TSTP Solution File: SEU303+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU303+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:32:53 EDT 2024
% Result : Theorem 0.21s 0.39s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 232
% Syntax : Number of formulae : 628 ( 216 unt; 0 def)
% Number of atoms : 1467 ( 19 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 1228 ( 389 ~; 323 |; 311 &)
% ( 149 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 168 ( 166 usr; 149 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 24 con; 0-2 aty)
% Number of variables : 336 ( 267 !; 69 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1235,plain,
$false,
inference(avatar_sat_refutation,[],[f321,f326,f331,f336,f341,f346,f351,f356,f361,f366,f371,f376,f381,f386,f391,f396,f401,f406,f411,f416,f421,f426,f431,f436,f441,f446,f451,f456,f461,f466,f471,f476,f481,f486,f491,f496,f501,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,f655,f659,f663,f667,f671,f675,f679,f683,f687,f691,f696,f701,f705,f709,f713,f717,f721,f725,f729,f733,f737,f807,f812,f816,f820,f824,f828,f832,f836,f840,f844,f848,f852,f857,f890,f895,f899,f903,f916,f920,f924,f929,f934,f938,f942,f946,f950,f954,f973,f1006,f1010,f1033,f1038,f1043,f1047,f1051,f1055,f1095,f1100,f1104,f1120,f1125,f1131,f1137,f1142,f1148,f1153,f1159,f1165,f1170,f1176,f1182,f1187,f1193,f1202,f1207,f1212,f1217,f1222,f1227,f1233,f1234]) ).
fof(f1234,plain,
( ~ spl27_1
| ~ spl27_2
| ~ spl27_3
| spl27_4
| ~ spl27_125
| ~ spl27_126 ),
inference(avatar_split_clause,[],[f1115,f1097,f1093,f333,f328,f323,f318]) ).
fof(f318,plain,
( spl27_1
<=> relation(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_1])]) ).
fof(f323,plain,
( spl27_2
<=> function(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_2])]) ).
fof(f328,plain,
( spl27_3
<=> finite(relation_dom(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_3])]) ).
fof(f333,plain,
( spl27_4
<=> finite(relation_rng(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_4])]) ).
fof(f1093,plain,
( spl27_125
<=> ! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_125])]) ).
fof(f1097,plain,
( spl27_126
<=> relation_rng(sK0) = relation_image(sK0,relation_dom(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_126])]) ).
fof(f1115,plain,
( finite(relation_rng(sK0))
| ~ finite(relation_dom(sK0))
| ~ function(sK0)
| ~ relation(sK0)
| ~ spl27_125
| ~ spl27_126 ),
inference(superposition,[],[f1094,f1099]) ).
fof(f1099,plain,
( relation_rng(sK0) = relation_image(sK0,relation_dom(sK0))
| ~ spl27_126 ),
inference(avatar_component_clause,[],[f1097]) ).
fof(f1094,plain,
( ! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl27_125 ),
inference(avatar_component_clause,[],[f1093]) ).
fof(f1233,plain,
( spl27_148
| ~ spl27_13
| ~ spl27_93 ),
inference(avatar_split_clause,[],[f861,f822,f378,f1230]) ).
fof(f1230,plain,
( spl27_148
<=> empty_set = sK7 ),
introduced(avatar_definition,[new_symbols(naming,[spl27_148])]) ).
fof(f378,plain,
( spl27_13
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_13])]) ).
fof(f822,plain,
( spl27_93
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_93])]) ).
fof(f861,plain,
( empty_set = sK7
| ~ spl27_13
| ~ spl27_93 ),
inference(resolution,[],[f823,f380]) ).
fof(f380,plain,
( empty(sK7)
| ~ spl27_13 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f823,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl27_93 ),
inference(avatar_component_clause,[],[f822]) ).
fof(f1227,plain,
( spl27_147
| ~ spl27_69
| ~ spl27_87 ),
inference(avatar_split_clause,[],[f797,f731,f657,f1225]) ).
fof(f1225,plain,
( spl27_147
<=> ! [X0] : ordinal(sK4(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_147])]) ).
fof(f657,plain,
( spl27_69
<=> ! [X0] : empty(sK4(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_69])]) ).
fof(f731,plain,
( spl27_87
<=> ! [X0] :
( ordinal(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_87])]) ).
fof(f797,plain,
( ! [X0] : ordinal(sK4(X0))
| ~ spl27_69
| ~ spl27_87 ),
inference(resolution,[],[f732,f658]) ).
fof(f658,plain,
( ! [X0] : empty(sK4(X0))
| ~ spl27_69 ),
inference(avatar_component_clause,[],[f657]) ).
fof(f732,plain,
( ! [X0] :
( ~ empty(X0)
| ordinal(X0) )
| ~ spl27_87 ),
inference(avatar_component_clause,[],[f731]) ).
fof(f1222,plain,
( spl27_146
| ~ spl27_69
| ~ spl27_86 ),
inference(avatar_split_clause,[],[f789,f727,f657,f1220]) ).
fof(f1220,plain,
( spl27_146
<=> ! [X0] : epsilon_connected(sK4(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_146])]) ).
fof(f727,plain,
( spl27_86
<=> ! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_86])]) ).
fof(f789,plain,
( ! [X0] : epsilon_connected(sK4(X0))
| ~ spl27_69
| ~ spl27_86 ),
inference(resolution,[],[f728,f658]) ).
fof(f728,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_connected(X0) )
| ~ spl27_86 ),
inference(avatar_component_clause,[],[f727]) ).
fof(f1217,plain,
( spl27_145
| ~ spl27_69
| ~ spl27_85 ),
inference(avatar_split_clause,[],[f781,f723,f657,f1215]) ).
fof(f1215,plain,
( spl27_145
<=> ! [X0] : epsilon_transitive(sK4(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_145])]) ).
fof(f723,plain,
( spl27_85
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_85])]) ).
fof(f781,plain,
( ! [X0] : epsilon_transitive(sK4(X0))
| ~ spl27_69
| ~ spl27_85 ),
inference(resolution,[],[f724,f658]) ).
fof(f724,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_transitive(X0) )
| ~ spl27_85 ),
inference(avatar_component_clause,[],[f723]) ).
fof(f1212,plain,
( spl27_144
| ~ spl27_69
| ~ spl27_84 ),
inference(avatar_split_clause,[],[f773,f719,f657,f1210]) ).
fof(f1210,plain,
( spl27_144
<=> ! [X0] : relation(sK4(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_144])]) ).
fof(f719,plain,
( spl27_84
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_84])]) ).
fof(f773,plain,
( ! [X0] : relation(sK4(X0))
| ~ spl27_69
| ~ spl27_84 ),
inference(resolution,[],[f720,f658]) ).
fof(f720,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl27_84 ),
inference(avatar_component_clause,[],[f719]) ).
fof(f1207,plain,
( spl27_143
| ~ spl27_69
| ~ spl27_83 ),
inference(avatar_split_clause,[],[f765,f715,f657,f1205]) ).
fof(f1205,plain,
( spl27_143
<=> ! [X0] : function(sK4(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_143])]) ).
fof(f715,plain,
( spl27_83
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_83])]) ).
fof(f765,plain,
( ! [X0] : function(sK4(X0))
| ~ spl27_69
| ~ spl27_83 ),
inference(resolution,[],[f716,f658]) ).
fof(f716,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl27_83 ),
inference(avatar_component_clause,[],[f715]) ).
fof(f1202,plain,
( spl27_142
| ~ spl27_69
| ~ spl27_82 ),
inference(avatar_split_clause,[],[f757,f711,f657,f1200]) ).
fof(f1200,plain,
( spl27_142
<=> ! [X0] : finite(sK4(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_142])]) ).
fof(f711,plain,
( spl27_82
<=> ! [X0] :
( finite(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_82])]) ).
fof(f757,plain,
( ! [X0] : finite(sK4(X0))
| ~ spl27_69
| ~ spl27_82 ),
inference(resolution,[],[f712,f658]) ).
fof(f712,plain,
( ! [X0] :
( ~ empty(X0)
| finite(X0) )
| ~ spl27_82 ),
inference(avatar_component_clause,[],[f711]) ).
fof(f1193,plain,
( spl27_141
| ~ spl27_58
| ~ spl27_87 ),
inference(avatar_split_clause,[],[f802,f731,f603,f1190]) ).
fof(f1190,plain,
( spl27_141
<=> ordinal(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_141])]) ).
fof(f603,plain,
( spl27_58
<=> empty(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_58])]) ).
fof(f802,plain,
( ordinal(sK24)
| ~ spl27_58
| ~ spl27_87 ),
inference(resolution,[],[f732,f605]) ).
fof(f605,plain,
( empty(sK24)
| ~ spl27_58 ),
inference(avatar_component_clause,[],[f603]) ).
fof(f1187,plain,
( spl27_140
| ~ spl27_32
| ~ spl27_87 ),
inference(avatar_split_clause,[],[f800,f731,f473,f1184]) ).
fof(f1184,plain,
( spl27_140
<=> ordinal(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_140])]) ).
fof(f473,plain,
( spl27_32
<=> empty(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_32])]) ).
fof(f800,plain,
( ordinal(sK14)
| ~ spl27_32
| ~ spl27_87 ),
inference(resolution,[],[f732,f475]) ).
fof(f475,plain,
( empty(sK14)
| ~ spl27_32 ),
inference(avatar_component_clause,[],[f473]) ).
fof(f1182,plain,
( spl27_139
| ~ spl27_13
| ~ spl27_87 ),
inference(avatar_split_clause,[],[f799,f731,f378,f1179]) ).
fof(f1179,plain,
( spl27_139
<=> ordinal(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_139])]) ).
fof(f799,plain,
( ordinal(sK7)
| ~ spl27_13
| ~ spl27_87 ),
inference(resolution,[],[f732,f380]) ).
fof(f1176,plain,
( spl27_138
| ~ spl27_58
| ~ spl27_86 ),
inference(avatar_split_clause,[],[f794,f727,f603,f1173]) ).
fof(f1173,plain,
( spl27_138
<=> epsilon_connected(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_138])]) ).
fof(f794,plain,
( epsilon_connected(sK24)
| ~ spl27_58
| ~ spl27_86 ),
inference(resolution,[],[f728,f605]) ).
fof(f1170,plain,
( spl27_137
| ~ spl27_32
| ~ spl27_86 ),
inference(avatar_split_clause,[],[f792,f727,f473,f1167]) ).
fof(f1167,plain,
( spl27_137
<=> epsilon_connected(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_137])]) ).
fof(f792,plain,
( epsilon_connected(sK14)
| ~ spl27_32
| ~ spl27_86 ),
inference(resolution,[],[f728,f475]) ).
fof(f1165,plain,
( spl27_136
| ~ spl27_13
| ~ spl27_86 ),
inference(avatar_split_clause,[],[f791,f727,f378,f1162]) ).
fof(f1162,plain,
( spl27_136
<=> epsilon_connected(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_136])]) ).
fof(f791,plain,
( epsilon_connected(sK7)
| ~ spl27_13
| ~ spl27_86 ),
inference(resolution,[],[f728,f380]) ).
fof(f1159,plain,
( spl27_135
| ~ spl27_58
| ~ spl27_85 ),
inference(avatar_split_clause,[],[f786,f723,f603,f1156]) ).
fof(f1156,plain,
( spl27_135
<=> epsilon_transitive(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_135])]) ).
fof(f786,plain,
( epsilon_transitive(sK24)
| ~ spl27_58
| ~ spl27_85 ),
inference(resolution,[],[f724,f605]) ).
fof(f1153,plain,
( spl27_134
| ~ spl27_32
| ~ spl27_85 ),
inference(avatar_split_clause,[],[f784,f723,f473,f1150]) ).
fof(f1150,plain,
( spl27_134
<=> epsilon_transitive(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_134])]) ).
fof(f784,plain,
( epsilon_transitive(sK14)
| ~ spl27_32
| ~ spl27_85 ),
inference(resolution,[],[f724,f475]) ).
fof(f1148,plain,
( spl27_133
| ~ spl27_13
| ~ spl27_85 ),
inference(avatar_split_clause,[],[f783,f723,f378,f1145]) ).
fof(f1145,plain,
( spl27_133
<=> epsilon_transitive(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_133])]) ).
fof(f783,plain,
( epsilon_transitive(sK7)
| ~ spl27_13
| ~ spl27_85 ),
inference(resolution,[],[f724,f380]) ).
fof(f1142,plain,
( spl27_132
| ~ spl27_64
| ~ spl27_84 ),
inference(avatar_split_clause,[],[f779,f719,f633,f1139]) ).
fof(f1139,plain,
( spl27_132
<=> relation(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_132])]) ).
fof(f633,plain,
( spl27_64
<=> empty(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_64])]) ).
fof(f779,plain,
( relation(sK26)
| ~ spl27_64
| ~ spl27_84 ),
inference(resolution,[],[f720,f635]) ).
fof(f635,plain,
( empty(sK26)
| ~ spl27_64 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f1137,plain,
( spl27_131
| ~ spl27_13
| ~ spl27_84 ),
inference(avatar_split_clause,[],[f775,f719,f378,f1134]) ).
fof(f1134,plain,
( spl27_131
<=> relation(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_131])]) ).
fof(f775,plain,
( relation(sK7)
| ~ spl27_13
| ~ spl27_84 ),
inference(resolution,[],[f720,f380]) ).
fof(f1131,plain,
( spl27_130
| ~ spl27_64
| ~ spl27_83 ),
inference(avatar_split_clause,[],[f771,f715,f633,f1128]) ).
fof(f1128,plain,
( spl27_130
<=> function(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_130])]) ).
fof(f771,plain,
( function(sK26)
| ~ spl27_64
| ~ spl27_83 ),
inference(resolution,[],[f716,f635]) ).
fof(f1125,plain,
( spl27_129
| ~ spl27_32
| ~ spl27_83 ),
inference(avatar_split_clause,[],[f768,f715,f473,f1122]) ).
fof(f1122,plain,
( spl27_129
<=> function(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_129])]) ).
fof(f768,plain,
( function(sK14)
| ~ spl27_32
| ~ spl27_83 ),
inference(resolution,[],[f716,f475]) ).
fof(f1120,plain,
( spl27_128
| ~ spl27_13
| ~ spl27_83 ),
inference(avatar_split_clause,[],[f767,f715,f378,f1117]) ).
fof(f1117,plain,
( spl27_128
<=> function(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_128])]) ).
fof(f767,plain,
( function(sK7)
| ~ spl27_13
| ~ spl27_83 ),
inference(resolution,[],[f716,f380]) ).
fof(f1104,plain,
spl27_127,
inference(avatar_split_clause,[],[f257,f1102]) ).
fof(f1102,plain,
( spl27_127
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_127])]) ).
fof(f257,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f126]) ).
fof(f126,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f1100,plain,
( spl27_126
| ~ spl27_1
| ~ spl27_119 ),
inference(avatar_split_clause,[],[f1059,f1031,f318,f1097]) ).
fof(f1031,plain,
( spl27_119
<=> ! [X0] :
( relation_rng(X0) = relation_image(X0,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_119])]) ).
fof(f1059,plain,
( relation_rng(sK0) = relation_image(sK0,relation_dom(sK0))
| ~ spl27_1
| ~ spl27_119 ),
inference(resolution,[],[f1032,f320]) ).
fof(f320,plain,
( relation(sK0)
| ~ spl27_1 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f1032,plain,
( ! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_image(X0,relation_dom(X0)) )
| ~ spl27_119 ),
inference(avatar_component_clause,[],[f1031]) ).
fof(f1095,plain,
spl27_125,
inference(avatar_split_clause,[],[f252,f1093]) ).
fof(f252,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f119]) ).
fof(f119,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( ( finite(X1)
& function(X0)
& relation(X0) )
=> finite(relation_image(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_finset_1) ).
fof(f1055,plain,
spl27_124,
inference(avatar_split_clause,[],[f258,f1053]) ).
fof(f1053,plain,
( spl27_124
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_124])]) ).
fof(f258,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f1051,plain,
spl27_123,
inference(avatar_split_clause,[],[f234,f1049]) ).
fof(f1049,plain,
( spl27_123
<=> ! [X0] :
( ordinal(relation_dom(X0))
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_123])]) ).
fof(f234,plain,
! [X0] :
( ordinal(relation_dom(X0))
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ( ordinal(relation_dom(X0))
& epsilon_connected(relation_dom(X0))
& epsilon_transitive(relation_dom(X0)) )
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f111]) ).
fof(f111,plain,
! [X0] :
( ( ordinal(relation_dom(X0))
& epsilon_connected(relation_dom(X0))
& epsilon_transitive(relation_dom(X0)) )
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ( transfinite_sequence(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(relation_dom(X0))
& epsilon_connected(relation_dom(X0))
& epsilon_transitive(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_ordinal1) ).
fof(f1047,plain,
spl27_122,
inference(avatar_split_clause,[],[f233,f1045]) ).
fof(f1045,plain,
( spl27_122
<=> ! [X0] :
( epsilon_connected(relation_dom(X0))
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_122])]) ).
fof(f233,plain,
! [X0] :
( epsilon_connected(relation_dom(X0))
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f1043,plain,
spl27_121,
inference(avatar_split_clause,[],[f232,f1041]) ).
fof(f1041,plain,
( spl27_121
<=> ! [X0] :
( epsilon_transitive(relation_dom(X0))
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_121])]) ).
fof(f232,plain,
! [X0] :
( epsilon_transitive(relation_dom(X0))
| ~ transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f1038,plain,
( spl27_120
| ~ spl27_64
| ~ spl27_82 ),
inference(avatar_split_clause,[],[f763,f711,f633,f1035]) ).
fof(f1035,plain,
( spl27_120
<=> finite(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_120])]) ).
fof(f763,plain,
( finite(sK26)
| ~ spl27_64
| ~ spl27_82 ),
inference(resolution,[],[f712,f635]) ).
fof(f1033,plain,
spl27_119,
inference(avatar_split_clause,[],[f222,f1031]) ).
fof(f222,plain,
! [X0] :
( relation_rng(X0) = relation_image(X0,relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0] :
( relation_rng(X0) = relation_image(X0,relation_dom(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] :
( relation(X0)
=> relation_rng(X0) = relation_image(X0,relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
fof(f1010,plain,
spl27_118,
inference(avatar_split_clause,[],[f251,f1008]) ).
fof(f1008,plain,
( spl27_118
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_118])]) ).
fof(f251,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f1006,plain,
spl27_117,
inference(avatar_split_clause,[],[f205,f1004]) ).
fof(f1004,plain,
( spl27_117
<=> ! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_117])]) ).
fof(f205,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( finite(X1)
| ~ element(X1,powerset(X0)) )
| ~ finite(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( finite(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> finite(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(f973,plain,
( spl27_116
| ~ spl27_58
| ~ spl27_82 ),
inference(avatar_split_clause,[],[f762,f711,f603,f970]) ).
fof(f970,plain,
( spl27_116
<=> finite(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_116])]) ).
fof(f762,plain,
( finite(sK24)
| ~ spl27_58
| ~ spl27_82 ),
inference(resolution,[],[f712,f605]) ).
fof(f954,plain,
spl27_115,
inference(avatar_split_clause,[],[f255,f952]) ).
fof(f952,plain,
( spl27_115
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_115])]) ).
fof(f255,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f950,plain,
spl27_114,
inference(avatar_split_clause,[],[f254,f948]) ).
fof(f948,plain,
( spl27_114
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_114])]) ).
fof(f254,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f59]) ).
fof(f59,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f946,plain,
spl27_113,
inference(avatar_split_clause,[],[f227,f944]) ).
fof(f944,plain,
( spl27_113
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_113])]) ).
fof(f227,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f105]) ).
fof(f105,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f942,plain,
spl27_112,
inference(avatar_split_clause,[],[f226,f940]) ).
fof(f940,plain,
( spl27_112
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_112])]) ).
fof(f226,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f103]) ).
fof(f103,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f938,plain,
spl27_111,
inference(avatar_split_clause,[],[f210,f936]) ).
fof(f936,plain,
( spl27_111
<=> ! [X0,X1] :
( ordinal(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_111])]) ).
fof(f210,plain,
! [X0,X1] :
( ordinal(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ( ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1) )
| ~ element(X1,X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( element(X1,X0)
=> ( ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_arytm_3) ).
fof(f934,plain,
spl27_110,
inference(avatar_split_clause,[],[f209,f932]) ).
fof(f932,plain,
( spl27_110
<=> ! [X0,X1] :
( epsilon_connected(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_110])]) ).
fof(f209,plain,
! [X0,X1] :
( epsilon_connected(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f929,plain,
( spl27_109
| ~ spl27_53
| ~ spl27_82 ),
inference(avatar_split_clause,[],[f761,f711,f578,f926]) ).
fof(f926,plain,
( spl27_109
<=> finite(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_109])]) ).
fof(f578,plain,
( spl27_53
<=> empty(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_53])]) ).
fof(f761,plain,
( finite(sK23)
| ~ spl27_53
| ~ spl27_82 ),
inference(resolution,[],[f712,f580]) ).
fof(f580,plain,
( empty(sK23)
| ~ spl27_53 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f924,plain,
spl27_108,
inference(avatar_split_clause,[],[f208,f922]) ).
fof(f922,plain,
( spl27_108
<=> ! [X0,X1] :
( epsilon_transitive(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_108])]) ).
fof(f208,plain,
! [X0,X1] :
( epsilon_transitive(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f920,plain,
spl27_107,
inference(avatar_split_clause,[],[f202,f918]) ).
fof(f918,plain,
( spl27_107
<=> ! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_107])]) ).
fof(f202,plain,
! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0] :
( ( finite(sK2(X0))
& ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f89,f133]) ).
fof(f133,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK2(X0))
& ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(f916,plain,
spl27_106,
inference(avatar_split_clause,[],[f200,f914]) ).
fof(f914,plain,
( spl27_106
<=> ! [X0] :
( element(sK1(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_106])]) ).
fof(f200,plain,
! [X0] :
( element(sK1(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ( ~ empty(sK1(X0))
& element(sK1(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f88,f131]) ).
fof(f131,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK1(X0))
& element(sK1(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f903,plain,
spl27_105,
inference(avatar_split_clause,[],[f250,f901]) ).
fof(f901,plain,
( spl27_105
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_105])]) ).
fof(f250,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f899,plain,
spl27_104,
inference(avatar_split_clause,[],[f249,f897]) ).
fof(f897,plain,
( spl27_104
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_104])]) ).
fof(f249,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f895,plain,
spl27_103,
inference(avatar_split_clause,[],[f228,f893]) ).
fof(f893,plain,
( spl27_103
<=> ! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_103])]) ).
fof(f228,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f107]) ).
fof(f107,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f890,plain,
( spl27_102
| ~ spl27_32
| ~ spl27_82 ),
inference(avatar_split_clause,[],[f760,f711,f473,f887]) ).
fof(f887,plain,
( spl27_102
<=> finite(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_102])]) ).
fof(f760,plain,
( finite(sK14)
| ~ spl27_32
| ~ spl27_82 ),
inference(resolution,[],[f712,f475]) ).
fof(f857,plain,
( spl27_101
| ~ spl27_13
| ~ spl27_82 ),
inference(avatar_split_clause,[],[f759,f711,f378,f854]) ).
fof(f854,plain,
( spl27_101
<=> finite(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_101])]) ).
fof(f759,plain,
( finite(sK7)
| ~ spl27_13
| ~ spl27_82 ),
inference(resolution,[],[f712,f380]) ).
fof(f852,plain,
spl27_100,
inference(avatar_split_clause,[],[f256,f850]) ).
fof(f850,plain,
( spl27_100
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_100])]) ).
fof(f256,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f848,plain,
spl27_99,
inference(avatar_split_clause,[],[f240,f846]) ).
fof(f846,plain,
( spl27_99
<=> ! [X0] : element(sK5(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_99])]) ).
fof(f240,plain,
! [X0] : element(sK5(X0),powerset(X0)),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0] :
( finite(sK5(X0))
& ordinal(sK5(X0))
& epsilon_connected(sK5(X0))
& epsilon_transitive(sK5(X0))
& function(sK5(X0))
& relation(sK5(X0))
& empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f81,f139]) ).
fof(f139,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK5(X0))
& ordinal(sK5(X0))
& epsilon_connected(sK5(X0))
& epsilon_transitive(sK5(X0))
& function(sK5(X0))
& relation(sK5(X0))
& empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0] :
? [X1] :
( finite(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f78]) ).
fof(f78,plain,
! [X0] :
? [X1] :
( finite(X1)
& natural(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f37]) ).
fof(f37,axiom,
! [X0] :
? [X1] :
( finite(X1)
& natural(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& one_to_one(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_finset_1) ).
fof(f844,plain,
spl27_98,
inference(avatar_split_clause,[],[f238,f842]) ).
fof(f842,plain,
( spl27_98
<=> ! [X0] : element(sK4(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_98])]) ).
fof(f238,plain,
! [X0] : element(sK4(X0),powerset(X0)),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
! [X0] :
( empty(sK4(X0))
& element(sK4(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f42,f137]) ).
fof(f137,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK4(X0))
& element(sK4(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f42,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f840,plain,
spl27_97,
inference(avatar_split_clause,[],[f221,f838]) ).
fof(f838,plain,
( spl27_97
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_97])]) ).
fof(f221,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f836,plain,
spl27_96,
inference(avatar_split_clause,[],[f220,f834]) ).
fof(f834,plain,
( spl27_96
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_96])]) ).
fof(f220,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f832,plain,
spl27_95,
inference(avatar_split_clause,[],[f219,f830]) ).
fof(f830,plain,
( spl27_95
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_95])]) ).
fof(f219,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f828,plain,
spl27_94,
inference(avatar_split_clause,[],[f218,f826]) ).
fof(f826,plain,
( spl27_94
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_94])]) ).
fof(f218,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f824,plain,
spl27_93,
inference(avatar_split_clause,[],[f214,f822]) ).
fof(f214,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f820,plain,
spl27_92,
inference(avatar_split_clause,[],[f204,f818]) ).
fof(f818,plain,
( spl27_92
<=> ! [X0] :
( finite(sK2(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_92])]) ).
fof(f204,plain,
! [X0] :
( finite(sK2(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f816,plain,
spl27_91,
inference(avatar_split_clause,[],[f203,f814]) ).
fof(f814,plain,
( spl27_91
<=> ! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_91])]) ).
fof(f203,plain,
! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f812,plain,
( spl27_90
| ~ spl27_6
| ~ spl27_82 ),
inference(avatar_split_clause,[],[f756,f711,f343,f809]) ).
fof(f809,plain,
( spl27_90
<=> finite(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_90])]) ).
fof(f343,plain,
( spl27_6
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_6])]) ).
fof(f756,plain,
( finite(empty_set)
| ~ spl27_6
| ~ spl27_82 ),
inference(resolution,[],[f712,f345]) ).
fof(f345,plain,
( empty(empty_set)
| ~ spl27_6 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f807,plain,
spl27_89,
inference(avatar_split_clause,[],[f201,f805]) ).
fof(f805,plain,
( spl27_89
<=> ! [X0] :
( ~ empty(sK1(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_89])]) ).
fof(f201,plain,
! [X0] :
( ~ empty(sK1(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f737,plain,
spl27_88,
inference(avatar_split_clause,[],[f237,f735]) ).
fof(f735,plain,
( spl27_88
<=> ! [X0] : element(sK3(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_88])]) ).
fof(f237,plain,
! [X0] : element(sK3(X0),X0),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] : element(sK3(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f13,f135]) ).
fof(f135,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK3(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f13,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f733,plain,
spl27_87,
inference(avatar_split_clause,[],[f217,f731]) ).
fof(f217,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f729,plain,
spl27_86,
inference(avatar_split_clause,[],[f216,f727]) ).
fof(f216,plain,
! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f725,plain,
spl27_85,
inference(avatar_split_clause,[],[f215,f723]) ).
fof(f215,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f721,plain,
spl27_84,
inference(avatar_split_clause,[],[f213,f719]) ).
fof(f213,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f717,plain,
spl27_83,
inference(avatar_split_clause,[],[f212,f715]) ).
fof(f212,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f713,plain,
spl27_82,
inference(avatar_split_clause,[],[f211,f711]) ).
fof(f211,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> finite(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
fof(f709,plain,
spl27_81,
inference(avatar_split_clause,[],[f207,f707]) ).
fof(f707,plain,
( spl27_81
<=> ! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_81])]) ).
fof(f207,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f705,plain,
spl27_80,
inference(avatar_split_clause,[],[f206,f703]) ).
fof(f703,plain,
( spl27_80
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_80])]) ).
fof(f206,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f701,plain,
spl27_79,
inference(avatar_split_clause,[],[f312,f698]) ).
fof(f698,plain,
( spl27_79
<=> element(sK26,positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_79])]) ).
fof(f312,plain,
element(sK26,positive_rationals),
inference(cnf_transformation,[],[f182]) ).
fof(f182,plain,
( ordinal(sK26)
& epsilon_connected(sK26)
& epsilon_transitive(sK26)
& empty(sK26)
& element(sK26,positive_rationals) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f82,f181]) ).
fof(f181,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& element(X0,positive_rationals) )
=> ( ordinal(sK26)
& epsilon_connected(sK26)
& epsilon_transitive(sK26)
& empty(sK26)
& element(sK26,positive_rationals) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& element(X0,positive_rationals) ),
inference(pure_predicate_removal,[],[f44]) ).
fof(f44,axiom,
? [X0] :
( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& element(X0,positive_rationals) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_arytm_3) ).
fof(f696,plain,
spl27_78,
inference(avatar_split_clause,[],[f307,f693]) ).
fof(f693,plain,
( spl27_78
<=> element(sK25,positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_78])]) ).
fof(f307,plain,
element(sK25,positive_rationals),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
( ordinal(sK25)
& epsilon_connected(sK25)
& epsilon_transitive(sK25)
& ~ empty(sK25)
& element(sK25,positive_rationals) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f36,f179]) ).
fof(f179,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0)
& element(X0,positive_rationals) )
=> ( ordinal(sK25)
& epsilon_connected(sK25)
& epsilon_transitive(sK25)
& ~ empty(sK25)
& element(sK25,positive_rationals) ) ),
introduced(choice_axiom,[]) ).
fof(f36,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0)
& element(X0,positive_rationals) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_arytm_3) ).
fof(f691,plain,
spl27_77,
inference(avatar_split_clause,[],[f248,f689]) ).
fof(f689,plain,
( spl27_77
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_77])]) ).
fof(f248,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f52]) ).
fof(f52,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f687,plain,
spl27_76,
inference(avatar_split_clause,[],[f247,f685]) ).
fof(f685,plain,
( spl27_76
<=> ! [X0] : finite(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_76])]) ).
fof(f247,plain,
! [X0] : finite(sK5(X0)),
inference(cnf_transformation,[],[f140]) ).
fof(f683,plain,
spl27_75,
inference(avatar_split_clause,[],[f246,f681]) ).
fof(f681,plain,
( spl27_75
<=> ! [X0] : ordinal(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_75])]) ).
fof(f246,plain,
! [X0] : ordinal(sK5(X0)),
inference(cnf_transformation,[],[f140]) ).
fof(f679,plain,
spl27_74,
inference(avatar_split_clause,[],[f245,f677]) ).
fof(f677,plain,
( spl27_74
<=> ! [X0] : epsilon_connected(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_74])]) ).
fof(f245,plain,
! [X0] : epsilon_connected(sK5(X0)),
inference(cnf_transformation,[],[f140]) ).
fof(f675,plain,
spl27_73,
inference(avatar_split_clause,[],[f244,f673]) ).
fof(f673,plain,
( spl27_73
<=> ! [X0] : epsilon_transitive(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_73])]) ).
fof(f244,plain,
! [X0] : epsilon_transitive(sK5(X0)),
inference(cnf_transformation,[],[f140]) ).
fof(f671,plain,
spl27_72,
inference(avatar_split_clause,[],[f243,f669]) ).
fof(f669,plain,
( spl27_72
<=> ! [X0] : function(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_72])]) ).
fof(f243,plain,
! [X0] : function(sK5(X0)),
inference(cnf_transformation,[],[f140]) ).
fof(f667,plain,
spl27_71,
inference(avatar_split_clause,[],[f242,f665]) ).
fof(f665,plain,
( spl27_71
<=> ! [X0] : relation(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_71])]) ).
fof(f242,plain,
! [X0] : relation(sK5(X0)),
inference(cnf_transformation,[],[f140]) ).
fof(f663,plain,
spl27_70,
inference(avatar_split_clause,[],[f241,f661]) ).
fof(f661,plain,
( spl27_70
<=> ! [X0] : empty(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_70])]) ).
fof(f241,plain,
! [X0] : empty(sK5(X0)),
inference(cnf_transformation,[],[f140]) ).
fof(f659,plain,
spl27_69,
inference(avatar_split_clause,[],[f239,f657]) ).
fof(f239,plain,
! [X0] : empty(sK4(X0)),
inference(cnf_transformation,[],[f138]) ).
fof(f655,plain,
spl27_68,
inference(avatar_split_clause,[],[f199,f653]) ).
fof(f653,plain,
( spl27_68
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_68])]) ).
fof(f199,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f651,plain,
spl27_67,
inference(avatar_split_clause,[],[f316,f648]) ).
fof(f648,plain,
( spl27_67
<=> ordinal(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_67])]) ).
fof(f316,plain,
ordinal(sK26),
inference(cnf_transformation,[],[f182]) ).
fof(f646,plain,
spl27_66,
inference(avatar_split_clause,[],[f315,f643]) ).
fof(f643,plain,
( spl27_66
<=> epsilon_connected(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_66])]) ).
fof(f315,plain,
epsilon_connected(sK26),
inference(cnf_transformation,[],[f182]) ).
fof(f641,plain,
spl27_65,
inference(avatar_split_clause,[],[f314,f638]) ).
fof(f638,plain,
( spl27_65
<=> epsilon_transitive(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_65])]) ).
fof(f314,plain,
epsilon_transitive(sK26),
inference(cnf_transformation,[],[f182]) ).
fof(f636,plain,
spl27_64,
inference(avatar_split_clause,[],[f313,f633]) ).
fof(f313,plain,
empty(sK26),
inference(cnf_transformation,[],[f182]) ).
fof(f631,plain,
spl27_63,
inference(avatar_split_clause,[],[f311,f628]) ).
fof(f628,plain,
( spl27_63
<=> ordinal(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_63])]) ).
fof(f311,plain,
ordinal(sK25),
inference(cnf_transformation,[],[f180]) ).
fof(f626,plain,
spl27_62,
inference(avatar_split_clause,[],[f310,f623]) ).
fof(f623,plain,
( spl27_62
<=> epsilon_connected(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_62])]) ).
fof(f310,plain,
epsilon_connected(sK25),
inference(cnf_transformation,[],[f180]) ).
fof(f621,plain,
spl27_61,
inference(avatar_split_clause,[],[f309,f618]) ).
fof(f618,plain,
( spl27_61
<=> epsilon_transitive(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_61])]) ).
fof(f309,plain,
epsilon_transitive(sK25),
inference(cnf_transformation,[],[f180]) ).
fof(f616,plain,
~ spl27_60,
inference(avatar_split_clause,[],[f308,f613]) ).
fof(f613,plain,
( spl27_60
<=> empty(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_60])]) ).
fof(f308,plain,
~ empty(sK25),
inference(cnf_transformation,[],[f180]) ).
fof(f611,plain,
spl27_59,
inference(avatar_split_clause,[],[f306,f608]) ).
fof(f608,plain,
( spl27_59
<=> function(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_59])]) ).
fof(f306,plain,
function(sK24),
inference(cnf_transformation,[],[f178]) ).
fof(f178,plain,
( function(sK24)
& empty(sK24)
& relation(sK24) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f38,f177]) ).
fof(f177,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK24)
& empty(sK24)
& relation(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f38,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f606,plain,
spl27_58,
inference(avatar_split_clause,[],[f305,f603]) ).
fof(f305,plain,
empty(sK24),
inference(cnf_transformation,[],[f178]) ).
fof(f601,plain,
spl27_57,
inference(avatar_split_clause,[],[f304,f598]) ).
fof(f598,plain,
( spl27_57
<=> relation(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_57])]) ).
fof(f304,plain,
relation(sK24),
inference(cnf_transformation,[],[f178]) ).
fof(f596,plain,
spl27_56,
inference(avatar_split_clause,[],[f303,f593]) ).
fof(f593,plain,
( spl27_56
<=> ordinal(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_56])]) ).
fof(f303,plain,
ordinal(sK23),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
( ordinal(sK23)
& epsilon_connected(sK23)
& epsilon_transitive(sK23)
& empty(sK23)
& function(sK23)
& relation(sK23) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f76,f175]) ).
fof(f175,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(sK23)
& epsilon_connected(sK23)
& epsilon_transitive(sK23)
& empty(sK23)
& function(sK23)
& relation(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f39]) ).
fof(f39,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(f591,plain,
spl27_55,
inference(avatar_split_clause,[],[f302,f588]) ).
fof(f588,plain,
( spl27_55
<=> epsilon_connected(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_55])]) ).
fof(f302,plain,
epsilon_connected(sK23),
inference(cnf_transformation,[],[f176]) ).
fof(f586,plain,
spl27_54,
inference(avatar_split_clause,[],[f301,f583]) ).
fof(f583,plain,
( spl27_54
<=> epsilon_transitive(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_54])]) ).
fof(f301,plain,
epsilon_transitive(sK23),
inference(cnf_transformation,[],[f176]) ).
fof(f581,plain,
spl27_53,
inference(avatar_split_clause,[],[f300,f578]) ).
fof(f300,plain,
empty(sK23),
inference(cnf_transformation,[],[f176]) ).
fof(f576,plain,
spl27_52,
inference(avatar_split_clause,[],[f299,f573]) ).
fof(f573,plain,
( spl27_52
<=> function(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_52])]) ).
fof(f299,plain,
function(sK23),
inference(cnf_transformation,[],[f176]) ).
fof(f571,plain,
spl27_51,
inference(avatar_split_clause,[],[f298,f568]) ).
fof(f568,plain,
( spl27_51
<=> relation(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_51])]) ).
fof(f298,plain,
relation(sK23),
inference(cnf_transformation,[],[f176]) ).
fof(f566,plain,
spl27_50,
inference(avatar_split_clause,[],[f297,f563]) ).
fof(f563,plain,
( spl27_50
<=> function(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_50])]) ).
fof(f297,plain,
function(sK22),
inference(cnf_transformation,[],[f174]) ).
fof(f174,plain,
( function(sK22)
& relation(sK22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f77,f173]) ).
fof(f173,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK22)
& relation(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f46]) ).
fof(f46,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f561,plain,
spl27_49,
inference(avatar_split_clause,[],[f296,f558]) ).
fof(f558,plain,
( spl27_49
<=> relation(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_49])]) ).
fof(f296,plain,
relation(sK22),
inference(cnf_transformation,[],[f174]) ).
fof(f556,plain,
spl27_48,
inference(avatar_split_clause,[],[f295,f553]) ).
fof(f553,plain,
( spl27_48
<=> transfinite_sequence(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_48])]) ).
fof(f295,plain,
transfinite_sequence(sK21),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
( transfinite_sequence(sK21)
& function(sK21)
& relation(sK21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f67,f171]) ).
fof(f171,plain,
( ? [X0] :
( transfinite_sequence(X0)
& function(X0)
& relation(X0) )
=> ( transfinite_sequence(sK21)
& function(sK21)
& relation(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
? [X0] :
( transfinite_sequence(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f40]) ).
fof(f40,axiom,
? [X0] :
( ordinal_yielding(X0)
& transfinite_sequence(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal2) ).
fof(f551,plain,
spl27_47,
inference(avatar_split_clause,[],[f294,f548]) ).
fof(f548,plain,
( spl27_47
<=> function(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_47])]) ).
fof(f294,plain,
function(sK21),
inference(cnf_transformation,[],[f172]) ).
fof(f546,plain,
spl27_46,
inference(avatar_split_clause,[],[f293,f543]) ).
fof(f543,plain,
( spl27_46
<=> relation(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_46])]) ).
fof(f293,plain,
relation(sK21),
inference(cnf_transformation,[],[f172]) ).
fof(f541,plain,
spl27_45,
inference(avatar_split_clause,[],[f292,f538]) ).
fof(f538,plain,
( spl27_45
<=> transfinite_sequence(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_45])]) ).
fof(f292,plain,
transfinite_sequence(sK20),
inference(cnf_transformation,[],[f170]) ).
fof(f170,plain,
( transfinite_sequence(sK20)
& function(sK20)
& relation(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f50,f169]) ).
fof(f169,plain,
( ? [X0] :
( transfinite_sequence(X0)
& function(X0)
& relation(X0) )
=> ( transfinite_sequence(sK20)
& function(sK20)
& relation(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f50,axiom,
? [X0] :
( transfinite_sequence(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_ordinal1) ).
fof(f536,plain,
spl27_44,
inference(avatar_split_clause,[],[f291,f533]) ).
fof(f533,plain,
( spl27_44
<=> function(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_44])]) ).
fof(f291,plain,
function(sK20),
inference(cnf_transformation,[],[f170]) ).
fof(f531,plain,
spl27_43,
inference(avatar_split_clause,[],[f290,f528]) ).
fof(f528,plain,
( spl27_43
<=> relation(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_43])]) ).
fof(f290,plain,
relation(sK20),
inference(cnf_transformation,[],[f170]) ).
fof(f526,plain,
spl27_42,
inference(avatar_split_clause,[],[f289,f523]) ).
fof(f523,plain,
( spl27_42
<=> function(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_42])]) ).
fof(f289,plain,
function(sK19),
inference(cnf_transformation,[],[f168]) ).
fof(f168,plain,
( function(sK19)
& relation(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f69,f167]) ).
fof(f167,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK19)
& relation(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f29]) ).
fof(f29,axiom,
? [X0] :
( function_yielding(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funcop_1) ).
fof(f521,plain,
spl27_41,
inference(avatar_split_clause,[],[f288,f518]) ).
fof(f518,plain,
( spl27_41
<=> relation(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_41])]) ).
fof(f288,plain,
relation(sK19),
inference(cnf_transformation,[],[f168]) ).
fof(f516,plain,
spl27_40,
inference(avatar_split_clause,[],[f287,f513]) ).
fof(f513,plain,
( spl27_40
<=> function(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_40])]) ).
fof(f287,plain,
function(sK18),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
( function(sK18)
& relation(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f30,f165]) ).
fof(f165,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK18)
& relation(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f30,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f511,plain,
spl27_39,
inference(avatar_split_clause,[],[f286,f508]) ).
fof(f508,plain,
( spl27_39
<=> relation(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_39])]) ).
fof(f286,plain,
relation(sK18),
inference(cnf_transformation,[],[f166]) ).
fof(f506,plain,
spl27_38,
inference(avatar_split_clause,[],[f285,f503]) ).
fof(f503,plain,
( spl27_38
<=> function(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_38])]) ).
fof(f285,plain,
function(sK17),
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
( function(sK17)
& relation(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f73,f163]) ).
fof(f163,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK17)
& relation(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f49]) ).
fof(f49,axiom,
? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(f501,plain,
spl27_37,
inference(avatar_split_clause,[],[f284,f498]) ).
fof(f498,plain,
( spl27_37
<=> relation(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_37])]) ).
fof(f284,plain,
relation(sK17),
inference(cnf_transformation,[],[f164]) ).
fof(f496,plain,
spl27_36,
inference(avatar_split_clause,[],[f283,f493]) ).
fof(f493,plain,
( spl27_36
<=> relation(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_36])]) ).
fof(f283,plain,
relation(sK16),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
relation(sK16),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f72,f161]) ).
fof(f161,plain,
( ? [X0] : relation(X0)
=> relation(sK16) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f48]) ).
fof(f48,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f491,plain,
spl27_35,
inference(avatar_split_clause,[],[f282,f488]) ).
fof(f488,plain,
( spl27_35
<=> function(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_35])]) ).
fof(f282,plain,
function(sK15),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
( function(sK15)
& relation(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f71,f159]) ).
fof(f159,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK15)
& relation(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f51]) ).
fof(f51,axiom,
? [X0] :
( function(X0)
& relation_non_empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_funct_1) ).
fof(f486,plain,
spl27_34,
inference(avatar_split_clause,[],[f281,f483]) ).
fof(f483,plain,
( spl27_34
<=> relation(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_34])]) ).
fof(f281,plain,
relation(sK15),
inference(cnf_transformation,[],[f160]) ).
fof(f481,plain,
spl27_33,
inference(avatar_split_clause,[],[f280,f478]) ).
fof(f478,plain,
( spl27_33
<=> relation(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_33])]) ).
fof(f280,plain,
relation(sK14),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
( relation(sK14)
& empty(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f33,f157]) ).
fof(f157,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK14)
& empty(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f33,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f476,plain,
spl27_32,
inference(avatar_split_clause,[],[f279,f473]) ).
fof(f279,plain,
empty(sK14),
inference(cnf_transformation,[],[f158]) ).
fof(f471,plain,
spl27_31,
inference(avatar_split_clause,[],[f278,f468]) ).
fof(f468,plain,
( spl27_31
<=> ordinal(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_31])]) ).
fof(f278,plain,
ordinal(sK13),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
( ordinal(sK13)
& epsilon_connected(sK13)
& epsilon_transitive(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f68,f155]) ).
fof(f155,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK13)
& epsilon_connected(sK13)
& epsilon_transitive(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
inference(pure_predicate_removal,[],[f32]) ).
fof(f32,axiom,
? [X0] :
( being_limit_ordinal(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal2) ).
fof(f466,plain,
spl27_30,
inference(avatar_split_clause,[],[f277,f463]) ).
fof(f463,plain,
( spl27_30
<=> epsilon_connected(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_30])]) ).
fof(f277,plain,
epsilon_connected(sK13),
inference(cnf_transformation,[],[f156]) ).
fof(f461,plain,
spl27_29,
inference(avatar_split_clause,[],[f276,f458]) ).
fof(f458,plain,
( spl27_29
<=> epsilon_transitive(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_29])]) ).
fof(f276,plain,
epsilon_transitive(sK13),
inference(cnf_transformation,[],[f156]) ).
fof(f456,plain,
spl27_28,
inference(avatar_split_clause,[],[f275,f453]) ).
fof(f453,plain,
( spl27_28
<=> ordinal(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_28])]) ).
fof(f275,plain,
ordinal(sK12),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f31,f153]) ).
fof(f153,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f31,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f451,plain,
spl27_27,
inference(avatar_split_clause,[],[f274,f448]) ).
fof(f448,plain,
( spl27_27
<=> epsilon_connected(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_27])]) ).
fof(f274,plain,
epsilon_connected(sK12),
inference(cnf_transformation,[],[f154]) ).
fof(f446,plain,
spl27_26,
inference(avatar_split_clause,[],[f273,f443]) ).
fof(f443,plain,
( spl27_26
<=> epsilon_transitive(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_26])]) ).
fof(f273,plain,
epsilon_transitive(sK12),
inference(cnf_transformation,[],[f154]) ).
fof(f441,plain,
spl27_25,
inference(avatar_split_clause,[],[f272,f438]) ).
fof(f438,plain,
( spl27_25
<=> relation(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_25])]) ).
fof(f272,plain,
relation(sK11),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
( relation(sK11)
& ~ empty(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f41,f151]) ).
fof(f151,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK11)
& ~ empty(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f41,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f436,plain,
~ spl27_24,
inference(avatar_split_clause,[],[f271,f433]) ).
fof(f433,plain,
( spl27_24
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_24])]) ).
fof(f271,plain,
~ empty(sK11),
inference(cnf_transformation,[],[f152]) ).
fof(f431,plain,
spl27_23,
inference(avatar_split_clause,[],[f270,f428]) ).
fof(f428,plain,
( spl27_23
<=> ordinal(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_23])]) ).
fof(f270,plain,
ordinal(sK10),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
( ordinal(sK10)
& epsilon_connected(sK10)
& epsilon_transitive(sK10)
& ~ empty(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f84,f149]) ).
fof(f149,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK10)
& epsilon_connected(sK10)
& epsilon_transitive(sK10)
& ~ empty(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
inference(pure_predicate_removal,[],[f27]) ).
fof(f27,axiom,
? [X0] :
( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(f426,plain,
spl27_22,
inference(avatar_split_clause,[],[f269,f423]) ).
fof(f423,plain,
( spl27_22
<=> epsilon_connected(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_22])]) ).
fof(f269,plain,
epsilon_connected(sK10),
inference(cnf_transformation,[],[f150]) ).
fof(f421,plain,
spl27_21,
inference(avatar_split_clause,[],[f268,f418]) ).
fof(f418,plain,
( spl27_21
<=> epsilon_transitive(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_21])]) ).
fof(f268,plain,
epsilon_transitive(sK10),
inference(cnf_transformation,[],[f150]) ).
fof(f416,plain,
~ spl27_20,
inference(avatar_split_clause,[],[f267,f413]) ).
fof(f413,plain,
( spl27_20
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_20])]) ).
fof(f267,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f150]) ).
fof(f411,plain,
spl27_19,
inference(avatar_split_clause,[],[f266,f408]) ).
fof(f408,plain,
( spl27_19
<=> ordinal(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_19])]) ).
fof(f266,plain,
ordinal(sK9),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
( ordinal(sK9)
& epsilon_connected(sK9)
& epsilon_transitive(sK9)
& ~ empty(sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f47,f147]) ).
fof(f147,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK9)
& epsilon_connected(sK9)
& epsilon_transitive(sK9)
& ~ empty(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f47,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f406,plain,
spl27_18,
inference(avatar_split_clause,[],[f265,f403]) ).
fof(f403,plain,
( spl27_18
<=> epsilon_connected(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_18])]) ).
fof(f265,plain,
epsilon_connected(sK9),
inference(cnf_transformation,[],[f148]) ).
fof(f401,plain,
spl27_17,
inference(avatar_split_clause,[],[f264,f398]) ).
fof(f398,plain,
( spl27_17
<=> epsilon_transitive(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_17])]) ).
fof(f264,plain,
epsilon_transitive(sK9),
inference(cnf_transformation,[],[f148]) ).
fof(f396,plain,
~ spl27_16,
inference(avatar_split_clause,[],[f263,f393]) ).
fof(f393,plain,
( spl27_16
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_16])]) ).
fof(f263,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f148]) ).
fof(f391,plain,
spl27_15,
inference(avatar_split_clause,[],[f262,f388]) ).
fof(f388,plain,
( spl27_15
<=> finite(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_15])]) ).
fof(f262,plain,
finite(sK8),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
( finite(sK8)
& ~ empty(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f28,f145]) ).
fof(f145,plain,
( ? [X0] :
( finite(X0)
& ~ empty(X0) )
=> ( finite(sK8)
& ~ empty(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] :
( finite(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f386,plain,
~ spl27_14,
inference(avatar_split_clause,[],[f261,f383]) ).
fof(f383,plain,
( spl27_14
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_14])]) ).
fof(f261,plain,
~ empty(sK8),
inference(cnf_transformation,[],[f146]) ).
fof(f381,plain,
spl27_13,
inference(avatar_split_clause,[],[f260,f378]) ).
fof(f260,plain,
empty(sK7),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
empty(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f35,f143]) ).
fof(f143,plain,
( ? [X0] : empty(X0)
=> empty(sK7) ),
introduced(choice_axiom,[]) ).
fof(f35,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f376,plain,
~ spl27_12,
inference(avatar_split_clause,[],[f259,f373]) ).
fof(f373,plain,
( spl27_12
<=> empty(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_12])]) ).
fof(f259,plain,
~ empty(sK6),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
~ empty(sK6),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f43,f141]) ).
fof(f141,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK6) ),
introduced(choice_axiom,[]) ).
fof(f43,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f371,plain,
spl27_11,
inference(avatar_split_clause,[],[f198,f368]) ).
fof(f368,plain,
( spl27_11
<=> ordinal(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_11])]) ).
fof(f198,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f74]) ).
fof(f74,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f18]) ).
fof(f18,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f366,plain,
spl27_10,
inference(avatar_split_clause,[],[f197,f363]) ).
fof(f363,plain,
( spl27_10
<=> epsilon_connected(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_10])]) ).
fof(f197,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f80]) ).
fof(f361,plain,
spl27_9,
inference(avatar_split_clause,[],[f196,f358]) ).
fof(f358,plain,
( spl27_9
<=> epsilon_transitive(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_9])]) ).
fof(f196,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f80]) ).
fof(f356,plain,
spl27_8,
inference(avatar_split_clause,[],[f194,f353]) ).
fof(f353,plain,
( spl27_8
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_8])]) ).
fof(f194,plain,
function(empty_set),
inference(cnf_transformation,[],[f80]) ).
fof(f351,plain,
spl27_7,
inference(avatar_split_clause,[],[f190,f348]) ).
fof(f348,plain,
( spl27_7
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_7])]) ).
fof(f190,plain,
relation(empty_set),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f346,plain,
spl27_6,
inference(avatar_split_clause,[],[f188,f343]) ).
fof(f188,plain,
empty(empty_set),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f341,plain,
~ spl27_5,
inference(avatar_split_clause,[],[f187,f338]) ).
fof(f338,plain,
( spl27_5
<=> empty(positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl27_5])]) ).
fof(f187,plain,
~ empty(positive_rationals),
inference(cnf_transformation,[],[f25]) ).
fof(f25,axiom,
~ empty(positive_rationals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_arytm_3) ).
fof(f336,plain,
~ spl27_4,
inference(avatar_split_clause,[],[f186,f333]) ).
fof(f186,plain,
~ finite(relation_rng(sK0)),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
( ~ finite(relation_rng(sK0))
& finite(relation_dom(sK0))
& function(sK0)
& relation(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f87,f129]) ).
fof(f129,plain,
( ? [X0] :
( ~ finite(relation_rng(X0))
& finite(relation_dom(X0))
& function(X0)
& relation(X0) )
=> ( ~ finite(relation_rng(sK0))
& finite(relation_dom(sK0))
& function(sK0)
& relation(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
? [X0] :
( ~ finite(relation_rng(X0))
& finite(relation_dom(X0))
& function(X0)
& relation(X0) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
? [X0] :
( ~ finite(relation_rng(X0))
& finite(relation_dom(X0))
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( finite(relation_dom(X0))
=> finite(relation_rng(X0)) ) ),
inference(negated_conjecture,[],[f56]) ).
fof(f56,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( finite(relation_dom(X0))
=> finite(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finset_1) ).
fof(f331,plain,
spl27_3,
inference(avatar_split_clause,[],[f185,f328]) ).
fof(f185,plain,
finite(relation_dom(sK0)),
inference(cnf_transformation,[],[f130]) ).
fof(f326,plain,
spl27_2,
inference(avatar_split_clause,[],[f184,f323]) ).
fof(f184,plain,
function(sK0),
inference(cnf_transformation,[],[f130]) ).
fof(f321,plain,
spl27_1,
inference(avatar_split_clause,[],[f183,f318]) ).
fof(f183,plain,
relation(sK0),
inference(cnf_transformation,[],[f130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU303+3 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 11:04:42 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (9495)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (9499)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.36 TRYING [1]
% 0.14/0.36 TRYING [2]
% 0.14/0.36 TRYING [3]
% 0.14/0.37 TRYING [4]
% 0.14/0.37 % (9498)WARNING: value z3 for option sas not known
% 0.14/0.37 % (9496)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (9497)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (9498)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (9500)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 % (9501)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 % (9502)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37 TRYING [5]
% 0.21/0.37 TRYING [6]
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.38 TRYING [1]
% 0.21/0.38 TRYING [2]
% 0.21/0.38 TRYING [3]
% 0.21/0.38 % (9500)First to succeed.
% 0.21/0.38 % (9501)Also succeeded, but the first one will report.
% 0.21/0.38 TRYING [4]
% 0.21/0.38 TRYING [7]
% 0.21/0.39 % (9498)Also succeeded, but the first one will report.
% 0.21/0.39 % (9500)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9495"
% 0.21/0.39 TRYING [3]
% 0.21/0.39 % (9500)Refutation found. Thanks to Tanya!
% 0.21/0.39 % SZS status Theorem for theBenchmark
% 0.21/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.39 % (9500)------------------------------
% 0.21/0.39 % (9500)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.39 % (9500)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (9500)Memory used [KB]: 1227
% 0.21/0.39 % (9500)Time elapsed: 0.020 s
% 0.21/0.39 % (9500)Instructions burned: 28 (million)
% 0.21/0.39 % (9495)Success in time 0.037 s
%------------------------------------------------------------------------------