TSTP Solution File: ALG216+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG216+1 : TPTP v8.2.0. Released v3.4.0.
% 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 : Mon May 20 18:36:06 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 190
% Syntax : Number of formulae : 564 ( 142 unt; 0 def)
% Number of atoms : 1854 ( 72 equ)
% Maximal formula atoms : 42 ( 3 avg)
% Number of connectives : 2176 ( 886 ~; 875 |; 231 &)
% ( 123 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 148 ( 146 usr; 123 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 15 con; 0-3 aty)
% Number of variables : 470 ( 411 !; 59 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f923,plain,
$false,
inference(avatar_sat_refutation,[],[f221,f226,f231,f236,f241,f246,f251,f256,f261,f266,f271,f276,f281,f286,f291,f296,f301,f306,f311,f316,f321,f326,f331,f336,f341,f346,f351,f356,f361,f366,f371,f376,f381,f385,f389,f393,f402,f406,f410,f414,f418,f422,f426,f430,f434,f438,f442,f451,f462,f466,f470,f474,f479,f483,f491,f495,f499,f503,f508,f512,f516,f520,f524,f528,f532,f537,f541,f545,f562,f573,f577,f587,f591,f596,f600,f615,f619,f631,f641,f645,f649,f659,f668,f677,f682,f687,f693,f698,f703,f708,f713,f725,f734,f738,f744,f748,f752,f759,f763,f764,f765,f769,f771,f790,f799,f807,f811,f820,f824,f830,f834,f840,f845,f849,f853,f866,f870,f874,f879,f890,f901,f906,f910,f914,f922]) ).
fof(f922,plain,
( spl21_1
| ~ spl21_2
| ~ spl21_3
| ~ spl21_4
| ~ spl21_5
| ~ spl21_6
| ~ spl21_7
| ~ spl21_8
| ~ spl21_9
| ~ spl21_10
| spl21_11
| ~ spl21_12
| ~ spl21_13
| ~ spl21_14
| ~ spl21_15
| ~ spl21_16
| ~ spl21_17
| ~ spl21_18
| ~ spl21_120
| spl21_19
| ~ spl21_37
| ~ spl21_81 ),
inference(avatar_split_clause,[],[f915,f643,f395,f308,f898,f303,f298,f293,f288,f283,f278,f273,f268,f263,f258,f253,f248,f243,f238,f233,f228,f223,f218]) ).
fof(f218,plain,
( spl21_1
<=> v3_struct_0(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_1])]) ).
fof(f223,plain,
( spl21_2
<=> v3_rlvect_1(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_2])]) ).
fof(f228,plain,
( spl21_3
<=> v4_rlvect_1(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_3])]) ).
fof(f233,plain,
( spl21_4
<=> v5_rlvect_1(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_4])]) ).
fof(f238,plain,
( spl21_5
<=> v6_rlvect_1(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_5])]) ).
fof(f243,plain,
( spl21_6
<=> v4_group_1(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_6])]) ).
fof(f248,plain,
( spl21_7
<=> v6_vectsp_1(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_7])]) ).
fof(f253,plain,
( spl21_8
<=> v7_vectsp_1(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_8])]) ).
fof(f258,plain,
( spl21_9
<=> v8_vectsp_1(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_9])]) ).
fof(f263,plain,
( spl21_10
<=> l3_vectsp_1(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_10])]) ).
fof(f268,plain,
( spl21_11
<=> v3_struct_0(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_11])]) ).
fof(f273,plain,
( spl21_12
<=> v3_rlvect_1(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_12])]) ).
fof(f278,plain,
( spl21_13
<=> v4_rlvect_1(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_13])]) ).
fof(f283,plain,
( spl21_14
<=> v5_rlvect_1(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_14])]) ).
fof(f288,plain,
( spl21_15
<=> v6_rlvect_1(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_15])]) ).
fof(f293,plain,
( spl21_16
<=> v5_vectsp_2(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_16])]) ).
fof(f298,plain,
( spl21_17
<=> l1_vectsp_2(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_17])]) ).
fof(f303,plain,
( spl21_18
<=> m1_subset_1(sK2,u1_struct_0(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_18])]) ).
fof(f898,plain,
( spl21_120
<=> m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_120])]) ).
fof(f308,plain,
( spl21_19
<=> k1_rlvect_1(sK0) = k2_group_1(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_19])]) ).
fof(f395,plain,
( spl21_37
<=> v1_rmod_5(k8_rlvect_2(sK1,sK2,k1_rlvect_1(sK1)),sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_37])]) ).
fof(f643,plain,
( spl21_81
<=> ! [X2,X0,X1] :
( k1_rlvect_1(X0) = k2_group_1(X0)
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1)
| ~ m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_81])]) ).
fof(f915,plain,
( k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ m1_subset_1(sK2,u1_struct_0(sK1))
| ~ l1_vectsp_2(sK1,sK0)
| ~ v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| ~ spl21_37
| ~ spl21_81 ),
inference(resolution,[],[f397,f644]) ).
fof(f644,plain,
( ! [X2,X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1)
| k1_rlvect_1(X0) = k2_group_1(X0)
| ~ m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) )
| ~ spl21_81 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f397,plain,
( v1_rmod_5(k8_rlvect_2(sK1,sK2,k1_rlvect_1(sK1)),sK0,sK1)
| ~ spl21_37 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f914,plain,
( ~ spl21_104
| ~ spl21_62
| spl21_120 ),
inference(avatar_split_clause,[],[f902,f898,f514,f787]) ).
fof(f787,plain,
( spl21_104
<=> l2_struct_0(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_104])]) ).
fof(f514,plain,
( spl21_62
<=> ! [X0] :
( m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ l2_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_62])]) ).
fof(f902,plain,
( ~ l2_struct_0(sK1)
| ~ spl21_62
| spl21_120 ),
inference(resolution,[],[f900,f515]) ).
fof(f515,plain,
( ! [X0] :
( m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ l2_struct_0(X0) )
| ~ spl21_62 ),
inference(avatar_component_clause,[],[f514]) ).
fof(f900,plain,
( ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| spl21_120 ),
inference(avatar_component_clause,[],[f898]) ).
fof(f910,plain,
( spl21_122
| ~ spl21_70
| ~ spl21_74 ),
inference(avatar_split_clause,[],[f604,f589,f560,f908]) ).
fof(f908,plain,
( spl21_122
<=> ! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| v1_xboole_0(k1_zfmisc_1(u1_struct_0(X0)))
| r2_hidden(sK7(X0),k1_zfmisc_1(u1_struct_0(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_122])]) ).
fof(f560,plain,
( spl21_70
<=> ! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_70])]) ).
fof(f589,plain,
( spl21_74
<=> ! [X0] :
( m1_subset_1(sK7(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_74])]) ).
fof(f604,plain,
( ! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| v1_xboole_0(k1_zfmisc_1(u1_struct_0(X0)))
| r2_hidden(sK7(X0),k1_zfmisc_1(u1_struct_0(X0))) )
| ~ spl21_70
| ~ spl21_74 ),
inference(resolution,[],[f590,f561]) ).
fof(f561,plain,
( ! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| v1_xboole_0(X1)
| r2_hidden(X0,X1) )
| ~ spl21_70 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f590,plain,
( ! [X0] :
( m1_subset_1(sK7(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) )
| ~ spl21_74 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f906,plain,
( spl21_121
| ~ spl21_70
| ~ spl21_73 ),
inference(avatar_split_clause,[],[f602,f585,f560,f904]) ).
fof(f904,plain,
( spl21_121
<=> ! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| v1_xboole_0(k1_zfmisc_1(u1_struct_0(X0)))
| r2_hidden(sK6(X0),k1_zfmisc_1(u1_struct_0(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_121])]) ).
fof(f585,plain,
( spl21_73
<=> ! [X0] :
( m1_subset_1(sK6(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_73])]) ).
fof(f602,plain,
( ! [X0] :
( ~ l1_struct_0(X0)
| v3_struct_0(X0)
| v1_xboole_0(k1_zfmisc_1(u1_struct_0(X0)))
| r2_hidden(sK6(X0),k1_zfmisc_1(u1_struct_0(X0))) )
| ~ spl21_70
| ~ spl21_73 ),
inference(resolution,[],[f586,f561]) ).
fof(f586,plain,
( ! [X0] :
( m1_subset_1(sK6(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) )
| ~ spl21_73 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f901,plain,
( spl21_1
| ~ spl21_2
| ~ spl21_3
| ~ spl21_4
| ~ spl21_5
| ~ spl21_6
| ~ spl21_7
| ~ spl21_8
| ~ spl21_9
| ~ spl21_10
| spl21_11
| ~ spl21_12
| ~ spl21_13
| ~ spl21_14
| ~ spl21_15
| ~ spl21_16
| ~ spl21_17
| ~ spl21_120
| ~ spl21_18
| spl21_19
| ~ spl21_38
| ~ spl21_82 ),
inference(avatar_split_clause,[],[f650,f647,f399,f308,f303,f898,f298,f293,f288,f283,f278,f273,f268,f263,f258,f253,f248,f243,f238,f233,f228,f223,f218]) ).
fof(f399,plain,
( spl21_38
<=> v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),sK2),sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_38])]) ).
fof(f647,plain,
( spl21_82
<=> ! [X0,X1,X3] :
( k1_rlvect_1(X0) = k2_group_1(X0)
| ~ v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X3),X0,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_82])]) ).
fof(f650,plain,
( k1_rlvect_1(sK0) = k2_group_1(sK0)
| ~ m1_subset_1(sK2,u1_struct_0(sK1))
| ~ m1_subset_1(k1_rlvect_1(sK1),u1_struct_0(sK1))
| ~ l1_vectsp_2(sK1,sK0)
| ~ v5_vectsp_2(sK1,sK0)
| ~ v6_rlvect_1(sK1)
| ~ v5_rlvect_1(sK1)
| ~ v4_rlvect_1(sK1)
| ~ v3_rlvect_1(sK1)
| v3_struct_0(sK1)
| ~ l3_vectsp_1(sK0)
| ~ v8_vectsp_1(sK0)
| ~ v7_vectsp_1(sK0)
| ~ v6_vectsp_1(sK0)
| ~ v4_group_1(sK0)
| ~ v6_rlvect_1(sK0)
| ~ v5_rlvect_1(sK0)
| ~ v4_rlvect_1(sK0)
| ~ v3_rlvect_1(sK0)
| v3_struct_0(sK0)
| ~ spl21_38
| ~ spl21_82 ),
inference(resolution,[],[f648,f401]) ).
fof(f401,plain,
( v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),sK2),sK0,sK1)
| ~ spl21_38 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f648,plain,
( ! [X3,X0,X1] :
( ~ v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X3),X0,X1)
| k1_rlvect_1(X0) = k2_group_1(X0)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) )
| ~ spl21_82 ),
inference(avatar_component_clause,[],[f647]) ).
fof(f890,plain,
( spl21_11
| ~ spl21_96
| spl21_119
| ~ spl21_18
| ~ spl21_79 ),
inference(avatar_split_clause,[],[f634,f629,f303,f888,f728,f268]) ).
fof(f728,plain,
( spl21_96
<=> l1_struct_0(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_96])]) ).
fof(f888,plain,
( spl21_119
<=> ! [X0] :
( k8_rlvect_2(sK1,X0,sK2) = k8_rlvect_2(sK1,sK2,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_119])]) ).
fof(f629,plain,
( spl21_79
<=> ! [X2,X0,X1] :
( k8_rlvect_2(X0,X1,X2) = k8_rlvect_2(X0,X2,X1)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_79])]) ).
fof(f634,plain,
( ! [X0] :
( k8_rlvect_2(sK1,X0,sK2) = k8_rlvect_2(sK1,sK2,X0)
| ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ l1_struct_0(sK1)
| v3_struct_0(sK1) )
| ~ spl21_18
| ~ spl21_79 ),
inference(resolution,[],[f630,f305]) ).
fof(f305,plain,
( m1_subset_1(sK2,u1_struct_0(sK1))
| ~ spl21_18 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f630,plain,
( ! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| k8_rlvect_2(X0,X1,X2) = k8_rlvect_2(X0,X2,X1)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) )
| ~ spl21_79 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f879,plain,
( spl21_96
| ~ spl21_46
| ~ spl21_104 ),
inference(avatar_split_clause,[],[f815,f787,f432,f728]) ).
fof(f432,plain,
( spl21_46
<=> ! [X0] :
( l1_struct_0(X0)
| ~ l2_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_46])]) ).
fof(f815,plain,
( l1_struct_0(sK1)
| ~ spl21_46
| ~ spl21_104 ),
inference(resolution,[],[f789,f433]) ).
fof(f433,plain,
( ! [X0] :
( ~ l2_struct_0(X0)
| l1_struct_0(X0) )
| ~ spl21_46 ),
inference(avatar_component_clause,[],[f432]) ).
fof(f789,plain,
( l2_struct_0(sK1)
| ~ spl21_104 ),
inference(avatar_component_clause,[],[f787]) ).
fof(f874,plain,
( spl21_118
| ~ spl21_74
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f608,f598,f589,f872]) ).
fof(f872,plain,
( spl21_118
<=> ! [X0,X1] :
( m1_subset_1(X0,u1_struct_0(X1))
| ~ r2_hidden(X0,sK7(X1))
| ~ l1_struct_0(X1)
| v3_struct_0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_118])]) ).
fof(f598,plain,
( spl21_76
<=> ! [X2,X0,X1] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_76])]) ).
fof(f608,plain,
( ! [X0,X1] :
( m1_subset_1(X0,u1_struct_0(X1))
| ~ r2_hidden(X0,sK7(X1))
| ~ l1_struct_0(X1)
| v3_struct_0(X1) )
| ~ spl21_74
| ~ spl21_76 ),
inference(resolution,[],[f599,f590]) ).
fof(f599,plain,
( ! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| m1_subset_1(X0,X2)
| ~ r2_hidden(X0,X1) )
| ~ spl21_76 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f870,plain,
( spl21_117
| ~ spl21_73
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f607,f598,f585,f868]) ).
fof(f868,plain,
( spl21_117
<=> ! [X0,X1] :
( m1_subset_1(X0,u1_struct_0(X1))
| ~ r2_hidden(X0,sK6(X1))
| ~ l1_struct_0(X1)
| v3_struct_0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_117])]) ).
fof(f607,plain,
( ! [X0,X1] :
( m1_subset_1(X0,u1_struct_0(X1))
| ~ r2_hidden(X0,sK6(X1))
| ~ l1_struct_0(X1)
| v3_struct_0(X1) )
| ~ spl21_73
| ~ spl21_76 ),
inference(resolution,[],[f599,f586]) ).
fof(f866,plain,
( spl21_116
| ~ spl21_70
| ~ spl21_71 ),
inference(avatar_split_clause,[],[f578,f571,f560,f864]) ).
fof(f864,plain,
( spl21_116
<=> ! [X0] :
( ~ l1_group_1(X0)
| v3_struct_0(X0)
| v1_xboole_0(u1_struct_0(X0))
| r2_hidden(k2_group_1(X0),u1_struct_0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_116])]) ).
fof(f571,plain,
( spl21_71
<=> ! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| v3_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_71])]) ).
fof(f578,plain,
( ! [X0] :
( ~ l1_group_1(X0)
| v3_struct_0(X0)
| v1_xboole_0(u1_struct_0(X0))
| r2_hidden(k2_group_1(X0),u1_struct_0(X0)) )
| ~ spl21_70
| ~ spl21_71 ),
inference(resolution,[],[f572,f561]) ).
fof(f572,plain,
( ! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| v3_struct_0(X0) )
| ~ spl21_71 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f853,plain,
( spl21_115
| ~ spl21_61
| ~ spl21_70 ),
inference(avatar_split_clause,[],[f566,f560,f510,f851]) ).
fof(f851,plain,
( spl21_115
<=> ! [X0] :
( v1_xboole_0(k1_zfmisc_1(X0))
| r2_hidden(sK3(X0),k1_zfmisc_1(X0))
| v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_115])]) ).
fof(f510,plain,
( spl21_61
<=> ! [X0] :
( m1_subset_1(sK3(X0),k1_zfmisc_1(X0))
| v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_61])]) ).
fof(f566,plain,
( ! [X0] :
( v1_xboole_0(k1_zfmisc_1(X0))
| r2_hidden(sK3(X0),k1_zfmisc_1(X0))
| v1_xboole_0(X0) )
| ~ spl21_61
| ~ spl21_70 ),
inference(resolution,[],[f561,f511]) ).
fof(f511,plain,
( ! [X0] :
( m1_subset_1(sK3(X0),k1_zfmisc_1(X0))
| v1_xboole_0(X0) )
| ~ spl21_61 ),
inference(avatar_component_clause,[],[f510]) ).
fof(f849,plain,
( spl21_114
| ~ spl21_62
| ~ spl21_70 ),
inference(avatar_split_clause,[],[f564,f560,f514,f847]) ).
fof(f847,plain,
( spl21_114
<=> ! [X0] :
( v1_xboole_0(u1_struct_0(X0))
| r2_hidden(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ l2_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_114])]) ).
fof(f564,plain,
( ! [X0] :
( v1_xboole_0(u1_struct_0(X0))
| r2_hidden(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ l2_struct_0(X0) )
| ~ spl21_62
| ~ spl21_70 ),
inference(resolution,[],[f561,f515]) ).
fof(f845,plain,
( spl21_113
| ~ spl21_39
| ~ spl21_80 ),
inference(avatar_split_clause,[],[f715,f638,f404,f842]) ).
fof(f842,plain,
( spl21_113
<=> l1_group_1(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_113])]) ).
fof(f404,plain,
( spl21_39
<=> ! [X0] :
( l1_group_1(X0)
| ~ l1_vectsp_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_39])]) ).
fof(f638,plain,
( spl21_80
<=> l1_vectsp_1(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_80])]) ).
fof(f715,plain,
( l1_group_1(sK0)
| ~ spl21_39
| ~ spl21_80 ),
inference(resolution,[],[f640,f405]) ).
fof(f405,plain,
( ! [X0] :
( ~ l1_vectsp_1(X0)
| l1_group_1(X0) )
| ~ spl21_39 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f640,plain,
( l1_vectsp_1(sK0)
| ~ spl21_80 ),
inference(avatar_component_clause,[],[f638]) ).
fof(f840,plain,
( spl21_112
| ~ spl21_68
| ~ spl21_70 ),
inference(avatar_split_clause,[],[f563,f560,f539,f838]) ).
fof(f838,plain,
( spl21_112
<=> ! [X0,X1] :
( v1_xboole_0(k1_zfmisc_1(X0))
| r2_hidden(X1,k1_zfmisc_1(X0))
| ~ r1_tarski(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_112])]) ).
fof(f539,plain,
( spl21_68
<=> ! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_68])]) ).
fof(f563,plain,
( ! [X0,X1] :
( v1_xboole_0(k1_zfmisc_1(X0))
| r2_hidden(X1,k1_zfmisc_1(X0))
| ~ r1_tarski(X1,X0) )
| ~ spl21_68
| ~ spl21_70 ),
inference(resolution,[],[f561,f540]) ).
fof(f540,plain,
( ! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) )
| ~ spl21_68 ),
inference(avatar_component_clause,[],[f539]) ).
fof(f834,plain,
( spl21_111
| ~ spl21_61
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f606,f598,f510,f832]) ).
fof(f832,plain,
( spl21_111
<=> ! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,sK3(X1))
| v1_xboole_0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_111])]) ).
fof(f606,plain,
( ! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,sK3(X1))
| v1_xboole_0(X1) )
| ~ spl21_61
| ~ spl21_76 ),
inference(resolution,[],[f599,f511]) ).
fof(f830,plain,
( spl21_110
| ~ spl21_68
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f605,f598,f539,f828]) ).
fof(f828,plain,
( spl21_110
<=> ! [X2,X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X2)
| ~ r1_tarski(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_110])]) ).
fof(f605,plain,
( ! [X2,X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X2)
| ~ r1_tarski(X2,X1) )
| ~ spl21_68
| ~ spl21_76 ),
inference(resolution,[],[f599,f540]) ).
fof(f824,plain,
( spl21_109
| ~ spl21_47
| ~ spl21_76 ),
inference(avatar_split_clause,[],[f609,f598,f436,f822]) ).
fof(f822,plain,
( spl21_109
<=> ! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,sK8(k1_zfmisc_1(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_109])]) ).
fof(f436,plain,
( spl21_47
<=> ! [X0] : m1_subset_1(sK8(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_47])]) ).
fof(f609,plain,
( ! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,sK8(k1_zfmisc_1(X1))) )
| ~ spl21_47
| ~ spl21_76 ),
inference(resolution,[],[f599,f437]) ).
fof(f437,plain,
( ! [X0] : m1_subset_1(sK8(X0),X0)
| ~ spl21_47 ),
inference(avatar_component_clause,[],[f436]) ).
fof(f820,plain,
( spl21_108
| ~ spl21_68
| ~ spl21_72 ),
inference(avatar_split_clause,[],[f579,f575,f539,f818]) ).
fof(f818,plain,
( spl21_108
<=> ! [X2,X0,X1] :
( ~ v1_xboole_0(X0)
| ~ r2_hidden(X1,X2)
| ~ r1_tarski(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_108])]) ).
fof(f575,plain,
( spl21_72
<=> ! [X2,X0,X1] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_72])]) ).
fof(f579,plain,
( ! [X2,X0,X1] :
( ~ v1_xboole_0(X0)
| ~ r2_hidden(X1,X2)
| ~ r1_tarski(X2,X0) )
| ~ spl21_68
| ~ spl21_72 ),
inference(resolution,[],[f576,f540]) ).
fof(f576,plain,
( ! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ v1_xboole_0(X2)
| ~ r2_hidden(X0,X1) )
| ~ spl21_72 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f811,plain,
( spl21_107
| ~ spl21_47
| ~ spl21_72 ),
inference(avatar_split_clause,[],[f581,f575,f436,f809]) ).
fof(f809,plain,
( spl21_107
<=> ! [X0,X1] :
( ~ v1_xboole_0(X0)
| ~ r2_hidden(X1,sK8(k1_zfmisc_1(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_107])]) ).
fof(f581,plain,
( ! [X0,X1] :
( ~ v1_xboole_0(X0)
| ~ r2_hidden(X1,sK8(k1_zfmisc_1(X0))) )
| ~ spl21_47
| ~ spl21_72 ),
inference(resolution,[],[f576,f437]) ).
fof(f807,plain,
( spl21_106
| ~ spl21_29
| ~ spl21_35
| ~ spl21_52
| ~ spl21_53
| ~ spl21_70 ),
inference(avatar_split_clause,[],[f569,f560,f472,f468,f387,f358,f805]) ).
fof(f805,plain,
( spl21_106
<=> ! [X0] :
( r2_hidden(sK18,k1_zfmisc_1(X0))
| v1_xboole_0(k1_zfmisc_1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_106])]) ).
fof(f358,plain,
( spl21_29
<=> v1_xboole_0(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_29])]) ).
fof(f387,plain,
( spl21_35
<=> ! [X0] : v1_xboole_0(sK9(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_35])]) ).
fof(f468,plain,
( spl21_52
<=> ! [X0] :
( k1_xboole_0 = X0
| ~ v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_52])]) ).
fof(f472,plain,
( spl21_53
<=> ! [X0] : m1_subset_1(sK9(X0),k1_zfmisc_1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_53])]) ).
fof(f569,plain,
( ! [X0] :
( r2_hidden(sK18,k1_zfmisc_1(X0))
| v1_xboole_0(k1_zfmisc_1(X0)) )
| ~ spl21_29
| ~ spl21_35
| ~ spl21_52
| ~ spl21_53
| ~ spl21_70 ),
inference(forward_demodulation,[],[f568,f487]) ).
fof(f487,plain,
( ! [X0] : sK9(X0) = sK18
| ~ spl21_29
| ~ spl21_35
| ~ spl21_52 ),
inference(forward_demodulation,[],[f486,f485]) ).
fof(f485,plain,
( k1_xboole_0 = sK18
| ~ spl21_29
| ~ spl21_52 ),
inference(resolution,[],[f469,f360]) ).
fof(f360,plain,
( v1_xboole_0(sK18)
| ~ spl21_29 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f469,plain,
( ! [X0] :
( ~ v1_xboole_0(X0)
| k1_xboole_0 = X0 )
| ~ spl21_52 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f486,plain,
( ! [X0] : k1_xboole_0 = sK9(X0)
| ~ spl21_35
| ~ spl21_52 ),
inference(resolution,[],[f469,f388]) ).
fof(f388,plain,
( ! [X0] : v1_xboole_0(sK9(X0))
| ~ spl21_35 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f568,plain,
( ! [X0] :
( v1_xboole_0(k1_zfmisc_1(X0))
| r2_hidden(sK9(X0),k1_zfmisc_1(X0)) )
| ~ spl21_53
| ~ spl21_70 ),
inference(resolution,[],[f561,f473]) ).
fof(f473,plain,
( ! [X0] : m1_subset_1(sK9(X0),k1_zfmisc_1(X0))
| ~ spl21_53 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f799,plain,
( spl21_105
| ~ spl21_47
| ~ spl21_70 ),
inference(avatar_split_clause,[],[f567,f560,f436,f797]) ).
fof(f797,plain,
( spl21_105
<=> ! [X0] :
( v1_xboole_0(X0)
| r2_hidden(sK8(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_105])]) ).
fof(f567,plain,
( ! [X0] :
( v1_xboole_0(X0)
| r2_hidden(sK8(X0),X0) )
| ~ spl21_47
| ~ spl21_70 ),
inference(resolution,[],[f561,f437]) ).
fof(f790,plain,
( spl21_104
| ~ spl21_45
| ~ spl21_84 ),
inference(avatar_split_clause,[],[f785,f656,f428,f787]) ).
fof(f428,plain,
( spl21_45
<=> ! [X0] :
( l2_struct_0(X0)
| ~ l1_rlvect_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_45])]) ).
fof(f656,plain,
( spl21_84
<=> l1_rlvect_1(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_84])]) ).
fof(f785,plain,
( l2_struct_0(sK1)
| ~ spl21_45
| ~ spl21_84 ),
inference(resolution,[],[f658,f429]) ).
fof(f429,plain,
( ! [X0] :
( ~ l1_rlvect_1(X0)
| l2_struct_0(X0) )
| ~ spl21_45 ),
inference(avatar_component_clause,[],[f428]) ).
fof(f658,plain,
( l1_rlvect_1(sK1)
| ~ spl21_84 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f771,plain,
( spl21_101
| ~ spl21_52
| ~ spl21_95 ),
inference(avatar_split_clause,[],[f766,f722,f468,f750]) ).
fof(f750,plain,
( spl21_101
<=> ! [X0] :
( sK18 = X0
| ~ v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_101])]) ).
fof(f722,plain,
( spl21_95
<=> k1_xboole_0 = sK18 ),
introduced(avatar_definition,[new_symbols(naming,[spl21_95])]) ).
fof(f766,plain,
( ! [X0] :
( sK18 = X0
| ~ v1_xboole_0(X0) )
| ~ spl21_52
| ~ spl21_95 ),
inference(forward_demodulation,[],[f469,f724]) ).
fof(f724,plain,
( k1_xboole_0 = sK18
| ~ spl21_95 ),
inference(avatar_component_clause,[],[f722]) ).
fof(f769,plain,
( spl21_83
| ~ spl21_46
| ~ spl21_75 ),
inference(avatar_split_clause,[],[f672,f593,f432,f652]) ).
fof(f652,plain,
( spl21_83
<=> l1_struct_0(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_83])]) ).
fof(f593,plain,
( spl21_75
<=> l2_struct_0(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_75])]) ).
fof(f672,plain,
( l1_struct_0(sK0)
| ~ spl21_46
| ~ spl21_75 ),
inference(resolution,[],[f595,f433]) ).
fof(f595,plain,
( l2_struct_0(sK0)
| ~ spl21_75 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f765,plain,
( ~ spl21_20
| ~ spl21_102 ),
inference(avatar_contradiction_clause,[],[f760]) ).
fof(f760,plain,
( $false
| ~ spl21_20
| ~ spl21_102 ),
inference(resolution,[],[f755,f315]) ).
fof(f315,plain,
( v1_xboole_0(k1_xboole_0)
| ~ spl21_20 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f313,plain,
( spl21_20
<=> v1_xboole_0(k1_xboole_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_20])]) ).
fof(f755,plain,
( ! [X0] : ~ v1_xboole_0(X0)
| ~ spl21_102 ),
inference(avatar_component_clause,[],[f754]) ).
fof(f754,plain,
( spl21_102
<=> ! [X0] : ~ v1_xboole_0(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_102])]) ).
fof(f764,plain,
( ~ spl21_29
| ~ spl21_102 ),
inference(avatar_contradiction_clause,[],[f761]) ).
fof(f761,plain,
( $false
| ~ spl21_29
| ~ spl21_102 ),
inference(resolution,[],[f755,f360]) ).
fof(f763,plain,
( ~ spl21_35
| ~ spl21_102 ),
inference(avatar_contradiction_clause,[],[f762]) ).
fof(f762,plain,
( $false
| ~ spl21_35
| ~ spl21_102 ),
inference(resolution,[],[f755,f388]) ).
fof(f759,plain,
( spl21_102
| spl21_103
| ~ spl21_29
| ~ spl21_35
| ~ spl21_52
| ~ spl21_53
| ~ spl21_72 ),
inference(avatar_split_clause,[],[f583,f575,f472,f468,f387,f358,f757,f754]) ).
fof(f757,plain,
( spl21_103
<=> ! [X1] : ~ r2_hidden(X1,sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_103])]) ).
fof(f583,plain,
( ! [X0,X1] :
( ~ r2_hidden(X1,sK18)
| ~ v1_xboole_0(X0) )
| ~ spl21_29
| ~ spl21_35
| ~ spl21_52
| ~ spl21_53
| ~ spl21_72 ),
inference(forward_demodulation,[],[f582,f487]) ).
fof(f582,plain,
( ! [X0,X1] :
( ~ v1_xboole_0(X0)
| ~ r2_hidden(X1,sK9(X0)) )
| ~ spl21_53
| ~ spl21_72 ),
inference(resolution,[],[f576,f473]) ).
fof(f752,plain,
( spl21_101
| ~ spl21_29
| ~ spl21_69 ),
inference(avatar_split_clause,[],[f556,f543,f358,f750]) ).
fof(f543,plain,
( spl21_69
<=> ! [X0,X1] :
( ~ v1_xboole_0(X1)
| X0 = X1
| ~ v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_69])]) ).
fof(f556,plain,
( ! [X0] :
( sK18 = X0
| ~ v1_xboole_0(X0) )
| ~ spl21_29
| ~ spl21_69 ),
inference(resolution,[],[f544,f360]) ).
fof(f544,plain,
( ! [X0,X1] :
( ~ v1_xboole_0(X1)
| X0 = X1
| ~ v1_xboole_0(X0) )
| ~ spl21_69 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f748,plain,
( spl21_100
| ~ spl21_56
| ~ spl21_63 ),
inference(avatar_split_clause,[],[f550,f518,f489,f746]) ).
fof(f746,plain,
( spl21_100
<=> ! [X0] :
( l1_rlvect_1(sK4(X0))
| ~ l1_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_100])]) ).
fof(f489,plain,
( spl21_56
<=> ! [X0] :
( l1_vectsp_2(sK4(X0),X0)
| ~ l1_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_56])]) ).
fof(f518,plain,
( spl21_63
<=> ! [X0,X1] :
( l1_rlvect_1(X1)
| ~ l1_vectsp_2(X1,X0)
| ~ l1_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_63])]) ).
fof(f550,plain,
( ! [X0] :
( l1_rlvect_1(sK4(X0))
| ~ l1_struct_0(X0) )
| ~ spl21_56
| ~ spl21_63 ),
inference(duplicate_literal_removal,[],[f547]) ).
fof(f547,plain,
( ! [X0] :
( l1_rlvect_1(sK4(X0))
| ~ l1_struct_0(X0)
| ~ l1_struct_0(X0) )
| ~ spl21_56
| ~ spl21_63 ),
inference(resolution,[],[f519,f490]) ).
fof(f490,plain,
( ! [X0] :
( l1_vectsp_2(sK4(X0),X0)
| ~ l1_struct_0(X0) )
| ~ spl21_56 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f519,plain,
( ! [X0,X1] :
( ~ l1_vectsp_2(X1,X0)
| l1_rlvect_1(X1)
| ~ l1_struct_0(X0) )
| ~ spl21_63 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f744,plain,
( spl21_99
| ~ spl21_57
| ~ spl21_63 ),
inference(avatar_split_clause,[],[f549,f518,f493,f742]) ).
fof(f742,plain,
( spl21_99
<=> ! [X0] :
( l1_rlvect_1(sK5(X0))
| ~ l1_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_99])]) ).
fof(f493,plain,
( spl21_57
<=> ! [X0] :
( l1_vectsp_2(sK5(X0),X0)
| ~ l1_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_57])]) ).
fof(f549,plain,
( ! [X0] :
( l1_rlvect_1(sK5(X0))
| ~ l1_struct_0(X0) )
| ~ spl21_57
| ~ spl21_63 ),
inference(duplicate_literal_removal,[],[f548]) ).
fof(f548,plain,
( ! [X0] :
( l1_rlvect_1(sK5(X0))
| ~ l1_struct_0(X0)
| ~ l1_struct_0(X0) )
| ~ spl21_57
| ~ spl21_63 ),
inference(resolution,[],[f519,f494]) ).
fof(f494,plain,
( ! [X0] :
( l1_vectsp_2(sK5(X0),X0)
| ~ l1_struct_0(X0) )
| ~ spl21_57 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f738,plain,
( spl21_98
| ~ spl21_29
| ~ spl21_35
| ~ spl21_52 ),
inference(avatar_split_clause,[],[f487,f468,f387,f358,f736]) ).
fof(f736,plain,
( spl21_98
<=> ! [X0] : sK9(X0) = sK18 ),
introduced(avatar_definition,[new_symbols(naming,[spl21_98])]) ).
fof(f734,plain,
( spl21_11
| ~ spl21_96
| spl21_97
| ~ spl21_18
| ~ spl21_77 ),
inference(avatar_split_clause,[],[f622,f613,f303,f732,f728,f268]) ).
fof(f732,plain,
( spl21_97
<=> ! [X0] :
( k8_rlvect_2(sK1,X0,sK2) = k2_tarski(X0,sK2)
| ~ m1_subset_1(X0,u1_struct_0(sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_97])]) ).
fof(f613,plain,
( spl21_77
<=> ! [X2,X0,X1] :
( k8_rlvect_2(X0,X1,X2) = k2_tarski(X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_77])]) ).
fof(f622,plain,
( ! [X0] :
( k8_rlvect_2(sK1,X0,sK2) = k2_tarski(X0,sK2)
| ~ m1_subset_1(X0,u1_struct_0(sK1))
| ~ l1_struct_0(sK1)
| v3_struct_0(sK1) )
| ~ spl21_18
| ~ spl21_77 ),
inference(resolution,[],[f614,f305]) ).
fof(f614,plain,
( ! [X2,X0,X1] :
( ~ m1_subset_1(X2,u1_struct_0(X0))
| k8_rlvect_2(X0,X1,X2) = k2_tarski(X1,X2)
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) )
| ~ spl21_77 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f725,plain,
( spl21_95
| ~ spl21_29
| ~ spl21_52 ),
inference(avatar_split_clause,[],[f485,f468,f358,f722]) ).
fof(f713,plain,
( spl21_94
| ~ spl21_30
| ~ spl21_46 ),
inference(avatar_split_clause,[],[f458,f432,f363,f710]) ).
fof(f710,plain,
( spl21_94
<=> l1_struct_0(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_94])]) ).
fof(f363,plain,
( spl21_30
<=> l2_struct_0(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_30])]) ).
fof(f458,plain,
( l1_struct_0(sK19)
| ~ spl21_30
| ~ spl21_46 ),
inference(resolution,[],[f433,f365]) ).
fof(f365,plain,
( l2_struct_0(sK19)
| ~ spl21_30 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f708,plain,
( spl21_93
| ~ spl21_27
| ~ spl21_46 ),
inference(avatar_split_clause,[],[f457,f432,f348,f705]) ).
fof(f705,plain,
( spl21_93
<=> l1_struct_0(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_93])]) ).
fof(f348,plain,
( spl21_27
<=> l2_struct_0(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_27])]) ).
fof(f457,plain,
( l1_struct_0(sK16)
| ~ spl21_27
| ~ spl21_46 ),
inference(resolution,[],[f433,f350]) ).
fof(f350,plain,
( l2_struct_0(sK16)
| ~ spl21_27 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f703,plain,
( spl21_92
| ~ spl21_26
| ~ spl21_45 ),
inference(avatar_split_clause,[],[f456,f428,f343,f700]) ).
fof(f700,plain,
( spl21_92
<=> l2_struct_0(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_92])]) ).
fof(f343,plain,
( spl21_26
<=> l1_rlvect_1(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_26])]) ).
fof(f456,plain,
( l2_struct_0(sK15)
| ~ spl21_26
| ~ spl21_45 ),
inference(resolution,[],[f429,f345]) ).
fof(f345,plain,
( l1_rlvect_1(sK15)
| ~ spl21_26 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f698,plain,
( spl21_91
| ~ spl21_25
| ~ spl21_44 ),
inference(avatar_split_clause,[],[f455,f424,f338,f695]) ).
fof(f695,plain,
( spl21_91
<=> l2_vectsp_1(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_91])]) ).
fof(f338,plain,
( spl21_25
<=> l3_vectsp_1(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_25])]) ).
fof(f424,plain,
( spl21_44
<=> ! [X0] :
( l2_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_44])]) ).
fof(f455,plain,
( l2_vectsp_1(sK14)
| ~ spl21_25
| ~ spl21_44 ),
inference(resolution,[],[f425,f340]) ).
fof(f340,plain,
( l3_vectsp_1(sK14)
| ~ spl21_25 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f425,plain,
( ! [X0] :
( ~ l3_vectsp_1(X0)
| l2_vectsp_1(X0) )
| ~ spl21_44 ),
inference(avatar_component_clause,[],[f424]) ).
fof(f693,plain,
( spl21_90
| ~ spl21_25
| ~ spl21_43 ),
inference(avatar_split_clause,[],[f453,f420,f338,f690]) ).
fof(f690,plain,
( spl21_90
<=> l1_rlvect_1(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_90])]) ).
fof(f420,plain,
( spl21_43
<=> ! [X0] :
( l1_rlvect_1(X0)
| ~ l3_vectsp_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_43])]) ).
fof(f453,plain,
( l1_rlvect_1(sK14)
| ~ spl21_25
| ~ spl21_43 ),
inference(resolution,[],[f421,f340]) ).
fof(f421,plain,
( ! [X0] :
( ~ l3_vectsp_1(X0)
| l1_rlvect_1(X0) )
| ~ spl21_43 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f687,plain,
( spl21_89
| ~ spl21_24
| ~ spl21_42 ),
inference(avatar_split_clause,[],[f446,f416,f333,f684]) ).
fof(f684,plain,
( spl21_89
<=> l1_struct_0(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_89])]) ).
fof(f333,plain,
( spl21_24
<=> l1_group_1(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_24])]) ).
fof(f416,plain,
( spl21_42
<=> ! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_42])]) ).
fof(f446,plain,
( l1_struct_0(sK13)
| ~ spl21_24
| ~ spl21_42 ),
inference(resolution,[],[f417,f335]) ).
fof(f335,plain,
( l1_group_1(sK13)
| ~ spl21_24 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f417,plain,
( ! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) )
| ~ spl21_42 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f682,plain,
( spl21_88
| ~ spl21_22
| ~ spl21_41 ),
inference(avatar_split_clause,[],[f445,f412,f323,f679]) ).
fof(f679,plain,
( spl21_88
<=> l2_struct_0(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_88])]) ).
fof(f323,plain,
( spl21_22
<=> l2_vectsp_1(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_22])]) ).
fof(f412,plain,
( spl21_41
<=> ! [X0] :
( l2_struct_0(X0)
| ~ l2_vectsp_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_41])]) ).
fof(f445,plain,
( l2_struct_0(sK11)
| ~ spl21_22
| ~ spl21_41 ),
inference(resolution,[],[f413,f325]) ).
fof(f325,plain,
( l2_vectsp_1(sK11)
| ~ spl21_22 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f413,plain,
( ! [X0] :
( ~ l2_vectsp_1(X0)
| l2_struct_0(X0) )
| ~ spl21_41 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f677,plain,
( spl21_87
| ~ spl21_22
| ~ spl21_40 ),
inference(avatar_split_clause,[],[f444,f408,f323,f674]) ).
fof(f674,plain,
( spl21_87
<=> l1_vectsp_1(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_87])]) ).
fof(f408,plain,
( spl21_40
<=> ! [X0] :
( l1_vectsp_1(X0)
| ~ l2_vectsp_1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_40])]) ).
fof(f444,plain,
( l1_vectsp_1(sK11)
| ~ spl21_22
| ~ spl21_40 ),
inference(resolution,[],[f409,f325]) ).
fof(f409,plain,
( ! [X0] :
( ~ l2_vectsp_1(X0)
| l1_vectsp_1(X0) )
| ~ spl21_40 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f668,plain,
( spl21_85
| spl21_86
| ~ spl21_18
| ~ spl21_70 ),
inference(avatar_split_clause,[],[f565,f560,f303,f665,f661]) ).
fof(f661,plain,
( spl21_85
<=> r2_hidden(sK2,u1_struct_0(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_85])]) ).
fof(f665,plain,
( spl21_86
<=> v1_xboole_0(u1_struct_0(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_86])]) ).
fof(f565,plain,
( v1_xboole_0(u1_struct_0(sK1))
| r2_hidden(sK2,u1_struct_0(sK1))
| ~ spl21_18
| ~ spl21_70 ),
inference(resolution,[],[f561,f305]) ).
fof(f659,plain,
( ~ spl21_83
| spl21_84
| ~ spl21_17
| ~ spl21_63 ),
inference(avatar_split_clause,[],[f546,f518,f298,f656,f652]) ).
fof(f546,plain,
( l1_rlvect_1(sK1)
| ~ l1_struct_0(sK0)
| ~ spl21_17
| ~ spl21_63 ),
inference(resolution,[],[f519,f300]) ).
fof(f300,plain,
( l1_vectsp_2(sK1,sK0)
| ~ spl21_17 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f649,plain,
spl21_82,
inference(avatar_split_clause,[],[f216,f647]) ).
fof(f216,plain,
! [X3,X0,X1] :
( k1_rlvect_1(X0) = k2_group_1(X0)
| ~ v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X3),X0,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(equality_resolution,[],[f177]) ).
fof(f177,plain,
! [X2,X3,X0,X1] :
( k1_rlvect_1(X1) != X2
| k1_rlvect_1(X0) = k2_group_1(X0)
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( k1_rlvect_1(X1) != X3
& k1_rlvect_1(X1) != X2 )
| k1_rlvect_1(X0) = k2_group_1(X0)
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1)) )
| ~ m1_subset_1(X2,u1_struct_0(X1)) )
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1) )
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( k1_rlvect_1(X1) != X3
& k1_rlvect_1(X1) != X2 )
| k1_rlvect_1(X0) = k2_group_1(X0)
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1)) )
| ~ m1_subset_1(X2,u1_struct_0(X1)) )
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1) )
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0] :
( ( l3_vectsp_1(X0)
& v8_vectsp_1(X0)
& v7_vectsp_1(X0)
& v6_vectsp_1(X0)
& v4_group_1(X0)
& v6_rlvect_1(X0)
& v5_rlvect_1(X0)
& v4_rlvect_1(X0)
& v3_rlvect_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l1_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
=> ( ( k1_rlvect_1(X1) != X3
& k1_rlvect_1(X1) != X2 )
| k1_rlvect_1(X0) = k2_group_1(X0) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_rmod_5) ).
fof(f645,plain,
spl21_81,
inference(avatar_split_clause,[],[f215,f643]) ).
fof(f215,plain,
! [X2,X0,X1] :
( k1_rlvect_1(X0) = k2_group_1(X0)
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1)
| ~ m1_subset_1(k1_rlvect_1(X1),u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(equality_resolution,[],[f178]) ).
fof(f178,plain,
! [X2,X3,X0,X1] :
( k1_rlvect_1(X1) != X3
| k1_rlvect_1(X0) = k2_group_1(X0)
| ~ v1_rmod_5(k8_rlvect_2(X1,X2,X3),X0,X1)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f641,plain,
( spl21_80
| ~ spl21_40
| ~ spl21_60 ),
inference(avatar_split_clause,[],[f554,f505,f408,f638]) ).
fof(f505,plain,
( spl21_60
<=> l2_vectsp_1(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_60])]) ).
fof(f554,plain,
( l1_vectsp_1(sK0)
| ~ spl21_40
| ~ spl21_60 ),
inference(resolution,[],[f507,f409]) ).
fof(f507,plain,
( l2_vectsp_1(sK0)
| ~ spl21_60 ),
inference(avatar_component_clause,[],[f505]) ).
fof(f631,plain,
spl21_79,
inference(avatar_split_clause,[],[f198,f629]) ).
fof(f198,plain,
! [X2,X0,X1] :
( k8_rlvect_2(X0,X1,X2) = k8_rlvect_2(X0,X2,X1)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2] :
( k8_rlvect_2(X0,X1,X2) = k8_rlvect_2(X0,X2,X1)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2] :
( k8_rlvect_2(X0,X1,X2) = k8_rlvect_2(X0,X2,X1)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X0))
& m1_subset_1(X1,u1_struct_0(X0))
& l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> k8_rlvect_2(X0,X1,X2) = k8_rlvect_2(X0,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k8_rlvect_2) ).
fof(f619,plain,
spl21_78,
inference(avatar_split_clause,[],[f199,f617]) ).
fof(f617,plain,
( spl21_78
<=> ! [X2,X0,X1] :
( m1_subset_1(k8_rlvect_2(X0,X1,X2),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_78])]) ).
fof(f199,plain,
! [X2,X0,X1] :
( m1_subset_1(k8_rlvect_2(X0,X1,X2),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2] :
( m1_subset_1(k8_rlvect_2(X0,X1,X2),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2] :
( m1_subset_1(k8_rlvect_2(X0,X1,X2),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X0))
& m1_subset_1(X1,u1_struct_0(X0))
& l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> m1_subset_1(k8_rlvect_2(X0,X1,X2),k1_zfmisc_1(u1_struct_0(X0))) ),
inference(pure_predicate_removal,[],[f49]) ).
fof(f49,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X0))
& m1_subset_1(X1,u1_struct_0(X0))
& l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> ( m1_subset_1(k8_rlvect_2(X0,X1,X2),k1_zfmisc_1(u1_struct_0(X0)))
& v1_finset_1(k8_rlvect_2(X0,X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_rlvect_2) ).
fof(f615,plain,
spl21_77,
inference(avatar_split_clause,[],[f197,f613]) ).
fof(f197,plain,
! [X2,X0,X1] :
( k8_rlvect_2(X0,X1,X2) = k2_tarski(X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( k8_rlvect_2(X0,X1,X2) = k2_tarski(X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2] :
( k8_rlvect_2(X0,X1,X2) = k2_tarski(X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X2,u1_struct_0(X0))
& m1_subset_1(X1,u1_struct_0(X0))
& l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> k8_rlvect_2(X0,X1,X2) = k2_tarski(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_rlvect_2) ).
fof(f600,plain,
spl21_76,
inference(avatar_split_clause,[],[f200,f598]) ).
fof(f200,plain,
! [X2,X0,X1] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(flattening,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X1,k1_zfmisc_1(X2))
& r2_hidden(X0,X1) )
=> m1_subset_1(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f596,plain,
( spl21_75
| ~ spl21_45
| ~ spl21_54 ),
inference(avatar_split_clause,[],[f533,f476,f428,f593]) ).
fof(f476,plain,
( spl21_54
<=> l1_rlvect_1(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_54])]) ).
fof(f533,plain,
( l2_struct_0(sK0)
| ~ spl21_45
| ~ spl21_54 ),
inference(resolution,[],[f478,f429]) ).
fof(f478,plain,
( l1_rlvect_1(sK0)
| ~ spl21_54 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f591,plain,
spl21_74,
inference(avatar_split_clause,[],[f183,f589]) ).
fof(f183,plain,
! [X0] :
( m1_subset_1(sK7(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ( ~ v1_xboole_0(sK7(X0))
& m1_subset_1(sK7(X0),k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f82,f111]) ).
fof(f111,plain,
! [X0] :
( ? [X1] :
( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
=> ( ~ v1_xboole_0(sK7(X0))
& m1_subset_1(sK7(X0),k1_zfmisc_1(u1_struct_0(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X0] :
( ? [X1] :
( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ? [X1] :
( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ( l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> ? [X1] :
( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
inference(pure_predicate_removal,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ( l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> ? [X1] :
( v1_finset_1(X1)
& ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_rlvect_2) ).
fof(f587,plain,
spl21_73,
inference(avatar_split_clause,[],[f181,f585]) ).
fof(f181,plain,
! [X0] :
( m1_subset_1(sK6(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( ( ~ v1_xboole_0(sK6(X0))
& m1_subset_1(sK6(X0),k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f80,f109]) ).
fof(f109,plain,
! [X0] :
( ? [X1] :
( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
=> ( ~ v1_xboole_0(sK6(X0))
& m1_subset_1(sK6(X0),k1_zfmisc_1(u1_struct_0(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0] :
( ? [X1] :
( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ? [X1] :
( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( ( l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> ? [X1] :
( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
fof(f577,plain,
spl21_72,
inference(avatar_split_clause,[],[f201,f575]) ).
fof(f201,plain,
! [X2,X0,X1] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] :
~ ( v1_xboole_0(X2)
& m1_subset_1(X1,k1_zfmisc_1(X2))
& r2_hidden(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f573,plain,
spl21_71,
inference(avatar_split_clause,[],[f179,f571]) ).
fof(f179,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f75]) ).
fof(f75,plain,
! [X0] :
( m1_subset_1(k2_group_1(X0),u1_struct_0(X0))
| ~ l1_group_1(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0] :
( ( l1_group_1(X0)
& ~ v3_struct_0(X0) )
=> m1_subset_1(k2_group_1(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_group_1) ).
fof(f562,plain,
spl21_70,
inference(avatar_split_clause,[],[f193,f560]) ).
fof(f193,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(flattening,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( m1_subset_1(X0,X1)
=> ( r2_hidden(X0,X1)
| v1_xboole_0(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f545,plain,
spl21_69,
inference(avatar_split_clause,[],[f195,f543]) ).
fof(f195,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| X0 = X1
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| X0 = X1
| ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
~ ( v1_xboole_0(X1)
& X0 != X1
& v1_xboole_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f541,plain,
spl21_68,
inference(avatar_split_clause,[],[f194,f539]) ).
fof(f194,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
=> m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(unused_predicate_definition_removal,[],[f41]) ).
fof(f41,axiom,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
<=> r1_tarski(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f537,plain,
spl21_67,
inference(avatar_split_clause,[],[f190,f535]) ).
fof(f535,plain,
( spl21_67
<=> ! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_67])]) ).
fof(f190,plain,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] : k2_tarski(X0,X1) = k2_tarski(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f532,plain,
spl21_66,
inference(avatar_split_clause,[],[f184,f530]) ).
fof(f530,plain,
( spl21_66
<=> ! [X0] :
( ~ v1_xboole_0(sK7(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_66])]) ).
fof(f184,plain,
! [X0] :
( ~ v1_xboole_0(sK7(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f528,plain,
spl21_65,
inference(avatar_split_clause,[],[f182,f526]) ).
fof(f526,plain,
( spl21_65
<=> ! [X0] :
( ~ v1_xboole_0(sK6(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_65])]) ).
fof(f182,plain,
! [X0] :
( ~ v1_xboole_0(sK6(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f524,plain,
spl21_64,
inference(avatar_split_clause,[],[f180,f522]) ).
fof(f522,plain,
( spl21_64
<=> ! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_64])]) ).
fof(f180,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ~ v1_xboole_0(u1_struct_0(X0))
| ~ l1_struct_0(X0)
| v3_struct_0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( ( l1_struct_0(X0)
& ~ v3_struct_0(X0) )
=> ~ v1_xboole_0(u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f520,plain,
spl21_63,
inference(avatar_split_clause,[],[f172,f518]) ).
fof(f172,plain,
! [X0,X1] :
( l1_rlvect_1(X1)
| ~ l1_vectsp_2(X1,X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( l1_rlvect_1(X1)
| ~ l1_vectsp_2(X1,X0) )
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] :
( l1_struct_0(X0)
=> ! [X1] :
( l1_vectsp_2(X1,X0)
=> l1_rlvect_1(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_vectsp_2) ).
fof(f516,plain,
spl21_62,
inference(avatar_split_clause,[],[f171,f514]) ).
fof(f171,plain,
! [X0] :
( m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ l2_struct_0(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0))
| ~ l2_struct_0(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0] :
( l2_struct_0(X0)
=> m1_subset_1(k1_rlvect_1(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_rlvect_1) ).
fof(f512,plain,
spl21_61,
inference(avatar_split_clause,[],[f161,f510]) ).
fof(f161,plain,
! [X0] :
( m1_subset_1(sK3(X0),k1_zfmisc_1(X0))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] :
( ( ~ v1_xboole_0(sK3(X0))
& m1_subset_1(sK3(X0),k1_zfmisc_1(X0)) )
| v1_xboole_0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f61,f103]) ).
fof(f103,plain,
! [X0] :
( ? [X1] :
( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(X0)) )
=> ( ~ v1_xboole_0(sK3(X0))
& m1_subset_1(sK3(X0),k1_zfmisc_1(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
! [X0] :
( ? [X1] :
( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(X0)) )
| v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ~ v1_xboole_0(X0)
=> ? [X1] :
( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f508,plain,
( spl21_60
| ~ spl21_10
| ~ spl21_44 ),
inference(avatar_split_clause,[],[f454,f424,f263,f505]) ).
fof(f454,plain,
( l2_vectsp_1(sK0)
| ~ spl21_10
| ~ spl21_44 ),
inference(resolution,[],[f425,f265]) ).
fof(f265,plain,
( l3_vectsp_1(sK0)
| ~ spl21_10 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f503,plain,
spl21_59,
inference(avatar_split_clause,[],[f192,f501]) ).
fof(f501,plain,
( spl21_59
<=> ! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_59])]) ).
fof(f192,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f499,plain,
spl21_58,
inference(avatar_split_clause,[],[f191,f497]) ).
fof(f497,plain,
( spl21_58
<=> ! [X0,X1] :
( ~ r2_hidden(X1,X0)
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_58])]) ).
fof(f191,plain,
! [X0,X1] :
( ~ r2_hidden(X1,X0)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( ~ r2_hidden(X1,X0)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> ~ r2_hidden(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f495,plain,
spl21_57,
inference(avatar_split_clause,[],[f174,f493]) ).
fof(f174,plain,
! [X0] :
( l1_vectsp_2(sK5(X0),X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( ( ~ v3_struct_0(sK5(X0))
& l1_vectsp_2(sK5(X0),X0) )
| ~ l1_struct_0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f71,f107]) ).
fof(f107,plain,
! [X0] :
( ? [X1] :
( ~ v3_struct_0(X1)
& l1_vectsp_2(X1,X0) )
=> ( ~ v3_struct_0(sK5(X0))
& l1_vectsp_2(sK5(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X0] :
( ? [X1] :
( ~ v3_struct_0(X1)
& l1_vectsp_2(X1,X0) )
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( l1_struct_0(X0)
=> ? [X1] :
( ~ v3_struct_0(X1)
& l1_vectsp_2(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc9_vectsp_2) ).
fof(f491,plain,
spl21_56,
inference(avatar_split_clause,[],[f173,f489]) ).
fof(f173,plain,
! [X0] :
( l1_vectsp_2(sK4(X0),X0)
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0] :
( l1_vectsp_2(sK4(X0),X0)
| ~ l1_struct_0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f70,f105]) ).
fof(f105,plain,
! [X0] :
( ? [X1] : l1_vectsp_2(X1,X0)
=> l1_vectsp_2(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X0] :
( ? [X1] : l1_vectsp_2(X1,X0)
| ~ l1_struct_0(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] :
( l1_struct_0(X0)
=> ? [X1] : l1_vectsp_2(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_vectsp_2) ).
fof(f483,plain,
spl21_55,
inference(avatar_split_clause,[],[f196,f481]) ).
fof(f481,plain,
( spl21_55
<=> ! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_55])]) ).
fof(f196,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] :
~ ( v1_xboole_0(X1)
& r2_hidden(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f479,plain,
( spl21_54
| ~ spl21_10
| ~ spl21_43 ),
inference(avatar_split_clause,[],[f452,f420,f263,f476]) ).
fof(f452,plain,
( l1_rlvect_1(sK0)
| ~ spl21_10
| ~ spl21_43 ),
inference(resolution,[],[f421,f265]) ).
fof(f474,plain,
spl21_53,
inference(avatar_split_clause,[],[f186,f472]) ).
fof(f186,plain,
! [X0] : m1_subset_1(sK9(X0),k1_zfmisc_1(X0)),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0] :
( v1_xboole_0(sK9(X0))
& m1_subset_1(sK9(X0),k1_zfmisc_1(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f15,f115]) ).
fof(f115,plain,
! [X0] :
( ? [X1] :
( v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(X0)) )
=> ( v1_xboole_0(sK9(X0))
& m1_subset_1(sK9(X0),k1_zfmisc_1(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f15,axiom,
! [X0] :
? [X1] :
( v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f470,plain,
spl21_52,
inference(avatar_split_clause,[],[f176,f468]) ).
fof(f176,plain,
! [X0] :
( k1_xboole_0 = X0
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( k1_xboole_0 = X0
| ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( v1_xboole_0(X0)
=> k1_xboole_0 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f466,plain,
spl21_51,
inference(avatar_split_clause,[],[f175,f464]) ).
fof(f464,plain,
( spl21_51
<=> ! [X0] :
( ~ v3_struct_0(sK5(X0))
| ~ l1_struct_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_51])]) ).
fof(f175,plain,
! [X0] :
( ~ v3_struct_0(sK5(X0))
| ~ l1_struct_0(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f462,plain,
spl21_50,
inference(avatar_split_clause,[],[f162,f460]) ).
fof(f460,plain,
( spl21_50
<=> ! [X0] :
( ~ v1_xboole_0(sK3(X0))
| v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_50])]) ).
fof(f162,plain,
! [X0] :
( ~ v1_xboole_0(sK3(X0))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f451,plain,
( spl21_49
| ~ spl21_23
| ~ spl21_39 ),
inference(avatar_split_clause,[],[f443,f404,f328,f448]) ).
fof(f448,plain,
( spl21_49
<=> l1_group_1(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_49])]) ).
fof(f328,plain,
( spl21_23
<=> l1_vectsp_1(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_23])]) ).
fof(f443,plain,
( l1_group_1(sK12)
| ~ spl21_23
| ~ spl21_39 ),
inference(resolution,[],[f405,f330]) ).
fof(f330,plain,
( l1_vectsp_1(sK12)
| ~ spl21_23 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f442,plain,
spl21_48,
inference(avatar_split_clause,[],[f189,f440]) ).
fof(f440,plain,
( spl21_48
<=> ! [X0,X1] : ~ v1_xboole_0(k2_tarski(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_48])]) ).
fof(f189,plain,
! [X0,X1] : ~ v1_xboole_0(k2_tarski(X0,X1)),
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] : ~ v1_xboole_0(k2_tarski(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f438,plain,
spl21_47,
inference(avatar_split_clause,[],[f185,f436]) ).
fof(f185,plain,
! [X0] : m1_subset_1(sK8(X0),X0),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0] : m1_subset_1(sK8(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f45,f113]) ).
fof(f113,plain,
! [X0] :
( ? [X1] : m1_subset_1(X1,X0)
=> m1_subset_1(sK8(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f45,axiom,
! [X0] :
? [X1] : m1_subset_1(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f434,plain,
spl21_46,
inference(avatar_split_clause,[],[f170,f432]) ).
fof(f170,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l2_struct_0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l2_struct_0(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( l2_struct_0(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_struct_0) ).
fof(f430,plain,
spl21_45,
inference(avatar_split_clause,[],[f169,f428]) ).
fof(f169,plain,
! [X0] :
( l2_struct_0(X0)
| ~ l1_rlvect_1(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( l2_struct_0(X0)
| ~ l1_rlvect_1(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( l1_rlvect_1(X0)
=> l2_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_rlvect_1) ).
fof(f426,plain,
spl21_44,
inference(avatar_split_clause,[],[f168,f424]) ).
fof(f168,plain,
! [X0] :
( l2_vectsp_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ( l2_vectsp_1(X0)
& l1_rlvect_1(X0) )
| ~ l3_vectsp_1(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( l3_vectsp_1(X0)
=> ( l2_vectsp_1(X0)
& l1_rlvect_1(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_vectsp_1) ).
fof(f422,plain,
spl21_43,
inference(avatar_split_clause,[],[f167,f420]) ).
fof(f167,plain,
! [X0] :
( l1_rlvect_1(X0)
| ~ l3_vectsp_1(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f418,plain,
spl21_42,
inference(avatar_split_clause,[],[f166,f416]) ).
fof(f166,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( l1_struct_0(X0)
| ~ l1_group_1(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( l1_group_1(X0)
=> l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_group_1) ).
fof(f414,plain,
spl21_41,
inference(avatar_split_clause,[],[f165,f412]) ).
fof(f165,plain,
! [X0] :
( l2_struct_0(X0)
| ~ l2_vectsp_1(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ( l2_struct_0(X0)
& l1_vectsp_1(X0) )
| ~ l2_vectsp_1(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( l2_vectsp_1(X0)
=> ( l2_struct_0(X0)
& l1_vectsp_1(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_vectsp_1) ).
fof(f410,plain,
spl21_40,
inference(avatar_split_clause,[],[f164,f408]) ).
fof(f164,plain,
! [X0] :
( l1_vectsp_1(X0)
| ~ l2_vectsp_1(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f406,plain,
spl21_39,
inference(avatar_split_clause,[],[f163,f404]) ).
fof(f163,plain,
! [X0] :
( l1_group_1(X0)
| ~ l1_vectsp_1(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( l1_group_1(X0)
| ~ l1_vectsp_1(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( l1_vectsp_1(X0)
=> l1_group_1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_vectsp_1) ).
fof(f402,plain,
( spl21_37
| spl21_38 ),
inference(avatar_split_clause,[],[f158,f399,f395]) ).
fof(f158,plain,
( v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),sK2),sK0,sK1)
| v1_rmod_5(k8_rlvect_2(sK1,sK2,k1_rlvect_1(sK1)),sK0,sK1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
( ( v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),sK2),sK0,sK1)
| v1_rmod_5(k8_rlvect_2(sK1,sK2,k1_rlvect_1(sK1)),sK0,sK1) )
& k1_rlvect_1(sK0) != k2_group_1(sK0)
& m1_subset_1(sK2,u1_struct_0(sK1))
& l1_vectsp_2(sK1,sK0)
& v5_vectsp_2(sK1,sK0)
& v6_rlvect_1(sK1)
& v5_rlvect_1(sK1)
& v4_rlvect_1(sK1)
& v3_rlvect_1(sK1)
& ~ v3_struct_0(sK1)
& l3_vectsp_1(sK0)
& v8_vectsp_1(sK0)
& v7_vectsp_1(sK0)
& v6_vectsp_1(sK0)
& v4_group_1(sK0)
& v6_rlvect_1(sK0)
& v5_rlvect_1(sK0)
& v4_rlvect_1(sK0)
& v3_rlvect_1(sK0)
& ~ v3_struct_0(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f60,f101,f100,f99]) ).
fof(f99,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ( v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X2),X0,X1)
| v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1) )
& k1_rlvect_1(X0) != k2_group_1(X0)
& m1_subset_1(X2,u1_struct_0(X1)) )
& l1_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
& l3_vectsp_1(X0)
& v8_vectsp_1(X0)
& v7_vectsp_1(X0)
& v6_vectsp_1(X0)
& v4_group_1(X0)
& v6_rlvect_1(X0)
& v5_rlvect_1(X0)
& v4_rlvect_1(X0)
& v3_rlvect_1(X0)
& ~ v3_struct_0(X0) )
=> ( ? [X1] :
( ? [X2] :
( ( v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X2),sK0,X1)
| v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),sK0,X1) )
& k1_rlvect_1(sK0) != k2_group_1(sK0)
& m1_subset_1(X2,u1_struct_0(X1)) )
& l1_vectsp_2(X1,sK0)
& v5_vectsp_2(X1,sK0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
& l3_vectsp_1(sK0)
& v8_vectsp_1(sK0)
& v7_vectsp_1(sK0)
& v6_vectsp_1(sK0)
& v4_group_1(sK0)
& v6_rlvect_1(sK0)
& v5_rlvect_1(sK0)
& v4_rlvect_1(sK0)
& v3_rlvect_1(sK0)
& ~ v3_struct_0(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
( ? [X1] :
( ? [X2] :
( ( v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X2),sK0,X1)
| v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),sK0,X1) )
& k1_rlvect_1(sK0) != k2_group_1(sK0)
& m1_subset_1(X2,u1_struct_0(X1)) )
& l1_vectsp_2(X1,sK0)
& v5_vectsp_2(X1,sK0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
=> ( ? [X2] :
( ( v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),X2),sK0,sK1)
| v1_rmod_5(k8_rlvect_2(sK1,X2,k1_rlvect_1(sK1)),sK0,sK1) )
& k1_rlvect_1(sK0) != k2_group_1(sK0)
& m1_subset_1(X2,u1_struct_0(sK1)) )
& l1_vectsp_2(sK1,sK0)
& v5_vectsp_2(sK1,sK0)
& v6_rlvect_1(sK1)
& v5_rlvect_1(sK1)
& v4_rlvect_1(sK1)
& v3_rlvect_1(sK1)
& ~ v3_struct_0(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
( ? [X2] :
( ( v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),X2),sK0,sK1)
| v1_rmod_5(k8_rlvect_2(sK1,X2,k1_rlvect_1(sK1)),sK0,sK1) )
& k1_rlvect_1(sK0) != k2_group_1(sK0)
& m1_subset_1(X2,u1_struct_0(sK1)) )
=> ( ( v1_rmod_5(k8_rlvect_2(sK1,k1_rlvect_1(sK1),sK2),sK0,sK1)
| v1_rmod_5(k8_rlvect_2(sK1,sK2,k1_rlvect_1(sK1)),sK0,sK1) )
& k1_rlvect_1(sK0) != k2_group_1(sK0)
& m1_subset_1(sK2,u1_struct_0(sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X2),X0,X1)
| v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1) )
& k1_rlvect_1(X0) != k2_group_1(X0)
& m1_subset_1(X2,u1_struct_0(X1)) )
& l1_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
& l3_vectsp_1(X0)
& v8_vectsp_1(X0)
& v7_vectsp_1(X0)
& v6_vectsp_1(X0)
& v4_group_1(X0)
& v6_rlvect_1(X0)
& v5_rlvect_1(X0)
& v4_rlvect_1(X0)
& v3_rlvect_1(X0)
& ~ v3_struct_0(X0) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X2),X0,X1)
| v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1) )
& k1_rlvect_1(X0) != k2_group_1(X0)
& m1_subset_1(X2,u1_struct_0(X1)) )
& l1_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
& l3_vectsp_1(X0)
& v8_vectsp_1(X0)
& v7_vectsp_1(X0)
& v6_vectsp_1(X0)
& v4_group_1(X0)
& v6_rlvect_1(X0)
& v5_rlvect_1(X0)
& v4_rlvect_1(X0)
& v3_rlvect_1(X0)
& ~ v3_struct_0(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( l3_vectsp_1(X0)
& v8_vectsp_1(X0)
& v7_vectsp_1(X0)
& v6_vectsp_1(X0)
& v4_group_1(X0)
& v6_rlvect_1(X0)
& v5_rlvect_1(X0)
& v4_rlvect_1(X0)
& v3_rlvect_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l1_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( k1_rlvect_1(X0) != k2_group_1(X0)
=> ( ~ v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X2),X0,X1)
& ~ v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1) ) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0] :
( ( l3_vectsp_1(X0)
& v8_vectsp_1(X0)
& v7_vectsp_1(X0)
& v6_vectsp_1(X0)
& v4_group_1(X0)
& v6_rlvect_1(X0)
& v5_rlvect_1(X0)
& v4_rlvect_1(X0)
& v3_rlvect_1(X0)
& ~ v3_struct_0(X0) )
=> ! [X1] :
( ( l1_vectsp_2(X1,X0)
& v5_vectsp_2(X1,X0)
& v6_rlvect_1(X1)
& v5_rlvect_1(X1)
& v4_rlvect_1(X1)
& v3_rlvect_1(X1)
& ~ v3_struct_0(X1) )
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ( k1_rlvect_1(X0) != k2_group_1(X0)
=> ( ~ v1_rmod_5(k8_rlvect_2(X1,k1_rlvect_1(X1),X2),X0,X1)
& ~ v1_rmod_5(k8_rlvect_2(X1,X2,k1_rlvect_1(X1)),X0,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_rmod_5) ).
fof(f393,plain,
spl21_36,
inference(avatar_split_clause,[],[f188,f391]) ).
fof(f391,plain,
( spl21_36
<=> ! [X0] : r1_tarski(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_36])]) ).
fof(f188,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f389,plain,
spl21_35,
inference(avatar_split_clause,[],[f187,f387]) ).
fof(f187,plain,
! [X0] : v1_xboole_0(sK9(X0)),
inference(cnf_transformation,[],[f116]) ).
fof(f385,plain,
spl21_34,
inference(avatar_split_clause,[],[f160,f383]) ).
fof(f383,plain,
( spl21_34
<=> ! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_34])]) ).
fof(f160,plain,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f381,plain,
~ spl21_33,
inference(avatar_split_clause,[],[f214,f378]) ).
fof(f378,plain,
( spl21_33
<=> v3_struct_0(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_33])]) ).
fof(f214,plain,
~ v3_struct_0(sK20),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
( ~ v3_struct_0(sK20)
& l1_struct_0(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f38,f137]) ).
fof(f137,plain,
( ? [X0] :
( ~ v3_struct_0(X0)
& l1_struct_0(X0) )
=> ( ~ v3_struct_0(sK20)
& l1_struct_0(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f38,axiom,
? [X0] :
( ~ v3_struct_0(X0)
& l1_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
fof(f376,plain,
spl21_32,
inference(avatar_split_clause,[],[f213,f373]) ).
fof(f373,plain,
( spl21_32
<=> l1_struct_0(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_32])]) ).
fof(f213,plain,
l1_struct_0(sK20),
inference(cnf_transformation,[],[f138]) ).
fof(f371,plain,
~ spl21_31,
inference(avatar_split_clause,[],[f212,f368]) ).
fof(f368,plain,
( spl21_31
<=> v3_struct_0(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_31])]) ).
fof(f212,plain,
~ v3_struct_0(sK19),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
( ~ v3_struct_0(sK19)
& l2_struct_0(sK19) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f39,f135]) ).
fof(f135,plain,
( ? [X0] :
( ~ v3_struct_0(X0)
& l2_struct_0(X0) )
=> ( ~ v3_struct_0(sK19)
& l2_struct_0(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f39,axiom,
? [X0] :
( ~ v3_struct_0(X0)
& l2_struct_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_struct_0) ).
fof(f366,plain,
spl21_30,
inference(avatar_split_clause,[],[f211,f363]) ).
fof(f211,plain,
l2_struct_0(sK19),
inference(cnf_transformation,[],[f136]) ).
fof(f361,plain,
spl21_29,
inference(avatar_split_clause,[],[f210,f358]) ).
fof(f210,plain,
v1_xboole_0(sK18),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
v1_xboole_0(sK18),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f13,f133]) ).
fof(f133,plain,
( ? [X0] : v1_xboole_0(X0)
=> v1_xboole_0(sK18) ),
introduced(choice_axiom,[]) ).
fof(f13,axiom,
? [X0] : v1_xboole_0(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f356,plain,
spl21_28,
inference(avatar_split_clause,[],[f209,f353]) ).
fof(f353,plain,
( spl21_28
<=> l1_struct_0(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_28])]) ).
fof(f209,plain,
l1_struct_0(sK17),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
l1_struct_0(sK17),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f25,f131]) ).
fof(f131,plain,
( ? [X0] : l1_struct_0(X0)
=> l1_struct_0(sK17) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
? [X0] : l1_struct_0(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
fof(f351,plain,
spl21_27,
inference(avatar_split_clause,[],[f208,f348]) ).
fof(f208,plain,
l2_struct_0(sK16),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
l2_struct_0(sK16),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f26,f129]) ).
fof(f129,plain,
( ? [X0] : l2_struct_0(X0)
=> l2_struct_0(sK16) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] : l2_struct_0(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_struct_0) ).
fof(f346,plain,
spl21_26,
inference(avatar_split_clause,[],[f207,f343]) ).
fof(f207,plain,
l1_rlvect_1(sK15),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
l1_rlvect_1(sK15),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f24,f127]) ).
fof(f127,plain,
( ? [X0] : l1_rlvect_1(X0)
=> l1_rlvect_1(sK15) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
? [X0] : l1_rlvect_1(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_rlvect_1) ).
fof(f341,plain,
spl21_25,
inference(avatar_split_clause,[],[f206,f338]) ).
fof(f206,plain,
l3_vectsp_1(sK14),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
l3_vectsp_1(sK14),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f44,f125]) ).
fof(f125,plain,
( ? [X0] : l3_vectsp_1(X0)
=> l3_vectsp_1(sK14) ),
introduced(choice_axiom,[]) ).
fof(f44,axiom,
? [X0] : l3_vectsp_1(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l3_vectsp_1) ).
fof(f336,plain,
spl21_24,
inference(avatar_split_clause,[],[f205,f333]) ).
fof(f205,plain,
l1_group_1(sK13),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
l1_group_1(sK13),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f23,f123]) ).
fof(f123,plain,
( ? [X0] : l1_group_1(X0)
=> l1_group_1(sK13) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
? [X0] : l1_group_1(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_group_1) ).
fof(f331,plain,
spl21_23,
inference(avatar_split_clause,[],[f204,f328]) ).
fof(f204,plain,
l1_vectsp_1(sK12),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
l1_vectsp_1(sK12),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f10,f121]) ).
fof(f121,plain,
( ? [X0] : l1_vectsp_1(X0)
=> l1_vectsp_1(sK12) ),
introduced(choice_axiom,[]) ).
fof(f10,axiom,
? [X0] : l1_vectsp_1(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_vectsp_1) ).
fof(f326,plain,
spl21_22,
inference(avatar_split_clause,[],[f203,f323]) ).
fof(f203,plain,
l2_vectsp_1(sK11),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
l2_vectsp_1(sK11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f27,f119]) ).
fof(f119,plain,
( ? [X0] : l2_vectsp_1(X0)
=> l2_vectsp_1(sK11) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] : l2_vectsp_1(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_vectsp_1) ).
fof(f321,plain,
~ spl21_21,
inference(avatar_split_clause,[],[f202,f318]) ).
fof(f318,plain,
( spl21_21
<=> v1_xboole_0(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl21_21])]) ).
fof(f202,plain,
~ v1_xboole_0(sK10),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
~ v1_xboole_0(sK10),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f16,f117]) ).
fof(f117,plain,
( ? [X0] : ~ v1_xboole_0(X0)
=> ~ v1_xboole_0(sK10) ),
introduced(choice_axiom,[]) ).
fof(f16,axiom,
? [X0] : ~ v1_xboole_0(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f316,plain,
spl21_20,
inference(avatar_split_clause,[],[f159,f313]) ).
fof(f159,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f311,plain,
~ spl21_19,
inference(avatar_split_clause,[],[f157,f308]) ).
fof(f157,plain,
k1_rlvect_1(sK0) != k2_group_1(sK0),
inference(cnf_transformation,[],[f102]) ).
fof(f306,plain,
spl21_18,
inference(avatar_split_clause,[],[f156,f303]) ).
fof(f156,plain,
m1_subset_1(sK2,u1_struct_0(sK1)),
inference(cnf_transformation,[],[f102]) ).
fof(f301,plain,
spl21_17,
inference(avatar_split_clause,[],[f155,f298]) ).
fof(f155,plain,
l1_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f102]) ).
fof(f296,plain,
spl21_16,
inference(avatar_split_clause,[],[f154,f293]) ).
fof(f154,plain,
v5_vectsp_2(sK1,sK0),
inference(cnf_transformation,[],[f102]) ).
fof(f291,plain,
spl21_15,
inference(avatar_split_clause,[],[f153,f288]) ).
fof(f153,plain,
v6_rlvect_1(sK1),
inference(cnf_transformation,[],[f102]) ).
fof(f286,plain,
spl21_14,
inference(avatar_split_clause,[],[f152,f283]) ).
fof(f152,plain,
v5_rlvect_1(sK1),
inference(cnf_transformation,[],[f102]) ).
fof(f281,plain,
spl21_13,
inference(avatar_split_clause,[],[f151,f278]) ).
fof(f151,plain,
v4_rlvect_1(sK1),
inference(cnf_transformation,[],[f102]) ).
fof(f276,plain,
spl21_12,
inference(avatar_split_clause,[],[f150,f273]) ).
fof(f150,plain,
v3_rlvect_1(sK1),
inference(cnf_transformation,[],[f102]) ).
fof(f271,plain,
~ spl21_11,
inference(avatar_split_clause,[],[f149,f268]) ).
fof(f149,plain,
~ v3_struct_0(sK1),
inference(cnf_transformation,[],[f102]) ).
fof(f266,plain,
spl21_10,
inference(avatar_split_clause,[],[f148,f263]) ).
fof(f148,plain,
l3_vectsp_1(sK0),
inference(cnf_transformation,[],[f102]) ).
fof(f261,plain,
spl21_9,
inference(avatar_split_clause,[],[f147,f258]) ).
fof(f147,plain,
v8_vectsp_1(sK0),
inference(cnf_transformation,[],[f102]) ).
fof(f256,plain,
spl21_8,
inference(avatar_split_clause,[],[f146,f253]) ).
fof(f146,plain,
v7_vectsp_1(sK0),
inference(cnf_transformation,[],[f102]) ).
fof(f251,plain,
spl21_7,
inference(avatar_split_clause,[],[f145,f248]) ).
fof(f145,plain,
v6_vectsp_1(sK0),
inference(cnf_transformation,[],[f102]) ).
fof(f246,plain,
spl21_6,
inference(avatar_split_clause,[],[f144,f243]) ).
fof(f144,plain,
v4_group_1(sK0),
inference(cnf_transformation,[],[f102]) ).
fof(f241,plain,
spl21_5,
inference(avatar_split_clause,[],[f143,f238]) ).
fof(f143,plain,
v6_rlvect_1(sK0),
inference(cnf_transformation,[],[f102]) ).
fof(f236,plain,
spl21_4,
inference(avatar_split_clause,[],[f142,f233]) ).
fof(f142,plain,
v5_rlvect_1(sK0),
inference(cnf_transformation,[],[f102]) ).
fof(f231,plain,
spl21_3,
inference(avatar_split_clause,[],[f141,f228]) ).
fof(f141,plain,
v4_rlvect_1(sK0),
inference(cnf_transformation,[],[f102]) ).
fof(f226,plain,
spl21_2,
inference(avatar_split_clause,[],[f140,f223]) ).
fof(f140,plain,
v3_rlvect_1(sK0),
inference(cnf_transformation,[],[f102]) ).
fof(f221,plain,
~ spl21_1,
inference(avatar_split_clause,[],[f139,f218]) ).
fof(f139,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ALG216+1 : TPTP v8.2.0. Released v3.4.0.
% 0.14/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.36 % Computer : n015.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat May 18 23:50:38 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.22/0.36 % (18500)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (18503)WARNING: value z3 for option sas not known
% 0.22/0.38 % (18501)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (18502)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (18504)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (18503)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)
% 0.22/0.38 % (18505)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)
% 0.22/0.38 % (18506)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)
% 0.22/0.38 % (18507)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)
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 TRYING [3]
% 0.22/0.40 % (18505)First to succeed.
% 0.22/0.40 TRYING [1]
% 0.22/0.40 % (18503)Also succeeded, but the first one will report.
% 0.22/0.40 TRYING [2]
% 0.22/0.40 % (18505)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18500"
% 0.22/0.40 % (18505)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.41 % (18505)------------------------------
% 0.22/0.41 % (18505)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.41 % (18505)Termination reason: Refutation
% 0.22/0.41
% 0.22/0.41 % (18505)Memory used [KB]: 1188
% 0.22/0.41 % (18505)Time elapsed: 0.022 s
% 0.22/0.41 % (18505)Instructions burned: 31 (million)
% 0.22/0.41 % (18500)Success in time 0.04 s
%------------------------------------------------------------------------------