TSTP Solution File: SEU096+1 by Vampire-SAT---4.8

View Problem - 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
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