TSTP Solution File: ALG178+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG178+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n005.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 04:27:07 EDT 2024
% Result : Theorem 0.14s 0.41s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 110
% Syntax : Number of formulae : 405 ( 16 unt; 0 def)
% Number of atoms : 1475 ( 277 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1977 ( 907 ~; 893 |; 37 &)
% ( 103 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 107 ( 105 usr; 104 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 400 ( 394 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1108,plain,
$false,
inference(avatar_sat_refutation,[],[f33,f37,f41,f45,f52,f57,f64,f68,f72,f81,f85,f89,f98,f102,f110,f114,f124,f128,f132,f144,f148,f152,f166,f170,f175,f189,f193,f203,f210,f215,f220,f230,f240,f244,f248,f252,f261,f279,f283,f291,f296,f300,f304,f316,f320,f324,f325,f329,f333,f353,f357,f361,f398,f402,f406,f435,f474,f478,f482,f502,f506,f510,f519,f523,f545,f549,f561,f572,f577,f582,f587,f592,f676,f719,f761,f765,f769,f773,f778,f782,f786,f790,f794,f798,f802,f806,f810,f841,f996,f1000,f1024,f1028,f1032,f1036,f1040,f1044,f1049,f1053,f1057,f1061,f1065,f1069,f1073,f1107]) ).
fof(f1107,plain,
( spl2_10
| ~ spl2_13
| ~ spl2_30
| ~ spl2_36
| ~ spl2_37
| ~ spl2_43
| ~ spl2_70
| ~ spl2_74
| ~ spl2_77 ),
inference(avatar_split_clause,[],[f855,f767,f716,f574,f298,f254,f250,f212,f95,f78]) ).
fof(f78,plain,
( spl2_10
<=> sK1 = op2(sK0,op2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).
fof(f95,plain,
( spl2_13
<=> sK1 = h(j(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).
fof(f212,plain,
( spl2_30
<=> j(op2(sK0,sK1)) = op1(j(sK0),j(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).
fof(f250,plain,
( spl2_36
<=> ! [X0] :
( ~ sorti1(X0)
| j(sK1) = op1(X0,op1(X0,j(sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_36])]) ).
fof(f254,plain,
( spl2_37
<=> sorti1(j(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_37])]) ).
fof(f298,plain,
( spl2_43
<=> ! [X0] :
( j(op2(sK0,h(X0))) = op1(j(sK0),j(h(X0)))
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_43])]) ).
fof(f574,plain,
( spl2_70
<=> op2(sK0,sK1) = h(j(op2(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_70])]) ).
fof(f716,plain,
( spl2_74
<=> sorti1(j(op2(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_74])]) ).
fof(f767,plain,
( spl2_77
<=> ! [X0] :
( op2(sK0,h(X0)) = h(j(op2(sK0,h(X0))))
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_77])]) ).
fof(f855,plain,
( sK1 = op2(sK0,op2(sK0,sK1))
| ~ spl2_13
| ~ spl2_30
| ~ spl2_36
| ~ spl2_37
| ~ spl2_43
| ~ spl2_70
| ~ spl2_74
| ~ spl2_77 ),
inference(forward_demodulation,[],[f854,f97]) ).
fof(f97,plain,
( sK1 = h(j(sK1))
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f854,plain,
( op2(sK0,op2(sK0,sK1)) = h(j(sK1))
| ~ spl2_30
| ~ spl2_36
| ~ spl2_37
| ~ spl2_43
| ~ spl2_70
| ~ spl2_74
| ~ spl2_77 ),
inference(forward_demodulation,[],[f853,f752]) ).
fof(f752,plain,
( j(sK1) = j(op2(sK0,op2(sK0,sK1)))
| ~ spl2_30
| ~ spl2_36
| ~ spl2_37
| ~ spl2_43
| ~ spl2_70
| ~ spl2_74 ),
inference(forward_demodulation,[],[f751,f385]) ).
fof(f385,plain,
( j(sK1) = op1(j(sK0),j(op2(sK0,sK1)))
| ~ spl2_30
| ~ spl2_36
| ~ spl2_37 ),
inference(forward_demodulation,[],[f371,f214]) ).
fof(f214,plain,
( j(op2(sK0,sK1)) = op1(j(sK0),j(sK1))
| ~ spl2_30 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f371,plain,
( j(sK1) = op1(j(sK0),op1(j(sK0),j(sK1)))
| ~ spl2_36
| ~ spl2_37 ),
inference(resolution,[],[f255,f251]) ).
fof(f251,plain,
( ! [X0] :
( ~ sorti1(X0)
| j(sK1) = op1(X0,op1(X0,j(sK1))) )
| ~ spl2_36 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f255,plain,
( sorti1(j(sK0))
| ~ spl2_37 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f751,plain,
( op1(j(sK0),j(op2(sK0,sK1))) = j(op2(sK0,op2(sK0,sK1)))
| ~ spl2_43
| ~ spl2_70
| ~ spl2_74 ),
inference(forward_demodulation,[],[f734,f576]) ).
fof(f576,plain,
( op2(sK0,sK1) = h(j(op2(sK0,sK1)))
| ~ spl2_70 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f734,plain,
( j(op2(sK0,h(j(op2(sK0,sK1))))) = op1(j(sK0),j(h(j(op2(sK0,sK1)))))
| ~ spl2_43
| ~ spl2_74 ),
inference(resolution,[],[f718,f299]) ).
fof(f299,plain,
( ! [X0] :
( ~ sorti1(X0)
| j(op2(sK0,h(X0))) = op1(j(sK0),j(h(X0))) )
| ~ spl2_43 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f718,plain,
( sorti1(j(op2(sK0,sK1)))
| ~ spl2_74 ),
inference(avatar_component_clause,[],[f716]) ).
fof(f853,plain,
( op2(sK0,op2(sK0,sK1)) = h(j(op2(sK0,op2(sK0,sK1))))
| ~ spl2_70
| ~ spl2_74
| ~ spl2_77 ),
inference(forward_demodulation,[],[f844,f576]) ).
fof(f844,plain,
( op2(sK0,h(j(op2(sK0,sK1)))) = h(j(op2(sK0,h(j(op2(sK0,sK1))))))
| ~ spl2_74
| ~ spl2_77 ),
inference(resolution,[],[f768,f718]) ).
fof(f768,plain,
( ! [X0] :
( ~ sorti1(X0)
| op2(sK0,h(X0)) = h(j(op2(sK0,h(X0)))) )
| ~ spl2_77 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f1073,plain,
( spl2_103
| ~ spl2_6
| ~ spl2_55 ),
inference(avatar_split_clause,[],[f431,f404,f54,f1071]) ).
fof(f1071,plain,
( spl2_103
<=> ! [X0] :
( j(op2(sK1,op2(X0,sK1))) = op1(j(sK1),j(op2(X0,sK1)))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_103])]) ).
fof(f54,plain,
( spl2_6
<=> sorti2(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).
fof(f404,plain,
( spl2_55
<=> ! [X0,X1] :
( ~ sorti2(X0)
| j(op2(sK1,op2(X0,X1))) = op1(j(sK1),j(op2(X0,X1)))
| ~ sorti2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_55])]) ).
fof(f431,plain,
( ! [X0] :
( j(op2(sK1,op2(X0,sK1))) = op1(j(sK1),j(op2(X0,sK1)))
| ~ sorti2(X0) )
| ~ spl2_6
| ~ spl2_55 ),
inference(resolution,[],[f405,f56]) ).
fof(f56,plain,
( sorti2(sK1)
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f405,plain,
( ! [X0,X1] :
( ~ sorti2(X1)
| j(op2(sK1,op2(X0,X1))) = op1(j(sK1),j(op2(X0,X1)))
| ~ sorti2(X0) )
| ~ spl2_55 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f1069,plain,
( spl2_102
| ~ spl2_5
| ~ spl2_55 ),
inference(avatar_split_clause,[],[f430,f404,f49,f1067]) ).
fof(f1067,plain,
( spl2_102
<=> ! [X0] :
( j(op2(sK1,op2(X0,sK0))) = op1(j(sK1),j(op2(X0,sK0)))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_102])]) ).
fof(f49,plain,
( spl2_5
<=> sorti2(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).
fof(f430,plain,
( ! [X0] :
( j(op2(sK1,op2(X0,sK0))) = op1(j(sK1),j(op2(X0,sK0)))
| ~ sorti2(X0) )
| ~ spl2_5
| ~ spl2_55 ),
inference(resolution,[],[f405,f51]) ).
fof(f51,plain,
( sorti2(sK0)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f1065,plain,
( spl2_101
| ~ spl2_6
| ~ spl2_54 ),
inference(avatar_split_clause,[],[f427,f400,f54,f1063]) ).
fof(f1063,plain,
( spl2_101
<=> ! [X0] :
( j(op2(sK0,op2(X0,sK1))) = op1(j(sK0),j(op2(X0,sK1)))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_101])]) ).
fof(f400,plain,
( spl2_54
<=> ! [X0,X1] :
( ~ sorti2(X0)
| j(op2(sK0,op2(X0,X1))) = op1(j(sK0),j(op2(X0,X1)))
| ~ sorti2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_54])]) ).
fof(f427,plain,
( ! [X0] :
( j(op2(sK0,op2(X0,sK1))) = op1(j(sK0),j(op2(X0,sK1)))
| ~ sorti2(X0) )
| ~ spl2_6
| ~ spl2_54 ),
inference(resolution,[],[f401,f56]) ).
fof(f401,plain,
( ! [X0,X1] :
( ~ sorti2(X1)
| j(op2(sK0,op2(X0,X1))) = op1(j(sK0),j(op2(X0,X1)))
| ~ sorti2(X0) )
| ~ spl2_54 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f1061,plain,
( spl2_100
| ~ spl2_5
| ~ spl2_54 ),
inference(avatar_split_clause,[],[f426,f400,f49,f1059]) ).
fof(f1059,plain,
( spl2_100
<=> ! [X0] :
( j(op2(sK0,op2(X0,sK0))) = op1(j(sK0),j(op2(X0,sK0)))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_100])]) ).
fof(f426,plain,
( ! [X0] :
( j(op2(sK0,op2(X0,sK0))) = op1(j(sK0),j(op2(X0,sK0)))
| ~ sorti2(X0) )
| ~ spl2_5
| ~ spl2_54 ),
inference(resolution,[],[f401,f51]) ).
fof(f1057,plain,
( spl2_99
| ~ spl2_6
| ~ spl2_51 ),
inference(avatar_split_clause,[],[f414,f355,f54,f1055]) ).
fof(f1055,plain,
( spl2_99
<=> ! [X0] :
( j(op2(op2(X0,sK1),sK1)) = op1(j(op2(X0,sK1)),j(sK1))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_99])]) ).
fof(f355,plain,
( spl2_51
<=> ! [X0,X1] :
( j(op2(op2(X0,X1),sK1)) = op1(j(op2(X0,X1)),j(sK1))
| ~ sorti2(X1)
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_51])]) ).
fof(f414,plain,
( ! [X0] :
( j(op2(op2(X0,sK1),sK1)) = op1(j(op2(X0,sK1)),j(sK1))
| ~ sorti2(X0) )
| ~ spl2_6
| ~ spl2_51 ),
inference(resolution,[],[f356,f56]) ).
fof(f356,plain,
( ! [X0,X1] :
( ~ sorti2(X1)
| j(op2(op2(X0,X1),sK1)) = op1(j(op2(X0,X1)),j(sK1))
| ~ sorti2(X0) )
| ~ spl2_51 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f1053,plain,
( spl2_98
| ~ spl2_5
| ~ spl2_51 ),
inference(avatar_split_clause,[],[f413,f355,f49,f1051]) ).
fof(f1051,plain,
( spl2_98
<=> ! [X0] :
( j(op2(op2(X0,sK0),sK1)) = op1(j(op2(X0,sK0)),j(sK1))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_98])]) ).
fof(f413,plain,
( ! [X0] :
( j(op2(op2(X0,sK0),sK1)) = op1(j(op2(X0,sK0)),j(sK1))
| ~ sorti2(X0) )
| ~ spl2_5
| ~ spl2_51 ),
inference(resolution,[],[f356,f51]) ).
fof(f1049,plain,
( spl2_97
| ~ spl2_7
| ~ spl2_38
| ~ spl2_69
| ~ spl2_77
| ~ spl2_79 ),
inference(avatar_split_clause,[],[f852,f775,f767,f569,f258,f61,f1046]) ).
fof(f1046,plain,
( spl2_97
<=> sK0 = op2(sK0,op2(sK0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_97])]) ).
fof(f61,plain,
( spl2_7
<=> sK0 = h(j(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).
fof(f258,plain,
( spl2_38
<=> sorti1(j(op2(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_38])]) ).
fof(f569,plain,
( spl2_69
<=> op2(sK0,sK0) = h(j(op2(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_69])]) ).
fof(f775,plain,
( spl2_79
<=> j(sK0) = j(op2(sK0,op2(sK0,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_79])]) ).
fof(f852,plain,
( sK0 = op2(sK0,op2(sK0,sK0))
| ~ spl2_7
| ~ spl2_38
| ~ spl2_69
| ~ spl2_77
| ~ spl2_79 ),
inference(forward_demodulation,[],[f851,f63]) ).
fof(f63,plain,
( sK0 = h(j(sK0))
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f61]) ).
fof(f851,plain,
( h(j(sK0)) = op2(sK0,op2(sK0,sK0))
| ~ spl2_38
| ~ spl2_69
| ~ spl2_77
| ~ spl2_79 ),
inference(forward_demodulation,[],[f850,f777]) ).
fof(f777,plain,
( j(sK0) = j(op2(sK0,op2(sK0,sK0)))
| ~ spl2_79 ),
inference(avatar_component_clause,[],[f775]) ).
fof(f850,plain,
( op2(sK0,op2(sK0,sK0)) = h(j(op2(sK0,op2(sK0,sK0))))
| ~ spl2_38
| ~ spl2_69
| ~ spl2_77 ),
inference(forward_demodulation,[],[f843,f571]) ).
fof(f571,plain,
( op2(sK0,sK0) = h(j(op2(sK0,sK0)))
| ~ spl2_69 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f843,plain,
( op2(sK0,h(j(op2(sK0,sK0)))) = h(j(op2(sK0,h(j(op2(sK0,sK0))))))
| ~ spl2_38
| ~ spl2_77 ),
inference(resolution,[],[f768,f260]) ).
fof(f260,plain,
( sorti1(j(op2(sK0,sK0)))
| ~ spl2_38 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f1044,plain,
( spl2_96
| ~ spl2_6
| ~ spl2_50 ),
inference(avatar_split_clause,[],[f410,f351,f54,f1042]) ).
fof(f1042,plain,
( spl2_96
<=> ! [X0] :
( j(op2(op2(X0,sK1),sK0)) = op1(j(op2(X0,sK1)),j(sK0))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_96])]) ).
fof(f351,plain,
( spl2_50
<=> ! [X0,X1] :
( j(op2(op2(X0,X1),sK0)) = op1(j(op2(X0,X1)),j(sK0))
| ~ sorti2(X1)
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_50])]) ).
fof(f410,plain,
( ! [X0] :
( j(op2(op2(X0,sK1),sK0)) = op1(j(op2(X0,sK1)),j(sK0))
| ~ sorti2(X0) )
| ~ spl2_6
| ~ spl2_50 ),
inference(resolution,[],[f352,f56]) ).
fof(f352,plain,
( ! [X0,X1] :
( ~ sorti2(X1)
| j(op2(op2(X0,X1),sK0)) = op1(j(op2(X0,X1)),j(sK0))
| ~ sorti2(X0) )
| ~ spl2_50 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f1040,plain,
( spl2_95
| ~ spl2_5
| ~ spl2_50 ),
inference(avatar_split_clause,[],[f409,f351,f49,f1038]) ).
fof(f1038,plain,
( spl2_95
<=> ! [X0] :
( j(op2(op2(X0,sK0),sK0)) = op1(j(op2(X0,sK0)),j(sK0))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_95])]) ).
fof(f409,plain,
( ! [X0] :
( j(op2(op2(X0,sK0),sK0)) = op1(j(op2(X0,sK0)),j(sK0))
| ~ sorti2(X0) )
| ~ spl2_5
| ~ spl2_50 ),
inference(resolution,[],[f352,f51]) ).
fof(f1036,plain,
( spl2_94
| ~ spl2_2
| ~ spl2_44 ),
inference(avatar_split_clause,[],[f311,f302,f35,f1034]) ).
fof(f1034,plain,
( spl2_94
<=> ! [X0] :
( j(op2(sK1,h(j(X0)))) = op1(j(sK1),j(h(j(X0))))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_94])]) ).
fof(f35,plain,
( spl2_2
<=> ! [X6] :
( sorti1(j(X6))
| ~ sorti2(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).
fof(f302,plain,
( spl2_44
<=> ! [X0] :
( j(op2(sK1,h(X0))) = op1(j(sK1),j(h(X0)))
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_44])]) ).
fof(f311,plain,
( ! [X0] :
( j(op2(sK1,h(j(X0)))) = op1(j(sK1),j(h(j(X0))))
| ~ sorti2(X0) )
| ~ spl2_2
| ~ spl2_44 ),
inference(resolution,[],[f303,f36]) ).
fof(f36,plain,
( ! [X6] :
( sorti1(j(X6))
| ~ sorti2(X6) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f35]) ).
fof(f303,plain,
( ! [X0] :
( ~ sorti1(X0)
| j(op2(sK1,h(X0))) = op1(j(sK1),j(h(X0))) )
| ~ spl2_44 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f1032,plain,
( spl2_93
| ~ spl2_2
| ~ spl2_43 ),
inference(avatar_split_clause,[],[f309,f298,f35,f1030]) ).
fof(f1030,plain,
( spl2_93
<=> ! [X0] :
( j(op2(sK0,h(j(X0)))) = op1(j(sK0),j(h(j(X0))))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_93])]) ).
fof(f309,plain,
( ! [X0] :
( j(op2(sK0,h(j(X0)))) = op1(j(sK0),j(h(j(X0))))
| ~ sorti2(X0) )
| ~ spl2_2
| ~ spl2_43 ),
inference(resolution,[],[f299,f36]) ).
fof(f1028,plain,
( spl2_92
| ~ spl2_2
| ~ spl2_42 ),
inference(avatar_split_clause,[],[f307,f294,f35,f1026]) ).
fof(f1026,plain,
( spl2_92
<=> ! [X0] :
( j(op2(h(j(X0)),sK1)) = op1(j(h(j(X0))),j(sK1))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_92])]) ).
fof(f294,plain,
( spl2_42
<=> ! [X0] :
( j(op2(h(X0),sK1)) = op1(j(h(X0)),j(sK1))
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_42])]) ).
fof(f307,plain,
( ! [X0] :
( j(op2(h(j(X0)),sK1)) = op1(j(h(j(X0))),j(sK1))
| ~ sorti2(X0) )
| ~ spl2_2
| ~ spl2_42 ),
inference(resolution,[],[f295,f36]) ).
fof(f295,plain,
( ! [X0] :
( ~ sorti1(X0)
| j(op2(h(X0),sK1)) = op1(j(h(X0)),j(sK1)) )
| ~ spl2_42 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f1024,plain,
( spl2_91
| ~ spl2_2
| ~ spl2_41 ),
inference(avatar_split_clause,[],[f305,f289,f35,f1022]) ).
fof(f1022,plain,
( spl2_91
<=> ! [X0] :
( j(op2(h(j(X0)),sK0)) = op1(j(h(j(X0))),j(sK0))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_91])]) ).
fof(f289,plain,
( spl2_41
<=> ! [X0] :
( j(op2(h(X0),sK0)) = op1(j(h(X0)),j(sK0))
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_41])]) ).
fof(f305,plain,
( ! [X0] :
( j(op2(h(j(X0)),sK0)) = op1(j(h(j(X0))),j(sK0))
| ~ sorti2(X0) )
| ~ spl2_2
| ~ spl2_41 ),
inference(resolution,[],[f290,f36]) ).
fof(f290,plain,
( ! [X0] :
( ~ sorti1(X0)
| j(op2(h(X0),sK0)) = op1(j(h(X0)),j(sK0)) )
| ~ spl2_41 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f1000,plain,
( spl2_90
| ~ spl2_2
| ~ spl2_40 ),
inference(avatar_split_clause,[],[f286,f281,f35,f998]) ).
fof(f998,plain,
( spl2_90
<=> ! [X0] :
( op2(h(j(X0)),sK1) = h(op1(j(X0),j(sK1)))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_90])]) ).
fof(f281,plain,
( spl2_40
<=> ! [X0] :
( op2(h(X0),sK1) = h(op1(X0,j(sK1)))
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_40])]) ).
fof(f286,plain,
( ! [X0] :
( op2(h(j(X0)),sK1) = h(op1(j(X0),j(sK1)))
| ~ sorti2(X0) )
| ~ spl2_2
| ~ spl2_40 ),
inference(resolution,[],[f282,f36]) ).
fof(f282,plain,
( ! [X0] :
( ~ sorti1(X0)
| op2(h(X0),sK1) = h(op1(X0,j(sK1))) )
| ~ spl2_40 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f996,plain,
( spl2_89
| ~ spl2_2
| ~ spl2_39 ),
inference(avatar_split_clause,[],[f284,f277,f35,f994]) ).
fof(f994,plain,
( spl2_89
<=> ! [X0] :
( op2(h(j(X0)),sK0) = h(op1(j(X0),j(sK0)))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_89])]) ).
fof(f277,plain,
( spl2_39
<=> ! [X0] :
( op2(h(X0),sK0) = h(op1(X0,j(sK0)))
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_39])]) ).
fof(f284,plain,
( ! [X0] :
( op2(h(j(X0)),sK0) = h(op1(j(X0),j(sK0)))
| ~ sorti2(X0) )
| ~ spl2_2
| ~ spl2_39 ),
inference(resolution,[],[f278,f36]) ).
fof(f278,plain,
( ! [X0] :
( ~ sorti1(X0)
| op2(h(X0),sK0) = h(op1(X0,j(sK0))) )
| ~ spl2_39 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f841,plain,
( ~ spl2_38
| spl2_88
| ~ spl2_1
| ~ spl2_69 ),
inference(avatar_split_clause,[],[f588,f569,f31,f838,f258]) ).
fof(f838,plain,
( spl2_88
<=> sorti2(op2(sK0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_88])]) ).
fof(f31,plain,
( spl2_1
<=> ! [X7] :
( sorti2(h(X7))
| ~ sorti1(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).
fof(f588,plain,
( sorti2(op2(sK0,sK0))
| ~ sorti1(j(op2(sK0,sK0)))
| ~ spl2_1
| ~ spl2_69 ),
inference(superposition,[],[f32,f571]) ).
fof(f32,plain,
( ! [X7] :
( sorti2(h(X7))
| ~ sorti1(X7) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f810,plain,
( spl2_87
| ~ spl2_6
| ~ spl2_48 ),
inference(avatar_split_clause,[],[f347,f327,f54,f808]) ).
fof(f808,plain,
( spl2_87
<=> ! [X0] :
( op2(h(X0),sK1) = h(j(op2(h(X0),sK1)))
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_87])]) ).
fof(f327,plain,
( spl2_48
<=> ! [X0,X1] :
( ~ sorti2(X0)
| op2(h(X1),X0) = h(j(op2(h(X1),X0)))
| ~ sorti1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_48])]) ).
fof(f347,plain,
( ! [X0] :
( op2(h(X0),sK1) = h(j(op2(h(X0),sK1)))
| ~ sorti1(X0) )
| ~ spl2_6
| ~ spl2_48 ),
inference(resolution,[],[f328,f56]) ).
fof(f328,plain,
( ! [X0,X1] :
( ~ sorti2(X0)
| op2(h(X1),X0) = h(j(op2(h(X1),X0)))
| ~ sorti1(X1) )
| ~ spl2_48 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f806,plain,
( spl2_86
| ~ spl2_5
| ~ spl2_48 ),
inference(avatar_split_clause,[],[f346,f327,f49,f804]) ).
fof(f804,plain,
( spl2_86
<=> ! [X0] :
( op2(h(X0),sK0) = h(j(op2(h(X0),sK0)))
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_86])]) ).
fof(f346,plain,
( ! [X0] :
( op2(h(X0),sK0) = h(j(op2(h(X0),sK0)))
| ~ sorti1(X0) )
| ~ spl2_5
| ~ spl2_48 ),
inference(resolution,[],[f328,f51]) ).
fof(f802,plain,
( spl2_85
| ~ spl2_6
| ~ spl2_47 ),
inference(avatar_split_clause,[],[f343,f322,f54,f800]) ).
fof(f800,plain,
( spl2_85
<=> ! [X0] :
( op1(j(sK1),X0) = j(h(op1(j(sK1),X0)))
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_85])]) ).
fof(f322,plain,
( spl2_47
<=> ! [X0,X1] :
( ~ sorti1(X0)
| op1(j(X1),X0) = j(h(op1(j(X1),X0)))
| ~ sorti2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_47])]) ).
fof(f343,plain,
( ! [X0] :
( op1(j(sK1),X0) = j(h(op1(j(sK1),X0)))
| ~ sorti1(X0) )
| ~ spl2_6
| ~ spl2_47 ),
inference(resolution,[],[f323,f56]) ).
fof(f323,plain,
( ! [X0,X1] :
( ~ sorti2(X1)
| op1(j(X1),X0) = j(h(op1(j(X1),X0)))
| ~ sorti1(X0) )
| ~ spl2_47 ),
inference(avatar_component_clause,[],[f322]) ).
fof(f798,plain,
( spl2_84
| ~ spl2_5
| ~ spl2_47 ),
inference(avatar_split_clause,[],[f342,f322,f49,f796]) ).
fof(f796,plain,
( spl2_84
<=> ! [X0] :
( op1(j(sK0),X0) = j(h(op1(j(sK0),X0)))
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_84])]) ).
fof(f342,plain,
( ! [X0] :
( op1(j(sK0),X0) = j(h(op1(j(sK0),X0)))
| ~ sorti1(X0) )
| ~ spl2_5
| ~ spl2_47 ),
inference(resolution,[],[f323,f51]) ).
fof(f794,plain,
( spl2_83
| ~ spl2_6
| ~ spl2_46 ),
inference(avatar_split_clause,[],[f339,f318,f54,f792]) ).
fof(f792,plain,
( spl2_83
<=> ! [X0] :
( j(op2(X0,sK1)) = j(h(j(op2(X0,sK1))))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_83])]) ).
fof(f318,plain,
( spl2_46
<=> ! [X0,X1] :
( j(op2(X0,X1)) = j(h(j(op2(X0,X1))))
| ~ sorti2(X1)
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_46])]) ).
fof(f339,plain,
( ! [X0] :
( j(op2(X0,sK1)) = j(h(j(op2(X0,sK1))))
| ~ sorti2(X0) )
| ~ spl2_6
| ~ spl2_46 ),
inference(resolution,[],[f319,f56]) ).
fof(f319,plain,
( ! [X0,X1] :
( ~ sorti2(X1)
| j(op2(X0,X1)) = j(h(j(op2(X0,X1))))
| ~ sorti2(X0) )
| ~ spl2_46 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f790,plain,
( spl2_82
| ~ spl2_5
| ~ spl2_46 ),
inference(avatar_split_clause,[],[f338,f318,f49,f788]) ).
fof(f788,plain,
( spl2_82
<=> ! [X0] :
( j(op2(X0,sK0)) = j(h(j(op2(X0,sK0))))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_82])]) ).
fof(f338,plain,
( ! [X0] :
( j(op2(X0,sK0)) = j(h(j(op2(X0,sK0))))
| ~ sorti2(X0) )
| ~ spl2_5
| ~ spl2_46 ),
inference(resolution,[],[f319,f51]) ).
fof(f786,plain,
( spl2_81
| ~ spl2_2
| ~ spl2_36 ),
inference(avatar_split_clause,[],[f274,f250,f35,f784]) ).
fof(f784,plain,
( spl2_81
<=> ! [X0] :
( j(sK1) = op1(j(X0),op1(j(X0),j(sK1)))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_81])]) ).
fof(f274,plain,
( ! [X0] :
( j(sK1) = op1(j(X0),op1(j(X0),j(sK1)))
| ~ sorti2(X0) )
| ~ spl2_2
| ~ spl2_36 ),
inference(resolution,[],[f251,f36]) ).
fof(f782,plain,
( spl2_80
| ~ spl2_2
| ~ spl2_35 ),
inference(avatar_split_clause,[],[f272,f246,f35,f780]) ).
fof(f780,plain,
( spl2_80
<=> ! [X0] :
( j(sK0) = op1(j(X0),op1(j(X0),j(sK0)))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_80])]) ).
fof(f246,plain,
( spl2_35
<=> ! [X0] :
( ~ sorti1(X0)
| j(sK0) = op1(X0,op1(X0,j(sK0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_35])]) ).
fof(f272,plain,
( ! [X0] :
( j(sK0) = op1(j(X0),op1(j(X0),j(sK0)))
| ~ sorti2(X0) )
| ~ spl2_2
| ~ spl2_35 ),
inference(resolution,[],[f247,f36]) ).
fof(f247,plain,
( ! [X0] :
( ~ sorti1(X0)
| j(sK0) = op1(X0,op1(X0,j(sK0))) )
| ~ spl2_35 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f778,plain,
( spl2_79
| ~ spl2_5
| ~ spl2_25
| ~ spl2_33
| ~ spl2_35
| ~ spl2_37
| ~ spl2_38
| ~ spl2_43 ),
inference(avatar_split_clause,[],[f465,f298,f258,f254,f246,f238,f172,f49,f775]) ).
fof(f172,plain,
( spl2_25
<=> j(op2(sK0,sK0)) = op1(j(sK0),j(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_25])]) ).
fof(f238,plain,
( spl2_33
<=> ! [X0] :
( ~ sorti2(X0)
| op2(sK0,X0) = h(j(op2(sK0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_33])]) ).
fof(f465,plain,
( j(sK0) = j(op2(sK0,op2(sK0,sK0)))
| ~ spl2_5
| ~ spl2_25
| ~ spl2_33
| ~ spl2_35
| ~ spl2_37
| ~ spl2_38
| ~ spl2_43 ),
inference(forward_demodulation,[],[f464,f384]) ).
fof(f384,plain,
( j(sK0) = op1(j(sK0),j(op2(sK0,sK0)))
| ~ spl2_25
| ~ spl2_35
| ~ spl2_37 ),
inference(forward_demodulation,[],[f370,f174]) ).
fof(f174,plain,
( j(op2(sK0,sK0)) = op1(j(sK0),j(sK0))
| ~ spl2_25 ),
inference(avatar_component_clause,[],[f172]) ).
fof(f370,plain,
( j(sK0) = op1(j(sK0),op1(j(sK0),j(sK0)))
| ~ spl2_35
| ~ spl2_37 ),
inference(resolution,[],[f255,f247]) ).
fof(f464,plain,
( op1(j(sK0),j(op2(sK0,sK0))) = j(op2(sK0,op2(sK0,sK0)))
| ~ spl2_5
| ~ spl2_33
| ~ spl2_38
| ~ spl2_43 ),
inference(forward_demodulation,[],[f450,f266]) ).
fof(f266,plain,
( op2(sK0,sK0) = h(j(op2(sK0,sK0)))
| ~ spl2_5
| ~ spl2_33 ),
inference(resolution,[],[f239,f51]) ).
fof(f239,plain,
( ! [X0] :
( ~ sorti2(X0)
| op2(sK0,X0) = h(j(op2(sK0,X0))) )
| ~ spl2_33 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f450,plain,
( j(op2(sK0,h(j(op2(sK0,sK0))))) = op1(j(sK0),j(h(j(op2(sK0,sK0)))))
| ~ spl2_38
| ~ spl2_43 ),
inference(resolution,[],[f260,f299]) ).
fof(f773,plain,
( spl2_78
| ~ spl2_1
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f269,f242,f31,f771]) ).
fof(f771,plain,
( spl2_78
<=> ! [X0] :
( op2(sK1,h(X0)) = h(j(op2(sK1,h(X0))))
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_78])]) ).
fof(f242,plain,
( spl2_34
<=> ! [X0] :
( ~ sorti2(X0)
| op2(sK1,X0) = h(j(op2(sK1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_34])]) ).
fof(f269,plain,
( ! [X0] :
( op2(sK1,h(X0)) = h(j(op2(sK1,h(X0))))
| ~ sorti1(X0) )
| ~ spl2_1
| ~ spl2_34 ),
inference(resolution,[],[f243,f32]) ).
fof(f243,plain,
( ! [X0] :
( ~ sorti2(X0)
| op2(sK1,X0) = h(j(op2(sK1,X0))) )
| ~ spl2_34 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f769,plain,
( spl2_77
| ~ spl2_1
| ~ spl2_33 ),
inference(avatar_split_clause,[],[f265,f238,f31,f767]) ).
fof(f265,plain,
( ! [X0] :
( op2(sK0,h(X0)) = h(j(op2(sK0,h(X0))))
| ~ sorti1(X0) )
| ~ spl2_1
| ~ spl2_33 ),
inference(resolution,[],[f239,f32]) ).
fof(f765,plain,
( spl2_76
| ~ spl2_2
| ~ spl2_32 ),
inference(avatar_split_clause,[],[f262,f228,f35,f763]) ).
fof(f763,plain,
( spl2_76
<=> ! [X0] :
( j(h(j(X0))) = j(h(j(h(j(X0)))))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_76])]) ).
fof(f228,plain,
( spl2_32
<=> ! [X0] :
( j(h(X0)) = j(h(j(h(X0))))
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_32])]) ).
fof(f262,plain,
( ! [X0] :
( j(h(j(X0))) = j(h(j(h(j(X0)))))
| ~ sorti2(X0) )
| ~ spl2_2
| ~ spl2_32 ),
inference(resolution,[],[f229,f36]) ).
fof(f229,plain,
( ! [X0] :
( ~ sorti1(X0)
| j(h(X0)) = j(h(j(h(X0)))) )
| ~ spl2_32 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f761,plain,
( spl2_75
| ~ spl2_1
| ~ spl2_19 ),
inference(avatar_split_clause,[],[f232,f130,f31,f759]) ).
fof(f759,plain,
( spl2_75
<=> ! [X0] :
( h(j(h(X0))) = h(j(h(j(h(X0)))))
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_75])]) ).
fof(f130,plain,
( spl2_19
<=> ! [X0] :
( h(j(X0)) = h(j(h(j(X0))))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).
fof(f232,plain,
( ! [X0] :
( h(j(h(X0))) = h(j(h(j(h(X0)))))
| ~ sorti1(X0) )
| ~ spl2_1
| ~ spl2_19 ),
inference(resolution,[],[f131,f32]) ).
fof(f131,plain,
( ! [X0] :
( ~ sorti2(X0)
| h(j(X0)) = h(j(h(j(X0)))) )
| ~ spl2_19 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f719,plain,
( ~ spl2_37
| ~ spl2_63
| spl2_74
| ~ spl2_11
| ~ spl2_30 ),
inference(avatar_split_clause,[],[f224,f212,f83,f716,f512,f254]) ).
fof(f512,plain,
( spl2_63
<=> sorti1(j(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_63])]) ).
fof(f83,plain,
( spl2_11
<=> ! [X0,X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).
fof(f224,plain,
( sorti1(j(op2(sK0,sK1)))
| ~ sorti1(j(sK1))
| ~ sorti1(j(sK0))
| ~ spl2_11
| ~ spl2_30 ),
inference(superposition,[],[f84,f214]) ).
fof(f84,plain,
( ! [X0,X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1)
| ~ sorti1(X0) )
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f676,plain,
( ~ spl2_63
| ~ spl2_37
| spl2_73
| ~ spl2_11
| ~ spl2_29 ),
inference(avatar_split_clause,[],[f223,f207,f83,f673,f254,f512]) ).
fof(f673,plain,
( spl2_73
<=> sorti1(j(op2(sK1,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_73])]) ).
fof(f207,plain,
( spl2_29
<=> j(op2(sK1,sK0)) = op1(j(sK1),j(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_29])]) ).
fof(f223,plain,
( sorti1(j(op2(sK1,sK0)))
| ~ sorti1(j(sK0))
| ~ sorti1(j(sK1))
| ~ spl2_11
| ~ spl2_29 ),
inference(superposition,[],[f84,f209]) ).
fof(f209,plain,
( j(op2(sK1,sK0)) = op1(j(sK1),j(sK0))
| ~ spl2_29 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f592,plain,
( ~ spl2_6
| ~ spl2_2
| spl2_63 ),
inference(avatar_split_clause,[],[f562,f512,f35,f54]) ).
fof(f562,plain,
( ~ sorti2(sK1)
| ~ spl2_2
| spl2_63 ),
inference(resolution,[],[f514,f36]) ).
fof(f514,plain,
( ~ sorti1(j(sK1))
| spl2_63 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f587,plain,
( spl2_72
| ~ spl2_6
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f271,f242,f54,f584]) ).
fof(f584,plain,
( spl2_72
<=> op2(sK1,sK1) = h(j(op2(sK1,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_72])]) ).
fof(f271,plain,
( op2(sK1,sK1) = h(j(op2(sK1,sK1)))
| ~ spl2_6
| ~ spl2_34 ),
inference(resolution,[],[f243,f56]) ).
fof(f582,plain,
( spl2_71
| ~ spl2_5
| ~ spl2_34 ),
inference(avatar_split_clause,[],[f270,f242,f49,f579]) ).
fof(f579,plain,
( spl2_71
<=> op2(sK1,sK0) = h(j(op2(sK1,sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_71])]) ).
fof(f270,plain,
( op2(sK1,sK0) = h(j(op2(sK1,sK0)))
| ~ spl2_5
| ~ spl2_34 ),
inference(resolution,[],[f243,f51]) ).
fof(f577,plain,
( spl2_70
| ~ spl2_6
| ~ spl2_33 ),
inference(avatar_split_clause,[],[f267,f238,f54,f574]) ).
fof(f267,plain,
( op2(sK0,sK1) = h(j(op2(sK0,sK1)))
| ~ spl2_6
| ~ spl2_33 ),
inference(resolution,[],[f239,f56]) ).
fof(f572,plain,
( spl2_69
| ~ spl2_5
| ~ spl2_33 ),
inference(avatar_split_clause,[],[f266,f238,f49,f569]) ).
fof(f561,plain,
( spl2_68
| ~ spl2_11
| ~ spl2_28 ),
inference(avatar_split_clause,[],[f205,f201,f83,f559]) ).
fof(f559,plain,
( spl2_68
<=> ! [X0,X3,X2,X1] :
( ~ sorti1(X0)
| op1(X1,op1(X2,X3)) = op1(X0,op1(X0,op1(X1,op1(X2,X3))))
| ~ sorti1(X1)
| ~ sorti1(X3)
| ~ sorti1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_68])]) ).
fof(f201,plain,
( spl2_28
<=> ! [X2,X0,X1] :
( op1(X1,X2) = op1(X0,op1(X0,op1(X1,X2)))
| ~ sorti1(X0)
| ~ sorti1(X2)
| ~ sorti1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_28])]) ).
fof(f205,plain,
( ! [X2,X3,X0,X1] :
( ~ sorti1(X0)
| op1(X1,op1(X2,X3)) = op1(X0,op1(X0,op1(X1,op1(X2,X3))))
| ~ sorti1(X1)
| ~ sorti1(X3)
| ~ sorti1(X2) )
| ~ spl2_11
| ~ spl2_28 ),
inference(resolution,[],[f202,f84]) ).
fof(f202,plain,
( ! [X2,X0,X1] :
( ~ sorti1(X2)
| ~ sorti1(X0)
| op1(X1,X2) = op1(X0,op1(X0,op1(X1,X2)))
| ~ sorti1(X1) )
| ~ spl2_28 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f549,plain,
( spl2_67
| ~ spl2_12
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f196,f191,f87,f547]) ).
fof(f547,plain,
( spl2_67
<=> ! [X0,X3,X2,X1] :
( ~ sorti2(X0)
| j(op2(op2(X1,X2),op2(X0,X3))) = op1(j(op2(X1,X2)),j(op2(X0,X3)))
| ~ sorti2(X3)
| ~ sorti2(X2)
| ~ sorti2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_67])]) ).
fof(f87,plain,
( spl2_12
<=> ! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).
fof(f191,plain,
( spl2_27
<=> ! [X2,X0,X1] :
( ~ sorti2(X0)
| ~ sorti2(X1)
| j(op2(X2,op2(X1,X0))) = op1(j(X2),j(op2(X1,X0)))
| ~ sorti2(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_27])]) ).
fof(f196,plain,
( ! [X2,X3,X0,X1] :
( ~ sorti2(X0)
| j(op2(op2(X1,X2),op2(X0,X3))) = op1(j(op2(X1,X2)),j(op2(X0,X3)))
| ~ sorti2(X3)
| ~ sorti2(X2)
| ~ sorti2(X1) )
| ~ spl2_12
| ~ spl2_27 ),
inference(resolution,[],[f192,f88]) ).
fof(f88,plain,
( ! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) )
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f192,plain,
( ! [X2,X0,X1] :
( ~ sorti2(X2)
| ~ sorti2(X1)
| j(op2(X2,op2(X1,X0))) = op1(j(X2),j(op2(X1,X0)))
| ~ sorti2(X0) )
| ~ spl2_27 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f545,plain,
( spl2_66
| ~ spl2_11
| ~ spl2_26 ),
inference(avatar_split_clause,[],[f195,f187,f83,f543]) ).
fof(f543,plain,
( spl2_66
<=> ! [X0,X3,X2,X1] :
( ~ sorti1(X0)
| h(op1(op1(X1,X2),op1(X0,X3))) = op2(h(op1(X1,X2)),h(op1(X0,X3)))
| ~ sorti1(X3)
| ~ sorti1(X2)
| ~ sorti1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_66])]) ).
fof(f187,plain,
( spl2_26
<=> ! [X2,X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| h(op1(X2,op1(X1,X0))) = op2(h(X2),h(op1(X1,X0)))
| ~ sorti1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_26])]) ).
fof(f195,plain,
( ! [X2,X3,X0,X1] :
( ~ sorti1(X0)
| h(op1(op1(X1,X2),op1(X0,X3))) = op2(h(op1(X1,X2)),h(op1(X0,X3)))
| ~ sorti1(X3)
| ~ sorti1(X2)
| ~ sorti1(X1) )
| ~ spl2_11
| ~ spl2_26 ),
inference(resolution,[],[f188,f84]) ).
fof(f188,plain,
( ! [X2,X0,X1] :
( ~ sorti1(X2)
| ~ sorti1(X1)
| h(op1(X2,op1(X1,X0))) = op2(h(X2),h(op1(X1,X0)))
| ~ sorti1(X0) )
| ~ spl2_26 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f523,plain,
( spl2_65
| ~ spl2_1
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f197,f191,f31,f521]) ).
fof(f521,plain,
( spl2_65
<=> ! [X2,X0,X1] :
( ~ sorti2(X0)
| j(op2(h(X1),op2(X0,X2))) = op1(j(h(X1)),j(op2(X0,X2)))
| ~ sorti2(X2)
| ~ sorti1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_65])]) ).
fof(f197,plain,
( ! [X2,X0,X1] :
( ~ sorti2(X0)
| j(op2(h(X1),op2(X0,X2))) = op1(j(h(X1)),j(op2(X0,X2)))
| ~ sorti2(X2)
| ~ sorti1(X1) )
| ~ spl2_1
| ~ spl2_27 ),
inference(resolution,[],[f192,f32]) ).
fof(f519,plain,
( ~ spl2_63
| spl2_64
| ~ spl2_11
| ~ spl2_31 ),
inference(avatar_split_clause,[],[f226,f217,f83,f516,f512]) ).
fof(f516,plain,
( spl2_64
<=> sorti1(j(op2(sK1,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_64])]) ).
fof(f217,plain,
( spl2_31
<=> j(op2(sK1,sK1)) = op1(j(sK1),j(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_31])]) ).
fof(f226,plain,
( sorti1(j(op2(sK1,sK1)))
| ~ sorti1(j(sK1))
| ~ spl2_11
| ~ spl2_31 ),
inference(duplicate_literal_removal,[],[f225]) ).
fof(f225,plain,
( sorti1(j(op2(sK1,sK1)))
| ~ sorti1(j(sK1))
| ~ sorti1(j(sK1))
| ~ spl2_11
| ~ spl2_31 ),
inference(superposition,[],[f84,f219]) ).
fof(f219,plain,
( j(op2(sK1,sK1)) = op1(j(sK1),j(sK1))
| ~ spl2_31 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f510,plain,
( spl2_62
| ~ spl2_2
| ~ spl2_26 ),
inference(avatar_split_clause,[],[f194,f187,f35,f508]) ).
fof(f508,plain,
( spl2_62
<=> ! [X2,X0,X1] :
( ~ sorti1(X0)
| h(op1(j(X1),op1(X0,X2))) = op2(h(j(X1)),h(op1(X0,X2)))
| ~ sorti1(X2)
| ~ sorti2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_62])]) ).
fof(f194,plain,
( ! [X2,X0,X1] :
( ~ sorti1(X0)
| h(op1(j(X1),op1(X0,X2))) = op2(h(j(X1)),h(op1(X0,X2)))
| ~ sorti1(X2)
| ~ sorti2(X1) )
| ~ spl2_2
| ~ spl2_26 ),
inference(resolution,[],[f188,f36]) ).
fof(f506,plain,
( spl2_61
| ~ spl2_12
| ~ spl2_24 ),
inference(avatar_split_clause,[],[f182,f168,f87,f504]) ).
fof(f504,plain,
( spl2_61
<=> ! [X2,X0,X1] :
( j(op2(op2(X0,X1),h(X2))) = op1(j(op2(X0,X1)),j(h(X2)))
| ~ sorti1(X2)
| ~ sorti2(X1)
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_61])]) ).
fof(f168,plain,
( spl2_24
<=> ! [X0,X1] :
( j(op2(X0,h(X1))) = op1(j(X0),j(h(X1)))
| ~ sorti2(X0)
| ~ sorti1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).
fof(f182,plain,
( ! [X2,X0,X1] :
( j(op2(op2(X0,X1),h(X2))) = op1(j(op2(X0,X1)),j(h(X2)))
| ~ sorti1(X2)
| ~ sorti2(X1)
| ~ sorti2(X0) )
| ~ spl2_12
| ~ spl2_24 ),
inference(resolution,[],[f169,f88]) ).
fof(f169,plain,
( ! [X0,X1] :
( ~ sorti2(X0)
| j(op2(X0,h(X1))) = op1(j(X0),j(h(X1)))
| ~ sorti1(X1) )
| ~ spl2_24 ),
inference(avatar_component_clause,[],[f168]) ).
fof(f502,plain,
( spl2_60
| ~ spl2_12
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f176,f164,f87,f500]) ).
fof(f500,plain,
( spl2_60
<=> ! [X2,X0,X1] :
( ~ sorti1(X0)
| h(op1(X0,j(op2(X1,X2)))) = op2(h(X0),h(j(op2(X1,X2))))
| ~ sorti2(X2)
| ~ sorti2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_60])]) ).
fof(f164,plain,
( spl2_23
<=> ! [X0,X1] :
( h(op1(X0,j(X1))) = op2(h(X0),h(j(X1)))
| ~ sorti1(X0)
| ~ sorti2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).
fof(f176,plain,
( ! [X2,X0,X1] :
( ~ sorti1(X0)
| h(op1(X0,j(op2(X1,X2)))) = op2(h(X0),h(j(op2(X1,X2))))
| ~ sorti2(X2)
| ~ sorti2(X1) )
| ~ spl2_12
| ~ spl2_23 ),
inference(resolution,[],[f165,f88]) ).
fof(f165,plain,
( ! [X0,X1] :
( ~ sorti2(X1)
| ~ sorti1(X0)
| h(op1(X0,j(X1))) = op2(h(X0),h(j(X1))) )
| ~ spl2_23 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f482,plain,
( spl2_59
| ~ spl2_2
| ~ spl2_28 ),
inference(avatar_split_clause,[],[f204,f201,f35,f480]) ).
fof(f480,plain,
( spl2_59
<=> ! [X2,X0,X1] :
( ~ sorti1(X0)
| op1(X1,j(X2)) = op1(X0,op1(X0,op1(X1,j(X2))))
| ~ sorti1(X1)
| ~ sorti2(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_59])]) ).
fof(f204,plain,
( ! [X2,X0,X1] :
( ~ sorti1(X0)
| op1(X1,j(X2)) = op1(X0,op1(X0,op1(X1,j(X2))))
| ~ sorti1(X1)
| ~ sorti2(X2) )
| ~ spl2_2
| ~ spl2_28 ),
inference(resolution,[],[f202,f36]) ).
fof(f478,plain,
( spl2_58
| ~ spl2_12
| ~ spl2_22 ),
inference(avatar_split_clause,[],[f159,f150,f87,f476]) ).
fof(f476,plain,
( spl2_58
<=> ! [X2,X0,X1] :
( ~ sorti1(X0)
| j(op2(X1,X2)) = op1(X0,op1(X0,j(op2(X1,X2))))
| ~ sorti2(X2)
| ~ sorti2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_58])]) ).
fof(f150,plain,
( spl2_22
<=> ! [X0,X1] :
( j(X1) = op1(X0,op1(X0,j(X1)))
| ~ sorti1(X0)
| ~ sorti2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).
fof(f159,plain,
( ! [X2,X0,X1] :
( ~ sorti1(X0)
| j(op2(X1,X2)) = op1(X0,op1(X0,j(op2(X1,X2))))
| ~ sorti2(X2)
| ~ sorti2(X1) )
| ~ spl2_12
| ~ spl2_22 ),
inference(resolution,[],[f151,f88]) ).
fof(f151,plain,
( ! [X0,X1] :
( ~ sorti2(X1)
| ~ sorti1(X0)
| j(X1) = op1(X0,op1(X0,j(X1))) )
| ~ spl2_22 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f474,plain,
( spl2_57
| ~ spl2_12
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f155,f146,f87,f472]) ).
fof(f472,plain,
( spl2_57
<=> ! [X2,X0,X1] :
( ~ sorti2(X0)
| op2(op2(X1,X2),X0) = h(j(op2(op2(X1,X2),X0)))
| ~ sorti2(X2)
| ~ sorti2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_57])]) ).
fof(f146,plain,
( spl2_21
<=> ! [X0,X1] :
( ~ sorti2(X0)
| ~ sorti2(X1)
| op2(X1,X0) = h(j(op2(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).
fof(f155,plain,
( ! [X2,X0,X1] :
( ~ sorti2(X0)
| op2(op2(X1,X2),X0) = h(j(op2(op2(X1,X2),X0)))
| ~ sorti2(X2)
| ~ sorti2(X1) )
| ~ spl2_12
| ~ spl2_21 ),
inference(resolution,[],[f147,f88]) ).
fof(f147,plain,
( ! [X0,X1] :
( ~ sorti2(X1)
| ~ sorti2(X0)
| op2(X1,X0) = h(j(op2(X1,X0))) )
| ~ spl2_21 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f435,plain,
( spl2_56
| ~ spl2_11
| ~ spl2_20 ),
inference(avatar_split_clause,[],[f154,f142,f83,f433]) ).
fof(f433,plain,
( spl2_56
<=> ! [X2,X0,X1] :
( ~ sorti1(X0)
| op1(op1(X1,X2),X0) = j(h(op1(op1(X1,X2),X0)))
| ~ sorti1(X2)
| ~ sorti1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_56])]) ).
fof(f142,plain,
( spl2_20
<=> ! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| op1(X1,X0) = j(h(op1(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).
fof(f154,plain,
( ! [X2,X0,X1] :
( ~ sorti1(X0)
| op1(op1(X1,X2),X0) = j(h(op1(op1(X1,X2),X0)))
| ~ sorti1(X2)
| ~ sorti1(X1) )
| ~ spl2_11
| ~ spl2_20 ),
inference(resolution,[],[f143,f84]) ).
fof(f143,plain,
( ! [X0,X1] :
( ~ sorti1(X1)
| ~ sorti1(X0)
| op1(X1,X0) = j(h(op1(X1,X0))) )
| ~ spl2_20 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f406,plain,
( spl2_55
| ~ spl2_6
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f199,f191,f54,f404]) ).
fof(f199,plain,
( ! [X0,X1] :
( ~ sorti2(X0)
| j(op2(sK1,op2(X0,X1))) = op1(j(sK1),j(op2(X0,X1)))
| ~ sorti2(X1) )
| ~ spl2_6
| ~ spl2_27 ),
inference(resolution,[],[f192,f56]) ).
fof(f402,plain,
( spl2_54
| ~ spl2_5
| ~ spl2_27 ),
inference(avatar_split_clause,[],[f198,f191,f49,f400]) ).
fof(f198,plain,
( ! [X0,X1] :
( ~ sorti2(X0)
| j(op2(sK0,op2(X0,X1))) = op1(j(sK0),j(op2(X0,X1)))
| ~ sorti2(X1) )
| ~ spl2_5
| ~ spl2_27 ),
inference(resolution,[],[f192,f51]) ).
fof(f398,plain,
( spl2_53
| ~ spl2_1
| ~ spl2_24 ),
inference(avatar_split_clause,[],[f183,f168,f31,f396]) ).
fof(f396,plain,
( spl2_53
<=> ! [X0,X1] :
( j(op2(h(X0),h(X1))) = op1(j(h(X0)),j(h(X1)))
| ~ sorti1(X1)
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_53])]) ).
fof(f183,plain,
( ! [X0,X1] :
( j(op2(h(X0),h(X1))) = op1(j(h(X0)),j(h(X1)))
| ~ sorti1(X1)
| ~ sorti1(X0) )
| ~ spl2_1
| ~ spl2_24 ),
inference(resolution,[],[f169,f32]) ).
fof(f361,plain,
( spl2_52
| ~ spl2_1
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f177,f164,f31,f359]) ).
fof(f359,plain,
( spl2_52
<=> ! [X0,X1] :
( ~ sorti1(X0)
| h(op1(X0,j(h(X1)))) = op2(h(X0),h(j(h(X1))))
| ~ sorti1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_52])]) ).
fof(f177,plain,
( ! [X0,X1] :
( ~ sorti1(X0)
| h(op1(X0,j(h(X1)))) = op2(h(X0),h(j(h(X1))))
| ~ sorti1(X1) )
| ~ spl2_1
| ~ spl2_23 ),
inference(resolution,[],[f165,f32]) ).
fof(f357,plain,
( spl2_51
| ~ spl2_12
| ~ spl2_18 ),
inference(avatar_split_clause,[],[f137,f126,f87,f355]) ).
fof(f126,plain,
( spl2_18
<=> ! [X0] :
( j(op2(X0,sK1)) = op1(j(X0),j(sK1))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).
fof(f137,plain,
( ! [X0,X1] :
( j(op2(op2(X0,X1),sK1)) = op1(j(op2(X0,X1)),j(sK1))
| ~ sorti2(X1)
| ~ sorti2(X0) )
| ~ spl2_12
| ~ spl2_18 ),
inference(resolution,[],[f127,f88]) ).
fof(f127,plain,
( ! [X0] :
( ~ sorti2(X0)
| j(op2(X0,sK1)) = op1(j(X0),j(sK1)) )
| ~ spl2_18 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f353,plain,
( spl2_50
| ~ spl2_12
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f133,f122,f87,f351]) ).
fof(f122,plain,
( spl2_17
<=> ! [X0] :
( j(op2(X0,sK0)) = op1(j(X0),j(sK0))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).
fof(f133,plain,
( ! [X0,X1] :
( j(op2(op2(X0,X1),sK0)) = op1(j(op2(X0,X1)),j(sK0))
| ~ sorti2(X1)
| ~ sorti2(X0) )
| ~ spl2_12
| ~ spl2_17 ),
inference(resolution,[],[f123,f88]) ).
fof(f123,plain,
( ! [X0] :
( ~ sorti2(X0)
| j(op2(X0,sK0)) = op1(j(X0),j(sK0)) )
| ~ spl2_17 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f333,plain,
( spl2_49
| ~ spl2_1
| ~ spl2_22 ),
inference(avatar_split_clause,[],[f160,f150,f31,f331]) ).
fof(f331,plain,
( spl2_49
<=> ! [X0,X1] :
( ~ sorti1(X0)
| j(h(X1)) = op1(X0,op1(X0,j(h(X1))))
| ~ sorti1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_49])]) ).
fof(f160,plain,
( ! [X0,X1] :
( ~ sorti1(X0)
| j(h(X1)) = op1(X0,op1(X0,j(h(X1))))
| ~ sorti1(X1) )
| ~ spl2_1
| ~ spl2_22 ),
inference(resolution,[],[f151,f32]) ).
fof(f329,plain,
( spl2_48
| ~ spl2_1
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f156,f146,f31,f327]) ).
fof(f156,plain,
( ! [X0,X1] :
( ~ sorti2(X0)
| op2(h(X1),X0) = h(j(op2(h(X1),X0)))
| ~ sorti1(X1) )
| ~ spl2_1
| ~ spl2_21 ),
inference(resolution,[],[f147,f32]) ).
fof(f325,plain,
( ~ spl2_5
| ~ spl2_2
| spl2_37 ),
inference(avatar_split_clause,[],[f292,f254,f35,f49]) ).
fof(f292,plain,
( ~ sorti2(sK0)
| ~ spl2_2
| spl2_37 ),
inference(resolution,[],[f256,f36]) ).
fof(f256,plain,
( ~ sorti1(j(sK0))
| spl2_37 ),
inference(avatar_component_clause,[],[f254]) ).
fof(f324,plain,
( spl2_47
| ~ spl2_2
| ~ spl2_20 ),
inference(avatar_split_clause,[],[f153,f142,f35,f322]) ).
fof(f153,plain,
( ! [X0,X1] :
( ~ sorti1(X0)
| op1(j(X1),X0) = j(h(op1(j(X1),X0)))
| ~ sorti2(X1) )
| ~ spl2_2
| ~ spl2_20 ),
inference(resolution,[],[f143,f36]) ).
fof(f320,plain,
( spl2_46
| ~ spl2_12
| ~ spl2_16 ),
inference(avatar_split_clause,[],[f117,f112,f87,f318]) ).
fof(f112,plain,
( spl2_16
<=> ! [X0] :
( j(X0) = j(h(j(X0)))
| ~ sorti2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).
fof(f117,plain,
( ! [X0,X1] :
( j(op2(X0,X1)) = j(h(j(op2(X0,X1))))
| ~ sorti2(X1)
| ~ sorti2(X0) )
| ~ spl2_12
| ~ spl2_16 ),
inference(resolution,[],[f113,f88]) ).
fof(f113,plain,
( ! [X0] :
( ~ sorti2(X0)
| j(X0) = j(h(j(X0))) )
| ~ spl2_16 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f316,plain,
( spl2_45
| ~ spl2_11
| ~ spl2_15 ),
inference(avatar_split_clause,[],[f116,f108,f83,f314]) ).
fof(f314,plain,
( spl2_45
<=> ! [X0,X1] :
( h(op1(X0,X1)) = h(j(h(op1(X0,X1))))
| ~ sorti1(X1)
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_45])]) ).
fof(f108,plain,
( spl2_15
<=> ! [X0] :
( h(X0) = h(j(h(X0)))
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).
fof(f116,plain,
( ! [X0,X1] :
( h(op1(X0,X1)) = h(j(h(op1(X0,X1))))
| ~ sorti1(X1)
| ~ sorti1(X0) )
| ~ spl2_11
| ~ spl2_15 ),
inference(resolution,[],[f109,f84]) ).
fof(f109,plain,
( ! [X0] :
( ~ sorti1(X0)
| h(X0) = h(j(h(X0))) )
| ~ spl2_15 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f304,plain,
( spl2_44
| ~ spl2_6
| ~ spl2_24 ),
inference(avatar_split_clause,[],[f185,f168,f54,f302]) ).
fof(f185,plain,
( ! [X0] :
( j(op2(sK1,h(X0))) = op1(j(sK1),j(h(X0)))
| ~ sorti1(X0) )
| ~ spl2_6
| ~ spl2_24 ),
inference(resolution,[],[f169,f56]) ).
fof(f300,plain,
( spl2_43
| ~ spl2_5
| ~ spl2_24 ),
inference(avatar_split_clause,[],[f184,f168,f49,f298]) ).
fof(f184,plain,
( ! [X0] :
( j(op2(sK0,h(X0))) = op1(j(sK0),j(h(X0)))
| ~ sorti1(X0) )
| ~ spl2_5
| ~ spl2_24 ),
inference(resolution,[],[f169,f51]) ).
fof(f296,plain,
( spl2_42
| ~ spl2_1
| ~ spl2_18 ),
inference(avatar_split_clause,[],[f138,f126,f31,f294]) ).
fof(f138,plain,
( ! [X0] :
( j(op2(h(X0),sK1)) = op1(j(h(X0)),j(sK1))
| ~ sorti1(X0) )
| ~ spl2_1
| ~ spl2_18 ),
inference(resolution,[],[f127,f32]) ).
fof(f291,plain,
( spl2_41
| ~ spl2_1
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f134,f122,f31,f289]) ).
fof(f134,plain,
( ! [X0] :
( j(op2(h(X0),sK0)) = op1(j(h(X0)),j(sK0))
| ~ sorti1(X0) )
| ~ spl2_1
| ~ spl2_17 ),
inference(resolution,[],[f123,f32]) ).
fof(f283,plain,
( spl2_40
| ~ spl2_6
| ~ spl2_13
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f181,f164,f95,f54,f281]) ).
fof(f181,plain,
( ! [X0] :
( op2(h(X0),sK1) = h(op1(X0,j(sK1)))
| ~ sorti1(X0) )
| ~ spl2_6
| ~ spl2_13
| ~ spl2_23 ),
inference(forward_demodulation,[],[f179,f97]) ).
fof(f179,plain,
( ! [X0] :
( ~ sorti1(X0)
| h(op1(X0,j(sK1))) = op2(h(X0),h(j(sK1))) )
| ~ spl2_6
| ~ spl2_23 ),
inference(resolution,[],[f165,f56]) ).
fof(f279,plain,
( spl2_39
| ~ spl2_5
| ~ spl2_7
| ~ spl2_23 ),
inference(avatar_split_clause,[],[f180,f164,f61,f49,f277]) ).
fof(f180,plain,
( ! [X0] :
( op2(h(X0),sK0) = h(op1(X0,j(sK0)))
| ~ sorti1(X0) )
| ~ spl2_5
| ~ spl2_7
| ~ spl2_23 ),
inference(forward_demodulation,[],[f178,f63]) ).
fof(f178,plain,
( ! [X0] :
( ~ sorti1(X0)
| h(op1(X0,j(sK0))) = op2(h(X0),h(j(sK0))) )
| ~ spl2_5
| ~ spl2_23 ),
inference(resolution,[],[f165,f51]) ).
fof(f261,plain,
( ~ spl2_37
| spl2_38
| ~ spl2_11
| ~ spl2_25 ),
inference(avatar_split_clause,[],[f222,f172,f83,f258,f254]) ).
fof(f222,plain,
( sorti1(j(op2(sK0,sK0)))
| ~ sorti1(j(sK0))
| ~ spl2_11
| ~ spl2_25 ),
inference(duplicate_literal_removal,[],[f221]) ).
fof(f221,plain,
( sorti1(j(op2(sK0,sK0)))
| ~ sorti1(j(sK0))
| ~ sorti1(j(sK0))
| ~ spl2_11
| ~ spl2_25 ),
inference(superposition,[],[f84,f174]) ).
fof(f252,plain,
( spl2_36
| ~ spl2_6
| ~ spl2_22 ),
inference(avatar_split_clause,[],[f162,f150,f54,f250]) ).
fof(f162,plain,
( ! [X0] :
( ~ sorti1(X0)
| j(sK1) = op1(X0,op1(X0,j(sK1))) )
| ~ spl2_6
| ~ spl2_22 ),
inference(resolution,[],[f151,f56]) ).
fof(f248,plain,
( spl2_35
| ~ spl2_5
| ~ spl2_22 ),
inference(avatar_split_clause,[],[f161,f150,f49,f246]) ).
fof(f161,plain,
( ! [X0] :
( ~ sorti1(X0)
| j(sK0) = op1(X0,op1(X0,j(sK0))) )
| ~ spl2_5
| ~ spl2_22 ),
inference(resolution,[],[f151,f51]) ).
fof(f244,plain,
( spl2_34
| ~ spl2_6
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f158,f146,f54,f242]) ).
fof(f158,plain,
( ! [X0] :
( ~ sorti2(X0)
| op2(sK1,X0) = h(j(op2(sK1,X0))) )
| ~ spl2_6
| ~ spl2_21 ),
inference(resolution,[],[f147,f56]) ).
fof(f240,plain,
( spl2_33
| ~ spl2_5
| ~ spl2_21 ),
inference(avatar_split_clause,[],[f157,f146,f49,f238]) ).
fof(f157,plain,
( ! [X0] :
( ~ sorti2(X0)
| op2(sK0,X0) = h(j(op2(sK0,X0))) )
| ~ spl2_5
| ~ spl2_21 ),
inference(resolution,[],[f147,f51]) ).
fof(f230,plain,
( spl2_32
| ~ spl2_1
| ~ spl2_16 ),
inference(avatar_split_clause,[],[f118,f112,f31,f228]) ).
fof(f118,plain,
( ! [X0] :
( j(h(X0)) = j(h(j(h(X0))))
| ~ sorti1(X0) )
| ~ spl2_1
| ~ spl2_16 ),
inference(resolution,[],[f113,f32]) ).
fof(f220,plain,
( spl2_31
| ~ spl2_6
| ~ spl2_18 ),
inference(avatar_split_clause,[],[f140,f126,f54,f217]) ).
fof(f140,plain,
( j(op2(sK1,sK1)) = op1(j(sK1),j(sK1))
| ~ spl2_6
| ~ spl2_18 ),
inference(resolution,[],[f127,f56]) ).
fof(f215,plain,
( spl2_30
| ~ spl2_5
| ~ spl2_18 ),
inference(avatar_split_clause,[],[f139,f126,f49,f212]) ).
fof(f139,plain,
( j(op2(sK0,sK1)) = op1(j(sK0),j(sK1))
| ~ spl2_5
| ~ spl2_18 ),
inference(resolution,[],[f127,f51]) ).
fof(f210,plain,
( spl2_29
| ~ spl2_6
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f136,f122,f54,f207]) ).
fof(f136,plain,
( j(op2(sK1,sK0)) = op1(j(sK1),j(sK0))
| ~ spl2_6
| ~ spl2_17 ),
inference(resolution,[],[f123,f56]) ).
fof(f203,plain,
( spl2_28
| ~ spl2_11
| ~ spl2_14 ),
inference(avatar_split_clause,[],[f104,f100,f83,f201]) ).
fof(f100,plain,
( spl2_14
<=> ! [X0,X1] :
( op1(X0,op1(X0,X1)) = X1
| ~ sorti1(X1)
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).
fof(f104,plain,
( ! [X2,X0,X1] :
( op1(X1,X2) = op1(X0,op1(X0,op1(X1,X2)))
| ~ sorti1(X0)
| ~ sorti1(X2)
| ~ sorti1(X1) )
| ~ spl2_11
| ~ spl2_14 ),
inference(resolution,[],[f101,f84]) ).
fof(f101,plain,
( ! [X0,X1] :
( ~ sorti1(X1)
| op1(X0,op1(X0,X1)) = X1
| ~ sorti1(X0) )
| ~ spl2_14 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f193,plain,
( spl2_27
| ~ spl2_9
| ~ spl2_12 ),
inference(avatar_split_clause,[],[f92,f87,f70,f191]) ).
fof(f70,plain,
( spl2_9
<=> ! [X2,X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3)
| ~ sorti2(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).
fof(f92,plain,
( ! [X2,X0,X1] :
( ~ sorti2(X0)
| ~ sorti2(X1)
| j(op2(X2,op2(X1,X0))) = op1(j(X2),j(op2(X1,X0)))
| ~ sorti2(X2) )
| ~ spl2_9
| ~ spl2_12 ),
inference(resolution,[],[f88,f71]) ).
fof(f71,plain,
( ! [X2,X3] :
( ~ sorti2(X3)
| j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X2) )
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f70]) ).
fof(f189,plain,
( spl2_26
| ~ spl2_8
| ~ spl2_11 ),
inference(avatar_split_clause,[],[f90,f83,f66,f187]) ).
fof(f66,plain,
( spl2_8
<=> ! [X4,X5] :
( h(op1(X4,X5)) = op2(h(X4),h(X5))
| ~ sorti1(X5)
| ~ sorti1(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).
fof(f90,plain,
( ! [X2,X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| h(op1(X2,op1(X1,X0))) = op2(h(X2),h(op1(X1,X0)))
| ~ sorti1(X2) )
| ~ spl2_8
| ~ spl2_11 ),
inference(resolution,[],[f84,f67]) ).
fof(f67,plain,
( ! [X4,X5] :
( ~ sorti1(X5)
| h(op1(X4,X5)) = op2(h(X4),h(X5))
| ~ sorti1(X4) )
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f66]) ).
fof(f175,plain,
( spl2_25
| ~ spl2_5
| ~ spl2_17 ),
inference(avatar_split_clause,[],[f135,f122,f49,f172]) ).
fof(f135,plain,
( j(op2(sK0,sK0)) = op1(j(sK0),j(sK0))
| ~ spl2_5
| ~ spl2_17 ),
inference(resolution,[],[f123,f51]) ).
fof(f170,plain,
( spl2_24
| ~ spl2_1
| ~ spl2_9 ),
inference(avatar_split_clause,[],[f74,f70,f31,f168]) ).
fof(f74,plain,
( ! [X0,X1] :
( j(op2(X0,h(X1))) = op1(j(X0),j(h(X1)))
| ~ sorti2(X0)
| ~ sorti1(X1) )
| ~ spl2_1
| ~ spl2_9 ),
inference(resolution,[],[f71,f32]) ).
fof(f166,plain,
( spl2_23
| ~ spl2_2
| ~ spl2_8 ),
inference(avatar_split_clause,[],[f73,f66,f35,f164]) ).
fof(f73,plain,
( ! [X0,X1] :
( h(op1(X0,j(X1))) = op2(h(X0),h(j(X1)))
| ~ sorti1(X0)
| ~ sorti2(X1) )
| ~ spl2_2
| ~ spl2_8 ),
inference(resolution,[],[f67,f36]) ).
fof(f152,plain,
( spl2_22
| ~ spl2_2
| ~ spl2_14 ),
inference(avatar_split_clause,[],[f103,f100,f35,f150]) ).
fof(f103,plain,
( ! [X0,X1] :
( j(X1) = op1(X0,op1(X0,j(X1)))
| ~ sorti1(X0)
| ~ sorti2(X1) )
| ~ spl2_2
| ~ spl2_14 ),
inference(resolution,[],[f101,f36]) ).
fof(f148,plain,
( spl2_21
| ~ spl2_3
| ~ spl2_12 ),
inference(avatar_split_clause,[],[f93,f87,f39,f146]) ).
fof(f39,plain,
( spl2_3
<=> ! [X1] :
( h(j(X1)) = X1
| ~ sorti2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).
fof(f93,plain,
( ! [X0,X1] :
( ~ sorti2(X0)
| ~ sorti2(X1)
| op2(X1,X0) = h(j(op2(X1,X0))) )
| ~ spl2_3
| ~ spl2_12 ),
inference(resolution,[],[f88,f40]) ).
fof(f40,plain,
( ! [X1] :
( ~ sorti2(X1)
| h(j(X1)) = X1 )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f144,plain,
( spl2_20
| ~ spl2_4
| ~ spl2_11 ),
inference(avatar_split_clause,[],[f91,f83,f43,f142]) ).
fof(f43,plain,
( spl2_4
<=> ! [X0] :
( j(h(X0)) = X0
| ~ sorti1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).
fof(f91,plain,
( ! [X0,X1] :
( ~ sorti1(X0)
| ~ sorti1(X1)
| op1(X1,X0) = j(h(op1(X1,X0))) )
| ~ spl2_4
| ~ spl2_11 ),
inference(resolution,[],[f84,f44]) ).
fof(f44,plain,
( ! [X0] :
( ~ sorti1(X0)
| j(h(X0)) = X0 )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f132,plain,
( spl2_19
| ~ spl2_2
| ~ spl2_15 ),
inference(avatar_split_clause,[],[f115,f108,f35,f130]) ).
fof(f115,plain,
( ! [X0] :
( h(j(X0)) = h(j(h(j(X0))))
| ~ sorti2(X0) )
| ~ spl2_2
| ~ spl2_15 ),
inference(resolution,[],[f109,f36]) ).
fof(f128,plain,
( spl2_18
| ~ spl2_6
| ~ spl2_9 ),
inference(avatar_split_clause,[],[f76,f70,f54,f126]) ).
fof(f76,plain,
( ! [X0] :
( j(op2(X0,sK1)) = op1(j(X0),j(sK1))
| ~ sorti2(X0) )
| ~ spl2_6
| ~ spl2_9 ),
inference(resolution,[],[f71,f56]) ).
fof(f124,plain,
( spl2_17
| ~ spl2_5
| ~ spl2_9 ),
inference(avatar_split_clause,[],[f75,f70,f49,f122]) ).
fof(f75,plain,
( ! [X0] :
( j(op2(X0,sK0)) = op1(j(X0),j(sK0))
| ~ sorti2(X0) )
| ~ spl2_5
| ~ spl2_9 ),
inference(resolution,[],[f71,f51]) ).
fof(f114,plain,
( spl2_16
| ~ spl2_2
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f47,f43,f35,f112]) ).
fof(f47,plain,
( ! [X0] :
( j(X0) = j(h(j(X0)))
| ~ sorti2(X0) )
| ~ spl2_2
| ~ spl2_4 ),
inference(resolution,[],[f44,f36]) ).
fof(f110,plain,
( spl2_15
| ~ spl2_1
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f46,f39,f31,f108]) ).
fof(f46,plain,
( ! [X0] :
( h(X0) = h(j(h(X0)))
| ~ sorti1(X0) )
| ~ spl2_1
| ~ spl2_3 ),
inference(resolution,[],[f40,f32]) ).
fof(f102,plain,
spl2_14,
inference(avatar_split_clause,[],[f28,f100]) ).
fof(f28,plain,
! [X0,X1] :
( op1(X0,op1(X0,X1)) = X1
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0] :
( ! [X1] :
( op1(X0,op1(X0,X1)) = X1
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> op1(X0,op1(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f98,plain,
( spl2_13
| ~ spl2_3
| ~ spl2_6 ),
inference(avatar_split_clause,[],[f59,f54,f39,f95]) ).
fof(f59,plain,
( sK1 = h(j(sK1))
| ~ spl2_3
| ~ spl2_6 ),
inference(resolution,[],[f56,f40]) ).
fof(f89,plain,
spl2_12,
inference(avatar_split_clause,[],[f29,f87]) ).
fof(f29,plain,
! [X0,X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1)
| ~ sorti2(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0] :
( ! [X1] :
( sorti2(op2(X0,X1))
| ~ sorti2(X1) )
| ~ sorti2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> sorti2(op2(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f85,plain,
spl2_11,
inference(avatar_split_clause,[],[f27,f83]) ).
fof(f27,plain,
! [X0,X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1)
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0] :
( ! [X1] :
( sorti1(op1(X0,X1))
| ~ sorti1(X1) )
| ~ sorti1(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( sorti1(X0)
=> ! [X1] :
( sorti1(X1)
=> sorti1(op1(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f81,plain,
~ spl2_10,
inference(avatar_split_clause,[],[f26,f78]) ).
fof(f26,plain,
sK1 != op2(sK0,op2(sK0,sK1)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
( sK1 != op2(sK0,op2(sK0,sK1))
& sorti2(sK1)
& sorti2(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f16,f15]) ).
fof(f15,plain,
( ? [X0] :
( ? [X1] :
( op2(X0,op2(X0,X1)) != X1
& sorti2(X1) )
& sorti2(X0) )
=> ( ? [X1] :
( op2(sK0,op2(sK0,X1)) != X1
& sorti2(X1) )
& sorti2(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
( ? [X1] :
( op2(sK0,op2(sK0,X1)) != X1
& sorti2(X1) )
=> ( sK1 != op2(sK0,op2(sK0,sK1))
& sorti2(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
? [X0] :
( ? [X1] :
( op2(X0,op2(X0,X1)) != X1
& sorti2(X1) )
& sorti2(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
~ ! [X0] :
( sorti2(X0)
=> ! [X1] :
( sorti2(X1)
=> op2(X0,op2(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f72,plain,
spl2_9,
inference(avatar_split_clause,[],[f21,f70]) ).
fof(f21,plain,
! [X2,X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3)
| ~ sorti2(X2) ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
( ! [X0] :
( j(h(X0)) = X0
| ~ sorti1(X0) )
& ! [X1] :
( h(j(X1)) = X1
| ~ sorti2(X1) )
& ! [X2] :
( ! [X3] :
( j(op2(X2,X3)) = op1(j(X2),j(X3))
| ~ sorti2(X3) )
| ~ sorti2(X2) )
& ! [X4] :
( ! [X5] :
( h(op1(X4,X5)) = op2(h(X4),h(X5))
| ~ sorti1(X5) )
| ~ sorti1(X4) )
& ! [X6] :
( sorti1(j(X6))
| ~ sorti2(X6) )
& ! [X7] :
( sorti2(h(X7))
| ~ sorti1(X7) ) ),
inference(rectify,[],[f9]) ).
fof(f9,plain,
( ! [X2] :
( j(h(X2)) = X2
| ~ sorti1(X2) )
& ! [X3] :
( h(j(X3)) = X3
| ~ sorti2(X3) )
& ! [X4] :
( ! [X5] :
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5) )
| ~ sorti2(X4) )
& ! [X6] :
( ! [X7] :
( h(op1(X6,X7)) = op2(h(X6),h(X7))
| ~ sorti1(X7) )
| ~ sorti1(X6) )
& ! [X0] :
( sorti1(j(X0))
| ~ sorti2(X0) )
& ! [X1] :
( sorti2(h(X1))
| ~ sorti1(X1) ) ),
inference(flattening,[],[f8]) ).
fof(f8,plain,
( ! [X2] :
( j(h(X2)) = X2
| ~ sorti1(X2) )
& ! [X3] :
( h(j(X3)) = X3
| ~ sorti2(X3) )
& ! [X4] :
( ! [X5] :
( j(op2(X4,X5)) = op1(j(X4),j(X5))
| ~ sorti2(X5) )
| ~ sorti2(X4) )
& ! [X6] :
( ! [X7] :
( h(op1(X6,X7)) = op2(h(X6),h(X7))
| ~ sorti1(X7) )
| ~ sorti1(X6) )
& ! [X0] :
( sorti1(j(X0))
| ~ sorti2(X0) )
& ! [X1] :
( sorti2(h(X1))
| ~ sorti1(X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,plain,
~ ( ( ! [X0] :
( sorti2(X0)
=> sorti1(j(X0)) )
& ! [X1] :
( sorti1(X1)
=> sorti2(h(X1)) ) )
=> ~ ( ! [X2] :
( sorti1(X2)
=> j(h(X2)) = X2 )
& ! [X3] :
( sorti2(X3)
=> h(j(X3)) = X3 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X6] :
( sorti1(X6)
=> ! [X7] :
( sorti1(X7)
=> h(op1(X6,X7)) = op2(h(X6),h(X7)) ) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,negated_conjecture,
~ ( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) ) ) ),
inference(negated_conjecture,[],[f5]) ).
fof(f5,conjecture,
( ( ! [X1] :
( sorti2(X1)
=> sorti1(j(X1)) )
& ! [X0] :
( sorti1(X0)
=> sorti2(h(X0)) ) )
=> ~ ( ! [X7] :
( sorti1(X7)
=> j(h(X7)) = X7 )
& ! [X6] :
( sorti2(X6)
=> h(j(X6)) = X6 )
& ! [X4] :
( sorti2(X4)
=> ! [X5] :
( sorti2(X5)
=> j(op2(X4,X5)) = op1(j(X4),j(X5)) ) )
& ! [X2] :
( sorti1(X2)
=> ! [X3] :
( sorti1(X3)
=> h(op1(X2,X3)) = op2(h(X2),h(X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f68,plain,
spl2_8,
inference(avatar_split_clause,[],[f20,f66]) ).
fof(f20,plain,
! [X4,X5] :
( h(op1(X4,X5)) = op2(h(X4),h(X5))
| ~ sorti1(X5)
| ~ sorti1(X4) ),
inference(cnf_transformation,[],[f14]) ).
fof(f64,plain,
( spl2_7
| ~ spl2_3
| ~ spl2_5 ),
inference(avatar_split_clause,[],[f58,f49,f39,f61]) ).
fof(f58,plain,
( sK0 = h(j(sK0))
| ~ spl2_3
| ~ spl2_5 ),
inference(resolution,[],[f51,f40]) ).
fof(f57,plain,
spl2_6,
inference(avatar_split_clause,[],[f25,f54]) ).
fof(f25,plain,
sorti2(sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f52,plain,
spl2_5,
inference(avatar_split_clause,[],[f24,f49]) ).
fof(f24,plain,
sorti2(sK0),
inference(cnf_transformation,[],[f17]) ).
fof(f45,plain,
spl2_4,
inference(avatar_split_clause,[],[f23,f43]) ).
fof(f23,plain,
! [X0] :
( j(h(X0)) = X0
| ~ sorti1(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f41,plain,
spl2_3,
inference(avatar_split_clause,[],[f22,f39]) ).
fof(f22,plain,
! [X1] :
( h(j(X1)) = X1
| ~ sorti2(X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f37,plain,
spl2_2,
inference(avatar_split_clause,[],[f19,f35]) ).
fof(f19,plain,
! [X6] :
( sorti1(j(X6))
| ~ sorti2(X6) ),
inference(cnf_transformation,[],[f14]) ).
fof(f33,plain,
spl2_1,
inference(avatar_split_clause,[],[f18,f31]) ).
fof(f18,plain,
! [X7] :
( sorti2(h(X7))
| ~ sorti1(X7) ),
inference(cnf_transformation,[],[f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ALG178+1 : TPTP v8.1.2. Released v2.7.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n005.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 19:58:53 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (2367)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (2372)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (2370)WARNING: value z3 for option sas not known
% 0.14/0.38 % (2369)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (2368)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (2371)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (2370)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (2373)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)
% 0.14/0.38 % (2374)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [3]
% 0.14/0.39 TRYING [4]
% 0.14/0.39 TRYING [4]
% 0.14/0.40 TRYING [5]
% 0.14/0.40 TRYING [5]
% 0.14/0.40 % (2372)First to succeed.
% 0.14/0.41 % (2373)Also succeeded, but the first one will report.
% 0.14/0.41 % (2372)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2367"
% 0.14/0.41 % (2372)Refutation found. Thanks to Tanya!
% 0.14/0.41 % SZS status Theorem for theBenchmark
% 0.14/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.41 % (2372)------------------------------
% 0.14/0.41 % (2372)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.41 % (2372)Termination reason: Refutation
% 0.14/0.41
% 0.14/0.41 % (2372)Memory used [KB]: 1325
% 0.14/0.41 % (2372)Time elapsed: 0.034 s
% 0.14/0.41 % (2372)Instructions burned: 62 (million)
% 0.14/0.41 % (2367)Success in time 0.036 s
%------------------------------------------------------------------------------