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,bit1(X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
tff(f355,plain,
! [X0: int] :
( ord_less(int,X0,pls)
| ~ ord_less(int,bit1(X0),pls) ),
inference(cnf_transformation,[],[f251]) ).
tff(f628,plain,
spl0_27,
inference(avatar_split_clause,[],[f313,f626]) ).
tff(f313,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f12]) ).
tff(f12,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( one_one(X0) = number_number_of(X0,bit1(pls)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_numeral__1__eq__1) ).
tff(f623,plain,
spl0_26,
inference(avatar_split_clause,[],[f305,f621]) ).
tff(f305,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f188]) ).
tff(f188,plain,
! [X0: $tType] :
( ( one_one(X0) = number_number_of(X0,bit1(pls)) )
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f92]) ).
tff(f92,axiom,
! [X0: $tType] :
( number_semiring(X0)
=> ( one_one(X0) = number_number_of(X0,bit1(pls)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_semiring__numeral__1__eq__1) ).
tff(f615,plain,
( spl0_25
| ~ spl0_14
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f589,f581,f561,f612]) ).
tff(f581,plain,
( spl0_19
<=> ( one_one(int) = number_number_of(int,bit1(pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
tff(f589,plain,
( ( bit1(pls) = one_one(int) )
| ~ spl0_14
| ~ spl0_19 ),
inference(superposition,[],[f583,f562]) ).
tff(f583,plain,
( ( one_one(int) = number_number_of(int,bit1(pls)) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f581]) ).
tff(f608,plain,
spl0_24,
inference(avatar_split_clause,[],[f462,f606]) ).
tff(f462,plain,
! [X1: int] : ord_less(int,X1,plus_plus(int,X1,one_one(int))),
inference(equality_resolution,[],[f401]) ).
tff(f401,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f268]) ).
tff(f604,plain,
spl0_23,
inference(avatar_split_clause,[],[f383,f602]) ).
tff(f602,plain,
( spl0_23
<=> ! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit1(X1) != bit1(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
tff(f383,plain,
! [X0: int,X1: int] :
( ( X0 = X1 )
| ( bit1(X1) != bit1(X0) ) ),
inference(cnf_transformation,[],[f259]) ).
tff(f259,plain,
! [X0: int,X1: int] :
( ( ( bit1(X1) = bit1(X0) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( bit1(X1) != bit1(X0) ) ) ),
inference(nnf_transformation,[],[f170]) ).
tff(f170,plain,
! [X0: int,X1: int] :
( ( bit1(X1) = bit1(X0) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f19]) ).
tff(f19,axiom,
! [X7: int,X8: int] :
( ( bit1(X8) = bit1(X7) )
<=> ( X7 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_rel__simps_I51_J) ).
tff(f600,plain,
spl0_22,
inference(avatar_split_clause,[],[f312,f598]) ).
tff(f598,plain,
( spl0_22
<=> ! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
tff(f312,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f38]) ).
tff(f38,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( zero_zero(X0) = number_number_of(X0,pls) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_number__of__Pls) ).
tff(f596,plain,
spl0_21,
inference(avatar_split_clause,[],[f304,f594]) ).
tff(f594,plain,
( spl0_21
<=> ! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
tff(f304,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f187]) ).
tff(f187,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f57]) ).
tff(f57,axiom,
! [X0: $tType] :
( number_semiring(X0)
=> ( zero_zero(X0) = number_number_of(X0,pls) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_semiring__numeral__0__eq__0) ).
tff(f588,plain,
spl0_20,
inference(avatar_split_clause,[],[f432,f586]) ).
tff(f586,plain,
( spl0_20
<=> ! [X0: int,X1: int] : ( bit1(X1) != plus_plus(int,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
tff(f432,plain,
! [X0: int,X1: int] : ( bit1(X1) != plus_plus(int,X0,X0) ),
inference(definition_unfolding,[],[f365,f298]) ).
tff(f365,plain,
! [X0: int,X1: int] : ( bit1(X1) != bit0(X0) ),
inference(cnf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: int,X1: int] : ( bit1(X1) != bit0(X0) ),
inference(rectify,[],[f24]) ).
tff(f24,axiom,
! [X5: int,X6: int] : ( bit1(X6) != bit0(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_rel__simps_I50_J) ).
tff(f584,plain,
spl0_19,
inference(avatar_split_clause,[],[f286,f581]) ).
tff(f286,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[],[f94]) ).
tff(f94,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_one__is__num__one) ).
tff(f579,plain,
spl0_18,
inference(avatar_split_clause,[],[f297,f577]) ).
tff(f297,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(cnf_transformation,[],[f118]) ).
tff(f118,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = X0 ),
inference(rectify,[],[f71]) ).
tff(f71,axiom,
! [X6: int] : ( plus_plus(int,pls,X6) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_add__Pls) ).
tff(f575,plain,
spl0_17,
inference(avatar_split_clause,[],[f296,f573]) ).
tff(f296,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f117]) ).
tff(f117,plain,
! [X0: int] : ( plus_plus(int,X0,pls) = X0 ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X6: int] : ( plus_plus(int,X6,pls) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_add__Pls__right) ).
tff(f571,plain,
spl0_16,
inference(avatar_split_clause,[],[f295,f569]) ).
tff(f295,plain,
! [X0: int] : ( minus_minus(int,X0,pls) = X0 ),
inference(cnf_transformation,[],[f116]) ).
tff(f116,plain,
! [X0: int] : ( minus_minus(int,X0,pls) = X0 ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X6: int] : ( minus_minus(int,X6,pls) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_diff__bin__simps_I1_J) ).
tff(f567,plain,
spl0_15,
inference(avatar_split_clause,[],[f294,f565]) ).
tff(f565,plain,
( spl0_15
<=> ! [X0: int] : ( pls = times_times(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
tff(f294,plain,
! [X0: int] : ( pls = times_times(int,pls,X0) ),
inference(cnf_transformation,[],[f115]) ).
tff(f115,plain,
! [X0: int] : ( pls = times_times(int,pls,X0) ),
inference(rectify,[],[f32]) ).
tff(f32,axiom,
! [X1: int] : ( pls = times_times(int,pls,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_mult__Pls) ).
tff(f563,plain,
spl0_14,
inference(avatar_split_clause,[],[f293,f561]) ).
tff(f293,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f114]) ).
tff(f114,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(rectify,[],[f55]) ).
tff(f55,axiom,
! [X6: int] : ( number_number_of(int,X6) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_number__of__is__id) ).
tff(f559,plain,
spl0_13,
inference(avatar_split_clause,[],[f291,f557]) ).
tff(f291,plain,
! [X0: int] : ( pls != bit1(X0) ),
inference(cnf_transformation,[],[f112]) ).
tff(f112,plain,
! [X0: int] : ( pls != bit1(X0) ),
inference(rectify,[],[f22]) ).
tff(f22,axiom,
! [X6: int] : ( pls != bit1(X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_rel__simps_I46_J) ).
tff(f555,plain,
spl0_12,
inference(avatar_split_clause,[],[f283,f552]) ).
tff(f552,plain,
( spl0_12
<=> ( zero_zero(int) = pls ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
tff(f550,plain,
~ spl0_11,
inference(avatar_split_clause,[],[f281,f547]) ).
tff(f547,plain,
( spl0_11
<=> ord_less(int,pls,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
tff(f281,plain,
~ ord_less(int,pls,pls),
inference(cnf_transformation,[],[f30]) ).
tff(f30,axiom,
~ ord_less(int,pls,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_rel__simps_I2_J) ).
tff(f545,plain,
spl0_10,
inference(avatar_split_clause,[],[f280,f542]) ).
tff(f280,plain,
number_ring(int),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
number_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f540,plain,
spl0_9,
inference(avatar_split_clause,[],[f279,f537]) ).
tff(f537,plain,
( spl0_9
<=> linordered_idom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
tff(f279,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
linordered_idom(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
tff(f535,plain,
spl0_8,
inference(avatar_split_clause,[],[f278,f532]) ).
tff(f532,plain,
( spl0_8
<=> number(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
tff(f278,plain,
number(int),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
number(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
tff(f530,plain,
spl0_7,
inference(avatar_split_clause,[],[f277,f527]) ).
tff(f277,plain,
number_semiring(int),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
number_semiring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
tff(f525,plain,
spl0_6,
inference(avatar_split_clause,[],[f276,f522]) ).
tff(f522,plain,
( spl0_6
<=> semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
tff(f276,plain,
semiring(int),
inference(cnf_transformation,[],[f104]) ).
tff(f104,axiom,
semiring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
tff(f520,plain,
spl0_5,
inference(avatar_split_clause,[],[f275,f517]) ).
tff(f517,plain,
( spl0_5
<=> ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
tff(f275,plain,
ring(int),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
tff(f515,plain,
spl0_4,
inference(avatar_split_clause,[],[f274,f512]) ).
tff(f512,plain,
( spl0_4
<=> pp(fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
tff(f274,plain,
pp(fTrue),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
pp(fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
tff(f510,plain,
spl0_3,
inference(avatar_split_clause,[],[f273,f507]) ).
tff(f507,plain,
( spl0_3
<=> linord219039673up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
tff(f273,plain,
linord219039673up_add(int),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
linord219039673up_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
tff(f505,plain,
spl0_2,
inference(avatar_split_clause,[],[f272,f502]) ).
tff(f502,plain,
( spl0_2
<=> ring_char_0(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
tff(f272,plain,
ring_char_0(int),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
ring_char_0(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
tff(f500,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f271,f497]) ).
tff(f497,plain,
( spl0_1
<=> pp(fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
tff(f271,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : NUM957_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 23:41:09 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % (9858)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (9861)WARNING: value z3 for option sas not known
% 0.13/0.38 % (9862)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38 % (9865)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)
% 0.13/0.38 % (9864)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)
% 0.13/0.38 % (9860)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38 % (9861)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)
% 0.13/0.38 % (9863)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)
% 0.13/0.38 % (9865)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.38 % Exception at run slice level
% 0.13/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.38 % Exception at run slice level
% 0.13/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.38 % (9859)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.38 % Exception at run slice level
% 0.19/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.39 % (9867)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)
% 0.19/0.39 % (9866)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.19/0.40 % (9866)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.40 % (9867)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.19/0.40 % Exception at run slice level
% 0.19/0.40 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.40 % (9868)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)
% 0.19/0.40 % (9863)First to succeed.
% 0.19/0.41 % (9869)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)
% 0.19/0.42 % (9863)Refutation found. Thanks to Tanya!
% 0.19/0.42 % SZS status Theorem for theBenchmark
% 0.19/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.43 % (9863)------------------------------
% 0.19/0.43 % (9863)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.43 % (9863)Termination reason: Refutation
% 0.19/0.43
% 0.19/0.43 % (9863)Memory used [KB]: 1465
% 0.19/0.43 % (9863)Time elapsed: 0.041 s
% 0.19/0.43 % (9863)Instructions burned: 78 (million)
% 0.19/0.43 % (9863)------------------------------
% 0.19/0.43 % (9863)------------------------------
% 0.19/0.43 % (9858)Success in time 0.056 s
%------------------------------------------------------------------------------