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