TSTP Solution File: SEU096+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU096+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 : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:22:07 EDT 2024
% Result : Theorem 0.20s 0.39s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 224
% Syntax : Number of formulae : 608 ( 209 unt; 0 def)
% Number of atoms : 1422 ( 23 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 1190 ( 376 ~; 312 |; 305 &)
% ( 144 <=>; 53 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 163 ( 161 usr; 144 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 25 con; 0-2 aty)
% Number of variables : 332 ( 258 !; 74 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1178,plain,
$false,
inference(avatar_sat_refutation,[],[f309,f314,f319,f324,f329,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,f638,f642,f646,f650,f654,f658,f662,f666,f670,f674,f679,f684,f688,f692,f696,f700,f704,f708,f712,f716,f720,f790,f794,f798,f803,f807,f811,f815,f819,f823,f827,f844,f856,f860,f864,f878,f883,f887,f891,f895,f899,f903,f907,f911,f915,f920,f975,f980,f985,f1008,f1022,f1026,f1040,f1045,f1053,f1058,f1064,f1070,f1075,f1081,f1086,f1092,f1098,f1103,f1109,f1115,f1120,f1126,f1135,f1140,f1145,f1150,f1155,f1160,f1165,f1171,f1176,f1177]) ).
fof(f1177,plain,
( ~ spl28_1
| ~ spl28_2
| ~ spl28_5
| spl28_3
| ~ spl28_117
| ~ spl28_135 ),
inference(avatar_split_clause,[],[f1136,f1132,f1020,f316,f326,f311,f306]) ).
fof(f306,plain,
( spl28_1
<=> relation(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_1])]) ).
fof(f311,plain,
( spl28_2
<=> function(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_2])]) ).
fof(f326,plain,
( spl28_5
<=> finite(relation_inverse_image(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_5])]) ).
fof(f316,plain,
( spl28_3
<=> finite(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_3])]) ).
fof(f1020,plain,
( spl28_117
<=> ! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_117])]) ).
fof(f1132,plain,
( spl28_135
<=> sK0 = relation_image(sK1,relation_inverse_image(sK1,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_135])]) ).
fof(f1136,plain,
( finite(sK0)
| ~ finite(relation_inverse_image(sK1,sK0))
| ~ function(sK1)
| ~ relation(sK1)
| ~ spl28_117
| ~ spl28_135 ),
inference(superposition,[],[f1021,f1134]) ).
fof(f1134,plain,
( sK0 = relation_image(sK1,relation_inverse_image(sK1,sK0))
| ~ spl28_135 ),
inference(avatar_component_clause,[],[f1132]) ).
fof(f1021,plain,
( ! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) )
| ~ spl28_117 ),
inference(avatar_component_clause,[],[f1020]) ).
fof(f1176,plain,
( spl28_143
| ~ spl28_14
| ~ spl28_33
| ~ spl28_92 ),
inference(avatar_split_clause,[],[f836,f805,f466,f371,f1173]) ).
fof(f1173,plain,
( spl28_143
<=> sK8 = sK15 ),
introduced(avatar_definition,[new_symbols(naming,[spl28_143])]) ).
fof(f371,plain,
( spl28_14
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_14])]) ).
fof(f466,plain,
( spl28_33
<=> empty(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_33])]) ).
fof(f805,plain,
( spl28_92
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_92])]) ).
fof(f836,plain,
( sK8 = sK15
| ~ spl28_14
| ~ spl28_33
| ~ spl28_92 ),
inference(forward_demodulation,[],[f832,f831]) ).
fof(f831,plain,
( empty_set = sK8
| ~ spl28_14
| ~ spl28_92 ),
inference(resolution,[],[f806,f373]) ).
fof(f373,plain,
( empty(sK8)
| ~ spl28_14 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f806,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl28_92 ),
inference(avatar_component_clause,[],[f805]) ).
fof(f832,plain,
( empty_set = sK15
| ~ spl28_33
| ~ spl28_92 ),
inference(resolution,[],[f806,f468]) ).
fof(f468,plain,
( empty(sK15)
| ~ spl28_33 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f1171,plain,
( spl28_142
| ~ spl28_14
| ~ spl28_92 ),
inference(avatar_split_clause,[],[f831,f805,f371,f1168]) ).
fof(f1168,plain,
( spl28_142
<=> empty_set = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl28_142])]) ).
fof(f1165,plain,
( spl28_141
| ~ spl28_68
| ~ spl28_86 ),
inference(avatar_split_clause,[],[f780,f714,f640,f1163]) ).
fof(f1163,plain,
( spl28_141
<=> ! [X0] : ordinal(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_141])]) ).
fof(f640,plain,
( spl28_68
<=> ! [X0] : empty(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_68])]) ).
fof(f714,plain,
( spl28_86
<=> ! [X0] :
( ordinal(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_86])]) ).
fof(f780,plain,
( ! [X0] : ordinal(sK5(X0))
| ~ spl28_68
| ~ spl28_86 ),
inference(resolution,[],[f715,f641]) ).
fof(f641,plain,
( ! [X0] : empty(sK5(X0))
| ~ spl28_68 ),
inference(avatar_component_clause,[],[f640]) ).
fof(f715,plain,
( ! [X0] :
( ~ empty(X0)
| ordinal(X0) )
| ~ spl28_86 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f1160,plain,
( spl28_140
| ~ spl28_68
| ~ spl28_85 ),
inference(avatar_split_clause,[],[f772,f710,f640,f1158]) ).
fof(f1158,plain,
( spl28_140
<=> ! [X0] : epsilon_connected(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_140])]) ).
fof(f710,plain,
( spl28_85
<=> ! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_85])]) ).
fof(f772,plain,
( ! [X0] : epsilon_connected(sK5(X0))
| ~ spl28_68
| ~ spl28_85 ),
inference(resolution,[],[f711,f641]) ).
fof(f711,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_connected(X0) )
| ~ spl28_85 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f1155,plain,
( spl28_139
| ~ spl28_68
| ~ spl28_84 ),
inference(avatar_split_clause,[],[f764,f706,f640,f1153]) ).
fof(f1153,plain,
( spl28_139
<=> ! [X0] : epsilon_transitive(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_139])]) ).
fof(f706,plain,
( spl28_84
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_84])]) ).
fof(f764,plain,
( ! [X0] : epsilon_transitive(sK5(X0))
| ~ spl28_68
| ~ spl28_84 ),
inference(resolution,[],[f707,f641]) ).
fof(f707,plain,
( ! [X0] :
( ~ empty(X0)
| epsilon_transitive(X0) )
| ~ spl28_84 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f1150,plain,
( spl28_138
| ~ spl28_68
| ~ spl28_83 ),
inference(avatar_split_clause,[],[f756,f702,f640,f1148]) ).
fof(f1148,plain,
( spl28_138
<=> ! [X0] : relation(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_138])]) ).
fof(f702,plain,
( spl28_83
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_83])]) ).
fof(f756,plain,
( ! [X0] : relation(sK5(X0))
| ~ spl28_68
| ~ spl28_83 ),
inference(resolution,[],[f703,f641]) ).
fof(f703,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl28_83 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f1145,plain,
( spl28_137
| ~ spl28_68
| ~ spl28_82 ),
inference(avatar_split_clause,[],[f748,f698,f640,f1143]) ).
fof(f1143,plain,
( spl28_137
<=> ! [X0] : function(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_137])]) ).
fof(f698,plain,
( spl28_82
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_82])]) ).
fof(f748,plain,
( ! [X0] : function(sK5(X0))
| ~ spl28_68
| ~ spl28_82 ),
inference(resolution,[],[f699,f641]) ).
fof(f699,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl28_82 ),
inference(avatar_component_clause,[],[f698]) ).
fof(f1140,plain,
( spl28_136
| ~ spl28_68
| ~ spl28_81 ),
inference(avatar_split_clause,[],[f740,f694,f640,f1138]) ).
fof(f1138,plain,
( spl28_136
<=> ! [X0] : finite(sK5(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_136])]) ).
fof(f694,plain,
( spl28_81
<=> ! [X0] :
( finite(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_81])]) ).
fof(f740,plain,
( ! [X0] : finite(sK5(X0))
| ~ spl28_68
| ~ spl28_81 ),
inference(resolution,[],[f695,f641]) ).
fof(f695,plain,
( ! [X0] :
( ~ empty(X0)
| finite(X0) )
| ~ spl28_81 ),
inference(avatar_component_clause,[],[f694]) ).
fof(f1135,plain,
( ~ spl28_1
| ~ spl28_2
| spl28_135
| ~ spl28_4
| ~ spl28_119 ),
inference(avatar_split_clause,[],[f1047,f1038,f321,f1132,f311,f306]) ).
fof(f321,plain,
( spl28_4
<=> subset(sK0,relation_rng(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_4])]) ).
fof(f1038,plain,
( spl28_119
<=> ! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_119])]) ).
fof(f1047,plain,
( sK0 = relation_image(sK1,relation_inverse_image(sK1,sK0))
| ~ function(sK1)
| ~ relation(sK1)
| ~ spl28_4
| ~ spl28_119 ),
inference(resolution,[],[f1039,f323]) ).
fof(f323,plain,
( subset(sK0,relation_rng(sK1))
| ~ spl28_4 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f1039,plain,
( ! [X0,X1] :
( ~ subset(X0,relation_rng(X1))
| relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ function(X1)
| ~ relation(X1) )
| ~ spl28_119 ),
inference(avatar_component_clause,[],[f1038]) ).
fof(f1126,plain,
( spl28_134
| ~ spl28_57
| ~ spl28_86 ),
inference(avatar_split_clause,[],[f785,f714,f586,f1123]) ).
fof(f1123,plain,
( spl28_134
<=> ordinal(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_134])]) ).
fof(f586,plain,
( spl28_57
<=> empty(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_57])]) ).
fof(f785,plain,
( ordinal(sK25)
| ~ spl28_57
| ~ spl28_86 ),
inference(resolution,[],[f715,f588]) ).
fof(f588,plain,
( empty(sK25)
| ~ spl28_57 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f1120,plain,
( spl28_133
| ~ spl28_33
| ~ spl28_86 ),
inference(avatar_split_clause,[],[f783,f714,f466,f1117]) ).
fof(f1117,plain,
( spl28_133
<=> ordinal(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_133])]) ).
fof(f783,plain,
( ordinal(sK15)
| ~ spl28_33
| ~ spl28_86 ),
inference(resolution,[],[f715,f468]) ).
fof(f1115,plain,
( spl28_132
| ~ spl28_14
| ~ spl28_86 ),
inference(avatar_split_clause,[],[f782,f714,f371,f1112]) ).
fof(f1112,plain,
( spl28_132
<=> ordinal(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_132])]) ).
fof(f782,plain,
( ordinal(sK8)
| ~ spl28_14
| ~ spl28_86 ),
inference(resolution,[],[f715,f373]) ).
fof(f1109,plain,
( spl28_131
| ~ spl28_57
| ~ spl28_85 ),
inference(avatar_split_clause,[],[f777,f710,f586,f1106]) ).
fof(f1106,plain,
( spl28_131
<=> epsilon_connected(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_131])]) ).
fof(f777,plain,
( epsilon_connected(sK25)
| ~ spl28_57
| ~ spl28_85 ),
inference(resolution,[],[f711,f588]) ).
fof(f1103,plain,
( spl28_130
| ~ spl28_33
| ~ spl28_85 ),
inference(avatar_split_clause,[],[f775,f710,f466,f1100]) ).
fof(f1100,plain,
( spl28_130
<=> epsilon_connected(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_130])]) ).
fof(f775,plain,
( epsilon_connected(sK15)
| ~ spl28_33
| ~ spl28_85 ),
inference(resolution,[],[f711,f468]) ).
fof(f1098,plain,
( spl28_129
| ~ spl28_14
| ~ spl28_85 ),
inference(avatar_split_clause,[],[f774,f710,f371,f1095]) ).
fof(f1095,plain,
( spl28_129
<=> epsilon_connected(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_129])]) ).
fof(f774,plain,
( epsilon_connected(sK8)
| ~ spl28_14
| ~ spl28_85 ),
inference(resolution,[],[f711,f373]) ).
fof(f1092,plain,
( spl28_128
| ~ spl28_57
| ~ spl28_84 ),
inference(avatar_split_clause,[],[f769,f706,f586,f1089]) ).
fof(f1089,plain,
( spl28_128
<=> epsilon_transitive(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_128])]) ).
fof(f769,plain,
( epsilon_transitive(sK25)
| ~ spl28_57
| ~ spl28_84 ),
inference(resolution,[],[f707,f588]) ).
fof(f1086,plain,
( spl28_127
| ~ spl28_33
| ~ spl28_84 ),
inference(avatar_split_clause,[],[f767,f706,f466,f1083]) ).
fof(f1083,plain,
( spl28_127
<=> epsilon_transitive(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_127])]) ).
fof(f767,plain,
( epsilon_transitive(sK15)
| ~ spl28_33
| ~ spl28_84 ),
inference(resolution,[],[f707,f468]) ).
fof(f1081,plain,
( spl28_126
| ~ spl28_14
| ~ spl28_84 ),
inference(avatar_split_clause,[],[f766,f706,f371,f1078]) ).
fof(f1078,plain,
( spl28_126
<=> epsilon_transitive(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_126])]) ).
fof(f766,plain,
( epsilon_transitive(sK8)
| ~ spl28_14
| ~ spl28_84 ),
inference(resolution,[],[f707,f373]) ).
fof(f1075,plain,
( spl28_125
| ~ spl28_63
| ~ spl28_83 ),
inference(avatar_split_clause,[],[f762,f702,f616,f1072]) ).
fof(f1072,plain,
( spl28_125
<=> relation(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_125])]) ).
fof(f616,plain,
( spl28_63
<=> empty(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_63])]) ).
fof(f762,plain,
( relation(sK27)
| ~ spl28_63
| ~ spl28_83 ),
inference(resolution,[],[f703,f618]) ).
fof(f618,plain,
( empty(sK27)
| ~ spl28_63 ),
inference(avatar_component_clause,[],[f616]) ).
fof(f1070,plain,
( spl28_124
| ~ spl28_14
| ~ spl28_83 ),
inference(avatar_split_clause,[],[f758,f702,f371,f1067]) ).
fof(f1067,plain,
( spl28_124
<=> relation(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_124])]) ).
fof(f758,plain,
( relation(sK8)
| ~ spl28_14
| ~ spl28_83 ),
inference(resolution,[],[f703,f373]) ).
fof(f1064,plain,
( spl28_123
| ~ spl28_63
| ~ spl28_82 ),
inference(avatar_split_clause,[],[f754,f698,f616,f1061]) ).
fof(f1061,plain,
( spl28_123
<=> function(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_123])]) ).
fof(f754,plain,
( function(sK27)
| ~ spl28_63
| ~ spl28_82 ),
inference(resolution,[],[f699,f618]) ).
fof(f1058,plain,
( spl28_122
| ~ spl28_33
| ~ spl28_82 ),
inference(avatar_split_clause,[],[f751,f698,f466,f1055]) ).
fof(f1055,plain,
( spl28_122
<=> function(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_122])]) ).
fof(f751,plain,
( function(sK15)
| ~ spl28_33
| ~ spl28_82 ),
inference(resolution,[],[f699,f468]) ).
fof(f1053,plain,
( spl28_121
| ~ spl28_14
| ~ spl28_82 ),
inference(avatar_split_clause,[],[f750,f698,f371,f1050]) ).
fof(f1050,plain,
( spl28_121
<=> function(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_121])]) ).
fof(f750,plain,
( function(sK8)
| ~ spl28_14
| ~ spl28_82 ),
inference(resolution,[],[f699,f373]) ).
fof(f1045,plain,
( spl28_120
| ~ spl28_63
| ~ spl28_81 ),
inference(avatar_split_clause,[],[f746,f694,f616,f1042]) ).
fof(f1042,plain,
( spl28_120
<=> finite(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_120])]) ).
fof(f746,plain,
( finite(sK27)
| ~ spl28_63
| ~ spl28_81 ),
inference(resolution,[],[f695,f618]) ).
fof(f1040,plain,
spl28_119,
inference(avatar_split_clause,[],[f242,f1038]) ).
fof(f242,plain,
! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( subset(X0,relation_rng(X1))
=> relation_image(X1,relation_inverse_image(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).
fof(f1026,plain,
spl28_118,
inference(avatar_split_clause,[],[f247,f1024]) ).
fof(f1024,plain,
( spl28_118
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_118])]) ).
fof(f247,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f119]) ).
fof(f119,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f1022,plain,
spl28_117,
inference(avatar_split_clause,[],[f240,f1020]) ).
fof(f240,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f111]) ).
fof(f111,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(f1008,plain,
spl28_116,
inference(avatar_split_clause,[],[f248,f1006]) ).
fof(f1006,plain,
( spl28_116
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_116])]) ).
fof(f248,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f985,plain,
spl28_115,
inference(avatar_split_clause,[],[f239,f983]) ).
fof(f983,plain,
( spl28_115
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_115])]) ).
fof(f239,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f980,plain,
( spl28_114
| ~ spl28_57
| ~ spl28_81 ),
inference(avatar_split_clause,[],[f745,f694,f586,f977]) ).
fof(f977,plain,
( spl28_114
<=> finite(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_114])]) ).
fof(f745,plain,
( finite(sK25)
| ~ spl28_57
| ~ spl28_81 ),
inference(resolution,[],[f695,f588]) ).
fof(f975,plain,
spl28_113,
inference(avatar_split_clause,[],[f200,f973]) ).
fof(f973,plain,
( spl28_113
<=> ! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_113])]) ).
fof(f200,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,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(f920,plain,
( spl28_112
| ~ spl28_52
| ~ spl28_81 ),
inference(avatar_split_clause,[],[f744,f694,f561,f917]) ).
fof(f917,plain,
( spl28_112
<=> finite(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_112])]) ).
fof(f561,plain,
( spl28_52
<=> empty(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_52])]) ).
fof(f744,plain,
( finite(sK24)
| ~ spl28_52
| ~ spl28_81 ),
inference(resolution,[],[f695,f563]) ).
fof(f563,plain,
( empty(sK24)
| ~ spl28_52 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f915,plain,
spl28_111,
inference(avatar_split_clause,[],[f245,f913]) ).
fof(f913,plain,
( spl28_111
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_111])]) ).
fof(f245,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f911,plain,
spl28_110,
inference(avatar_split_clause,[],[f244,f909]) ).
fof(f909,plain,
( spl28_110
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_110])]) ).
fof(f244,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f907,plain,
spl28_109,
inference(avatar_split_clause,[],[f243,f905]) ).
fof(f905,plain,
( spl28_109
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_109])]) ).
fof(f243,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f134]) ).
fof(f903,plain,
spl28_108,
inference(avatar_split_clause,[],[f218,f901]) ).
fof(f901,plain,
( spl28_108
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_108])]) ).
fof(f218,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f899,plain,
spl28_107,
inference(avatar_split_clause,[],[f205,f897]) ).
fof(f897,plain,
( spl28_107
<=> ! [X0,X1] :
( ordinal(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_107])]) ).
fof(f205,plain,
! [X0,X1] :
( ordinal(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,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(f895,plain,
spl28_106,
inference(avatar_split_clause,[],[f204,f893]) ).
fof(f893,plain,
( spl28_106
<=> ! [X0,X1] :
( epsilon_connected(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_106])]) ).
fof(f204,plain,
! [X0,X1] :
( epsilon_connected(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f891,plain,
spl28_105,
inference(avatar_split_clause,[],[f203,f889]) ).
fof(f889,plain,
( spl28_105
<=> ! [X0,X1] :
( epsilon_transitive(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_105])]) ).
fof(f203,plain,
! [X0,X1] :
( epsilon_transitive(X1)
| ~ element(X1,X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f887,plain,
spl28_104,
inference(avatar_split_clause,[],[f197,f885]) ).
fof(f885,plain,
( spl28_104
<=> ! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_104])]) ).
fof(f197,plain,
! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ( finite(sK3(X0))
& ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f87,f126]) ).
fof(f126,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(f87,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(f883,plain,
spl28_103,
inference(avatar_split_clause,[],[f195,f881]) ).
fof(f881,plain,
( spl28_103
<=> ! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_103])]) ).
fof(f195,plain,
! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f86,f124]) ).
fof(f124,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f878,plain,
( spl28_102
| ~ spl28_33
| ~ spl28_81 ),
inference(avatar_split_clause,[],[f743,f694,f466,f875]) ).
fof(f875,plain,
( spl28_102
<=> finite(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_102])]) ).
fof(f743,plain,
( finite(sK15)
| ~ spl28_33
| ~ spl28_81 ),
inference(resolution,[],[f695,f468]) ).
fof(f864,plain,
spl28_101,
inference(avatar_split_clause,[],[f238,f862]) ).
fof(f862,plain,
( spl28_101
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_101])]) ).
fof(f238,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f860,plain,
spl28_100,
inference(avatar_split_clause,[],[f237,f858]) ).
fof(f858,plain,
( spl28_100
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_100])]) ).
fof(f237,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,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(f856,plain,
spl28_99,
inference(avatar_split_clause,[],[f219,f854]) ).
fof(f854,plain,
( spl28_99
<=> ! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_99])]) ).
fof(f219,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f101]) ).
fof(f101,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(f844,plain,
( spl28_98
| ~ spl28_14
| ~ spl28_81 ),
inference(avatar_split_clause,[],[f742,f694,f371,f841]) ).
fof(f841,plain,
( spl28_98
<=> finite(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_98])]) ).
fof(f742,plain,
( finite(sK8)
| ~ spl28_14
| ~ spl28_81 ),
inference(resolution,[],[f695,f373]) ).
fof(f827,plain,
spl28_97,
inference(avatar_split_clause,[],[f246,f825]) ).
fof(f825,plain,
( spl28_97
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_97])]) ).
fof(f246,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f823,plain,
spl28_96,
inference(avatar_split_clause,[],[f228,f821]) ).
fof(f821,plain,
( spl28_96
<=> ! [X0] : element(sK6(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_96])]) ).
fof(f228,plain,
! [X0] : element(sK6(X0),powerset(X0)),
inference(cnf_transformation,[],[f133]) ).
fof(f133,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])],[f81,f132]) ).
fof(f132,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(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,[],[f77]) ).
fof(f77,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,[],[f34]) ).
fof(f34,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(f819,plain,
spl28_95,
inference(avatar_split_clause,[],[f226,f817]) ).
fof(f817,plain,
( spl28_95
<=> ! [X0] : element(sK5(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_95])]) ).
fof(f226,plain,
! [X0] : element(sK5(X0),powerset(X0)),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0] :
( empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f39,f130]) ).
fof(f130,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK5(X0))
& element(sK5(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f39,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f815,plain,
spl28_94,
inference(avatar_split_clause,[],[f214,f813]) ).
fof(f813,plain,
( spl28_94
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_94])]) ).
fof(f214,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f811,plain,
spl28_93,
inference(avatar_split_clause,[],[f213,f809]) ).
fof(f809,plain,
( spl28_93
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_93])]) ).
fof(f213,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f807,plain,
spl28_92,
inference(avatar_split_clause,[],[f209,f805]) ).
fof(f209,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f803,plain,
( spl28_91
| ~ spl28_7
| ~ spl28_81 ),
inference(avatar_split_clause,[],[f739,f694,f336,f800]) ).
fof(f800,plain,
( spl28_91
<=> finite(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_91])]) ).
fof(f336,plain,
( spl28_7
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_7])]) ).
fof(f739,plain,
( finite(empty_set)
| ~ spl28_7
| ~ spl28_81 ),
inference(resolution,[],[f695,f338]) ).
fof(f338,plain,
( empty(empty_set)
| ~ spl28_7 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f798,plain,
spl28_90,
inference(avatar_split_clause,[],[f199,f796]) ).
fof(f796,plain,
( spl28_90
<=> ! [X0] :
( finite(sK3(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_90])]) ).
fof(f199,plain,
! [X0] :
( finite(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f794,plain,
spl28_89,
inference(avatar_split_clause,[],[f198,f792]) ).
fof(f792,plain,
( spl28_89
<=> ! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_89])]) ).
fof(f198,plain,
! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f790,plain,
spl28_88,
inference(avatar_split_clause,[],[f196,f788]) ).
fof(f788,plain,
( spl28_88
<=> ! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_88])]) ).
fof(f196,plain,
! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f720,plain,
spl28_87,
inference(avatar_split_clause,[],[f225,f718]) ).
fof(f718,plain,
( spl28_87
<=> ! [X0] : element(sK4(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_87])]) ).
fof(f225,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0] : element(sK4(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f13,f128]) ).
fof(f128,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK4(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(f716,plain,
spl28_86,
inference(avatar_split_clause,[],[f212,f714]) ).
fof(f212,plain,
! [X0] :
( ordinal(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,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(f712,plain,
spl28_85,
inference(avatar_split_clause,[],[f211,f710]) ).
fof(f211,plain,
! [X0] :
( epsilon_connected(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f708,plain,
spl28_84,
inference(avatar_split_clause,[],[f210,f706]) ).
fof(f210,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f704,plain,
spl28_83,
inference(avatar_split_clause,[],[f208,f702]) ).
fof(f208,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,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(f700,plain,
spl28_82,
inference(avatar_split_clause,[],[f207,f698]) ).
fof(f207,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,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(f696,plain,
spl28_81,
inference(avatar_split_clause,[],[f206,f694]) ).
fof(f206,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,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(f692,plain,
spl28_80,
inference(avatar_split_clause,[],[f202,f690]) ).
fof(f690,plain,
( spl28_80
<=> ! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_80])]) ).
fof(f202,plain,
! [X0] :
( epsilon_connected(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,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(f688,plain,
spl28_79,
inference(avatar_split_clause,[],[f201,f686]) ).
fof(f686,plain,
( spl28_79
<=> ! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_79])]) ).
fof(f201,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f684,plain,
spl28_78,
inference(avatar_split_clause,[],[f300,f681]) ).
fof(f681,plain,
( spl28_78
<=> element(sK27,positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_78])]) ).
fof(f300,plain,
element(sK27,positive_rationals),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
( ordinal(sK27)
& epsilon_connected(sK27)
& epsilon_transitive(sK27)
& empty(sK27)
& element(sK27,positive_rationals) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f79,f175]) ).
fof(f175,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(f79,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& element(X0,positive_rationals) ),
inference(pure_predicate_removal,[],[f41]) ).
fof(f41,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(f679,plain,
spl28_77,
inference(avatar_split_clause,[],[f295,f676]) ).
fof(f676,plain,
( spl28_77
<=> element(sK26,positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_77])]) ).
fof(f295,plain,
element(sK26,positive_rationals),
inference(cnf_transformation,[],[f174]) ).
fof(f174,plain,
( ordinal(sK26)
& epsilon_connected(sK26)
& epsilon_transitive(sK26)
& ~ empty(sK26)
& element(sK26,positive_rationals) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f33,f173]) ).
fof(f173,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(f33,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(f674,plain,
spl28_76,
inference(avatar_split_clause,[],[f236,f672]) ).
fof(f672,plain,
( spl28_76
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_76])]) ).
fof(f236,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f670,plain,
spl28_75,
inference(avatar_split_clause,[],[f235,f668]) ).
fof(f668,plain,
( spl28_75
<=> ! [X0] : finite(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_75])]) ).
fof(f235,plain,
! [X0] : finite(sK6(X0)),
inference(cnf_transformation,[],[f133]) ).
fof(f666,plain,
spl28_74,
inference(avatar_split_clause,[],[f234,f664]) ).
fof(f664,plain,
( spl28_74
<=> ! [X0] : ordinal(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_74])]) ).
fof(f234,plain,
! [X0] : ordinal(sK6(X0)),
inference(cnf_transformation,[],[f133]) ).
fof(f662,plain,
spl28_73,
inference(avatar_split_clause,[],[f233,f660]) ).
fof(f660,plain,
( spl28_73
<=> ! [X0] : epsilon_connected(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_73])]) ).
fof(f233,plain,
! [X0] : epsilon_connected(sK6(X0)),
inference(cnf_transformation,[],[f133]) ).
fof(f658,plain,
spl28_72,
inference(avatar_split_clause,[],[f232,f656]) ).
fof(f656,plain,
( spl28_72
<=> ! [X0] : epsilon_transitive(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_72])]) ).
fof(f232,plain,
! [X0] : epsilon_transitive(sK6(X0)),
inference(cnf_transformation,[],[f133]) ).
fof(f654,plain,
spl28_71,
inference(avatar_split_clause,[],[f231,f652]) ).
fof(f652,plain,
( spl28_71
<=> ! [X0] : function(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_71])]) ).
fof(f231,plain,
! [X0] : function(sK6(X0)),
inference(cnf_transformation,[],[f133]) ).
fof(f650,plain,
spl28_70,
inference(avatar_split_clause,[],[f230,f648]) ).
fof(f648,plain,
( spl28_70
<=> ! [X0] : relation(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_70])]) ).
fof(f230,plain,
! [X0] : relation(sK6(X0)),
inference(cnf_transformation,[],[f133]) ).
fof(f646,plain,
spl28_69,
inference(avatar_split_clause,[],[f229,f644]) ).
fof(f644,plain,
( spl28_69
<=> ! [X0] : empty(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_69])]) ).
fof(f229,plain,
! [X0] : empty(sK6(X0)),
inference(cnf_transformation,[],[f133]) ).
fof(f642,plain,
spl28_68,
inference(avatar_split_clause,[],[f227,f640]) ).
fof(f227,plain,
! [X0] : empty(sK5(X0)),
inference(cnf_transformation,[],[f131]) ).
fof(f638,plain,
spl28_67,
inference(avatar_split_clause,[],[f194,f636]) ).
fof(f636,plain,
( spl28_67
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_67])]) ).
fof(f194,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(f634,plain,
spl28_66,
inference(avatar_split_clause,[],[f304,f631]) ).
fof(f631,plain,
( spl28_66
<=> ordinal(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_66])]) ).
fof(f304,plain,
ordinal(sK27),
inference(cnf_transformation,[],[f176]) ).
fof(f629,plain,
spl28_65,
inference(avatar_split_clause,[],[f303,f626]) ).
fof(f626,plain,
( spl28_65
<=> epsilon_connected(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_65])]) ).
fof(f303,plain,
epsilon_connected(sK27),
inference(cnf_transformation,[],[f176]) ).
fof(f624,plain,
spl28_64,
inference(avatar_split_clause,[],[f302,f621]) ).
fof(f621,plain,
( spl28_64
<=> epsilon_transitive(sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_64])]) ).
fof(f302,plain,
epsilon_transitive(sK27),
inference(cnf_transformation,[],[f176]) ).
fof(f619,plain,
spl28_63,
inference(avatar_split_clause,[],[f301,f616]) ).
fof(f301,plain,
empty(sK27),
inference(cnf_transformation,[],[f176]) ).
fof(f614,plain,
spl28_62,
inference(avatar_split_clause,[],[f299,f611]) ).
fof(f611,plain,
( spl28_62
<=> ordinal(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_62])]) ).
fof(f299,plain,
ordinal(sK26),
inference(cnf_transformation,[],[f174]) ).
fof(f609,plain,
spl28_61,
inference(avatar_split_clause,[],[f298,f606]) ).
fof(f606,plain,
( spl28_61
<=> epsilon_connected(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_61])]) ).
fof(f298,plain,
epsilon_connected(sK26),
inference(cnf_transformation,[],[f174]) ).
fof(f604,plain,
spl28_60,
inference(avatar_split_clause,[],[f297,f601]) ).
fof(f601,plain,
( spl28_60
<=> epsilon_transitive(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_60])]) ).
fof(f297,plain,
epsilon_transitive(sK26),
inference(cnf_transformation,[],[f174]) ).
fof(f599,plain,
~ spl28_59,
inference(avatar_split_clause,[],[f296,f596]) ).
fof(f596,plain,
( spl28_59
<=> empty(sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_59])]) ).
fof(f296,plain,
~ empty(sK26),
inference(cnf_transformation,[],[f174]) ).
fof(f594,plain,
spl28_58,
inference(avatar_split_clause,[],[f294,f591]) ).
fof(f591,plain,
( spl28_58
<=> function(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_58])]) ).
fof(f294,plain,
function(sK25),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
( function(sK25)
& empty(sK25)
& relation(sK25) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f35,f171]) ).
fof(f171,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK25)
& empty(sK25)
& relation(sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f35,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f589,plain,
spl28_57,
inference(avatar_split_clause,[],[f293,f586]) ).
fof(f293,plain,
empty(sK25),
inference(cnf_transformation,[],[f172]) ).
fof(f584,plain,
spl28_56,
inference(avatar_split_clause,[],[f292,f581]) ).
fof(f581,plain,
( spl28_56
<=> relation(sK25) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_56])]) ).
fof(f292,plain,
relation(sK25),
inference(cnf_transformation,[],[f172]) ).
fof(f579,plain,
spl28_55,
inference(avatar_split_clause,[],[f291,f576]) ).
fof(f576,plain,
( spl28_55
<=> ordinal(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_55])]) ).
fof(f291,plain,
ordinal(sK24),
inference(cnf_transformation,[],[f170]) ).
fof(f170,plain,
( ordinal(sK24)
& epsilon_connected(sK24)
& epsilon_transitive(sK24)
& empty(sK24)
& function(sK24)
& relation(sK24) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f74,f169]) ).
fof(f169,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(f74,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f36]) ).
fof(f36,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(f574,plain,
spl28_54,
inference(avatar_split_clause,[],[f290,f571]) ).
fof(f571,plain,
( spl28_54
<=> epsilon_connected(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_54])]) ).
fof(f290,plain,
epsilon_connected(sK24),
inference(cnf_transformation,[],[f170]) ).
fof(f569,plain,
spl28_53,
inference(avatar_split_clause,[],[f289,f566]) ).
fof(f566,plain,
( spl28_53
<=> epsilon_transitive(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_53])]) ).
fof(f289,plain,
epsilon_transitive(sK24),
inference(cnf_transformation,[],[f170]) ).
fof(f564,plain,
spl28_52,
inference(avatar_split_clause,[],[f288,f561]) ).
fof(f288,plain,
empty(sK24),
inference(cnf_transformation,[],[f170]) ).
fof(f559,plain,
spl28_51,
inference(avatar_split_clause,[],[f287,f556]) ).
fof(f556,plain,
( spl28_51
<=> function(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_51])]) ).
fof(f287,plain,
function(sK24),
inference(cnf_transformation,[],[f170]) ).
fof(f554,plain,
spl28_50,
inference(avatar_split_clause,[],[f286,f551]) ).
fof(f551,plain,
( spl28_50
<=> relation(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_50])]) ).
fof(f286,plain,
relation(sK24),
inference(cnf_transformation,[],[f170]) ).
fof(f549,plain,
spl28_49,
inference(avatar_split_clause,[],[f285,f546]) ).
fof(f546,plain,
( spl28_49
<=> function(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_49])]) ).
fof(f285,plain,
function(sK23),
inference(cnf_transformation,[],[f168]) ).
fof(f168,plain,
( function(sK23)
& relation(sK23) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f78,f167]) ).
fof(f167,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK23)
& relation(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f43]) ).
fof(f43,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f544,plain,
spl28_48,
inference(avatar_split_clause,[],[f284,f541]) ).
fof(f541,plain,
( spl28_48
<=> relation(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_48])]) ).
fof(f284,plain,
relation(sK23),
inference(cnf_transformation,[],[f168]) ).
fof(f539,plain,
spl28_47,
inference(avatar_split_clause,[],[f283,f536]) ).
fof(f536,plain,
( spl28_47
<=> function(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_47])]) ).
fof(f283,plain,
function(sK22),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
( function(sK22)
& relation(sK22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f65,f165]) ).
fof(f165,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK22)
& relation(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f63]) ).
fof(f63,plain,
? [X0] :
( transfinite_sequence(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f37]) ).
fof(f37,axiom,
? [X0] :
( ordinal_yielding(X0)
& transfinite_sequence(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal2) ).
fof(f534,plain,
spl28_46,
inference(avatar_split_clause,[],[f282,f531]) ).
fof(f531,plain,
( spl28_46
<=> relation(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_46])]) ).
fof(f282,plain,
relation(sK22),
inference(cnf_transformation,[],[f166]) ).
fof(f529,plain,
spl28_45,
inference(avatar_split_clause,[],[f281,f526]) ).
fof(f526,plain,
( spl28_45
<=> function(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_45])]) ).
fof(f281,plain,
function(sK21),
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
( function(sK21)
& relation(sK21) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f64,f163]) ).
fof(f163,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK21)
& relation(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f47]) ).
fof(f47,axiom,
? [X0] :
( transfinite_sequence(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_ordinal1) ).
fof(f524,plain,
spl28_44,
inference(avatar_split_clause,[],[f280,f521]) ).
fof(f521,plain,
( spl28_44
<=> relation(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_44])]) ).
fof(f280,plain,
relation(sK21),
inference(cnf_transformation,[],[f164]) ).
fof(f519,plain,
spl28_43,
inference(avatar_split_clause,[],[f279,f516]) ).
fof(f516,plain,
( spl28_43
<=> function(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_43])]) ).
fof(f279,plain,
function(sK20),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
( function(sK20)
& relation(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f67,f161]) ).
fof(f161,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK20)
& relation(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f26]) ).
fof(f26,axiom,
? [X0] :
( function_yielding(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funcop_1) ).
fof(f514,plain,
spl28_42,
inference(avatar_split_clause,[],[f278,f511]) ).
fof(f511,plain,
( spl28_42
<=> relation(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_42])]) ).
fof(f278,plain,
relation(sK20),
inference(cnf_transformation,[],[f162]) ).
fof(f509,plain,
spl28_41,
inference(avatar_split_clause,[],[f277,f506]) ).
fof(f506,plain,
( spl28_41
<=> function(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_41])]) ).
fof(f277,plain,
function(sK19),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
( function(sK19)
& relation(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f27,f159]) ).
fof(f159,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK19)
& relation(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f504,plain,
spl28_40,
inference(avatar_split_clause,[],[f276,f501]) ).
fof(f501,plain,
( spl28_40
<=> relation(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_40])]) ).
fof(f276,plain,
relation(sK19),
inference(cnf_transformation,[],[f160]) ).
fof(f499,plain,
spl28_39,
inference(avatar_split_clause,[],[f275,f496]) ).
fof(f496,plain,
( spl28_39
<=> function(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_39])]) ).
fof(f275,plain,
function(sK18),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
( function(sK18)
& relation(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f70,f157]) ).
fof(f157,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK18)
& relation(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f46]) ).
fof(f46,axiom,
? [X0] :
( function(X0)
& relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(f494,plain,
spl28_38,
inference(avatar_split_clause,[],[f274,f491]) ).
fof(f491,plain,
( spl28_38
<=> relation(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_38])]) ).
fof(f274,plain,
relation(sK18),
inference(cnf_transformation,[],[f158]) ).
fof(f489,plain,
spl28_37,
inference(avatar_split_clause,[],[f273,f486]) ).
fof(f486,plain,
( spl28_37
<=> relation(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_37])]) ).
fof(f273,plain,
relation(sK17),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
relation(sK17),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f72,f155]) ).
fof(f155,plain,
( ? [X0] : relation(X0)
=> relation(sK17) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f45]) ).
fof(f45,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f484,plain,
spl28_36,
inference(avatar_split_clause,[],[f272,f481]) ).
fof(f481,plain,
( spl28_36
<=> function(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_36])]) ).
fof(f272,plain,
function(sK16),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
( function(sK16)
& relation(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f69,f153]) ).
fof(f153,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK16)
& relation(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f48]) ).
fof(f48,axiom,
? [X0] :
( function(X0)
& relation_non_empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_funct_1) ).
fof(f479,plain,
spl28_35,
inference(avatar_split_clause,[],[f271,f476]) ).
fof(f476,plain,
( spl28_35
<=> relation(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_35])]) ).
fof(f271,plain,
relation(sK16),
inference(cnf_transformation,[],[f154]) ).
fof(f474,plain,
spl28_34,
inference(avatar_split_clause,[],[f270,f471]) ).
fof(f471,plain,
( spl28_34
<=> relation(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_34])]) ).
fof(f270,plain,
relation(sK15),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
( relation(sK15)
& empty(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f30,f151]) ).
fof(f151,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK15)
& empty(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f30,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f469,plain,
spl28_33,
inference(avatar_split_clause,[],[f269,f466]) ).
fof(f269,plain,
empty(sK15),
inference(cnf_transformation,[],[f152]) ).
fof(f464,plain,
spl28_32,
inference(avatar_split_clause,[],[f268,f461]) ).
fof(f461,plain,
( spl28_32
<=> ordinal(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_32])]) ).
fof(f268,plain,
ordinal(sK14),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
( ordinal(sK14)
& epsilon_connected(sK14)
& epsilon_transitive(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f66,f149]) ).
fof(f149,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK14)
& epsilon_connected(sK14)
& epsilon_transitive(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
inference(pure_predicate_removal,[],[f29]) ).
fof(f29,axiom,
? [X0] :
( being_limit_ordinal(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal2) ).
fof(f459,plain,
spl28_31,
inference(avatar_split_clause,[],[f267,f456]) ).
fof(f456,plain,
( spl28_31
<=> epsilon_connected(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_31])]) ).
fof(f267,plain,
epsilon_connected(sK14),
inference(cnf_transformation,[],[f150]) ).
fof(f454,plain,
spl28_30,
inference(avatar_split_clause,[],[f266,f451]) ).
fof(f451,plain,
( spl28_30
<=> epsilon_transitive(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_30])]) ).
fof(f266,plain,
epsilon_transitive(sK14),
inference(cnf_transformation,[],[f150]) ).
fof(f449,plain,
spl28_29,
inference(avatar_split_clause,[],[f265,f446]) ).
fof(f446,plain,
( spl28_29
<=> ordinal(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_29])]) ).
fof(f265,plain,
ordinal(sK13),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
( ordinal(sK13)
& epsilon_connected(sK13)
& epsilon_transitive(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f28,f147]) ).
fof(f147,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK13)
& epsilon_connected(sK13)
& epsilon_transitive(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f444,plain,
spl28_28,
inference(avatar_split_clause,[],[f264,f441]) ).
fof(f441,plain,
( spl28_28
<=> epsilon_connected(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_28])]) ).
fof(f264,plain,
epsilon_connected(sK13),
inference(cnf_transformation,[],[f148]) ).
fof(f439,plain,
spl28_27,
inference(avatar_split_clause,[],[f263,f436]) ).
fof(f436,plain,
( spl28_27
<=> epsilon_transitive(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_27])]) ).
fof(f263,plain,
epsilon_transitive(sK13),
inference(cnf_transformation,[],[f148]) ).
fof(f434,plain,
spl28_26,
inference(avatar_split_clause,[],[f262,f431]) ).
fof(f431,plain,
( spl28_26
<=> relation(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_26])]) ).
fof(f262,plain,
relation(sK12),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
( relation(sK12)
& ~ empty(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f38,f145]) ).
fof(f145,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK12)
& ~ empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f38,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f429,plain,
~ spl28_25,
inference(avatar_split_clause,[],[f261,f426]) ).
fof(f426,plain,
( spl28_25
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_25])]) ).
fof(f261,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f146]) ).
fof(f424,plain,
spl28_24,
inference(avatar_split_clause,[],[f260,f421]) ).
fof(f421,plain,
( spl28_24
<=> ordinal(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_24])]) ).
fof(f260,plain,
ordinal(sK11),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
( ordinal(sK11)
& epsilon_connected(sK11)
& epsilon_transitive(sK11)
& ~ empty(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f82,f143]) ).
fof(f143,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(f82,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
inference(pure_predicate_removal,[],[f24]) ).
fof(f24,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(f419,plain,
spl28_23,
inference(avatar_split_clause,[],[f259,f416]) ).
fof(f416,plain,
( spl28_23
<=> epsilon_connected(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_23])]) ).
fof(f259,plain,
epsilon_connected(sK11),
inference(cnf_transformation,[],[f144]) ).
fof(f414,plain,
spl28_22,
inference(avatar_split_clause,[],[f258,f411]) ).
fof(f411,plain,
( spl28_22
<=> epsilon_transitive(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_22])]) ).
fof(f258,plain,
epsilon_transitive(sK11),
inference(cnf_transformation,[],[f144]) ).
fof(f409,plain,
~ spl28_21,
inference(avatar_split_clause,[],[f257,f406]) ).
fof(f406,plain,
( spl28_21
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_21])]) ).
fof(f257,plain,
~ empty(sK11),
inference(cnf_transformation,[],[f144]) ).
fof(f404,plain,
spl28_20,
inference(avatar_split_clause,[],[f256,f401]) ).
fof(f401,plain,
( spl28_20
<=> ordinal(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_20])]) ).
fof(f256,plain,
ordinal(sK10),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
( ordinal(sK10)
& epsilon_connected(sK10)
& epsilon_transitive(sK10)
& ~ empty(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f44,f141]) ).
fof(f141,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(f44,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f399,plain,
spl28_19,
inference(avatar_split_clause,[],[f255,f396]) ).
fof(f396,plain,
( spl28_19
<=> epsilon_connected(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_19])]) ).
fof(f255,plain,
epsilon_connected(sK10),
inference(cnf_transformation,[],[f142]) ).
fof(f394,plain,
spl28_18,
inference(avatar_split_clause,[],[f254,f391]) ).
fof(f391,plain,
( spl28_18
<=> epsilon_transitive(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_18])]) ).
fof(f254,plain,
epsilon_transitive(sK10),
inference(cnf_transformation,[],[f142]) ).
fof(f389,plain,
~ spl28_17,
inference(avatar_split_clause,[],[f253,f386]) ).
fof(f386,plain,
( spl28_17
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_17])]) ).
fof(f253,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f142]) ).
fof(f384,plain,
spl28_16,
inference(avatar_split_clause,[],[f252,f381]) ).
fof(f381,plain,
( spl28_16
<=> finite(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_16])]) ).
fof(f252,plain,
finite(sK9),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
( finite(sK9)
& ~ empty(sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f25,f139]) ).
fof(f139,plain,
( ? [X0] :
( finite(X0)
& ~ empty(X0) )
=> ( finite(sK9)
& ~ empty(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
? [X0] :
( finite(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f379,plain,
~ spl28_15,
inference(avatar_split_clause,[],[f251,f376]) ).
fof(f376,plain,
( spl28_15
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_15])]) ).
fof(f251,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f140]) ).
fof(f374,plain,
spl28_14,
inference(avatar_split_clause,[],[f250,f371]) ).
fof(f250,plain,
empty(sK8),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
empty(sK8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f32,f137]) ).
fof(f137,plain,
( ? [X0] : empty(X0)
=> empty(sK8) ),
introduced(choice_axiom,[]) ).
fof(f32,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f369,plain,
~ spl28_13,
inference(avatar_split_clause,[],[f249,f366]) ).
fof(f366,plain,
( spl28_13
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_13])]) ).
fof(f249,plain,
~ empty(sK7),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
~ empty(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f40,f135]) ).
fof(f135,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK7) ),
introduced(choice_axiom,[]) ).
fof(f40,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f364,plain,
spl28_12,
inference(avatar_split_clause,[],[f193,f361]) ).
fof(f361,plain,
( spl28_12
<=> ordinal(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_12])]) ).
fof(f193,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f75]) ).
fof(f75,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,[],[f71]) ).
fof(f71,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(f359,plain,
spl28_11,
inference(avatar_split_clause,[],[f192,f356]) ).
fof(f356,plain,
( spl28_11
<=> epsilon_connected(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_11])]) ).
fof(f192,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f75]) ).
fof(f354,plain,
spl28_10,
inference(avatar_split_clause,[],[f191,f351]) ).
fof(f351,plain,
( spl28_10
<=> epsilon_transitive(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_10])]) ).
fof(f191,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f75]) ).
fof(f349,plain,
spl28_9,
inference(avatar_split_clause,[],[f189,f346]) ).
fof(f346,plain,
( spl28_9
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_9])]) ).
fof(f189,plain,
function(empty_set),
inference(cnf_transformation,[],[f75]) ).
fof(f344,plain,
spl28_8,
inference(avatar_split_clause,[],[f185,f341]) ).
fof(f341,plain,
( spl28_8
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_8])]) ).
fof(f185,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(f339,plain,
spl28_7,
inference(avatar_split_clause,[],[f183,f336]) ).
fof(f183,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(f334,plain,
~ spl28_6,
inference(avatar_split_clause,[],[f182,f331]) ).
fof(f331,plain,
( spl28_6
<=> empty(positive_rationals) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_6])]) ).
fof(f182,plain,
~ empty(positive_rationals),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
~ empty(positive_rationals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_arytm_3) ).
fof(f329,plain,
spl28_5,
inference(avatar_split_clause,[],[f180,f326]) ).
fof(f180,plain,
finite(relation_inverse_image(sK1,sK0)),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
( ~ finite(sK0)
& finite(relation_inverse_image(sK1,sK0))
& subset(sK0,relation_rng(sK1))
& function(sK1)
& relation(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f85,f122]) ).
fof(f122,plain,
( ? [X0,X1] :
( ~ finite(X0)
& finite(relation_inverse_image(X1,X0))
& subset(X0,relation_rng(X1))
& function(X1)
& relation(X1) )
=> ( ~ finite(sK0)
& finite(relation_inverse_image(sK1,sK0))
& subset(sK0,relation_rng(sK1))
& function(sK1)
& relation(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
? [X0,X1] :
( ~ finite(X0)
& finite(relation_inverse_image(X1,X0))
& subset(X0,relation_rng(X1))
& function(X1)
& relation(X1) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
? [X0,X1] :
( ~ finite(X0)
& finite(relation_inverse_image(X1,X0))
& subset(X0,relation_rng(X1))
& function(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,negated_conjecture,
~ ! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ( finite(relation_inverse_image(X1,X0))
& subset(X0,relation_rng(X1)) )
=> finite(X0) ) ),
inference(negated_conjecture,[],[f53]) ).
fof(f53,conjecture,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( ( finite(relation_inverse_image(X1,X0))
& subset(X0,relation_rng(X1)) )
=> finite(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finset_1) ).
fof(f324,plain,
spl28_4,
inference(avatar_split_clause,[],[f179,f321]) ).
fof(f179,plain,
subset(sK0,relation_rng(sK1)),
inference(cnf_transformation,[],[f123]) ).
fof(f319,plain,
~ spl28_3,
inference(avatar_split_clause,[],[f181,f316]) ).
fof(f181,plain,
~ finite(sK0),
inference(cnf_transformation,[],[f123]) ).
fof(f314,plain,
spl28_2,
inference(avatar_split_clause,[],[f178,f311]) ).
fof(f178,plain,
function(sK1),
inference(cnf_transformation,[],[f123]) ).
fof(f309,plain,
spl28_1,
inference(avatar_split_clause,[],[f177,f306]) ).
fof(f177,plain,
relation(sK1),
inference(cnf_transformation,[],[f123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU096+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 21:14:58 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (32156)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (32159)WARNING: value z3 for option sas not known
% 0.14/0.37 % (32160)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (32158)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 % (32157)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (32159)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 % (32161)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 % (32163)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 % (32162)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)
% 0.20/0.38 TRYING [1]
% 0.20/0.38 TRYING [2]
% 0.20/0.38 TRYING [3]
% 0.20/0.38 TRYING [1]
% 0.20/0.38 TRYING [4]
% 0.20/0.38 TRYING [2]
% 0.20/0.38 TRYING [1]
% 0.20/0.38 TRYING [2]
% 0.20/0.38 % (32161)First to succeed.
% 0.20/0.39 TRYING [3]
% 0.20/0.39 TRYING [4]
% 0.20/0.39 TRYING [5]
% 0.20/0.39 % (32159)Also succeeded, but the first one will report.
% 0.20/0.39 TRYING [3]
% 0.20/0.39 % (32162)Also succeeded, but the first one will report.
% 0.20/0.39 % (32161)Refutation found. Thanks to Tanya!
% 0.20/0.39 % SZS status Theorem for theBenchmark
% 0.20/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.40 % (32161)------------------------------
% 0.20/0.40 % (32161)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.40 % (32161)Termination reason: Refutation
% 0.20/0.40
% 0.20/0.40 % (32161)Memory used [KB]: 1200
% 0.20/0.40 % (32161)Time elapsed: 0.018 s
% 0.20/0.40 % (32161)Instructions burned: 26 (million)
% 0.20/0.40 % (32161)------------------------------
% 0.20/0.40 % (32161)------------------------------
% 0.20/0.40 % (32156)Success in time 0.036 s
%------------------------------------------------------------------------------