TSTP Solution File: SWV184+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV184+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 16:42:11 EDT 2024
% Result : Theorem 0.13s 0.40s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 232
% Syntax : Number of formulae : 660 ( 229 unt; 0 def)
% Number of atoms : 1817 ( 228 equ)
% Maximal formula atoms : 27 ( 2 avg)
% Number of connectives : 1828 ( 671 ~; 586 |; 360 &)
% ( 154 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 168 ( 166 usr; 153 prp; 0-2 aty)
% Number of functors : 53 ( 53 usr; 20 con; 0-3 aty)
% Number of variables : 776 ( 682 !; 94 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1358,plain,
$false,
inference(avatar_sat_refutation,[],[f476,f481,f486,f491,f495,f500,f506,f511,f516,f521,f526,f531,f536,f541,f546,f551,f556,f561,f566,f571,f576,f581,f586,f591,f596,f601,f606,f611,f616,f621,f626,f631,f636,f641,f646,f651,f656,f660,f664,f675,f679,f685,f691,f697,f704,f709,f713,f718,f723,f728,f733,f743,f749,f771,f776,f780,f822,f826,f830,f834,f855,f861,f866,f871,f877,f881,f885,f890,f894,f899,f903,f908,f912,f917,f921,f926,f930,f934,f939,f943,f948,f952,f957,f961,f966,f970,f975,f979,f984,f988,f993,f997,f1002,f1006,f1011,f1016,f1020,f1025,f1029,f1034,f1038,f1043,f1047,f1052,f1056,f1061,f1065,f1070,f1074,f1079,f1083,f1088,f1092,f1097,f1101,f1105,f1110,f1114,f1118,f1122,f1126,f1130,f1134,f1138,f1142,f1146,f1150,f1154,f1158,f1162,f1167,f1171,f1175,f1179,f1183,f1187,f1191,f1195,f1199,f1203,f1207,f1212,f1216,f1220,f1224,f1228,f1232,f1236,f1240,f1244,f1309,f1357]) ).
fof(f1357,plain,
( ~ spl41_3
| spl41_4
| ~ spl41_2
| ~ spl41_44 ),
inference(avatar_split_clause,[],[f692,f689,f478,f488,f483]) ).
fof(f483,plain,
( spl41_3
<=> leq(sK13,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_3])]) ).
fof(f488,plain,
( spl41_4
<=> init = a_select2(sigmaold_init,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_4])]) ).
fof(f478,plain,
( spl41_2
<=> leq(n0,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_2])]) ).
fof(f689,plain,
( spl41_44
<=> ! [X1] :
( init = a_select2(sigmaold_init,X1)
| ~ leq(n0,X1)
| ~ leq(X1,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_44])]) ).
fof(f692,plain,
( init = a_select2(sigmaold_init,sK13)
| ~ leq(sK13,n4)
| ~ spl41_2
| ~ spl41_44 ),
inference(resolution,[],[f690,f480]) ).
fof(f480,plain,
( leq(n0,sK13)
| ~ spl41_2 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f690,plain,
( ! [X1] :
( ~ leq(n0,X1)
| init = a_select2(sigmaold_init,X1)
| ~ leq(X1,n4) )
| ~ spl41_44 ),
inference(avatar_component_clause,[],[f689]) ).
fof(f1309,plain,
( ~ spl41_3
| spl41_152
| ~ spl41_2
| ~ spl41_43 ),
inference(avatar_split_clause,[],[f686,f683,f478,f1306,f483]) ).
fof(f1306,plain,
( spl41_152
<=> init = a_select2(rhoold_init,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_152])]) ).
fof(f683,plain,
( spl41_43
<=> ! [X2] :
( init = a_select2(rhoold_init,X2)
| ~ leq(n0,X2)
| ~ leq(X2,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_43])]) ).
fof(f686,plain,
( init = a_select2(rhoold_init,sK13)
| ~ leq(sK13,n4)
| ~ spl41_2
| ~ spl41_43 ),
inference(resolution,[],[f684,f480]) ).
fof(f684,plain,
( ! [X2] :
( ~ leq(n0,X2)
| init = a_select2(rhoold_init,X2)
| ~ leq(X2,n4) )
| ~ spl41_43 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f1244,plain,
( spl41_151
| ~ spl41_54
| ~ spl41_114 ),
inference(avatar_split_clause,[],[f1093,f1090,f746,f1242]) ).
fof(f1242,plain,
( spl41_151
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK40(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_151])]) ).
fof(f746,plain,
( spl41_54
<=> n0 = tptp_float_0_0 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_54])]) ).
fof(f1090,plain,
( spl41_114
<=> ! [X0,X1] :
( leq(n0,sK40(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_114])]) ).
fof(f1093,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK40(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl41_54
| ~ spl41_114 ),
inference(forward_demodulation,[],[f1091,f748]) ).
fof(f748,plain,
( n0 = tptp_float_0_0
| ~ spl41_54 ),
inference(avatar_component_clause,[],[f746]) ).
fof(f1091,plain,
( ! [X0,X1] :
( leq(n0,sK40(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl41_114 ),
inference(avatar_component_clause,[],[f1090]) ).
fof(f1240,plain,
( spl41_150
| ~ spl41_54
| ~ spl41_112 ),
inference(avatar_split_clause,[],[f1084,f1081,f746,f1238]) ).
fof(f1238,plain,
( spl41_150
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK39(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_150])]) ).
fof(f1081,plain,
( spl41_112
<=> ! [X0,X1] :
( leq(n0,sK39(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_112])]) ).
fof(f1084,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK39(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl41_54
| ~ spl41_112 ),
inference(forward_demodulation,[],[f1082,f748]) ).
fof(f1082,plain,
( ! [X0,X1] :
( leq(n0,sK39(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl41_112 ),
inference(avatar_component_clause,[],[f1081]) ).
fof(f1236,plain,
( spl41_149
| ~ spl41_54
| ~ spl41_110 ),
inference(avatar_split_clause,[],[f1075,f1072,f746,f1234]) ).
fof(f1234,plain,
( spl41_149
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK38(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_149])]) ).
fof(f1072,plain,
( spl41_110
<=> ! [X0,X1] :
( leq(n0,sK38(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_110])]) ).
fof(f1075,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK38(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl41_54
| ~ spl41_110 ),
inference(forward_demodulation,[],[f1073,f748]) ).
fof(f1073,plain,
( ! [X0,X1] :
( leq(n0,sK38(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl41_110 ),
inference(avatar_component_clause,[],[f1072]) ).
fof(f1232,plain,
( spl41_148
| ~ spl41_54
| ~ spl41_108 ),
inference(avatar_split_clause,[],[f1066,f1063,f746,f1230]) ).
fof(f1230,plain,
( spl41_148
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK37(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_148])]) ).
fof(f1063,plain,
( spl41_108
<=> ! [X0,X1] :
( leq(n0,sK37(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_108])]) ).
fof(f1066,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK37(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl41_54
| ~ spl41_108 ),
inference(forward_demodulation,[],[f1064,f748]) ).
fof(f1064,plain,
( ! [X0,X1] :
( leq(n0,sK37(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl41_108 ),
inference(avatar_component_clause,[],[f1063]) ).
fof(f1228,plain,
( spl41_147
| ~ spl41_54
| ~ spl41_106 ),
inference(avatar_split_clause,[],[f1057,f1054,f746,f1226]) ).
fof(f1226,plain,
( spl41_147
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK36(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_147])]) ).
fof(f1054,plain,
( spl41_106
<=> ! [X0,X1] :
( leq(n0,sK36(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_106])]) ).
fof(f1057,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK36(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl41_54
| ~ spl41_106 ),
inference(forward_demodulation,[],[f1055,f748]) ).
fof(f1055,plain,
( ! [X0,X1] :
( leq(n0,sK36(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl41_106 ),
inference(avatar_component_clause,[],[f1054]) ).
fof(f1224,plain,
( spl41_146
| ~ spl41_54
| ~ spl41_104 ),
inference(avatar_split_clause,[],[f1048,f1045,f746,f1222]) ).
fof(f1222,plain,
( spl41_146
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK35(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_146])]) ).
fof(f1045,plain,
( spl41_104
<=> ! [X0,X1] :
( leq(n0,sK35(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_104])]) ).
fof(f1048,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK35(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl41_54
| ~ spl41_104 ),
inference(forward_demodulation,[],[f1046,f748]) ).
fof(f1046,plain,
( ! [X0,X1] :
( leq(n0,sK35(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl41_104 ),
inference(avatar_component_clause,[],[f1045]) ).
fof(f1220,plain,
( spl41_145
| ~ spl41_54
| ~ spl41_102 ),
inference(avatar_split_clause,[],[f1039,f1036,f746,f1218]) ).
fof(f1218,plain,
( spl41_145
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK32(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_145])]) ).
fof(f1036,plain,
( spl41_102
<=> ! [X0,X1] :
( leq(n0,sK32(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_102])]) ).
fof(f1039,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK32(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl41_54
| ~ spl41_102 ),
inference(forward_demodulation,[],[f1037,f748]) ).
fof(f1037,plain,
( ! [X0,X1] :
( leq(n0,sK32(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl41_102 ),
inference(avatar_component_clause,[],[f1036]) ).
fof(f1216,plain,
( spl41_144
| ~ spl41_54
| ~ spl41_100 ),
inference(avatar_split_clause,[],[f1030,f1027,f746,f1214]) ).
fof(f1214,plain,
( spl41_144
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK31(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_144])]) ).
fof(f1027,plain,
( spl41_100
<=> ! [X0,X1] :
( leq(n0,sK31(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_100])]) ).
fof(f1030,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK31(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl41_54
| ~ spl41_100 ),
inference(forward_demodulation,[],[f1028,f748]) ).
fof(f1028,plain,
( ! [X0,X1] :
( leq(n0,sK31(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl41_100 ),
inference(avatar_component_clause,[],[f1027]) ).
fof(f1212,plain,
( ~ spl41_3
| spl41_143
| ~ spl41_2
| ~ spl41_42 ),
inference(avatar_split_clause,[],[f680,f677,f478,f1209,f483]) ).
fof(f1209,plain,
( spl41_143
<=> init = a_select2(muold_init,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_143])]) ).
fof(f677,plain,
( spl41_42
<=> ! [X3] :
( init = a_select2(muold_init,X3)
| ~ leq(n0,X3)
| ~ leq(X3,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_42])]) ).
fof(f680,plain,
( init = a_select2(muold_init,sK13)
| ~ leq(sK13,n4)
| ~ spl41_2
| ~ spl41_42 ),
inference(resolution,[],[f678,f480]) ).
fof(f678,plain,
( ! [X3] :
( ~ leq(n0,X3)
| init = a_select2(muold_init,X3)
| ~ leq(X3,n4) )
| ~ spl41_42 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f1207,plain,
( spl41_142
| ~ spl41_54
| ~ spl41_98 ),
inference(avatar_split_clause,[],[f1021,f1018,f746,f1205]) ).
fof(f1205,plain,
( spl41_142
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK29(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_142])]) ).
fof(f1018,plain,
( spl41_98
<=> ! [X0,X1] :
( leq(n0,sK29(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_98])]) ).
fof(f1021,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK29(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl41_54
| ~ spl41_98 ),
inference(forward_demodulation,[],[f1019,f748]) ).
fof(f1019,plain,
( ! [X0,X1] :
( leq(n0,sK29(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl41_98 ),
inference(avatar_component_clause,[],[f1018]) ).
fof(f1203,plain,
( spl41_141
| ~ spl41_54
| ~ spl41_95 ),
inference(avatar_split_clause,[],[f1007,f1004,f746,f1201]) ).
fof(f1201,plain,
( spl41_141
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK28(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_141])]) ).
fof(f1004,plain,
( spl41_95
<=> ! [X0,X1] :
( leq(n0,sK28(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_95])]) ).
fof(f1007,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK28(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl41_54
| ~ spl41_95 ),
inference(forward_demodulation,[],[f1005,f748]) ).
fof(f1005,plain,
( ! [X0,X1] :
( leq(n0,sK28(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl41_95 ),
inference(avatar_component_clause,[],[f1004]) ).
fof(f1199,plain,
( spl41_140
| ~ spl41_54
| ~ spl41_93 ),
inference(avatar_split_clause,[],[f998,f995,f746,f1197]) ).
fof(f1197,plain,
( spl41_140
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK27(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_140])]) ).
fof(f995,plain,
( spl41_93
<=> ! [X0,X1] :
( leq(n0,sK27(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_93])]) ).
fof(f998,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK27(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl41_54
| ~ spl41_93 ),
inference(forward_demodulation,[],[f996,f748]) ).
fof(f996,plain,
( ! [X0,X1] :
( leq(n0,sK27(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl41_93 ),
inference(avatar_component_clause,[],[f995]) ).
fof(f1195,plain,
( spl41_139
| ~ spl41_54
| ~ spl41_91 ),
inference(avatar_split_clause,[],[f989,f986,f746,f1193]) ).
fof(f1193,plain,
( spl41_139
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK26(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_139])]) ).
fof(f986,plain,
( spl41_91
<=> ! [X0,X1] :
( leq(n0,sK26(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_91])]) ).
fof(f989,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK26(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl41_54
| ~ spl41_91 ),
inference(forward_demodulation,[],[f987,f748]) ).
fof(f987,plain,
( ! [X0,X1] :
( leq(n0,sK26(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl41_91 ),
inference(avatar_component_clause,[],[f986]) ).
fof(f1191,plain,
( spl41_138
| ~ spl41_54
| ~ spl41_89 ),
inference(avatar_split_clause,[],[f980,f977,f746,f1189]) ).
fof(f1189,plain,
( spl41_138
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK25(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_138])]) ).
fof(f977,plain,
( spl41_89
<=> ! [X0,X1] :
( leq(n0,sK25(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_89])]) ).
fof(f980,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK25(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl41_54
| ~ spl41_89 ),
inference(forward_demodulation,[],[f978,f748]) ).
fof(f978,plain,
( ! [X0,X1] :
( leq(n0,sK25(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl41_89 ),
inference(avatar_component_clause,[],[f977]) ).
fof(f1187,plain,
( spl41_137
| ~ spl41_54
| ~ spl41_87 ),
inference(avatar_split_clause,[],[f971,f968,f746,f1185]) ).
fof(f1185,plain,
( spl41_137
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK24(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_137])]) ).
fof(f968,plain,
( spl41_87
<=> ! [X0,X1] :
( leq(n0,sK24(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_87])]) ).
fof(f971,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK24(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl41_54
| ~ spl41_87 ),
inference(forward_demodulation,[],[f969,f748]) ).
fof(f969,plain,
( ! [X0,X1] :
( leq(n0,sK24(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl41_87 ),
inference(avatar_component_clause,[],[f968]) ).
fof(f1183,plain,
( spl41_136
| ~ spl41_54
| ~ spl41_85 ),
inference(avatar_split_clause,[],[f962,f959,f746,f1181]) ).
fof(f1181,plain,
( spl41_136
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK23(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_136])]) ).
fof(f959,plain,
( spl41_85
<=> ! [X0,X1] :
( leq(n0,sK23(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_85])]) ).
fof(f962,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK23(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl41_54
| ~ spl41_85 ),
inference(forward_demodulation,[],[f960,f748]) ).
fof(f960,plain,
( ! [X0,X1] :
( leq(n0,sK23(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl41_85 ),
inference(avatar_component_clause,[],[f959]) ).
fof(f1179,plain,
( spl41_135
| ~ spl41_54
| ~ spl41_83 ),
inference(avatar_split_clause,[],[f953,f950,f746,f1177]) ).
fof(f1177,plain,
( spl41_135
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK22(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_135])]) ).
fof(f950,plain,
( spl41_83
<=> ! [X0,X1] :
( leq(n0,sK22(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_83])]) ).
fof(f953,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK22(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl41_54
| ~ spl41_83 ),
inference(forward_demodulation,[],[f951,f748]) ).
fof(f951,plain,
( ! [X0,X1] :
( leq(n0,sK22(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl41_83 ),
inference(avatar_component_clause,[],[f950]) ).
fof(f1175,plain,
( spl41_134
| ~ spl41_54
| ~ spl41_81 ),
inference(avatar_split_clause,[],[f944,f941,f746,f1173]) ).
fof(f1173,plain,
( spl41_134
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK21(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_134])]) ).
fof(f941,plain,
( spl41_81
<=> ! [X0,X1] :
( leq(n0,sK21(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_81])]) ).
fof(f944,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK21(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl41_54
| ~ spl41_81 ),
inference(forward_demodulation,[],[f942,f748]) ).
fof(f942,plain,
( ! [X0,X1] :
( leq(n0,sK21(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl41_81 ),
inference(avatar_component_clause,[],[f941]) ).
fof(f1171,plain,
( spl41_133
| ~ spl41_54
| ~ spl41_79 ),
inference(avatar_split_clause,[],[f935,f932,f746,f1169]) ).
fof(f1169,plain,
( spl41_133
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK20(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_133])]) ).
fof(f932,plain,
( spl41_79
<=> ! [X0,X1] :
( leq(n0,sK20(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_79])]) ).
fof(f935,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK20(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl41_54
| ~ spl41_79 ),
inference(forward_demodulation,[],[f933,f748]) ).
fof(f933,plain,
( ! [X0,X1] :
( leq(n0,sK20(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl41_79 ),
inference(avatar_component_clause,[],[f932]) ).
fof(f1167,plain,
( spl41_132
| ~ spl41_28
| ~ spl41_54 ),
inference(avatar_split_clause,[],[f756,f746,f608,f1164]) ).
fof(f1164,plain,
( spl41_132
<=> init = a_select3(center_init,sK13,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_132])]) ).
fof(f608,plain,
( spl41_28
<=> init = a_select3(center_init,sK13,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_28])]) ).
fof(f756,plain,
( init = a_select3(center_init,sK13,tptp_float_0_0)
| ~ spl41_28
| ~ spl41_54 ),
inference(superposition,[],[f610,f748]) ).
fof(f610,plain,
( init = a_select3(center_init,sK13,n0)
| ~ spl41_28 ),
inference(avatar_component_clause,[],[f608]) ).
fof(f1162,plain,
( spl41_131
| ~ spl41_54
| ~ spl41_76 ),
inference(avatar_split_clause,[],[f922,f919,f746,f1160]) ).
fof(f1160,plain,
( spl41_131
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK19(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_131])]) ).
fof(f919,plain,
( spl41_76
<=> ! [X0,X1] :
( leq(n0,sK19(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_76])]) ).
fof(f922,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK19(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl41_54
| ~ spl41_76 ),
inference(forward_demodulation,[],[f920,f748]) ).
fof(f920,plain,
( ! [X0,X1] :
( leq(n0,sK19(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl41_76 ),
inference(avatar_component_clause,[],[f919]) ).
fof(f1158,plain,
( spl41_130
| ~ spl41_54
| ~ spl41_74 ),
inference(avatar_split_clause,[],[f913,f910,f746,f1156]) ).
fof(f1156,plain,
( spl41_130
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK18(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_130])]) ).
fof(f910,plain,
( spl41_74
<=> ! [X0,X1] :
( leq(n0,sK18(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_74])]) ).
fof(f913,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK18(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl41_54
| ~ spl41_74 ),
inference(forward_demodulation,[],[f911,f748]) ).
fof(f911,plain,
( ! [X0,X1] :
( leq(n0,sK18(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl41_74 ),
inference(avatar_component_clause,[],[f910]) ).
fof(f1154,plain,
( spl41_129
| ~ spl41_54
| ~ spl41_72 ),
inference(avatar_split_clause,[],[f904,f901,f746,f1152]) ).
fof(f1152,plain,
( spl41_129
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK17(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_129])]) ).
fof(f901,plain,
( spl41_72
<=> ! [X0,X1] :
( leq(n0,sK17(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_72])]) ).
fof(f904,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK17(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl41_54
| ~ spl41_72 ),
inference(forward_demodulation,[],[f902,f748]) ).
fof(f902,plain,
( ! [X0,X1] :
( leq(n0,sK17(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl41_72 ),
inference(avatar_component_clause,[],[f901]) ).
fof(f1150,plain,
( spl41_128
| ~ spl41_54
| ~ spl41_70 ),
inference(avatar_split_clause,[],[f895,f892,f746,f1148]) ).
fof(f1148,plain,
( spl41_128
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK16(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_128])]) ).
fof(f892,plain,
( spl41_70
<=> ! [X0,X1] :
( leq(n0,sK16(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_70])]) ).
fof(f895,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK16(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl41_54
| ~ spl41_70 ),
inference(forward_demodulation,[],[f893,f748]) ).
fof(f893,plain,
( ! [X0,X1] :
( leq(n0,sK16(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl41_70 ),
inference(avatar_component_clause,[],[f892]) ).
fof(f1146,plain,
( spl41_127
| ~ spl41_54
| ~ spl41_68 ),
inference(avatar_split_clause,[],[f886,f883,f746,f1144]) ).
fof(f1144,plain,
( spl41_127
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK15(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_127])]) ).
fof(f883,plain,
( spl41_68
<=> ! [X0,X1] :
( leq(n0,sK15(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_68])]) ).
fof(f886,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK15(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl41_54
| ~ spl41_68 ),
inference(forward_demodulation,[],[f884,f748]) ).
fof(f884,plain,
( ! [X0,X1] :
( leq(n0,sK15(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl41_68 ),
inference(avatar_component_clause,[],[f883]) ).
fof(f1142,plain,
( spl41_126
| ~ spl41_54
| ~ spl41_65 ),
inference(avatar_split_clause,[],[f872,f869,f746,f1140]) ).
fof(f1140,plain,
( spl41_126
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK14(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_126])]) ).
fof(f869,plain,
( spl41_65
<=> ! [X0,X1] :
( leq(n0,sK14(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_65])]) ).
fof(f872,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK14(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl41_54
| ~ spl41_65 ),
inference(forward_demodulation,[],[f870,f748]) ).
fof(f870,plain,
( ! [X0,X1] :
( leq(n0,sK14(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl41_65 ),
inference(avatar_component_clause,[],[f869]) ).
fof(f1138,plain,
( spl41_125
| ~ spl41_54
| ~ spl41_64 ),
inference(avatar_split_clause,[],[f867,f864,f746,f1136]) ).
fof(f1136,plain,
( spl41_125
<=> ! [X0,X1] :
( leq(tptp_float_0_0,X1)
| ~ leq(minus(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_125])]) ).
fof(f864,plain,
( spl41_64
<=> ! [X0,X1] :
( leq(n0,X1)
| ~ leq(minus(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_64])]) ).
fof(f867,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,X1)
| ~ leq(minus(X0,X1),X0) )
| ~ spl41_54
| ~ spl41_64 ),
inference(forward_demodulation,[],[f865,f748]) ).
fof(f865,plain,
( ! [X0,X1] :
( leq(n0,X1)
| ~ leq(minus(X0,X1),X0) )
| ~ spl41_64 ),
inference(avatar_component_clause,[],[f864]) ).
fof(f1134,plain,
( spl41_124
| ~ spl41_54
| ~ spl41_63 ),
inference(avatar_split_clause,[],[f862,f859,f746,f1132]) ).
fof(f1132,plain,
( spl41_124
<=> ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(uniform_int_rnd(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_124])]) ).
fof(f859,plain,
( spl41_63
<=> ! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_63])]) ).
fof(f862,plain,
( ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(uniform_int_rnd(X1,X0),X0) )
| ~ spl41_54
| ~ spl41_63 ),
inference(forward_demodulation,[],[f860,f748]) ).
fof(f860,plain,
( ! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) )
| ~ spl41_63 ),
inference(avatar_component_clause,[],[f859]) ).
fof(f1130,plain,
( spl41_123
| ~ spl41_54
| ~ spl41_62 ),
inference(avatar_split_clause,[],[f857,f853,f746,f1128]) ).
fof(f1128,plain,
( spl41_123
<=> ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(tptp_float_0_0,uniform_int_rnd(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_123])]) ).
fof(f853,plain,
( spl41_62
<=> ! [X0,X1] :
( leq(n0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_62])]) ).
fof(f857,plain,
( ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(tptp_float_0_0,uniform_int_rnd(X1,X0)) )
| ~ spl41_54
| ~ spl41_62 ),
inference(forward_demodulation,[],[f856,f748]) ).
fof(f856,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) )
| ~ spl41_54
| ~ spl41_62 ),
inference(forward_demodulation,[],[f854,f748]) ).
fof(f854,plain,
( ! [X0,X1] :
( leq(n0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) )
| ~ spl41_62 ),
inference(avatar_component_clause,[],[f853]) ).
fof(f1126,plain,
spl41_122,
inference(avatar_split_clause,[],[f448,f1124]) ).
fof(f1124,plain,
( spl41_122
<=> ! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,minus(X1,n1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_122])]) ).
fof(f448,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,minus(X1,n1)) ),
inference(definition_unfolding,[],[f354,f310]) ).
fof(f310,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_minus_1) ).
fof(f354,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,pred(X1)) ),
inference(cnf_transformation,[],[f208]) ).
fof(f208,plain,
! [X0,X1] :
( ( leq(X0,pred(X1))
| ~ gt(X1,X0) )
& ( gt(X1,X0)
| ~ leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred) ).
fof(f1122,plain,
spl41_121,
inference(avatar_split_clause,[],[f447,f1120]) ).
fof(f1120,plain,
( spl41_121
<=> ! [X0,X1] :
( leq(X0,minus(X1,n1))
| ~ gt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_121])]) ).
fof(f447,plain,
! [X0,X1] :
( leq(X0,minus(X1,n1))
| ~ gt(X1,X0) ),
inference(definition_unfolding,[],[f355,f310]) ).
fof(f355,plain,
! [X0,X1] :
( leq(X0,pred(X1))
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f1118,plain,
spl41_120,
inference(avatar_split_clause,[],[f446,f1116]) ).
fof(f1116,plain,
( spl41_120
<=> ! [X0,X1] :
( gt(plus(X1,n1),X0)
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_120])]) ).
fof(f446,plain,
! [X0,X1] :
( gt(plus(X1,n1),X0)
| ~ leq(X0,X1) ),
inference(definition_unfolding,[],[f352,f308]) ).
fof(f308,plain,
! [X0] : succ(X0) = plus(X0,n1),
inference(cnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] : succ(X0) = plus(X0,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_1_r) ).
fof(f352,plain,
! [X0,X1] :
( gt(succ(X1),X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0,X1] :
( ( leq(X0,X1)
| ~ gt(succ(X1),X0) )
& ( gt(succ(X1),X0)
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> gt(succ(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
fof(f1114,plain,
spl41_119,
inference(avatar_split_clause,[],[f445,f1112]) ).
fof(f1112,plain,
( spl41_119
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ gt(plus(X1,n1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_119])]) ).
fof(f445,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(plus(X1,n1),X0) ),
inference(definition_unfolding,[],[f353,f308]) ).
fof(f353,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(succ(X1),X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f1110,plain,
( ~ spl41_118
| spl41_40
| ~ spl41_54 ),
inference(avatar_split_clause,[],[f761,f746,f668,f1107]) ).
fof(f1107,plain,
( spl41_118
<=> init = a_select2(rho_init,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_118])]) ).
fof(f668,plain,
( spl41_40
<=> init = a_select2(rho_init,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_40])]) ).
fof(f761,plain,
( init != a_select2(rho_init,tptp_float_0_0)
| spl41_40
| ~ spl41_54 ),
inference(superposition,[],[f669,f748]) ).
fof(f669,plain,
( init != a_select2(rho_init,n0)
| spl41_40 ),
inference(avatar_component_clause,[],[f668]) ).
fof(f1105,plain,
spl41_117,
inference(avatar_split_clause,[],[f444,f1103]) ).
fof(f1103,plain,
( spl41_117
<=> ! [X0,X1] :
( gt(X1,X0)
| ~ leq(plus(X0,n1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_117])]) ).
fof(f444,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(plus(X0,n1),X1) ),
inference(definition_unfolding,[],[f331,f308]) ).
fof(f331,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(succ(X0),X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(succ(X0),X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] :
( leq(succ(X0),X1)
=> gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ_gt) ).
fof(f1101,plain,
spl41_116,
inference(avatar_split_clause,[],[f443,f1099]) ).
fof(f1099,plain,
( spl41_116
<=> ! [X0,X1] :
( leq(X0,plus(X1,n1))
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_116])]) ).
fof(f443,plain,
! [X0,X1] :
( leq(X0,plus(X1,n1))
| ~ leq(X0,X1) ),
inference(definition_unfolding,[],[f327,f308]) ).
fof(f327,plain,
! [X0,X1] :
( leq(X0,succ(X1))
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1] :
( leq(X0,succ(X1))
| ~ leq(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
=> leq(X0,succ(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_succ) ).
fof(f1097,plain,
spl41_115,
inference(avatar_split_clause,[],[f422,f1095]) ).
fof(f1095,plain,
( spl41_115
<=> ! [X0,X1] :
( leq(sK40(X0,X1),X1)
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_115])]) ).
fof(f422,plain,
! [X0,X1] :
( leq(sK40(X0,X1),X1)
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0,X1] :
( ( a_select3(X0,sK39(X0,X1),sK40(X0,X1)) != a_select3(X0,sK40(X0,X1),sK39(X0,X1))
& leq(sK40(X0,X1),X1)
& leq(n0,sK40(X0,X1))
& leq(sK39(X0,X1),X1)
& leq(n0,sK39(X0,X1)) )
| ~ sP10(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39,sK40])],[f253,f254]) ).
fof(f254,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK39(X0,X1),sK40(X0,X1)) != a_select3(X0,sK40(X0,X1),sK39(X0,X1))
& leq(sK40(X0,X1),X1)
& leq(n0,sK40(X0,X1))
& leq(sK39(X0,X1),X1)
& leq(n0,sK39(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f253,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP10(X0,X1) ),
inference(rectify,[],[f252]) ).
fof(f252,plain,
! [X3,X7] :
( ? [X12,X13] :
( a_select3(X3,X12,X13) != a_select3(X3,X13,X12)
& leq(X13,X7)
& leq(n0,X13)
& leq(X12,X7)
& leq(n0,X12) )
| ~ sP10(X3,X7) ),
inference(nnf_transformation,[],[f188]) ).
fof(f188,plain,
! [X3,X7] :
( ? [X12,X13] :
( a_select3(X3,X12,X13) != a_select3(X3,X13,X12)
& leq(X13,X7)
& leq(n0,X13)
& leq(X12,X7)
& leq(n0,X12) )
| ~ sP10(X3,X7) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f1092,plain,
spl41_114,
inference(avatar_split_clause,[],[f421,f1090]) ).
fof(f421,plain,
! [X0,X1] :
( leq(n0,sK40(X0,X1))
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f1088,plain,
spl41_113,
inference(avatar_split_clause,[],[f420,f1086]) ).
fof(f1086,plain,
( spl41_113
<=> ! [X0,X1] :
( leq(sK39(X0,X1),X1)
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_113])]) ).
fof(f420,plain,
! [X0,X1] :
( leq(sK39(X0,X1),X1)
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f1083,plain,
spl41_112,
inference(avatar_split_clause,[],[f419,f1081]) ).
fof(f419,plain,
! [X0,X1] :
( leq(n0,sK39(X0,X1))
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f1079,plain,
spl41_111,
inference(avatar_split_clause,[],[f417,f1077]) ).
fof(f1077,plain,
( spl41_111
<=> ! [X0,X1] :
( leq(sK38(X0,X1),X1)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_111])]) ).
fof(f417,plain,
! [X0,X1] :
( leq(sK38(X0,X1),X1)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f251,plain,
! [X0,X1] :
( ( a_select3(X0,sK37(X0,X1),sK38(X0,X1)) != a_select3(X0,sK38(X0,X1),sK37(X0,X1))
& leq(sK38(X0,X1),X1)
& leq(n0,sK38(X0,X1))
& leq(sK37(X0,X1),X1)
& leq(n0,sK37(X0,X1)) )
| ~ sP11(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38])],[f249,f250]) ).
fof(f250,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK37(X0,X1),sK38(X0,X1)) != a_select3(X0,sK38(X0,X1),sK37(X0,X1))
& leq(sK38(X0,X1),X1)
& leq(n0,sK38(X0,X1))
& leq(sK37(X0,X1),X1)
& leq(n0,sK37(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f249,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP11(X0,X1) ),
inference(rectify,[],[f248]) ).
fof(f248,plain,
! [X0,X6] :
( ? [X10,X11] :
( a_select3(X0,X10,X11) != a_select3(X0,X11,X10)
& leq(X11,X6)
& leq(n0,X11)
& leq(X10,X6)
& leq(n0,X10) )
| ~ sP11(X0,X6) ),
inference(nnf_transformation,[],[f189]) ).
fof(f189,plain,
! [X0,X6] :
( ? [X10,X11] :
( a_select3(X0,X10,X11) != a_select3(X0,X11,X10)
& leq(X11,X6)
& leq(n0,X11)
& leq(X10,X6)
& leq(n0,X10) )
| ~ sP11(X0,X6) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f1074,plain,
spl41_110,
inference(avatar_split_clause,[],[f416,f1072]) ).
fof(f416,plain,
! [X0,X1] :
( leq(n0,sK38(X0,X1))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f1070,plain,
spl41_109,
inference(avatar_split_clause,[],[f415,f1068]) ).
fof(f1068,plain,
( spl41_109
<=> ! [X0,X1] :
( leq(sK37(X0,X1),X1)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_109])]) ).
fof(f415,plain,
! [X0,X1] :
( leq(sK37(X0,X1),X1)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f1065,plain,
spl41_108,
inference(avatar_split_clause,[],[f414,f1063]) ).
fof(f414,plain,
! [X0,X1] :
( leq(n0,sK37(X0,X1))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f1061,plain,
spl41_107,
inference(avatar_split_clause,[],[f412,f1059]) ).
fof(f1059,plain,
( spl41_107
<=> ! [X0,X1] :
( leq(sK36(X0,X1),X1)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_107])]) ).
fof(f412,plain,
! [X0,X1] :
( leq(sK36(X0,X1),X1)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f247,plain,
! [X0,X1] :
( ( a_select3(X0,sK35(X0,X1),sK36(X0,X1)) != a_select3(X0,sK36(X0,X1),sK35(X0,X1))
& leq(sK36(X0,X1),X1)
& leq(n0,sK36(X0,X1))
& leq(sK35(X0,X1),X1)
& leq(n0,sK35(X0,X1)) )
| ~ sP12(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36])],[f245,f246]) ).
fof(f246,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK35(X0,X1),sK36(X0,X1)) != a_select3(X0,sK36(X0,X1),sK35(X0,X1))
& leq(sK36(X0,X1),X1)
& leq(n0,sK36(X0,X1))
& leq(sK35(X0,X1),X1)
& leq(n0,sK35(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f245,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP12(X0,X1) ),
inference(rectify,[],[f244]) ).
fof(f244,plain,
! [X5,X6] :
( ? [X8,X9] :
( a_select3(X5,X8,X9) != a_select3(X5,X9,X8)
& leq(X9,X6)
& leq(n0,X9)
& leq(X8,X6)
& leq(n0,X8) )
| ~ sP12(X5,X6) ),
inference(nnf_transformation,[],[f190]) ).
fof(f190,plain,
! [X5,X6] :
( ? [X8,X9] :
( a_select3(X5,X8,X9) != a_select3(X5,X9,X8)
& leq(X9,X6)
& leq(n0,X9)
& leq(X8,X6)
& leq(n0,X8) )
| ~ sP12(X5,X6) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f1056,plain,
spl41_106,
inference(avatar_split_clause,[],[f411,f1054]) ).
fof(f411,plain,
! [X0,X1] :
( leq(n0,sK36(X0,X1))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f1052,plain,
spl41_105,
inference(avatar_split_clause,[],[f410,f1050]) ).
fof(f1050,plain,
( spl41_105
<=> ! [X0,X1] :
( leq(sK35(X0,X1),X1)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_105])]) ).
fof(f410,plain,
! [X0,X1] :
( leq(sK35(X0,X1),X1)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f1047,plain,
spl41_104,
inference(avatar_split_clause,[],[f409,f1045]) ).
fof(f409,plain,
! [X0,X1] :
( leq(n0,sK35(X0,X1))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f1043,plain,
spl41_103,
inference(avatar_split_clause,[],[f397,f1041]) ).
fof(f1041,plain,
( spl41_103
<=> ! [X0,X1] :
( leq(sK32(X0,X1),X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_103])]) ).
fof(f397,plain,
! [X0,X1] :
( leq(sK32(X0,X1),X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f238,plain,
! [X0,X1] :
( ( a_select3(X0,sK31(X0,X1),sK32(X0,X1)) != a_select3(X0,sK32(X0,X1),sK31(X0,X1))
& leq(sK32(X0,X1),X1)
& leq(n0,sK32(X0,X1))
& leq(sK31(X0,X1),X1)
& leq(n0,sK31(X0,X1)) )
| ~ sP8(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32])],[f236,f237]) ).
fof(f237,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK31(X0,X1),sK32(X0,X1)) != a_select3(X0,sK32(X0,X1),sK31(X0,X1))
& leq(sK32(X0,X1),X1)
& leq(n0,sK32(X0,X1))
& leq(sK31(X0,X1),X1)
& leq(n0,sK31(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f236,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP8(X0,X1) ),
inference(rectify,[],[f235]) ).
fof(f235,plain,
! [X1,X3] :
( ? [X4,X5] :
( a_select3(X1,X4,X5) != a_select3(X1,X5,X4)
& leq(X5,X3)
& leq(n0,X5)
& leq(X4,X3)
& leq(n0,X4) )
| ~ sP8(X1,X3) ),
inference(nnf_transformation,[],[f184]) ).
fof(f184,plain,
! [X1,X3] :
( ? [X4,X5] :
( a_select3(X1,X4,X5) != a_select3(X1,X5,X4)
& leq(X5,X3)
& leq(n0,X5)
& leq(X4,X3)
& leq(n0,X4) )
| ~ sP8(X1,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f1038,plain,
spl41_102,
inference(avatar_split_clause,[],[f396,f1036]) ).
fof(f396,plain,
! [X0,X1] :
( leq(n0,sK32(X0,X1))
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f1034,plain,
spl41_101,
inference(avatar_split_clause,[],[f395,f1032]) ).
fof(f1032,plain,
( spl41_101
<=> ! [X0,X1] :
( leq(sK31(X0,X1),X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_101])]) ).
fof(f395,plain,
! [X0,X1] :
( leq(sK31(X0,X1),X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f1029,plain,
spl41_100,
inference(avatar_split_clause,[],[f394,f1027]) ).
fof(f394,plain,
! [X0,X1] :
( leq(n0,sK31(X0,X1))
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f1025,plain,
spl41_99,
inference(avatar_split_clause,[],[f386,f1023]) ).
fof(f1023,plain,
( spl41_99
<=> ! [X0,X1] :
( leq(sK29(X0,X1),X1)
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_99])]) ).
fof(f386,plain,
! [X0,X1] :
( leq(sK29(X0,X1),X1)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0,X1] :
( ( a_select3(X0,sK28(X0,X1),sK29(X0,X1)) != a_select3(X0,sK29(X0,X1),sK28(X0,X1))
& leq(sK29(X0,X1),X1)
& leq(n0,sK29(X0,X1))
& leq(sK28(X0,X1),X1)
& leq(n0,sK28(X0,X1)) )
| ~ sP7(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f229,f230]) ).
fof(f230,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK28(X0,X1),sK29(X0,X1)) != a_select3(X0,sK29(X0,X1),sK28(X0,X1))
& leq(sK29(X0,X1),X1)
& leq(n0,sK29(X0,X1))
& leq(sK28(X0,X1),X1)
& leq(n0,sK28(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f229,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP7(X0,X1) ),
inference(rectify,[],[f228]) ).
fof(f228,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP7(X1,X2) ),
inference(nnf_transformation,[],[f182]) ).
fof(f182,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP7(X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f1020,plain,
spl41_98,
inference(avatar_split_clause,[],[f385,f1018]) ).
fof(f385,plain,
! [X0,X1] :
( leq(n0,sK29(X0,X1))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f1016,plain,
( ~ spl41_97
| spl41_41
| ~ spl41_54 ),
inference(avatar_split_clause,[],[f762,f746,f672,f1013]) ).
fof(f1013,plain,
( spl41_97
<=> leq(tptp_float_0_0,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_97])]) ).
fof(f672,plain,
( spl41_41
<=> leq(n0,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_41])]) ).
fof(f762,plain,
( ~ leq(tptp_float_0_0,n4)
| spl41_41
| ~ spl41_54 ),
inference(superposition,[],[f674,f748]) ).
fof(f674,plain,
( ~ leq(n0,n4)
| spl41_41 ),
inference(avatar_component_clause,[],[f672]) ).
fof(f1011,plain,
spl41_96,
inference(avatar_split_clause,[],[f384,f1009]) ).
fof(f1009,plain,
( spl41_96
<=> ! [X0,X1] :
( leq(sK28(X0,X1),X1)
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_96])]) ).
fof(f384,plain,
! [X0,X1] :
( leq(sK28(X0,X1),X1)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f1006,plain,
spl41_95,
inference(avatar_split_clause,[],[f383,f1004]) ).
fof(f383,plain,
! [X0,X1] :
( leq(n0,sK28(X0,X1))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f1002,plain,
spl41_94,
inference(avatar_split_clause,[],[f380,f1000]) ).
fof(f1000,plain,
( spl41_94
<=> ! [X0,X1] :
( leq(sK27(X0,X1),X1)
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_94])]) ).
fof(f380,plain,
! [X0,X1] :
( leq(sK27(X0,X1),X1)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
fof(f226,plain,
! [X0,X1] :
( ( a_select3(X0,sK26(X0,X1),sK27(X0,X1)) != a_select3(X0,sK27(X0,X1),sK26(X0,X1))
& leq(sK27(X0,X1),X1)
& leq(n0,sK27(X0,X1))
& leq(sK26(X0,X1),X1)
& leq(n0,sK26(X0,X1)) )
| ~ sP5(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f224,f225]) ).
fof(f225,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK26(X0,X1),sK27(X0,X1)) != a_select3(X0,sK27(X0,X1),sK26(X0,X1))
& leq(sK27(X0,X1),X1)
& leq(n0,sK27(X0,X1))
& leq(sK26(X0,X1),X1)
& leq(n0,sK26(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f224,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP5(X0,X1) ),
inference(rectify,[],[f223]) ).
fof(f223,plain,
! [X0,X2] :
( ? [X5,X6] :
( a_select3(X0,X5,X6) != a_select3(X0,X6,X5)
& leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) )
| ~ sP5(X0,X2) ),
inference(nnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0,X2] :
( ? [X5,X6] :
( a_select3(X0,X5,X6) != a_select3(X0,X6,X5)
& leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) )
| ~ sP5(X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f997,plain,
spl41_93,
inference(avatar_split_clause,[],[f379,f995]) ).
fof(f379,plain,
! [X0,X1] :
( leq(n0,sK27(X0,X1))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
fof(f993,plain,
spl41_92,
inference(avatar_split_clause,[],[f378,f991]) ).
fof(f991,plain,
( spl41_92
<=> ! [X0,X1] :
( leq(sK26(X0,X1),X1)
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_92])]) ).
fof(f378,plain,
! [X0,X1] :
( leq(sK26(X0,X1),X1)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
fof(f988,plain,
spl41_91,
inference(avatar_split_clause,[],[f377,f986]) ).
fof(f377,plain,
! [X0,X1] :
( leq(n0,sK26(X0,X1))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
fof(f984,plain,
spl41_90,
inference(avatar_split_clause,[],[f375,f982]) ).
fof(f982,plain,
( spl41_90
<=> ! [X0,X1] :
( leq(sK25(X0,X1),X1)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_90])]) ).
fof(f375,plain,
! [X0,X1] :
( leq(sK25(X0,X1),X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f222,plain,
! [X0,X1] :
( ( a_select3(X0,sK24(X0,X1),sK25(X0,X1)) != a_select3(X0,sK25(X0,X1),sK24(X0,X1))
& leq(sK25(X0,X1),X1)
& leq(n0,sK25(X0,X1))
& leq(sK24(X0,X1),X1)
& leq(n0,sK24(X0,X1)) )
| ~ sP6(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f220,f221]) ).
fof(f221,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK24(X0,X1),sK25(X0,X1)) != a_select3(X0,sK25(X0,X1),sK24(X0,X1))
& leq(sK25(X0,X1),X1)
& leq(n0,sK25(X0,X1))
& leq(sK24(X0,X1),X1)
& leq(n0,sK24(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f220,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f219]) ).
fof(f219,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP6(X1,X2) ),
inference(nnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP6(X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f979,plain,
spl41_89,
inference(avatar_split_clause,[],[f374,f977]) ).
fof(f374,plain,
! [X0,X1] :
( leq(n0,sK25(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f975,plain,
spl41_88,
inference(avatar_split_clause,[],[f373,f973]) ).
fof(f973,plain,
( spl41_88
<=> ! [X0,X1] :
( leq(sK24(X0,X1),X1)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_88])]) ).
fof(f373,plain,
! [X0,X1] :
( leq(sK24(X0,X1),X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f970,plain,
spl41_87,
inference(avatar_split_clause,[],[f372,f968]) ).
fof(f372,plain,
! [X0,X1] :
( leq(n0,sK24(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f966,plain,
spl41_86,
inference(avatar_split_clause,[],[f369,f964]) ).
fof(f964,plain,
( spl41_86
<=> ! [X0,X1] :
( leq(sK23(X0,X1),X1)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_86])]) ).
fof(f369,plain,
! [X0,X1] :
( leq(sK23(X0,X1),X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0,X1] :
( ( a_select3(X0,sK22(X0,X1),sK23(X0,X1)) != a_select3(X0,sK23(X0,X1),sK22(X0,X1))
& leq(sK23(X0,X1),X1)
& leq(n0,sK23(X0,X1))
& leq(sK22(X0,X1),X1)
& leq(n0,sK22(X0,X1)) )
| ~ sP3(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f215,f216]) ).
fof(f216,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK22(X0,X1),sK23(X0,X1)) != a_select3(X0,sK23(X0,X1),sK22(X0,X1))
& leq(sK23(X0,X1),X1)
& leq(n0,sK23(X0,X1))
& leq(sK22(X0,X1),X1)
& leq(n0,sK22(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f215,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f214]) ).
fof(f214,plain,
! [X0,X2] :
( ? [X5,X6] :
( a_select3(X0,X5,X6) != a_select3(X0,X6,X5)
& leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) )
| ~ sP3(X0,X2) ),
inference(nnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0,X2] :
( ? [X5,X6] :
( a_select3(X0,X5,X6) != a_select3(X0,X6,X5)
& leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) )
| ~ sP3(X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f961,plain,
spl41_85,
inference(avatar_split_clause,[],[f368,f959]) ).
fof(f368,plain,
! [X0,X1] :
( leq(n0,sK23(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f957,plain,
spl41_84,
inference(avatar_split_clause,[],[f367,f955]) ).
fof(f955,plain,
( spl41_84
<=> ! [X0,X1] :
( leq(sK22(X0,X1),X1)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_84])]) ).
fof(f367,plain,
! [X0,X1] :
( leq(sK22(X0,X1),X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f952,plain,
spl41_83,
inference(avatar_split_clause,[],[f366,f950]) ).
fof(f366,plain,
! [X0,X1] :
( leq(n0,sK22(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f948,plain,
spl41_82,
inference(avatar_split_clause,[],[f364,f946]) ).
fof(f946,plain,
( spl41_82
<=> ! [X0,X1] :
( leq(sK21(X0,X1),X1)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_82])]) ).
fof(f364,plain,
! [X0,X1] :
( leq(sK21(X0,X1),X1)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0,X1] :
( ( a_select3(X0,sK20(X0,X1),sK21(X0,X1)) != a_select3(X0,sK21(X0,X1),sK20(X0,X1))
& leq(sK21(X0,X1),X1)
& leq(n0,sK21(X0,X1))
& leq(sK20(X0,X1),X1)
& leq(n0,sK20(X0,X1)) )
| ~ sP4(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f211,f212]) ).
fof(f212,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK20(X0,X1),sK21(X0,X1)) != a_select3(X0,sK21(X0,X1),sK20(X0,X1))
& leq(sK21(X0,X1),X1)
& leq(n0,sK21(X0,X1))
& leq(sK20(X0,X1),X1)
& leq(n0,sK20(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f211,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP4(X0,X1) ),
inference(rectify,[],[f210]) ).
fof(f210,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP4(X1,X2) ),
inference(nnf_transformation,[],[f177]) ).
fof(f177,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP4(X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f943,plain,
spl41_81,
inference(avatar_split_clause,[],[f363,f941]) ).
fof(f363,plain,
! [X0,X1] :
( leq(n0,sK21(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f939,plain,
spl41_80,
inference(avatar_split_clause,[],[f362,f937]) ).
fof(f937,plain,
( spl41_80
<=> ! [X0,X1] :
( leq(sK20(X0,X1),X1)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_80])]) ).
fof(f362,plain,
! [X0,X1] :
( leq(sK20(X0,X1),X1)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f934,plain,
spl41_79,
inference(avatar_split_clause,[],[f361,f932]) ).
fof(f361,plain,
! [X0,X1] :
( leq(n0,sK20(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f930,plain,
spl41_78,
inference(avatar_split_clause,[],[f358,f928]) ).
fof(f928,plain,
( spl41_78
<=> ! [X2,X0,X1] : a_select2(tptp_update2(X0,X1,X2),X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_78])]) ).
fof(f358,plain,
! [X2,X0,X1] : a_select2(tptp_update2(X0,X1,X2),X1) = X2,
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2] : a_select2(tptp_update2(X0,X1,X2),X1) = X2,
inference(rectify,[],[f48]) ).
fof(f48,axiom,
! [X0,X6,X16] : a_select2(tptp_update2(X0,X6,X16),X6) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sel2_update_1) ).
fof(f926,plain,
spl41_77,
inference(avatar_split_clause,[],[f349,f924]) ).
fof(f924,plain,
( spl41_77
<=> ! [X0,X1] :
( leq(sK19(X0,X1),X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_77])]) ).
fof(f349,plain,
! [X0,X1] :
( leq(sK19(X0,X1),X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f205,plain,
! [X0,X1] :
( ( a_select3(X0,sK18(X0,X1),sK19(X0,X1)) != a_select3(X0,sK19(X0,X1),sK18(X0,X1))
& leq(sK19(X0,X1),X1)
& leq(n0,sK19(X0,X1))
& leq(sK18(X0,X1),X1)
& leq(n0,sK18(X0,X1)) )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f203,f204]) ).
fof(f204,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK18(X0,X1),sK19(X0,X1)) != a_select3(X0,sK19(X0,X1),sK18(X0,X1))
& leq(sK19(X0,X1),X1)
& leq(n0,sK19(X0,X1))
& leq(sK18(X0,X1),X1)
& leq(n0,sK18(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f203,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f174]) ).
fof(f174,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP2(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f921,plain,
spl41_76,
inference(avatar_split_clause,[],[f348,f919]) ).
fof(f348,plain,
! [X0,X1] :
( leq(n0,sK19(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f917,plain,
spl41_75,
inference(avatar_split_clause,[],[f347,f915]) ).
fof(f915,plain,
( spl41_75
<=> ! [X0,X1] :
( leq(sK18(X0,X1),X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_75])]) ).
fof(f347,plain,
! [X0,X1] :
( leq(sK18(X0,X1),X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f912,plain,
spl41_74,
inference(avatar_split_clause,[],[f346,f910]) ).
fof(f346,plain,
! [X0,X1] :
( leq(n0,sK18(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f908,plain,
spl41_73,
inference(avatar_split_clause,[],[f343,f906]) ).
fof(f906,plain,
( spl41_73
<=> ! [X0,X1] :
( leq(sK17(X0,X1),X1)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_73])]) ).
fof(f343,plain,
! [X0,X1] :
( leq(sK17(X0,X1),X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0,X1] :
( ( a_select3(X0,sK16(X0,X1),sK17(X0,X1)) != a_select3(X0,sK17(X0,X1),sK16(X0,X1))
& leq(sK17(X0,X1),X1)
& leq(n0,sK17(X0,X1))
& leq(sK16(X0,X1),X1)
& leq(n0,sK16(X0,X1)) )
| ~ sP1(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f199,f200]) ).
fof(f200,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK16(X0,X1),sK17(X0,X1)) != a_select3(X0,sK17(X0,X1),sK16(X0,X1))
& leq(sK17(X0,X1),X1)
& leq(n0,sK17(X0,X1))
& leq(sK16(X0,X1),X1)
& leq(n0,sK16(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f199,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP1(X0,X1) ),
inference(nnf_transformation,[],[f172]) ).
fof(f172,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP1(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f903,plain,
spl41_72,
inference(avatar_split_clause,[],[f342,f901]) ).
fof(f342,plain,
! [X0,X1] :
( leq(n0,sK17(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
fof(f899,plain,
spl41_71,
inference(avatar_split_clause,[],[f341,f897]) ).
fof(f897,plain,
( spl41_71
<=> ! [X0,X1] :
( leq(sK16(X0,X1),X1)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_71])]) ).
fof(f341,plain,
! [X0,X1] :
( leq(sK16(X0,X1),X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
fof(f894,plain,
spl41_70,
inference(avatar_split_clause,[],[f340,f892]) ).
fof(f340,plain,
! [X0,X1] :
( leq(n0,sK16(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
fof(f890,plain,
spl41_69,
inference(avatar_split_clause,[],[f337,f888]) ).
fof(f888,plain,
( spl41_69
<=> ! [X0,X1] :
( leq(sK15(X0,X1),X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_69])]) ).
fof(f337,plain,
! [X0,X1] :
( leq(sK15(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f197,plain,
! [X0,X1] :
( ( a_select3(X0,sK14(X0,X1),sK15(X0,X1)) != a_select3(X0,sK15(X0,X1),sK14(X0,X1))
& leq(sK15(X0,X1),X1)
& leq(n0,sK15(X0,X1))
& leq(sK14(X0,X1),X1)
& leq(n0,sK14(X0,X1)) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f195,f196]) ).
fof(f196,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK14(X0,X1),sK15(X0,X1)) != a_select3(X0,sK15(X0,X1),sK14(X0,X1))
& leq(sK15(X0,X1),X1)
& leq(n0,sK15(X0,X1))
& leq(sK14(X0,X1),X1)
& leq(n0,sK14(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f195,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP0(X0,X1) ),
inference(nnf_transformation,[],[f170]) ).
fof(f170,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP0(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f885,plain,
spl41_68,
inference(avatar_split_clause,[],[f336,f883]) ).
fof(f336,plain,
! [X0,X1] :
( leq(n0,sK15(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f881,plain,
spl41_67,
inference(avatar_split_clause,[],[f335,f879]) ).
fof(f879,plain,
( spl41_67
<=> ! [X0,X1] :
( leq(sK14(X0,X1),X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_67])]) ).
fof(f335,plain,
! [X0,X1] :
( leq(sK14(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f877,plain,
( spl41_66
| ~ spl41_1
| ~ spl41_56 ),
inference(avatar_split_clause,[],[f803,f774,f473,f874]) ).
fof(f874,plain,
( spl41_66
<=> leq(n1,loopcounter) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_66])]) ).
fof(f473,plain,
( spl41_1
<=> gt(loopcounter,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_1])]) ).
fof(f774,plain,
( spl41_56
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_56])]) ).
fof(f803,plain,
( leq(n1,loopcounter)
| ~ spl41_1
| ~ spl41_56 ),
inference(resolution,[],[f775,f475]) ).
fof(f475,plain,
( gt(loopcounter,n1)
| ~ spl41_1 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f775,plain,
( ! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,X1) )
| ~ spl41_56 ),
inference(avatar_component_clause,[],[f774]) ).
fof(f871,plain,
spl41_65,
inference(avatar_split_clause,[],[f334,f869]) ).
fof(f334,plain,
! [X0,X1] :
( leq(n0,sK14(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f866,plain,
spl41_64,
inference(avatar_split_clause,[],[f332,f864]) ).
fof(f332,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ leq(minus(X0,X1),X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ leq(minus(X0,X1),X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
( leq(minus(X0,X1),X0)
=> leq(n0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_minus) ).
fof(f861,plain,
spl41_63,
inference(avatar_split_clause,[],[f329,f859]) ).
fof(f329,plain,
! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( leq(n0,X0)
=> leq(uniform_int_rnd(X1,X0),X0) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X3] :
( leq(n0,X0)
=> leq(uniform_int_rnd(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniform_int_rand_ranges_hi) ).
fof(f855,plain,
spl41_62,
inference(avatar_split_clause,[],[f328,f853]) ).
fof(f328,plain,
! [X0,X1] :
( leq(n0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0,X1] :
( leq(n0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( leq(n0,X0)
=> leq(n0,uniform_int_rnd(X1,X0)) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X0,X3] :
( leq(n0,X0)
=> leq(n0,uniform_int_rnd(X3,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniform_int_rand_ranges_lo) ).
fof(f834,plain,
spl41_61,
inference(avatar_split_clause,[],[f434,f832]) ).
fof(f832,plain,
( spl41_61
<=> ! [X0] : plus(X0,n1) = plus(n1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_61])]) ).
fof(f434,plain,
! [X0] : plus(X0,n1) = plus(n1,X0),
inference(definition_unfolding,[],[f309,f308]) ).
fof(f309,plain,
! [X0] : succ(X0) = plus(n1,X0),
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] : succ(X0) = plus(n1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_plus_1_l) ).
fof(f830,plain,
spl41_60,
inference(avatar_split_clause,[],[f433,f828]) ).
fof(f828,plain,
( spl41_60
<=> ! [X0] : plus(minus(X0,n1),n1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_60])]) ).
fof(f433,plain,
! [X0] : plus(minus(X0,n1),n1) = X0,
inference(definition_unfolding,[],[f306,f308,f310]) ).
fof(f306,plain,
! [X0] : succ(pred(X0)) = X0,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] : succ(pred(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_pred) ).
fof(f826,plain,
spl41_59,
inference(avatar_split_clause,[],[f432,f824]) ).
fof(f824,plain,
( spl41_59
<=> ! [X0] : minus(plus(X0,n1),n1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_59])]) ).
fof(f432,plain,
! [X0] : minus(plus(X0,n1),n1) = X0,
inference(definition_unfolding,[],[f305,f310,f308]) ).
fof(f305,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] : pred(succ(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_succ) ).
fof(f822,plain,
( spl41_58
| ~ spl41_2
| ~ spl41_54 ),
inference(avatar_split_clause,[],[f750,f746,f478,f819]) ).
fof(f819,plain,
( spl41_58
<=> leq(tptp_float_0_0,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_58])]) ).
fof(f750,plain,
( leq(tptp_float_0_0,sK13)
| ~ spl41_2
| ~ spl41_54 ),
inference(superposition,[],[f480,f748]) ).
fof(f780,plain,
( spl41_57
| ~ spl41_54
| ~ spl41_55 ),
inference(avatar_split_clause,[],[f772,f769,f746,f778]) ).
fof(f778,plain,
( spl41_57
<=> ! [X0] : tptp_float_0_0 = sum(tptp_float_0_0,tptp_minus_1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_57])]) ).
fof(f769,plain,
( spl41_55
<=> ! [X0] : tptp_float_0_0 = sum(n0,tptp_minus_1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_55])]) ).
fof(f772,plain,
( ! [X0] : tptp_float_0_0 = sum(tptp_float_0_0,tptp_minus_1,X0)
| ~ spl41_54
| ~ spl41_55 ),
inference(forward_demodulation,[],[f770,f748]) ).
fof(f770,plain,
( ! [X0] : tptp_float_0_0 = sum(n0,tptp_minus_1,X0)
| ~ spl41_55 ),
inference(avatar_component_clause,[],[f769]) ).
fof(f776,plain,
spl41_56,
inference(avatar_split_clause,[],[f330,f774]) ).
fof(f330,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( gt(X1,X0)
=> leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt1) ).
fof(f771,plain,
spl41_55,
inference(avatar_split_clause,[],[f311,f769]) ).
fof(f311,plain,
! [X0] : tptp_float_0_0 = sum(n0,tptp_minus_1,X0),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0] : tptp_float_0_0 = sum(n0,tptp_minus_1,X0),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X22] : sum(n0,tptp_minus_1,X22) = tptp_float_0_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_plus_base_float) ).
fof(f749,plain,
( spl41_54
| ~ spl41_53 ),
inference(avatar_split_clause,[],[f744,f741,f746]) ).
fof(f741,plain,
( spl41_53
<=> ! [X0] : n0 = sum(n0,tptp_minus_1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_53])]) ).
fof(f744,plain,
( n0 = tptp_float_0_0
| ~ spl41_53 ),
inference(forward_demodulation,[],[f742,f311]) ).
fof(f742,plain,
( ! [X0] : n0 = sum(n0,tptp_minus_1,X0)
| ~ spl41_53 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f743,plain,
spl41_53,
inference(avatar_split_clause,[],[f307,f741]) ).
fof(f307,plain,
! [X0] : n0 = sum(n0,tptp_minus_1,X0),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0] : n0 = sum(n0,tptp_minus_1,X0),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X22] : n0 = sum(n0,tptp_minus_1,X22),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_plus_base) ).
fof(f733,plain,
spl41_52,
inference(avatar_split_clause,[],[f463,f730]) ).
fof(f730,plain,
( spl41_52
<=> n5 = plus(n4,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_52])]) ).
fof(f463,plain,
n5 = plus(n4,n1),
inference(forward_demodulation,[],[f462,f459]) ).
fof(f459,plain,
n4 = plus(n3,n1),
inference(forward_demodulation,[],[f458,f456]) ).
fof(f456,plain,
n3 = plus(n2,n1),
inference(forward_demodulation,[],[f455,f454]) ).
fof(f454,plain,
n2 = plus(n1,n1),
inference(forward_demodulation,[],[f427,f425]) ).
fof(f425,plain,
n1 = plus(n0,n1),
inference(definition_unfolding,[],[f296,f308]) ).
fof(f296,plain,
n1 = succ(n0),
inference(cnf_transformation,[],[f91]) ).
fof(f91,axiom,
n1 = succ(n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
fof(f427,plain,
n2 = plus(plus(n0,n1),n1),
inference(definition_unfolding,[],[f298,f308,f308]) ).
fof(f298,plain,
n2 = succ(succ(n0)),
inference(cnf_transformation,[],[f92]) ).
fof(f92,axiom,
n2 = succ(succ(n0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_2) ).
fof(f455,plain,
n3 = plus(plus(n1,n1),n1),
inference(forward_demodulation,[],[f428,f425]) ).
fof(f428,plain,
n3 = plus(plus(plus(n0,n1),n1),n1),
inference(definition_unfolding,[],[f299,f308,f308,f308]) ).
fof(f299,plain,
n3 = succ(succ(succ(n0))),
inference(cnf_transformation,[],[f93]) ).
fof(f93,axiom,
n3 = succ(succ(succ(n0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_3) ).
fof(f458,plain,
n4 = plus(plus(n2,n1),n1),
inference(forward_demodulation,[],[f457,f454]) ).
fof(f457,plain,
n4 = plus(plus(plus(n1,n1),n1),n1),
inference(forward_demodulation,[],[f429,f425]) ).
fof(f429,plain,
n4 = plus(plus(plus(plus(n0,n1),n1),n1),n1),
inference(definition_unfolding,[],[f300,f308,f308,f308,f308]) ).
fof(f300,plain,
n4 = succ(succ(succ(succ(n0)))),
inference(cnf_transformation,[],[f89]) ).
fof(f89,axiom,
n4 = succ(succ(succ(succ(n0)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_4) ).
fof(f462,plain,
n5 = plus(plus(n3,n1),n1),
inference(forward_demodulation,[],[f461,f456]) ).
fof(f461,plain,
n5 = plus(plus(plus(n2,n1),n1),n1),
inference(forward_demodulation,[],[f460,f454]) ).
fof(f460,plain,
n5 = plus(plus(plus(plus(n1,n1),n1),n1),n1),
inference(forward_demodulation,[],[f430,f425]) ).
fof(f430,plain,
n5 = plus(plus(plus(plus(plus(n0,n1),n1),n1),n1),n1),
inference(definition_unfolding,[],[f301,f308,f308,f308,f308,f308]) ).
fof(f301,plain,
n5 = succ(succ(succ(succ(succ(n0))))),
inference(cnf_transformation,[],[f90]) ).
fof(f90,axiom,
n5 = succ(succ(succ(succ(succ(n0))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_5) ).
fof(f728,plain,
spl41_51,
inference(avatar_split_clause,[],[f459,f725]) ).
fof(f725,plain,
( spl41_51
<=> n4 = plus(n3,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_51])]) ).
fof(f723,plain,
spl41_50,
inference(avatar_split_clause,[],[f456,f720]) ).
fof(f720,plain,
( spl41_50
<=> n3 = plus(n2,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_50])]) ).
fof(f718,plain,
spl41_49,
inference(avatar_split_clause,[],[f454,f715]) ).
fof(f715,plain,
( spl41_49
<=> n2 = plus(n1,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_49])]) ).
fof(f713,plain,
spl41_48,
inference(avatar_split_clause,[],[f431,f711]) ).
fof(f711,plain,
( spl41_48
<=> ! [X0] : gt(plus(X0,n1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_48])]) ).
fof(f431,plain,
! [X0] : gt(plus(X0,n1),X0),
inference(definition_unfolding,[],[f304,f308]) ).
fof(f304,plain,
! [X0] : gt(succ(X0),X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : gt(succ(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_succ) ).
fof(f709,plain,
spl41_47,
inference(avatar_split_clause,[],[f426,f706]) ).
fof(f706,plain,
( spl41_47
<=> n0 = plus(tptp_minus_1,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_47])]) ).
fof(f426,plain,
n0 = plus(tptp_minus_1,n1),
inference(definition_unfolding,[],[f297,f308]) ).
fof(f297,plain,
n0 = succ(tptp_minus_1),
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
n0 = succ(tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
fof(f704,plain,
spl41_46,
inference(avatar_split_clause,[],[f425,f701]) ).
fof(f701,plain,
( spl41_46
<=> n1 = plus(n0,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_46])]) ).
fof(f697,plain,
spl41_45,
inference(avatar_split_clause,[],[f258,f695]) ).
fof(f695,plain,
( spl41_45
<=> ! [X6,X7] :
( init = a_select3(q_init,X6,X7)
| ~ leq(X7,n4)
| ~ leq(n0,X7)
| ~ leq(X6,n135299)
| ~ leq(n0,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_45])]) ).
fof(f258,plain,
! [X6,X7] :
( init = a_select3(q_init,X6,X7)
| ~ leq(X7,n4)
| ~ leq(n0,X7)
| ~ leq(X6,n135299)
| ~ leq(n0,X6) ),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
( init != a_select2(sigmaold_init,sK13)
& leq(sK13,n4)
& leq(n0,sK13)
& ( ! [X1] :
( init = a_select2(sigmaold_init,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X1) )
| ~ gt(loopcounter,n1) )
& ( ! [X2] :
( init = a_select2(rhoold_init,X2)
| ~ leq(X2,n4)
| ~ leq(n0,X2) )
| ~ gt(loopcounter,n1) )
& ( ! [X3] :
( init = a_select2(muold_init,X3)
| ~ leq(X3,n4)
| ~ leq(n0,X3) )
| ~ gt(loopcounter,n1) )
& ! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(X4,n4)
| ~ leq(n0,X4) )
& ! [X5] :
( init = a_select2(rho_init,X5)
| ~ leq(X5,n4)
| ~ leq(n0,X5) )
& ! [X6] :
( ! [X7] :
( init = a_select3(q_init,X6,X7)
| ~ leq(X7,n4)
| ~ leq(n0,X7) )
| ~ leq(X6,n135299)
| ~ leq(n0,X6) )
& gt(loopcounter,n1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f192,f193]) ).
fof(f193,plain,
( ? [X0] :
( init != a_select2(sigmaold_init,X0)
& leq(X0,n4)
& leq(n0,X0) )
=> ( init != a_select2(sigmaold_init,sK13)
& leq(sK13,n4)
& leq(n0,sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f192,plain,
( ? [X0] :
( init != a_select2(sigmaold_init,X0)
& leq(X0,n4)
& leq(n0,X0) )
& ( ! [X1] :
( init = a_select2(sigmaold_init,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X1) )
| ~ gt(loopcounter,n1) )
& ( ! [X2] :
( init = a_select2(rhoold_init,X2)
| ~ leq(X2,n4)
| ~ leq(n0,X2) )
| ~ gt(loopcounter,n1) )
& ( ! [X3] :
( init = a_select2(muold_init,X3)
| ~ leq(X3,n4)
| ~ leq(n0,X3) )
| ~ gt(loopcounter,n1) )
& ! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(X4,n4)
| ~ leq(n0,X4) )
& ! [X5] :
( init = a_select2(rho_init,X5)
| ~ leq(X5,n4)
| ~ leq(n0,X5) )
& ! [X6] :
( ! [X7] :
( init = a_select3(q_init,X6,X7)
| ~ leq(X7,n4)
| ~ leq(n0,X7) )
| ~ leq(X6,n135299)
| ~ leq(n0,X6) )
& gt(loopcounter,n1) ),
inference(rectify,[],[f117]) ).
fof(f117,plain,
( ? [X7] :
( init != a_select2(sigmaold_init,X7)
& leq(X7,n4)
& leq(n0,X7) )
& ( ! [X0] :
( init = a_select2(sigmaold_init,X0)
| ~ leq(X0,n4)
| ~ leq(n0,X0) )
| ~ gt(loopcounter,n1) )
& ( ! [X1] :
( init = a_select2(rhoold_init,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X1) )
| ~ gt(loopcounter,n1) )
& ( ! [X2] :
( init = a_select2(muold_init,X2)
| ~ leq(X2,n4)
| ~ leq(n0,X2) )
| ~ gt(loopcounter,n1) )
& ! [X3] :
( init = a_select3(center_init,X3,n0)
| ~ leq(X3,n4)
| ~ leq(n0,X3) )
& ! [X4] :
( init = a_select2(rho_init,X4)
| ~ leq(X4,n4)
| ~ leq(n0,X4) )
& ! [X5] :
( ! [X6] :
( init = a_select3(q_init,X5,X6)
| ~ leq(X6,n4)
| ~ leq(n0,X6) )
| ~ leq(X5,n135299)
| ~ leq(n0,X5) )
& gt(loopcounter,n1) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
( ? [X7] :
( init != a_select2(sigmaold_init,X7)
& leq(X7,n4)
& leq(n0,X7) )
& ( ! [X0] :
( init = a_select2(sigmaold_init,X0)
| ~ leq(X0,n4)
| ~ leq(n0,X0) )
| ~ gt(loopcounter,n1) )
& ( ! [X1] :
( init = a_select2(rhoold_init,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X1) )
| ~ gt(loopcounter,n1) )
& ( ! [X2] :
( init = a_select2(muold_init,X2)
| ~ leq(X2,n4)
| ~ leq(n0,X2) )
| ~ gt(loopcounter,n1) )
& ! [X3] :
( init = a_select3(center_init,X3,n0)
| ~ leq(X3,n4)
| ~ leq(n0,X3) )
& ! [X4] :
( init = a_select2(rho_init,X4)
| ~ leq(X4,n4)
| ~ leq(n0,X4) )
& ! [X5] :
( ! [X6] :
( init = a_select3(q_init,X5,X6)
| ~ leq(X6,n4)
| ~ leq(n0,X6) )
| ~ leq(X5,n135299)
| ~ leq(n0,X5) )
& gt(loopcounter,n1) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,plain,
~ ( ( ( gt(loopcounter,n1)
=> ! [X0] :
( ( leq(X0,n4)
& leq(n0,X0) )
=> init = a_select2(sigmaold_init,X0) ) )
& ( gt(loopcounter,n1)
=> ! [X1] :
( ( leq(X1,n4)
& leq(n0,X1) )
=> init = a_select2(rhoold_init,X1) ) )
& ( gt(loopcounter,n1)
=> ! [X2] :
( ( leq(X2,n4)
& leq(n0,X2) )
=> init = a_select2(muold_init,X2) ) )
& ! [X3] :
( ( leq(X3,n4)
& leq(n0,X3) )
=> init = a_select3(center_init,X3,n0) )
& ! [X4] :
( ( leq(X4,n4)
& leq(n0,X4) )
=> init = a_select2(rho_init,X4) )
& ! [X5] :
( ( leq(X5,n135299)
& leq(n0,X5) )
=> ! [X6] :
( ( leq(X6,n4)
& leq(n0,X6) )
=> init = a_select3(q_init,X5,X6) ) )
& gt(loopcounter,n1) )
=> ! [X7] :
( ( leq(X7,n4)
& leq(n0,X7) )
=> init = a_select2(sigmaold_init,X7) ) ),
inference(rectify,[],[f54]) ).
fof(f54,negated_conjecture,
~ ( ( ( gt(loopcounter,n1)
=> ! [X27] :
( ( leq(X27,n4)
& leq(n0,X27) )
=> init = a_select2(sigmaold_init,X27) ) )
& ( gt(loopcounter,n1)
=> ! [X21] :
( ( leq(X21,n4)
& leq(n0,X21) )
=> init = a_select2(rhoold_init,X21) ) )
& ( gt(loopcounter,n1)
=> ! [X20] :
( ( leq(X20,n4)
& leq(n0,X20) )
=> init = a_select2(muold_init,X20) ) )
& ! [X19] :
( ( leq(X19,n4)
& leq(n0,X19) )
=> init = a_select3(center_init,X19,n0) )
& ! [X3] :
( ( leq(X3,n4)
& leq(n0,X3) )
=> init = a_select2(rho_init,X3) )
& ! [X13] :
( ( leq(X13,n135299)
& leq(n0,X13) )
=> ! [X17] :
( ( leq(X17,n4)
& leq(n0,X17) )
=> a_select3(q_init,X13,X17) = init ) )
& gt(loopcounter,n1) )
=> ! [X28] :
( ( leq(X28,n4)
& leq(n0,X28) )
=> init = a_select2(sigmaold_init,X28) ) ),
inference(negated_conjecture,[],[f53]) ).
fof(f53,conjecture,
( ( ( gt(loopcounter,n1)
=> ! [X27] :
( ( leq(X27,n4)
& leq(n0,X27) )
=> init = a_select2(sigmaold_init,X27) ) )
& ( gt(loopcounter,n1)
=> ! [X21] :
( ( leq(X21,n4)
& leq(n0,X21) )
=> init = a_select2(rhoold_init,X21) ) )
& ( gt(loopcounter,n1)
=> ! [X20] :
( ( leq(X20,n4)
& leq(n0,X20) )
=> init = a_select2(muold_init,X20) ) )
& ! [X19] :
( ( leq(X19,n4)
& leq(n0,X19) )
=> init = a_select3(center_init,X19,n0) )
& ! [X3] :
( ( leq(X3,n4)
& leq(n0,X3) )
=> init = a_select2(rho_init,X3) )
& ! [X13] :
( ( leq(X13,n135299)
& leq(n0,X13) )
=> ! [X17] :
( ( leq(X17,n4)
& leq(n0,X17) )
=> a_select3(q_init,X13,X17) = init ) )
& gt(loopcounter,n1) )
=> ! [X28] :
( ( leq(X28,n4)
& leq(n0,X28) )
=> init = a_select2(sigmaold_init,X28) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_init_0096) ).
fof(f691,plain,
( ~ spl41_1
| spl41_44 ),
inference(avatar_split_clause,[],[f263,f689,f473]) ).
fof(f263,plain,
! [X1] :
( init = a_select2(sigmaold_init,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X1)
| ~ gt(loopcounter,n1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f685,plain,
( ~ spl41_1
| spl41_43 ),
inference(avatar_split_clause,[],[f262,f683,f473]) ).
fof(f262,plain,
! [X2] :
( init = a_select2(rhoold_init,X2)
| ~ leq(X2,n4)
| ~ leq(n0,X2)
| ~ gt(loopcounter,n1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f679,plain,
( ~ spl41_1
| spl41_42 ),
inference(avatar_split_clause,[],[f261,f677,f473]) ).
fof(f261,plain,
! [X3] :
( init = a_select2(muold_init,X3)
| ~ leq(X3,n4)
| ~ leq(n0,X3)
| ~ gt(loopcounter,n1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f675,plain,
( spl41_40
| ~ spl41_41
| ~ spl41_5
| ~ spl41_39 ),
inference(avatar_split_clause,[],[f666,f662,f493,f672,f668]) ).
fof(f493,plain,
( spl41_5
<=> ! [X5] :
( init = a_select2(rho_init,X5)
| ~ leq(X5,n4)
| ~ leq(n0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_5])]) ).
fof(f662,plain,
( spl41_39
<=> ! [X0] : leq(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_39])]) ).
fof(f666,plain,
( ~ leq(n0,n4)
| init = a_select2(rho_init,n0)
| ~ spl41_5
| ~ spl41_39 ),
inference(resolution,[],[f663,f494]) ).
fof(f494,plain,
( ! [X5] :
( ~ leq(n0,X5)
| ~ leq(X5,n4)
| init = a_select2(rho_init,X5) )
| ~ spl41_5 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f663,plain,
( ! [X0] : leq(X0,X0)
| ~ spl41_39 ),
inference(avatar_component_clause,[],[f662]) ).
fof(f664,plain,
spl41_39,
inference(avatar_split_clause,[],[f303,f662]) ).
fof(f303,plain,
! [X0] : leq(X0,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : leq(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_leq) ).
fof(f660,plain,
spl41_38,
inference(avatar_split_clause,[],[f302,f658]) ).
fof(f658,plain,
( spl41_38
<=> ! [X0] : ~ gt(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_38])]) ).
fof(f302,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f656,plain,
spl41_37,
inference(avatar_split_clause,[],[f295,f653]) ).
fof(f653,plain,
( spl41_37
<=> gt(n0,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_37])]) ).
fof(f295,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[],[f61]) ).
fof(f61,axiom,
gt(n0,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
fof(f651,plain,
spl41_36,
inference(avatar_split_clause,[],[f294,f648]) ).
fof(f648,plain,
( spl41_36
<=> gt(n1,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_36])]) ).
fof(f294,plain,
gt(n1,n0),
inference(cnf_transformation,[],[f68]) ).
fof(f68,axiom,
gt(n1,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_0) ).
fof(f646,plain,
spl41_35,
inference(avatar_split_clause,[],[f293,f643]) ).
fof(f643,plain,
( spl41_35
<=> gt(n1,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_35])]) ).
fof(f293,plain,
gt(n1,tptp_minus_1),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
gt(n1,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_tptp_minus_1) ).
fof(f641,plain,
spl41_34,
inference(avatar_split_clause,[],[f292,f638]) ).
fof(f638,plain,
( spl41_34
<=> gt(n4,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_34])]) ).
fof(f292,plain,
gt(n4,n0),
inference(cnf_transformation,[],[f65]) ).
fof(f65,axiom,
gt(n4,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_0) ).
fof(f636,plain,
spl41_33,
inference(avatar_split_clause,[],[f291,f633]) ).
fof(f633,plain,
( spl41_33
<=> gt(n4,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_33])]) ).
fof(f291,plain,
gt(n4,n1),
inference(cnf_transformation,[],[f71]) ).
fof(f71,axiom,
gt(n4,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_1) ).
fof(f631,plain,
spl41_32,
inference(avatar_split_clause,[],[f290,f628]) ).
fof(f628,plain,
( spl41_32
<=> gt(n4,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_32])]) ).
fof(f290,plain,
gt(n4,n2),
inference(cnf_transformation,[],[f76]) ).
fof(f76,axiom,
gt(n4,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_2) ).
fof(f626,plain,
spl41_31,
inference(avatar_split_clause,[],[f289,f623]) ).
fof(f623,plain,
( spl41_31
<=> gt(n4,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_31])]) ).
fof(f289,plain,
gt(n4,n3),
inference(cnf_transformation,[],[f80]) ).
fof(f80,axiom,
gt(n4,n3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_3) ).
fof(f621,plain,
spl41_30,
inference(avatar_split_clause,[],[f288,f618]) ).
fof(f618,plain,
( spl41_30
<=> gt(n4,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_30])]) ).
fof(f288,plain,
gt(n4,tptp_minus_1),
inference(cnf_transformation,[],[f58]) ).
fof(f58,axiom,
gt(n4,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_4_tptp_minus_1) ).
fof(f616,plain,
spl41_29,
inference(avatar_split_clause,[],[f287,f613]) ).
fof(f613,plain,
( spl41_29
<=> gt(n2,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_29])]) ).
fof(f287,plain,
gt(n2,n0),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
gt(n2,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_0) ).
fof(f611,plain,
( spl41_28
| ~ spl41_3
| ~ spl41_2
| ~ spl41_6 ),
inference(avatar_split_clause,[],[f501,f498,f478,f483,f608]) ).
fof(f498,plain,
( spl41_6
<=> ! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(X4,n4)
| ~ leq(n0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_6])]) ).
fof(f501,plain,
( ~ leq(sK13,n4)
| init = a_select3(center_init,sK13,n0)
| ~ spl41_2
| ~ spl41_6 ),
inference(resolution,[],[f499,f480]) ).
fof(f499,plain,
( ! [X4] :
( ~ leq(n0,X4)
| ~ leq(X4,n4)
| init = a_select3(center_init,X4,n0) )
| ~ spl41_6 ),
inference(avatar_component_clause,[],[f498]) ).
fof(f606,plain,
spl41_27,
inference(avatar_split_clause,[],[f286,f603]) ).
fof(f603,plain,
( spl41_27
<=> gt(n2,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_27])]) ).
fof(f286,plain,
gt(n2,n1),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
gt(n2,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_1) ).
fof(f601,plain,
spl41_26,
inference(avatar_split_clause,[],[f285,f598]) ).
fof(f598,plain,
( spl41_26
<=> gt(n2,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_26])]) ).
fof(f285,plain,
gt(n2,tptp_minus_1),
inference(cnf_transformation,[],[f63]) ).
fof(f63,axiom,
gt(n2,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_2_tptp_minus_1) ).
fof(f596,plain,
spl41_25,
inference(avatar_split_clause,[],[f284,f593]) ).
fof(f593,plain,
( spl41_25
<=> gt(n3,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_25])]) ).
fof(f284,plain,
gt(n3,n0),
inference(cnf_transformation,[],[f70]) ).
fof(f70,axiom,
gt(n3,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_0) ).
fof(f591,plain,
spl41_24,
inference(avatar_split_clause,[],[f283,f588]) ).
fof(f588,plain,
( spl41_24
<=> gt(n3,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_24])]) ).
fof(f283,plain,
gt(n3,n1),
inference(cnf_transformation,[],[f75]) ).
fof(f75,axiom,
gt(n3,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_1) ).
fof(f586,plain,
spl41_23,
inference(avatar_split_clause,[],[f282,f583]) ).
fof(f583,plain,
( spl41_23
<=> gt(n3,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_23])]) ).
fof(f282,plain,
gt(n3,n2),
inference(cnf_transformation,[],[f79]) ).
fof(f79,axiom,
gt(n3,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_2) ).
fof(f581,plain,
spl41_22,
inference(avatar_split_clause,[],[f281,f578]) ).
fof(f578,plain,
( spl41_22
<=> gt(n3,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_22])]) ).
fof(f281,plain,
gt(n3,tptp_minus_1),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
gt(n3,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_3_tptp_minus_1) ).
fof(f576,plain,
spl41_21,
inference(avatar_split_clause,[],[f280,f573]) ).
fof(f573,plain,
( spl41_21
<=> gt(n5,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_21])]) ).
fof(f280,plain,
gt(n5,n0),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
gt(n5,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_0) ).
fof(f571,plain,
spl41_20,
inference(avatar_split_clause,[],[f279,f568]) ).
fof(f568,plain,
( spl41_20
<=> gt(n5,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_20])]) ).
fof(f279,plain,
gt(n5,n1),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
gt(n5,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_1) ).
fof(f566,plain,
spl41_19,
inference(avatar_split_clause,[],[f278,f563]) ).
fof(f563,plain,
( spl41_19
<=> gt(n5,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_19])]) ).
fof(f278,plain,
gt(n5,n4),
inference(cnf_transformation,[],[f55]) ).
fof(f55,axiom,
gt(n5,n4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_4) ).
fof(f561,plain,
spl41_18,
inference(avatar_split_clause,[],[f277,f558]) ).
fof(f558,plain,
( spl41_18
<=> gt(n5,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_18])]) ).
fof(f277,plain,
gt(n5,n2),
inference(cnf_transformation,[],[f77]) ).
fof(f77,axiom,
gt(n5,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_2) ).
fof(f556,plain,
spl41_17,
inference(avatar_split_clause,[],[f276,f553]) ).
fof(f553,plain,
( spl41_17
<=> gt(n5,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_17])]) ).
fof(f276,plain,
gt(n5,n3),
inference(cnf_transformation,[],[f81]) ).
fof(f81,axiom,
gt(n5,n3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_3) ).
fof(f551,plain,
spl41_16,
inference(avatar_split_clause,[],[f275,f548]) ).
fof(f548,plain,
( spl41_16
<=> gt(n5,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_16])]) ).
fof(f275,plain,
gt(n5,tptp_minus_1),
inference(cnf_transformation,[],[f59]) ).
fof(f59,axiom,
gt(n5,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_5_tptp_minus_1) ).
fof(f546,plain,
spl41_15,
inference(avatar_split_clause,[],[f274,f543]) ).
fof(f543,plain,
( spl41_15
<=> gt(n135299,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_15])]) ).
fof(f274,plain,
gt(n135299,n0),
inference(cnf_transformation,[],[f67]) ).
fof(f67,axiom,
gt(n135299,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135299_0) ).
fof(f541,plain,
spl41_14,
inference(avatar_split_clause,[],[f273,f538]) ).
fof(f538,plain,
( spl41_14
<=> gt(n135299,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_14])]) ).
fof(f273,plain,
gt(n135299,n1),
inference(cnf_transformation,[],[f73]) ).
fof(f73,axiom,
gt(n135299,n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135299_1) ).
fof(f536,plain,
spl41_13,
inference(avatar_split_clause,[],[f272,f533]) ).
fof(f533,plain,
( spl41_13
<=> gt(n135299,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_13])]) ).
fof(f272,plain,
gt(n135299,n4),
inference(cnf_transformation,[],[f56]) ).
fof(f56,axiom,
gt(n135299,n4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135299_4) ).
fof(f531,plain,
spl41_12,
inference(avatar_split_clause,[],[f271,f528]) ).
fof(f528,plain,
( spl41_12
<=> gt(n135299,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_12])]) ).
fof(f271,plain,
gt(n135299,n2),
inference(cnf_transformation,[],[f78]) ).
fof(f78,axiom,
gt(n135299,n2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135299_2) ).
fof(f526,plain,
spl41_11,
inference(avatar_split_clause,[],[f270,f523]) ).
fof(f523,plain,
( spl41_11
<=> gt(n135299,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_11])]) ).
fof(f270,plain,
gt(n135299,n3),
inference(cnf_transformation,[],[f82]) ).
fof(f82,axiom,
gt(n135299,n3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135299_3) ).
fof(f521,plain,
spl41_10,
inference(avatar_split_clause,[],[f269,f518]) ).
fof(f518,plain,
( spl41_10
<=> gt(n135299,n5) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_10])]) ).
fof(f269,plain,
gt(n135299,n5),
inference(cnf_transformation,[],[f57]) ).
fof(f57,axiom,
gt(n135299,n5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135299_5) ).
fof(f516,plain,
spl41_9,
inference(avatar_split_clause,[],[f268,f513]) ).
fof(f513,plain,
( spl41_9
<=> gt(n135299,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_9])]) ).
fof(f268,plain,
gt(n135299,tptp_minus_1),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
gt(n135299,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_135299_tptp_minus_1) ).
fof(f511,plain,
~ spl41_8,
inference(avatar_split_clause,[],[f267,f508]) ).
fof(f508,plain,
( spl41_8
<=> def = use ),
introduced(avatar_definition,[new_symbols(naming,[spl41_8])]) ).
fof(f267,plain,
def != use,
inference(cnf_transformation,[],[f52]) ).
fof(f52,axiom,
def != use,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',defuse) ).
fof(f506,plain,
( spl41_7
| ~ spl41_3
| ~ spl41_2
| ~ spl41_5 ),
inference(avatar_split_clause,[],[f496,f493,f478,f483,f503]) ).
fof(f503,plain,
( spl41_7
<=> init = a_select2(rho_init,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_7])]) ).
fof(f496,plain,
( ~ leq(sK13,n4)
| init = a_select2(rho_init,sK13)
| ~ spl41_2
| ~ spl41_5 ),
inference(resolution,[],[f494,f480]) ).
fof(f500,plain,
spl41_6,
inference(avatar_split_clause,[],[f260,f498]) ).
fof(f260,plain,
! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(X4,n4)
| ~ leq(n0,X4) ),
inference(cnf_transformation,[],[f194]) ).
fof(f495,plain,
spl41_5,
inference(avatar_split_clause,[],[f259,f493]) ).
fof(f259,plain,
! [X5] :
( init = a_select2(rho_init,X5)
| ~ leq(X5,n4)
| ~ leq(n0,X5) ),
inference(cnf_transformation,[],[f194]) ).
fof(f491,plain,
~ spl41_4,
inference(avatar_split_clause,[],[f266,f488]) ).
fof(f266,plain,
init != a_select2(sigmaold_init,sK13),
inference(cnf_transformation,[],[f194]) ).
fof(f486,plain,
spl41_3,
inference(avatar_split_clause,[],[f265,f483]) ).
fof(f265,plain,
leq(sK13,n4),
inference(cnf_transformation,[],[f194]) ).
fof(f481,plain,
spl41_2,
inference(avatar_split_clause,[],[f264,f478]) ).
fof(f264,plain,
leq(n0,sK13),
inference(cnf_transformation,[],[f194]) ).
fof(f476,plain,
spl41_1,
inference(avatar_split_clause,[],[f257,f473]) ).
fof(f257,plain,
gt(loopcounter,n1),
inference(cnf_transformation,[],[f194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV184+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.10/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n023.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 : Tue Apr 30 05:02:55 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (17684)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (17687)WARNING: value z3 for option sas not known
% 0.13/0.37 % (17686)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37 % (17688)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37 % (17691)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.37 % (17690)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.37 % (17687)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37 % (17689)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.37 % (17685)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.39 % (17689)First to succeed.
% 0.13/0.40 % (17689)Refutation found. Thanks to Tanya!
% 0.13/0.40 % SZS status Theorem for theBenchmark
% 0.13/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.40 % (17689)------------------------------
% 0.13/0.40 % (17689)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.40 % (17689)Termination reason: Refutation
% 0.13/0.40
% 0.13/0.40 % (17689)Memory used [KB]: 1505
% 0.13/0.40 % (17689)Time elapsed: 0.029 s
% 0.13/0.40 % (17689)Instructions burned: 50 (million)
% 0.13/0.40 % (17689)------------------------------
% 0.13/0.40 % (17689)------------------------------
% 0.13/0.40 % (17684)Success in time 0.048 s
%------------------------------------------------------------------------------