TSTP Solution File: SEU097+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU097+1 : 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 : n008.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 09:26:59 EDT 2024
% Result : Theorem 0.15s 0.36s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 231
% Syntax : Number of formulae : 620 ( 229 unt; 0 def)
% Number of atoms : 1375 ( 36 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 1093 ( 338 ~; 271 |; 289 &)
% ( 142 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 161 ( 159 usr; 142 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 25 con; 0-2 aty)
% Number of variables : 372 ( 298 !; 74 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1203,plain,
$false,
inference(avatar_sat_refutation,[],[f334,f339,f344,f349,f354,f359,f364,f369,f374,f379,f384,f389,f394,f399,f404,f409,f414,f419,f424,f429,f434,f439,f444,f449,f454,f459,f464,f469,f474,f479,f484,f489,f494,f499,f504,f509,f514,f519,f524,f529,f534,f539,f544,f549,f554,f559,f564,f569,f574,f579,f584,f589,f594,f599,f604,f609,f614,f619,f624,f629,f634,f639,f644,f649,f653,f657,f661,f665,f669,f673,f677,f681,f685,f689,f694,f699,f703,f707,f711,f715,f719,f723,f727,f731,f735,f782,f810,f814,f818,f822,f826,f830,f835,f839,f843,f847,f851,f855,f860,f876,f880,f884,f888,f893,f898,f902,f921,f925,f930,f935,f939,f943,f947,f951,f955,f959,f972,f1020,f1032,f1036,f1040,f1045,f1049,f1053,f1091,f1105,f1114,f1131,f1137,f1143,f1148,f1154,f1159,f1161,f1166,f1172,f1177,f1183,f1189,f1194,f1200,f1202]) ).
fof(f1202,plain,
( ~ spl28_2
| ~ spl28_103
| spl28_128 ),
inference(avatar_split_clause,[],[f1126,f1111,f886,f336]) ).
fof(f336,plain,
( spl28_2
<=> finite(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_2])]) ).
fof(f886,plain,
( spl28_103
<=> ! [X0,X1] :
( finite(set_difference(X0,X1))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_103])]) ).
fof(f1111,plain,
( spl28_128
<=> finite(set_difference(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_128])]) ).
fof(f1126,plain,
( ~ finite(sK1)
| ~ spl28_103
| spl28_128 ),
inference(resolution,[],[f1113,f887]) ).
fof(f887,plain,
( ! [X0,X1] :
( finite(set_difference(X0,X1))
| ~ finite(X0) )
| ~ spl28_103 ),
inference(avatar_component_clause,[],[f886]) ).
fof(f1113,plain,
( ~ finite(set_difference(sK1,sK0))
| spl28_128 ),
inference(avatar_component_clause,[],[f1111]) ).
fof(f1200,plain,
( spl28_141
| ~ spl28_55
| ~ spl28_84 ),
inference(avatar_split_clause,[],[f805,f729,f601,f1197]) ).
fof(f1197,plain,
( spl28_141
<=> ordinal(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_141])]) ).
fof(f601,plain,
( spl28_55
<=> empty(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_55])]) ).
fof(f729,plain,
( spl28_84
<=> ! [X0] :
( ordinal(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_84])]) ).
fof(f805,plain,
( ordinal(sK25)
| ~ spl28_55
| ~ spl28_84 ),
inference(resolution,[],[f730,f603]) ).
fof(f603,plain,
( empty(sK25)
| ~ spl28_55 ),
inference(avatar_component_clause,[],[f601]) ).
fof(f730,plain,
( ! [X0] :
( ~ empty(X0)
| ordinal(X0) )
| ~ spl28_84 ),
inference(avatar_component_clause,[],[f729]) ).
fof(f1194,plain,
( spl28_140
| ~ spl28_31
| ~ spl28_84 ),
inference(avatar_split_clause,[],[f803,f729,f481,f1191]) ).
fof(f1191,plain,
( spl28_140
<=> ordinal(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_140])]) ).
fof(f481,plain,
( spl28_31
<=> empty(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_31])]) ).
fof(f803,plain,
( ordinal(sK15)
| ~ spl28_31
| ~ spl28_84 ),
inference(resolution,[],[f730,f483]) ).
fof(f483,plain,
( empty(sK15)
| ~ spl28_31 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f1189,plain,
( spl28_139
| ~ spl28_12
| ~ spl28_84 ),
inference(avatar_split_clause,[],[f802,f729,f386,f1186]) ).
fof(f1186,plain,
( spl28_139
<=> ordinal(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_139])]) ).
fof(f386,plain,
( spl28_12
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_12])]) ).
fof(f802,plain,
( ordinal(sK8)
| ~ spl28_12
| ~ spl28_84 ),
inference(resolution,[],[f730,f388]) ).
fof(f388,plain,
( empty(sK8)
| ~ spl28_12 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f1183,plain,
( spl28_138
| ~ spl28_55
| ~ spl28_83 ),
inference(avatar_split_clause,[],[f797,f725,f601,f1180]) ).
fof(f1180,plain,
( spl28_138
<=> epsilon_connected(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_138])]) ).
fof(f725,plain,
( spl28_83
<=> ! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_83])]) ).
fof(f797,plain,
( epsilon_connected(sK25)
| ~ spl28_55
| ~ spl28_83 ),
inference(resolution,[],[f726,f603]) ).
fof(f726,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_connected(X0) )
| ~ spl28_83 ),
inference(avatar_component_clause,[],[f725]) ).
fof(f1177,plain,
( spl28_137
| ~ spl28_31
| ~ spl28_83 ),
inference(avatar_split_clause,[],[f795,f725,f481,f1174]) ).
fof(f1174,plain,
( spl28_137
<=> epsilon_connected(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_137])]) ).
fof(f795,plain,
( epsilon_connected(sK15)
| ~ spl28_31
| ~ spl28_83 ),
inference(resolution,[],[f726,f483]) ).
fof(f1172,plain,
( spl28_136
| ~ spl28_12
| ~ spl28_83 ),
inference(avatar_split_clause,[],[f794,f725,f386,f1169]) ).
fof(f1169,plain,
( spl28_136
<=> epsilon_connected(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_136])]) ).
fof(f794,plain,
( epsilon_connected(sK8)
| ~ spl28_12
| ~ spl28_83 ),
inference(resolution,[],[f726,f388]) ).
fof(f1166,plain,
( spl28_135
| ~ spl28_55
| ~ spl28_82 ),
inference(avatar_split_clause,[],[f789,f721,f601,f1163]) ).
fof(f1163,plain,
( spl28_135
<=> epsilon_transitive(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_135])]) ).
fof(f721,plain,
( spl28_82
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_82])]) ).
fof(f789,plain,
( epsilon_transitive(sK25)
| ~ spl28_55
| ~ spl28_82 ),
inference(resolution,[],[f722,f603]) ).
fof(f722,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_transitive(X0) )
| ~ spl28_82 ),
inference(avatar_component_clause,[],[f721]) ).
fof(f1161,plain,
( ~ spl28_1
| ~ spl28_103
| spl28_127 ),
inference(avatar_split_clause,[],[f1125,f1107,f886,f331]) ).
fof(f331,plain,
( spl28_1
<=> finite(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_1])]) ).
fof(f1107,plain,
( spl28_127
<=> finite(set_difference(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_127])]) ).
fof(f1125,plain,
( ~ finite(sK0)
| ~ spl28_103
| spl28_127 ),
inference(resolution,[],[f1109,f887]) ).
fof(f1109,plain,
( ~ finite(set_difference(sK0,sK1))
| spl28_127 ),
inference(avatar_component_clause,[],[f1107]) ).
fof(f1159,plain,
( spl28_134
| ~ spl28_31
| ~ spl28_82 ),
inference(avatar_split_clause,[],[f787,f721,f481,f1156]) ).
fof(f1156,plain,
( spl28_134
<=> epsilon_transitive(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_134])]) ).
fof(f787,plain,
( epsilon_transitive(sK15)
| ~ spl28_31
| ~ spl28_82 ),
inference(resolution,[],[f722,f483]) ).
fof(f1154,plain,
( spl28_133
| ~ spl28_12
| ~ spl28_82 ),
inference(avatar_split_clause,[],[f786,f721,f386,f1151]) ).
fof(f1151,plain,
( spl28_133
<=> epsilon_transitive(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_133])]) ).
fof(f786,plain,
( epsilon_transitive(sK8)
| ~ spl28_12
| ~ spl28_82 ),
inference(resolution,[],[f722,f388]) ).
fof(f1148,plain,
( spl28_132
| ~ spl28_61
| ~ spl28_81 ),
inference(avatar_split_clause,[],[f777,f717,f631,f1145]) ).
fof(f1145,plain,
( spl28_132
<=> relation(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_132])]) ).
fof(f631,plain,
( spl28_61
<=> empty(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_61])]) ).
fof(f717,plain,
( spl28_81
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_81])]) ).
fof(f777,plain,
( relation(sK27)
| ~ spl28_61
| ~ spl28_81 ),
inference(resolution,[],[f718,f633]) ).
fof(f633,plain,
( empty(sK27)
| ~ spl28_61 ),
inference(avatar_component_clause,[],[f631]) ).
fof(f718,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl28_81 ),
inference(avatar_component_clause,[],[f717]) ).
fof(f1143,plain,
( spl28_131
| ~ spl28_12
| ~ spl28_81 ),
inference(avatar_split_clause,[],[f773,f717,f386,f1140]) ).
fof(f1140,plain,
( spl28_131
<=> relation(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_131])]) ).
fof(f773,plain,
( relation(sK8)
| ~ spl28_12
| ~ spl28_81 ),
inference(resolution,[],[f718,f388]) ).
fof(f1137,plain,
( spl28_130
| ~ spl28_61
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f769,f713,f631,f1134]) ).
fof(f1134,plain,
( spl28_130
<=> function(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_130])]) ).
fof(f713,plain,
( spl28_80
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_80])]) ).
fof(f769,plain,
( function(sK27)
| ~ spl28_61
| ~ spl28_80 ),
inference(resolution,[],[f714,f633]) ).
fof(f714,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl28_80 ),
inference(avatar_component_clause,[],[f713]) ).
fof(f1131,plain,
( spl28_129
| ~ spl28_31
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f766,f713,f481,f1128]) ).
fof(f1128,plain,
( spl28_129
<=> function(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_129])]) ).
fof(f766,plain,
( function(sK15)
| ~ spl28_31
| ~ spl28_80 ),
inference(resolution,[],[f714,f483]) ).
fof(f1114,plain,
( ~ spl28_127
| ~ spl28_128
| spl28_3
| ~ spl28_121 ),
inference(avatar_split_clause,[],[f1073,f1038,f341,f1111,f1107]) ).
fof(f341,plain,
( spl28_3
<=> finite(set_union2(set_difference(sK0,sK1),set_difference(sK1,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_3])]) ).
fof(f1038,plain,
( spl28_121
<=> ! [X0,X1] :
( finite(set_union2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_121])]) ).
fof(f1073,plain,
( ~ finite(set_difference(sK1,sK0))
| ~ finite(set_difference(sK0,sK1))
| spl28_3
| ~ spl28_121 ),
inference(resolution,[],[f1039,f343]) ).
fof(f343,plain,
( ~ finite(set_union2(set_difference(sK0,sK1),set_difference(sK1,sK0)))
| spl28_3 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f1039,plain,
( ! [X0,X1] :
( finite(set_union2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) )
| ~ spl28_121 ),
inference(avatar_component_clause,[],[f1038]) ).
fof(f1105,plain,
spl28_126,
inference(avatar_split_clause,[],[f268,f1103]) ).
fof(f1103,plain,
( spl28_126
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_126])]) ).
fof(f268,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f134]) ).
fof(f134,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f1091,plain,
spl28_125,
inference(avatar_split_clause,[],[f269,f1089]) ).
fof(f1089,plain,
( spl28_125
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_125])]) ).
fof(f269,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f1053,plain,
spl28_124,
inference(avatar_split_clause,[],[f264,f1051]) ).
fof(f1051,plain,
( spl28_124
<=> ! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_124])]) ).
fof(f264,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f129]) ).
fof(f129,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(f1049,plain,
spl28_123,
inference(avatar_split_clause,[],[f263,f1047]) ).
fof(f1047,plain,
( spl28_123
<=> ! [X0,X1] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_123])]) ).
fof(f263,plain,
! [X0,X1] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0,X1] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f127]) ).
fof(f127,plain,
! [X0,X1] :
( relation(set_difference(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_difference(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_relat_1) ).
fof(f1045,plain,
( spl28_122
| ~ spl28_12
| ~ spl28_80 ),
inference(avatar_split_clause,[],[f765,f713,f386,f1042]) ).
fof(f1042,plain,
( spl28_122
<=> function(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_122])]) ).
fof(f765,plain,
( function(sK8)
| ~ spl28_12
| ~ spl28_80 ),
inference(resolution,[],[f714,f388]) ).
fof(f1040,plain,
spl28_121,
inference(avatar_split_clause,[],[f261,f1038]) ).
fof(f261,plain,
! [X0,X1] :
( finite(set_union2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0,X1] :
( finite(set_union2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(flattening,[],[f123]) ).
fof(f123,plain,
! [X0,X1] :
( finite(set_union2(X0,X1))
| ~ finite(X1)
| ~ finite(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
fof(f1036,plain,
spl28_120,
inference(avatar_split_clause,[],[f260,f1034]) ).
fof(f1034,plain,
( spl28_120
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_120])]) ).
fof(f260,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f121]) ).
fof(f121,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f1032,plain,
spl28_119,
inference(avatar_split_clause,[],[f216,f1030]) ).
fof(f1030,plain,
( spl28_119
<=> ! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_119])]) ).
fof(f216,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,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/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(f1020,plain,
( spl28_118
| ~ spl28_12
| ~ spl28_94
| ~ spl28_116 ),
inference(avatar_split_clause,[],[f960,f957,f837,f386,f1018]) ).
fof(f1018,plain,
( spl28_118
<=> ! [X0] : set_union2(set_difference(X0,sK8),sK8) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl28_118])]) ).
fof(f837,plain,
( spl28_94
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_94])]) ).
fof(f957,plain,
( spl28_116
<=> ! [X0] : set_union2(set_difference(X0,empty_set),empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl28_116])]) ).
fof(f960,plain,
( ! [X0] : set_union2(set_difference(X0,sK8),sK8) = X0
| ~ spl28_12
| ~ spl28_94
| ~ spl28_116 ),
inference(forward_demodulation,[],[f958,f864]) ).
fof(f864,plain,
( empty_set = sK8
| ~ spl28_12
| ~ spl28_94 ),
inference(resolution,[],[f838,f388]) ).
fof(f838,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl28_94 ),
inference(avatar_component_clause,[],[f837]) ).
fof(f958,plain,
( ! [X0] : set_union2(set_difference(X0,empty_set),empty_set) = X0
| ~ spl28_116 ),
inference(avatar_component_clause,[],[f957]) ).
fof(f972,plain,
( spl28_117
| ~ spl28_61
| ~ spl28_79 ),
inference(avatar_split_clause,[],[f761,f709,f631,f969]) ).
fof(f969,plain,
( spl28_117
<=> finite(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_117])]) ).
fof(f709,plain,
( spl28_79
<=> ! [X0] :
( finite(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_79])]) ).
fof(f761,plain,
( finite(sK27)
| ~ spl28_61
| ~ spl28_79 ),
inference(resolution,[],[f710,f633]) ).
fof(f710,plain,
( ! [X0] :
( ~ empty(X0)
| finite(X0) )
| ~ spl28_79 ),
inference(avatar_component_clause,[],[f709]) ).
fof(f959,plain,
spl28_116,
inference(avatar_split_clause,[],[f329,f957]) ).
fof(f329,plain,
! [X0] : set_union2(set_difference(X0,empty_set),empty_set) = X0,
inference(forward_demodulation,[],[f327,f207]) ).
fof(f207,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0] : empty_set = set_difference(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
fof(f327,plain,
! [X0] : set_union2(set_difference(X0,empty_set),set_difference(empty_set,X0)) = X0,
inference(definition_unfolding,[],[f208,f253]) ).
fof(f253,plain,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] : symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
fof(f208,plain,
! [X0] : symmetric_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0] : symmetric_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_boole) ).
fof(f955,plain,
spl28_115,
inference(avatar_split_clause,[],[f266,f953]) ).
fof(f953,plain,
( spl28_115
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_115])]) ).
fof(f266,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f951,plain,
spl28_114,
inference(avatar_split_clause,[],[f265,f949]) ).
fof(f949,plain,
( spl28_114
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_114])]) ).
fof(f265,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f64]) ).
fof(f64,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f947,plain,
spl28_113,
inference(avatar_split_clause,[],[f252,f945]) ).
fof(f945,plain,
( spl28_113
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_113])]) ).
fof(f252,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f943,plain,
spl28_112,
inference(avatar_split_clause,[],[f221,f941]) ).
fof(f941,plain,
( spl28_112
<=> ! [X0,X1] :
( ordinal(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_112])]) ).
fof(f221,plain,
! [X0,X1] :
( ordinal(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,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/sandbox2/benchmark/theBenchmark.p',cc1_arytm_3) ).
fof(f939,plain,
spl28_111,
inference(avatar_split_clause,[],[f220,f937]) ).
fof(f937,plain,
( spl28_111
<=> ! [X0,X1] :
( epsilon_connected(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_111])]) ).
fof(f220,plain,
! [X0,X1] :
( epsilon_connected(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f935,plain,
spl28_110,
inference(avatar_split_clause,[],[f219,f933]) ).
fof(f933,plain,
( spl28_110
<=> ! [X0,X1] :
( epsilon_transitive(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_110])]) ).
fof(f219,plain,
! [X0,X1] :
( epsilon_transitive(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f930,plain,
( spl28_109
| ~ spl28_55
| ~ spl28_79 ),
inference(avatar_split_clause,[],[f760,f709,f601,f927]) ).
fof(f927,plain,
( spl28_109
<=> finite(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_109])]) ).
fof(f760,plain,
( finite(sK25)
| ~ spl28_55
| ~ spl28_79 ),
inference(resolution,[],[f710,f603]) ).
fof(f925,plain,
spl28_108,
inference(avatar_split_clause,[],[f213,f923]) ).
fof(f923,plain,
( spl28_108
<=> ! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_108])]) ).
fof(f213,plain,
! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0] :
( ( finite(sK3(X0))
& ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f98,f141]) ).
fof(f141,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK3(X0))
& ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f98,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(f921,plain,
spl28_107,
inference(avatar_split_clause,[],[f211,f919]) ).
fof(f919,plain,
( spl28_107
<=> ! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_107])]) ).
fof(f211,plain,
! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0] :
( ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f97,f139]) ).
fof(f139,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f902,plain,
spl28_106,
inference(avatar_split_clause,[],[f259,f900]) ).
fof(f900,plain,
( spl28_106
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_106])]) ).
fof(f259,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f898,plain,
spl28_105,
inference(avatar_split_clause,[],[f258,f896]) ).
fof(f896,plain,
( spl28_105
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_105])]) ).
fof(f258,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,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/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f893,plain,
( spl28_104
| ~ spl28_50
| ~ spl28_79 ),
inference(avatar_split_clause,[],[f759,f709,f576,f890]) ).
fof(f890,plain,
( spl28_104
<=> finite(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_104])]) ).
fof(f576,plain,
( spl28_50
<=> empty(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_50])]) ).
fof(f759,plain,
( finite(sK24)
| ~ spl28_50
| ~ spl28_79 ),
inference(resolution,[],[f710,f578]) ).
fof(f578,plain,
( empty(sK24)
| ~ spl28_50 ),
inference(avatar_component_clause,[],[f576]) ).
fof(f888,plain,
spl28_103,
inference(avatar_split_clause,[],[f256,f886]) ).
fof(f256,plain,
! [X0,X1] :
( finite(set_difference(X0,X1))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( finite(set_difference(X0,X1))
| ~ finite(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( finite(X0)
=> finite(set_difference(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
fof(f884,plain,
spl28_102,
inference(avatar_split_clause,[],[f255,f882]) ).
fof(f882,plain,
( spl28_102
<=> ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_102])]) ).
fof(f255,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f880,plain,
spl28_101,
inference(avatar_split_clause,[],[f254,f878]) ).
fof(f878,plain,
( spl28_101
<=> ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_101])]) ).
fof(f254,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f876,plain,
spl28_100,
inference(avatar_split_clause,[],[f232,f874]) ).
fof(f874,plain,
( spl28_100
<=> ! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_100])]) ).
fof(f232,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f109]) ).
fof(f109,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/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f860,plain,
( spl28_99
| ~ spl28_31
| ~ spl28_79 ),
inference(avatar_split_clause,[],[f758,f709,f481,f857]) ).
fof(f857,plain,
( spl28_99
<=> finite(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_99])]) ).
fof(f758,plain,
( finite(sK15)
| ~ spl28_31
| ~ spl28_79 ),
inference(resolution,[],[f710,f483]) ).
fof(f855,plain,
spl28_98,
inference(avatar_split_clause,[],[f267,f853]) ).
fof(f853,plain,
( spl28_98
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_98])]) ).
fof(f267,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f851,plain,
spl28_97,
inference(avatar_split_clause,[],[f250,f849]) ).
fof(f849,plain,
( spl28_97
<=> ! [X0] : set_union2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl28_97])]) ).
fof(f250,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f847,plain,
spl28_96,
inference(avatar_split_clause,[],[f241,f845]) ).
fof(f845,plain,
( spl28_96
<=> ! [X0] : element(sK6(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_96])]) ).
fof(f241,plain,
! [X0] : element(sK6(X0),powerset(X0)),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( finite(sK6(X0))
& ordinal(sK6(X0))
& epsilon_connected(sK6(X0))
& epsilon_transitive(sK6(X0))
& function(sK6(X0))
& relation(sK6(X0))
& empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f92,f147]) ).
fof(f147,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK6(X0))
& ordinal(sK6(X0))
& epsilon_connected(sK6(X0))
& epsilon_transitive(sK6(X0))
& function(sK6(X0))
& relation(sK6(X0))
& empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f92,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,[],[f86]) ).
fof(f86,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,[],[f41]) ).
fof(f41,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/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).
fof(f843,plain,
spl28_95,
inference(avatar_split_clause,[],[f239,f841]) ).
fof(f841,plain,
( spl28_95
<=> ! [X0] : element(sK5(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_95])]) ).
fof(f239,plain,
! [X0] : element(sK5(X0),powerset(X0)),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0] :
( empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f46,f145]) ).
fof(f145,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f46,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f839,plain,
spl28_94,
inference(avatar_split_clause,[],[f225,f837]) ).
fof(f225,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f835,plain,
( spl28_93
| ~ spl28_12
| ~ spl28_79 ),
inference(avatar_split_clause,[],[f757,f709,f386,f832]) ).
fof(f832,plain,
( spl28_93
<=> finite(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_93])]) ).
fof(f757,plain,
( finite(sK8)
| ~ spl28_12
| ~ spl28_79 ),
inference(resolution,[],[f710,f388]) ).
fof(f830,plain,
spl28_92,
inference(avatar_split_clause,[],[f215,f828]) ).
fof(f828,plain,
( spl28_92
<=> ! [X0] :
( finite(sK3(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_92])]) ).
fof(f215,plain,
! [X0] :
( finite(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f826,plain,
spl28_91,
inference(avatar_split_clause,[],[f214,f824]) ).
fof(f824,plain,
( spl28_91
<=> ! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_91])]) ).
fof(f214,plain,
! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f822,plain,
spl28_90,
inference(avatar_split_clause,[],[f212,f820]) ).
fof(f820,plain,
( spl28_90
<=> ! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_90])]) ).
fof(f212,plain,
! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f818,plain,
spl28_89,
inference(avatar_split_clause,[],[f210,f816]) ).
fof(f816,plain,
( spl28_89
<=> ! [X0] : set_union2(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl28_89])]) ).
fof(f210,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(f814,plain,
spl28_88,
inference(avatar_split_clause,[],[f209,f812]) ).
fof(f812,plain,
( spl28_88
<=> ! [X0] : set_difference(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl28_88])]) ).
fof(f209,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(f810,plain,
spl28_87,
inference(avatar_split_clause,[],[f207,f808]) ).
fof(f808,plain,
( spl28_87
<=> ! [X0] : empty_set = set_difference(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_87])]) ).
fof(f782,plain,
( spl28_86
| ~ spl28_5
| ~ spl28_79 ),
inference(avatar_split_clause,[],[f754,f709,f351,f779]) ).
fof(f779,plain,
( spl28_86
<=> finite(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_86])]) ).
fof(f351,plain,
( spl28_5
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_5])]) ).
fof(f754,plain,
( finite(empty_set)
| ~ spl28_5
| ~ spl28_79 ),
inference(resolution,[],[f710,f353]) ).
fof(f353,plain,
( empty(empty_set)
| ~ spl28_5 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f735,plain,
spl28_85,
inference(avatar_split_clause,[],[f238,f733]) ).
fof(f733,plain,
( spl28_85
<=> ! [X0] : element(sK4(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_85])]) ).
fof(f238,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0] : element(sK4(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f16,f143]) ).
fof(f143,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f16,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f731,plain,
spl28_84,
inference(avatar_split_clause,[],[f228,f729]) ).
fof(f228,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,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/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f727,plain,
spl28_83,
inference(avatar_split_clause,[],[f227,f725]) ).
fof(f227,plain,
! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f723,plain,
spl28_82,
inference(avatar_split_clause,[],[f226,f721]) ).
fof(f226,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f719,plain,
spl28_81,
inference(avatar_split_clause,[],[f224,f717]) ).
fof(f224,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f715,plain,
spl28_80,
inference(avatar_split_clause,[],[f223,f713]) ).
fof(f223,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f711,plain,
spl28_79,
inference(avatar_split_clause,[],[f222,f709]) ).
fof(f222,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> finite(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
fof(f707,plain,
spl28_78,
inference(avatar_split_clause,[],[f218,f705]) ).
fof(f705,plain,
( spl28_78
<=> ! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_78])]) ).
fof(f218,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,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/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f703,plain,
spl28_77,
inference(avatar_split_clause,[],[f217,f701]) ).
fof(f701,plain,
( spl28_77
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_77])]) ).
fof(f217,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f699,plain,
spl28_76,
inference(avatar_split_clause,[],[f321,f696]) ).
fof(f696,plain,
( spl28_76
<=> element(sK27,positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_76])]) ).
fof(f321,plain,
element(sK27,positive_rationals),
inference(cnf_transformation,[],[f190]) ).
fof(f190,plain,
( ordinal(sK27)
& epsilon_connected(sK27)
& epsilon_transitive(sK27)
& empty(sK27)
& element(sK27,positive_rationals) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f91,f189]) ).
fof(f189,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& element(X0,positive_rationals) )
=> ( ordinal(sK27)
& epsilon_connected(sK27)
& epsilon_transitive(sK27)
& empty(sK27)
& element(sK27,positive_rationals) ) ),
introduced(choice_axiom,[]) ).
fof(f91,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& element(X0,positive_rationals) ),
inference(pure_predicate_removal,[],[f48]) ).
fof(f48,axiom,
? [X0] :
( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& element(X0,positive_rationals) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_arytm_3) ).
fof(f694,plain,
spl28_75,
inference(avatar_split_clause,[],[f316,f691]) ).
fof(f691,plain,
( spl28_75
<=> element(sK26,positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_75])]) ).
fof(f316,plain,
element(sK26,positive_rationals),
inference(cnf_transformation,[],[f188]) ).
fof(f188,plain,
( ordinal(sK26)
& epsilon_connected(sK26)
& epsilon_transitive(sK26)
& ~ empty(sK26)
& element(sK26,positive_rationals) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f40,f187]) ).
fof(f187,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(f40,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0)
& element(X0,positive_rationals) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_arytm_3) ).
fof(f689,plain,
spl28_74,
inference(avatar_split_clause,[],[f249,f687]) ).
fof(f687,plain,
( spl28_74
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_74])]) ).
fof(f249,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f56]) ).
fof(f56,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f685,plain,
spl28_73,
inference(avatar_split_clause,[],[f248,f683]) ).
fof(f683,plain,
( spl28_73
<=> ! [X0] : finite(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_73])]) ).
fof(f248,plain,
! [X0] : finite(sK6(X0)),
inference(cnf_transformation,[],[f148]) ).
fof(f681,plain,
spl28_72,
inference(avatar_split_clause,[],[f247,f679]) ).
fof(f679,plain,
( spl28_72
<=> ! [X0] : ordinal(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_72])]) ).
fof(f247,plain,
! [X0] : ordinal(sK6(X0)),
inference(cnf_transformation,[],[f148]) ).
fof(f677,plain,
spl28_71,
inference(avatar_split_clause,[],[f246,f675]) ).
fof(f675,plain,
( spl28_71
<=> ! [X0] : epsilon_connected(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_71])]) ).
fof(f246,plain,
! [X0] : epsilon_connected(sK6(X0)),
inference(cnf_transformation,[],[f148]) ).
fof(f673,plain,
spl28_70,
inference(avatar_split_clause,[],[f245,f671]) ).
fof(f671,plain,
( spl28_70
<=> ! [X0] : epsilon_transitive(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_70])]) ).
fof(f245,plain,
! [X0] : epsilon_transitive(sK6(X0)),
inference(cnf_transformation,[],[f148]) ).
fof(f669,plain,
spl28_69,
inference(avatar_split_clause,[],[f244,f667]) ).
fof(f667,plain,
( spl28_69
<=> ! [X0] : function(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_69])]) ).
fof(f244,plain,
! [X0] : function(sK6(X0)),
inference(cnf_transformation,[],[f148]) ).
fof(f665,plain,
spl28_68,
inference(avatar_split_clause,[],[f243,f663]) ).
fof(f663,plain,
( spl28_68
<=> ! [X0] : relation(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_68])]) ).
fof(f243,plain,
! [X0] : relation(sK6(X0)),
inference(cnf_transformation,[],[f148]) ).
fof(f661,plain,
spl28_67,
inference(avatar_split_clause,[],[f242,f659]) ).
fof(f659,plain,
( spl28_67
<=> ! [X0] : empty(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_67])]) ).
fof(f242,plain,
! [X0] : empty(sK6(X0)),
inference(cnf_transformation,[],[f148]) ).
fof(f657,plain,
spl28_66,
inference(avatar_split_clause,[],[f240,f655]) ).
fof(f655,plain,
( spl28_66
<=> ! [X0] : empty(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_66])]) ).
fof(f240,plain,
! [X0] : empty(sK5(X0)),
inference(cnf_transformation,[],[f146]) ).
fof(f653,plain,
spl28_65,
inference(avatar_split_clause,[],[f206,f651]) ).
fof(f651,plain,
( spl28_65
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_65])]) ).
fof(f206,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f649,plain,
spl28_64,
inference(avatar_split_clause,[],[f325,f646]) ).
fof(f646,plain,
( spl28_64
<=> ordinal(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_64])]) ).
fof(f325,plain,
ordinal(sK27),
inference(cnf_transformation,[],[f190]) ).
fof(f644,plain,
spl28_63,
inference(avatar_split_clause,[],[f324,f641]) ).
fof(f641,plain,
( spl28_63
<=> epsilon_connected(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_63])]) ).
fof(f324,plain,
epsilon_connected(sK27),
inference(cnf_transformation,[],[f190]) ).
fof(f639,plain,
spl28_62,
inference(avatar_split_clause,[],[f323,f636]) ).
fof(f636,plain,
( spl28_62
<=> epsilon_transitive(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_62])]) ).
fof(f323,plain,
epsilon_transitive(sK27),
inference(cnf_transformation,[],[f190]) ).
fof(f634,plain,
spl28_61,
inference(avatar_split_clause,[],[f322,f631]) ).
fof(f322,plain,
empty(sK27),
inference(cnf_transformation,[],[f190]) ).
fof(f629,plain,
spl28_60,
inference(avatar_split_clause,[],[f320,f626]) ).
fof(f626,plain,
( spl28_60
<=> ordinal(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_60])]) ).
fof(f320,plain,
ordinal(sK26),
inference(cnf_transformation,[],[f188]) ).
fof(f624,plain,
spl28_59,
inference(avatar_split_clause,[],[f319,f621]) ).
fof(f621,plain,
( spl28_59
<=> epsilon_connected(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_59])]) ).
fof(f319,plain,
epsilon_connected(sK26),
inference(cnf_transformation,[],[f188]) ).
fof(f619,plain,
spl28_58,
inference(avatar_split_clause,[],[f318,f616]) ).
fof(f616,plain,
( spl28_58
<=> epsilon_transitive(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_58])]) ).
fof(f318,plain,
epsilon_transitive(sK26),
inference(cnf_transformation,[],[f188]) ).
fof(f614,plain,
~ spl28_57,
inference(avatar_split_clause,[],[f317,f611]) ).
fof(f611,plain,
( spl28_57
<=> empty(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_57])]) ).
fof(f317,plain,
~ empty(sK26),
inference(cnf_transformation,[],[f188]) ).
fof(f609,plain,
spl28_56,
inference(avatar_split_clause,[],[f315,f606]) ).
fof(f606,plain,
( spl28_56
<=> function(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_56])]) ).
fof(f315,plain,
function(sK25),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
( function(sK25)
& empty(sK25)
& relation(sK25) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f42,f185]) ).
fof(f185,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK25)
& empty(sK25)
& relation(sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f42,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f604,plain,
spl28_55,
inference(avatar_split_clause,[],[f314,f601]) ).
fof(f314,plain,
empty(sK25),
inference(cnf_transformation,[],[f186]) ).
fof(f599,plain,
spl28_54,
inference(avatar_split_clause,[],[f313,f596]) ).
fof(f596,plain,
( spl28_54
<=> relation(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_54])]) ).
fof(f313,plain,
relation(sK25),
inference(cnf_transformation,[],[f186]) ).
fof(f594,plain,
spl28_53,
inference(avatar_split_clause,[],[f312,f591]) ).
fof(f591,plain,
( spl28_53
<=> ordinal(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_53])]) ).
fof(f312,plain,
ordinal(sK24),
inference(cnf_transformation,[],[f184]) ).
fof(f184,plain,
( ordinal(sK24)
& epsilon_connected(sK24)
& epsilon_transitive(sK24)
& empty(sK24)
& function(sK24)
& relation(sK24) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f89,f183]) ).
fof(f183,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(sK24)
& epsilon_connected(sK24)
& epsilon_transitive(sK24)
& empty(sK24)
& function(sK24)
& relation(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f43]) ).
fof(f43,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(f589,plain,
spl28_52,
inference(avatar_split_clause,[],[f311,f586]) ).
fof(f586,plain,
( spl28_52
<=> epsilon_connected(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_52])]) ).
fof(f311,plain,
epsilon_connected(sK24),
inference(cnf_transformation,[],[f184]) ).
fof(f584,plain,
spl28_51,
inference(avatar_split_clause,[],[f310,f581]) ).
fof(f581,plain,
( spl28_51
<=> epsilon_transitive(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_51])]) ).
fof(f310,plain,
epsilon_transitive(sK24),
inference(cnf_transformation,[],[f184]) ).
fof(f579,plain,
spl28_50,
inference(avatar_split_clause,[],[f309,f576]) ).
fof(f309,plain,
empty(sK24),
inference(cnf_transformation,[],[f184]) ).
fof(f574,plain,
spl28_49,
inference(avatar_split_clause,[],[f308,f571]) ).
fof(f571,plain,
( spl28_49
<=> function(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_49])]) ).
fof(f308,plain,
function(sK24),
inference(cnf_transformation,[],[f184]) ).
fof(f569,plain,
spl28_48,
inference(avatar_split_clause,[],[f307,f566]) ).
fof(f566,plain,
( spl28_48
<=> relation(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_48])]) ).
fof(f307,plain,
relation(sK24),
inference(cnf_transformation,[],[f184]) ).
fof(f564,plain,
spl28_47,
inference(avatar_split_clause,[],[f306,f561]) ).
fof(f561,plain,
( spl28_47
<=> function(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_47])]) ).
fof(f306,plain,
function(sK23),
inference(cnf_transformation,[],[f182]) ).
fof(f182,plain,
( function(sK23)
& relation(sK23) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f85,f181]) ).
fof(f181,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK23)
& relation(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f50]) ).
fof(f50,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f559,plain,
spl28_46,
inference(avatar_split_clause,[],[f305,f556]) ).
fof(f556,plain,
( spl28_46
<=> relation(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_46])]) ).
fof(f305,plain,
relation(sK23),
inference(cnf_transformation,[],[f182]) ).
fof(f554,plain,
spl28_45,
inference(avatar_split_clause,[],[f304,f551]) ).
fof(f551,plain,
( spl28_45
<=> function(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_45])]) ).
fof(f304,plain,
function(sK22),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
( function(sK22)
& relation(sK22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f78,f179]) ).
fof(f179,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK22)
& relation(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f76]) ).
fof(f76,plain,
? [X0] :
( transfinite_sequence(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f44]) ).
fof(f44,axiom,
? [X0] :
( ordinal_yielding(X0)
& transfinite_sequence(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal2) ).
fof(f549,plain,
spl28_44,
inference(avatar_split_clause,[],[f303,f546]) ).
fof(f546,plain,
( spl28_44
<=> relation(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_44])]) ).
fof(f303,plain,
relation(sK22),
inference(cnf_transformation,[],[f180]) ).
fof(f544,plain,
spl28_43,
inference(avatar_split_clause,[],[f302,f541]) ).
fof(f541,plain,
( spl28_43
<=> function(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_43])]) ).
fof(f302,plain,
function(sK21),
inference(cnf_transformation,[],[f178]) ).
fof(f178,plain,
( function(sK21)
& relation(sK21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f77,f177]) ).
fof(f177,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK21)
& relation(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f54]) ).
fof(f54,axiom,
? [X0] :
( transfinite_sequence(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_ordinal1) ).
fof(f539,plain,
spl28_42,
inference(avatar_split_clause,[],[f301,f536]) ).
fof(f536,plain,
( spl28_42
<=> relation(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_42])]) ).
fof(f301,plain,
relation(sK21),
inference(cnf_transformation,[],[f178]) ).
fof(f534,plain,
spl28_41,
inference(avatar_split_clause,[],[f300,f531]) ).
fof(f531,plain,
( spl28_41
<=> function(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_41])]) ).
fof(f300,plain,
function(sK20),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
( function(sK20)
& relation(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f80,f175]) ).
fof(f175,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK20)
& relation(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f33]) ).
fof(f33,axiom,
? [X0] :
( function_yielding(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funcop_1) ).
fof(f529,plain,
spl28_40,
inference(avatar_split_clause,[],[f299,f526]) ).
fof(f526,plain,
( spl28_40
<=> relation(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_40])]) ).
fof(f299,plain,
relation(sK20),
inference(cnf_transformation,[],[f176]) ).
fof(f524,plain,
spl28_39,
inference(avatar_split_clause,[],[f298,f521]) ).
fof(f521,plain,
( spl28_39
<=> function(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_39])]) ).
fof(f298,plain,
function(sK19),
inference(cnf_transformation,[],[f174]) ).
fof(f174,plain,
( function(sK19)
& relation(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f34,f173]) ).
fof(f173,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK19)
& relation(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f34,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f519,plain,
spl28_38,
inference(avatar_split_clause,[],[f297,f516]) ).
fof(f516,plain,
( spl28_38
<=> relation(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_38])]) ).
fof(f297,plain,
relation(sK19),
inference(cnf_transformation,[],[f174]) ).
fof(f514,plain,
spl28_37,
inference(avatar_split_clause,[],[f296,f511]) ).
fof(f511,plain,
( spl28_37
<=> function(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_37])]) ).
fof(f296,plain,
function(sK18),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
( function(sK18)
& relation(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f84,f171]) ).
fof(f171,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK18)
& relation(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f53]) ).
fof(f53,axiom,
? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(f509,plain,
spl28_36,
inference(avatar_split_clause,[],[f295,f506]) ).
fof(f506,plain,
( spl28_36
<=> relation(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_36])]) ).
fof(f295,plain,
relation(sK18),
inference(cnf_transformation,[],[f172]) ).
fof(f504,plain,
spl28_35,
inference(avatar_split_clause,[],[f294,f501]) ).
fof(f501,plain,
( spl28_35
<=> relation(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_35])]) ).
fof(f294,plain,
relation(sK17),
inference(cnf_transformation,[],[f170]) ).
fof(f170,plain,
relation(sK17),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f83,f169]) ).
fof(f169,plain,
( ? [X0] : relation(X0)
=> relation(sK17) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f52]) ).
fof(f52,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f499,plain,
spl28_34,
inference(avatar_split_clause,[],[f293,f496]) ).
fof(f496,plain,
( spl28_34
<=> function(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_34])]) ).
fof(f293,plain,
function(sK16),
inference(cnf_transformation,[],[f168]) ).
fof(f168,plain,
( function(sK16)
& relation(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f75,f167]) ).
fof(f167,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK16)
& relation(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f55]) ).
fof(f55,axiom,
? [X0] :
( function(X0)
& relation_non_empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_funct_1) ).
fof(f494,plain,
spl28_33,
inference(avatar_split_clause,[],[f292,f491]) ).
fof(f491,plain,
( spl28_33
<=> relation(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_33])]) ).
fof(f292,plain,
relation(sK16),
inference(cnf_transformation,[],[f168]) ).
fof(f489,plain,
spl28_32,
inference(avatar_split_clause,[],[f291,f486]) ).
fof(f486,plain,
( spl28_32
<=> relation(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_32])]) ).
fof(f291,plain,
relation(sK15),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
( relation(sK15)
& empty(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f37,f165]) ).
fof(f165,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK15)
& empty(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f37,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f484,plain,
spl28_31,
inference(avatar_split_clause,[],[f290,f481]) ).
fof(f290,plain,
empty(sK15),
inference(cnf_transformation,[],[f166]) ).
fof(f479,plain,
spl28_30,
inference(avatar_split_clause,[],[f289,f476]) ).
fof(f476,plain,
( spl28_30
<=> ordinal(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_30])]) ).
fof(f289,plain,
ordinal(sK14),
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
( ordinal(sK14)
& epsilon_connected(sK14)
& epsilon_transitive(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f79,f163]) ).
fof(f163,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK14)
& epsilon_connected(sK14)
& epsilon_transitive(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
inference(pure_predicate_removal,[],[f36]) ).
fof(f36,axiom,
? [X0] :
( being_limit_ordinal(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal2) ).
fof(f474,plain,
spl28_29,
inference(avatar_split_clause,[],[f288,f471]) ).
fof(f471,plain,
( spl28_29
<=> epsilon_connected(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_29])]) ).
fof(f288,plain,
epsilon_connected(sK14),
inference(cnf_transformation,[],[f164]) ).
fof(f469,plain,
spl28_28,
inference(avatar_split_clause,[],[f287,f466]) ).
fof(f466,plain,
( spl28_28
<=> epsilon_transitive(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_28])]) ).
fof(f287,plain,
epsilon_transitive(sK14),
inference(cnf_transformation,[],[f164]) ).
fof(f464,plain,
spl28_27,
inference(avatar_split_clause,[],[f286,f461]) ).
fof(f461,plain,
( spl28_27
<=> ordinal(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_27])]) ).
fof(f286,plain,
ordinal(sK13),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
( ordinal(sK13)
& epsilon_connected(sK13)
& epsilon_transitive(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f35,f161]) ).
fof(f161,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK13)
& epsilon_connected(sK13)
& epsilon_transitive(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f35,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f459,plain,
spl28_26,
inference(avatar_split_clause,[],[f285,f456]) ).
fof(f456,plain,
( spl28_26
<=> epsilon_connected(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_26])]) ).
fof(f285,plain,
epsilon_connected(sK13),
inference(cnf_transformation,[],[f162]) ).
fof(f454,plain,
spl28_25,
inference(avatar_split_clause,[],[f284,f451]) ).
fof(f451,plain,
( spl28_25
<=> epsilon_transitive(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_25])]) ).
fof(f284,plain,
epsilon_transitive(sK13),
inference(cnf_transformation,[],[f162]) ).
fof(f449,plain,
spl28_24,
inference(avatar_split_clause,[],[f283,f446]) ).
fof(f446,plain,
( spl28_24
<=> relation(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_24])]) ).
fof(f283,plain,
relation(sK12),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
( relation(sK12)
& ~ empty(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f45,f159]) ).
fof(f159,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK12)
& ~ empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f45,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f444,plain,
~ spl28_23,
inference(avatar_split_clause,[],[f282,f441]) ).
fof(f441,plain,
( spl28_23
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_23])]) ).
fof(f282,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f160]) ).
fof(f439,plain,
spl28_22,
inference(avatar_split_clause,[],[f281,f436]) ).
fof(f436,plain,
( spl28_22
<=> ordinal(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_22])]) ).
fof(f281,plain,
ordinal(sK11),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
( ordinal(sK11)
& epsilon_connected(sK11)
& epsilon_transitive(sK11)
& ~ empty(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f90,f157]) ).
fof(f157,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK11)
& epsilon_connected(sK11)
& epsilon_transitive(sK11)
& ~ empty(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
inference(pure_predicate_removal,[],[f31]) ).
fof(f31,axiom,
? [X0] :
( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(f434,plain,
spl28_21,
inference(avatar_split_clause,[],[f280,f431]) ).
fof(f431,plain,
( spl28_21
<=> epsilon_connected(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_21])]) ).
fof(f280,plain,
epsilon_connected(sK11),
inference(cnf_transformation,[],[f158]) ).
fof(f429,plain,
spl28_20,
inference(avatar_split_clause,[],[f279,f426]) ).
fof(f426,plain,
( spl28_20
<=> epsilon_transitive(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_20])]) ).
fof(f279,plain,
epsilon_transitive(sK11),
inference(cnf_transformation,[],[f158]) ).
fof(f424,plain,
~ spl28_19,
inference(avatar_split_clause,[],[f278,f421]) ).
fof(f421,plain,
( spl28_19
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_19])]) ).
fof(f278,plain,
~ empty(sK11),
inference(cnf_transformation,[],[f158]) ).
fof(f419,plain,
spl28_18,
inference(avatar_split_clause,[],[f277,f416]) ).
fof(f416,plain,
( spl28_18
<=> ordinal(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_18])]) ).
fof(f277,plain,
ordinal(sK10),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
( ordinal(sK10)
& epsilon_connected(sK10)
& epsilon_transitive(sK10)
& ~ empty(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f51,f155]) ).
fof(f155,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(f51,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f414,plain,
spl28_17,
inference(avatar_split_clause,[],[f276,f411]) ).
fof(f411,plain,
( spl28_17
<=> epsilon_connected(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_17])]) ).
fof(f276,plain,
epsilon_connected(sK10),
inference(cnf_transformation,[],[f156]) ).
fof(f409,plain,
spl28_16,
inference(avatar_split_clause,[],[f275,f406]) ).
fof(f406,plain,
( spl28_16
<=> epsilon_transitive(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_16])]) ).
fof(f275,plain,
epsilon_transitive(sK10),
inference(cnf_transformation,[],[f156]) ).
fof(f404,plain,
~ spl28_15,
inference(avatar_split_clause,[],[f274,f401]) ).
fof(f401,plain,
( spl28_15
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_15])]) ).
fof(f274,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f156]) ).
fof(f399,plain,
spl28_14,
inference(avatar_split_clause,[],[f273,f396]) ).
fof(f396,plain,
( spl28_14
<=> finite(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_14])]) ).
fof(f273,plain,
finite(sK9),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
( finite(sK9)
& ~ empty(sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f32,f153]) ).
fof(f153,plain,
( ? [X0] :
( finite(X0)
& ~ empty(X0) )
=> ( finite(sK9)
& ~ empty(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f32,axiom,
? [X0] :
( finite(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f394,plain,
~ spl28_13,
inference(avatar_split_clause,[],[f272,f391]) ).
fof(f391,plain,
( spl28_13
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_13])]) ).
fof(f272,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f154]) ).
fof(f389,plain,
spl28_12,
inference(avatar_split_clause,[],[f271,f386]) ).
fof(f271,plain,
empty(sK8),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
empty(sK8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f39,f151]) ).
fof(f151,plain,
( ? [X0] : empty(X0)
=> empty(sK8) ),
introduced(choice_axiom,[]) ).
fof(f39,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f384,plain,
~ spl28_11,
inference(avatar_split_clause,[],[f270,f381]) ).
fof(f381,plain,
( spl28_11
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_11])]) ).
fof(f270,plain,
~ empty(sK7),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
~ empty(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f47,f149]) ).
fof(f149,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK7) ),
introduced(choice_axiom,[]) ).
fof(f47,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f379,plain,
spl28_10,
inference(avatar_split_clause,[],[f205,f376]) ).
fof(f376,plain,
( spl28_10
<=> ordinal(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_10])]) ).
fof(f205,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f87]) ).
fof(f87,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,[],[f81]) ).
fof(f81,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,[],[f21]) ).
fof(f21,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/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f374,plain,
spl28_9,
inference(avatar_split_clause,[],[f204,f371]) ).
fof(f371,plain,
( spl28_9
<=> epsilon_connected(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_9])]) ).
fof(f204,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f87]) ).
fof(f369,plain,
spl28_8,
inference(avatar_split_clause,[],[f203,f366]) ).
fof(f366,plain,
( spl28_8
<=> epsilon_transitive(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_8])]) ).
fof(f203,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f87]) ).
fof(f364,plain,
spl28_7,
inference(avatar_split_clause,[],[f201,f361]) ).
fof(f361,plain,
( spl28_7
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_7])]) ).
fof(f201,plain,
function(empty_set),
inference(cnf_transformation,[],[f87]) ).
fof(f359,plain,
spl28_6,
inference(avatar_split_clause,[],[f197,f356]) ).
fof(f356,plain,
( spl28_6
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_6])]) ).
fof(f197,plain,
relation(empty_set),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f354,plain,
spl28_5,
inference(avatar_split_clause,[],[f195,f351]) ).
fof(f195,plain,
empty(empty_set),
inference(cnf_transformation,[],[f20]) ).
fof(f20,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f349,plain,
~ spl28_4,
inference(avatar_split_clause,[],[f194,f346]) ).
fof(f346,plain,
( spl28_4
<=> empty(positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_4])]) ).
fof(f194,plain,
~ empty(positive_rationals),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
~ empty(positive_rationals),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_arytm_3) ).
fof(f344,plain,
~ spl28_3,
inference(avatar_split_clause,[],[f326,f341]) ).
fof(f326,plain,
~ finite(set_union2(set_difference(sK0,sK1),set_difference(sK1,sK0))),
inference(definition_unfolding,[],[f193,f253]) ).
fof(f193,plain,
~ finite(symmetric_difference(sK0,sK1)),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
( ~ finite(symmetric_difference(sK0,sK1))
& finite(sK1)
& finite(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f96,f137]) ).
fof(f137,plain,
( ? [X0,X1] :
( ~ finite(symmetric_difference(X0,X1))
& finite(X1)
& finite(X0) )
=> ( ~ finite(symmetric_difference(sK0,sK1))
& finite(sK1)
& finite(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
? [X0,X1] :
( ~ finite(symmetric_difference(X0,X1))
& finite(X1)
& finite(X0) ),
inference(flattening,[],[f95]) ).
fof(f95,plain,
? [X0,X1] :
( ~ finite(symmetric_difference(X0,X1))
& finite(X1)
& finite(X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,negated_conjecture,
~ ! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite(symmetric_difference(X0,X1)) ),
inference(negated_conjecture,[],[f60]) ).
fof(f60,conjecture,
! [X0,X1] :
( ( finite(X1)
& finite(X0) )
=> finite(symmetric_difference(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finset_1) ).
fof(f339,plain,
spl28_2,
inference(avatar_split_clause,[],[f192,f336]) ).
fof(f192,plain,
finite(sK1),
inference(cnf_transformation,[],[f138]) ).
fof(f334,plain,
spl28_1,
inference(avatar_split_clause,[],[f191,f331]) ).
fof(f191,plain,
finite(sK0),
inference(cnf_transformation,[],[f138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU097+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Fri May 3 10:59:42 EDT 2024
% 0.15/0.34 % CPUTime :
% 0.15/0.34 % (2392)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.35 % (2400)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)
% 0.15/0.36 % (2398)WARNING: value z3 for option sas not known
% 0.15/0.36 % (2401)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)
% 0.15/0.36 % (2399)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.36 % (2396)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.36 % (2397)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.36 % (2400)First to succeed.
% 0.15/0.36 % (2398)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)
% 0.15/0.36 % (2402)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)
% 0.15/0.36 % (2400)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2392"
% 0.15/0.36 TRYING [1]
% 0.15/0.36 TRYING [2]
% 0.15/0.36 % (2400)Refutation found. Thanks to Tanya!
% 0.15/0.36 % SZS status Theorem for theBenchmark
% 0.15/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.37 % (2400)------------------------------
% 0.15/0.37 % (2400)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.37 % (2400)Termination reason: Refutation
% 0.15/0.37
% 0.15/0.37 % (2400)Memory used [KB]: 1209
% 0.15/0.37 % (2400)Time elapsed: 0.012 s
% 0.15/0.37 % (2400)Instructions burned: 28 (million)
% 0.15/0.37 % (2392)Success in time 0.023 s
%------------------------------------------------------------------------------