TSTP Solution File: SEU223+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU223+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n026.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 15:24:48 EDT 2024

% Result   : Theorem 0.15s 0.39s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :  137
% Syntax   : Number of formulae    :  401 (  99 unt;   0 def)
%            Number of atoms       : 1087 ( 110 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 1192 ( 506   ~; 465   |;  96   &)
%                                         (  90 <=>;  35  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   96 (  94 usr;  87 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;  12 con; 0-2 aty)
%            Number of variables   :  381 ( 344   !;  37   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f700,plain,
    $false,
    inference(avatar_sat_refutation,[],[f172,f177,f182,f187,f192,f197,f202,f207,f212,f217,f222,f227,f232,f237,f242,f247,f252,f257,f262,f267,f272,f277,f281,f285,f289,f293,f297,f301,f316,f320,f324,f328,f332,f336,f340,f344,f348,f353,f369,f373,f377,f382,f388,f392,f396,f400,f404,f427,f431,f435,f439,f455,f459,f469,f479,f485,f496,f501,f508,f513,f519,f525,f529,f534,f540,f545,f550,f564,f569,f574,f580,f584,f588,f595,f617,f623,f627,f646,f650,f658,f659,f663,f667,f690,f694,f699]) ).

fof(f699,plain,
    ( ~ spl15_1
    | ~ spl15_2
    | ~ spl15_50
    | spl15_77 ),
    inference(avatar_split_clause,[],[f619,f614,f433,f174,f169]) ).

fof(f169,plain,
    ( spl15_1
  <=> relation(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).

fof(f174,plain,
    ( spl15_2
  <=> function(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).

fof(f433,plain,
    ( spl15_50
  <=> ! [X0,X1] :
        ( function(relation_dom_restriction(X0,X1))
        | ~ function(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_50])]) ).

fof(f614,plain,
    ( spl15_77
  <=> function(relation_dom_restriction(sK2,sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_77])]) ).

fof(f619,plain,
    ( ~ function(sK2)
    | ~ relation(sK2)
    | ~ spl15_50
    | spl15_77 ),
    inference(resolution,[],[f616,f434]) ).

fof(f434,plain,
    ( ! [X0,X1] :
        ( function(relation_dom_restriction(X0,X1))
        | ~ function(X0)
        | ~ relation(X0) )
    | ~ spl15_50 ),
    inference(avatar_component_clause,[],[f433]) ).

fof(f616,plain,
    ( ~ function(relation_dom_restriction(sK2,sK0))
    | spl15_77 ),
    inference(avatar_component_clause,[],[f614]) ).

fof(f694,plain,
    ( spl15_86
    | ~ spl15_43
    | ~ spl15_54 ),
    inference(avatar_split_clause,[],[f471,f467,f386,f692]) ).

fof(f692,plain,
    ( spl15_86
  <=> ! [X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,sK3(X1))
        | empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_86])]) ).

fof(f386,plain,
    ( spl15_43
  <=> ! [X0] :
        ( element(sK3(X0),powerset(X0))
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_43])]) ).

fof(f467,plain,
    ( spl15_54
  <=> ! [X2,X0,X1] :
        ( element(X0,X2)
        | ~ element(X1,powerset(X2))
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_54])]) ).

fof(f471,plain,
    ( ! [X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,sK3(X1))
        | empty(X1) )
    | ~ spl15_43
    | ~ spl15_54 ),
    inference(resolution,[],[f468,f387]) ).

fof(f387,plain,
    ( ! [X0] :
        ( element(sK3(X0),powerset(X0))
        | empty(X0) )
    | ~ spl15_43 ),
    inference(avatar_component_clause,[],[f386]) ).

fof(f468,plain,
    ( ! [X2,X0,X1] :
        ( ~ element(X1,powerset(X2))
        | element(X0,X2)
        | ~ in(X0,X1) )
    | ~ spl15_54 ),
    inference(avatar_component_clause,[],[f467]) ).

fof(f690,plain,
    ( spl15_85
    | ~ spl15_46
    | ~ spl15_54 ),
    inference(avatar_split_clause,[],[f470,f467,f398,f688]) ).

fof(f688,plain,
    ( spl15_85
  <=> ! [X2,X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,X2)
        | ~ subset(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_85])]) ).

fof(f398,plain,
    ( spl15_46
  <=> ! [X0,X1] :
        ( element(X0,powerset(X1))
        | ~ subset(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_46])]) ).

fof(f470,plain,
    ( ! [X2,X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,X2)
        | ~ subset(X2,X1) )
    | ~ spl15_46
    | ~ spl15_54 ),
    inference(resolution,[],[f468,f399]) ).

fof(f399,plain,
    ( ! [X0,X1] :
        ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
    | ~ spl15_46 ),
    inference(avatar_component_clause,[],[f398]) ).

fof(f667,plain,
    ( spl15_84
    | ~ spl15_28
    | ~ spl15_54 ),
    inference(avatar_split_clause,[],[f472,f467,f299,f665]) ).

fof(f665,plain,
    ( spl15_84
  <=> ! [X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,sK4(powerset(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_84])]) ).

fof(f299,plain,
    ( spl15_28
  <=> ! [X0] : element(sK4(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_28])]) ).

fof(f472,plain,
    ( ! [X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,sK4(powerset(X1))) )
    | ~ spl15_28
    | ~ spl15_54 ),
    inference(resolution,[],[f468,f300]) ).

fof(f300,plain,
    ( ! [X0] : element(sK4(X0),X0)
    | ~ spl15_28 ),
    inference(avatar_component_clause,[],[f299]) ).

fof(f663,plain,
    ( spl15_83
    | ~ spl15_46
    | ~ spl15_53 ),
    inference(avatar_split_clause,[],[f460,f457,f398,f661]) ).

fof(f661,plain,
    ( spl15_83
  <=> ! [X2,X0,X1] :
        ( ~ empty(X0)
        | ~ in(X1,X2)
        | ~ subset(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_83])]) ).

fof(f457,plain,
    ( spl15_53
  <=> ! [X2,X0,X1] :
        ( ~ empty(X2)
        | ~ element(X1,powerset(X2))
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_53])]) ).

fof(f460,plain,
    ( ! [X2,X0,X1] :
        ( ~ empty(X0)
        | ~ in(X1,X2)
        | ~ subset(X2,X0) )
    | ~ spl15_46
    | ~ spl15_53 ),
    inference(resolution,[],[f458,f399]) ).

fof(f458,plain,
    ( ! [X2,X0,X1] :
        ( ~ element(X1,powerset(X2))
        | ~ empty(X2)
        | ~ in(X0,X1) )
    | ~ spl15_53 ),
    inference(avatar_component_clause,[],[f457]) ).

fof(f659,plain,
    ( ~ spl15_1
    | ~ spl15_39
    | spl15_76 ),
    inference(avatar_split_clause,[],[f618,f610,f367,f169]) ).

fof(f367,plain,
    ( spl15_39
  <=> ! [X0,X1] :
        ( relation(relation_dom_restriction(X0,X1))
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_39])]) ).

fof(f610,plain,
    ( spl15_76
  <=> relation(relation_dom_restriction(sK2,sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_76])]) ).

fof(f618,plain,
    ( ~ relation(sK2)
    | ~ spl15_39
    | spl15_76 ),
    inference(resolution,[],[f612,f368]) ).

fof(f368,plain,
    ( ! [X0,X1] :
        ( relation(relation_dom_restriction(X0,X1))
        | ~ relation(X0) )
    | ~ spl15_39 ),
    inference(avatar_component_clause,[],[f367]) ).

fof(f612,plain,
    ( ~ relation(relation_dom_restriction(sK2,sK0))
    | spl15_76 ),
    inference(avatar_component_clause,[],[f610]) ).

fof(f658,plain,
    ( spl15_82
    | ~ spl15_33
    | ~ spl15_47 ),
    inference(avatar_split_clause,[],[f416,f402,f330,f656]) ).

fof(f656,plain,
    ( spl15_82
  <=> ! [X0,X1] :
        ( relation_dom(X1) = X0
        | ~ empty(X0)
        | ~ empty(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_82])]) ).

fof(f330,plain,
    ( spl15_33
  <=> ! [X0] :
        ( empty(relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_33])]) ).

fof(f402,plain,
    ( spl15_47
  <=> ! [X0,X1] :
        ( ~ empty(X1)
        | X0 = X1
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_47])]) ).

fof(f416,plain,
    ( ! [X0,X1] :
        ( relation_dom(X1) = X0
        | ~ empty(X0)
        | ~ empty(X1) )
    | ~ spl15_33
    | ~ spl15_47 ),
    inference(resolution,[],[f403,f331]) ).

fof(f331,plain,
    ( ! [X0] :
        ( empty(relation_dom(X0))
        | ~ empty(X0) )
    | ~ spl15_33 ),
    inference(avatar_component_clause,[],[f330]) ).

fof(f403,plain,
    ( ! [X0,X1] :
        ( ~ empty(X1)
        | X0 = X1
        | ~ empty(X0) )
    | ~ spl15_47 ),
    inference(avatar_component_clause,[],[f402]) ).

fof(f650,plain,
    ( spl15_81
    | ~ spl15_28
    | ~ spl15_53 ),
    inference(avatar_split_clause,[],[f462,f457,f299,f648]) ).

fof(f648,plain,
    ( spl15_81
  <=> ! [X0,X1] :
        ( ~ empty(X0)
        | ~ in(X1,sK4(powerset(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_81])]) ).

fof(f462,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | ~ in(X1,sK4(powerset(X0))) )
    | ~ spl15_28
    | ~ spl15_53 ),
    inference(resolution,[],[f458,f300]) ).

fof(f646,plain,
    ( spl15_80
    | ~ spl15_8
    | ~ spl15_24
    | ~ spl15_32
    | ~ spl15_35
    | ~ spl15_48 ),
    inference(avatar_split_clause,[],[f445,f425,f338,f326,f283,f204,f644]) ).

fof(f644,plain,
    ( spl15_80
  <=> ! [X0] :
        ( in(sK8,powerset(X0))
        | empty(powerset(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_80])]) ).

fof(f204,plain,
    ( spl15_8
  <=> empty(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_8])]) ).

fof(f283,plain,
    ( spl15_24
  <=> ! [X0] : empty(sK5(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_24])]) ).

fof(f326,plain,
    ( spl15_32
  <=> ! [X0] :
        ( empty_set = X0
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_32])]) ).

fof(f338,plain,
    ( spl15_35
  <=> ! [X0] : element(sK5(X0),powerset(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_35])]) ).

fof(f425,plain,
    ( spl15_48
  <=> ! [X0,X1] :
        ( in(X0,X1)
        | empty(X1)
        | ~ element(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_48])]) ).

fof(f445,plain,
    ( ! [X0] :
        ( in(sK8,powerset(X0))
        | empty(powerset(X0)) )
    | ~ spl15_8
    | ~ spl15_24
    | ~ spl15_32
    | ~ spl15_35
    | ~ spl15_48 ),
    inference(forward_demodulation,[],[f444,f356]) ).

fof(f356,plain,
    ( empty_set = sK8
    | ~ spl15_8
    | ~ spl15_32 ),
    inference(resolution,[],[f327,f206]) ).

fof(f206,plain,
    ( empty(sK8)
    | ~ spl15_8 ),
    inference(avatar_component_clause,[],[f204]) ).

fof(f327,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | empty_set = X0 )
    | ~ spl15_32 ),
    inference(avatar_component_clause,[],[f326]) ).

fof(f444,plain,
    ( ! [X0] :
        ( in(empty_set,powerset(X0))
        | empty(powerset(X0)) )
    | ~ spl15_24
    | ~ spl15_32
    | ~ spl15_35
    | ~ spl15_48 ),
    inference(forward_demodulation,[],[f443,f355]) ).

fof(f355,plain,
    ( ! [X0] : empty_set = sK5(X0)
    | ~ spl15_24
    | ~ spl15_32 ),
    inference(resolution,[],[f327,f284]) ).

fof(f284,plain,
    ( ! [X0] : empty(sK5(X0))
    | ~ spl15_24 ),
    inference(avatar_component_clause,[],[f283]) ).

fof(f443,plain,
    ( ! [X0] :
        ( empty(powerset(X0))
        | in(sK5(X0),powerset(X0)) )
    | ~ spl15_35
    | ~ spl15_48 ),
    inference(resolution,[],[f426,f339]) ).

fof(f339,plain,
    ( ! [X0] : element(sK5(X0),powerset(X0))
    | ~ spl15_35 ),
    inference(avatar_component_clause,[],[f338]) ).

fof(f426,plain,
    ( ! [X0,X1] :
        ( ~ element(X0,X1)
        | empty(X1)
        | in(X0,X1) )
    | ~ spl15_48 ),
    inference(avatar_component_clause,[],[f425]) ).

fof(f627,plain,
    ( spl15_79
    | ~ spl15_28
    | ~ spl15_48 ),
    inference(avatar_split_clause,[],[f442,f425,f299,f625]) ).

fof(f625,plain,
    ( spl15_79
  <=> ! [X0] :
        ( empty(X0)
        | in(sK4(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_79])]) ).

fof(f442,plain,
    ( ! [X0] :
        ( empty(X0)
        | in(sK4(X0),X0) )
    | ~ spl15_28
    | ~ spl15_48 ),
    inference(resolution,[],[f426,f300]) ).

fof(f623,plain,
    ( spl15_78
    | ~ spl15_8
    | ~ spl15_32
    | ~ spl15_33 ),
    inference(avatar_split_clause,[],[f364,f330,f326,f204,f621]) ).

fof(f621,plain,
    ( spl15_78
  <=> ! [X0] :
        ( relation_dom(X0) = sK8
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_78])]) ).

fof(f364,plain,
    ( ! [X0] :
        ( relation_dom(X0) = sK8
        | ~ empty(X0) )
    | ~ spl15_8
    | ~ spl15_32
    | ~ spl15_33 ),
    inference(forward_demodulation,[],[f361,f356]) ).

fof(f361,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | empty_set = relation_dom(X0) )
    | ~ spl15_32
    | ~ spl15_33 ),
    inference(resolution,[],[f331,f327]) ).

fof(f617,plain,
    ( ~ spl15_76
    | ~ spl15_77
    | ~ spl15_1
    | ~ spl15_2
    | spl15_22
    | ~ spl15_3
    | ~ spl15_57 ),
    inference(avatar_split_clause,[],[f497,f494,f179,f274,f174,f169,f614,f610]) ).

fof(f274,plain,
    ( spl15_22
  <=> apply(relation_dom_restriction(sK2,sK0),sK1) = apply(sK2,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_22])]) ).

fof(f179,plain,
    ( spl15_3
  <=> in(sK1,relation_dom(relation_dom_restriction(sK2,sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).

fof(f494,plain,
    ( spl15_57
  <=> ! [X4,X0,X2] :
        ( apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
        | ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
        | ~ function(X2)
        | ~ relation(X2)
        | ~ function(relation_dom_restriction(X2,X0))
        | ~ relation(relation_dom_restriction(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_57])]) ).

fof(f497,plain,
    ( apply(relation_dom_restriction(sK2,sK0),sK1) = apply(sK2,sK1)
    | ~ function(sK2)
    | ~ relation(sK2)
    | ~ function(relation_dom_restriction(sK2,sK0))
    | ~ relation(relation_dom_restriction(sK2,sK0))
    | ~ spl15_3
    | ~ spl15_57 ),
    inference(resolution,[],[f495,f181]) ).

fof(f181,plain,
    ( in(sK1,relation_dom(relation_dom_restriction(sK2,sK0)))
    | ~ spl15_3 ),
    inference(avatar_component_clause,[],[f179]) ).

fof(f495,plain,
    ( ! [X2,X0,X4] :
        ( ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
        | apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
        | ~ function(X2)
        | ~ relation(X2)
        | ~ function(relation_dom_restriction(X2,X0))
        | ~ relation(relation_dom_restriction(X2,X0)) )
    | ~ spl15_57 ),
    inference(avatar_component_clause,[],[f494]) ).

fof(f595,plain,
    ( spl15_74
    | spl15_75
    | ~ spl15_8
    | ~ spl15_24
    | ~ spl15_32
    | ~ spl15_35
    | ~ spl15_53 ),
    inference(avatar_split_clause,[],[f465,f457,f338,f326,f283,f204,f593,f590]) ).

fof(f590,plain,
    ( spl15_74
  <=> ! [X0] : ~ empty(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_74])]) ).

fof(f593,plain,
    ( spl15_75
  <=> ! [X1] : ~ in(X1,sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_75])]) ).

fof(f465,plain,
    ( ! [X0,X1] :
        ( ~ in(X1,sK8)
        | ~ empty(X0) )
    | ~ spl15_8
    | ~ spl15_24
    | ~ spl15_32
    | ~ spl15_35
    | ~ spl15_53 ),
    inference(forward_demodulation,[],[f464,f356]) ).

fof(f464,plain,
    ( ! [X0,X1] :
        ( ~ in(X1,empty_set)
        | ~ empty(X0) )
    | ~ spl15_24
    | ~ spl15_32
    | ~ spl15_35
    | ~ spl15_53 ),
    inference(forward_demodulation,[],[f463,f355]) ).

fof(f463,plain,
    ( ! [X0,X1] :
        ( ~ empty(X0)
        | ~ in(X1,sK5(X0)) )
    | ~ spl15_35
    | ~ spl15_53 ),
    inference(resolution,[],[f458,f339]) ).

fof(f588,plain,
    ( spl15_73
    | ~ spl15_8
    | ~ spl15_47 ),
    inference(avatar_split_clause,[],[f418,f402,f204,f586]) ).

fof(f586,plain,
    ( spl15_73
  <=> ! [X0] :
        ( sK8 = X0
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_73])]) ).

fof(f418,plain,
    ( ! [X0] :
        ( sK8 = X0
        | ~ empty(X0) )
    | ~ spl15_8
    | ~ spl15_47 ),
    inference(resolution,[],[f403,f206]) ).

fof(f584,plain,
    ( spl15_72
    | ~ spl15_8
    | ~ spl15_30
    | ~ spl15_32
    | ~ spl15_45 ),
    inference(avatar_split_clause,[],[f410,f394,f326,f318,f204,f582]) ).

fof(f582,plain,
    ( spl15_72
  <=> ! [X0] : sK8 = set_intersection2(sK8,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_72])]) ).

fof(f318,plain,
    ( spl15_30
  <=> ! [X0] : empty_set = set_intersection2(X0,empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_30])]) ).

fof(f394,plain,
    ( spl15_45
  <=> ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_45])]) ).

fof(f410,plain,
    ( ! [X0] : sK8 = set_intersection2(sK8,X0)
    | ~ spl15_8
    | ~ spl15_30
    | ~ spl15_32
    | ~ spl15_45 ),
    inference(forward_demodulation,[],[f406,f356]) ).

fof(f406,plain,
    ( ! [X0] : empty_set = set_intersection2(empty_set,X0)
    | ~ spl15_30
    | ~ spl15_45 ),
    inference(superposition,[],[f395,f319]) ).

fof(f319,plain,
    ( ! [X0] : empty_set = set_intersection2(X0,empty_set)
    | ~ spl15_30 ),
    inference(avatar_component_clause,[],[f318]) ).

fof(f395,plain,
    ( ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0)
    | ~ spl15_45 ),
    inference(avatar_component_clause,[],[f394]) ).

fof(f580,plain,
    ( spl15_71
    | ~ spl15_26
    | ~ spl15_33 ),
    inference(avatar_split_clause,[],[f363,f330,f291,f578]) ).

fof(f578,plain,
    ( spl15_71
  <=> ! [X0] :
        ( ~ empty(X0)
        | function(relation_dom(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_71])]) ).

fof(f291,plain,
    ( spl15_26
  <=> ! [X0] :
        ( function(X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_26])]) ).

fof(f363,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | function(relation_dom(X0)) )
    | ~ spl15_26
    | ~ spl15_33 ),
    inference(resolution,[],[f331,f292]) ).

fof(f292,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | function(X0) )
    | ~ spl15_26 ),
    inference(avatar_component_clause,[],[f291]) ).

fof(f574,plain,
    ( spl15_70
    | ~ spl15_6
    | ~ spl15_65 ),
    inference(avatar_split_clause,[],[f553,f537,f194,f571]) ).

fof(f571,plain,
    ( spl15_70
  <=> relation_empty_yielding(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_70])]) ).

fof(f194,plain,
    ( spl15_6
  <=> relation_empty_yielding(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_6])]) ).

fof(f537,plain,
    ( spl15_65
  <=> empty_set = sK8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_65])]) ).

fof(f553,plain,
    ( relation_empty_yielding(sK8)
    | ~ spl15_6
    | ~ spl15_65 ),
    inference(superposition,[],[f196,f539]) ).

fof(f539,plain,
    ( empty_set = sK8
    | ~ spl15_65 ),
    inference(avatar_component_clause,[],[f537]) ).

fof(f196,plain,
    ( relation_empty_yielding(empty_set)
    | ~ spl15_6 ),
    inference(avatar_component_clause,[],[f194]) ).

fof(f569,plain,
    ( spl15_69
    | ~ spl15_65
    | ~ spl15_68 ),
    inference(avatar_split_clause,[],[f565,f562,f537,f567]) ).

fof(f567,plain,
    ( spl15_69
  <=> ! [X0] : sK5(X0) = sK8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_69])]) ).

fof(f562,plain,
    ( spl15_68
  <=> ! [X0] : empty_set = sK5(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_68])]) ).

fof(f565,plain,
    ( ! [X0] : sK5(X0) = sK8
    | ~ spl15_65
    | ~ spl15_68 ),
    inference(forward_demodulation,[],[f563,f539]) ).

fof(f563,plain,
    ( ! [X0] : empty_set = sK5(X0)
    | ~ spl15_68 ),
    inference(avatar_component_clause,[],[f562]) ).

fof(f564,plain,
    ( spl15_68
    | ~ spl15_24
    | ~ spl15_32 ),
    inference(avatar_split_clause,[],[f355,f326,f283,f562]) ).

fof(f550,plain,
    ( spl15_67
    | ~ spl15_8
    | ~ spl15_20
    | ~ spl15_32 ),
    inference(avatar_split_clause,[],[f360,f326,f264,f204,f547]) ).

fof(f547,plain,
    ( spl15_67
  <=> sK8 = sK14 ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_67])]) ).

fof(f264,plain,
    ( spl15_20
  <=> empty(sK14) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_20])]) ).

fof(f360,plain,
    ( sK8 = sK14
    | ~ spl15_8
    | ~ spl15_20
    | ~ spl15_32 ),
    inference(forward_demodulation,[],[f358,f356]) ).

fof(f358,plain,
    ( empty_set = sK14
    | ~ spl15_20
    | ~ spl15_32 ),
    inference(resolution,[],[f327,f266]) ).

fof(f266,plain,
    ( empty(sK14)
    | ~ spl15_20 ),
    inference(avatar_component_clause,[],[f264]) ).

fof(f545,plain,
    ( spl15_66
    | ~ spl15_8
    | ~ spl15_11
    | ~ spl15_32 ),
    inference(avatar_split_clause,[],[f359,f326,f219,f204,f542]) ).

fof(f542,plain,
    ( spl15_66
  <=> sK8 = sK10 ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_66])]) ).

fof(f219,plain,
    ( spl15_11
  <=> empty(sK10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_11])]) ).

fof(f359,plain,
    ( sK8 = sK10
    | ~ spl15_8
    | ~ spl15_11
    | ~ spl15_32 ),
    inference(forward_demodulation,[],[f357,f356]) ).

fof(f357,plain,
    ( empty_set = sK10
    | ~ spl15_11
    | ~ spl15_32 ),
    inference(resolution,[],[f327,f221]) ).

fof(f221,plain,
    ( empty(sK10)
    | ~ spl15_11 ),
    inference(avatar_component_clause,[],[f219]) ).

fof(f540,plain,
    ( spl15_65
    | ~ spl15_8
    | ~ spl15_32 ),
    inference(avatar_split_clause,[],[f356,f326,f204,f537]) ).

fof(f534,plain,
    ( spl15_64
    | ~ spl15_24
    | ~ spl15_27 ),
    inference(avatar_split_clause,[],[f308,f295,f283,f532]) ).

fof(f532,plain,
    ( spl15_64
  <=> ! [X0] : relation(sK5(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_64])]) ).

fof(f295,plain,
    ( spl15_27
  <=> ! [X0] :
        ( relation(X0)
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_27])]) ).

fof(f308,plain,
    ( ! [X0] : relation(sK5(X0))
    | ~ spl15_24
    | ~ spl15_27 ),
    inference(resolution,[],[f296,f284]) ).

fof(f296,plain,
    ( ! [X0] :
        ( ~ empty(X0)
        | relation(X0) )
    | ~ spl15_27 ),
    inference(avatar_component_clause,[],[f295]) ).

fof(f529,plain,
    ( spl15_63
    | ~ spl15_24
    | ~ spl15_26 ),
    inference(avatar_split_clause,[],[f303,f291,f283,f527]) ).

fof(f527,plain,
    ( spl15_63
  <=> ! [X0] : function(sK5(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_63])]) ).

fof(f303,plain,
    ( ! [X0] : function(sK5(X0))
    | ~ spl15_24
    | ~ spl15_26 ),
    inference(resolution,[],[f292,f284]) ).

fof(f525,plain,
    ( spl15_62
    | ~ spl15_8
    | ~ spl15_27 ),
    inference(avatar_split_clause,[],[f309,f295,f204,f522]) ).

fof(f522,plain,
    ( spl15_62
  <=> relation(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_62])]) ).

fof(f309,plain,
    ( relation(sK8)
    | ~ spl15_8
    | ~ spl15_27 ),
    inference(resolution,[],[f296,f206]) ).

fof(f519,plain,
    ( spl15_61
    | ~ spl15_11
    | ~ spl15_26 ),
    inference(avatar_split_clause,[],[f305,f291,f219,f516]) ).

fof(f516,plain,
    ( spl15_61
  <=> function(sK10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_61])]) ).

fof(f305,plain,
    ( function(sK10)
    | ~ spl15_11
    | ~ spl15_26 ),
    inference(resolution,[],[f292,f221]) ).

fof(f513,plain,
    ( spl15_60
    | ~ spl15_3
    | ~ spl15_41 ),
    inference(avatar_split_clause,[],[f384,f375,f179,f510]) ).

fof(f510,plain,
    ( spl15_60
  <=> element(sK1,relation_dom(relation_dom_restriction(sK2,sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_60])]) ).

fof(f375,plain,
    ( spl15_41
  <=> ! [X0,X1] :
        ( element(X0,X1)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_41])]) ).

fof(f384,plain,
    ( element(sK1,relation_dom(relation_dom_restriction(sK2,sK0)))
    | ~ spl15_3
    | ~ spl15_41 ),
    inference(resolution,[],[f376,f181]) ).

fof(f376,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,X1)
        | element(X0,X1) )
    | ~ spl15_41 ),
    inference(avatar_component_clause,[],[f375]) ).

fof(f508,plain,
    ( ~ spl15_59
    | ~ spl15_3
    | ~ spl15_40 ),
    inference(avatar_split_clause,[],[f383,f371,f179,f505]) ).

fof(f505,plain,
    ( spl15_59
  <=> in(relation_dom(relation_dom_restriction(sK2,sK0)),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_59])]) ).

fof(f371,plain,
    ( spl15_40
  <=> ! [X0,X1] :
        ( ~ in(X1,X0)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_40])]) ).

fof(f383,plain,
    ( ~ in(relation_dom(relation_dom_restriction(sK2,sK0)),sK1)
    | ~ spl15_3
    | ~ spl15_40 ),
    inference(resolution,[],[f372,f181]) ).

fof(f372,plain,
    ( ! [X0,X1] :
        ( ~ in(X1,X0)
        | ~ in(X0,X1) )
    | ~ spl15_40 ),
    inference(avatar_component_clause,[],[f371]) ).

fof(f501,plain,
    spl15_58,
    inference(avatar_split_clause,[],[f144,f499]) ).

fof(f499,plain,
    ( spl15_58
  <=> ! [X2,X0,X1] :
        ( relation_dom_restriction(X2,X0) = X1
        | apply(X1,sK6(X1,X2)) != apply(X2,sK6(X1,X2))
        | relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
        | ~ function(X2)
        | ~ relation(X2)
        | ~ function(X1)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_58])]) ).

fof(f144,plain,
    ! [X2,X0,X1] :
      ( relation_dom_restriction(X2,X0) = X1
      | apply(X1,sK6(X1,X2)) != apply(X2,sK6(X1,X2))
      | relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_dom_restriction(X2,X0) = X1
              | ( apply(X1,sK6(X1,X2)) != apply(X2,sK6(X1,X2))
                & in(sK6(X1,X2),relation_dom(X1)) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
            & ( ( ! [X4] :
                    ( apply(X1,X4) = apply(X2,X4)
                    | ~ in(X4,relation_dom(X1)) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
              | relation_dom_restriction(X2,X0) != X1 ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f86,f87]) ).

fof(f87,plain,
    ! [X1,X2] :
      ( ? [X3] :
          ( apply(X1,X3) != apply(X2,X3)
          & in(X3,relation_dom(X1)) )
     => ( apply(X1,sK6(X1,X2)) != apply(X2,sK6(X1,X2))
        & in(sK6(X1,X2),relation_dom(X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_dom_restriction(X2,X0) = X1
              | ? [X3] :
                  ( apply(X1,X3) != apply(X2,X3)
                  & in(X3,relation_dom(X1)) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
            & ( ( ! [X4] :
                    ( apply(X1,X4) = apply(X2,X4)
                    | ~ in(X4,relation_dom(X1)) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
              | relation_dom_restriction(X2,X0) != X1 ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(rectify,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_dom_restriction(X2,X0) = X1
              | ? [X3] :
                  ( apply(X1,X3) != apply(X2,X3)
                  & in(X3,relation_dom(X1)) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
            & ( ( ! [X3] :
                    ( apply(X1,X3) = apply(X2,X3)
                    | ~ in(X3,relation_dom(X1)) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
              | relation_dom_restriction(X2,X0) != X1 ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( relation_dom_restriction(X2,X0) = X1
              | ? [X3] :
                  ( apply(X1,X3) != apply(X2,X3)
                  & in(X3,relation_dom(X1)) )
              | relation_dom(X1) != set_intersection2(relation_dom(X2),X0) )
            & ( ( ! [X3] :
                    ( apply(X1,X3) = apply(X2,X3)
                    | ~ in(X3,relation_dom(X1)) )
                & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
              | relation_dom_restriction(X2,X0) != X1 ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(nnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( relation_dom_restriction(X2,X0) = X1
          <=> ( ! [X3] :
                  ( apply(X1,X3) = apply(X2,X3)
                  | ~ in(X3,relation_dom(X1)) )
              & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f66]) ).

fof(f66,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( relation_dom_restriction(X2,X0) = X1
          <=> ( ! [X3] :
                  ( apply(X1,X3) = apply(X2,X3)
                  | ~ in(X3,relation_dom(X1)) )
              & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( relation_dom_restriction(X2,X0) = X1
          <=> ( ! [X3] :
                  ( in(X3,relation_dom(X1))
                 => apply(X1,X3) = apply(X2,X3) )
              & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).

fof(f496,plain,
    spl15_57,
    inference(avatar_split_clause,[],[f166,f494]) ).

fof(f166,plain,
    ! [X2,X0,X4] :
      ( apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
      | ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(relation_dom_restriction(X2,X0))
      | ~ relation(relation_dom_restriction(X2,X0)) ),
    inference(equality_resolution,[],[f142]) ).

fof(f142,plain,
    ! [X2,X0,X1,X4] :
      ( apply(X1,X4) = apply(X2,X4)
      | ~ in(X4,relation_dom(X1))
      | relation_dom_restriction(X2,X0) != X1
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f485,plain,
    spl15_56,
    inference(avatar_split_clause,[],[f143,f483]) ).

fof(f483,plain,
    ( spl15_56
  <=> ! [X2,X0,X1] :
        ( relation_dom_restriction(X2,X0) = X1
        | in(sK6(X1,X2),relation_dom(X1))
        | relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
        | ~ function(X2)
        | ~ relation(X2)
        | ~ function(X1)
        | ~ relation(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_56])]) ).

fof(f143,plain,
    ! [X2,X0,X1] :
      ( relation_dom_restriction(X2,X0) = X1
      | in(sK6(X1,X2),relation_dom(X1))
      | relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f479,plain,
    spl15_55,
    inference(avatar_split_clause,[],[f167,f477]) ).

fof(f477,plain,
    ( spl15_55
  <=> ! [X2,X0] :
        ( relation_dom(relation_dom_restriction(X2,X0)) = set_intersection2(relation_dom(X2),X0)
        | ~ function(X2)
        | ~ relation(X2)
        | ~ function(relation_dom_restriction(X2,X0))
        | ~ relation(relation_dom_restriction(X2,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_55])]) ).

fof(f167,plain,
    ! [X2,X0] :
      ( relation_dom(relation_dom_restriction(X2,X0)) = set_intersection2(relation_dom(X2),X0)
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(relation_dom_restriction(X2,X0))
      | ~ relation(relation_dom_restriction(X2,X0)) ),
    inference(equality_resolution,[],[f141]) ).

fof(f141,plain,
    ! [X2,X0,X1] :
      ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
      | relation_dom_restriction(X2,X0) != X1
      | ~ function(X2)
      | ~ relation(X2)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f469,plain,
    spl15_54,
    inference(avatar_split_clause,[],[f149,f467]) ).

fof(f149,plain,
    ! [X2,X0,X1] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0,X1,X2] :
      ( ( element(X1,powerset(X2))
        & in(X0,X1) )
     => element(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).

fof(f459,plain,
    spl15_53,
    inference(avatar_split_clause,[],[f150,f457]) ).

fof(f150,plain,
    ! [X2,X0,X1] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1,X2] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0,X1,X2] :
      ~ ( empty(X2)
        & element(X1,powerset(X2))
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).

fof(f455,plain,
    ( ~ spl15_52
    | ~ spl15_33
    | spl15_42 ),
    inference(avatar_split_clause,[],[f414,f379,f330,f452]) ).

fof(f452,plain,
    ( spl15_52
  <=> empty(relation_dom_restriction(sK2,sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_52])]) ).

fof(f379,plain,
    ( spl15_42
  <=> empty(relation_dom(relation_dom_restriction(sK2,sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_42])]) ).

fof(f414,plain,
    ( ~ empty(relation_dom_restriction(sK2,sK0))
    | ~ spl15_33
    | spl15_42 ),
    inference(resolution,[],[f381,f331]) ).

fof(f381,plain,
    ( ~ empty(relation_dom(relation_dom_restriction(sK2,sK0)))
    | spl15_42 ),
    inference(avatar_component_clause,[],[f379]) ).

fof(f439,plain,
    spl15_51,
    inference(avatar_split_clause,[],[f145,f437]) ).

fof(f437,plain,
    ( spl15_51
  <=> ! [X0,X1] :
        ( relation(set_intersection2(X0,X1))
        | ~ relation(X1)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_51])]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( relation(set_intersection2(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( relation(set_intersection2(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(flattening,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( relation(set_intersection2(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0,X1] :
      ( ( relation(X1)
        & relation(X0) )
     => relation(set_intersection2(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).

fof(f435,plain,
    spl15_50,
    inference(avatar_split_clause,[],[f140,f433]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( function(relation_dom_restriction(X0,X1))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f64]) ).

fof(f64,plain,
    ! [X0,X1] :
      ( ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,axiom,
    ! [X0,X1] :
      ( ( function(X0)
        & relation(X0) )
     => ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).

fof(f431,plain,
    spl15_49,
    inference(avatar_split_clause,[],[f138,f429]) ).

fof(f429,plain,
    ( spl15_49
  <=> ! [X0,X1] :
        ( relation_empty_yielding(relation_dom_restriction(X0,X1))
        | ~ relation_empty_yielding(X0)
        | ~ relation(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_49])]) ).

fof(f138,plain,
    ! [X0,X1] :
      ( relation_empty_yielding(relation_dom_restriction(X0,X1))
      | ~ relation_empty_yielding(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ( relation_empty_yielding(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ relation_empty_yielding(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ( relation_empty_yielding(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ relation_empty_yielding(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( ( relation_empty_yielding(X0)
        & relation(X0) )
     => ( relation_empty_yielding(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc13_relat_1) ).

fof(f427,plain,
    spl15_48,
    inference(avatar_split_clause,[],[f136,f425]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).

fof(f404,plain,
    spl15_47,
    inference(avatar_split_clause,[],[f147,f402]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | X0 = X1
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & X0 != X1
        & empty(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).

fof(f400,plain,
    spl15_46,
    inference(avatar_split_clause,[],[f146,f398]) ).

fof(f146,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
     => element(X0,powerset(X1)) ),
    inference(unused_predicate_definition_removal,[],[f15]) ).

fof(f15,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

fof(f396,plain,
    spl15_45,
    inference(avatar_split_clause,[],[f132,f394]) ).

fof(f132,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f392,plain,
    spl15_44,
    inference(avatar_split_clause,[],[f124,f390]) ).

fof(f390,plain,
    ( spl15_44
  <=> ! [X0] :
        ( ~ empty(relation_dom(X0))
        | ~ relation(X0)
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_44])]) ).

fof(f124,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(flattening,[],[f53]) ).

fof(f53,plain,
    ! [X0] :
      ( ~ empty(relation_dom(X0))
      | ~ relation(X0)
      | empty(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0] :
      ( ( relation(X0)
        & ~ empty(X0) )
     => ~ empty(relation_dom(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).

fof(f388,plain,
    spl15_43,
    inference(avatar_split_clause,[],[f117,f386]) ).

fof(f117,plain,
    ! [X0] :
      ( element(sK3(X0),powerset(X0))
      | empty(X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0] :
      ( ( ~ empty(sK3(X0))
        & element(sK3(X0),powerset(X0)) )
      | empty(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f48,f78]) ).

fof(f78,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ empty(X1)
          & element(X1,powerset(X0)) )
     => ( ~ empty(sK3(X0))
        & element(sK3(X0),powerset(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ empty(X1)
          & element(X1,powerset(X0)) )
      | empty(X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,axiom,
    ! [X0] :
      ( ~ empty(X0)
     => ? [X1] :
          ( ~ empty(X1)
          & element(X1,powerset(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).

fof(f382,plain,
    ( ~ spl15_42
    | ~ spl15_3
    | ~ spl15_37 ),
    inference(avatar_split_clause,[],[f365,f346,f179,f379]) ).

fof(f346,plain,
    ( spl15_37
  <=> ! [X0,X1] :
        ( ~ empty(X1)
        | ~ in(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_37])]) ).

fof(f365,plain,
    ( ~ empty(relation_dom(relation_dom_restriction(sK2,sK0)))
    | ~ spl15_3
    | ~ spl15_37 ),
    inference(resolution,[],[f347,f181]) ).

fof(f347,plain,
    ( ! [X0,X1] :
        ( ~ in(X0,X1)
        | ~ empty(X1) )
    | ~ spl15_37 ),
    inference(avatar_component_clause,[],[f346]) ).

fof(f377,plain,
    spl15_41,
    inference(avatar_split_clause,[],[f135,f375]) ).

fof(f135,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => element(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).

fof(f373,plain,
    spl15_40,
    inference(avatar_split_clause,[],[f134,f371]) ).

fof(f134,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => ~ in(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(f369,plain,
    spl15_39,
    inference(avatar_split_clause,[],[f133,f367]) ).

fof(f133,plain,
    ! [X0,X1] :
      ( relation(relation_dom_restriction(X0,X1))
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( relation(relation_dom_restriction(X0,X1))
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0,X1] :
      ( relation(X0)
     => relation(relation_dom_restriction(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).

fof(f353,plain,
    ( spl15_38
    | ~ spl15_8
    | ~ spl15_26 ),
    inference(avatar_split_clause,[],[f304,f291,f204,f350]) ).

fof(f350,plain,
    ( spl15_38
  <=> function(sK8) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_38])]) ).

fof(f304,plain,
    ( function(sK8)
    | ~ spl15_8
    | ~ spl15_26 ),
    inference(resolution,[],[f292,f206]) ).

fof(f348,plain,
    spl15_37,
    inference(avatar_split_clause,[],[f148,f346]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ~ empty(X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,axiom,
    ! [X0,X1] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(f344,plain,
    spl15_36,
    inference(avatar_split_clause,[],[f131,f342]) ).

fof(f342,plain,
    ( spl15_36
  <=> ! [X0] : set_intersection2(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_36])]) ).

fof(f131,plain,
    ! [X0] : set_intersection2(X0,X0) = X0,
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0] : set_intersection2(X0,X0) = X0,
    inference(rectify,[],[f21]) ).

fof(f21,axiom,
    ! [X0,X1] : set_intersection2(X0,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).

fof(f340,plain,
    spl15_35,
    inference(avatar_split_clause,[],[f128,f338]) ).

fof(f128,plain,
    ! [X0] : element(sK5(X0),powerset(X0)),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0] :
      ( empty(sK5(X0))
      & element(sK5(X0),powerset(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f29,f82]) ).

fof(f82,plain,
    ! [X0] :
      ( ? [X1] :
          ( empty(X1)
          & element(X1,powerset(X0)) )
     => ( empty(sK5(X0))
        & element(sK5(X0),powerset(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,axiom,
    ! [X0] :
    ? [X1] :
      ( empty(X1)
      & element(X1,powerset(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).

fof(f336,plain,
    spl15_34,
    inference(avatar_split_clause,[],[f123,f334]) ).

fof(f334,plain,
    ( spl15_34
  <=> ! [X0] :
        ( relation(relation_dom(X0))
        | ~ empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_34])]) ).

fof(f123,plain,
    ! [X0] :
      ( relation(relation_dom(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ( relation(relation_dom(X0))
        & empty(relation_dom(X0)) )
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0] :
      ( empty(X0)
     => ( relation(relation_dom(X0))
        & empty(relation_dom(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).

fof(f332,plain,
    spl15_33,
    inference(avatar_split_clause,[],[f122,f330]) ).

fof(f122,plain,
    ! [X0] :
      ( empty(relation_dom(X0))
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f52]) ).

fof(f328,plain,
    spl15_32,
    inference(avatar_split_clause,[],[f121,f326]) ).

fof(f121,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(f324,plain,
    spl15_31,
    inference(avatar_split_clause,[],[f118,f322]) ).

fof(f322,plain,
    ( spl15_31
  <=> ! [X0] :
        ( ~ empty(sK3(X0))
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_31])]) ).

fof(f118,plain,
    ! [X0] :
      ( ~ empty(sK3(X0))
      | empty(X0) ),
    inference(cnf_transformation,[],[f79]) ).

fof(f320,plain,
    spl15_30,
    inference(avatar_split_clause,[],[f116,f318]) ).

fof(f116,plain,
    ! [X0] : empty_set = set_intersection2(X0,empty_set),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] : empty_set = set_intersection2(X0,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).

fof(f316,plain,
    ( spl15_29
    | ~ spl15_4
    | ~ spl15_26 ),
    inference(avatar_split_clause,[],[f302,f291,f184,f313]) ).

fof(f313,plain,
    ( spl15_29
  <=> function(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_29])]) ).

fof(f184,plain,
    ( spl15_4
  <=> empty(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).

fof(f302,plain,
    ( function(empty_set)
    | ~ spl15_4
    | ~ spl15_26 ),
    inference(resolution,[],[f292,f186]) ).

fof(f186,plain,
    ( empty(empty_set)
    | ~ spl15_4 ),
    inference(avatar_component_clause,[],[f184]) ).

fof(f301,plain,
    spl15_28,
    inference(avatar_split_clause,[],[f127,f299]) ).

fof(f127,plain,
    ! [X0] : element(sK4(X0),X0),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0] : element(sK4(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f6,f80]) ).

fof(f80,plain,
    ! [X0] :
      ( ? [X1] : element(X1,X0)
     => element(sK4(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f6,axiom,
    ! [X0] :
    ? [X1] : element(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(f297,plain,
    spl15_27,
    inference(avatar_split_clause,[],[f120,f295]) ).

fof(f120,plain,
    ! [X0] :
      ( relation(X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0] :
      ( relation(X0)
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0] :
      ( empty(X0)
     => relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).

fof(f293,plain,
    spl15_26,
    inference(avatar_split_clause,[],[f119,f291]) ).

fof(f119,plain,
    ! [X0] :
      ( function(X0)
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( function(X0)
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( empty(X0)
     => function(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).

fof(f289,plain,
    spl15_25,
    inference(avatar_split_clause,[],[f130,f287]) ).

fof(f287,plain,
    ( spl15_25
  <=> ! [X0] : subset(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_25])]) ).

fof(f130,plain,
    ! [X0] : subset(X0,X0),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0] : subset(X0,X0),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] : subset(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

fof(f285,plain,
    spl15_24,
    inference(avatar_split_clause,[],[f129,f283]) ).

fof(f129,plain,
    ! [X0] : empty(sK5(X0)),
    inference(cnf_transformation,[],[f83]) ).

fof(f281,plain,
    spl15_23,
    inference(avatar_split_clause,[],[f115,f279]) ).

fof(f279,plain,
    ( spl15_23
  <=> ! [X0] : ~ empty(powerset(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_23])]) ).

fof(f115,plain,
    ! [X0] : ~ empty(powerset(X0)),
    inference(cnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0] : ~ empty(powerset(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).

fof(f277,plain,
    ~ spl15_22,
    inference(avatar_split_clause,[],[f108,f274]) ).

fof(f108,plain,
    apply(relation_dom_restriction(sK2,sK0),sK1) != apply(sK2,sK1),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ( apply(relation_dom_restriction(sK2,sK0),sK1) != apply(sK2,sK1)
    & in(sK1,relation_dom(relation_dom_restriction(sK2,sK0)))
    & function(sK2)
    & relation(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f47,f76]) ).

fof(f76,plain,
    ( ? [X0,X1,X2] :
        ( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
        & in(X1,relation_dom(relation_dom_restriction(X2,X0)))
        & function(X2)
        & relation(X2) )
   => ( apply(relation_dom_restriction(sK2,sK0),sK1) != apply(sK2,sK1)
      & in(sK1,relation_dom(relation_dom_restriction(sK2,sK0)))
      & function(sK2)
      & relation(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ? [X0,X1,X2] :
      ( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
      & in(X1,relation_dom(relation_dom_restriction(X2,X0)))
      & function(X2)
      & relation(X2) ),
    inference(flattening,[],[f46]) ).

fof(f46,plain,
    ? [X0,X1,X2] :
      ( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
      & in(X1,relation_dom(relation_dom_restriction(X2,X0)))
      & function(X2)
      & relation(X2) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( function(X2)
          & relation(X2) )
       => ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
         => apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
    inference(negated_conjecture,[],[f38]) ).

fof(f38,conjecture,
    ! [X0,X1,X2] :
      ( ( function(X2)
        & relation(X2) )
     => ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
       => apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_funct_1) ).

fof(f272,plain,
    spl15_21,
    inference(avatar_split_clause,[],[f165,f269]) ).

fof(f269,plain,
    ( spl15_21
  <=> function(sK14) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_21])]) ).

fof(f165,plain,
    function(sK14),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ( function(sK14)
    & empty(sK14)
    & relation(sK14) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f26,f103]) ).

fof(f103,plain,
    ( ? [X0] :
        ( function(X0)
        & empty(X0)
        & relation(X0) )
   => ( function(sK14)
      & empty(sK14)
      & relation(sK14) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,axiom,
    ? [X0] :
      ( function(X0)
      & empty(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).

fof(f267,plain,
    spl15_20,
    inference(avatar_split_clause,[],[f164,f264]) ).

fof(f164,plain,
    empty(sK14),
    inference(cnf_transformation,[],[f104]) ).

fof(f262,plain,
    spl15_19,
    inference(avatar_split_clause,[],[f163,f259]) ).

fof(f259,plain,
    ( spl15_19
  <=> relation(sK14) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_19])]) ).

fof(f163,plain,
    relation(sK14),
    inference(cnf_transformation,[],[f104]) ).

fof(f257,plain,
    spl15_18,
    inference(avatar_split_clause,[],[f162,f254]) ).

fof(f254,plain,
    ( spl15_18
  <=> function(sK13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_18])]) ).

fof(f162,plain,
    function(sK13),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ( function(sK13)
    & relation(sK13) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f45,f101]) ).

fof(f101,plain,
    ( ? [X0] :
        ( function(X0)
        & relation(X0) )
   => ( function(sK13)
      & relation(sK13) ) ),
    introduced(choice_axiom,[]) ).

fof(f45,plain,
    ? [X0] :
      ( function(X0)
      & relation(X0) ),
    inference(pure_predicate_removal,[],[f27]) ).

fof(f27,axiom,
    ? [X0] :
      ( one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).

fof(f252,plain,
    spl15_17,
    inference(avatar_split_clause,[],[f161,f249]) ).

fof(f249,plain,
    ( spl15_17
  <=> relation(sK13) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_17])]) ).

fof(f161,plain,
    relation(sK13),
    inference(cnf_transformation,[],[f102]) ).

fof(f247,plain,
    spl15_16,
    inference(avatar_split_clause,[],[f160,f244]) ).

fof(f244,plain,
    ( spl15_16
  <=> function(sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_16])]) ).

fof(f160,plain,
    function(sK12),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ( function(sK12)
    & relation(sK12) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f25,f99]) ).

fof(f99,plain,
    ( ? [X0] :
        ( function(X0)
        & relation(X0) )
   => ( function(sK12)
      & relation(sK12) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,axiom,
    ? [X0] :
      ( function(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).

fof(f242,plain,
    spl15_15,
    inference(avatar_split_clause,[],[f159,f239]) ).

fof(f239,plain,
    ( spl15_15
  <=> relation(sK12) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_15])]) ).

fof(f159,plain,
    relation(sK12),
    inference(cnf_transformation,[],[f100]) ).

fof(f237,plain,
    spl15_14,
    inference(avatar_split_clause,[],[f158,f234]) ).

fof(f234,plain,
    ( spl15_14
  <=> relation_empty_yielding(sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_14])]) ).

fof(f158,plain,
    relation_empty_yielding(sK11),
    inference(cnf_transformation,[],[f98]) ).

fof(f98,plain,
    ( relation_empty_yielding(sK11)
    & relation(sK11) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f33,f97]) ).

fof(f97,plain,
    ( ? [X0] :
        ( relation_empty_yielding(X0)
        & relation(X0) )
   => ( relation_empty_yielding(sK11)
      & relation(sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,axiom,
    ? [X0] :
      ( relation_empty_yielding(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).

fof(f232,plain,
    spl15_13,
    inference(avatar_split_clause,[],[f157,f229]) ).

fof(f229,plain,
    ( spl15_13
  <=> relation(sK11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_13])]) ).

fof(f157,plain,
    relation(sK11),
    inference(cnf_transformation,[],[f98]) ).

fof(f227,plain,
    spl15_12,
    inference(avatar_split_clause,[],[f156,f224]) ).

fof(f224,plain,
    ( spl15_12
  <=> relation(sK10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_12])]) ).

fof(f156,plain,
    relation(sK10),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ( relation(sK10)
    & empty(sK10) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f31,f95]) ).

fof(f95,plain,
    ( ? [X0] :
        ( relation(X0)
        & empty(X0) )
   => ( relation(sK10)
      & empty(sK10) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,axiom,
    ? [X0] :
      ( relation(X0)
      & empty(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).

fof(f222,plain,
    spl15_11,
    inference(avatar_split_clause,[],[f155,f219]) ).

fof(f155,plain,
    empty(sK10),
    inference(cnf_transformation,[],[f96]) ).

fof(f217,plain,
    spl15_10,
    inference(avatar_split_clause,[],[f154,f214]) ).

fof(f214,plain,
    ( spl15_10
  <=> relation(sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_10])]) ).

fof(f154,plain,
    relation(sK9),
    inference(cnf_transformation,[],[f94]) ).

fof(f94,plain,
    ( relation(sK9)
    & ~ empty(sK9) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f32,f93]) ).

fof(f93,plain,
    ( ? [X0] :
        ( relation(X0)
        & ~ empty(X0) )
   => ( relation(sK9)
      & ~ empty(sK9) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,axiom,
    ? [X0] :
      ( relation(X0)
      & ~ empty(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).

fof(f212,plain,
    ~ spl15_9,
    inference(avatar_split_clause,[],[f153,f209]) ).

fof(f209,plain,
    ( spl15_9
  <=> empty(sK9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_9])]) ).

fof(f153,plain,
    ~ empty(sK9),
    inference(cnf_transformation,[],[f94]) ).

fof(f207,plain,
    spl15_8,
    inference(avatar_split_clause,[],[f152,f204]) ).

fof(f152,plain,
    empty(sK8),
    inference(cnf_transformation,[],[f92]) ).

fof(f92,plain,
    empty(sK8),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f34,f91]) ).

fof(f91,plain,
    ( ? [X0] : empty(X0)
   => empty(sK8) ),
    introduced(choice_axiom,[]) ).

fof(f34,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(f202,plain,
    ~ spl15_7,
    inference(avatar_split_clause,[],[f151,f199]) ).

fof(f199,plain,
    ( spl15_7
  <=> empty(sK7) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_7])]) ).

fof(f151,plain,
    ~ empty(sK7),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ~ empty(sK7),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f35,f89]) ).

fof(f89,plain,
    ( ? [X0] : ~ empty(X0)
   => ~ empty(sK7) ),
    introduced(choice_axiom,[]) ).

fof(f35,axiom,
    ? [X0] : ~ empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).

fof(f197,plain,
    spl15_6,
    inference(avatar_split_clause,[],[f114,f194]) ).

fof(f114,plain,
    relation_empty_yielding(empty_set),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ( relation_empty_yielding(empty_set)
    & relation(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).

fof(f192,plain,
    spl15_5,
    inference(avatar_split_clause,[],[f111,f189]) ).

fof(f189,plain,
    ( spl15_5
  <=> relation(empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl15_5])]) ).

fof(f111,plain,
    relation(empty_set),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ( relation(empty_set)
    & empty(empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).

fof(f187,plain,
    spl15_4,
    inference(avatar_split_clause,[],[f109,f184]) ).

fof(f109,plain,
    empty(empty_set),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).

fof(f182,plain,
    spl15_3,
    inference(avatar_split_clause,[],[f107,f179]) ).

fof(f107,plain,
    in(sK1,relation_dom(relation_dom_restriction(sK2,sK0))),
    inference(cnf_transformation,[],[f77]) ).

fof(f177,plain,
    spl15_2,
    inference(avatar_split_clause,[],[f106,f174]) ).

fof(f106,plain,
    function(sK2),
    inference(cnf_transformation,[],[f77]) ).

fof(f172,plain,
    spl15_1,
    inference(avatar_split_clause,[],[f105,f169]) ).

fof(f105,plain,
    relation(sK2),
    inference(cnf_transformation,[],[f77]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU223+3 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n026.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon Apr 29 20:58:04 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (18499)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (18502)WARNING: value z3 for option sas not known
% 0.15/0.38  % (18500)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (18501)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (18503)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (18502)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38  % (18504)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38  % (18506)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38  % (18505)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [3]
% 0.15/0.39  TRYING [1]
% 0.15/0.39  TRYING [2]
% 0.15/0.39  % (18504)First to succeed.
% 0.15/0.39  TRYING [1]
% 0.15/0.39  TRYING [3]
% 0.15/0.39  TRYING [2]
% 0.15/0.39  % (18505)Also succeeded, but the first one will report.
% 0.15/0.39  TRYING [4]
% 0.15/0.39  % (18502)Also succeeded, but the first one will report.
% 0.15/0.39  % (18504)Refutation found. Thanks to Tanya!
% 0.15/0.39  % SZS status Theorem for theBenchmark
% 0.15/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40  % (18504)------------------------------
% 0.15/0.40  % (18504)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.40  % (18504)Termination reason: Refutation
% 0.15/0.40  
% 0.15/0.40  % (18504)Memory used [KB]: 1039
% 0.15/0.40  % (18504)Time elapsed: 0.016 s
% 0.15/0.40  % (18504)Instructions burned: 22 (million)
% 0.15/0.40  % (18504)------------------------------
% 0.15/0.40  % (18504)------------------------------
% 0.15/0.40  % (18499)Success in time 0.033 s
%------------------------------------------------------------------------------