TSTP Solution File: SEU129+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU129+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:27:08 EDT 2024
% Result : Theorem 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 128
% Syntax : Number of formulae : 388 ( 93 unt; 0 def)
% Number of atoms : 1073 ( 104 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 1159 ( 474 ~; 462 |; 103 &)
% ( 98 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 91 ( 89 usr; 84 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 591 ( 559 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f812,plain,
$false,
inference(avatar_sat_refutation,[],[f167,f172,f177,f182,f187,f191,f195,f199,f203,f207,f211,f215,f219,f223,f227,f231,f241,f247,f252,f259,f263,f267,f271,f275,f279,f298,f303,f307,f311,f315,f347,f356,f360,f364,f368,f394,f398,f403,f408,f412,f416,f433,f437,f451,f455,f459,f463,f482,f486,f499,f503,f507,f511,f524,f528,f532,f557,f561,f567,f571,f575,f579,f609,f613,f655,f664,f668,f692,f700,f704,f712,f716,f720,f724,f737,f750,f754,f758,f762,f766,f801,f811]) ).
fof(f811,plain,
( spl13_70
| ~ spl13_78 ),
inference(avatar_contradiction_clause,[],[f802]) ).
fof(f802,plain,
( $false
| spl13_70
| ~ spl13_78 ),
inference(resolution,[],[f736,f687]) ).
fof(f687,plain,
( ~ subset(set_intersection2(sK2,sK4),sK3)
| spl13_70 ),
inference(avatar_component_clause,[],[f685]) ).
fof(f685,plain,
( spl13_70
<=> subset(set_intersection2(sK2,sK4),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_70])]) ).
fof(f736,plain,
( ! [X0] : subset(set_intersection2(sK2,X0),sK3)
| ~ spl13_78 ),
inference(avatar_component_clause,[],[f735]) ).
fof(f735,plain,
( spl13_78
<=> ! [X0] : subset(set_intersection2(sK2,X0),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_78])]) ).
fof(f801,plain,
( spl13_71
| ~ spl13_81 ),
inference(avatar_contradiction_clause,[],[f789]) ).
fof(f789,plain,
( $false
| spl13_71
| ~ spl13_81 ),
inference(resolution,[],[f757,f691]) ).
fof(f691,plain,
( ~ subset(set_intersection2(sK2,sK4),sK4)
| spl13_71 ),
inference(avatar_component_clause,[],[f689]) ).
fof(f689,plain,
( spl13_71
<=> subset(set_intersection2(sK2,sK4),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_71])]) ).
fof(f757,plain,
( ! [X0,X1] : subset(set_intersection2(X1,X0),X0)
| ~ spl13_81 ),
inference(avatar_component_clause,[],[f756]) ).
fof(f756,plain,
( spl13_81
<=> ! [X0,X1] : subset(set_intersection2(X1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_81])]) ).
fof(f766,plain,
( spl13_83
| ~ spl13_16
| ~ spl13_34 ),
inference(avatar_split_clause,[],[f381,f362,f229,f764]) ).
fof(f764,plain,
( spl13_83
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_83])]) ).
fof(f229,plain,
( spl13_16
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_16])]) ).
fof(f362,plain,
( spl13_34
<=> ! [X0,X1] :
( in(sK6(X0,X1),X1)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_34])]) ).
fof(f381,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ empty(X1) )
| ~ spl13_16
| ~ spl13_34 ),
inference(resolution,[],[f363,f230]) ).
fof(f230,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl13_16 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f363,plain,
( ! [X0,X1] :
( in(sK6(X0,X1),X1)
| disjoint(X0,X1) )
| ~ spl13_34 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f762,plain,
( spl13_82
| ~ spl13_16
| ~ spl13_33 ),
inference(avatar_split_clause,[],[f376,f358,f229,f760]) ).
fof(f760,plain,
( spl13_82
<=> ! [X0,X1] :
( disjoint(X0,X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_82])]) ).
fof(f358,plain,
( spl13_33
<=> ! [X0,X1] :
( in(sK6(X0,X1),X0)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_33])]) ).
fof(f376,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| ~ empty(X0) )
| ~ spl13_16
| ~ spl13_33 ),
inference(resolution,[],[f359,f230]) ).
fof(f359,plain,
( ! [X0,X1] :
( in(sK6(X0,X1),X0)
| disjoint(X0,X1) )
| ~ spl13_33 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f758,plain,
( spl13_81
| ~ spl13_10
| ~ spl13_28 ),
inference(avatar_split_clause,[],[f335,f305,f205,f756]) ).
fof(f205,plain,
( spl13_10
<=> ! [X0,X1] : subset(set_intersection2(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_10])]) ).
fof(f305,plain,
( spl13_28
<=> ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_28])]) ).
fof(f335,plain,
( ! [X0,X1] : subset(set_intersection2(X1,X0),X0)
| ~ spl13_10
| ~ spl13_28 ),
inference(superposition,[],[f206,f306]) ).
fof(f306,plain,
( ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0)
| ~ spl13_28 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f206,plain,
( ! [X0,X1] : subset(set_intersection2(X0,X1),X0)
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f754,plain,
( spl13_80
| ~ spl13_9
| ~ spl13_27 ),
inference(avatar_split_clause,[],[f321,f301,f201,f752]) ).
fof(f752,plain,
( spl13_80
<=> ! [X0,X1] : subset(X0,set_union2(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_80])]) ).
fof(f201,plain,
( spl13_9
<=> ! [X0,X1] : subset(X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_9])]) ).
fof(f301,plain,
( spl13_27
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_27])]) ).
fof(f321,plain,
( ! [X0,X1] : subset(X0,set_union2(X1,X0))
| ~ spl13_9
| ~ spl13_27 ),
inference(superposition,[],[f202,f302]) ).
fof(f302,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)
| ~ spl13_27 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f202,plain,
( ! [X0,X1] : subset(X0,set_union2(X0,X1))
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f750,plain,
( spl13_79
| ~ spl13_10
| ~ spl13_18 ),
inference(avatar_split_clause,[],[f254,f245,f205,f748]) ).
fof(f748,plain,
( spl13_79
<=> ! [X0] : sK12 = set_intersection2(sK12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_79])]) ).
fof(f245,plain,
( spl13_18
<=> ! [X0] :
( ~ subset(X0,sK12)
| sK12 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_18])]) ).
fof(f254,plain,
( ! [X0] : sK12 = set_intersection2(sK12,X0)
| ~ spl13_10
| ~ spl13_18 ),
inference(resolution,[],[f246,f206]) ).
fof(f246,plain,
( ! [X0] :
( ~ subset(X0,sK12)
| sK12 = X0 )
| ~ spl13_18 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f737,plain,
( spl13_78
| ~ spl13_10
| ~ spl13_66 ),
inference(avatar_split_clause,[],[f671,f653,f205,f735]) ).
fof(f653,plain,
( spl13_66
<=> ! [X0] :
( subset(X0,sK3)
| ~ subset(X0,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_66])]) ).
fof(f671,plain,
( ! [X0] : subset(set_intersection2(sK2,X0),sK3)
| ~ spl13_10
| ~ spl13_66 ),
inference(resolution,[],[f654,f206]) ).
fof(f654,plain,
( ! [X0] :
( ~ subset(X0,sK2)
| subset(X0,sK3) )
| ~ spl13_66 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f724,plain,
( spl13_77
| ~ spl13_11
| ~ spl13_19
| ~ spl13_25 ),
inference(avatar_split_clause,[],[f294,f277,f249,f209,f722]) ).
fof(f722,plain,
( spl13_77
<=> ! [X0] : sP1(sK12,X0,sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_77])]) ).
fof(f209,plain,
( spl13_11
<=> ! [X0] : empty_set = set_intersection2(X0,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_11])]) ).
fof(f249,plain,
( spl13_19
<=> empty_set = sK12 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_19])]) ).
fof(f277,plain,
( spl13_25
<=> ! [X0,X1] : sP1(X1,X0,set_intersection2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_25])]) ).
fof(f294,plain,
( ! [X0] : sP1(sK12,X0,sK12)
| ~ spl13_11
| ~ spl13_19
| ~ spl13_25 ),
inference(forward_demodulation,[],[f292,f251]) ).
fof(f251,plain,
( empty_set = sK12
| ~ spl13_19 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f292,plain,
( ! [X0] : sP1(empty_set,X0,empty_set)
| ~ spl13_11
| ~ spl13_25 ),
inference(superposition,[],[f278,f210]) ).
fof(f210,plain,
( ! [X0] : empty_set = set_intersection2(X0,empty_set)
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f278,plain,
( ! [X0,X1] : sP1(X1,X0,set_intersection2(X0,X1))
| ~ spl13_25 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f720,plain,
( spl13_76
| ~ spl13_15
| ~ spl13_25 ),
inference(avatar_split_clause,[],[f293,f277,f225,f718]) ).
fof(f718,plain,
( spl13_76
<=> ! [X0] : sP1(X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_76])]) ).
fof(f225,plain,
( spl13_15
<=> ! [X0] : set_intersection2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_15])]) ).
fof(f293,plain,
( ! [X0] : sP1(X0,X0,X0)
| ~ spl13_15
| ~ spl13_25 ),
inference(superposition,[],[f278,f226]) ).
fof(f226,plain,
( ! [X0] : set_intersection2(X0,X0) = X0
| ~ spl13_15 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f716,plain,
( spl13_75
| ~ spl13_12
| ~ spl13_19
| ~ spl13_24 ),
inference(avatar_split_clause,[],[f291,f273,f249,f213,f714]) ).
fof(f714,plain,
( spl13_75
<=> ! [X0] : sP0(sK12,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_75])]) ).
fof(f213,plain,
( spl13_12
<=> ! [X0] : set_union2(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_12])]) ).
fof(f273,plain,
( spl13_24
<=> ! [X0,X1] : sP0(X1,X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_24])]) ).
fof(f291,plain,
( ! [X0] : sP0(sK12,X0,X0)
| ~ spl13_12
| ~ spl13_19
| ~ spl13_24 ),
inference(forward_demodulation,[],[f289,f251]) ).
fof(f289,plain,
( ! [X0] : sP0(empty_set,X0,X0)
| ~ spl13_12
| ~ spl13_24 ),
inference(superposition,[],[f274,f214]) ).
fof(f214,plain,
( ! [X0] : set_union2(X0,empty_set) = X0
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f274,plain,
( ! [X0,X1] : sP0(X1,X0,set_union2(X0,X1))
| ~ spl13_24 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f712,plain,
( spl13_74
| ~ spl13_14
| ~ spl13_24 ),
inference(avatar_split_clause,[],[f290,f273,f221,f710]) ).
fof(f710,plain,
( spl13_74
<=> ! [X0] : sP0(X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_74])]) ).
fof(f221,plain,
( spl13_14
<=> ! [X0] : set_union2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_14])]) ).
fof(f290,plain,
( ! [X0] : sP0(X0,X0,X0)
| ~ spl13_14
| ~ spl13_24 ),
inference(superposition,[],[f274,f222]) ).
fof(f222,plain,
( ! [X0] : set_union2(X0,X0) = X0
| ~ spl13_14 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f704,plain,
( spl13_73
| ~ spl13_8
| ~ spl13_19
| ~ spl13_34 ),
inference(avatar_split_clause,[],[f383,f362,f249,f197,f702]) ).
fof(f702,plain,
( spl13_73
<=> ! [X0] : disjoint(X0,sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_73])]) ).
fof(f197,plain,
( spl13_8
<=> ! [X2] : ~ in(X2,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_8])]) ).
fof(f383,plain,
( ! [X0] : disjoint(X0,sK12)
| ~ spl13_8
| ~ spl13_19
| ~ spl13_34 ),
inference(forward_demodulation,[],[f379,f251]) ).
fof(f379,plain,
( ! [X0] : disjoint(X0,empty_set)
| ~ spl13_8
| ~ spl13_34 ),
inference(resolution,[],[f363,f198]) ).
fof(f198,plain,
( ! [X2] : ~ in(X2,empty_set)
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f700,plain,
( spl13_72
| ~ spl13_8
| ~ spl13_19
| ~ spl13_33 ),
inference(avatar_split_clause,[],[f378,f358,f249,f197,f698]) ).
fof(f698,plain,
( spl13_72
<=> ! [X0] : disjoint(sK12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_72])]) ).
fof(f378,plain,
( ! [X0] : disjoint(sK12,X0)
| ~ spl13_8
| ~ spl13_19
| ~ spl13_33 ),
inference(forward_demodulation,[],[f374,f251]) ).
fof(f374,plain,
( ! [X0] : disjoint(empty_set,X0)
| ~ spl13_8
| ~ spl13_33 ),
inference(resolution,[],[f359,f198]) ).
fof(f692,plain,
( ~ spl13_70
| ~ spl13_71
| spl13_2
| ~ spl13_56 ),
inference(avatar_split_clause,[],[f533,f526,f169,f689,f685]) ).
fof(f169,plain,
( spl13_2
<=> subset(set_intersection2(sK2,sK4),set_intersection2(sK3,sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).
fof(f526,plain,
( spl13_56
<=> ! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_56])]) ).
fof(f533,plain,
( ~ subset(set_intersection2(sK2,sK4),sK4)
| ~ subset(set_intersection2(sK2,sK4),sK3)
| spl13_2
| ~ spl13_56 ),
inference(resolution,[],[f527,f171]) ).
fof(f171,plain,
( ~ subset(set_intersection2(sK2,sK4),set_intersection2(sK3,sK4))
| spl13_2 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f527,plain,
( ! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) )
| ~ spl13_56 ),
inference(avatar_component_clause,[],[f526]) ).
fof(f668,plain,
( spl13_69
| ~ spl13_1
| ~ spl13_45 ),
inference(avatar_split_clause,[],[f475,f453,f164,f666]) ).
fof(f666,plain,
( spl13_69
<=> ! [X0] :
( ~ in(X0,sK2)
| in(X0,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_69])]) ).
fof(f164,plain,
( spl13_1
<=> subset(sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).
fof(f453,plain,
( spl13_45
<=> ! [X0,X1,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_45])]) ).
fof(f475,plain,
( ! [X0] :
( ~ in(X0,sK2)
| in(X0,sK3) )
| ~ spl13_1
| ~ spl13_45 ),
inference(resolution,[],[f454,f166]) ).
fof(f166,plain,
( subset(sK2,sK3)
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f454,plain,
( ! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) )
| ~ spl13_45 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f664,plain,
( ~ spl13_67
| spl13_68
| ~ spl13_1
| ~ spl13_44 ),
inference(avatar_split_clause,[],[f468,f449,f164,f661,f657]) ).
fof(f657,plain,
( spl13_67
<=> subset(sK3,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_67])]) ).
fof(f661,plain,
( spl13_68
<=> sK2 = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_68])]) ).
fof(f449,plain,
( spl13_44
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_44])]) ).
fof(f468,plain,
( sK2 = sK3
| ~ subset(sK3,sK2)
| ~ spl13_1
| ~ spl13_44 ),
inference(resolution,[],[f450,f166]) ).
fof(f450,plain,
( ! [X0,X1] :
( ~ subset(X1,X0)
| X0 = X1
| ~ subset(X0,X1) )
| ~ spl13_44 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f655,plain,
( spl13_66
| ~ spl13_1
| ~ spl13_43 ),
inference(avatar_split_clause,[],[f446,f435,f164,f653]) ).
fof(f435,plain,
( spl13_43
<=> ! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_43])]) ).
fof(f446,plain,
( ! [X0] :
( subset(X0,sK3)
| ~ subset(X0,sK2) )
| ~ spl13_1
| ~ spl13_43 ),
inference(resolution,[],[f436,f166]) ).
fof(f436,plain,
( ! [X2,X0,X1] :
( ~ subset(X1,X2)
| subset(X0,X2)
| ~ subset(X0,X1) )
| ~ spl13_43 ),
inference(avatar_component_clause,[],[f435]) ).
fof(f613,plain,
spl13_65,
inference(avatar_split_clause,[],[f153,f611]) ).
fof(f611,plain,
( spl13_65
<=> ! [X2,X0,X1] :
( sP1(X0,X1,X2)
| ~ in(sK10(X0,X1,X2),X0)
| ~ in(sK10(X0,X1,X2),X1)
| ~ in(sK10(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_65])]) ).
fof(f153,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| ~ in(sK10(X0,X1,X2),X0)
| ~ in(sK10(X0,X1,X2),X1)
| ~ in(sK10(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( ( ~ in(sK10(X0,X1,X2),X0)
| ~ in(sK10(X0,X1,X2),X1)
| ~ in(sK10(X0,X1,X2),X2) )
& ( ( in(sK10(X0,X1,X2),X0)
& in(sK10(X0,X1,X2),X1) )
| in(sK10(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f92,f93]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( ~ in(sK10(X0,X1,X2),X0)
| ~ in(sK10(X0,X1,X2),X1)
| ~ in(sK10(X0,X1,X2),X2) )
& ( ( in(sK10(X0,X1,X2),X0)
& in(sK10(X0,X1,X2),X1) )
| in(sK10(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f91]) ).
fof(f91,plain,
! [X1,X0,X2] :
( ( sP1(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP1(X1,X0,X2) ) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X1,X0,X2] :
( ( sP1(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP1(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X1,X0,X2] :
( sP1(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f609,plain,
spl13_64,
inference(avatar_split_clause,[],[f143,f607]) ).
fof(f607,plain,
( spl13_64
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK9(X0,X1,X2),X0)
| in(sK9(X0,X1,X2),X1)
| in(sK9(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_64])]) ).
fof(f143,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK9(X0,X1,X2),X0)
| in(sK9(X0,X1,X2),X1)
| in(sK9(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ( ~ in(sK9(X0,X1,X2),X0)
& ~ in(sK9(X0,X1,X2),X1) )
| ~ in(sK9(X0,X1,X2),X2) )
& ( in(sK9(X0,X1,X2),X0)
| in(sK9(X0,X1,X2),X1)
| in(sK9(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f86,f87]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK9(X0,X1,X2),X0)
& ~ in(sK9(X0,X1,X2),X1) )
| ~ in(sK9(X0,X1,X2),X2) )
& ( in(sK9(X0,X1,X2),X0)
| in(sK9(X0,X1,X2),X1)
| in(sK9(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f85]) ).
fof(f85,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f579,plain,
spl13_63,
inference(avatar_split_clause,[],[f152,f577]) ).
fof(f577,plain,
( spl13_63
<=> ! [X2,X0,X1] :
( sP1(X0,X1,X2)
| in(sK10(X0,X1,X2),X0)
| in(sK10(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_63])]) ).
fof(f152,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| in(sK10(X0,X1,X2),X0)
| in(sK10(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f575,plain,
spl13_62,
inference(avatar_split_clause,[],[f151,f573]) ).
fof(f573,plain,
( spl13_62
<=> ! [X2,X0,X1] :
( sP1(X0,X1,X2)
| in(sK10(X0,X1,X2),X1)
| in(sK10(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_62])]) ).
fof(f151,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| in(sK10(X0,X1,X2),X1)
| in(sK10(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f571,plain,
spl13_61,
inference(avatar_split_clause,[],[f145,f569]) ).
fof(f569,plain,
( spl13_61
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK9(X0,X1,X2),X0)
| ~ in(sK9(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_61])]) ).
fof(f145,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK9(X0,X1,X2),X0)
| ~ in(sK9(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f567,plain,
spl13_60,
inference(avatar_split_clause,[],[f144,f565]) ).
fof(f565,plain,
( spl13_60
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK9(X0,X1,X2),X1)
| ~ in(sK9(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_60])]) ).
fof(f144,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(sK9(X0,X1,X2),X1)
| ~ in(sK9(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f561,plain,
spl13_59,
inference(avatar_split_clause,[],[f150,f559]) ).
fof(f559,plain,
( spl13_59
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_59])]) ).
fof(f150,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f557,plain,
spl13_58,
inference(avatar_split_clause,[],[f140,f555]) ).
fof(f555,plain,
( spl13_58
<=> ! [X2,X4,X0,X1] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_58])]) ).
fof(f140,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f532,plain,
spl13_57,
inference(avatar_split_clause,[],[f114,f530]) ).
fof(f530,plain,
( spl13_57
<=> ! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_57])]) ).
fof(f114,plain,
! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f528,plain,
spl13_56,
inference(avatar_split_clause,[],[f113,f526]) ).
fof(f113,plain,
! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f524,plain,
( spl13_54
| ~ spl13_55
| ~ spl13_21
| ~ spl13_36 ),
inference(avatar_split_clause,[],[f439,f391,f261,f521,f517]) ).
fof(f517,plain,
( spl13_54
<=> empty(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_54])]) ).
fof(f521,plain,
( spl13_55
<=> empty(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_55])]) ).
fof(f261,plain,
( spl13_21
<=> ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_21])]) ).
fof(f391,plain,
( spl13_36
<=> sK3 = set_union2(sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_36])]) ).
fof(f439,plain,
( ~ empty(sK3)
| empty(sK2)
| ~ spl13_21
| ~ spl13_36 ),
inference(superposition,[],[f262,f393]) ).
fof(f393,plain,
( sK3 = set_union2(sK2,sK3)
| ~ spl13_36 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f262,plain,
( ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) )
| ~ spl13_21 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f511,plain,
spl13_53,
inference(avatar_split_clause,[],[f149,f509]) ).
fof(f509,plain,
( spl13_53
<=> ! [X4,X0,X2,X1] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_53])]) ).
fof(f149,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f507,plain,
spl13_52,
inference(avatar_split_clause,[],[f148,f505]) ).
fof(f505,plain,
( spl13_52
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_52])]) ).
fof(f148,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f503,plain,
spl13_51,
inference(avatar_split_clause,[],[f142,f501]) ).
fof(f501,plain,
( spl13_51
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_51])]) ).
fof(f142,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f499,plain,
spl13_50,
inference(avatar_split_clause,[],[f141,f497]) ).
fof(f497,plain,
( spl13_50
<=> ! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_50])]) ).
fof(f141,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f486,plain,
spl13_49,
inference(avatar_split_clause,[],[f106,f484]) ).
fof(f484,plain,
( spl13_49
<=> ! [X0,X1] :
( in(sK5(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_49])]) ).
fof(f106,plain,
! [X0,X1] :
( in(sK5(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( in(sK5(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f46,f69]) ).
fof(f69,plain,
! [X0,X1] :
( ? [X3] : in(X3,set_intersection2(X0,X1))
=> in(sK5(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( ? [X3] : in(X3,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f482,plain,
( spl13_48
| ~ spl13_24
| ~ spl13_36 ),
inference(avatar_split_clause,[],[f438,f391,f273,f479]) ).
fof(f479,plain,
( spl13_48
<=> sP0(sK3,sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_48])]) ).
fof(f438,plain,
( sP0(sK3,sK2,sK3)
| ~ spl13_24
| ~ spl13_36 ),
inference(superposition,[],[f274,f393]) ).
fof(f463,plain,
spl13_47,
inference(avatar_split_clause,[],[f155,f461]) ).
fof(f461,plain,
( spl13_47
<=> ! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ sP1(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_47])]) ).
fof(f155,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ sP1(X1,X0,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP1(X1,X0,X2) )
& ( sP1(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP1(X1,X0,X2) ),
inference(definition_folding,[],[f8,f65]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f459,plain,
spl13_46,
inference(avatar_split_clause,[],[f147,f457]) ).
fof(f457,plain,
( spl13_46
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP0(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_46])]) ).
fof(f147,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP0(X1,X0,X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f6,f63]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f455,plain,
spl13_45,
inference(avatar_split_clause,[],[f135,f453]) ).
fof(f135,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK8(X0,X1),X1)
& in(sK8(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f81,f82]) ).
fof(f82,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK8(X0,X1),X1)
& in(sK8(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f451,plain,
spl13_44,
inference(avatar_split_clause,[],[f132,f449]) ).
fof(f132,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f437,plain,
spl13_43,
inference(avatar_split_clause,[],[f112,f435]) ).
fof(f112,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f433,plain,
spl13_42,
inference(avatar_split_clause,[],[f110,f431]) ).
fof(f431,plain,
( spl13_42
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_42])]) ).
fof(f110,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ( in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f47,f71]) ).
fof(f71,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
=> ( in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X3] :
~ ( in(X3,X1)
& in(X3,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f416,plain,
( spl13_41
| ~ spl13_19
| ~ spl13_38 ),
inference(avatar_split_clause,[],[f404,f401,f249,f414]) ).
fof(f414,plain,
( spl13_41
<=> ! [X0,X1] :
( set_intersection2(X0,X1) != sK12
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_41])]) ).
fof(f401,plain,
( spl13_38
<=> ! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_38])]) ).
fof(f404,plain,
( ! [X0,X1] :
( set_intersection2(X0,X1) != sK12
| disjoint(X0,X1) )
| ~ spl13_19
| ~ spl13_38 ),
inference(forward_demodulation,[],[f402,f251]) ).
fof(f402,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
| ~ spl13_38 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f412,plain,
spl13_40,
inference(avatar_split_clause,[],[f137,f410]) ).
fof(f410,plain,
( spl13_40
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(sK8(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_40])]) ).
fof(f137,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f408,plain,
spl13_39,
inference(avatar_split_clause,[],[f136,f406]) ).
fof(f406,plain,
( spl13_39
<=> ! [X0,X1] :
( subset(X0,X1)
| in(sK8(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_39])]) ).
fof(f136,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f403,plain,
spl13_38,
inference(avatar_split_clause,[],[f134,f401]) ).
fof(f134,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f398,plain,
spl13_37,
inference(avatar_split_clause,[],[f133,f396]) ).
fof(f396,plain,
( spl13_37
<=> ! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_37])]) ).
fof(f133,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f394,plain,
( spl13_36
| ~ spl13_1
| ~ spl13_35 ),
inference(avatar_split_clause,[],[f388,f366,f164,f391]) ).
fof(f366,plain,
( spl13_35
<=> ! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_35])]) ).
fof(f388,plain,
( sK3 = set_union2(sK2,sK3)
| ~ spl13_1
| ~ spl13_35 ),
inference(resolution,[],[f367,f166]) ).
fof(f367,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 )
| ~ spl13_35 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f368,plain,
spl13_35,
inference(avatar_split_clause,[],[f111,f366]) ).
fof(f111,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f364,plain,
spl13_34,
inference(avatar_split_clause,[],[f109,f362]) ).
fof(f109,plain,
! [X0,X1] :
( in(sK6(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f360,plain,
spl13_33,
inference(avatar_split_clause,[],[f108,f358]) ).
fof(f108,plain,
! [X0,X1] :
( in(sK6(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f356,plain,
spl13_32,
inference(avatar_split_clause,[],[f107,f354]) ).
fof(f354,plain,
( spl13_32
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_32])]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f347,plain,
( spl13_31
| ~ spl13_6
| ~ spl13_19 ),
inference(avatar_split_clause,[],[f287,f249,f189,f345]) ).
fof(f345,plain,
( spl13_31
<=> ! [X0] : subset(sK12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_31])]) ).
fof(f189,plain,
( spl13_6
<=> ! [X0] : subset(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).
fof(f287,plain,
( ! [X0] : subset(sK12,X0)
| ~ spl13_6
| ~ spl13_19 ),
inference(superposition,[],[f190,f251]) ).
fof(f190,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f315,plain,
( spl13_30
| ~ spl13_19
| ~ spl13_26 ),
inference(avatar_split_clause,[],[f299,f296,f249,f313]) ).
fof(f313,plain,
( spl13_30
<=> ! [X0] :
( sK12 = X0
| in(sK7(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_30])]) ).
fof(f296,plain,
( spl13_26
<=> ! [X0] :
( empty_set = X0
| in(sK7(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_26])]) ).
fof(f299,plain,
( ! [X0] :
( sK12 = X0
| in(sK7(X0),X0) )
| ~ spl13_19
| ~ spl13_26 ),
inference(forward_demodulation,[],[f297,f251]) ).
fof(f297,plain,
( ! [X0] :
( empty_set = X0
| in(sK7(X0),X0) )
| ~ spl13_26 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f311,plain,
spl13_29,
inference(avatar_split_clause,[],[f138,f309]) ).
fof(f309,plain,
( spl13_29
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_29])]) ).
fof(f138,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f307,plain,
spl13_28,
inference(avatar_split_clause,[],[f125,f305]) ).
fof(f125,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f303,plain,
spl13_27,
inference(avatar_split_clause,[],[f124,f301]) ).
fof(f124,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f298,plain,
spl13_26,
inference(avatar_split_clause,[],[f120,f296]) ).
fof(f120,plain,
! [X0] :
( empty_set = X0
| in(sK7(X0),X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ( empty_set = X0
| in(sK7(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f74,f75]) ).
fof(f75,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK7(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f73]) ).
fof(f73,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f279,plain,
spl13_25,
inference(avatar_split_clause,[],[f162,f277]) ).
fof(f162,plain,
! [X0,X1] : sP1(X1,X0,set_intersection2(X0,X1)),
inference(equality_resolution,[],[f154]) ).
fof(f154,plain,
! [X2,X0,X1] :
( sP1(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f95]) ).
fof(f275,plain,
spl13_24,
inference(avatar_split_clause,[],[f161,f273]) ).
fof(f161,plain,
! [X0,X1] : sP0(X1,X0,set_union2(X0,X1)),
inference(equality_resolution,[],[f146]) ).
fof(f146,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f89]) ).
fof(f271,plain,
spl13_23,
inference(avatar_split_clause,[],[f129,f269]) ).
fof(f269,plain,
( spl13_23
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_23])]) ).
fof(f129,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f267,plain,
spl13_22,
inference(avatar_split_clause,[],[f128,f265]) ).
fof(f265,plain,
( spl13_22
<=> ! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_22])]) ).
fof(f128,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f263,plain,
spl13_21,
inference(avatar_split_clause,[],[f127,f261]) ).
fof(f127,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f259,plain,
spl13_20,
inference(avatar_split_clause,[],[f126,f257]) ).
fof(f257,plain,
( spl13_20
<=> ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_20])]) ).
fof(f126,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f252,plain,
( spl13_19
| ~ spl13_5
| ~ spl13_13 ),
inference(avatar_split_clause,[],[f235,f217,f184,f249]) ).
fof(f184,plain,
( spl13_5
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).
fof(f217,plain,
( spl13_13
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_13])]) ).
fof(f235,plain,
( empty_set = sK12
| ~ spl13_5
| ~ spl13_13 ),
inference(resolution,[],[f218,f186]) ).
fof(f186,plain,
( empty(sK12)
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f184]) ).
fof(f218,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl13_13 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f247,plain,
( spl13_18
| ~ spl13_5
| ~ spl13_13
| ~ spl13_17 ),
inference(avatar_split_clause,[],[f243,f239,f217,f184,f245]) ).
fof(f239,plain,
( spl13_17
<=> ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_17])]) ).
fof(f243,plain,
( ! [X0] :
( ~ subset(X0,sK12)
| sK12 = X0 )
| ~ spl13_5
| ~ spl13_13
| ~ spl13_17 ),
inference(forward_demodulation,[],[f242,f235]) ).
fof(f242,plain,
( ! [X0] :
( sK12 = X0
| ~ subset(X0,empty_set) )
| ~ spl13_5
| ~ spl13_13
| ~ spl13_17 ),
inference(forward_demodulation,[],[f240,f235]) ).
fof(f240,plain,
( ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) )
| ~ spl13_17 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f241,plain,
spl13_17,
inference(avatar_split_clause,[],[f103,f239]) ).
fof(f103,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f231,plain,
spl13_16,
inference(avatar_split_clause,[],[f139,f229]) ).
fof(f139,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f227,plain,
spl13_15,
inference(avatar_split_clause,[],[f123,f225]) ).
fof(f123,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f223,plain,
spl13_14,
inference(avatar_split_clause,[],[f122,f221]) ).
fof(f122,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f219,plain,
spl13_13,
inference(avatar_split_clause,[],[f118,f217]) ).
fof(f118,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f215,plain,
spl13_12,
inference(avatar_split_clause,[],[f117,f213]) ).
fof(f117,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(f211,plain,
spl13_11,
inference(avatar_split_clause,[],[f116,f209]) ).
fof(f116,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] : empty_set = set_intersection2(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(f207,plain,
spl13_10,
inference(avatar_split_clause,[],[f105,f205]) ).
fof(f105,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f203,plain,
spl13_9,
inference(avatar_split_clause,[],[f104,f201]) ).
fof(f104,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f199,plain,
spl13_8,
inference(avatar_split_clause,[],[f158,f197]) ).
fof(f158,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f119]) ).
fof(f119,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f76]) ).
fof(f195,plain,
spl13_7,
inference(avatar_split_clause,[],[f121,f193]) ).
fof(f193,plain,
( spl13_7
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_7])]) ).
fof(f121,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f191,plain,
spl13_6,
inference(avatar_split_clause,[],[f102,f189]) ).
fof(f102,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f187,plain,
spl13_5,
inference(avatar_split_clause,[],[f157,f184]) ).
fof(f157,plain,
empty(sK12),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
empty(sK12),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f18,f98]) ).
fof(f98,plain,
( ? [X0] : empty(X0)
=> empty(sK12) ),
introduced(choice_axiom,[]) ).
fof(f18,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f182,plain,
~ spl13_4,
inference(avatar_split_clause,[],[f156,f179]) ).
fof(f179,plain,
( spl13_4
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).
fof(f156,plain,
~ empty(sK11),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
~ empty(sK11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f19,f96]) ).
fof(f96,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK11) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f177,plain,
spl13_3,
inference(avatar_split_clause,[],[f115,f174]) ).
fof(f174,plain,
( spl13_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).
fof(f115,plain,
empty(empty_set),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f172,plain,
~ spl13_2,
inference(avatar_split_clause,[],[f101,f169]) ).
fof(f101,plain,
~ subset(set_intersection2(sK2,sK4),set_intersection2(sK3,sK4)),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
( ~ subset(set_intersection2(sK2,sK4),set_intersection2(sK3,sK4))
& subset(sK2,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f44,f67]) ).
fof(f67,plain,
( ? [X0,X1,X2] :
( ~ subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
& subset(X0,X1) )
=> ( ~ subset(set_intersection2(sK2,sK4),set_intersection2(sK3,sK4))
& subset(sK2,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f44,plain,
? [X0,X1,X2] :
( ~ subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
& subset(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
inference(negated_conjecture,[],[f27]) ).
fof(f27,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(f167,plain,
spl13_1,
inference(avatar_split_clause,[],[f100,f164]) ).
fof(f100,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU129+2 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 11:47:36 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (7079)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (7083)WARNING: value z3 for option sas not known
% 0.15/0.38 % (7082)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 % (7081)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (7083)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 % (7084)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (7085)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 % (7086)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 % (7087)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 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 TRYING [1]
% 0.15/0.39 TRYING [4]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 % (7085)First to succeed.
% 0.15/0.40 % (7085)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7079"
% 0.15/0.40 TRYING [4]
% 0.15/0.40 % (7085)Refutation found. Thanks to Tanya!
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40 % (7085)------------------------------
% 0.15/0.40 % (7085)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.40 % (7085)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (7085)Memory used [KB]: 1100
% 0.15/0.40 % (7085)Time elapsed: 0.022 s
% 0.15/0.40 % (7085)Instructions burned: 29 (million)
% 0.15/0.40 % (7079)Success in time 0.039 s
%------------------------------------------------------------------------------