TSTP Solution File: NUM925+5 by Vampire-SAT---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.9
% Problem : NUM925+5 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d SAT
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 13:28:41 EDT 2024
% Result : Theorem 1.10s 0.51s
% Output : Refutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 331
% Syntax : Number of formulae : 1102 ( 331 unt; 0 def)
% Number of atoms : 2715 ( 789 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 2770 (1157 ~;1118 |; 108 &)
% ( 282 <=>; 105 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 216 ( 214 usr; 201 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 1381 (1381 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3096,plain,
$false,
inference(avatar_sat_refutation,[],[f724,f729,f734,f739,f744,f749,f754,f759,f764,f769,f774,f779,f784,f789,f794,f799,f804,f809,f814,f819,f824,f829,f834,f839,f844,f849,f854,f859,f864,f869,f874,f879,f883,f887,f892,f896,f902,f906,f912,f919,f923,f927,f931,f941,f945,f949,f953,f958,f962,f966,f989,f993,f997,f1001,f1005,f1009,f1014,f1040,f1050,f1057,f1061,f1065,f1069,f1073,f1077,f1081,f1085,f1089,f1093,f1097,f1101,f1120,f1146,f1150,f1157,f1161,f1165,f1169,f1173,f1177,f1181,f1185,f1195,f1264,f1268,f1277,f1281,f1285,f1289,f1293,f1297,f1302,f1311,f1316,f1325,f1329,f1352,f1356,f1360,f1364,f1368,f1404,f1408,f1412,f1418,f1422,f1426,f1430,f1434,f1438,f1442,f1446,f1450,f1454,f1459,f1463,f1467,f1471,f1475,f1480,f1485,f1489,f1493,f1505,f1854,f1858,f1875,f1912,f1916,f1920,f1924,f1928,f1932,f1936,f1940,f1996,f2000,f2004,f2009,f2013,f2017,f2027,f2031,f2096,f2100,f2104,f2111,f2124,f2129,f2133,f2137,f2141,f2145,f2214,f2219,f2223,f2227,f2232,f2236,f2296,f2300,f2326,f2330,f2390,f2394,f2398,f2440,f2445,f2464,f2468,f2473,f2490,f2494,f2679,f2684,f2730,f2734,f2778,f2796,f2800,f2818,f2824,f2838,f2869,f2873,f2877,f2882,f2886,f2890,f2894,f2898,f3061,f3065,f3069,f3073,f3077,f3081,f3085,f3089,f3094,f3095]) ).
fof(f3095,plain,
( spl0_22
| ~ spl0_57
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f3016,f2879,f1011,f826]) ).
fof(f826,plain,
( spl0_22
<=> ord_less(int,pls,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1011,plain,
( spl0_57
<=> ord_less(int,pls,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f2879,plain,
( spl0_187
<=> pls = plus_plus(int,one_one(int),semiring_1_of_nat(int,n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f3016,plain,
( ord_less(int,pls,pls)
| ~ spl0_57
| ~ spl0_187 ),
inference(superposition,[],[f1013,f2881]) ).
fof(f2881,plain,
( pls = plus_plus(int,one_one(int),semiring_1_of_nat(int,n))
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f2879]) ).
fof(f1013,plain,
( ord_less(int,pls,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f1011]) ).
fof(f3094,plain,
( ~ spl0_21
| spl0_200
| ~ spl0_17
| ~ spl0_23
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f2114,f2109,f831,f801,f3091,f821]) ).
fof(f821,plain,
( spl0_21
<=> power(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f3091,plain,
( spl0_200
<=> one_one(int) = power_power(int,pls,zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f801,plain,
( spl0_17
<=> semiring_0(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f831,plain,
( spl0_23
<=> pls = zero_zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f2109,plain,
( spl0_148
<=> ! [X0] :
( one_one(X0) = power_power(X0,zero_zero(X0),zero_zero(nat))
| ~ power(X0)
| ~ semiring_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f2114,plain,
( one_one(int) = power_power(int,pls,zero_zero(nat))
| ~ power(int)
| ~ spl0_17
| ~ spl0_23
| ~ spl0_148 ),
inference(forward_demodulation,[],[f2113,f833]) ).
fof(f833,plain,
( pls = zero_zero(int)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f831]) ).
fof(f2113,plain,
( ~ power(int)
| one_one(int) = power_power(int,zero_zero(int),zero_zero(nat))
| ~ spl0_17
| ~ spl0_148 ),
inference(resolution,[],[f2110,f803]) ).
fof(f803,plain,
( semiring_0(int)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f801]) ).
fof(f2110,plain,
( ! [X0] :
( ~ semiring_0(X0)
| ~ power(X0)
| one_one(X0) = power_power(X0,zero_zero(X0),zero_zero(nat)) )
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f2109]) ).
fof(f3089,plain,
( spl0_199
| ~ spl0_56
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f1802,f1457,f1007,f3087]) ).
fof(f3087,plain,
( spl0_199
<=> ! [X0] : pls != plus_plus(int,one_one(int),plus_plus(int,X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1007,plain,
( spl0_56
<=> ! [X0] : pls != plus_plus(int,plus_plus(int,one_one(int),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f1457,plain,
( spl0_115
<=> ! [X2,X0,X1] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,plus_plus(int,X0,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f1802,plain,
( ! [X0] : pls != plus_plus(int,one_one(int),plus_plus(int,X0,X0))
| ~ spl0_56
| ~ spl0_115 ),
inference(superposition,[],[f1008,f1458]) ).
fof(f1458,plain,
( ! [X2,X0,X1] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,plus_plus(int,X0,X1),X2)
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1457]) ).
fof(f1008,plain,
( ! [X0] : pls != plus_plus(int,plus_plus(int,one_one(int),X0),X0)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f1007]) ).
fof(f3085,plain,
( spl0_198
| ~ spl0_30
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f1209,f1163,f866,f3083]) ).
fof(f3083,plain,
( spl0_198
<=> ! [X0] :
( ord_less(int,number_number_of(int,X0),pls)
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f866,plain,
( spl0_30
<=> pls = number_number_of(int,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1163,plain,
( spl0_77
<=> ! [X0,X1] :
( ord_less(int,number_number_of(int,X0),number_number_of(int,X1))
| ~ ord_less(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1209,plain,
( ! [X0] :
( ord_less(int,number_number_of(int,X0),pls)
| ~ ord_less(int,X0,pls) )
| ~ spl0_30
| ~ spl0_77 ),
inference(superposition,[],[f1164,f868]) ).
fof(f868,plain,
( pls = number_number_of(int,pls)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f866]) ).
fof(f1164,plain,
( ! [X0,X1] :
( ord_less(int,number_number_of(int,X0),number_number_of(int,X1))
| ~ ord_less(int,X0,X1) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1163]) ).
fof(f3081,plain,
( spl0_197
| ~ spl0_30
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f1207,f1163,f866,f3079]) ).
fof(f3079,plain,
( spl0_197
<=> ! [X0] :
( ord_less(int,pls,number_number_of(int,X0))
| ~ ord_less(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1207,plain,
( ! [X0] :
( ord_less(int,pls,number_number_of(int,X0))
| ~ ord_less(int,pls,X0) )
| ~ spl0_30
| ~ spl0_77 ),
inference(superposition,[],[f1164,f868]) ).
fof(f3077,plain,
( spl0_196
| ~ spl0_30
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f1204,f1159,f866,f3075]) ).
fof(f3075,plain,
( spl0_196
<=> ! [X0] :
( ~ ord_less(int,number_number_of(int,X0),pls)
| ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f1159,plain,
( spl0_76
<=> ! [X0,X1] :
( ord_less(int,X0,X1)
| ~ ord_less(int,number_number_of(int,X0),number_number_of(int,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1204,plain,
( ! [X0] :
( ~ ord_less(int,number_number_of(int,X0),pls)
| ord_less(int,X0,pls) )
| ~ spl0_30
| ~ spl0_76 ),
inference(superposition,[],[f1160,f868]) ).
fof(f1160,plain,
( ! [X0,X1] :
( ~ ord_less(int,number_number_of(int,X0),number_number_of(int,X1))
| ord_less(int,X0,X1) )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f3073,plain,
( spl0_195
| ~ spl0_30
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f1202,f1159,f866,f3071]) ).
fof(f3071,plain,
( spl0_195
<=> ! [X0] :
( ~ ord_less(int,pls,number_number_of(int,X0))
| ord_less(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f1202,plain,
( ! [X0] :
( ~ ord_less(int,pls,number_number_of(int,X0))
| ord_less(int,pls,X0) )
| ~ spl0_30
| ~ spl0_76 ),
inference(superposition,[],[f1160,f868]) ).
fof(f3069,plain,
( spl0_194
| ~ spl0_46
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f1045,f1007,f947,f3067]) ).
fof(f3067,plain,
( spl0_194
<=> ! [X0] : pls != plus_plus(int,X0,plus_plus(int,one_one(int),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f947,plain,
( spl0_46
<=> ! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f1045,plain,
( ! [X0] : pls != plus_plus(int,X0,plus_plus(int,one_one(int),X0))
| ~ spl0_46
| ~ spl0_56 ),
inference(superposition,[],[f1008,f948]) ).
fof(f948,plain,
( ! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0)
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f947]) ).
fof(f3065,plain,
( spl0_193
| ~ spl0_46
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f1042,f1007,f947,f3063]) ).
fof(f3063,plain,
( spl0_193
<=> ! [X0] : pls != plus_plus(int,plus_plus(int,X0,one_one(int)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1042,plain,
( ! [X0] : pls != plus_plus(int,plus_plus(int,X0,one_one(int)),X0)
| ~ spl0_46
| ~ spl0_56 ),
inference(superposition,[],[f1008,f948]) ).
fof(f3061,plain,
( spl0_192
| ~ spl0_37
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f1032,f1003,f899,f3059]) ).
fof(f3059,plain,
( spl0_192
<=> ! [X0] :
( one_one(int) != semiring_1_of_nat(int,X0)
| one_one(nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f899,plain,
( spl0_37
<=> one_one(int) = semiring_1_of_nat(int,one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1003,plain,
( spl0_55
<=> ! [X0,X1] :
( X0 = X1
| semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1032,plain,
( ! [X0] :
( one_one(int) != semiring_1_of_nat(int,X0)
| one_one(nat) = X0 )
| ~ spl0_37
| ~ spl0_55 ),
inference(superposition,[],[f1004,f901]) ).
fof(f901,plain,
( one_one(int) = semiring_1_of_nat(int,one_one(nat))
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f899]) ).
fof(f1004,plain,
( ! [X0,X1] :
( semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1)
| X0 = X1 )
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f1003]) ).
fof(f2898,plain,
( spl0_191
| ~ spl0_34
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f1199,f1155,f885,f2896]) ).
fof(f2896,plain,
( spl0_191
<=> ! [X0] :
( ord_less(int,X0,one_one(int))
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f885,plain,
( spl0_34
<=> ! [X0] : plus_plus(int,pls,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1155,plain,
( spl0_75
<=> ! [X0,X1] :
( ord_less(int,X0,plus_plus(int,X1,one_one(int)))
| ~ ord_less(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1199,plain,
( ! [X0] :
( ord_less(int,X0,one_one(int))
| ~ ord_less(int,X0,pls) )
| ~ spl0_34
| ~ spl0_75 ),
inference(superposition,[],[f1156,f886]) ).
fof(f886,plain,
( ! [X0] : plus_plus(int,pls,X0) = X0
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f885]) ).
fof(f1156,plain,
( ! [X0,X1] :
( ord_less(int,X0,plus_plus(int,X1,one_one(int)))
| ~ ord_less(int,X0,X1) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f1155]) ).
fof(f2894,plain,
( spl0_190
| ~ spl0_19
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f1128,f1083,f811,f2892]) ).
fof(f2892,plain,
( spl0_190
<=> ! [X0] : semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,ti(nat,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f811,plain,
( spl0_19
<=> number_semiring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f1083,plain,
( spl0_67
<=> ! [X0,X1] :
( semiring_1_of_nat(X1,X0) = semiring_1_of_nat(X1,ti(nat,X0))
| ~ number_semiring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1128,plain,
( ! [X0] : semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,ti(nat,X0))
| ~ spl0_19
| ~ spl0_67 ),
inference(resolution,[],[f1084,f813]) ).
fof(f813,plain,
( number_semiring(int)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f811]) ).
fof(f1084,plain,
( ! [X0,X1] :
( ~ number_semiring(X1)
| semiring_1_of_nat(X1,X0) = semiring_1_of_nat(X1,ti(nat,X0)) )
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f1083]) ).
fof(f2890,plain,
( spl0_189
| ~ spl0_18
| ~ spl0_67 ),
inference(avatar_split_clause,[],[f1127,f1083,f806,f2888]) ).
fof(f2888,plain,
( spl0_189
<=> ! [X0] : semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,ti(nat,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f806,plain,
( spl0_18
<=> number_semiring(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1127,plain,
( ! [X0] : semiring_1_of_nat(nat,X0) = semiring_1_of_nat(nat,ti(nat,X0))
| ~ spl0_18
| ~ spl0_67 ),
inference(resolution,[],[f1084,f808]) ).
fof(f808,plain,
( number_semiring(nat)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f806]) ).
fof(f2886,plain,
( spl0_188
| ~ spl0_18
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f1125,f1079,f806,f2884]) ).
fof(f2884,plain,
( spl0_188
<=> ! [X0] : semiring_1_of_nat(nat,X0) = ti(nat,semiring_1_of_nat(nat,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1079,plain,
( spl0_66
<=> ! [X0,X1] :
( semiring_1_of_nat(X1,X0) = ti(X1,semiring_1_of_nat(X1,X0))
| ~ number_semiring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1125,plain,
( ! [X0] : semiring_1_of_nat(nat,X0) = ti(nat,semiring_1_of_nat(nat,X0))
| ~ spl0_18
| ~ spl0_66 ),
inference(resolution,[],[f1080,f808]) ).
fof(f1080,plain,
( ! [X0,X1] :
( ~ number_semiring(X1)
| semiring_1_of_nat(X1,X0) = ti(X1,semiring_1_of_nat(X1,X0)) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f1079]) ).
fof(f2882,plain,
( spl0_187
| ~ spl0_40
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2841,f2836,f916,f2879]) ).
fof(f916,plain,
( spl0_40
<=> pls = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(nat,one_one(nat),one_one(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f2836,plain,
( spl0_183
<=> ! [X0] :
( pls = X0
| pls != power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f2841,plain,
( pls = plus_plus(int,one_one(int),semiring_1_of_nat(int,n))
| ~ spl0_40
| ~ spl0_183 ),
inference(trivial_inequality_removal,[],[f2839]) ).
fof(f2839,plain,
( pls != pls
| pls = plus_plus(int,one_one(int),semiring_1_of_nat(int,n))
| ~ spl0_40
| ~ spl0_183 ),
inference(superposition,[],[f2837,f918]) ).
fof(f918,plain,
( pls = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(nat,one_one(nat),one_one(nat)))
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f916]) ).
fof(f2837,plain,
( ! [X0] :
( pls != power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat)))
| pls = X0 )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f2836]) ).
fof(f2877,plain,
( spl0_186
| ~ spl0_9
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f1124,f1075,f761,f2875]) ).
fof(f2875,plain,
( spl0_186
<=> ! [X0] : number_number_of(int,X0) = number_number_of(int,ti(int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f761,plain,
( spl0_9
<=> number(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1075,plain,
( spl0_65
<=> ! [X0,X1] :
( number_number_of(X1,X0) = number_number_of(X1,ti(int,X0))
| ~ number(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1124,plain,
( ! [X0] : number_number_of(int,X0) = number_number_of(int,ti(int,X0))
| ~ spl0_9
| ~ spl0_65 ),
inference(resolution,[],[f1076,f763]) ).
fof(f763,plain,
( number(int)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f761]) ).
fof(f1076,plain,
( ! [X0,X1] :
( ~ number(X1)
| number_number_of(X1,X0) = number_number_of(X1,ti(int,X0)) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f1075]) ).
fof(f2873,plain,
( spl0_185
| ~ spl0_8
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f1123,f1075,f756,f2871]) ).
fof(f2871,plain,
( spl0_185
<=> ! [X0] : number_number_of(nat,X0) = number_number_of(nat,ti(int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f756,plain,
( spl0_8
<=> number(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f1123,plain,
( ! [X0] : number_number_of(nat,X0) = number_number_of(nat,ti(int,X0))
| ~ spl0_8
| ~ spl0_65 ),
inference(resolution,[],[f1076,f758]) ).
fof(f758,plain,
( number(nat)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f756]) ).
fof(f2869,plain,
( spl0_184
| ~ spl0_8
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f1121,f1071,f756,f2867]) ).
fof(f2867,plain,
( spl0_184
<=> ! [X0] : number_number_of(nat,X0) = ti(nat,number_number_of(nat,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1071,plain,
( spl0_64
<=> ! [X0,X1] :
( number_number_of(X1,X0) = ti(X1,number_number_of(X1,X0))
| ~ number(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1121,plain,
( ! [X0] : number_number_of(nat,X0) = ti(nat,number_number_of(nat,X0))
| ~ spl0_8
| ~ spl0_64 ),
inference(resolution,[],[f1072,f758]) ).
fof(f1072,plain,
( ! [X0,X1] :
( ~ number(X1)
| number_number_of(X1,X0) = ti(X1,number_number_of(X1,X0)) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1071]) ).
fof(f2838,plain,
( ~ spl0_4
| spl0_183
| ~ spl0_23
| ~ spl0_34
| ~ spl0_40
| ~ spl0_83
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f2694,f2677,f1193,f916,f885,f831,f2836,f736]) ).
fof(f736,plain,
( spl0_4
<=> linordered_idom(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1193,plain,
( spl0_83
<=> ! [X0] : ti(int,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f2677,plain,
( spl0_174
<=> ! [X2,X0,X1] :
( zero_zero(X0) != plus_plus(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))))
| ti(X0,X2) = zero_zero(X0)
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f2694,plain,
( ! [X0] :
( pls = X0
| pls != power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat)))
| ~ linordered_idom(int) )
| ~ spl0_23
| ~ spl0_34
| ~ spl0_40
| ~ spl0_83
| ~ spl0_174 ),
inference(forward_demodulation,[],[f2693,f833]) ).
fof(f2693,plain,
( ! [X0] :
( zero_zero(int) = X0
| pls != power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat)))
| ~ linordered_idom(int) )
| ~ spl0_23
| ~ spl0_34
| ~ spl0_40
| ~ spl0_83
| ~ spl0_174 ),
inference(forward_demodulation,[],[f2692,f1194]) ).
fof(f1194,plain,
( ! [X0] : ti(int,X0) = X0
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f1193]) ).
fof(f2692,plain,
( ! [X0] :
( pls != power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat)))
| zero_zero(int) = ti(int,X0)
| ~ linordered_idom(int) )
| ~ spl0_23
| ~ spl0_34
| ~ spl0_40
| ~ spl0_174 ),
inference(forward_demodulation,[],[f2691,f833]) ).
fof(f2691,plain,
( ! [X0] :
( zero_zero(int) != power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat)))
| zero_zero(int) = ti(int,X0)
| ~ linordered_idom(int) )
| ~ spl0_34
| ~ spl0_40
| ~ spl0_174 ),
inference(forward_demodulation,[],[f2685,f886]) ).
fof(f2685,plain,
( ! [X0] :
( zero_zero(int) != plus_plus(int,pls,power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat))))
| zero_zero(int) = ti(int,X0)
| ~ linordered_idom(int) )
| ~ spl0_40
| ~ spl0_174 ),
inference(superposition,[],[f2678,f918]) ).
fof(f2678,plain,
( ! [X2,X0,X1] :
( zero_zero(X0) != plus_plus(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))))
| ti(X0,X2) = zero_zero(X0)
| ~ linordered_idom(X0) )
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f2677]) ).
fof(f2824,plain,
( spl0_182
| ~ spl0_18
| ~ spl0_114
| ~ spl0_115
| ~ spl0_141
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f2820,f2816,f2015,f1457,f1452,f806,f2822]) ).
fof(f2822,plain,
( spl0_182
<=> ! [X0] : power_power(int,X0,number_number_of(nat,plus_plus(int,one_one(int),plus_plus(int,one_one(int),plus_plus(int,one_one(int),one_one(int)))))) = power_power(int,power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat))),plus_plus(nat,one_one(nat),one_one(nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1452,plain,
( spl0_114
<=> ! [X2,X0,X1] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,X1,plus_plus(int,X0,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f2015,plain,
( spl0_141
<=> ! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,one_one(int),one_one(int)))
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f2816,plain,
( spl0_181
<=> ! [X0] : power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f2820,plain,
( ! [X0] : power_power(int,X0,number_number_of(nat,plus_plus(int,one_one(int),plus_plus(int,one_one(int),plus_plus(int,one_one(int),one_one(int)))))) = power_power(int,power_power(int,X0,plus_plus(nat,one_one(nat),one_one(nat))),plus_plus(nat,one_one(nat),one_one(nat)))
| ~ spl0_18
| ~ spl0_114
| ~ spl0_115
| ~ spl0_141
| ~ spl0_181 ),
inference(forward_demodulation,[],[f2819,f2022]) ).
fof(f2022,plain,
( plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))
| ~ spl0_18
| ~ spl0_141 ),
inference(resolution,[],[f2016,f808]) ).
fof(f2016,plain,
( ! [X0] :
( ~ number_semiring(X0)
| plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,one_one(int),one_one(int))) )
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f2015]) ).
fof(f2819,plain,
( ! [X0] : power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,one_one(int),plus_plus(int,one_one(int),plus_plus(int,one_one(int),one_one(int))))))
| ~ spl0_114
| ~ spl0_115
| ~ spl0_181 ),
inference(forward_demodulation,[],[f2817,f1820]) ).
fof(f1820,plain,
( ! [X2,X3,X0,X1] : plus_plus(int,X3,plus_plus(int,X0,plus_plus(int,X1,X2))) = plus_plus(int,plus_plus(int,X0,X1),plus_plus(int,X3,X2))
| ~ spl0_114
| ~ spl0_115 ),
inference(superposition,[],[f1453,f1458]) ).
fof(f1453,plain,
( ! [X2,X0,X1] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,X1,plus_plus(int,X0,X2))
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1452]) ).
fof(f2817,plain,
( ! [X0] : power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int)))))
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f2816]) ).
fof(f2818,plain,
spl0_181,
inference(avatar_split_clause,[],[f656,f2816]) ).
fof(f656,plain,
! [X0] : power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))),number_number_of(nat,plus_plus(int,one_one(int),one_one(int)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),one_one(int)),plus_plus(int,one_one(int),one_one(int))))),
inference(forward_demodulation,[],[f655,f417]) ).
fof(f417,plain,
! [X0] : plus_plus(int,X0,pls) = X0,
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
! [X0] : plus_plus(int,X0,pls) = X0,
inference(rectify,[],[f108]) ).
fof(f108,axiom,
! [X18] : plus_plus(int,X18,pls) = X18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f655,plain,
! [X0] : power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))),number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)),plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls))))),
inference(forward_demodulation,[],[f578,f417]) ).
fof(f578,plain,
! [X0] : power_power(int,power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) = power_power(int,X0,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)),plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))),
inference(definition_unfolding,[],[f426,f421,f425,f421,f425,f421,f421,f425]) ).
fof(f425,plain,
! [X0] : bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0),
inference(cnf_transformation,[],[f169]) ).
fof(f169,plain,
! [X0] : bit1(X0) = plus_plus(int,plus_plus(int,one_one(int),X0),X0),
inference(rectify,[],[f125]) ).
fof(f125,axiom,
! [X18] : bit1(X18) = plus_plus(int,plus_plus(int,one_one(int),X18),X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f421,plain,
! [X0] : bit0(X0) = plus_plus(int,X0,X0),
inference(cnf_transformation,[],[f165]) ).
fof(f165,plain,
! [X0] : bit0(X0) = plus_plus(int,X0,X0),
inference(rectify,[],[f111]) ).
fof(f111,axiom,
! [X18] : bit0(X18) = plus_plus(int,X18,X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f426,plain,
! [X0] : power_power(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))) = power_power(int,X0,number_number_of(nat,bit0(bit0(bit1(pls))))),
inference(cnf_transformation,[],[f170]) ).
fof(f170,plain,
! [X0] : power_power(int,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))) = power_power(int,X0,number_number_of(nat,bit0(bit0(bit1(pls))))),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X8] : power_power(int,power_power(int,X8,number_number_of(nat,bit0(bit1(pls)))),number_number_of(nat,bit0(bit1(pls)))) = power_power(int,X8,number_number_of(nat,bit0(bit0(bit1(pls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2800,plain,
( spl0_180
| ~ spl0_55
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2305,f2216,f1003,f2798]) ).
fof(f2798,plain,
( spl0_180
<=> ! [X0] :
( pls != semiring_1_of_nat(int,X0)
| plus_plus(nat,one_one(nat),n) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f2216,plain,
( spl0_156
<=> pls = semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f2305,plain,
( ! [X0] :
( pls != semiring_1_of_nat(int,X0)
| plus_plus(nat,one_one(nat),n) = X0 )
| ~ spl0_55
| ~ spl0_156 ),
inference(superposition,[],[f1004,f2218]) ).
fof(f2218,plain,
( pls = semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n))
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f2216]) ).
fof(f2796,plain,
spl0_179,
inference(avatar_split_clause,[],[f667,f2794]) ).
fof(f2794,plain,
( spl0_179
<=> ! [X2,X0,X1] :
( ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat)))))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0)
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f667,plain,
! [X2,X0,X1] :
( ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat)))))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f589,f575]) ).
fof(f575,plain,
plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))),
inference(definition_unfolding,[],[f414,f421,f425]) ).
fof(f414,plain,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
number_number_of(nat,bit0(bit1(pls))) = plus_plus(nat,one_one(nat),one_one(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f589,plain,
! [X2,X0,X1] :
( ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0)
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f440,f421,f425,f421,f425]) ).
fof(f440,plain,
! [X2,X0,X1] :
( ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0)
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f333,plain,
! [X0] :
( ! [X1,X2] :
( ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))))
| ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) ) )
& ( ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0)
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))) ) )
| ~ linordered_idom(X0) ),
inference(flattening,[],[f332]) ).
fof(f332,plain,
! [X0] :
( ! [X1,X2] :
( ( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))))
| ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) ) )
& ( ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0)
| ~ ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f259]) ).
fof(f259,plain,
! [X0] :
( ! [X1,X2] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))))
<=> ( ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0) ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0] :
( linordered_idom(X0)
=> ! [X1,X2] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))))
<=> ( ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0) ) ) ),
inference(rectify,[],[f130]) ).
fof(f130,axiom,
! [X0] :
( linordered_idom(X0)
=> ! [X3,X4] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X3,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X4,number_number_of(nat,bit0(bit1(pls))))))
<=> ( zero_zero(X0) != ti(X0,X4)
| zero_zero(X0) != ti(X0,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2778,plain,
spl0_178,
inference(avatar_split_clause,[],[f662,f2776]) ).
fof(f2776,plain,
( spl0_178
<=> ! [X2,X0,X1] :
( zero_zero(X0) = plus_plus(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0)
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f662,plain,
! [X2,X0,X1] :
( zero_zero(X0) = plus_plus(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f584,f575]) ).
fof(f584,plain,
! [X2,X0,X1] :
( zero_zero(X0) = plus_plus(X0,power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f439,f421,f425,f421,f425]) ).
fof(f439,plain,
! [X2,X0,X1] :
( zero_zero(X0) = plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f331]) ).
fof(f331,plain,
! [X0] :
( ! [X1,X2] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0) )
& ( ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) )
| zero_zero(X0) != plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))) ) )
| ~ linordered_idom(X0) ),
inference(flattening,[],[f330]) ).
fof(f330,plain,
! [X0] :
( ! [X1,X2] :
( ( zero_zero(X0) = plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
| ti(X0,X2) != zero_zero(X0)
| ti(X0,X1) != zero_zero(X0) )
& ( ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) )
| zero_zero(X0) != plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f258]) ).
fof(f258,plain,
! [X0] :
( ! [X1,X2] :
( zero_zero(X0) = plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
<=> ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( linordered_idom(X0)
=> ! [X1,X2] :
( zero_zero(X0) = plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
<=> ( ti(X0,X2) = zero_zero(X0)
& ti(X0,X1) = zero_zero(X0) ) ) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( linordered_idom(X0)
=> ! [X3,X4] :
( zero_zero(X0) = plus_plus(X0,power_power(X0,X3,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X4,number_number_of(nat,bit0(bit1(pls)))))
<=> ( zero_zero(X0) = ti(X0,X4)
& zero_zero(X0) = ti(X0,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2734,plain,
spl0_177,
inference(avatar_split_clause,[],[f666,f2732]) ).
fof(f2732,plain,
( spl0_177
<=> ! [X2,X0,X1] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat)))))
| ti(X0,X1) = zero_zero(X0)
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f666,plain,
! [X2,X0,X1] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat)))))
| ti(X0,X1) = zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f588,f575]) ).
fof(f588,plain,
! [X2,X0,X1] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))))
| ti(X0,X1) = zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f441,f421,f425,f421,f425]) ).
fof(f441,plain,
! [X2,X0,X1] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))))
| ti(X0,X1) = zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f2730,plain,
spl0_176,
inference(avatar_split_clause,[],[f665,f2728]) ).
fof(f2728,plain,
( spl0_176
<=> ! [X2,X0,X1] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat)))))
| ti(X0,X2) = zero_zero(X0)
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f665,plain,
! [X2,X0,X1] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat)))))
| ti(X0,X2) = zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f587,f575]) ).
fof(f587,plain,
! [X2,X0,X1] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))))
| ti(X0,X2) = zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f442,f421,f425,f421,f425]) ).
fof(f442,plain,
! [X2,X0,X1] :
( ord_less(X0,zero_zero(X0),plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls))))))
| ti(X0,X2) = zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f2684,plain,
spl0_175,
inference(avatar_split_clause,[],[f664,f2682]) ).
fof(f2682,plain,
( spl0_175
<=> ! [X2,X0,X1] :
( zero_zero(X0) != plus_plus(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))))
| ti(X0,X1) = zero_zero(X0)
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f664,plain,
! [X2,X0,X1] :
( zero_zero(X0) != plus_plus(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))))
| ti(X0,X1) = zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f586,f575]) ).
fof(f586,plain,
! [X2,X0,X1] :
( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != plus_plus(X0,power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f437,f421,f425,f421,f425]) ).
fof(f437,plain,
! [X2,X0,X1] :
( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f331]) ).
fof(f2679,plain,
spl0_174,
inference(avatar_split_clause,[],[f663,f2677]) ).
fof(f663,plain,
! [X2,X0,X1] :
( zero_zero(X0) != plus_plus(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),power_power(X0,X2,plus_plus(nat,one_one(nat),one_one(nat))))
| ti(X0,X2) = zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f585,f575]) ).
fof(f585,plain,
! [X2,X0,X1] :
( ti(X0,X2) = zero_zero(X0)
| zero_zero(X0) != plus_plus(X0,power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),power_power(X0,X2,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f438,f421,f425,f421,f425]) ).
fof(f438,plain,
! [X2,X0,X1] :
( ti(X0,X2) = zero_zero(X0)
| zero_zero(X0) != plus_plus(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),power_power(X0,X2,number_number_of(nat,bit0(bit1(pls)))))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f331]) ).
fof(f2494,plain,
( spl0_173
| ~ spl0_115
| ~ spl0_171 ),
inference(avatar_split_clause,[],[f2475,f2471,f1457,f2492]) ).
fof(f2492,plain,
( spl0_173
<=> ! [X0,X1] : plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X0,X1)),plus_plus(int,X0,X1)) = plus_plus(int,X0,plus_plus(int,one_one(int),plus_plus(int,X0,plus_plus(int,X1,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f2471,plain,
( spl0_171
<=> ! [X0,X1] : plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X0,X1)),plus_plus(int,X0,X1)) = plus_plus(int,plus_plus(int,X0,plus_plus(int,one_one(int),X0)),plus_plus(int,X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f2475,plain,
( ! [X0,X1] : plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X0,X1)),plus_plus(int,X0,X1)) = plus_plus(int,X0,plus_plus(int,one_one(int),plus_plus(int,X0,plus_plus(int,X1,X1))))
| ~ spl0_115
| ~ spl0_171 ),
inference(forward_demodulation,[],[f2474,f1458]) ).
fof(f2474,plain,
( ! [X0,X1] : plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X0,X1)),plus_plus(int,X0,X1)) = plus_plus(int,X0,plus_plus(int,plus_plus(int,one_one(int),X0),plus_plus(int,X1,X1)))
| ~ spl0_115
| ~ spl0_171 ),
inference(forward_demodulation,[],[f2472,f1458]) ).
fof(f2472,plain,
( ! [X0,X1] : plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X0,X1)),plus_plus(int,X0,X1)) = plus_plus(int,plus_plus(int,X0,plus_plus(int,one_one(int),X0)),plus_plus(int,X1,X1))
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f2471]) ).
fof(f2490,plain,
( spl0_172
| ~ spl0_115
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f2469,f2466,f1457,f2488]) ).
fof(f2488,plain,
( spl0_172
<=> ! [X0,X1] : plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X0,X1)),plus_plus(int,X0,X1)) = plus_plus(int,X0,plus_plus(int,X0,plus_plus(int,X1,plus_plus(int,one_one(int),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f2466,plain,
( spl0_170
<=> ! [X0,X1] : plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X0,X1)),plus_plus(int,X0,X1)) = plus_plus(int,plus_plus(int,X0,X0),plus_plus(int,X1,plus_plus(int,one_one(int),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f2469,plain,
( ! [X0,X1] : plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X0,X1)),plus_plus(int,X0,X1)) = plus_plus(int,X0,plus_plus(int,X0,plus_plus(int,X1,plus_plus(int,one_one(int),X1))))
| ~ spl0_115
| ~ spl0_170 ),
inference(forward_demodulation,[],[f2467,f1458]) ).
fof(f2467,plain,
( ! [X0,X1] : plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X0,X1)),plus_plus(int,X0,X1)) = plus_plus(int,plus_plus(int,X0,X0),plus_plus(int,X1,plus_plus(int,one_one(int),X1)))
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f2466]) ).
fof(f2473,plain,
spl0_171,
inference(avatar_split_clause,[],[f707,f2471]) ).
fof(f707,plain,
! [X0,X1] : plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X0,X1)),plus_plus(int,X0,X1)) = plus_plus(int,plus_plus(int,X0,plus_plus(int,one_one(int),X0)),plus_plus(int,X1,X1)),
inference(forward_demodulation,[],[f620,f503]) ).
fof(f503,plain,
! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0,X1] : plus_plus(int,X0,X1) = plus_plus(int,X1,X0),
inference(rectify,[],[f80]) ).
fof(f80,axiom,
! [X14,X6] : plus_plus(int,X14,X6) = plus_plus(int,X6,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f620,plain,
! [X0,X1] : plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X0,X1)),plus_plus(int,X0,X1)) = plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),plus_plus(int,X1,X1)),
inference(definition_unfolding,[],[f506,f425,f425,f421]) ).
fof(f506,plain,
! [X0,X1] : bit1(plus_plus(int,X0,X1)) = plus_plus(int,bit1(X0),bit0(X1)),
inference(cnf_transformation,[],[f210]) ).
fof(f210,plain,
! [X0,X1] : bit1(plus_plus(int,X0,X1)) = plus_plus(int,bit1(X0),bit0(X1)),
inference(rectify,[],[f123]) ).
fof(f123,axiom,
! [X18,X28] : plus_plus(int,bit1(X18),bit0(X28)) = bit1(plus_plus(int,X18,X28)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2468,plain,
spl0_170,
inference(avatar_split_clause,[],[f706,f2466]) ).
fof(f706,plain,
! [X0,X1] : plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X0,X1)),plus_plus(int,X0,X1)) = plus_plus(int,plus_plus(int,X0,X0),plus_plus(int,X1,plus_plus(int,one_one(int),X1))),
inference(forward_demodulation,[],[f618,f503]) ).
fof(f618,plain,
! [X0,X1] : plus_plus(int,plus_plus(int,one_one(int),plus_plus(int,X0,X1)),plus_plus(int,X0,X1)) = plus_plus(int,plus_plus(int,X0,X0),plus_plus(int,plus_plus(int,one_one(int),X1),X1)),
inference(definition_unfolding,[],[f504,f425,f421,f425]) ).
fof(f504,plain,
! [X0,X1] : bit1(plus_plus(int,X0,X1)) = plus_plus(int,bit0(X0),bit1(X1)),
inference(cnf_transformation,[],[f208]) ).
fof(f208,plain,
! [X0,X1] : bit1(plus_plus(int,X0,X1)) = plus_plus(int,bit0(X0),bit1(X1)),
inference(rectify,[],[f124]) ).
fof(f124,axiom,
! [X18,X28] : bit1(plus_plus(int,X18,X28)) = plus_plus(int,bit0(X18),bit1(X28)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2464,plain,
spl0_169,
inference(avatar_split_clause,[],[f477,f2462]) ).
fof(f2462,plain,
( spl0_169
<=> ! [X2,X0,X1] :
( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,X2))
| zero_zero(nat) = number_number_of(nat,X2)
| ti(X0,X1) != zero_zero(X0)
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f477,plain,
! [X2,X0,X1] :
( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,X2))
| zero_zero(nat) = number_number_of(nat,X2)
| ti(X0,X1) != zero_zero(X0)
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f342]) ).
fof(f342,plain,
! [X0] :
( ! [X1,X2] :
( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,X2))
| zero_zero(nat) = number_number_of(nat,X2)
| ti(X0,X1) != zero_zero(X0) )
& ( ( zero_zero(nat) != number_number_of(nat,X2)
& ti(X0,X1) = zero_zero(X0) )
| zero_zero(X0) != power_power(X0,X1,number_number_of(nat,X2)) ) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(flattening,[],[f341]) ).
fof(f341,plain,
! [X0] :
( ! [X1,X2] :
( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,X2))
| zero_zero(nat) = number_number_of(nat,X2)
| ti(X0,X1) != zero_zero(X0) )
& ( ( zero_zero(nat) != number_number_of(nat,X2)
& ti(X0,X1) = zero_zero(X0) )
| zero_zero(X0) != power_power(X0,X1,number_number_of(nat,X2)) ) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(nnf_transformation,[],[f293]) ).
fof(f293,plain,
! [X0] :
( ! [X1,X2] :
( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,X2))
<=> ( zero_zero(nat) != number_number_of(nat,X2)
& ti(X0,X1) = zero_zero(X0) ) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(flattening,[],[f292]) ).
fof(f292,plain,
! [X0] :
( ! [X1,X2] :
( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,X2))
<=> ( zero_zero(nat) != number_number_of(nat,X2)
& ti(X0,X1) = zero_zero(X0) ) )
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(ennf_transformation,[],[f193]) ).
fof(f193,plain,
! [X0] :
( ( zero_neq_one(X0)
& no_zero_divisors(X0)
& mult_zero(X0)
& power(X0) )
=> ! [X1,X2] :
( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,X2))
<=> ( zero_zero(nat) != number_number_of(nat,X2)
& ti(X0,X1) = zero_zero(X0) ) ) ),
inference(rectify,[],[f119]) ).
fof(f119,axiom,
! [X0] :
( ( zero_neq_one(X0)
& no_zero_divisors(X0)
& mult_zero(X0)
& power(X0) )
=> ! [X5,X22] :
( zero_zero(X0) = power_power(X0,X5,number_number_of(nat,X22))
<=> ( zero_zero(nat) != number_number_of(nat,X22)
& zero_zero(X0) = ti(X0,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2445,plain,
spl0_168,
inference(avatar_split_clause,[],[f575,f2442]) ).
fof(f2442,plain,
( spl0_168
<=> plus_plus(nat,one_one(nat),one_one(nat)) = number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f2440,plain,
( spl0_167
| ~ spl0_50
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f2312,f2216,f964,f2437]) ).
fof(f2437,plain,
( spl0_167
<=> zero_zero(nat) = plus_plus(nat,one_one(nat),n) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f964,plain,
( spl0_50
<=> ! [X0] :
( pls != semiring_1_of_nat(int,X0)
| zero_zero(nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f2312,plain,
( zero_zero(nat) = plus_plus(nat,one_one(nat),n)
| ~ spl0_50
| ~ spl0_156 ),
inference(trivial_inequality_removal,[],[f2304]) ).
fof(f2304,plain,
( pls != pls
| zero_zero(nat) = plus_plus(nat,one_one(nat),n)
| ~ spl0_50
| ~ spl0_156 ),
inference(superposition,[],[f965,f2218]) ).
fof(f965,plain,
( ! [X0] :
( pls != semiring_1_of_nat(int,X0)
| zero_zero(nat) = X0 )
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f964]) ).
fof(f2398,plain,
spl0_166,
inference(avatar_split_clause,[],[f513,f2396]) ).
fof(f2396,plain,
( spl0_166
<=> ! [X0,X1] :
( plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) = number_number_of(nat,plus_plus(int,X1,X0))
| ord_less(int,X0,pls)
| ord_less(int,X1,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f513,plain,
! [X0,X1] :
( plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) = number_number_of(nat,plus_plus(int,X1,X0))
| ord_less(int,X0,pls)
| ord_less(int,X1,pls) ),
inference(cnf_transformation,[],[f300]) ).
fof(f300,plain,
! [X0,X1] :
( ( ( ( plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) = number_number_of(nat,plus_plus(int,X1,X0))
| ord_less(int,X0,pls) )
& ( number_number_of(nat,X1) = plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less(int,X0,pls) ) )
| ord_less(int,X1,pls) )
& ( number_number_of(nat,X0) = plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less(int,X1,pls) ) ),
inference(ennf_transformation,[],[f215]) ).
fof(f215,plain,
! [X0,X1] :
( ( ~ ord_less(int,X1,pls)
=> ( ( ~ ord_less(int,X0,pls)
=> plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) = number_number_of(nat,plus_plus(int,X1,X0)) )
& ( ord_less(int,X0,pls)
=> number_number_of(nat,X1) = plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ) )
& ( ord_less(int,X1,pls)
=> number_number_of(nat,X0) = plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0)) ) ),
inference(rectify,[],[f69]) ).
fof(f69,axiom,
! [X21,X7] :
( ( ~ ord_less(int,X7,pls)
=> ( ( ~ ord_less(int,X21,pls)
=> plus_plus(nat,number_number_of(nat,X7),number_number_of(nat,X21)) = number_number_of(nat,plus_plus(int,X7,X21)) )
& ( ord_less(int,X21,pls)
=> number_number_of(nat,X7) = plus_plus(nat,number_number_of(nat,X7),number_number_of(nat,X21)) ) ) )
& ( ord_less(int,X7,pls)
=> number_number_of(nat,X21) = plus_plus(nat,number_number_of(nat,X7),number_number_of(nat,X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2394,plain,
spl0_165,
inference(avatar_split_clause,[],[f475,f2392]) ).
fof(f2392,plain,
( spl0_165
<=> ! [X2,X0,X1] :
( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != power_power(X0,X1,number_number_of(nat,X2))
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f475,plain,
! [X2,X0,X1] :
( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != power_power(X0,X1,number_number_of(nat,X2))
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f342]) ).
fof(f2390,plain,
spl0_164,
inference(avatar_split_clause,[],[f454,f2388]) ).
fof(f2388,plain,
( spl0_164
<=> ! [X0,X3,X2,X1] :
( plus_plus(X0,number_number_of(X0,X1),plus_plus(X0,number_number_of(X0,X2),X3)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X1,X2)),X3)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f454,plain,
! [X2,X3,X0,X1] :
( plus_plus(X0,number_number_of(X0,X1),plus_plus(X0,number_number_of(X0,X2),X3)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X1,X2)),X3)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f271,plain,
! [X0] :
( ! [X1,X2,X3] : plus_plus(X0,number_number_of(X0,X1),plus_plus(X0,number_number_of(X0,X2),X3)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X1,X2)),X3)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f184]) ).
fof(f184,plain,
! [X0] :
( number_ring(X0)
=> ! [X1,X2,X3] : plus_plus(X0,number_number_of(X0,X1),plus_plus(X0,number_number_of(X0,X2),X3)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X1,X2)),X3) ),
inference(rectify,[],[f120]) ).
fof(f120,axiom,
! [X0] :
( number_ring(X0)
=> ! [X7,X6,X14] : plus_plus(X0,number_number_of(X0,X7),plus_plus(X0,number_number_of(X0,X6),X14)) = plus_plus(X0,number_number_of(X0,plus_plus(int,X7,X6)),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2330,plain,
spl0_163,
inference(avatar_split_clause,[],[f715,f2328]) ).
fof(f2328,plain,
( spl0_163
<=> ! [X0,X1] :
( ~ ord_less(int,plus_plus(int,X0,plus_plus(int,one_one(int),X0)),plus_plus(int,X1,plus_plus(int,one_one(int),X1)))
| ord_less(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f715,plain,
! [X0,X1] :
( ~ ord_less(int,plus_plus(int,X0,plus_plus(int,one_one(int),X0)),plus_plus(int,X1,plus_plus(int,one_one(int),X1)))
| ord_less(int,X0,X1) ),
inference(forward_demodulation,[],[f714,f503]) ).
fof(f714,plain,
! [X0,X1] :
( ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),plus_plus(int,X1,plus_plus(int,one_one(int),X1)))
| ord_less(int,X0,X1) ),
inference(forward_demodulation,[],[f634,f503]) ).
fof(f634,plain,
! [X0,X1] :
( ord_less(int,X0,X1)
| ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),plus_plus(int,plus_plus(int,one_one(int),X1),X1)) ),
inference(definition_unfolding,[],[f535,f425,f425]) ).
fof(f535,plain,
! [X0,X1] :
( ord_less(int,X0,X1)
| ~ ord_less(int,bit1(X0),bit1(X1)) ),
inference(cnf_transformation,[],[f360]) ).
fof(f360,plain,
! [X0,X1] :
( ( ord_less(int,bit1(X0),bit1(X1))
| ~ ord_less(int,X0,X1) )
& ( ord_less(int,X0,X1)
| ~ ord_less(int,bit1(X0),bit1(X1)) ) ),
inference(nnf_transformation,[],[f229]) ).
fof(f229,plain,
! [X0,X1] :
( ord_less(int,bit1(X0),bit1(X1))
<=> ord_less(int,X0,X1) ),
inference(rectify,[],[f63]) ).
fof(f63,axiom,
! [X16,X17] :
( ord_less(int,bit1(X16),bit1(X17))
<=> ord_less(int,X16,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2326,plain,
spl0_162,
inference(avatar_split_clause,[],[f713,f2324]) ).
fof(f2324,plain,
( spl0_162
<=> ! [X0,X1] :
( ord_less(int,plus_plus(int,X0,plus_plus(int,one_one(int),X0)),plus_plus(int,X1,plus_plus(int,one_one(int),X1)))
| ~ ord_less(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f713,plain,
! [X0,X1] :
( ord_less(int,plus_plus(int,X0,plus_plus(int,one_one(int),X0)),plus_plus(int,X1,plus_plus(int,one_one(int),X1)))
| ~ ord_less(int,X0,X1) ),
inference(forward_demodulation,[],[f712,f503]) ).
fof(f712,plain,
! [X0,X1] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),plus_plus(int,X1,plus_plus(int,one_one(int),X1)))
| ~ ord_less(int,X0,X1) ),
inference(forward_demodulation,[],[f633,f503]) ).
fof(f633,plain,
! [X0,X1] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),plus_plus(int,plus_plus(int,one_one(int),X1),X1))
| ~ ord_less(int,X0,X1) ),
inference(definition_unfolding,[],[f536,f425,f425]) ).
fof(f536,plain,
! [X0,X1] :
( ord_less(int,bit1(X0),bit1(X1))
| ~ ord_less(int,X0,X1) ),
inference(cnf_transformation,[],[f360]) ).
fof(f2300,plain,
( ~ spl0_32
| ~ spl0_147 ),
inference(avatar_contradiction_clause,[],[f2299]) ).
fof(f2299,plain,
( $false
| ~ spl0_32
| ~ spl0_147 ),
inference(trivial_inequality_removal,[],[f2297]) ).
fof(f2297,plain,
( zero_zero(nat) != zero_zero(nat)
| ~ spl0_32
| ~ spl0_147 ),
inference(superposition,[],[f2107,f878]) ).
fof(f878,plain,
( zero_zero(nat) = number_number_of(nat,pls)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f876]) ).
fof(f876,plain,
( spl0_32
<=> zero_zero(nat) = number_number_of(nat,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f2107,plain,
( ! [X1] : zero_zero(nat) != number_number_of(nat,X1)
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f2106]) ).
fof(f2106,plain,
( spl0_147
<=> ! [X1] : zero_zero(nat) != number_number_of(nat,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f2296,plain,
( spl0_161
| spl0_147 ),
inference(avatar_split_clause,[],[f690,f2106,f2294]) ).
fof(f2294,plain,
( spl0_161
<=> ! [X0,X1] :
( zero_zero(X0) != power_power(X0,X1,zero_zero(nat))
| ~ power(X0)
| ~ mult_zero(X0)
| ~ no_zero_divisors(X0)
| ~ zero_neq_one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f690,plain,
! [X2,X0,X1] :
( zero_zero(nat) != number_number_of(nat,X2)
| zero_zero(X0) != power_power(X0,X1,zero_zero(nat))
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(inner_rewriting,[],[f476]) ).
fof(f476,plain,
! [X2,X0,X1] :
( zero_zero(nat) != number_number_of(nat,X2)
| zero_zero(X0) != power_power(X0,X1,number_number_of(nat,X2))
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f342]) ).
fof(f2236,plain,
spl0_160,
inference(avatar_split_clause,[],[f661,f2234]) ).
fof(f2234,plain,
( spl0_160
<=> ! [X0,X1] :
( ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))))
| ti(X0,X1) != zero_zero(X0)
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f661,plain,
! [X0,X1] :
( ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))))
| ti(X0,X1) != zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f583,f575]) ).
fof(f583,plain,
! [X0,X1] :
( ti(X0,X1) != zero_zero(X0)
| ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f435,f421,f425]) ).
fof(f435,plain,
! [X0,X1] :
( ti(X0,X1) != zero_zero(X0)
| ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f329]) ).
fof(f329,plain,
! [X0] :
( ! [X1] :
( ( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ti(X0,X1) = zero_zero(X0) )
& ( ti(X0,X1) != zero_zero(X0)
| ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f257]) ).
fof(f257,plain,
! [X0] :
( ! [X1] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
<=> ti(X0,X1) != zero_zero(X0) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f175]) ).
fof(f175,plain,
! [X0] :
( linordered_idom(X0)
=> ! [X1] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
<=> ti(X0,X1) != zero_zero(X0) ) ),
inference(rectify,[],[f128]) ).
fof(f128,axiom,
! [X0] :
( linordered_idom(X0)
=> ! [X5] :
( ord_less(X0,zero_zero(X0),power_power(X0,X5,number_number_of(nat,bit0(bit1(pls)))))
<=> zero_zero(X0) != ti(X0,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2232,plain,
spl0_159,
inference(avatar_split_clause,[],[f660,f2230]) ).
fof(f2230,plain,
( spl0_159
<=> ! [X0,X1] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))))
| ti(X0,X1) = zero_zero(X0)
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f660,plain,
! [X0,X1] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))))
| ti(X0,X1) = zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f582,f575]) ).
fof(f582,plain,
! [X0,X1] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))))
| ti(X0,X1) = zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f436,f421,f425]) ).
fof(f436,plain,
! [X0,X1] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ti(X0,X1) = zero_zero(X0)
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f329]) ).
fof(f2227,plain,
spl0_158,
inference(avatar_split_clause,[],[f619,f2225]) ).
fof(f2225,plain,
( spl0_158
<=> ! [X0,X1] : plus_plus(int,plus_plus(int,X0,X0),plus_plus(int,X1,X1)) = plus_plus(int,plus_plus(int,X0,X1),plus_plus(int,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f619,plain,
! [X0,X1] : plus_plus(int,plus_plus(int,X0,X0),plus_plus(int,X1,X1)) = plus_plus(int,plus_plus(int,X0,X1),plus_plus(int,X0,X1)),
inference(definition_unfolding,[],[f505,f421,f421,f421]) ).
fof(f505,plain,
! [X0,X1] : plus_plus(int,bit0(X0),bit0(X1)) = bit0(plus_plus(int,X0,X1)),
inference(cnf_transformation,[],[f209]) ).
fof(f209,plain,
! [X0,X1] : plus_plus(int,bit0(X0),bit0(X1)) = bit0(plus_plus(int,X0,X1)),
inference(rectify,[],[f110]) ).
fof(f110,axiom,
! [X18,X28] : plus_plus(int,bit0(X18),bit0(X28)) = bit0(plus_plus(int,X18,X28)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2223,plain,
spl0_157,
inference(avatar_split_clause,[],[f548,f2221]) ).
fof(f2221,plain,
( spl0_157
<=> ! [X2,X0,X1] : plus_plus(int,semiring_1_of_nat(int,X0),plus_plus(int,semiring_1_of_nat(int,X1),X2)) = plus_plus(int,semiring_1_of_nat(int,plus_plus(nat,X0,X1)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f548,plain,
! [X2,X0,X1] : plus_plus(int,semiring_1_of_nat(int,X0),plus_plus(int,semiring_1_of_nat(int,X1),X2)) = plus_plus(int,semiring_1_of_nat(int,plus_plus(nat,X0,X1)),X2),
inference(cnf_transformation,[],[f236]) ).
fof(f236,plain,
! [X0,X1,X2] : plus_plus(int,semiring_1_of_nat(int,X0),plus_plus(int,semiring_1_of_nat(int,X1),X2)) = plus_plus(int,semiring_1_of_nat(int,plus_plus(nat,X0,X1)),X2),
inference(rectify,[],[f55]) ).
fof(f55,axiom,
! [X12,X13,X14] : plus_plus(int,semiring_1_of_nat(int,X12),plus_plus(int,semiring_1_of_nat(int,X13),X14)) = plus_plus(int,semiring_1_of_nat(int,plus_plus(nat,X12,X13)),X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2219,plain,
( ~ spl0_1
| spl0_156
| ~ spl0_23
| ~ spl0_37
| ~ spl0_40
| ~ spl0_83
| ~ spl0_111
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f2207,f2143,f1440,f1193,f916,f899,f831,f2216,f721]) ).
fof(f721,plain,
( spl0_1
<=> ring_11004092258visors(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f1440,plain,
( spl0_111
<=> ! [X0,X1] : semiring_1_of_nat(int,plus_plus(nat,X0,X1)) = plus_plus(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f2143,plain,
( spl0_154
<=> ! [X0,X1] :
( zero_zero(X0) != power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat)))
| ti(X0,X1) = zero_zero(X0)
| ~ ring_11004092258visors(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f2207,plain,
( pls = semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n))
| ~ ring_11004092258visors(int)
| ~ spl0_23
| ~ spl0_37
| ~ spl0_40
| ~ spl0_83
| ~ spl0_111
| ~ spl0_154 ),
inference(forward_demodulation,[],[f2206,f833]) ).
fof(f2206,plain,
( zero_zero(int) = semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n))
| ~ ring_11004092258visors(int)
| ~ spl0_23
| ~ spl0_37
| ~ spl0_40
| ~ spl0_83
| ~ spl0_111
| ~ spl0_154 ),
inference(forward_demodulation,[],[f2205,f1570]) ).
fof(f1570,plain,
( ! [X0] : semiring_1_of_nat(int,plus_plus(nat,one_one(nat),X0)) = plus_plus(int,one_one(int),semiring_1_of_nat(int,X0))
| ~ spl0_37
| ~ spl0_111 ),
inference(superposition,[],[f1441,f901]) ).
fof(f1441,plain,
( ! [X0,X1] : semiring_1_of_nat(int,plus_plus(nat,X0,X1)) = plus_plus(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X1))
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f1440]) ).
fof(f2205,plain,
( zero_zero(int) = plus_plus(int,one_one(int),semiring_1_of_nat(int,n))
| ~ ring_11004092258visors(int)
| ~ spl0_23
| ~ spl0_40
| ~ spl0_83
| ~ spl0_154 ),
inference(forward_demodulation,[],[f2204,f1194]) ).
fof(f2204,plain,
( zero_zero(int) = ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))
| ~ ring_11004092258visors(int)
| ~ spl0_23
| ~ spl0_40
| ~ spl0_154 ),
inference(trivial_inequality_removal,[],[f2203]) ).
fof(f2203,plain,
( pls != pls
| zero_zero(int) = ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))
| ~ ring_11004092258visors(int)
| ~ spl0_23
| ~ spl0_40
| ~ spl0_154 ),
inference(forward_demodulation,[],[f2201,f833]) ).
fof(f2201,plain,
( pls != zero_zero(int)
| zero_zero(int) = ti(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)))
| ~ ring_11004092258visors(int)
| ~ spl0_40
| ~ spl0_154 ),
inference(superposition,[],[f2144,f918]) ).
fof(f2144,plain,
( ! [X0,X1] :
( zero_zero(X0) != power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat)))
| ti(X0,X1) = zero_zero(X0)
| ~ ring_11004092258visors(X0) )
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f2143]) ).
fof(f2214,plain,
spl0_155,
inference(avatar_split_clause,[],[f570,f2212]) ).
fof(f2212,plain,
( spl0_155
<=> ! [X0] : plus_plus(int,plus_plus(int,one_one(int),X0),X0) = plus_plus(int,plus_plus(int,one_one(int),ti(int,X0)),ti(int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f570,plain,
! [X0] : plus_plus(int,plus_plus(int,one_one(int),X0),X0) = plus_plus(int,plus_plus(int,one_one(int),ti(int,X0)),ti(int,X0)),
inference(definition_unfolding,[],[f374,f425,f425]) ).
fof(f374,plain,
! [X0] : bit1(X0) = bit1(ti(int,X0)),
inference(cnf_transformation,[],[f159]) ).
fof(f159,plain,
! [X0] : bit1(X0) = bit1(ti(int,X0)),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X1] : bit1(ti(int,X1)) = bit1(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2145,plain,
spl0_154,
inference(avatar_split_clause,[],[f658,f2143]) ).
fof(f658,plain,
! [X0,X1] :
( zero_zero(X0) != power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat)))
| ti(X0,X1) = zero_zero(X0)
| ~ ring_11004092258visors(X0) ),
inference(forward_demodulation,[],[f580,f575]) ).
fof(f580,plain,
! [X0,X1] :
( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))
| ~ ring_11004092258visors(X0) ),
inference(definition_unfolding,[],[f427,f421,f425]) ).
fof(f427,plain,
! [X0,X1] :
( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))
| ~ ring_11004092258visors(X0) ),
inference(cnf_transformation,[],[f326]) ).
fof(f326,plain,
! [X0] :
( ! [X1] :
( ( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))
| ti(X0,X1) != zero_zero(X0) )
& ( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))) ) )
| ~ ring_11004092258visors(X0) ),
inference(nnf_transformation,[],[f252]) ).
fof(f252,plain,
! [X0] :
( ! [X1] :
( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))
<=> ti(X0,X1) = zero_zero(X0) )
| ~ ring_11004092258visors(X0) ),
inference(ennf_transformation,[],[f171]) ).
fof(f171,plain,
! [X0] :
( ring_11004092258visors(X0)
=> ! [X1] :
( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))
<=> ti(X0,X1) = zero_zero(X0) ) ),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ring_11004092258visors(X0)
=> ! [X5] :
( zero_zero(X0) = power_power(X0,X5,number_number_of(nat,bit0(bit1(pls))))
<=> zero_zero(X0) = ti(X0,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2141,plain,
spl0_153,
inference(avatar_split_clause,[],[f657,f2139]) ).
fof(f2139,plain,
( spl0_153
<=> ! [X0,X1] :
( zero_zero(X0) = power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat)))
| ti(X0,X1) != zero_zero(X0)
| ~ ring_11004092258visors(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f657,plain,
! [X0,X1] :
( zero_zero(X0) = power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat)))
| ti(X0,X1) != zero_zero(X0)
| ~ ring_11004092258visors(X0) ),
inference(forward_demodulation,[],[f579,f575]) ).
fof(f579,plain,
! [X0,X1] :
( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))
| ti(X0,X1) != zero_zero(X0)
| ~ ring_11004092258visors(X0) ),
inference(definition_unfolding,[],[f428,f421,f425]) ).
fof(f428,plain,
! [X0,X1] :
( zero_zero(X0) = power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))
| ti(X0,X1) != zero_zero(X0)
| ~ ring_11004092258visors(X0) ),
inference(cnf_transformation,[],[f326]) ).
fof(f2137,plain,
spl0_152,
inference(avatar_split_clause,[],[f624,f2135]) ).
fof(f2135,plain,
( spl0_152
<=> ! [X0,X1] :
( X0 = X1
| plus_plus(int,plus_plus(int,one_one(int),X0),X0) != plus_plus(int,plus_plus(int,one_one(int),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f624,plain,
! [X0,X1] :
( X0 = X1
| plus_plus(int,plus_plus(int,one_one(int),X0),X0) != plus_plus(int,plus_plus(int,one_one(int),X1),X1) ),
inference(definition_unfolding,[],[f521,f425,f425]) ).
fof(f521,plain,
! [X0,X1] :
( X0 = X1
| bit1(X1) != bit1(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f353,plain,
! [X0,X1] :
( ( bit1(X1) = bit1(X0)
| X0 != X1 )
& ( X0 = X1
| bit1(X1) != bit1(X0) ) ),
inference(nnf_transformation,[],[f222]) ).
fof(f222,plain,
! [X0,X1] :
( bit1(X1) = bit1(X0)
<=> X0 = X1 ),
inference(rectify,[],[f75]) ).
fof(f75,axiom,
! [X10,X11] :
( bit1(X10) = bit1(X11)
<=> X10 = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2133,plain,
spl0_151,
inference(avatar_split_clause,[],[f512,f2131]) ).
fof(f2131,plain,
( spl0_151
<=> ! [X0,X1] :
( number_number_of(nat,X1) = plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less(int,X0,pls)
| ord_less(int,X1,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f512,plain,
! [X0,X1] :
( number_number_of(nat,X1) = plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less(int,X0,pls)
| ord_less(int,X1,pls) ),
inference(cnf_transformation,[],[f300]) ).
fof(f2129,plain,
( ~ spl0_20
| spl0_150
| ~ spl0_16
| ~ spl0_62 ),
inference(avatar_split_clause,[],[f1106,f1063,f796,f2126,f816]) ).
fof(f816,plain,
( spl0_20
<=> power(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f2126,plain,
( spl0_150
<=> zero_zero(nat) = ti(nat,zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f796,plain,
( spl0_16
<=> semiring_0(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1063,plain,
( spl0_62
<=> ! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ semiring_0(X0)
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1106,plain,
( zero_zero(nat) = ti(nat,zero_zero(nat))
| ~ power(nat)
| ~ spl0_16
| ~ spl0_62 ),
inference(resolution,[],[f1064,f798]) ).
fof(f798,plain,
( semiring_0(nat)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f796]) ).
fof(f1064,plain,
( ! [X0] :
( ~ semiring_0(X0)
| zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ power(X0) )
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f1063]) ).
fof(f2124,plain,
spl0_149,
inference(avatar_split_clause,[],[f481,f2122]) ).
fof(f2122,plain,
( spl0_149
<=> ! [X0,X1] :
( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1))
| zero_zero(nat) = number_number_of(nat,X1)
| ~ semiring_0(X0)
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f481,plain,
! [X0,X1] :
( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1))
| zero_zero(nat) = number_number_of(nat,X1)
| ~ semiring_0(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f299,plain,
! [X0] :
( ! [X1] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1))
| zero_zero(nat) = number_number_of(nat,X1) )
& ( one_one(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1))
| zero_zero(nat) != number_number_of(nat,X1) ) )
| ~ semiring_0(X0)
| ~ power(X0) ),
inference(flattening,[],[f298]) ).
fof(f298,plain,
! [X0] :
( ! [X1] :
( ( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1))
| zero_zero(nat) = number_number_of(nat,X1) )
& ( one_one(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1))
| zero_zero(nat) != number_number_of(nat,X1) ) )
| ~ semiring_0(X0)
| ~ power(X0) ),
inference(ennf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0] :
( ( semiring_0(X0)
& power(X0) )
=> ! [X1] :
( ( zero_zero(nat) != number_number_of(nat,X1)
=> zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1)) )
& ( zero_zero(nat) = number_number_of(nat,X1)
=> one_one(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1)) ) ) ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X0] :
( ( semiring_0(X0)
& power(X0) )
=> ! [X6] :
( ( number_number_of(nat,X6) != zero_zero(nat)
=> zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X6)) )
& ( number_number_of(nat,X6) = zero_zero(nat)
=> one_one(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2111,plain,
( spl0_147
| spl0_148 ),
inference(avatar_split_clause,[],[f691,f2109,f2106]) ).
fof(f691,plain,
! [X0,X1] :
( one_one(X0) = power_power(X0,zero_zero(X0),zero_zero(nat))
| zero_zero(nat) != number_number_of(nat,X1)
| ~ semiring_0(X0)
| ~ power(X0) ),
inference(inner_rewriting,[],[f480]) ).
fof(f480,plain,
! [X0,X1] :
( one_one(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,X1))
| zero_zero(nat) != number_number_of(nat,X1)
| ~ semiring_0(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f2104,plain,
spl0_146,
inference(avatar_split_clause,[],[f562,f2102]) ).
fof(f2102,plain,
( spl0_146
<=> ! [X2,X0,X1] :
( power_power(X2,X0,X1) = power_power(X2,ti(X2,X0),X1)
| ~ zero_neq_one(X2)
| ~ no_zero_divisors(X2)
| ~ mult_zero(X2)
| ~ power(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f562,plain,
! [X2,X0,X1] :
( power_power(X2,X0,X1) = power_power(X2,ti(X2,X0),X1)
| ~ zero_neq_one(X2)
| ~ no_zero_divisors(X2)
| ~ mult_zero(X2)
| ~ power(X2) ),
inference(cnf_transformation,[],[f319]) ).
fof(f319,plain,
! [X0,X1,X2] :
( power_power(X2,X0,X1) = power_power(X2,ti(X2,X0),X1)
| ~ zero_neq_one(X2)
| ~ no_zero_divisors(X2)
| ~ mult_zero(X2)
| ~ power(X2) ),
inference(flattening,[],[f318]) ).
fof(f318,plain,
! [X0,X1,X2] :
( power_power(X2,X0,X1) = power_power(X2,ti(X2,X0),X1)
| ~ zero_neq_one(X2)
| ~ no_zero_divisors(X2)
| ~ mult_zero(X2)
| ~ power(X2) ),
inference(ennf_transformation,[],[f248]) ).
fof(f248,plain,
! [X0,X1,X2] :
( ( zero_neq_one(X2)
& no_zero_divisors(X2)
& mult_zero(X2)
& power(X2) )
=> power_power(X2,X0,X1) = power_power(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X1,X2,X0] :
( ( zero_neq_one(X0)
& no_zero_divisors(X0)
& mult_zero(X0)
& power(X0) )
=> power_power(X0,ti(X0,X1),X2) = power_power(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2100,plain,
spl0_145,
inference(avatar_split_clause,[],[f561,f2098]) ).
fof(f2098,plain,
( spl0_145
<=> ! [X2,X0,X1] :
( power_power(X2,X0,X1) = ti(X2,power_power(X2,X0,X1))
| ~ zero_neq_one(X2)
| ~ no_zero_divisors(X2)
| ~ mult_zero(X2)
| ~ power(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f561,plain,
! [X2,X0,X1] :
( power_power(X2,X0,X1) = ti(X2,power_power(X2,X0,X1))
| ~ zero_neq_one(X2)
| ~ no_zero_divisors(X2)
| ~ mult_zero(X2)
| ~ power(X2) ),
inference(cnf_transformation,[],[f317]) ).
fof(f317,plain,
! [X0,X1,X2] :
( power_power(X2,X0,X1) = ti(X2,power_power(X2,X0,X1))
| ~ zero_neq_one(X2)
| ~ no_zero_divisors(X2)
| ~ mult_zero(X2)
| ~ power(X2) ),
inference(flattening,[],[f316]) ).
fof(f316,plain,
! [X0,X1,X2] :
( power_power(X2,X0,X1) = ti(X2,power_power(X2,X0,X1))
| ~ zero_neq_one(X2)
| ~ no_zero_divisors(X2)
| ~ mult_zero(X2)
| ~ power(X2) ),
inference(ennf_transformation,[],[f247]) ).
fof(f247,plain,
! [X0,X1,X2] :
( ( zero_neq_one(X2)
& no_zero_divisors(X2)
& mult_zero(X2)
& power(X2) )
=> power_power(X2,X0,X1) = ti(X2,power_power(X2,X0,X1)) ),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X1,X2,X0] :
( ( zero_neq_one(X0)
& no_zero_divisors(X0)
& mult_zero(X0)
& power(X0) )
=> power_power(X0,X1,X2) = ti(X0,power_power(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2096,plain,
spl0_144,
inference(avatar_split_clause,[],[f560,f2094]) ).
fof(f2094,plain,
( spl0_144
<=> ! [X2,X0,X1] :
( power_power(X2,X0,X1) = power_power(X2,X0,ti(nat,X1))
| ~ zero_neq_one(X2)
| ~ no_zero_divisors(X2)
| ~ mult_zero(X2)
| ~ power(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f560,plain,
! [X2,X0,X1] :
( power_power(X2,X0,X1) = power_power(X2,X0,ti(nat,X1))
| ~ zero_neq_one(X2)
| ~ no_zero_divisors(X2)
| ~ mult_zero(X2)
| ~ power(X2) ),
inference(cnf_transformation,[],[f315]) ).
fof(f315,plain,
! [X0,X1,X2] :
( power_power(X2,X0,X1) = power_power(X2,X0,ti(nat,X1))
| ~ zero_neq_one(X2)
| ~ no_zero_divisors(X2)
| ~ mult_zero(X2)
| ~ power(X2) ),
inference(flattening,[],[f314]) ).
fof(f314,plain,
! [X0,X1,X2] :
( power_power(X2,X0,X1) = power_power(X2,X0,ti(nat,X1))
| ~ zero_neq_one(X2)
| ~ no_zero_divisors(X2)
| ~ mult_zero(X2)
| ~ power(X2) ),
inference(ennf_transformation,[],[f246]) ).
fof(f246,plain,
! [X0,X1,X2] :
( ( zero_neq_one(X2)
& no_zero_divisors(X2)
& mult_zero(X2)
& power(X2) )
=> power_power(X2,X0,X1) = power_power(X2,X0,ti(nat,X1)) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X1,X2,X0] :
( ( zero_neq_one(X0)
& no_zero_divisors(X0)
& mult_zero(X0)
& power(X0) )
=> power_power(X0,X1,X2) = power_power(X0,X1,ti(nat,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2031,plain,
spl0_143,
inference(avatar_split_clause,[],[f709,f2029]) ).
fof(f2029,plain,
( spl0_143
<=> ! [X0,X1] :
( ~ ord_less(int,plus_plus(int,X0,plus_plus(int,one_one(int),X0)),plus_plus(int,X1,X1))
| ord_less(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f709,plain,
! [X0,X1] :
( ~ ord_less(int,plus_plus(int,X0,plus_plus(int,one_one(int),X0)),plus_plus(int,X1,X1))
| ord_less(int,X0,X1) ),
inference(forward_demodulation,[],[f630,f503]) ).
fof(f630,plain,
! [X0,X1] :
( ord_less(int,X0,X1)
| ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),plus_plus(int,X1,X1)) ),
inference(definition_unfolding,[],[f531,f425,f421]) ).
fof(f531,plain,
! [X0,X1] :
( ord_less(int,X0,X1)
| ~ ord_less(int,bit1(X0),bit0(X1)) ),
inference(cnf_transformation,[],[f358]) ).
fof(f358,plain,
! [X0,X1] :
( ( ord_less(int,bit1(X0),bit0(X1))
| ~ ord_less(int,X0,X1) )
& ( ord_less(int,X0,X1)
| ~ ord_less(int,bit1(X0),bit0(X1)) ) ),
inference(nnf_transformation,[],[f227]) ).
fof(f227,plain,
! [X0,X1] :
( ord_less(int,bit1(X0),bit0(X1))
<=> ord_less(int,X0,X1) ),
inference(rectify,[],[f85]) ).
fof(f85,axiom,
! [X16,X17] :
( ord_less(int,bit1(X16),bit0(X17))
<=> ord_less(int,X16,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2027,plain,
spl0_142,
inference(avatar_split_clause,[],[f708,f2025]) ).
fof(f2025,plain,
( spl0_142
<=> ! [X0,X1] :
( ord_less(int,plus_plus(int,X0,plus_plus(int,one_one(int),X0)),plus_plus(int,X1,X1))
| ~ ord_less(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f708,plain,
! [X0,X1] :
( ord_less(int,plus_plus(int,X0,plus_plus(int,one_one(int),X0)),plus_plus(int,X1,X1))
| ~ ord_less(int,X0,X1) ),
inference(forward_demodulation,[],[f629,f503]) ).
fof(f629,plain,
! [X0,X1] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),plus_plus(int,X1,X1))
| ~ ord_less(int,X0,X1) ),
inference(definition_unfolding,[],[f532,f425,f421]) ).
fof(f532,plain,
! [X0,X1] :
( ord_less(int,bit1(X0),bit0(X1))
| ~ ord_less(int,X0,X1) ),
inference(cnf_transformation,[],[f358]) ).
fof(f2017,plain,
spl0_141,
inference(avatar_split_clause,[],[f681,f2015]) ).
fof(f681,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,one_one(int),one_one(int)))
| ~ number_semiring(X0) ),
inference(forward_demodulation,[],[f680,f417]) ).
fof(f680,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))
| ~ number_semiring(X0) ),
inference(forward_demodulation,[],[f597,f417]) ).
fof(f597,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))
| ~ number_semiring(X0) ),
inference(definition_unfolding,[],[f460,f421,f425]) ).
fof(f460,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls)))
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f276,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls)))
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( number_semiring(X0)
=> plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2013,plain,
spl0_140,
inference(avatar_split_clause,[],[f677,f2011]) ).
fof(f2011,plain,
( spl0_140
<=> ! [X0,X1] :
( 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_140])]) ).
fof(f677,plain,
! [X0,X1] :
( 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) ),
inference(forward_demodulation,[],[f676,f417]) ).
fof(f676,plain,
! [X0,X1] :
( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,plus_plus(int,one_one(int),pls)))
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f594,f417]) ).
fof(f594,plain,
! [X0,X1] :
( plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,plus_plus(int,plus_plus(int,one_one(int),pls),pls)))
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f451,f425]) ).
fof(f451,plain,
! [X0,X1] :
( 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,[],[f268]) ).
fof(f268,plain,
! [X0] :
( ! [X1] : 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,[],[f181]) ).
fof(f181,plain,
! [X0] :
( number_ring(X0)
=> ! [X1] : plus_plus(X0,number_number_of(X0,X1),one_one(X0)) = number_number_of(X0,plus_plus(int,X1,bit1(pls))) ),
inference(rectify,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( number_ring(X0)
=> ! [X7] : plus_plus(X0,number_number_of(X0,X7),one_one(X0)) = number_number_of(X0,plus_plus(int,X7,bit1(pls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2009,plain,
( ~ spl0_20
| spl0_139
| ~ spl0_16
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f1104,f1059,f796,f2006,f816]) ).
fof(f2006,plain,
( spl0_139
<=> one_one(nat) = ti(nat,one_one(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1059,plain,
( spl0_61
<=> ! [X0] :
( one_one(X0) = ti(X0,one_one(X0))
| ~ semiring_0(X0)
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1104,plain,
( one_one(nat) = ti(nat,one_one(nat))
| ~ power(nat)
| ~ spl0_16
| ~ spl0_61 ),
inference(resolution,[],[f1060,f798]) ).
fof(f1060,plain,
( ! [X0] :
( ~ semiring_0(X0)
| one_one(X0) = ti(X0,one_one(X0))
| ~ power(X0) )
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f1059]) ).
fof(f2004,plain,
spl0_138,
inference(avatar_split_clause,[],[f675,f2002]) ).
fof(f2002,plain,
( spl0_138
<=> ! [X0,X1] :
( 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_138])]) ).
fof(f675,plain,
! [X0,X1] :
( 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) ),
inference(forward_demodulation,[],[f674,f417]) ).
fof(f674,plain,
! [X0,X1] :
( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,plus_plus(int,one_one(int),pls),X1))
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f593,f417]) ).
fof(f593,plain,
! [X0,X1] :
( plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),X1))
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f450,f425]) ).
fof(f450,plain,
! [X0,X1] :
( 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,[],[f267]) ).
fof(f267,plain,
! [X0] :
( ! [X1] : 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,[],[f180]) ).
fof(f180,plain,
! [X0] :
( number_ring(X0)
=> ! [X1] : plus_plus(X0,one_one(X0),number_number_of(X0,X1)) = number_number_of(X0,plus_plus(int,bit1(pls),X1)) ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X0] :
( number_ring(X0)
=> ! [X6] : plus_plus(X0,one_one(X0),number_number_of(X0,X6)) = number_number_of(X0,plus_plus(int,bit1(pls),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f2000,plain,
spl0_137,
inference(avatar_split_clause,[],[f673,f1998]) ).
fof(f1998,plain,
( spl0_137
<=> ! [X0] :
( 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_137])]) ).
fof(f673,plain,
! [X0] :
( 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) ),
inference(forward_demodulation,[],[f672,f417]) ).
fof(f672,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,plus_plus(int,one_one(int),pls),plus_plus(int,one_one(int),pls)))
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f592,f417]) ).
fof(f592,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f447,f421,f425]) ).
fof(f447,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls)))
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f264,plain,
! [X0] :
( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls)))
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( number_ring(X0)
=> plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1996,plain,
spl0_136,
inference(avatar_split_clause,[],[f452,f1994]) ).
fof(f1994,plain,
( spl0_136
<=> ! [X2,X0,X1] :
( number_number_of(X0,plus_plus(int,X1,X2)) = plus_plus(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f452,plain,
! [X2,X0,X1] :
( number_number_of(X0,plus_plus(int,X1,X2)) = plus_plus(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f269]) ).
fof(f269,plain,
! [X0] :
( ! [X1,X2] : number_number_of(X0,plus_plus(int,X1,X2)) = plus_plus(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0] :
( number_ring(X0)
=> ! [X1,X2] : number_number_of(X0,plus_plus(int,X1,X2)) = plus_plus(X0,number_number_of(X0,X1),number_number_of(X0,X2)) ),
inference(rectify,[],[f122]) ).
fof(f122,axiom,
! [X0] :
( number_ring(X0)
=> ! [X7,X6] : number_number_of(X0,plus_plus(int,X7,X6)) = plus_plus(X0,number_number_of(X0,X7),number_number_of(X0,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1940,plain,
( spl0_135
| ~ spl0_19
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f1103,f1055,f811,f1938]) ).
fof(f1938,plain,
( spl0_135
<=> ! [X0] : semiring_1_of_nat(int,X0) = number_number_of(int,semiring_1_of_nat(int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1055,plain,
( spl0_60
<=> ! [X0,X1] :
( semiring_1_of_nat(X0,X1) = number_number_of(X0,semiring_1_of_nat(int,X1))
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1103,plain,
( ! [X0] : semiring_1_of_nat(int,X0) = number_number_of(int,semiring_1_of_nat(int,X0))
| ~ spl0_19
| ~ spl0_60 ),
inference(resolution,[],[f1056,f813]) ).
fof(f1056,plain,
( ! [X0,X1] :
( ~ number_semiring(X0)
| semiring_1_of_nat(X0,X1) = number_number_of(X0,semiring_1_of_nat(int,X1)) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f1936,plain,
spl0_134,
inference(avatar_split_clause,[],[f689,f1934]) ).
fof(f1934,plain,
( spl0_134
<=> ! [X0,X1] :
( 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_134])]) ).
fof(f689,plain,
! [X0,X1] :
( ord_less(int,X1,one_one(int))
| ~ ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f688,f417]) ).
fof(f688,plain,
! [X0,X1] :
( ord_less(int,X1,plus_plus(int,one_one(int),pls))
| ~ ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f601,f417]) ).
fof(f601,plain,
! [X0,X1] :
( ord_less(int,X1,plus_plus(int,plus_plus(int,one_one(int),pls),pls))
| ~ ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f468,f425]) ).
fof(f468,plain,
! [X0,X1] :
( 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,[],[f338]) ).
fof(f338,plain,
! [X0] :
( ! [X1] :
( ( 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,[],[f285]) ).
fof(f285,plain,
! [X0] :
( ! [X1] :
( 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,[],[f284]) ).
fof(f284,plain,
! [X0] :
( ! [X1] :
( 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,[],[f190]) ).
fof(f190,plain,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1] :
( ord_less(X0,number_number_of(X0,X1),one_one(X0))
<=> ord_less(int,X1,bit1(pls)) ) ),
inference(rectify,[],[f95]) ).
fof(f95,axiom,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X3] :
( ord_less(X0,number_number_of(X0,X3),one_one(X0))
<=> ord_less(int,X3,bit1(pls)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1932,plain,
spl0_133,
inference(avatar_split_clause,[],[f687,f1930]) ).
fof(f1930,plain,
( spl0_133
<=> ! [X0,X1] :
( ~ 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_133])]) ).
fof(f687,plain,
! [X0,X1] :
( ~ ord_less(int,X1,one_one(int))
| ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f686,f417]) ).
fof(f686,plain,
! [X0,X1] :
( ~ ord_less(int,X1,plus_plus(int,one_one(int),pls))
| ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f600,f417]) ).
fof(f600,plain,
! [X0,X1] :
( ord_less(X0,number_number_of(X0,X1),one_one(X0))
| ~ ord_less(int,X1,plus_plus(int,plus_plus(int,one_one(int),pls),pls))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f469,f425]) ).
fof(f469,plain,
! [X0,X1] :
( 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,[],[f338]) ).
fof(f1928,plain,
spl0_132,
inference(avatar_split_clause,[],[f685,f1926]) ).
fof(f1926,plain,
( spl0_132
<=> ! [X0,X1] :
( 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_132])]) ).
fof(f685,plain,
! [X0,X1] :
( ord_less(int,one_one(int),X1)
| ~ ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f684,f417]) ).
fof(f684,plain,
! [X0,X1] :
( ord_less(int,plus_plus(int,one_one(int),pls),X1)
| ~ ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f599,f417]) ).
fof(f599,plain,
! [X0,X1] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),X1)
| ~ ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f464,f425]) ).
fof(f464,plain,
! [X0,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(cnf_transformation,[],[f336]) ).
fof(f336,plain,
! [X0] :
( ! [X1] :
( ( 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,[],[f281]) ).
fof(f281,plain,
! [X0] :
( ! [X1] :
( 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,[],[f280]) ).
fof(f280,plain,
! [X0] :
( ! [X1] :
( 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,[],[f188]) ).
fof(f188,plain,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1] :
( ord_less(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less(int,bit1(pls),X1) ) ),
inference(rectify,[],[f96]) ).
fof(f96,axiom,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X4] :
( ord_less(X0,one_one(X0),number_number_of(X0,X4))
<=> ord_less(int,bit1(pls),X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1924,plain,
spl0_131,
inference(avatar_split_clause,[],[f683,f1922]) ).
fof(f1922,plain,
( spl0_131
<=> ! [X0,X1] :
( ~ 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_131])]) ).
fof(f683,plain,
! [X0,X1] :
( ~ ord_less(int,one_one(int),X1)
| ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f682,f417]) ).
fof(f682,plain,
! [X0,X1] :
( ~ ord_less(int,plus_plus(int,one_one(int),pls),X1)
| ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f598,f417]) ).
fof(f598,plain,
! [X0,X1] :
( ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f465,f425]) ).
fof(f465,plain,
! [X0,X1] :
( 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,[],[f336]) ).
fof(f1920,plain,
spl0_130,
inference(avatar_split_clause,[],[f511,f1918]) ).
fof(f1918,plain,
( spl0_130
<=> ! [X0,X1] :
( number_number_of(nat,X0) = plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less(int,X1,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f511,plain,
! [X0,X1] :
( number_number_of(nat,X0) = plus_plus(nat,number_number_of(nat,X1),number_number_of(nat,X0))
| ~ ord_less(int,X1,pls) ),
inference(cnf_transformation,[],[f300]) ).
fof(f1916,plain,
spl0_129,
inference(avatar_split_clause,[],[f473,f1914]) ).
fof(f1914,plain,
( spl0_129
<=> ! [X2,X0,X1] :
( ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ ord_less(int,X1,X2)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f473,plain,
! [X2,X0,X1] :
( ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ ord_less(int,X1,X2)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f340]) ).
fof(f340,plain,
! [X0] :
( ! [X1,X2] :
( ( ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ ord_less(int,X1,X2) )
& ( ord_less(int,X1,X2)
| ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f289]) ).
fof(f289,plain,
! [X0] :
( ! [X1,X2] :
( ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
<=> ord_less(int,X1,X2) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f288]) ).
fof(f288,plain,
! [X0] :
( ! [X1,X2] :
( ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
<=> ord_less(int,X1,X2) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f192]) ).
fof(f192,plain,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1,X2] :
( ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
<=> ord_less(int,X1,X2) ) ),
inference(rectify,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X3,X4] :
( ord_less(X0,number_number_of(X0,X3),number_number_of(X0,X4))
<=> ord_less(int,X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1912,plain,
spl0_128,
inference(avatar_split_clause,[],[f472,f1910]) ).
fof(f1910,plain,
( spl0_128
<=> ! [X2,X0,X1] :
( ord_less(int,X1,X2)
| ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f472,plain,
! [X2,X0,X1] :
( ord_less(int,X1,X2)
| ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f340]) ).
fof(f1875,plain,
( spl0_127
| ~ spl0_18
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f1102,f1055,f806,f1873]) ).
fof(f1873,plain,
( spl0_127
<=> ! [X0] : semiring_1_of_nat(nat,X0) = number_number_of(nat,semiring_1_of_nat(int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1102,plain,
( ! [X0] : semiring_1_of_nat(nat,X0) = number_number_of(nat,semiring_1_of_nat(int,X0))
| ~ spl0_18
| ~ spl0_60 ),
inference(resolution,[],[f1056,f808]) ).
fof(f1858,plain,
( spl0_126
| ~ spl0_115
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1481,f1478,f1457,f1856]) ).
fof(f1856,plain,
( spl0_126
<=> ! [X0] :
( ~ ord_less(int,plus_plus(int,one_one(int),plus_plus(int,X0,X0)),pls)
| ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1478,plain,
( spl0_120
<=> ! [X0] :
( ord_less(int,X0,pls)
| ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1481,plain,
( ! [X0] :
( ~ ord_less(int,plus_plus(int,one_one(int),plus_plus(int,X0,X0)),pls)
| ord_less(int,X0,pls) )
| ~ spl0_115
| ~ spl0_120 ),
inference(forward_demodulation,[],[f1479,f1458]) ).
fof(f1479,plain,
( ! [X0] :
( ord_less(int,X0,pls)
| ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls) )
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1478]) ).
fof(f1854,plain,
( spl0_125
| ~ spl0_115
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1476,f1473,f1457,f1852]) ).
fof(f1852,plain,
( spl0_125
<=> ! [X0] :
( ord_less(int,plus_plus(int,one_one(int),plus_plus(int,X0,X0)),pls)
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1473,plain,
( spl0_119
<=> ! [X0] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls)
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1476,plain,
( ! [X0] :
( ord_less(int,plus_plus(int,one_one(int),plus_plus(int,X0,X0)),pls)
| ~ ord_less(int,X0,pls) )
| ~ spl0_115
| ~ spl0_119 ),
inference(forward_demodulation,[],[f1474,f1458]) ).
fof(f1474,plain,
( ! [X0] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls)
| ~ ord_less(int,X0,pls) )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1473]) ).
fof(f1505,plain,
( spl0_124
| ~ spl0_43
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f979,f947,f929,f1503]) ).
fof(f1503,plain,
( spl0_124
<=> ! [X0] : ord_less(int,X0,plus_plus(int,one_one(int),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f929,plain,
( spl0_43
<=> ! [X1] : ord_less(int,X1,plus_plus(int,X1,one_one(int))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f979,plain,
( ! [X0] : ord_less(int,X0,plus_plus(int,one_one(int),X0))
| ~ spl0_43
| ~ spl0_46 ),
inference(superposition,[],[f930,f948]) ).
fof(f930,plain,
( ! [X1] : ord_less(int,X1,plus_plus(int,X1,one_one(int)))
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f929]) ).
fof(f1493,plain,
spl0_123,
inference(avatar_split_clause,[],[f679,f1491]) ).
fof(f1491,plain,
( spl0_123
<=> ! [X0] :
( zero_zero(X0) = power_power(X0,zero_zero(X0),plus_plus(nat,one_one(nat),one_one(nat)))
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f679,plain,
! [X0] :
( zero_zero(X0) = power_power(X0,zero_zero(X0),plus_plus(nat,one_one(nat),one_one(nat)))
| ~ semiring_1(X0) ),
inference(forward_demodulation,[],[f596,f575]) ).
fof(f596,plain,
! [X0] :
( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))
| ~ semiring_1(X0) ),
inference(definition_unfolding,[],[f456,f421,f425]) ).
fof(f456,plain,
! [X0] :
( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls))))
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f273,plain,
! [X0] :
( zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls))))
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( semiring_1(X0)
=> zero_zero(X0) = power_power(X0,zero_zero(X0),number_number_of(nat,bit0(bit1(pls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1489,plain,
spl0_122,
inference(avatar_split_clause,[],[f678,f1487]) ).
fof(f1487,plain,
( spl0_122
<=> ! [X0] :
( one_one(X0) = power_power(X0,one_one(X0),plus_plus(nat,one_one(nat),one_one(nat)))
| ~ semiring_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f678,plain,
! [X0] :
( one_one(X0) = power_power(X0,one_one(X0),plus_plus(nat,one_one(nat),one_one(nat)))
| ~ semiring_1(X0) ),
inference(forward_demodulation,[],[f595,f575]) ).
fof(f595,plain,
! [X0] :
( one_one(X0) = power_power(X0,one_one(X0),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))
| ~ semiring_1(X0) ),
inference(definition_unfolding,[],[f455,f421,f425]) ).
fof(f455,plain,
! [X0] :
( one_one(X0) = power_power(X0,one_one(X0),number_number_of(nat,bit0(bit1(pls))))
| ~ semiring_1(X0) ),
inference(cnf_transformation,[],[f272]) ).
fof(f272,plain,
! [X0] :
( one_one(X0) = power_power(X0,one_one(X0),number_number_of(nat,bit0(bit1(pls))))
| ~ semiring_1(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( semiring_1(X0)
=> one_one(X0) = power_power(X0,one_one(X0),number_number_of(nat,bit0(bit1(pls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1485,plain,
spl0_121,
inference(avatar_split_clause,[],[f659,f1483]) ).
fof(f1483,plain,
( spl0_121
<=> ! [X0,X1] :
( ~ ord_less(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),zero_zero(X0))
| ~ linordered_idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f659,plain,
! [X0,X1] :
( ~ ord_less(X0,power_power(X0,X1,plus_plus(nat,one_one(nat),one_one(nat))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(forward_demodulation,[],[f581,f575]) ).
fof(f581,plain,
! [X0,X1] :
( ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(definition_unfolding,[],[f432,f421,f425]) ).
fof(f432,plain,
! [X0,X1] :
( ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0] :
( ! [X1] : ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f173]) ).
fof(f173,plain,
! [X0] :
( linordered_idom(X0)
=> ! [X1] : ~ ord_less(X0,power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0)) ),
inference(rectify,[],[f129]) ).
fof(f129,axiom,
! [X0] :
( linordered_idom(X0)
=> ! [X29] : ~ ord_less(X0,power_power(X0,X29,number_number_of(nat,bit0(bit1(pls)))),zero_zero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1480,plain,
spl0_120,
inference(avatar_split_clause,[],[f611,f1478]) ).
fof(f611,plain,
! [X0] :
( ord_less(int,X0,pls)
| ~ ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls) ),
inference(definition_unfolding,[],[f490,f425]) ).
fof(f490,plain,
! [X0] :
( ord_less(int,X0,pls)
| ~ ord_less(int,bit1(X0),pls) ),
inference(cnf_transformation,[],[f347]) ).
fof(f347,plain,
! [X0] :
( ( 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,[],[f199]) ).
fof(f199,plain,
! [X0] :
( ord_less(int,bit1(X0),pls)
<=> ord_less(int,X0,pls) ),
inference(rectify,[],[f84]) ).
fof(f84,axiom,
! [X10] :
( ord_less(int,bit1(X10),pls)
<=> ord_less(int,X10,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1475,plain,
spl0_119,
inference(avatar_split_clause,[],[f610,f1473]) ).
fof(f610,plain,
! [X0] :
( ord_less(int,plus_plus(int,plus_plus(int,one_one(int),X0),X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(definition_unfolding,[],[f491,f425]) ).
fof(f491,plain,
! [X0] :
( ord_less(int,bit1(X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(cnf_transformation,[],[f347]) ).
fof(f1471,plain,
spl0_118,
inference(avatar_split_clause,[],[f565,f1469]) ).
fof(f1469,plain,
( spl0_118
<=> ! [X2,X0,X1] :
( power_power(X2,X0,X1) = power_power(X2,ti(X2,X0),X1)
| ~ semiring_0(X2)
| ~ power(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f565,plain,
! [X2,X0,X1] :
( power_power(X2,X0,X1) = power_power(X2,ti(X2,X0),X1)
| ~ semiring_0(X2)
| ~ power(X2) ),
inference(cnf_transformation,[],[f325]) ).
fof(f325,plain,
! [X0,X1,X2] :
( power_power(X2,X0,X1) = power_power(X2,ti(X2,X0),X1)
| ~ semiring_0(X2)
| ~ power(X2) ),
inference(flattening,[],[f324]) ).
fof(f324,plain,
! [X0,X1,X2] :
( power_power(X2,X0,X1) = power_power(X2,ti(X2,X0),X1)
| ~ semiring_0(X2)
| ~ power(X2) ),
inference(ennf_transformation,[],[f251]) ).
fof(f251,plain,
! [X0,X1,X2] :
( ( semiring_0(X2)
& power(X2) )
=> power_power(X2,X0,X1) = power_power(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X1,X2,X0] :
( ( semiring_0(X0)
& power(X0) )
=> power_power(X0,ti(X0,X1),X2) = power_power(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1467,plain,
spl0_117,
inference(avatar_split_clause,[],[f564,f1465]) ).
fof(f1465,plain,
( spl0_117
<=> ! [X2,X0,X1] :
( power_power(X2,X0,X1) = ti(X2,power_power(X2,X0,X1))
| ~ semiring_0(X2)
| ~ power(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f564,plain,
! [X2,X0,X1] :
( power_power(X2,X0,X1) = ti(X2,power_power(X2,X0,X1))
| ~ semiring_0(X2)
| ~ power(X2) ),
inference(cnf_transformation,[],[f323]) ).
fof(f323,plain,
! [X0,X1,X2] :
( power_power(X2,X0,X1) = ti(X2,power_power(X2,X0,X1))
| ~ semiring_0(X2)
| ~ power(X2) ),
inference(flattening,[],[f322]) ).
fof(f322,plain,
! [X0,X1,X2] :
( power_power(X2,X0,X1) = ti(X2,power_power(X2,X0,X1))
| ~ semiring_0(X2)
| ~ power(X2) ),
inference(ennf_transformation,[],[f250]) ).
fof(f250,plain,
! [X0,X1,X2] :
( ( semiring_0(X2)
& power(X2) )
=> power_power(X2,X0,X1) = ti(X2,power_power(X2,X0,X1)) ),
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X1,X2,X0] :
( ( semiring_0(X0)
& power(X0) )
=> power_power(X0,X1,X2) = ti(X0,power_power(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1463,plain,
spl0_116,
inference(avatar_split_clause,[],[f563,f1461]) ).
fof(f1461,plain,
( spl0_116
<=> ! [X2,X0,X1] :
( power_power(X2,X0,X1) = power_power(X2,X0,ti(nat,X1))
| ~ semiring_0(X2)
| ~ power(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f563,plain,
! [X2,X0,X1] :
( power_power(X2,X0,X1) = power_power(X2,X0,ti(nat,X1))
| ~ semiring_0(X2)
| ~ power(X2) ),
inference(cnf_transformation,[],[f321]) ).
fof(f321,plain,
! [X0,X1,X2] :
( power_power(X2,X0,X1) = power_power(X2,X0,ti(nat,X1))
| ~ semiring_0(X2)
| ~ power(X2) ),
inference(flattening,[],[f320]) ).
fof(f320,plain,
! [X0,X1,X2] :
( power_power(X2,X0,X1) = power_power(X2,X0,ti(nat,X1))
| ~ semiring_0(X2)
| ~ power(X2) ),
inference(ennf_transformation,[],[f249]) ).
fof(f249,plain,
! [X0,X1,X2] :
( ( semiring_0(X2)
& power(X2) )
=> power_power(X2,X0,X1) = power_power(X2,X0,ti(nat,X1)) ),
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X1,X2,X0] :
( ( semiring_0(X0)
& power(X0) )
=> power_power(X0,X1,X2) = power_power(X0,X1,ti(nat,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1459,plain,
spl0_115,
inference(avatar_split_clause,[],[f547,f1457]) ).
fof(f547,plain,
! [X2,X0,X1] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,plus_plus(int,X0,X1),X2),
inference(cnf_transformation,[],[f235]) ).
fof(f235,plain,
! [X0,X1,X2] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,plus_plus(int,X0,X1),X2),
inference(rectify,[],[f78]) ).
fof(f78,axiom,
! [X23,X24,X25] : plus_plus(int,plus_plus(int,X23,X24),X25) = plus_plus(int,X23,plus_plus(int,X24,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1454,plain,
spl0_114,
inference(avatar_split_clause,[],[f546,f1452]) ).
fof(f546,plain,
! [X2,X0,X1] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,X1,plus_plus(int,X0,X2)),
inference(cnf_transformation,[],[f234]) ).
fof(f234,plain,
! [X0,X1,X2] : plus_plus(int,X0,plus_plus(int,X1,X2)) = plus_plus(int,X1,plus_plus(int,X0,X2)),
inference(rectify,[],[f79]) ).
fof(f79,axiom,
! [X8,X9,X14] : plus_plus(int,X8,plus_plus(int,X9,X14)) = plus_plus(int,X9,plus_plus(int,X8,X14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1450,plain,
spl0_113,
inference(avatar_split_clause,[],[f541,f1448]) ).
fof(f1448,plain,
( spl0_113
<=> ! [X0,X1] :
( X0 = X1
| ord_less(int,X0,X1)
| ~ ord_less(int,X0,plus_plus(int,X1,one_one(int))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f541,plain,
! [X0,X1] :
( X0 = X1
| ord_less(int,X0,X1)
| ~ ord_less(int,X0,plus_plus(int,X1,one_one(int))) ),
inference(cnf_transformation,[],[f364]) ).
fof(f364,plain,
! [X0,X1] :
( ( ord_less(int,X0,plus_plus(int,X1,one_one(int)))
| ( X0 != X1
& ~ ord_less(int,X0,X1) ) )
& ( X0 = X1
| ord_less(int,X0,X1)
| ~ ord_less(int,X0,plus_plus(int,X1,one_one(int))) ) ),
inference(flattening,[],[f363]) ).
fof(f363,plain,
! [X0,X1] :
( ( ord_less(int,X0,plus_plus(int,X1,one_one(int)))
| ( X0 != X1
& ~ ord_less(int,X0,X1) ) )
& ( X0 = X1
| ord_less(int,X0,X1)
| ~ ord_less(int,X0,plus_plus(int,X1,one_one(int))) ) ),
inference(nnf_transformation,[],[f232]) ).
fof(f232,plain,
! [X0,X1] :
( ord_less(int,X0,plus_plus(int,X1,one_one(int)))
<=> ( X0 = X1
| ord_less(int,X0,X1) ) ),
inference(rectify,[],[f93]) ).
fof(f93,axiom,
! [X22,X27] :
( ord_less(int,X22,plus_plus(int,X27,one_one(int)))
<=> ( X22 = X27
| ord_less(int,X22,X27) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1446,plain,
spl0_112,
inference(avatar_split_clause,[],[f510,f1444]) ).
fof(f1444,plain,
( spl0_112
<=> ! [X0,X1] : plus_plus(int,number_number_of(int,X0),number_number_of(int,X1)) = number_number_of(int,plus_plus(int,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f510,plain,
! [X0,X1] : plus_plus(int,number_number_of(int,X0),number_number_of(int,X1)) = number_number_of(int,plus_plus(int,X0,X1)),
inference(cnf_transformation,[],[f214]) ).
fof(f214,plain,
! [X0,X1] : plus_plus(int,number_number_of(int,X0),number_number_of(int,X1)) = number_number_of(int,plus_plus(int,X0,X1)),
inference(rectify,[],[f50]) ).
fof(f50,axiom,
! [X7,X6] : plus_plus(int,number_number_of(int,X7),number_number_of(int,X6)) = number_number_of(int,plus_plus(int,X7,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1442,plain,
spl0_111,
inference(avatar_split_clause,[],[f509,f1440]) ).
fof(f509,plain,
! [X0,X1] : semiring_1_of_nat(int,plus_plus(nat,X0,X1)) = plus_plus(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X1)),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0,X1] : semiring_1_of_nat(int,plus_plus(nat,X0,X1)) = plus_plus(int,semiring_1_of_nat(int,X0),semiring_1_of_nat(int,X1)),
inference(rectify,[],[f56]) ).
fof(f56,axiom,
! [X12,X13] : semiring_1_of_nat(int,plus_plus(nat,X12,X13)) = plus_plus(int,semiring_1_of_nat(int,X12),semiring_1_of_nat(int,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1438,plain,
spl0_110,
inference(avatar_split_clause,[],[f474,f1436]) ).
fof(f1436,plain,
( spl0_110
<=> ! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f474,plain,
! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f291]) ).
fof(f291,plain,
! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(flattening,[],[f290]) ).
fof(f290,plain,
! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ zero_neq_one(X0)
| ~ no_zero_divisors(X0)
| ~ mult_zero(X0)
| ~ power(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ( zero_neq_one(X0)
& no_zero_divisors(X0)
& mult_zero(X0)
& power(X0) )
=> zero_zero(X0) = ti(X0,zero_zero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1434,plain,
spl0_109,
inference(avatar_split_clause,[],[f471,f1432]) ).
fof(f1432,plain,
( spl0_109
<=> ! [X0,X1] :
( 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_109])]) ).
fof(f471,plain,
! [X0,X1] :
( 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,[],[f339]) ).
fof(f339,plain,
! [X0] :
( ! [X1] :
( ( 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,[],[f287]) ).
fof(f287,plain,
! [X0] :
( ! [X1] :
( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less(int,X1,pls) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f286]) ).
fof(f286,plain,
! [X0] :
( ! [X1] :
( 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,[],[f191]) ).
fof(f191,plain,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1] :
( ord_less(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less(int,X1,pls) ) ),
inference(rectify,[],[f82]) ).
fof(f82,axiom,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X3] :
( ord_less(X0,number_number_of(X0,X3),zero_zero(X0))
<=> ord_less(int,X3,pls) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1430,plain,
spl0_108,
inference(avatar_split_clause,[],[f470,f1428]) ).
fof(f1428,plain,
( spl0_108
<=> ! [X0,X1] :
( 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_108])]) ).
fof(f470,plain,
! [X0,X1] :
( 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,[],[f339]) ).
fof(f1426,plain,
spl0_107,
inference(avatar_split_clause,[],[f467,f1424]) ).
fof(f1424,plain,
( spl0_107
<=> ! [X0,X1] :
( 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_107])]) ).
fof(f467,plain,
! [X0,X1] :
( 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,[],[f337]) ).
fof(f337,plain,
! [X0] :
( ! [X1] :
( ( 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,[],[f283]) ).
fof(f283,plain,
! [X0] :
( ! [X1] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less(int,pls,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f282]) ).
fof(f282,plain,
! [X0] :
( ! [X1] :
( 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,[],[f189]) ).
fof(f189,plain,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less(int,pls,X1) ) ),
inference(rectify,[],[f83]) ).
fof(f83,axiom,
! [X0] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X4] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X4))
<=> ord_less(int,pls,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1422,plain,
spl0_106,
inference(avatar_split_clause,[],[f466,f1420]) ).
fof(f1420,plain,
( spl0_106
<=> ! [X0,X1] :
( 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_106])]) ).
fof(f466,plain,
! [X0,X1] :
( 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,[],[f337]) ).
fof(f1418,plain,
spl0_105,
inference(avatar_split_clause,[],[f434,f1416]) ).
fof(f1416,plain,
( spl0_105
<=> ! [X0,X1] :
( 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_105])]) ).
fof(f434,plain,
! [X0,X1] :
( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ ord_less(X0,X1,zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f328,plain,
! [X0] :
( ! [X1] :
( ( 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,[],[f256]) ).
fof(f256,plain,
! [X0] :
( ! [X1] :
( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
<=> ord_less(X0,X1,zero_zero(X0)) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f174]) ).
fof(f174,plain,
! [X0] :
( linordered_idom(X0)
=> ! [X1] :
( ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
<=> ord_less(X0,X1,zero_zero(X0)) ) ),
inference(rectify,[],[f77]) ).
fof(f77,axiom,
! [X0] :
( linordered_idom(X0)
=> ! [X5] :
( ord_less(X0,plus_plus(X0,X5,X5),zero_zero(X0))
<=> ord_less(X0,X5,zero_zero(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1412,plain,
spl0_104,
inference(avatar_split_clause,[],[f433,f1410]) ).
fof(f1410,plain,
( spl0_104
<=> ! [X0,X1] :
( 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_104])]) ).
fof(f433,plain,
! [X0,X1] :
( ord_less(X0,X1,zero_zero(X0))
| ~ ord_less(X0,plus_plus(X0,X1,X1),zero_zero(X0))
| ~ linordered_idom(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f1408,plain,
spl0_103,
inference(avatar_split_clause,[],[f431,f1406]) ).
fof(f1406,plain,
( spl0_103
<=> ! [X0,X1] :
( zero_zero(X0) = plus_plus(X0,X1,X1)
| ti(X0,X1) != zero_zero(X0)
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f431,plain,
! [X0,X1] :
( zero_zero(X0) = plus_plus(X0,X1,X1)
| ti(X0,X1) != zero_zero(X0)
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f327,plain,
! [X0] :
( ! [X1] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1)
| ti(X0,X1) != zero_zero(X0) )
& ( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != plus_plus(X0,X1,X1) ) )
| ~ linord219039673up_add(X0) ),
inference(nnf_transformation,[],[f254]) ).
fof(f254,plain,
! [X0] :
( ! [X1] :
( zero_zero(X0) = plus_plus(X0,X1,X1)
<=> ti(X0,X1) = zero_zero(X0) )
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f172]) ).
fof(f172,plain,
! [X0] :
( linord219039673up_add(X0)
=> ! [X1] :
( zero_zero(X0) = plus_plus(X0,X1,X1)
<=> ti(X0,X1) = zero_zero(X0) ) ),
inference(rectify,[],[f98]) ).
fof(f98,axiom,
! [X0] :
( linord219039673up_add(X0)
=> ! [X5] :
( zero_zero(X0) = plus_plus(X0,X5,X5)
<=> zero_zero(X0) = ti(X0,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1404,plain,
spl0_102,
inference(avatar_split_clause,[],[f430,f1402]) ).
fof(f1402,plain,
( spl0_102
<=> ! [X0,X1] :
( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != plus_plus(X0,X1,X1)
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f430,plain,
! [X0,X1] :
( ti(X0,X1) = zero_zero(X0)
| zero_zero(X0) != plus_plus(X0,X1,X1)
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f1368,plain,
spl0_101,
inference(avatar_split_clause,[],[f626,f1366]) ).
fof(f1366,plain,
( spl0_101
<=> ! [X0,X1] :
( ord_less(int,X0,X1)
| ~ ord_less(int,plus_plus(int,X0,X0),plus_plus(int,X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f626,plain,
! [X0,X1] :
( ord_less(int,X0,X1)
| ~ ord_less(int,plus_plus(int,X0,X0),plus_plus(int,X1,X1)) ),
inference(definition_unfolding,[],[f527,f421,f421]) ).
fof(f527,plain,
! [X0,X1] :
( ord_less(int,X0,X1)
| ~ ord_less(int,bit0(X0),bit0(X1)) ),
inference(cnf_transformation,[],[f356]) ).
fof(f356,plain,
! [X0,X1] :
( ( ord_less(int,bit0(X0),bit0(X1))
| ~ ord_less(int,X0,X1) )
& ( ord_less(int,X0,X1)
| ~ ord_less(int,bit0(X0),bit0(X1)) ) ),
inference(nnf_transformation,[],[f225]) ).
fof(f225,plain,
! [X0,X1] :
( ord_less(int,bit0(X0),bit0(X1))
<=> ord_less(int,X0,X1) ),
inference(rectify,[],[f67]) ).
fof(f67,axiom,
! [X10,X11] :
( ord_less(int,bit0(X10),bit0(X11))
<=> ord_less(int,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1364,plain,
spl0_100,
inference(avatar_split_clause,[],[f625,f1362]) ).
fof(f1362,plain,
( spl0_100
<=> ! [X0,X1] :
( ord_less(int,plus_plus(int,X0,X0),plus_plus(int,X1,X1))
| ~ ord_less(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f625,plain,
! [X0,X1] :
( ord_less(int,plus_plus(int,X0,X0),plus_plus(int,X1,X1))
| ~ ord_less(int,X0,X1) ),
inference(definition_unfolding,[],[f528,f421,f421]) ).
fof(f528,plain,
! [X0,X1] :
( ord_less(int,bit0(X0),bit0(X1))
| ~ ord_less(int,X0,X1) ),
inference(cnf_transformation,[],[f356]) ).
fof(f1360,plain,
spl0_99,
inference(avatar_split_clause,[],[f559,f1358]) ).
fof(f1358,plain,
( spl0_99
<=> ! [X2,X0,X1] :
( ord_less(int,plus_plus(int,X1,X0),plus_plus(int,X2,X0))
| ~ ord_less(int,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f559,plain,
! [X2,X0,X1] :
( ord_less(int,plus_plus(int,X1,X0),plus_plus(int,X2,X0))
| ~ ord_less(int,X1,X2) ),
inference(cnf_transformation,[],[f313]) ).
fof(f313,plain,
! [X0,X1,X2] :
( ord_less(int,plus_plus(int,X1,X0),plus_plus(int,X2,X0))
| ~ ord_less(int,X1,X2) ),
inference(ennf_transformation,[],[f245]) ).
fof(f245,plain,
! [X0,X1,X2] :
( ord_less(int,X1,X2)
=> ord_less(int,plus_plus(int,X1,X0),plus_plus(int,X2,X0)) ),
inference(rectify,[],[f68]) ).
fof(f68,axiom,
! [X18,X19,X20] :
( ord_less(int,X19,X20)
=> ord_less(int,plus_plus(int,X19,X18),plus_plus(int,X20,X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1356,plain,
( spl0_98
| ~ spl0_33
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1347,f1327,f881,f1354]) ).
fof(f1354,plain,
( spl0_98
<=> ! [X0] : one_one(int) != plus_plus(int,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f881,plain,
( spl0_33
<=> ! [X0] : plus_plus(int,X0,pls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1327,plain,
( spl0_96
<=> ! [X0,X1] : plus_plus(int,plus_plus(int,one_one(int),X0),X0) != plus_plus(int,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1347,plain,
( ! [X0] : one_one(int) != plus_plus(int,X0,X0)
| ~ spl0_33
| ~ spl0_96 ),
inference(forward_demodulation,[],[f1341,f882]) ).
fof(f882,plain,
( ! [X0] : plus_plus(int,X0,pls) = X0
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f881]) ).
fof(f1341,plain,
( ! [X0] : plus_plus(int,X0,X0) != plus_plus(int,one_one(int),pls)
| ~ spl0_33
| ~ spl0_96 ),
inference(superposition,[],[f1328,f882]) ).
fof(f1328,plain,
( ! [X0,X1] : plus_plus(int,plus_plus(int,one_one(int),X0),X0) != plus_plus(int,X1,X1)
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1327]) ).
fof(f1352,plain,
spl0_97,
inference(avatar_split_clause,[],[f462,f1350]) ).
fof(f1350,plain,
( spl0_97
<=> ! [X2,X0,X1] :
( 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_97])]) ).
fof(f462,plain,
! [X2,X0,X1] :
( X1 = X2
| number_number_of(X0,X1) != number_number_of(X0,X2)
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f335]) ).
fof(f335,plain,
! [X0] :
( ! [X1,X2] :
( ( 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,[],[f279]) ).
fof(f279,plain,
! [X0] :
( ! [X1,X2] :
( number_number_of(X0,X1) = number_number_of(X0,X2)
<=> X1 = X2 )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f278]) ).
fof(f278,plain,
! [X0] :
( ! [X1,X2] :
( number_number_of(X0,X1) = number_number_of(X0,X2)
<=> X1 = X2 )
| ~ ring_char_0(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f187]) ).
fof(f187,plain,
! [X0] :
( ( ring_char_0(X0)
& number_ring(X0) )
=> ! [X1,X2] :
( number_number_of(X0,X1) = number_number_of(X0,X2)
<=> X1 = X2 ) ),
inference(rectify,[],[f73]) ).
fof(f73,axiom,
! [X0] :
( ( ring_char_0(X0)
& number_ring(X0) )
=> ! [X3,X4] :
( number_number_of(X0,X3) = number_number_of(X0,X4)
<=> X3 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1329,plain,
spl0_96,
inference(avatar_split_clause,[],[f616,f1327]) ).
fof(f616,plain,
! [X0,X1] : plus_plus(int,plus_plus(int,one_one(int),X0),X0) != plus_plus(int,X1,X1),
inference(definition_unfolding,[],[f500,f421,f425]) ).
fof(f500,plain,
! [X0,X1] : bit0(X1) != bit1(X0),
inference(cnf_transformation,[],[f204]) ).
fof(f204,plain,
! [X0,X1] : bit0(X1) != bit1(X0),
inference(rectify,[],[f101]) ).
fof(f101,axiom,
! [X18,X28] : bit1(X18) != bit0(X28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1325,plain,
( ~ spl0_95
| ~ spl0_46
| spl0_72 ),
inference(avatar_split_clause,[],[f1152,f1117,f947,f1322]) ).
fof(f1322,plain,
( spl0_95
<=> pls = plus_plus(int,pls,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1117,plain,
( spl0_72
<=> pls = plus_plus(int,one_one(int),pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1152,plain,
( pls != plus_plus(int,pls,one_one(int))
| ~ spl0_46
| spl0_72 ),
inference(superposition,[],[f1119,f948]) ).
fof(f1119,plain,
( pls != plus_plus(int,one_one(int),pls)
| spl0_72 ),
inference(avatar_component_clause,[],[f1117]) ).
fof(f1316,plain,
spl0_94,
inference(avatar_split_clause,[],[f574,f1313]) ).
fof(f1313,plain,
( spl0_94
<=> one_one(int) = number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f574,plain,
one_one(int) = number_number_of(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),
inference(definition_unfolding,[],[f411,f425]) ).
fof(f411,plain,
one_one(int) = number_number_of(int,bit1(pls)),
inference(cnf_transformation,[],[f70]) ).
fof(f70,axiom,
one_one(int) = number_number_of(int,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1311,plain,
( spl0_93
| ~ spl0_33
| ~ spl0_34
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f1306,f1299,f885,f881,f1308]) ).
fof(f1308,plain,
( spl0_93
<=> one_one(nat) = number_number_of(nat,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1299,plain,
( spl0_92
<=> one_one(nat) = number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),pls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1306,plain,
( one_one(nat) = number_number_of(nat,one_one(int))
| ~ spl0_33
| ~ spl0_34
| ~ spl0_92 ),
inference(forward_demodulation,[],[f1305,f882]) ).
fof(f1305,plain,
( one_one(nat) = number_number_of(nat,plus_plus(int,one_one(int),pls))
| ~ spl0_34
| ~ spl0_92 ),
inference(forward_demodulation,[],[f1304,f886]) ).
fof(f1304,plain,
( one_one(nat) = number_number_of(nat,plus_plus(int,pls,plus_plus(int,one_one(int),pls)))
| ~ spl0_92 ),
inference(forward_demodulation,[],[f1303,f546]) ).
fof(f1303,plain,
( one_one(nat) = number_number_of(nat,plus_plus(int,one_one(int),plus_plus(int,pls,pls)))
| ~ spl0_92 ),
inference(forward_demodulation,[],[f1301,f547]) ).
fof(f1301,plain,
( one_one(nat) = number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),pls))
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f1299]) ).
fof(f1302,plain,
spl0_92,
inference(avatar_split_clause,[],[f572,f1299]) ).
fof(f572,plain,
one_one(nat) = number_number_of(nat,plus_plus(int,plus_plus(int,one_one(int),pls),pls)),
inference(definition_unfolding,[],[f408,f425]) ).
fof(f408,plain,
one_one(nat) = number_number_of(nat,bit1(pls)),
inference(cnf_transformation,[],[f71]) ).
fof(f71,axiom,
one_one(nat) = number_number_of(nat,bit1(pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1297,plain,
spl0_91,
inference(avatar_split_clause,[],[f558,f1295]) ).
fof(f1295,plain,
( spl0_91
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ number_semiring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f558,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ number_semiring(X2) ),
inference(cnf_transformation,[],[f312]) ).
fof(f312,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ number_semiring(X2) ),
inference(ennf_transformation,[],[f244]) ).
fof(f244,plain,
! [X0,X1,X2] :
( number_semiring(X2)
=> plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X2,X0] :
( number_semiring(X0)
=> plus_plus(X0,ti(X0,X1),X2) = plus_plus(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1293,plain,
spl0_90,
inference(avatar_split_clause,[],[f557,f1291]) ).
fof(f1291,plain,
( spl0_90
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ number_semiring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f557,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ number_semiring(X2) ),
inference(cnf_transformation,[],[f311]) ).
fof(f311,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ number_semiring(X2) ),
inference(ennf_transformation,[],[f243]) ).
fof(f243,plain,
! [X0,X1,X2] :
( number_semiring(X2)
=> plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1)) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X2,X0] :
( number_semiring(X0)
=> plus_plus(X0,X1,X2) = plus_plus(X0,X1,ti(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1289,plain,
spl0_89,
inference(avatar_split_clause,[],[f556,f1287]) ).
fof(f1287,plain,
( spl0_89
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ number_semiring(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f556,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ number_semiring(X2) ),
inference(cnf_transformation,[],[f310]) ).
fof(f310,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ number_semiring(X2) ),
inference(ennf_transformation,[],[f242]) ).
fof(f242,plain,
! [X0,X1,X2] :
( number_semiring(X2)
=> plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1)) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X1,X2,X0] :
( number_semiring(X0)
=> plus_plus(X0,X1,X2) = ti(X0,plus_plus(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1285,plain,
spl0_88,
inference(avatar_split_clause,[],[f551,f1283]) ).
fof(f1283,plain,
( spl0_88
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ linord219039673up_add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f551,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ linord219039673up_add(X2) ),
inference(cnf_transformation,[],[f307]) ).
fof(f307,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1)
| ~ linord219039673up_add(X2) ),
inference(ennf_transformation,[],[f239]) ).
fof(f239,plain,
! [X0,X1,X2] :
( linord219039673up_add(X2)
=> plus_plus(X2,X0,X1) = plus_plus(X2,ti(X2,X0),X1) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X2,X0] :
( linord219039673up_add(X0)
=> plus_plus(X0,ti(X0,X1),X2) = plus_plus(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1281,plain,
spl0_87,
inference(avatar_split_clause,[],[f550,f1279]) ).
fof(f1279,plain,
( spl0_87
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ linord219039673up_add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f550,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ linord219039673up_add(X2) ),
inference(cnf_transformation,[],[f306]) ).
fof(f306,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1))
| ~ linord219039673up_add(X2) ),
inference(ennf_transformation,[],[f238]) ).
fof(f238,plain,
! [X0,X1,X2] :
( linord219039673up_add(X2)
=> plus_plus(X2,X0,X1) = plus_plus(X2,X0,ti(X2,X1)) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X2,X0] :
( linord219039673up_add(X0)
=> plus_plus(X0,X1,X2) = plus_plus(X0,X1,ti(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1277,plain,
spl0_86,
inference(avatar_split_clause,[],[f549,f1275]) ).
fof(f1275,plain,
( spl0_86
<=> ! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ linord219039673up_add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f549,plain,
! [X2,X0,X1] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ linord219039673up_add(X2) ),
inference(cnf_transformation,[],[f305]) ).
fof(f305,plain,
! [X0,X1,X2] :
( plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1))
| ~ linord219039673up_add(X2) ),
inference(ennf_transformation,[],[f237]) ).
fof(f237,plain,
! [X0,X1,X2] :
( linord219039673up_add(X2)
=> plus_plus(X2,X0,X1) = ti(X2,plus_plus(X2,X0,X1)) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X2,X0] :
( linord219039673up_add(X0)
=> plus_plus(X0,X1,X2) = ti(X0,plus_plus(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1268,plain,
spl0_85,
inference(avatar_split_clause,[],[f507,f1266]) ).
fof(f1266,plain,
( spl0_85
<=> ! [X0,X1] : power_power(int,semiring_1_of_nat(int,X0),X1) = semiring_1_of_nat(int,power_power(nat,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f507,plain,
! [X0,X1] : power_power(int,semiring_1_of_nat(int,X0),X1) = semiring_1_of_nat(int,power_power(nat,X0,X1)),
inference(cnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0,X1] : power_power(int,semiring_1_of_nat(int,X0),X1) = semiring_1_of_nat(int,power_power(nat,X0,X1)),
inference(rectify,[],[f54]) ).
fof(f54,axiom,
! [X12,X13] : power_power(int,semiring_1_of_nat(int,X12),X13) = semiring_1_of_nat(int,power_power(nat,X12,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1264,plain,
spl0_84,
inference(avatar_split_clause,[],[f569,f1262]) ).
fof(f1262,plain,
( spl0_84
<=> ! [X0] : plus_plus(int,X0,X0) = plus_plus(int,ti(int,X0),ti(int,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f569,plain,
! [X0] : plus_plus(int,X0,X0) = plus_plus(int,ti(int,X0),ti(int,X0)),
inference(definition_unfolding,[],[f373,f421,f421]) ).
fof(f373,plain,
! [X0] : bit0(X0) = bit0(ti(int,X0)),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0] : bit0(X0) = bit0(ti(int,X0)),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X1] : bit0(ti(int,X1)) = bit0(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1195,plain,
( spl0_83
| ~ spl0_5
| ~ spl0_30
| ~ spl0_33
| ~ spl0_73 ),
inference(avatar_split_clause,[],[f1188,f1144,f881,f866,f741,f1193]) ).
fof(f741,plain,
( spl0_5
<=> number_ring(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1144,plain,
( spl0_73
<=> ! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,X1,number_number_of(X0,pls))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1188,plain,
( ! [X0] : ti(int,X0) = X0
| ~ spl0_5
| ~ spl0_30
| ~ spl0_33
| ~ spl0_73 ),
inference(forward_demodulation,[],[f1187,f882]) ).
fof(f1187,plain,
( ! [X0] : ti(int,X0) = plus_plus(int,X0,pls)
| ~ spl0_5
| ~ spl0_30
| ~ spl0_73 ),
inference(forward_demodulation,[],[f1186,f868]) ).
fof(f1186,plain,
( ! [X0] : ti(int,X0) = plus_plus(int,X0,number_number_of(int,pls))
| ~ spl0_5
| ~ spl0_73 ),
inference(resolution,[],[f1145,f743]) ).
fof(f743,plain,
( number_ring(int)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f1145,plain,
( ! [X0,X1] :
( ~ number_ring(X0)
| ti(X0,X1) = plus_plus(X0,X1,number_number_of(X0,pls)) )
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f1144]) ).
fof(f1185,plain,
spl0_82,
inference(avatar_split_clause,[],[f622,f1183]) ).
fof(f1183,plain,
( spl0_82
<=> ! [X0,X1] :
( X0 = X1
| plus_plus(int,X0,X0) != plus_plus(int,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f622,plain,
! [X0,X1] :
( X0 = X1
| plus_plus(int,X0,X0) != plus_plus(int,X1,X1) ),
inference(definition_unfolding,[],[f519,f421,f421]) ).
fof(f519,plain,
! [X0,X1] :
( X0 = X1
| bit0(X1) != bit0(X0) ),
inference(cnf_transformation,[],[f352]) ).
fof(f352,plain,
! [X0,X1] :
( ( bit0(X1) = bit0(X0)
| X0 != X1 )
& ( X0 = X1
| bit0(X1) != bit0(X0) ) ),
inference(nnf_transformation,[],[f221]) ).
fof(f221,plain,
! [X0,X1] :
( bit0(X1) = bit0(X0)
<=> X0 = X1 ),
inference(rectify,[],[f76]) ).
fof(f76,axiom,
! [X10,X11] :
( bit0(X10) = bit0(X11)
<=> X10 = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1181,plain,
spl0_81,
inference(avatar_split_clause,[],[f555,f1179]) ).
fof(f1179,plain,
( spl0_81
<=> ! [X2,X0,X1] :
( ord_less(X2,ti(X2,X0),X1)
| ~ ord_less(X2,X0,X1)
| ~ linordered_idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f555,plain,
! [X2,X0,X1] :
( ord_less(X2,ti(X2,X0),X1)
| ~ ord_less(X2,X0,X1)
| ~ linordered_idom(X2) ),
inference(cnf_transformation,[],[f367]) ).
fof(f367,plain,
! [X0,X1,X2] :
( ( ( ord_less(X2,ti(X2,X0),X1)
| ~ ord_less(X2,X0,X1) )
& ( ord_less(X2,X0,X1)
| ~ ord_less(X2,ti(X2,X0),X1) ) )
| ~ linordered_idom(X2) ),
inference(nnf_transformation,[],[f309]) ).
fof(f309,plain,
! [X0,X1,X2] :
( ( ord_less(X2,ti(X2,X0),X1)
<=> ord_less(X2,X0,X1) )
| ~ linordered_idom(X2) ),
inference(ennf_transformation,[],[f241]) ).
fof(f241,plain,
! [X0,X1,X2] :
( linordered_idom(X2)
=> ( ord_less(X2,ti(X2,X0),X1)
<=> ord_less(X2,X0,X1) ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X1,X2,X0] :
( linordered_idom(X0)
=> ( ord_less(X0,ti(X0,X1),X2)
<=> ord_less(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1177,plain,
spl0_80,
inference(avatar_split_clause,[],[f554,f1175]) ).
fof(f1175,plain,
( spl0_80
<=> ! [X2,X0,X1] :
( ord_less(X2,X0,X1)
| ~ ord_less(X2,ti(X2,X0),X1)
| ~ linordered_idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f554,plain,
! [X2,X0,X1] :
( ord_less(X2,X0,X1)
| ~ ord_less(X2,ti(X2,X0),X1)
| ~ linordered_idom(X2) ),
inference(cnf_transformation,[],[f367]) ).
fof(f1173,plain,
spl0_79,
inference(avatar_split_clause,[],[f553,f1171]) ).
fof(f1171,plain,
( spl0_79
<=> ! [X2,X0,X1] :
( ord_less(X2,X0,ti(X2,X1))
| ~ ord_less(X2,X0,X1)
| ~ linordered_idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f553,plain,
! [X2,X0,X1] :
( ord_less(X2,X0,ti(X2,X1))
| ~ ord_less(X2,X0,X1)
| ~ linordered_idom(X2) ),
inference(cnf_transformation,[],[f366]) ).
fof(f366,plain,
! [X0,X1,X2] :
( ( ( ord_less(X2,X0,ti(X2,X1))
| ~ ord_less(X2,X0,X1) )
& ( ord_less(X2,X0,X1)
| ~ ord_less(X2,X0,ti(X2,X1)) ) )
| ~ linordered_idom(X2) ),
inference(nnf_transformation,[],[f308]) ).
fof(f308,plain,
! [X0,X1,X2] :
( ( ord_less(X2,X0,ti(X2,X1))
<=> ord_less(X2,X0,X1) )
| ~ linordered_idom(X2) ),
inference(ennf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0,X1,X2] :
( linordered_idom(X2)
=> ( ord_less(X2,X0,ti(X2,X1))
<=> ord_less(X2,X0,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X1,X2,X0] :
( linordered_idom(X0)
=> ( ord_less(X0,X1,ti(X0,X2))
<=> ord_less(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1169,plain,
spl0_78,
inference(avatar_split_clause,[],[f552,f1167]) ).
fof(f1167,plain,
( spl0_78
<=> ! [X2,X0,X1] :
( ord_less(X2,X0,X1)
| ~ ord_less(X2,X0,ti(X2,X1))
| ~ linordered_idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f552,plain,
! [X2,X0,X1] :
( ord_less(X2,X0,X1)
| ~ ord_less(X2,X0,ti(X2,X1))
| ~ linordered_idom(X2) ),
inference(cnf_transformation,[],[f366]) ).
fof(f1165,plain,
spl0_77,
inference(avatar_split_clause,[],[f545,f1163]) ).
fof(f545,plain,
! [X0,X1] :
( ord_less(int,number_number_of(int,X0),number_number_of(int,X1))
| ~ ord_less(int,X0,X1) ),
inference(cnf_transformation,[],[f365]) ).
fof(f365,plain,
! [X0,X1] :
( ( ord_less(int,number_number_of(int,X0),number_number_of(int,X1))
| ~ ord_less(int,X0,X1) )
& ( ord_less(int,X0,X1)
| ~ ord_less(int,number_number_of(int,X0),number_number_of(int,X1)) ) ),
inference(nnf_transformation,[],[f233]) ).
fof(f233,plain,
! [X0,X1] :
( ord_less(int,number_number_of(int,X0),number_number_of(int,X1))
<=> ord_less(int,X0,X1) ),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X10,X11] :
( ord_less(int,number_number_of(int,X10),number_number_of(int,X11))
<=> ord_less(int,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1161,plain,
spl0_76,
inference(avatar_split_clause,[],[f544,f1159]) ).
fof(f544,plain,
! [X0,X1] :
( ord_less(int,X0,X1)
| ~ ord_less(int,number_number_of(int,X0),number_number_of(int,X1)) ),
inference(cnf_transformation,[],[f365]) ).
fof(f1157,plain,
spl0_75,
inference(avatar_split_clause,[],[f542,f1155]) ).
fof(f542,plain,
! [X0,X1] :
( ord_less(int,X0,plus_plus(int,X1,one_one(int)))
| ~ ord_less(int,X0,X1) ),
inference(cnf_transformation,[],[f364]) ).
fof(f1150,plain,
spl0_74,
inference(avatar_split_clause,[],[f449,f1148]) ).
fof(f1148,plain,
( spl0_74
<=> ! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,number_number_of(X0,pls),X1)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f449,plain,
! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,number_number_of(X0,pls),X1)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f266,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = plus_plus(X0,number_number_of(X0,pls),X1)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( number_ring(X0)
=> ! [X1] : ti(X0,X1) = plus_plus(X0,number_number_of(X0,pls),X1) ),
inference(rectify,[],[f117]) ).
fof(f117,axiom,
! [X0] :
( number_ring(X0)
=> ! [X29] : plus_plus(X0,number_number_of(X0,pls),X29) = ti(X0,X29) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1146,plain,
spl0_73,
inference(avatar_split_clause,[],[f448,f1144]) ).
fof(f448,plain,
! [X0,X1] :
( ti(X0,X1) = plus_plus(X0,X1,number_number_of(X0,pls))
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f265]) ).
fof(f265,plain,
! [X0] :
( ! [X1] : ti(X0,X1) = plus_plus(X0,X1,number_number_of(X0,pls))
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0] :
( number_ring(X0)
=> ! [X1] : ti(X0,X1) = plus_plus(X0,X1,number_number_of(X0,pls)) ),
inference(rectify,[],[f118]) ).
fof(f118,axiom,
! [X0] :
( number_ring(X0)
=> ! [X29] : ti(X0,X29) = plus_plus(X0,X29,number_number_of(X0,pls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1120,plain,
( ~ spl0_72
| ~ spl0_33
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f1041,f1007,f881,f1117]) ).
fof(f1041,plain,
( pls != plus_plus(int,one_one(int),pls)
| ~ spl0_33
| ~ spl0_56 ),
inference(superposition,[],[f1008,f882]) ).
fof(f1101,plain,
spl0_71,
inference(avatar_split_clause,[],[f609,f1099]) ).
fof(f1099,plain,
( spl0_71
<=> ! [X0] :
( ord_less(int,X0,pls)
| ~ ord_less(int,plus_plus(int,X0,X0),pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f609,plain,
! [X0] :
( ord_less(int,X0,pls)
| ~ ord_less(int,plus_plus(int,X0,X0),pls) ),
inference(definition_unfolding,[],[f488,f421]) ).
fof(f488,plain,
! [X0] :
( ord_less(int,X0,pls)
| ~ ord_less(int,bit0(X0),pls) ),
inference(cnf_transformation,[],[f346]) ).
fof(f346,plain,
! [X0] :
( ( 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,[],[f198]) ).
fof(f198,plain,
! [X0] :
( ord_less(int,bit0(X0),pls)
<=> ord_less(int,X0,pls) ),
inference(rectify,[],[f87]) ).
fof(f87,axiom,
! [X10] :
( ord_less(int,bit0(X10),pls)
<=> ord_less(int,X10,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1097,plain,
spl0_70,
inference(avatar_split_clause,[],[f608,f1095]) ).
fof(f1095,plain,
( spl0_70
<=> ! [X0] :
( ord_less(int,plus_plus(int,X0,X0),pls)
| ~ ord_less(int,X0,pls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f608,plain,
! [X0] :
( ord_less(int,plus_plus(int,X0,X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(definition_unfolding,[],[f489,f421]) ).
fof(f489,plain,
! [X0] :
( ord_less(int,bit0(X0),pls)
| ~ ord_less(int,X0,pls) ),
inference(cnf_transformation,[],[f346]) ).
fof(f1093,plain,
spl0_69,
inference(avatar_split_clause,[],[f607,f1091]) ).
fof(f1091,plain,
( spl0_69
<=> ! [X0] :
( ord_less(int,pls,X0)
| ~ ord_less(int,pls,plus_plus(int,X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f607,plain,
! [X0] :
( ord_less(int,pls,X0)
| ~ ord_less(int,pls,plus_plus(int,X0,X0)) ),
inference(definition_unfolding,[],[f486,f421]) ).
fof(f486,plain,
! [X0] :
( ord_less(int,pls,X0)
| ~ ord_less(int,pls,bit0(X0)) ),
inference(cnf_transformation,[],[f345]) ).
fof(f345,plain,
! [X0] :
( ( 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,[],[f197]) ).
fof(f197,plain,
! [X0] :
( ord_less(int,pls,bit0(X0))
<=> ord_less(int,pls,X0) ),
inference(rectify,[],[f88]) ).
fof(f88,axiom,
! [X10] :
( ord_less(int,pls,bit0(X10))
<=> ord_less(int,pls,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1089,plain,
spl0_68,
inference(avatar_split_clause,[],[f606,f1087]) ).
fof(f1087,plain,
( spl0_68
<=> ! [X0] :
( ord_less(int,pls,plus_plus(int,X0,X0))
| ~ ord_less(int,pls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f606,plain,
! [X0] :
( ord_less(int,pls,plus_plus(int,X0,X0))
| ~ ord_less(int,pls,X0) ),
inference(definition_unfolding,[],[f487,f421]) ).
fof(f487,plain,
! [X0] :
( ord_less(int,pls,bit0(X0))
| ~ ord_less(int,pls,X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f1085,plain,
spl0_67,
inference(avatar_split_clause,[],[f518,f1083]) ).
fof(f518,plain,
! [X0,X1] :
( semiring_1_of_nat(X1,X0) = semiring_1_of_nat(X1,ti(nat,X0))
| ~ number_semiring(X1) ),
inference(cnf_transformation,[],[f304]) ).
fof(f304,plain,
! [X0,X1] :
( semiring_1_of_nat(X1,X0) = semiring_1_of_nat(X1,ti(nat,X0))
| ~ number_semiring(X1) ),
inference(ennf_transformation,[],[f220]) ).
fof(f220,plain,
! [X0,X1] :
( number_semiring(X1)
=> semiring_1_of_nat(X1,X0) = semiring_1_of_nat(X1,ti(nat,X0)) ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X1,X0] :
( number_semiring(X0)
=> semiring_1_of_nat(X0,ti(nat,X1)) = semiring_1_of_nat(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1081,plain,
spl0_66,
inference(avatar_split_clause,[],[f517,f1079]) ).
fof(f517,plain,
! [X0,X1] :
( semiring_1_of_nat(X1,X0) = ti(X1,semiring_1_of_nat(X1,X0))
| ~ number_semiring(X1) ),
inference(cnf_transformation,[],[f303]) ).
fof(f303,plain,
! [X0,X1] :
( semiring_1_of_nat(X1,X0) = ti(X1,semiring_1_of_nat(X1,X0))
| ~ number_semiring(X1) ),
inference(ennf_transformation,[],[f219]) ).
fof(f219,plain,
! [X0,X1] :
( number_semiring(X1)
=> semiring_1_of_nat(X1,X0) = ti(X1,semiring_1_of_nat(X1,X0)) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X1,X0] :
( number_semiring(X0)
=> semiring_1_of_nat(X0,X1) = ti(X0,semiring_1_of_nat(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1077,plain,
spl0_65,
inference(avatar_split_clause,[],[f516,f1075]) ).
fof(f516,plain,
! [X0,X1] :
( number_number_of(X1,X0) = number_number_of(X1,ti(int,X0))
| ~ number(X1) ),
inference(cnf_transformation,[],[f302]) ).
fof(f302,plain,
! [X0,X1] :
( number_number_of(X1,X0) = number_number_of(X1,ti(int,X0))
| ~ number(X1) ),
inference(ennf_transformation,[],[f218]) ).
fof(f218,plain,
! [X0,X1] :
( number(X1)
=> number_number_of(X1,X0) = number_number_of(X1,ti(int,X0)) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X1,X0] :
( number(X0)
=> number_number_of(X0,ti(int,X1)) = number_number_of(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1073,plain,
spl0_64,
inference(avatar_split_clause,[],[f515,f1071]) ).
fof(f515,plain,
! [X0,X1] :
( number_number_of(X1,X0) = ti(X1,number_number_of(X1,X0))
| ~ number(X1) ),
inference(cnf_transformation,[],[f301]) ).
fof(f301,plain,
! [X0,X1] :
( number_number_of(X1,X0) = ti(X1,number_number_of(X1,X0))
| ~ number(X1) ),
inference(ennf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0,X1] :
( number(X1)
=> number_number_of(X1,X0) = ti(X1,number_number_of(X1,X0)) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X1,X0] :
( number(X0)
=> number_number_of(X0,X1) = ti(X0,number_number_of(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1069,plain,
spl0_63,
inference(avatar_split_clause,[],[f514,f1067]) ).
fof(f1067,plain,
( spl0_63
<=> ! [X0,X1] :
( ord_less(int,X1,X0)
| X0 = X1
| ord_less(int,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f514,plain,
! [X0,X1] :
( ord_less(int,X1,X0)
| X0 = X1
| ord_less(int,X0,X1) ),
inference(cnf_transformation,[],[f216]) ).
fof(f216,plain,
! [X0,X1] :
( ord_less(int,X1,X0)
| X0 = X1
| ord_less(int,X0,X1) ),
inference(rectify,[],[f48]) ).
fof(f48,axiom,
! [X8,X9] :
( ord_less(int,X9,X8)
| X8 = X9
| ord_less(int,X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1065,plain,
spl0_62,
inference(avatar_split_clause,[],[f479,f1063]) ).
fof(f479,plain,
! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ semiring_0(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f297,plain,
! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ semiring_0(X0)
| ~ power(X0) ),
inference(flattening,[],[f296]) ).
fof(f296,plain,
! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ semiring_0(X0)
| ~ power(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ( semiring_0(X0)
& power(X0) )
=> zero_zero(X0) = ti(X0,zero_zero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1061,plain,
spl0_61,
inference(avatar_split_clause,[],[f478,f1059]) ).
fof(f478,plain,
! [X0] :
( one_one(X0) = ti(X0,one_one(X0))
| ~ semiring_0(X0)
| ~ power(X0) ),
inference(cnf_transformation,[],[f295]) ).
fof(f295,plain,
! [X0] :
( one_one(X0) = ti(X0,one_one(X0))
| ~ semiring_0(X0)
| ~ power(X0) ),
inference(flattening,[],[f294]) ).
fof(f294,plain,
! [X0] :
( one_one(X0) = ti(X0,one_one(X0))
| ~ semiring_0(X0)
| ~ power(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ( semiring_0(X0)
& power(X0) )
=> one_one(X0) = ti(X0,one_one(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1057,plain,
spl0_60,
inference(avatar_split_clause,[],[f461,f1055]) ).
fof(f461,plain,
! [X0,X1] :
( semiring_1_of_nat(X0,X1) = number_number_of(X0,semiring_1_of_nat(int,X1))
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f277]) ).
fof(f277,plain,
! [X0] :
( ! [X1] : semiring_1_of_nat(X0,X1) = number_number_of(X0,semiring_1_of_nat(int,X1))
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0] :
( number_semiring(X0)
=> ! [X1] : semiring_1_of_nat(X0,X1) = number_number_of(X0,semiring_1_of_nat(int,X1)) ),
inference(rectify,[],[f127]) ).
fof(f127,axiom,
! [X0] :
( number_semiring(X0)
=> ! [X13] : number_number_of(X0,semiring_1_of_nat(int,X13)) = semiring_1_of_nat(X0,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1050,plain,
spl0_59,
inference(avatar_split_clause,[],[f567,f1048]) ).
fof(f1048,plain,
( spl0_59
<=> ! [X0] : plus_plus(int,X0,X0) = ti(int,plus_plus(int,X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f567,plain,
! [X0] : plus_plus(int,X0,X0) = ti(int,plus_plus(int,X0,X0)),
inference(definition_unfolding,[],[f371,f421,f421]) ).
fof(f371,plain,
! [X0] : bit0(X0) = ti(int,bit0(X0)),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0] : bit0(X0) = ti(int,bit0(X0)),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X1] : bit0(X1) = ti(int,bit0(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1040,plain,
( spl0_58
| ~ spl0_5
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f984,f960,f741,f1037]) ).
fof(f1037,plain,
( spl0_58
<=> one_one(int) = number_number_of(int,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f960,plain,
( spl0_49
<=> ! [X0] :
( one_one(X0) = number_number_of(X0,one_one(int))
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f984,plain,
( one_one(int) = number_number_of(int,one_one(int))
| ~ spl0_5
| ~ spl0_49 ),
inference(resolution,[],[f961,f743]) ).
fof(f961,plain,
( ! [X0] :
( ~ number_ring(X0)
| one_one(X0) = number_number_of(X0,one_one(int)) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f960]) ).
fof(f1014,plain,
spl0_57,
inference(avatar_split_clause,[],[f650,f1011]) ).
fof(f650,plain,
ord_less(int,pls,plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(forward_demodulation,[],[f413,f398]) ).
fof(f398,plain,
pls = zero_zero(int),
inference(cnf_transformation,[],[f106]) ).
fof(f106,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f413,plain,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1009,plain,
spl0_56,
inference(avatar_split_clause,[],[f576,f1007]) ).
fof(f576,plain,
! [X0] : pls != plus_plus(int,plus_plus(int,one_one(int),X0),X0),
inference(definition_unfolding,[],[f415,f425]) ).
fof(f415,plain,
! [X0] : pls != bit1(X0),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
! [X0] : pls != bit1(X0),
inference(rectify,[],[f100]) ).
fof(f100,axiom,
! [X28] : pls != bit1(X28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1005,plain,
spl0_55,
inference(avatar_split_clause,[],[f539,f1003]) ).
fof(f539,plain,
! [X0,X1] :
( X0 = X1
| semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ),
inference(cnf_transformation,[],[f362]) ).
fof(f362,plain,
! [X0,X1] :
( ( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1)
| X0 != X1 )
& ( X0 = X1
| semiring_1_of_nat(int,X0) != semiring_1_of_nat(int,X1) ) ),
inference(nnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0,X1] :
( semiring_1_of_nat(int,X0) = semiring_1_of_nat(int,X1)
<=> X0 = X1 ),
inference(rectify,[],[f81]) ).
fof(f81,axiom,
! [X26,X15] :
( semiring_1_of_nat(int,X15) = semiring_1_of_nat(int,X26)
<=> X15 = X26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1001,plain,
spl0_54,
inference(avatar_split_clause,[],[f526,f999]) ).
fof(f999,plain,
( spl0_54
<=> ! [X0,X1] :
( ord_less(nat,ti(nat,X0),X1)
| ~ ord_less(nat,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f526,plain,
! [X0,X1] :
( ord_less(nat,ti(nat,X0),X1)
| ~ ord_less(nat,X0,X1) ),
inference(cnf_transformation,[],[f355]) ).
fof(f355,plain,
! [X0,X1] :
( ( ord_less(nat,ti(nat,X0),X1)
| ~ ord_less(nat,X0,X1) )
& ( ord_less(nat,X0,X1)
| ~ ord_less(nat,ti(nat,X0),X1) ) ),
inference(nnf_transformation,[],[f224]) ).
fof(f224,plain,
! [X0,X1] :
( ord_less(nat,ti(nat,X0),X1)
<=> ord_less(nat,X0,X1) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X1,X2] :
( ord_less(nat,ti(nat,X1),X2)
<=> ord_less(nat,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f997,plain,
spl0_53,
inference(avatar_split_clause,[],[f525,f995]) ).
fof(f995,plain,
( spl0_53
<=> ! [X0,X1] :
( ord_less(nat,X0,X1)
| ~ ord_less(nat,ti(nat,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f525,plain,
! [X0,X1] :
( ord_less(nat,X0,X1)
| ~ ord_less(nat,ti(nat,X0),X1) ),
inference(cnf_transformation,[],[f355]) ).
fof(f993,plain,
spl0_52,
inference(avatar_split_clause,[],[f524,f991]) ).
fof(f991,plain,
( spl0_52
<=> ! [X0,X1] :
( ord_less(nat,X0,ti(nat,X1))
| ~ ord_less(nat,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f524,plain,
! [X0,X1] :
( ord_less(nat,X0,ti(nat,X1))
| ~ ord_less(nat,X0,X1) ),
inference(cnf_transformation,[],[f354]) ).
fof(f354,plain,
! [X0,X1] :
( ( ord_less(nat,X0,ti(nat,X1))
| ~ ord_less(nat,X0,X1) )
& ( ord_less(nat,X0,X1)
| ~ ord_less(nat,X0,ti(nat,X1)) ) ),
inference(nnf_transformation,[],[f223]) ).
fof(f223,plain,
! [X0,X1] :
( ord_less(nat,X0,ti(nat,X1))
<=> ord_less(nat,X0,X1) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X1,X2] :
( ord_less(nat,X1,ti(nat,X2))
<=> ord_less(nat,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f989,plain,
spl0_51,
inference(avatar_split_clause,[],[f523,f987]) ).
fof(f987,plain,
( spl0_51
<=> ! [X0,X1] :
( ord_less(nat,X0,X1)
| ~ ord_less(nat,X0,ti(nat,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f523,plain,
! [X0,X1] :
( ord_less(nat,X0,X1)
| ~ ord_less(nat,X0,ti(nat,X1)) ),
inference(cnf_transformation,[],[f354]) ).
fof(f966,plain,
spl0_50,
inference(avatar_split_clause,[],[f693,f964]) ).
fof(f693,plain,
! [X0] :
( pls != semiring_1_of_nat(int,X0)
| zero_zero(nat) = X0 ),
inference(forward_demodulation,[],[f492,f398]) ).
fof(f492,plain,
! [X0] :
( zero_zero(nat) = X0
| zero_zero(int) != semiring_1_of_nat(int,X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f348,plain,
! [X0] :
( ( zero_zero(int) = semiring_1_of_nat(int,X0)
| zero_zero(nat) != X0 )
& ( zero_zero(nat) = X0
| zero_zero(int) != semiring_1_of_nat(int,X0) ) ),
inference(nnf_transformation,[],[f200]) ).
fof(f200,plain,
! [X0] :
( zero_zero(int) = semiring_1_of_nat(int,X0)
<=> zero_zero(nat) = X0 ),
inference(rectify,[],[f60]) ).
fof(f60,axiom,
! [X15] :
( zero_zero(int) = semiring_1_of_nat(int,X15)
<=> zero_zero(nat) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f962,plain,
spl0_49,
inference(avatar_split_clause,[],[f669,f960]) ).
fof(f669,plain,
! [X0] :
( one_one(X0) = number_number_of(X0,one_one(int))
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f668,f417]) ).
fof(f668,plain,
! [X0] :
( one_one(X0) = number_number_of(X0,plus_plus(int,one_one(int),pls))
| ~ number_ring(X0) ),
inference(forward_demodulation,[],[f590,f417]) ).
fof(f590,plain,
! [X0] :
( one_one(X0) = number_number_of(X0,plus_plus(int,plus_plus(int,one_one(int),pls),pls))
| ~ number_ring(X0) ),
inference(definition_unfolding,[],[f445,f425]) ).
fof(f445,plain,
! [X0] :
( one_one(X0) = number_number_of(X0,bit1(pls))
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f262]) ).
fof(f262,plain,
! [X0] :
( one_one(X0) = number_number_of(X0,bit1(pls))
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( number_ring(X0)
=> one_one(X0) = number_number_of(X0,bit1(pls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f958,plain,
( ~ spl0_48
| ~ spl0_36
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f907,f899,f894,f955]) ).
fof(f955,plain,
( spl0_48
<=> ord_less(int,one_one(int),pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f894,plain,
( spl0_36
<=> ! [X0] : ~ ord_less(int,semiring_1_of_nat(int,X0),pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f907,plain,
( ~ ord_less(int,one_one(int),pls)
| ~ spl0_36
| ~ spl0_37 ),
inference(superposition,[],[f895,f901]) ).
fof(f895,plain,
( ! [X0] : ~ ord_less(int,semiring_1_of_nat(int,X0),pls)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f894]) ).
fof(f953,plain,
spl0_47,
inference(avatar_split_clause,[],[f603,f951]) ).
fof(f951,plain,
( spl0_47
<=> ! [X0] :
( pls = X0
| pls != plus_plus(int,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f603,plain,
! [X0] :
( pls = X0
| pls != plus_plus(int,X0,X0) ),
inference(definition_unfolding,[],[f482,f421]) ).
fof(f482,plain,
! [X0] :
( pls = X0
| pls != bit0(X0) ),
inference(cnf_transformation,[],[f343]) ).
fof(f343,plain,
! [X0] :
( ( pls = bit0(X0)
| pls != X0 )
& ( pls = X0
| pls != bit0(X0) ) ),
inference(nnf_transformation,[],[f195]) ).
fof(f195,plain,
! [X0] :
( pls = bit0(X0)
<=> pls = X0 ),
inference(rectify,[],[f104]) ).
fof(f104,axiom,
! [X11] :
( pls = bit0(X11)
<=> pls = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f949,plain,
spl0_46,
inference(avatar_split_clause,[],[f503,f947]) ).
fof(f945,plain,
spl0_45,
inference(avatar_split_clause,[],[f502,f943]) ).
fof(f943,plain,
( spl0_45
<=> ! [X0,X1] : ti(X0,X1) = ti(X0,ti(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f502,plain,
! [X0,X1] : ti(X0,X1) = ti(X0,ti(X0,X1)),
inference(cnf_transformation,[],[f206]) ).
fof(f206,plain,
! [X0,X1] : ti(X0,X1) = ti(X0,ti(X0,X1)),
inference(rectify,[],[f152]) ).
fof(f152,axiom,
! [X30,X31] : ti(X30,X31) = ti(X30,ti(X30,X31)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f941,plain,
spl0_44,
inference(avatar_split_clause,[],[f429,f939]) ).
fof(f939,plain,
( spl0_44
<=> ! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ linord219039673up_add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f429,plain,
! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f253]) ).
fof(f253,plain,
! [X0] :
( zero_zero(X0) = ti(X0,zero_zero(X0))
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( linord219039673up_add(X0)
=> zero_zero(X0) = ti(X0,zero_zero(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f931,plain,
spl0_43,
inference(avatar_split_clause,[],[f644,f929]) ).
fof(f644,plain,
! [X1] : ord_less(int,X1,plus_plus(int,X1,one_one(int))),
inference(equality_resolution,[],[f543]) ).
fof(f543,plain,
! [X0,X1] :
( ord_less(int,X0,plus_plus(int,X1,one_one(int)))
| X0 != X1 ),
inference(cnf_transformation,[],[f364]) ).
fof(f927,plain,
spl0_42,
inference(avatar_split_clause,[],[f459,f925]) ).
fof(f925,plain,
( spl0_42
<=> ! [X0] :
( zero_zero(X0) = number_number_of(X0,pls)
| ~ number_semiring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f459,plain,
! [X0] :
( zero_zero(X0) = number_number_of(X0,pls)
| ~ number_semiring(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f275,plain,
! [X0] :
( zero_zero(X0) = number_number_of(X0,pls)
| ~ number_semiring(X0) ),
inference(ennf_transformation,[],[f114]) ).
fof(f114,axiom,
! [X0] :
( number_semiring(X0)
=> zero_zero(X0) = number_number_of(X0,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f923,plain,
spl0_41,
inference(avatar_split_clause,[],[f443,f921]) ).
fof(f921,plain,
( spl0_41
<=> ! [X0] :
( zero_zero(X0) = number_number_of(X0,pls)
| ~ number_ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f443,plain,
! [X0] :
( zero_zero(X0) = number_number_of(X0,pls)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f260]) ).
fof(f260,plain,
! [X0] :
( zero_zero(X0) = number_number_of(X0,pls)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f115]) ).
fof(f115,axiom,
! [X0] :
( number_ring(X0)
=> zero_zero(X0) = number_number_of(X0,pls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f919,plain,
( spl0_40
| ~ spl0_23
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f914,f909,f831,f916]) ).
fof(f909,plain,
( spl0_39
<=> zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f914,plain,
( pls = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(nat,one_one(nat),one_one(nat)))
| ~ spl0_23
| ~ spl0_39 ),
inference(forward_demodulation,[],[f913,f833]) ).
fof(f913,plain,
( zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),plus_plus(nat,one_one(nat),one_one(nat)))
| ~ spl0_39 ),
inference(forward_demodulation,[],[f911,f575]) ).
fof(f911,plain,
( zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls))))
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f909]) ).
fof(f912,plain,
spl0_39,
inference(avatar_split_clause,[],[f566,f909]) ).
fof(f566,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,plus_plus(int,plus_plus(int,plus_plus(int,one_one(int),pls),pls),plus_plus(int,plus_plus(int,one_one(int),pls),pls)))),
inference(definition_unfolding,[],[f368,f421,f425]) ).
fof(f368,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
zero_zero(int) = power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),
inference(flattening,[],[f154]) ).
fof(f154,negated_conjecture,
~ ( zero_zero(int) != power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) ),
inference(negated_conjecture,[],[f153]) ).
fof(f153,conjecture,
zero_zero(int) != power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f906,plain,
spl0_38,
inference(avatar_split_clause,[],[f420,f904]) ).
fof(f904,plain,
( spl0_38
<=> ! [X0] : undefined(X0) = ti(X0,undefined(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f420,plain,
! [X0] : undefined(X0) = ti(X0,undefined(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : undefined(X0) = ti(X0,undefined(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f902,plain,
spl0_37,
inference(avatar_split_clause,[],[f410,f899]) ).
fof(f410,plain,
one_one(int) = semiring_1_of_nat(int,one_one(nat)),
inference(cnf_transformation,[],[f57]) ).
fof(f57,axiom,
one_one(int) = semiring_1_of_nat(int,one_one(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f896,plain,
spl0_36,
inference(avatar_split_clause,[],[f651,f894]) ).
fof(f651,plain,
! [X0] : ~ ord_less(int,semiring_1_of_nat(int,X0),pls),
inference(forward_demodulation,[],[f419,f398]) ).
fof(f419,plain,
! [X0] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
! [X0] : ~ ord_less(int,semiring_1_of_nat(int,X0),zero_zero(int)),
inference(rectify,[],[f94]) ).
fof(f94,axiom,
! [X18] : ~ ord_less(int,semiring_1_of_nat(int,X18),zero_zero(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f892,plain,
spl0_35,
inference(avatar_split_clause,[],[f649,f889]) ).
fof(f889,plain,
( spl0_35
<=> pls = semiring_1_of_nat(int,zero_zero(nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f649,plain,
pls = semiring_1_of_nat(int,zero_zero(nat)),
inference(forward_demodulation,[],[f412,f398]) ).
fof(f412,plain,
zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)),
inference(cnf_transformation,[],[f61]) ).
fof(f61,axiom,
zero_zero(int) = semiring_1_of_nat(int,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f887,plain,
spl0_34,
inference(avatar_split_clause,[],[f418,f885]) ).
fof(f418,plain,
! [X0] : plus_plus(int,pls,X0) = X0,
inference(cnf_transformation,[],[f163]) ).
fof(f163,plain,
! [X0] : plus_plus(int,pls,X0) = X0,
inference(rectify,[],[f109]) ).
fof(f109,axiom,
! [X18] : plus_plus(int,pls,X18) = X18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f883,plain,
spl0_33,
inference(avatar_split_clause,[],[f417,f881]) ).
fof(f879,plain,
spl0_32,
inference(avatar_split_clause,[],[f404,f876]) ).
fof(f404,plain,
zero_zero(nat) = number_number_of(nat,pls),
inference(cnf_transformation,[],[f59]) ).
fof(f59,axiom,
zero_zero(nat) = number_number_of(nat,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f874,plain,
spl0_31,
inference(avatar_split_clause,[],[f648,f871]) ).
fof(f871,plain,
( spl0_31
<=> ord_less(int,pls,one_one(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f648,plain,
ord_less(int,pls,one_one(int)),
inference(forward_demodulation,[],[f407,f398]) ).
fof(f407,plain,
ord_less(int,zero_zero(int),one_one(int)),
inference(cnf_transformation,[],[f92]) ).
fof(f92,axiom,
ord_less(int,zero_zero(int),one_one(int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f869,plain,
spl0_30,
inference(avatar_split_clause,[],[f647,f866]) ).
fof(f647,plain,
pls = number_number_of(int,pls),
inference(forward_demodulation,[],[f406,f398]) ).
fof(f406,plain,
zero_zero(int) = number_number_of(int,pls),
inference(cnf_transformation,[],[f52]) ).
fof(f52,axiom,
zero_zero(int) = number_number_of(int,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f864,plain,
spl0_29,
inference(avatar_split_clause,[],[f403,f861]) ).
fof(f861,plain,
( spl0_29
<=> ord_less(int,one_one(int),t) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f403,plain,
ord_less(int,one_one(int),t),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
ord_less(int,one_one(int),t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f859,plain,
spl0_28,
inference(avatar_split_clause,[],[f402,f856]) ).
fof(f856,plain,
( spl0_28
<=> ord_less(nat,zero_zero(nat),n) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f402,plain,
ord_less(nat,zero_zero(nat),n),
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
ord_less(nat,zero_zero(nat),n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f854,plain,
spl0_27,
inference(avatar_split_clause,[],[f401,f851]) ).
fof(f851,plain,
( spl0_27
<=> t = ti(int,t) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f401,plain,
t = ti(int,t),
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
t = ti(int,t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f849,plain,
spl0_26,
inference(avatar_split_clause,[],[f370,f846]) ).
fof(f846,plain,
( spl0_26
<=> pls = ti(int,pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f370,plain,
pls = ti(int,pls),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
pls = ti(int,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f844,plain,
spl0_25,
inference(avatar_split_clause,[],[f369,f841]) ).
fof(f841,plain,
( spl0_25
<=> n = ti(nat,n) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f369,plain,
n = ti(nat,n),
inference(cnf_transformation,[],[f31]) ).
fof(f31,axiom,
n = ti(nat,n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f839,plain,
~ spl0_24,
inference(avatar_split_clause,[],[f645,f836]) ).
fof(f836,plain,
( spl0_24
<=> pls = one_one(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f645,plain,
pls != one_one(int),
inference(forward_demodulation,[],[f399,f398]) ).
fof(f399,plain,
zero_zero(int) != one_one(int),
inference(cnf_transformation,[],[f107]) ).
fof(f107,axiom,
zero_zero(int) != one_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f834,plain,
spl0_23,
inference(avatar_split_clause,[],[f398,f831]) ).
fof(f829,plain,
~ spl0_22,
inference(avatar_split_clause,[],[f396,f826]) ).
fof(f396,plain,
~ ord_less(int,pls,pls),
inference(cnf_transformation,[],[f65]) ).
fof(f65,axiom,
~ ord_less(int,pls,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f824,plain,
spl0_21,
inference(avatar_split_clause,[],[f395,f821]) ).
fof(f395,plain,
power(int),
inference(cnf_transformation,[],[f142]) ).
fof(f142,axiom,
power(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f819,plain,
spl0_20,
inference(avatar_split_clause,[],[f394,f816]) ).
fof(f394,plain,
power(nat),
inference(cnf_transformation,[],[f150]) ).
fof(f150,axiom,
power(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f814,plain,
spl0_19,
inference(avatar_split_clause,[],[f393,f811]) ).
fof(f393,plain,
number_semiring(int),
inference(cnf_transformation,[],[f135]) ).
fof(f135,axiom,
number_semiring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f809,plain,
spl0_18,
inference(avatar_split_clause,[],[f392,f806]) ).
fof(f392,plain,
number_semiring(nat),
inference(cnf_transformation,[],[f145]) ).
fof(f145,axiom,
number_semiring(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f804,plain,
spl0_17,
inference(avatar_split_clause,[],[f391,f801]) ).
fof(f391,plain,
semiring_0(int),
inference(cnf_transformation,[],[f138]) ).
fof(f138,axiom,
semiring_0(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f799,plain,
spl0_16,
inference(avatar_split_clause,[],[f390,f796]) ).
fof(f390,plain,
semiring_0(nat),
inference(cnf_transformation,[],[f148]) ).
fof(f148,axiom,
semiring_0(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f794,plain,
spl0_15,
inference(avatar_split_clause,[],[f389,f791]) ).
fof(f791,plain,
( spl0_15
<=> zero_neq_one(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f389,plain,
zero_neq_one(int),
inference(cnf_transformation,[],[f136]) ).
fof(f136,axiom,
zero_neq_one(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f789,plain,
spl0_14,
inference(avatar_split_clause,[],[f388,f786]) ).
fof(f786,plain,
( spl0_14
<=> mult_zero(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f388,plain,
mult_zero(int),
inference(cnf_transformation,[],[f139]) ).
fof(f139,axiom,
mult_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f784,plain,
spl0_13,
inference(avatar_split_clause,[],[f387,f781]) ).
fof(f781,plain,
( spl0_13
<=> no_zero_divisors(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f387,plain,
no_zero_divisors(int),
inference(cnf_transformation,[],[f133]) ).
fof(f133,axiom,
no_zero_divisors(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f779,plain,
spl0_12,
inference(avatar_split_clause,[],[f386,f776]) ).
fof(f776,plain,
( spl0_12
<=> no_zero_divisors(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f386,plain,
no_zero_divisors(nat),
inference(cnf_transformation,[],[f144]) ).
fof(f144,axiom,
no_zero_divisors(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f774,plain,
spl0_11,
inference(avatar_split_clause,[],[f385,f771]) ).
fof(f771,plain,
( spl0_11
<=> zero_neq_one(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f385,plain,
zero_neq_one(nat),
inference(cnf_transformation,[],[f146]) ).
fof(f146,axiom,
zero_neq_one(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f769,plain,
spl0_10,
inference(avatar_split_clause,[],[f384,f766]) ).
fof(f766,plain,
( spl0_10
<=> mult_zero(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f384,plain,
mult_zero(nat),
inference(cnf_transformation,[],[f149]) ).
fof(f149,axiom,
mult_zero(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f764,plain,
spl0_9,
inference(avatar_split_clause,[],[f383,f761]) ).
fof(f383,plain,
number(int),
inference(cnf_transformation,[],[f143]) ).
fof(f143,axiom,
number(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f759,plain,
spl0_8,
inference(avatar_split_clause,[],[f382,f756]) ).
fof(f382,plain,
number(nat),
inference(cnf_transformation,[],[f151]) ).
fof(f151,axiom,
number(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f754,plain,
spl0_7,
inference(avatar_split_clause,[],[f381,f751]) ).
fof(f751,plain,
( spl0_7
<=> semiring_1(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f381,plain,
semiring_1(int),
inference(cnf_transformation,[],[f137]) ).
fof(f137,axiom,
semiring_1(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f749,plain,
spl0_6,
inference(avatar_split_clause,[],[f380,f746]) ).
fof(f746,plain,
( spl0_6
<=> semiring_1(nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f380,plain,
semiring_1(nat),
inference(cnf_transformation,[],[f147]) ).
fof(f147,axiom,
semiring_1(nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f744,plain,
spl0_5,
inference(avatar_split_clause,[],[f379,f741]) ).
fof(f379,plain,
number_ring(int),
inference(cnf_transformation,[],[f141]) ).
fof(f141,axiom,
number_ring(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f739,plain,
spl0_4,
inference(avatar_split_clause,[],[f378,f736]) ).
fof(f378,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f134]) ).
fof(f134,axiom,
linordered_idom(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f734,plain,
spl0_3,
inference(avatar_split_clause,[],[f377,f731]) ).
fof(f731,plain,
( spl0_3
<=> linord219039673up_add(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f377,plain,
linord219039673up_add(int),
inference(cnf_transformation,[],[f131]) ).
fof(f131,axiom,
linord219039673up_add(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f729,plain,
spl0_2,
inference(avatar_split_clause,[],[f376,f726]) ).
fof(f726,plain,
( spl0_2
<=> ring_char_0(int) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f376,plain,
ring_char_0(int),
inference(cnf_transformation,[],[f140]) ).
fof(f140,axiom,
ring_char_0(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f724,plain,
spl0_1,
inference(avatar_split_clause,[],[f375,f721]) ).
fof(f375,plain,
ring_11004092258visors(int),
inference(cnf_transformation,[],[f132]) ).
fof(f132,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM925+5 : TPTP v8.2.0. Released v5.3.0.
% 0.07/0.13 % Command : run_vampire %s %d SAT
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Jun 22 23:54:39 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.13/0.37 Running first-order model finding
% 0.13/0.37 Running /export/starexec/sandbox/solver/bin/vampire --mode casc_sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.43 % (27096)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (27097)fmb+10_1:1_sil=256000:i=98885:tgt=full:fmbsr=1.3:fmbss=10_0 on theBenchmark for (3000ds/98885Mi)
% 0.21/0.43 % (27096)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (27101)ott+21_1:1_sil=4000:i=104:fsd=on:fd=off:newcnf=on_0 on theBenchmark for (3000ds/104Mi)
% 0.21/0.43 % (27096)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (27103)ott-4_1:1_sil=4000:sp=reverse_arity:lcm=predicate:newcnf=on:i=115:bce=on:fd=off:fs=off:fsr=off_0 on theBenchmark for (3000ds/115Mi)
% 0.21/0.43 % (27096)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (27099)fmb+10_1:1_sil=256000:fmbes=contour:i=214858:bce=on_0 on theBenchmark for (3000ds/214858Mi)
% 0.21/0.43 % (27096)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (27098)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency:i=99418_0 on theBenchmark for (3000ds/99418Mi)
% 0.21/0.43 % (27096)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (27102)ott+11_8:59_sil=16000:sp=occurrence:lsd=20:abs=on:i=146:aac=none:nm=16:fdi=10:rawr=on:nicw=on_0 on theBenchmark for (3000ds/146Mi)
% 0.21/0.44 % (27096)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.44 % (27100)fmb+10_1:1_sil=256000:fmbss=23:fmbes=contour:newcnf=on:fmbsr=1.14:i=152523:nm=2:gsp=on:rp=on_0 on theBenchmark for (3000ds/152523Mi)
% 0.21/0.49 % (27103)Instruction limit reached!
% 0.21/0.49 % (27103)------------------------------
% 0.21/0.49 % (27103)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.49 % (27103)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.49 % (27103)Termination reason: Time limit
% 0.21/0.49 % (27103)Termination phase: Saturation
% 0.21/0.49
% 0.21/0.49 % (27103)Memory used [KB]: 1768
% 0.21/0.49 % (27103)Time elapsed: 0.058 s
% 0.21/0.49 % (27103)Instructions burned: 117 (million)
% 0.21/0.49 % (27101)Instruction limit reached!
% 0.21/0.49 % (27101)------------------------------
% 0.21/0.49 % (27101)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.49 % (27101)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.49 % (27101)Termination reason: Time limit
% 0.21/0.49 % (27101)Termination phase: Saturation
% 0.21/0.49
% 0.21/0.49 % (27101)Memory used [KB]: 1692
% 0.21/0.49 % (27101)Time elapsed: 0.058 s
% 0.21/0.49 % (27101)Instructions burned: 104 (million)
% 0.21/0.49 TRYING [1]
% 0.21/0.50 TRYING [2]
% 0.21/0.50 % (27102)Instruction limit reached!
% 0.21/0.50 % (27102)------------------------------
% 0.21/0.50 % (27102)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.50 % (27102)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.50 % (27102)Termination reason: Time limit
% 0.21/0.50 % (27102)Termination phase: Saturation
% 0.21/0.50
% 0.21/0.50 % (27102)Memory used [KB]: 2046
% 0.21/0.50 % (27102)Time elapsed: 0.070 s
% 0.21/0.50 % (27102)Instructions burned: 147 (million)
% 0.21/0.50 % (27098)First to succeed.
% 1.10/0.51 % (27098)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-27096"
% 1.10/0.51 % (27096)Running in auto input_syntax mode. Trying TPTP
% 1.10/0.51 % (27098)Refutation found. Thanks to Tanya!
% 1.10/0.51 % SZS status Theorem for theBenchmark
% 1.10/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 1.10/0.52 % (27098)------------------------------
% 1.10/0.52 % (27098)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.10/0.52 % (27098)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.10/0.52 % (27098)Termination reason: Refutation
% 1.10/0.52
% 1.10/0.52 % (27098)Memory used [KB]: 2183
% 1.10/0.52 % (27098)Time elapsed: 0.080 s
% 1.10/0.52 % (27098)Instructions burned: 147 (million)
% 1.10/0.52 % (27098)------------------------------
% 1.10/0.52 % (27098)------------------------------
% 1.10/0.52 % (27096)Success in time 0.13 s
%------------------------------------------------------------------------------