TSTP Solution File: SEU413+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU413+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:34:18 EDT 2024
% Result : Theorem 0.11s 0.36s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 150
% Syntax : Number of formulae : 469 ( 83 unt; 0 def)
% Number of atoms : 1505 ( 69 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 1857 ( 821 ~; 781 |; 101 &)
% ( 114 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 122 ( 120 usr; 111 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-2 aty)
% Number of variables : 598 ( 562 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f780,plain,
$false,
inference(avatar_sat_refutation,[],[f140,f145,f150,f155,f160,f165,f170,f175,f180,f185,f190,f195,f200,f204,f208,f212,f216,f220,f224,f231,f235,f239,f243,f250,f254,f258,f262,f276,f280,f284,f288,f292,f296,f300,f313,f318,f322,f330,f334,f344,f349,f354,f358,f364,f368,f377,f392,f401,f409,f413,f420,f425,f436,f443,f448,f452,f464,f468,f472,f476,f480,f490,f498,f503,f508,f512,f518,f522,f530,f537,f541,f548,f555,f560,f564,f569,f574,f580,f585,f593,f607,f612,f625,f630,f634,f638,f642,f643,f652,f657,f661,f667,f676,f680,f684,f688,f700,f705,f710,f716,f728,f733,f738,f746,f753,f757,f770,f779]) ).
fof(f779,plain,
( ~ spl10_3
| spl10_4
| ~ spl10_6
| ~ spl10_5
| ~ spl10_7
| ~ spl10_92 ),
inference(avatar_split_clause,[],[f653,f650,f167,f157,f162,f152,f147]) ).
fof(f147,plain,
( spl10_3
<=> r2_hidden(sK3,u1_struct_0(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_3])]) ).
fof(f152,plain,
( spl10_4
<=> r2_hidden(sK2,u1_struct_0(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_4])]) ).
fof(f162,plain,
( spl10_6
<=> m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_6])]) ).
fof(f157,plain,
( spl10_5
<=> m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_5])]) ).
fof(f167,plain,
( spl10_7
<=> r1_orders_2(k1_latsum_1(sK0,sK1),sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_7])]) ).
fof(f650,plain,
( spl10_92
<=> ! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK0))
| ~ m1_subset_1(X0,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(X1,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ r1_orders_2(k1_latsum_1(sK0,sK1),X0,X1)
| ~ r2_hidden(X1,u1_struct_0(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_92])]) ).
fof(f653,plain,
( ~ m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1)))
| r2_hidden(sK2,u1_struct_0(sK0))
| ~ r2_hidden(sK3,u1_struct_0(sK0))
| ~ spl10_7
| ~ spl10_92 ),
inference(resolution,[],[f651,f169]) ).
fof(f169,plain,
( r1_orders_2(k1_latsum_1(sK0,sK1),sK2,sK3)
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f651,plain,
( ! [X0,X1] :
( ~ r1_orders_2(k1_latsum_1(sK0,sK1),X0,X1)
| ~ m1_subset_1(X0,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(X1,u1_struct_0(k1_latsum_1(sK0,sK1)))
| r2_hidden(X0,u1_struct_0(sK0))
| ~ r2_hidden(X1,u1_struct_0(sK0)) )
| ~ spl10_92 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f770,plain,
( ~ spl10_110
| ~ spl10_20
| ~ spl10_95 ),
inference(avatar_split_clause,[],[f748,f664,f229,f767]) ).
fof(f767,plain,
( spl10_110
<=> r2_hidden(u1_struct_0(sK1),sK4(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_110])]) ).
fof(f229,plain,
( spl10_20
<=> ! [X0,X1] :
( ~ r2_hidden(X1,X0)
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_20])]) ).
fof(f664,plain,
( spl10_95
<=> r2_hidden(sK4(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),u1_struct_0(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_95])]) ).
fof(f748,plain,
( ~ r2_hidden(u1_struct_0(sK1),sK4(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))))
| ~ spl10_20
| ~ spl10_95 ),
inference(resolution,[],[f666,f230]) ).
fof(f230,plain,
( ! [X0,X1] :
( ~ r2_hidden(X1,X0)
| ~ r2_hidden(X0,X1) )
| ~ spl10_20 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f666,plain,
( r2_hidden(sK4(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),u1_struct_0(sK1))
| ~ spl10_95 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f757,plain,
( spl10_109
| ~ spl10_2
| ~ spl10_103 ),
inference(avatar_split_clause,[],[f723,f714,f142,f755]) ).
fof(f755,plain,
( spl10_109
<=> ! [X0] :
( k1_latsum_1(X0,sK1) = g1_orders_2(u1_struct_0(k1_latsum_1(X0,sK1)),u1_orders_2(k1_latsum_1(X0,sK1)))
| ~ l1_orders_2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_109])]) ).
fof(f142,plain,
( spl10_2
<=> l1_orders_2(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_2])]) ).
fof(f714,plain,
( spl10_103
<=> ! [X0,X1] :
( k1_latsum_1(X0,X1) = g1_orders_2(u1_struct_0(k1_latsum_1(X0,X1)),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_103])]) ).
fof(f723,plain,
( ! [X0] :
( k1_latsum_1(X0,sK1) = g1_orders_2(u1_struct_0(k1_latsum_1(X0,sK1)),u1_orders_2(k1_latsum_1(X0,sK1)))
| ~ l1_orders_2(X0) )
| ~ spl10_2
| ~ spl10_103 ),
inference(resolution,[],[f715,f144]) ).
fof(f144,plain,
( l1_orders_2(sK1)
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f142]) ).
fof(f715,plain,
( ! [X0,X1] :
( ~ l1_orders_2(X1)
| k1_latsum_1(X0,X1) = g1_orders_2(u1_struct_0(k1_latsum_1(X0,X1)),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ l1_orders_2(X0) )
| ~ spl10_103 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f753,plain,
( spl10_108
| ~ spl10_1
| ~ spl10_103 ),
inference(avatar_split_clause,[],[f722,f714,f137,f751]) ).
fof(f751,plain,
( spl10_108
<=> ! [X0] :
( k1_latsum_1(X0,sK0) = g1_orders_2(u1_struct_0(k1_latsum_1(X0,sK0)),u1_orders_2(k1_latsum_1(X0,sK0)))
| ~ l1_orders_2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_108])]) ).
fof(f137,plain,
( spl10_1
<=> l1_orders_2(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_1])]) ).
fof(f722,plain,
( ! [X0] :
( k1_latsum_1(X0,sK0) = g1_orders_2(u1_struct_0(k1_latsum_1(X0,sK0)),u1_orders_2(k1_latsum_1(X0,sK0)))
| ~ l1_orders_2(X0) )
| ~ spl10_1
| ~ spl10_103 ),
inference(resolution,[],[f715,f139]) ).
fof(f139,plain,
( l1_orders_2(sK0)
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f746,plain,
( spl10_107
| ~ spl10_44
| ~ spl10_80 ),
inference(avatar_split_clause,[],[f581,f578,f362,f744]) ).
fof(f744,plain,
( spl10_107
<=> ! [X2,X0,X1] :
( ~ r2_hidden(X0,u1_struct_0(X1))
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X1)))
| r2_hidden(X2,u1_struct_0(X1))
| ~ v12_waybel_0(u1_struct_0(X1),X1)
| ~ l1_orders_2(X1)
| ~ r1_orders_2(k1_latsum_1(X1,X1),X2,X0)
| ~ m1_subset_1(X0,u1_struct_0(k1_latsum_1(X1,X1)))
| ~ m1_subset_1(X2,u1_struct_0(k1_latsum_1(X1,X1)))
| ~ l1_orders_2(k1_latsum_1(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_107])]) ).
fof(f362,plain,
( spl10_44
<=> ! [X2,X0,X1] :
( r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0))
| ~ r1_orders_2(X0,X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_44])]) ).
fof(f578,plain,
( spl10_80
<=> ! [X2,X0,X1] :
( ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ r2_hidden(X1,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X2,X1),u1_orders_2(k1_latsum_1(X0,X0)))
| r2_hidden(X2,u1_struct_0(X0))
| ~ v12_waybel_0(u1_struct_0(X0),X0)
| ~ l1_orders_2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_80])]) ).
fof(f581,plain,
( ! [X2,X0,X1] :
( ~ r2_hidden(X0,u1_struct_0(X1))
| ~ m1_subset_1(u1_struct_0(X1),k1_zfmisc_1(u1_struct_0(X1)))
| r2_hidden(X2,u1_struct_0(X1))
| ~ v12_waybel_0(u1_struct_0(X1),X1)
| ~ l1_orders_2(X1)
| ~ r1_orders_2(k1_latsum_1(X1,X1),X2,X0)
| ~ m1_subset_1(X0,u1_struct_0(k1_latsum_1(X1,X1)))
| ~ m1_subset_1(X2,u1_struct_0(k1_latsum_1(X1,X1)))
| ~ l1_orders_2(k1_latsum_1(X1,X1)) )
| ~ spl10_44
| ~ spl10_80 ),
inference(resolution,[],[f579,f363]) ).
fof(f363,plain,
( ! [X2,X0,X1] :
( r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0))
| ~ r1_orders_2(X0,X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0) )
| ~ spl10_44 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f579,plain,
( ! [X2,X0,X1] :
( ~ r2_hidden(k4_tarski(X2,X1),u1_orders_2(k1_latsum_1(X0,X0)))
| ~ r2_hidden(X1,u1_struct_0(X0))
| ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(u1_struct_0(X0)))
| r2_hidden(X2,u1_struct_0(X0))
| ~ v12_waybel_0(u1_struct_0(X0),X0)
| ~ l1_orders_2(X0) )
| ~ spl10_80 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f738,plain,
( spl10_106
| ~ spl10_25
| ~ spl10_81 ),
inference(avatar_split_clause,[],[f587,f583,f252,f736]) ).
fof(f736,plain,
( spl10_106
<=> ! [X0,X3,X2,X1] :
( ~ r1_tarski(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X0)),u1_struct_0(X1))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| r2_hidden(X2,u1_struct_0(X0))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X0)),X1)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0)
| ~ r2_hidden(X3,u1_struct_0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_106])]) ).
fof(f252,plain,
( spl10_25
<=> ! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_25])]) ).
fof(f583,plain,
( spl10_81
<=> ! [X0,X3,X2,X1] :
( ~ r2_hidden(X0,u1_struct_0(X1))
| ~ r2_hidden(k4_tarski(X2,X0),u1_orders_2(k1_latsum_1(X1,X3)))
| r2_hidden(X2,u1_struct_0(X1))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X3)),X3)
| ~ l1_orders_2(X3)
| ~ l1_orders_2(X1)
| ~ r1_tarski(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X3)),u1_struct_0(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_81])]) ).
fof(f587,plain,
( ! [X2,X3,X0,X1] :
( ~ r1_tarski(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X0)),u1_struct_0(X1))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| r2_hidden(X2,u1_struct_0(X0))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X0)),X1)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0)
| ~ r2_hidden(X3,u1_struct_0(X0)) )
| ~ spl10_25
| ~ spl10_81 ),
inference(superposition,[],[f584,f253]) ).
fof(f253,plain,
( ! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0)
| ~ spl10_25 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f584,plain,
( ! [X2,X3,X0,X1] :
( ~ r1_tarski(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X3)),u1_struct_0(X3))
| ~ r2_hidden(k4_tarski(X2,X0),u1_orders_2(k1_latsum_1(X1,X3)))
| r2_hidden(X2,u1_struct_0(X1))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X3)),X3)
| ~ l1_orders_2(X3)
| ~ l1_orders_2(X1)
| ~ r2_hidden(X0,u1_struct_0(X1)) )
| ~ spl10_81 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f733,plain,
( spl10_105
| ~ spl10_18
| ~ spl10_81 ),
inference(avatar_split_clause,[],[f589,f583,f218,f731]) ).
fof(f731,plain,
( spl10_105
<=> ! [X2,X0,X1] :
( ~ r1_tarski(u1_struct_0(X0),u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X1,X2),u1_orders_2(k1_latsum_1(X0,X0)))
| r2_hidden(X1,u1_struct_0(X0))
| ~ v12_waybel_0(u1_struct_0(X0),X0)
| ~ l1_orders_2(X0)
| ~ r2_hidden(X2,u1_struct_0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_105])]) ).
fof(f218,plain,
( spl10_18
<=> ! [X0] : k3_xboole_0(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl10_18])]) ).
fof(f589,plain,
( ! [X2,X0,X1] :
( ~ r1_tarski(u1_struct_0(X0),u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X1,X2),u1_orders_2(k1_latsum_1(X0,X0)))
| r2_hidden(X1,u1_struct_0(X0))
| ~ v12_waybel_0(u1_struct_0(X0),X0)
| ~ l1_orders_2(X0)
| ~ r2_hidden(X2,u1_struct_0(X0)) )
| ~ spl10_18
| ~ spl10_81 ),
inference(duplicate_literal_removal,[],[f586]) ).
fof(f586,plain,
( ! [X2,X0,X1] :
( ~ r1_tarski(u1_struct_0(X0),u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X1,X2),u1_orders_2(k1_latsum_1(X0,X0)))
| r2_hidden(X1,u1_struct_0(X0))
| ~ v12_waybel_0(u1_struct_0(X0),X0)
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X0)
| ~ r2_hidden(X2,u1_struct_0(X0)) )
| ~ spl10_18
| ~ spl10_81 ),
inference(superposition,[],[f584,f219]) ).
fof(f219,plain,
( ! [X0] : k3_xboole_0(X0,X0) = X0
| ~ spl10_18 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f728,plain,
( spl10_104
| ~ spl10_40
| ~ spl10_60 ),
inference(avatar_split_clause,[],[f485,f466,f342,f726]) ).
fof(f726,plain,
( spl10_104
<=> ! [X0] :
( g1_orders_2(X0,sK5(X0,X0)) = g1_orders_2(u1_struct_0(g1_orders_2(X0,sK5(X0,X0))),u1_orders_2(g1_orders_2(X0,sK5(X0,X0))))
| ~ l1_orders_2(g1_orders_2(X0,sK5(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_104])]) ).
fof(f342,plain,
( spl10_40
<=> ! [X0] :
( g1_orders_2(u1_struct_0(X0),u1_orders_2(X0)) = X0
| ~ v1_orders_2(X0)
| ~ l1_orders_2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_40])]) ).
fof(f466,plain,
( spl10_60
<=> ! [X0] : v1_orders_2(g1_orders_2(X0,sK5(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_60])]) ).
fof(f485,plain,
( ! [X0] :
( g1_orders_2(X0,sK5(X0,X0)) = g1_orders_2(u1_struct_0(g1_orders_2(X0,sK5(X0,X0))),u1_orders_2(g1_orders_2(X0,sK5(X0,X0))))
| ~ l1_orders_2(g1_orders_2(X0,sK5(X0,X0))) )
| ~ spl10_40
| ~ spl10_60 ),
inference(resolution,[],[f467,f343]) ).
fof(f343,plain,
( ! [X0] :
( ~ v1_orders_2(X0)
| g1_orders_2(u1_struct_0(X0),u1_orders_2(X0)) = X0
| ~ l1_orders_2(X0) )
| ~ spl10_40 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f467,plain,
( ! [X0] : v1_orders_2(g1_orders_2(X0,sK5(X0,X0)))
| ~ spl10_60 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f716,plain,
( spl10_103
| ~ spl10_32
| ~ spl10_78 ),
inference(avatar_split_clause,[],[f576,f567,f290,f714]) ).
fof(f290,plain,
( spl10_32
<=> ! [X0,X1] :
( l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_32])]) ).
fof(f567,plain,
( spl10_78
<=> ! [X0,X1] :
( k1_latsum_1(X0,X1) = g1_orders_2(u1_struct_0(k1_latsum_1(X0,X1)),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_78])]) ).
fof(f576,plain,
( ! [X0,X1] :
( k1_latsum_1(X0,X1) = g1_orders_2(u1_struct_0(k1_latsum_1(X0,X1)),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) )
| ~ spl10_32
| ~ spl10_78 ),
inference(duplicate_literal_removal,[],[f575]) ).
fof(f575,plain,
( ! [X0,X1] :
( k1_latsum_1(X0,X1) = g1_orders_2(u1_struct_0(k1_latsum_1(X0,X1)),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) )
| ~ spl10_32
| ~ spl10_78 ),
inference(resolution,[],[f568,f291]) ).
fof(f291,plain,
( ! [X0,X1] :
( l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) )
| ~ spl10_32 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f568,plain,
( ! [X0,X1] :
( ~ l1_orders_2(k1_latsum_1(X0,X1))
| k1_latsum_1(X0,X1) = g1_orders_2(u1_struct_0(k1_latsum_1(X0,X1)),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) )
| ~ spl10_78 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f710,plain,
( spl10_102
| ~ spl10_20
| ~ spl10_74 ),
inference(avatar_split_clause,[],[f550,f546,f229,f708]) ).
fof(f708,plain,
( spl10_102
<=> ! [X2,X0,X1] :
( v1_xboole_0(k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1)
| ~ r2_hidden(k1_zfmisc_1(k2_zfmisc_1(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_102])]) ).
fof(f546,plain,
( spl10_74
<=> ! [X2,X0,X1] :
( ~ m2_relset_1(X0,X1,X2)
| v1_xboole_0(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| r2_hidden(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_74])]) ).
fof(f550,plain,
( ! [X2,X0,X1] :
( v1_xboole_0(k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1)
| ~ r2_hidden(k1_zfmisc_1(k2_zfmisc_1(X0,X1)),X2) )
| ~ spl10_20
| ~ spl10_74 ),
inference(resolution,[],[f547,f230]) ).
fof(f547,plain,
( ! [X2,X0,X1] :
( r2_hidden(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| v1_xboole_0(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| ~ m2_relset_1(X0,X1,X2) )
| ~ spl10_74 ),
inference(avatar_component_clause,[],[f546]) ).
fof(f705,plain,
( spl10_101
| ~ spl10_36
| ~ spl10_73 ),
inference(avatar_split_clause,[],[f543,f539,f316,f703]) ).
fof(f703,plain,
( spl10_101
<=> ! [X0,X1] :
( ~ r2_hidden(X0,u1_orders_2(X1))
| m1_subset_1(X0,k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)))
| ~ l1_orders_2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_101])]) ).
fof(f316,plain,
( spl10_36
<=> ! [X0] :
( m2_relset_1(u1_orders_2(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_orders_2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_36])]) ).
fof(f539,plain,
( spl10_73
<=> ! [X0,X3,X2,X1] :
( m1_subset_1(X0,k2_zfmisc_1(X1,X2))
| ~ r2_hidden(X0,X3)
| ~ m2_relset_1(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_73])]) ).
fof(f543,plain,
( ! [X0,X1] :
( ~ r2_hidden(X0,u1_orders_2(X1))
| m1_subset_1(X0,k2_zfmisc_1(u1_struct_0(X1),u1_struct_0(X1)))
| ~ l1_orders_2(X1) )
| ~ spl10_36
| ~ spl10_73 ),
inference(resolution,[],[f540,f317]) ).
fof(f317,plain,
( ! [X0] :
( m2_relset_1(u1_orders_2(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_orders_2(X0) )
| ~ spl10_36 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f540,plain,
( ! [X2,X3,X0,X1] :
( ~ m2_relset_1(X3,X1,X2)
| ~ r2_hidden(X0,X3)
| m1_subset_1(X0,k2_zfmisc_1(X1,X2)) )
| ~ spl10_73 ),
inference(avatar_component_clause,[],[f539]) ).
fof(f700,plain,
( spl10_100
| ~ spl10_58
| ~ spl10_84 ),
inference(avatar_split_clause,[],[f668,f604,f450,f697]) ).
fof(f697,plain,
( spl10_100
<=> k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)) = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl10_100])]) ).
fof(f450,plain,
( spl10_58
<=> ! [X0] :
( sK8 = X0
| ~ v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_58])]) ).
fof(f604,plain,
( spl10_84
<=> v1_xboole_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_84])]) ).
fof(f668,plain,
( k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)) = sK8
| ~ spl10_58
| ~ spl10_84 ),
inference(resolution,[],[f606,f451]) ).
fof(f451,plain,
( ! [X0] :
( ~ v1_xboole_0(X0)
| sK8 = X0 )
| ~ spl10_58 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f606,plain,
( v1_xboole_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
| ~ spl10_84 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f688,plain,
( spl10_99
| ~ spl10_63
| ~ spl10_73 ),
inference(avatar_split_clause,[],[f544,f539,f478,f686]) ).
fof(f686,plain,
( spl10_99
<=> ! [X2,X0,X1] :
( ~ r2_hidden(X0,sK5(X1,X2))
| m1_subset_1(X0,k2_zfmisc_1(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_99])]) ).
fof(f478,plain,
( spl10_63
<=> ! [X0,X1] : m2_relset_1(sK5(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_63])]) ).
fof(f544,plain,
( ! [X2,X0,X1] :
( ~ r2_hidden(X0,sK5(X1,X2))
| m1_subset_1(X0,k2_zfmisc_1(X1,X2)) )
| ~ spl10_63
| ~ spl10_73 ),
inference(resolution,[],[f540,f479]) ).
fof(f479,plain,
( ! [X0,X1] : m2_relset_1(sK5(X0,X1),X0,X1)
| ~ spl10_63 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f684,plain,
( spl10_98
| ~ spl10_23
| ~ spl10_73 ),
inference(avatar_split_clause,[],[f542,f539,f241,f682]) ).
fof(f682,plain,
( spl10_98
<=> ! [X2,X0,X1] :
( ~ r2_hidden(X0,sK6(X1,X2))
| m1_subset_1(X0,k2_zfmisc_1(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_98])]) ).
fof(f241,plain,
( spl10_23
<=> ! [X0,X1] : m2_relset_1(sK6(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_23])]) ).
fof(f542,plain,
( ! [X2,X0,X1] :
( ~ r2_hidden(X0,sK6(X1,X2))
| m1_subset_1(X0,k2_zfmisc_1(X1,X2)) )
| ~ spl10_23
| ~ spl10_73 ),
inference(resolution,[],[f540,f242]) ).
fof(f242,plain,
( ! [X0,X1] : m2_relset_1(sK6(X0,X1),X0,X1)
| ~ spl10_23 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f680,plain,
( spl10_97
| ~ spl10_20
| ~ spl10_71 ),
inference(avatar_split_clause,[],[f532,f528,f229,f678]) ).
fof(f678,plain,
( spl10_97
<=> ! [X0,X1] :
( v1_xboole_0(k1_zfmisc_1(X0))
| ~ r1_tarski(X1,X0)
| ~ r2_hidden(k1_zfmisc_1(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_97])]) ).
fof(f528,plain,
( spl10_71
<=> ! [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,[spl10_71])]) ).
fof(f532,plain,
( ! [X0,X1] :
( v1_xboole_0(k1_zfmisc_1(X0))
| ~ r1_tarski(X1,X0)
| ~ r2_hidden(k1_zfmisc_1(X0),X1) )
| ~ spl10_20
| ~ spl10_71 ),
inference(resolution,[],[f529,f230]) ).
fof(f529,plain,
( ! [X0,X1] :
( r2_hidden(X1,k1_zfmisc_1(X0))
| v1_xboole_0(k1_zfmisc_1(X0))
| ~ r1_tarski(X1,X0) )
| ~ spl10_71 ),
inference(avatar_component_clause,[],[f528]) ).
fof(f676,plain,
( spl10_96
| ~ spl10_59
| ~ spl10_68 ),
inference(avatar_split_clause,[],[f514,f510,f462,f674]) ).
fof(f674,plain,
( spl10_96
<=> ! [X0] :
( m1_subset_1(sK4(sK4(k1_zfmisc_1(X0))),X0)
| v1_xboole_0(sK4(k1_zfmisc_1(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_96])]) ).
fof(f462,plain,
( spl10_59
<=> ! [X0] :
( v1_xboole_0(X0)
| r2_hidden(sK4(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_59])]) ).
fof(f510,plain,
( spl10_68
<=> ! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,sK4(k1_zfmisc_1(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_68])]) ).
fof(f514,plain,
( ! [X0] :
( m1_subset_1(sK4(sK4(k1_zfmisc_1(X0))),X0)
| v1_xboole_0(sK4(k1_zfmisc_1(X0))) )
| ~ spl10_59
| ~ spl10_68 ),
inference(resolution,[],[f511,f463]) ).
fof(f463,plain,
( ! [X0] :
( r2_hidden(sK4(X0),X0)
| v1_xboole_0(X0) )
| ~ spl10_59 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f511,plain,
( ! [X0,X1] :
( ~ r2_hidden(X0,sK4(k1_zfmisc_1(X1)))
| m1_subset_1(X0,X1) )
| ~ spl10_68 ),
inference(avatar_component_clause,[],[f510]) ).
fof(f667,plain,
( spl10_95
| spl10_48
| ~ spl10_28
| ~ spl10_83 ),
inference(avatar_split_clause,[],[f608,f600,f274,f389,f664]) ).
fof(f389,plain,
( spl10_48
<=> v1_xboole_0(u1_struct_0(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_48])]) ).
fof(f274,plain,
( spl10_28
<=> ! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_28])]) ).
fof(f600,plain,
( spl10_83
<=> m1_subset_1(sK4(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),u1_struct_0(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_83])]) ).
fof(f608,plain,
( v1_xboole_0(u1_struct_0(sK1))
| r2_hidden(sK4(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),u1_struct_0(sK1))
| ~ spl10_28
| ~ spl10_83 ),
inference(resolution,[],[f602,f275]) ).
fof(f275,plain,
( ! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| v1_xboole_0(X1)
| r2_hidden(X0,X1) )
| ~ spl10_28 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f602,plain,
( m1_subset_1(sK4(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),u1_struct_0(sK1))
| ~ spl10_83 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f661,plain,
( spl10_94
| ~ spl10_29
| ~ spl10_69 ),
inference(avatar_split_clause,[],[f524,f516,f278,f659]) ).
fof(f659,plain,
( spl10_94
<=> ! [X0] :
( ~ l1_orders_2(X0)
| v1_orders_2(g1_orders_2(u1_struct_0(X0),u1_orders_2(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_94])]) ).
fof(f278,plain,
( spl10_29
<=> ! [X0,X1] :
( v1_orders_2(g1_orders_2(X0,X1))
| ~ m1_relset_1(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_29])]) ).
fof(f516,plain,
( spl10_69
<=> ! [X0] :
( ~ l1_orders_2(X0)
| m1_relset_1(u1_orders_2(X0),u1_struct_0(X0),u1_struct_0(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_69])]) ).
fof(f524,plain,
( ! [X0] :
( ~ l1_orders_2(X0)
| v1_orders_2(g1_orders_2(u1_struct_0(X0),u1_orders_2(X0))) )
| ~ spl10_29
| ~ spl10_69 ),
inference(resolution,[],[f517,f279]) ).
fof(f279,plain,
( ! [X0,X1] :
( ~ m1_relset_1(X1,X0,X0)
| v1_orders_2(g1_orders_2(X0,X1)) )
| ~ spl10_29 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f517,plain,
( ! [X0] :
( m1_relset_1(u1_orders_2(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_orders_2(X0) )
| ~ spl10_69 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f657,plain,
( spl10_93
| ~ spl10_30
| ~ spl10_69 ),
inference(avatar_split_clause,[],[f523,f516,f282,f655]) ).
fof(f655,plain,
( spl10_93
<=> ! [X0] :
( ~ l1_orders_2(X0)
| l1_orders_2(g1_orders_2(u1_struct_0(X0),u1_orders_2(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_93])]) ).
fof(f282,plain,
( spl10_30
<=> ! [X0,X1] :
( l1_orders_2(g1_orders_2(X0,X1))
| ~ m1_relset_1(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_30])]) ).
fof(f523,plain,
( ! [X0] :
( ~ l1_orders_2(X0)
| l1_orders_2(g1_orders_2(u1_struct_0(X0),u1_orders_2(X0))) )
| ~ spl10_30
| ~ spl10_69 ),
inference(resolution,[],[f517,f283]) ).
fof(f283,plain,
( ! [X0,X1] :
( ~ m1_relset_1(X1,X0,X0)
| l1_orders_2(g1_orders_2(X0,X1)) )
| ~ spl10_30 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f652,plain,
( ~ spl10_87
| spl10_92
| ~ spl10_44
| ~ spl10_65 ),
inference(avatar_split_clause,[],[f499,f496,f362,f650,f622]) ).
fof(f622,plain,
( spl10_87
<=> l1_orders_2(k1_latsum_1(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_87])]) ).
fof(f496,plain,
( spl10_65
<=> ! [X0,X1] :
( ~ r2_hidden(X0,u1_struct_0(sK0))
| r2_hidden(X1,u1_struct_0(sK0))
| ~ r2_hidden(k4_tarski(X1,X0),u1_orders_2(k1_latsum_1(sK0,sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_65])]) ).
fof(f499,plain,
( ! [X0,X1] :
( r2_hidden(X0,u1_struct_0(sK0))
| ~ r2_hidden(X1,u1_struct_0(sK0))
| ~ r1_orders_2(k1_latsum_1(sK0,sK1),X0,X1)
| ~ m1_subset_1(X1,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(X0,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ l1_orders_2(k1_latsum_1(sK0,sK1)) )
| ~ spl10_44
| ~ spl10_65 ),
inference(resolution,[],[f497,f363]) ).
fof(f497,plain,
( ! [X0,X1] :
( ~ r2_hidden(k4_tarski(X1,X0),u1_orders_2(k1_latsum_1(sK0,sK1)))
| r2_hidden(X1,u1_struct_0(sK0))
| ~ r2_hidden(X0,u1_struct_0(sK0)) )
| ~ spl10_65 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f643,plain,
( ~ spl10_1
| ~ spl10_2
| ~ spl10_32
| spl10_87 ),
inference(avatar_split_clause,[],[f626,f622,f290,f142,f137]) ).
fof(f626,plain,
( ~ l1_orders_2(sK1)
| ~ l1_orders_2(sK0)
| ~ spl10_32
| spl10_87 ),
inference(resolution,[],[f624,f291]) ).
fof(f624,plain,
( ~ l1_orders_2(k1_latsum_1(sK0,sK1))
| spl10_87 ),
inference(avatar_component_clause,[],[f622]) ).
fof(f642,plain,
( spl10_91
| ~ spl10_59
| ~ spl10_66 ),
inference(avatar_split_clause,[],[f504,f501,f462,f640]) ).
fof(f640,plain,
( spl10_91
<=> ! [X0] :
( ~ v1_xboole_0(X0)
| v1_xboole_0(sK4(k1_zfmisc_1(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_91])]) ).
fof(f501,plain,
( spl10_66
<=> ! [X0,X1] :
( ~ v1_xboole_0(X0)
| ~ r2_hidden(X1,sK4(k1_zfmisc_1(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_66])]) ).
fof(f504,plain,
( ! [X0] :
( ~ v1_xboole_0(X0)
| v1_xboole_0(sK4(k1_zfmisc_1(X0))) )
| ~ spl10_59
| ~ spl10_66 ),
inference(resolution,[],[f502,f463]) ).
fof(f502,plain,
( ! [X0,X1] :
( ~ r2_hidden(X1,sK4(k1_zfmisc_1(X0)))
| ~ v1_xboole_0(X0) )
| ~ spl10_66 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f638,plain,
( spl10_90
| ~ spl10_29
| ~ spl10_62 ),
inference(avatar_split_clause,[],[f492,f474,f278,f636]) ).
fof(f636,plain,
( spl10_90
<=> ! [X0] : v1_orders_2(g1_orders_2(X0,sK6(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_90])]) ).
fof(f474,plain,
( spl10_62
<=> ! [X0,X1] : m1_relset_1(sK6(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_62])]) ).
fof(f492,plain,
( ! [X0] : v1_orders_2(g1_orders_2(X0,sK6(X0,X0)))
| ~ spl10_29
| ~ spl10_62 ),
inference(resolution,[],[f475,f279]) ).
fof(f475,plain,
( ! [X0,X1] : m1_relset_1(sK6(X0,X1),X0,X1)
| ~ spl10_62 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f634,plain,
( spl10_89
| ~ spl10_30
| ~ spl10_62 ),
inference(avatar_split_clause,[],[f491,f474,f282,f632]) ).
fof(f632,plain,
( spl10_89
<=> ! [X0] : l1_orders_2(g1_orders_2(X0,sK6(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_89])]) ).
fof(f491,plain,
( ! [X0] : l1_orders_2(g1_orders_2(X0,sK6(X0,X0)))
| ~ spl10_30
| ~ spl10_62 ),
inference(resolution,[],[f475,f283]) ).
fof(f630,plain,
( spl10_88
| ~ spl10_20
| ~ spl10_59 ),
inference(avatar_split_clause,[],[f482,f462,f229,f628]) ).
fof(f628,plain,
( spl10_88
<=> ! [X0] :
( v1_xboole_0(X0)
| ~ r2_hidden(X0,sK4(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_88])]) ).
fof(f482,plain,
( ! [X0] :
( v1_xboole_0(X0)
| ~ r2_hidden(X0,sK4(X0)) )
| ~ spl10_20
| ~ spl10_59 ),
inference(resolution,[],[f463,f230]) ).
fof(f625,plain,
( ~ spl10_86
| ~ spl10_87
| ~ spl10_5
| ~ spl10_6
| ~ spl10_7
| ~ spl10_75 ),
inference(avatar_split_clause,[],[f556,f553,f167,f162,f157,f622,f618]) ).
fof(f618,plain,
( spl10_86
<=> v1_xboole_0(u1_orders_2(k1_latsum_1(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_86])]) ).
fof(f553,plain,
( spl10_75
<=> ! [X2,X0,X1] :
( ~ r1_orders_2(X0,X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0)
| ~ v1_xboole_0(u1_orders_2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_75])]) ).
fof(f556,plain,
( ~ m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ l1_orders_2(k1_latsum_1(sK0,sK1))
| ~ v1_xboole_0(u1_orders_2(k1_latsum_1(sK0,sK1)))
| ~ spl10_7
| ~ spl10_75 ),
inference(resolution,[],[f554,f169]) ).
fof(f554,plain,
( ! [X2,X0,X1] :
( ~ r1_orders_2(X0,X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0)
| ~ v1_xboole_0(u1_orders_2(X0)) )
| ~ spl10_75 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f612,plain,
( spl10_85
| ~ spl10_16
| ~ spl10_53 ),
inference(avatar_split_clause,[],[f426,f422,f210,f610]) ).
fof(f610,plain,
( spl10_85
<=> ! [X0] : sK8 = k3_xboole_0(X0,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_85])]) ).
fof(f210,plain,
( spl10_16
<=> ! [X0] : k1_xboole_0 = k3_xboole_0(X0,k1_xboole_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_16])]) ).
fof(f422,plain,
( spl10_53
<=> k1_xboole_0 = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl10_53])]) ).
fof(f426,plain,
( ! [X0] : sK8 = k3_xboole_0(X0,sK8)
| ~ spl10_16
| ~ spl10_53 ),
inference(superposition,[],[f211,f424]) ).
fof(f424,plain,
( k1_xboole_0 = sK8
| ~ spl10_53 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f211,plain,
( ! [X0] : k1_xboole_0 = k3_xboole_0(X0,k1_xboole_0)
| ~ spl10_16 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f607,plain,
( spl10_83
| spl10_84
| ~ spl10_52
| ~ spl10_59 ),
inference(avatar_split_clause,[],[f484,f462,f418,f604,f600]) ).
fof(f418,plain,
( spl10_52
<=> ! [X0] :
( m1_subset_1(X0,u1_struct_0(sK1))
| ~ r2_hidden(X0,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_52])]) ).
fof(f484,plain,
( v1_xboole_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
| m1_subset_1(sK4(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))),u1_struct_0(sK1))
| ~ spl10_52
| ~ spl10_59 ),
inference(resolution,[],[f463,f419]) ).
fof(f419,plain,
( ! [X0] :
( ~ r2_hidden(X0,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
| m1_subset_1(X0,u1_struct_0(sK1)) )
| ~ spl10_52 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f593,plain,
( spl10_82
| ~ spl10_25
| ~ spl10_46 ),
inference(avatar_split_clause,[],[f381,f375,f252,f591]) ).
fof(f591,plain,
( spl10_82
<=> ! [X0,X3,X2,X1] :
( ~ m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X0)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(X2,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X3,X2),u1_orders_2(k1_latsum_1(X0,X1)))
| r2_hidden(X3,u1_struct_0(X0))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X0)),X1)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_82])]) ).
fof(f375,plain,
( spl10_46
<=> ! [X0,X3,X2,X1] :
( r2_hidden(X2,u1_struct_0(X0))
| ~ r2_hidden(X3,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_46])]) ).
fof(f381,plain,
( ! [X2,X3,X0,X1] :
( ~ m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X0)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(X2,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X3,X2),u1_orders_2(k1_latsum_1(X0,X1)))
| r2_hidden(X3,u1_struct_0(X0))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X0)),X1)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) )
| ~ spl10_25
| ~ spl10_46 ),
inference(superposition,[],[f376,f253]) ).
fof(f376,plain,
( ! [X2,X3,X0,X1] :
( ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ r2_hidden(X3,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| r2_hidden(X2,u1_struct_0(X0))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) )
| ~ spl10_46 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f585,plain,
( spl10_81
| ~ spl10_26
| ~ spl10_46 ),
inference(avatar_split_clause,[],[f379,f375,f256,f583]) ).
fof(f256,plain,
( spl10_26
<=> ! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_26])]) ).
fof(f379,plain,
( ! [X2,X3,X0,X1] :
( ~ r2_hidden(X0,u1_struct_0(X1))
| ~ r2_hidden(k4_tarski(X2,X0),u1_orders_2(k1_latsum_1(X1,X3)))
| r2_hidden(X2,u1_struct_0(X1))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X3)),X3)
| ~ l1_orders_2(X3)
| ~ l1_orders_2(X1)
| ~ r1_tarski(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X3)),u1_struct_0(X3)) )
| ~ spl10_26
| ~ spl10_46 ),
inference(resolution,[],[f376,f257]) ).
fof(f257,plain,
( ! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) )
| ~ spl10_26 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f580,plain,
( spl10_80
| ~ spl10_18
| ~ spl10_46 ),
inference(avatar_split_clause,[],[f383,f375,f218,f578]) ).
fof(f383,plain,
( ! [X2,X0,X1] :
( ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ r2_hidden(X1,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X2,X1),u1_orders_2(k1_latsum_1(X0,X0)))
| r2_hidden(X2,u1_struct_0(X0))
| ~ v12_waybel_0(u1_struct_0(X0),X0)
| ~ l1_orders_2(X0) )
| ~ spl10_18
| ~ spl10_46 ),
inference(duplicate_literal_removal,[],[f380]) ).
fof(f380,plain,
( ! [X2,X0,X1] :
( ~ m1_subset_1(u1_struct_0(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ r2_hidden(X1,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X2,X1),u1_orders_2(k1_latsum_1(X0,X0)))
| r2_hidden(X2,u1_struct_0(X0))
| ~ v12_waybel_0(u1_struct_0(X0),X0)
| ~ l1_orders_2(X0)
| ~ l1_orders_2(X0) )
| ~ spl10_18
| ~ spl10_46 ),
inference(superposition,[],[f376,f219]) ).
fof(f574,plain,
( ~ spl10_79
| ~ spl10_20
| ~ spl10_54 ),
inference(avatar_split_clause,[],[f438,f429,f229,f571]) ).
fof(f571,plain,
( spl10_79
<=> r2_hidden(k1_zfmisc_1(u1_struct_0(sK1)),k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_79])]) ).
fof(f429,plain,
( spl10_54
<=> r2_hidden(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_54])]) ).
fof(f438,plain,
( ~ r2_hidden(k1_zfmisc_1(u1_struct_0(sK1)),k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)))
| ~ spl10_20
| ~ spl10_54 ),
inference(resolution,[],[f431,f230]) ).
fof(f431,plain,
( r2_hidden(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ spl10_54 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f569,plain,
( spl10_78
| ~ spl10_31
| ~ spl10_40 ),
inference(avatar_split_clause,[],[f350,f342,f286,f567]) ).
fof(f286,plain,
( spl10_31
<=> ! [X0,X1] :
( v1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_31])]) ).
fof(f350,plain,
( ! [X0,X1] :
( k1_latsum_1(X0,X1) = g1_orders_2(u1_struct_0(k1_latsum_1(X0,X1)),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) )
| ~ spl10_31
| ~ spl10_40 ),
inference(resolution,[],[f343,f287]) ).
fof(f287,plain,
( ! [X0,X1] :
( v1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) )
| ~ spl10_31 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f564,plain,
( spl10_77
| ~ spl10_20
| ~ spl10_44 ),
inference(avatar_split_clause,[],[f370,f362,f229,f562]) ).
fof(f562,plain,
( spl10_77
<=> ! [X2,X0,X1] :
( ~ r1_orders_2(X0,X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0)
| ~ r2_hidden(u1_orders_2(X0),k4_tarski(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_77])]) ).
fof(f370,plain,
( ! [X2,X0,X1] :
( ~ r1_orders_2(X0,X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0)
| ~ r2_hidden(u1_orders_2(X0),k4_tarski(X1,X2)) )
| ~ spl10_20
| ~ spl10_44 ),
inference(resolution,[],[f363,f230]) ).
fof(f560,plain,
( spl10_76
| ~ spl10_21
| ~ spl10_44 ),
inference(avatar_split_clause,[],[f369,f362,f233,f558]) ).
fof(f558,plain,
( spl10_76
<=> ! [X2,X0,X1] :
( ~ r1_orders_2(X0,X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0)
| m1_subset_1(k4_tarski(X1,X2),u1_orders_2(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_76])]) ).
fof(f233,plain,
( spl10_21
<=> ! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_21])]) ).
fof(f369,plain,
( ! [X2,X0,X1] :
( ~ r1_orders_2(X0,X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0)
| m1_subset_1(k4_tarski(X1,X2),u1_orders_2(X0)) )
| ~ spl10_21
| ~ spl10_44 ),
inference(resolution,[],[f363,f234]) ).
fof(f234,plain,
( ! [X0,X1] :
( ~ r2_hidden(X0,X1)
| m1_subset_1(X0,X1) )
| ~ spl10_21 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f555,plain,
( spl10_75
| ~ spl10_19
| ~ spl10_44 ),
inference(avatar_split_clause,[],[f371,f362,f222,f553]) ).
fof(f222,plain,
( spl10_19
<=> ! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_19])]) ).
fof(f371,plain,
( ! [X2,X0,X1] :
( ~ r1_orders_2(X0,X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0)
| ~ v1_xboole_0(u1_orders_2(X0)) )
| ~ spl10_19
| ~ spl10_44 ),
inference(resolution,[],[f363,f223]) ).
fof(f223,plain,
( ! [X0,X1] :
( ~ r2_hidden(X0,X1)
| ~ v1_xboole_0(X1) )
| ~ spl10_19 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f548,plain,
( spl10_74
| ~ spl10_28
| ~ spl10_38 ),
inference(avatar_split_clause,[],[f336,f328,f274,f546]) ).
fof(f328,plain,
( spl10_38
<=> ! [X2,X0,X1] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_38])]) ).
fof(f336,plain,
( ! [X2,X0,X1] :
( ~ m2_relset_1(X0,X1,X2)
| v1_xboole_0(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))
| r2_hidden(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))) )
| ~ spl10_28
| ~ spl10_38 ),
inference(resolution,[],[f329,f275]) ).
fof(f329,plain,
( ! [X2,X0,X1] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1) )
| ~ spl10_38 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f541,plain,
( spl10_73
| ~ spl10_38
| ~ spl10_39 ),
inference(avatar_split_clause,[],[f339,f332,f328,f539]) ).
fof(f332,plain,
( spl10_39
<=> ! [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,[spl10_39])]) ).
fof(f339,plain,
( ! [X2,X3,X0,X1] :
( m1_subset_1(X0,k2_zfmisc_1(X1,X2))
| ~ r2_hidden(X0,X3)
| ~ m2_relset_1(X3,X1,X2) )
| ~ spl10_38
| ~ spl10_39 ),
inference(resolution,[],[f333,f329]) ).
fof(f333,plain,
( ! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| m1_subset_1(X0,X2)
| ~ r2_hidden(X0,X1) )
| ~ spl10_39 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f537,plain,
( spl10_72
| ~ spl10_37
| ~ spl10_38 ),
inference(avatar_split_clause,[],[f335,f328,f320,f535]) ).
fof(f535,plain,
( spl10_72
<=> ! [X2,X0,X1,X3] :
( ~ m2_relset_1(X0,X1,X2)
| ~ v1_xboole_0(k2_zfmisc_1(X1,X2))
| ~ r2_hidden(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_72])]) ).
fof(f320,plain,
( spl10_37
<=> ! [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,[spl10_37])]) ).
fof(f335,plain,
( ! [X2,X3,X0,X1] :
( ~ m2_relset_1(X0,X1,X2)
| ~ v1_xboole_0(k2_zfmisc_1(X1,X2))
| ~ r2_hidden(X3,X0) )
| ~ spl10_37
| ~ spl10_38 ),
inference(resolution,[],[f329,f321]) ).
fof(f321,plain,
( ! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ v1_xboole_0(X2)
| ~ r2_hidden(X0,X1) )
| ~ spl10_37 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f530,plain,
( spl10_71
| ~ spl10_26
| ~ spl10_28 ),
inference(avatar_split_clause,[],[f304,f274,f256,f528]) ).
fof(f304,plain,
( ! [X0,X1] :
( v1_xboole_0(k1_zfmisc_1(X0))
| r2_hidden(X1,k1_zfmisc_1(X0))
| ~ r1_tarski(X1,X0) )
| ~ spl10_26
| ~ spl10_28 ),
inference(resolution,[],[f275,f257]) ).
fof(f522,plain,
( spl10_70
| ~ spl10_26
| ~ spl10_39 ),
inference(avatar_split_clause,[],[f338,f332,f256,f520]) ).
fof(f520,plain,
( spl10_70
<=> ! [X2,X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X2)
| ~ r1_tarski(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_70])]) ).
fof(f338,plain,
( ! [X2,X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X2)
| ~ r1_tarski(X2,X1) )
| ~ spl10_26
| ~ spl10_39 ),
inference(resolution,[],[f333,f257]) ).
fof(f518,plain,
( spl10_69
| ~ spl10_33
| ~ spl10_36 ),
inference(avatar_split_clause,[],[f323,f316,f294,f516]) ).
fof(f294,plain,
( spl10_33
<=> ! [X2,X0,X1] :
( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_33])]) ).
fof(f323,plain,
( ! [X0] :
( ~ l1_orders_2(X0)
| m1_relset_1(u1_orders_2(X0),u1_struct_0(X0),u1_struct_0(X0)) )
| ~ spl10_33
| ~ spl10_36 ),
inference(resolution,[],[f317,f295]) ).
fof(f295,plain,
( ! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) )
| ~ spl10_33 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f512,plain,
( spl10_68
| ~ spl10_15
| ~ spl10_39 ),
inference(avatar_split_clause,[],[f340,f332,f206,f510]) ).
fof(f206,plain,
( spl10_15
<=> ! [X0] : m1_subset_1(sK4(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_15])]) ).
fof(f340,plain,
( ! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,sK4(k1_zfmisc_1(X1))) )
| ~ spl10_15
| ~ spl10_39 ),
inference(resolution,[],[f333,f207]) ).
fof(f207,plain,
( ! [X0] : m1_subset_1(sK4(X0),X0)
| ~ spl10_15 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f508,plain,
( spl10_67
| ~ spl10_26
| ~ spl10_37 ),
inference(avatar_split_clause,[],[f325,f320,f256,f506]) ).
fof(f506,plain,
( spl10_67
<=> ! [X2,X0,X1] :
( ~ v1_xboole_0(X0)
| ~ r2_hidden(X1,X2)
| ~ r1_tarski(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_67])]) ).
fof(f325,plain,
( ! [X2,X0,X1] :
( ~ v1_xboole_0(X0)
| ~ r2_hidden(X1,X2)
| ~ r1_tarski(X2,X0) )
| ~ spl10_26
| ~ spl10_37 ),
inference(resolution,[],[f321,f257]) ).
fof(f503,plain,
( spl10_66
| ~ spl10_15
| ~ spl10_37 ),
inference(avatar_split_clause,[],[f326,f320,f206,f501]) ).
fof(f326,plain,
( ! [X0,X1] :
( ~ v1_xboole_0(X0)
| ~ r2_hidden(X1,sK4(k1_zfmisc_1(X0))) )
| ~ spl10_15
| ~ spl10_37 ),
inference(resolution,[],[f321,f207]) ).
fof(f498,plain,
( ~ spl10_1
| ~ spl10_2
| ~ spl10_8
| spl10_65
| ~ spl10_13
| ~ spl10_46 ),
inference(avatar_split_clause,[],[f378,f375,f197,f496,f172,f142,f137]) ).
fof(f172,plain,
( spl10_8
<=> v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_8])]) ).
fof(f197,plain,
( spl10_13
<=> m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_13])]) ).
fof(f378,plain,
( ! [X0,X1] :
( ~ r2_hidden(X0,u1_struct_0(sK0))
| ~ r2_hidden(k4_tarski(X1,X0),u1_orders_2(k1_latsum_1(sK0,sK1)))
| r2_hidden(X1,u1_struct_0(sK0))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1)
| ~ l1_orders_2(sK1)
| ~ l1_orders_2(sK0) )
| ~ spl10_13
| ~ spl10_46 ),
inference(resolution,[],[f376,f199]) ).
fof(f199,plain,
( m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ spl10_13 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f490,plain,
( ~ spl10_64
| ~ spl10_20
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f415,f406,f229,f487]) ).
fof(f487,plain,
( spl10_64
<=> r2_hidden(u1_struct_0(k1_latsum_1(sK0,sK1)),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_64])]) ).
fof(f406,plain,
( spl10_51
<=> r2_hidden(sK3,u1_struct_0(k1_latsum_1(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_51])]) ).
fof(f415,plain,
( ~ r2_hidden(u1_struct_0(k1_latsum_1(sK0,sK1)),sK3)
| ~ spl10_20
| ~ spl10_51 ),
inference(resolution,[],[f408,f230]) ).
fof(f408,plain,
( r2_hidden(sK3,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ spl10_51 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f480,plain,
( spl10_63
| ~ spl10_22
| ~ spl10_34 ),
inference(avatar_split_clause,[],[f314,f298,f237,f478]) ).
fof(f237,plain,
( spl10_22
<=> ! [X0,X1] : m1_relset_1(sK5(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_22])]) ).
fof(f298,plain,
( spl10_34
<=> ! [X2,X0,X1] :
( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_34])]) ).
fof(f314,plain,
( ! [X0,X1] : m2_relset_1(sK5(X0,X1),X0,X1)
| ~ spl10_22
| ~ spl10_34 ),
inference(resolution,[],[f299,f238]) ).
fof(f238,plain,
( ! [X0,X1] : m1_relset_1(sK5(X0,X1),X0,X1)
| ~ spl10_22 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f299,plain,
( ! [X2,X0,X1] :
( ~ m1_relset_1(X2,X0,X1)
| m2_relset_1(X2,X0,X1) )
| ~ spl10_34 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f476,plain,
( spl10_62
| ~ spl10_23
| ~ spl10_33 ),
inference(avatar_split_clause,[],[f308,f294,f241,f474]) ).
fof(f308,plain,
( ! [X0,X1] : m1_relset_1(sK6(X0,X1),X0,X1)
| ~ spl10_23
| ~ spl10_33 ),
inference(resolution,[],[f295,f242]) ).
fof(f472,plain,
( spl10_61
| ~ spl10_22
| ~ spl10_30 ),
inference(avatar_split_clause,[],[f307,f282,f237,f470]) ).
fof(f470,plain,
( spl10_61
<=> ! [X0] : l1_orders_2(g1_orders_2(X0,sK5(X0,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_61])]) ).
fof(f307,plain,
( ! [X0] : l1_orders_2(g1_orders_2(X0,sK5(X0,X0)))
| ~ spl10_22
| ~ spl10_30 ),
inference(resolution,[],[f283,f238]) ).
fof(f468,plain,
( spl10_60
| ~ spl10_22
| ~ spl10_29 ),
inference(avatar_split_clause,[],[f306,f278,f237,f466]) ).
fof(f306,plain,
( ! [X0] : v1_orders_2(g1_orders_2(X0,sK5(X0,X0)))
| ~ spl10_22
| ~ spl10_29 ),
inference(resolution,[],[f279,f238]) ).
fof(f464,plain,
( spl10_59
| ~ spl10_15
| ~ spl10_28 ),
inference(avatar_split_clause,[],[f305,f274,f206,f462]) ).
fof(f305,plain,
( ! [X0] :
( v1_xboole_0(X0)
| r2_hidden(sK4(X0),X0) )
| ~ spl10_15
| ~ spl10_28 ),
inference(resolution,[],[f275,f207]) ).
fof(f452,plain,
( spl10_58
| ~ spl10_11
| ~ spl10_27 ),
inference(avatar_split_clause,[],[f272,f260,f187,f450]) ).
fof(f187,plain,
( spl10_11
<=> v1_xboole_0(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_11])]) ).
fof(f260,plain,
( spl10_27
<=> ! [X0,X1] :
( ~ v1_xboole_0(X1)
| X0 = X1
| ~ v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_27])]) ).
fof(f272,plain,
( ! [X0] :
( sK8 = X0
| ~ v1_xboole_0(X0) )
| ~ spl10_11
| ~ spl10_27 ),
inference(resolution,[],[f261,f189]) ).
fof(f189,plain,
( v1_xboole_0(sK8)
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f261,plain,
( ! [X0,X1] :
( ~ v1_xboole_0(X1)
| X0 = X1
| ~ v1_xboole_0(X0) )
| ~ spl10_27 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f448,plain,
( ~ spl10_57
| ~ spl10_20
| ~ spl10_49 ),
inference(avatar_split_clause,[],[f403,f394,f229,f445]) ).
fof(f445,plain,
( spl10_57
<=> r2_hidden(u1_struct_0(k1_latsum_1(sK0,sK1)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_57])]) ).
fof(f394,plain,
( spl10_49
<=> r2_hidden(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_49])]) ).
fof(f403,plain,
( ~ r2_hidden(u1_struct_0(k1_latsum_1(sK0,sK1)),sK2)
| ~ spl10_20
| ~ spl10_49 ),
inference(resolution,[],[f396,f230]) ).
fof(f396,plain,
( r2_hidden(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ spl10_49 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f443,plain,
( spl10_56
| ~ spl10_11
| ~ spl10_16
| ~ spl10_17
| ~ spl10_25 ),
inference(avatar_split_clause,[],[f267,f252,f214,f210,f187,f441]) ).
fof(f441,plain,
( spl10_56
<=> ! [X0] : sK8 = k3_xboole_0(sK8,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_56])]) ).
fof(f214,plain,
( spl10_17
<=> ! [X0] :
( k1_xboole_0 = X0
| ~ v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_17])]) ).
fof(f267,plain,
( ! [X0] : sK8 = k3_xboole_0(sK8,X0)
| ~ spl10_11
| ~ spl10_16
| ~ spl10_17
| ~ spl10_25 ),
inference(forward_demodulation,[],[f263,f226]) ).
fof(f226,plain,
( k1_xboole_0 = sK8
| ~ spl10_11
| ~ spl10_17 ),
inference(resolution,[],[f215,f189]) ).
fof(f215,plain,
( ! [X0] :
( ~ v1_xboole_0(X0)
| k1_xboole_0 = X0 )
| ~ spl10_17 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f263,plain,
( ! [X0] : k1_xboole_0 = k3_xboole_0(k1_xboole_0,X0)
| ~ spl10_16
| ~ spl10_25 ),
inference(superposition,[],[f253,f211]) ).
fof(f436,plain,
( spl10_54
| spl10_55
| ~ spl10_13
| ~ spl10_28 ),
inference(avatar_split_clause,[],[f303,f274,f197,f433,f429]) ).
fof(f433,plain,
( spl10_55
<=> v1_xboole_0(k1_zfmisc_1(u1_struct_0(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_55])]) ).
fof(f303,plain,
( v1_xboole_0(k1_zfmisc_1(u1_struct_0(sK1)))
| r2_hidden(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
| ~ spl10_13
| ~ spl10_28 ),
inference(resolution,[],[f275,f199]) ).
fof(f425,plain,
( spl10_53
| ~ spl10_11
| ~ spl10_17 ),
inference(avatar_split_clause,[],[f226,f214,f187,f422]) ).
fof(f420,plain,
( spl10_52
| ~ spl10_13
| ~ spl10_39 ),
inference(avatar_split_clause,[],[f337,f332,f197,f418]) ).
fof(f337,plain,
( ! [X0] :
( m1_subset_1(X0,u1_struct_0(sK1))
| ~ r2_hidden(X0,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))) )
| ~ spl10_13
| ~ spl10_39 ),
inference(resolution,[],[f333,f199]) ).
fof(f413,plain,
( ~ spl10_50
| ~ spl10_19
| ~ spl10_49 ),
inference(avatar_split_clause,[],[f404,f394,f222,f398]) ).
fof(f398,plain,
( spl10_50
<=> v1_xboole_0(u1_struct_0(k1_latsum_1(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_50])]) ).
fof(f404,plain,
( ~ v1_xboole_0(u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ spl10_19
| ~ spl10_49 ),
inference(resolution,[],[f396,f223]) ).
fof(f409,plain,
( spl10_51
| spl10_50
| ~ spl10_6
| ~ spl10_28 ),
inference(avatar_split_clause,[],[f302,f274,f162,f398,f406]) ).
fof(f302,plain,
( v1_xboole_0(u1_struct_0(k1_latsum_1(sK0,sK1)))
| r2_hidden(sK3,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ spl10_6
| ~ spl10_28 ),
inference(resolution,[],[f275,f164]) ).
fof(f164,plain,
( m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f401,plain,
( spl10_49
| spl10_50
| ~ spl10_5
| ~ spl10_28 ),
inference(avatar_split_clause,[],[f301,f274,f157,f398,f394]) ).
fof(f301,plain,
( v1_xboole_0(u1_struct_0(k1_latsum_1(sK0,sK1)))
| r2_hidden(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ spl10_5
| ~ spl10_28 ),
inference(resolution,[],[f275,f159]) ).
fof(f159,plain,
( m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f392,plain,
( spl10_47
| ~ spl10_48
| ~ spl10_13
| ~ spl10_37 ),
inference(avatar_split_clause,[],[f324,f320,f197,f389,f386]) ).
fof(f386,plain,
( spl10_47
<=> ! [X0] : ~ r2_hidden(X0,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_47])]) ).
fof(f324,plain,
( ! [X0] :
( ~ v1_xboole_0(u1_struct_0(sK1))
| ~ r2_hidden(X0,k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1))) )
| ~ spl10_13
| ~ spl10_37 ),
inference(resolution,[],[f321,f199]) ).
fof(f377,plain,
spl10_46,
inference(avatar_split_clause,[],[f107,f375]) ).
fof(f107,plain,
! [X2,X3,X0,X1] :
( r2_hidden(X2,u1_struct_0(X0))
| ~ r2_hidden(X3,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( r2_hidden(X2,u1_struct_0(X0))
| ~ r2_hidden(X3,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1) )
| ~ l1_orders_2(X1) )
| ~ l1_orders_2(X0) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( r2_hidden(X2,u1_struct_0(X0))
| ~ r2_hidden(X3,u1_struct_0(X0))
| ~ r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1) )
| ~ l1_orders_2(X1) )
| ~ l1_orders_2(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( l1_orders_2(X1)
=> ! [X2,X3] :
( ( r2_hidden(X3,u1_struct_0(X0))
& r2_hidden(k4_tarski(X2,X3),u1_orders_2(k1_latsum_1(X0,X1)))
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1) )
=> r2_hidden(X2,u1_struct_0(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_latsum_1) ).
fof(f368,plain,
spl10_45,
inference(avatar_split_clause,[],[f109,f366]) ).
fof(f366,plain,
( spl10_45
<=> ! [X2,X0,X1] :
( r1_orders_2(X0,X1,X2)
| ~ r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_45])]) ).
fof(f109,plain,
! [X2,X0,X1] :
( r1_orders_2(X0,X1,X2)
| ~ r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0))
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( r1_orders_2(X0,X1,X2)
| ~ r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0)) )
& ( r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0))
| ~ r1_orders_2(X0,X1,X2) ) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l1_orders_2(X0) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( r1_orders_2(X0,X1,X2)
<=> r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0)) )
| ~ m1_subset_1(X2,u1_struct_0(X0)) )
| ~ m1_subset_1(X1,u1_struct_0(X0)) )
| ~ l1_orders_2(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( m1_subset_1(X1,u1_struct_0(X0))
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X0))
=> ( r1_orders_2(X0,X1,X2)
<=> r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
fof(f364,plain,
spl10_44,
inference(avatar_split_clause,[],[f108,f362]) ).
fof(f108,plain,
! [X2,X0,X1] :
( r2_hidden(k4_tarski(X1,X2),u1_orders_2(X0))
| ~ r1_orders_2(X0,X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(X0))
| ~ m1_subset_1(X1,u1_struct_0(X0))
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f358,plain,
spl10_43,
inference(avatar_split_clause,[],[f120,f356]) ).
fof(f356,plain,
( spl10_43
<=> ! [X0,X3,X2,X1] :
( X1 = X3
| g1_orders_2(X0,X1) != g1_orders_2(X2,X3)
| ~ m1_relset_1(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_43])]) ).
fof(f120,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| g1_orders_2(X0,X1) != g1_orders_2(X2,X3)
| ~ m1_relset_1(X1,X0,X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( X1 = X3
& X0 = X2 )
| g1_orders_2(X0,X1) != g1_orders_2(X2,X3) )
| ~ m1_relset_1(X1,X0,X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( m1_relset_1(X1,X0,X0)
=> ! [X2,X3] :
( g1_orders_2(X0,X1) = g1_orders_2(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',free_g1_orders_2) ).
fof(f354,plain,
spl10_42,
inference(avatar_split_clause,[],[f119,f352]) ).
fof(f352,plain,
( spl10_42
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| g1_orders_2(X0,X1) != g1_orders_2(X2,X3)
| ~ m1_relset_1(X1,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_42])]) ).
fof(f119,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| g1_orders_2(X0,X1) != g1_orders_2(X2,X3)
| ~ m1_relset_1(X1,X0,X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f349,plain,
( spl10_41
| ~ spl10_3
| ~ spl10_21 ),
inference(avatar_split_clause,[],[f245,f233,f147,f346]) ).
fof(f346,plain,
( spl10_41
<=> m1_subset_1(sK3,u1_struct_0(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_41])]) ).
fof(f245,plain,
( m1_subset_1(sK3,u1_struct_0(sK0))
| ~ spl10_3
| ~ spl10_21 ),
inference(resolution,[],[f234,f149]) ).
fof(f149,plain,
( r2_hidden(sK3,u1_struct_0(sK0))
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f147]) ).
fof(f344,plain,
spl10_40,
inference(avatar_split_clause,[],[f106,f342]) ).
fof(f106,plain,
! [X0] :
( g1_orders_2(u1_struct_0(X0),u1_orders_2(X0)) = X0
| ~ v1_orders_2(X0)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( g1_orders_2(u1_struct_0(X0),u1_orders_2(X0)) = X0
| ~ v1_orders_2(X0)
| ~ l1_orders_2(X0) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
! [X0] :
( g1_orders_2(u1_struct_0(X0),u1_orders_2(X0)) = X0
| ~ v1_orders_2(X0)
| ~ l1_orders_2(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( l1_orders_2(X0)
=> ( v1_orders_2(X0)
=> g1_orders_2(u1_struct_0(X0),u1_orders_2(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).
fof(f334,plain,
spl10_39,
inference(avatar_split_clause,[],[f129,f332]) ).
fof(f129,plain,
! [X2,X0,X1] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,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(f330,plain,
spl10_38,
inference(avatar_split_clause,[],[f128,f328]) ).
fof(f128,plain,
! [X2,X0,X1] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
=> m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f322,plain,
spl10_37,
inference(avatar_split_clause,[],[f132,f320]) ).
fof(f132,plain,
! [X2,X0,X1] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,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(f318,plain,
spl10_36,
inference(avatar_split_clause,[],[f105,f316]) ).
fof(f105,plain,
! [X0] :
( m2_relset_1(u1_orders_2(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( m2_relset_1(u1_orders_2(X0),u1_struct_0(X0),u1_struct_0(X0))
| ~ l1_orders_2(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( l1_orders_2(X0)
=> m2_relset_1(u1_orders_2(X0),u1_struct_0(X0),u1_struct_0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_orders_2) ).
fof(f313,plain,
( ~ spl10_35
| ~ spl10_3
| ~ spl10_20 ),
inference(avatar_split_clause,[],[f244,f229,f147,f310]) ).
fof(f310,plain,
( spl10_35
<=> r2_hidden(u1_struct_0(sK0),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_35])]) ).
fof(f244,plain,
( ~ r2_hidden(u1_struct_0(sK0),sK3)
| ~ spl10_3
| ~ spl10_20 ),
inference(resolution,[],[f230,f149]) ).
fof(f300,plain,
spl10_34,
inference(avatar_split_clause,[],[f131,f298]) ).
fof(f131,plain,
! [X2,X0,X1] :
( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) )
& ( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f296,plain,
spl10_33,
inference(avatar_split_clause,[],[f130,f294]) ).
fof(f130,plain,
! [X2,X0,X1] :
( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f292,plain,
spl10_32,
inference(avatar_split_clause,[],[f122,f290]) ).
fof(f122,plain,
! [X0,X1] :
( l1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ( l1_orders_2(k1_latsum_1(X0,X1))
& v1_orders_2(k1_latsum_1(X0,X1)) )
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ( l1_orders_2(k1_latsum_1(X0,X1))
& v1_orders_2(k1_latsum_1(X0,X1)) )
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( l1_orders_2(X1)
& l1_orders_2(X0) )
=> ( l1_orders_2(k1_latsum_1(X0,X1))
& v1_orders_2(k1_latsum_1(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsum_1) ).
fof(f288,plain,
spl10_31,
inference(avatar_split_clause,[],[f121,f286]) ).
fof(f121,plain,
! [X0,X1] :
( v1_orders_2(k1_latsum_1(X0,X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f284,plain,
spl10_30,
inference(avatar_split_clause,[],[f118,f282]) ).
fof(f118,plain,
! [X0,X1] :
( l1_orders_2(g1_orders_2(X0,X1))
| ~ m1_relset_1(X1,X0,X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( ( l1_orders_2(g1_orders_2(X0,X1))
& v1_orders_2(g1_orders_2(X0,X1)) )
| ~ m1_relset_1(X1,X0,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( m1_relset_1(X1,X0,X0)
=> ( l1_orders_2(g1_orders_2(X0,X1))
& v1_orders_2(g1_orders_2(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_g1_orders_2) ).
fof(f280,plain,
spl10_29,
inference(avatar_split_clause,[],[f117,f278]) ).
fof(f117,plain,
! [X0,X1] :
( v1_orders_2(g1_orders_2(X0,X1))
| ~ m1_relset_1(X1,X0,X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f276,plain,
spl10_28,
inference(avatar_split_clause,[],[f116,f274]) ).
fof(f116,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,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(f262,plain,
spl10_27,
inference(avatar_split_clause,[],[f124,f260]) ).
fof(f124,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| X0 = X1
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| X0 = X1
| ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] :
~ ( v1_xboole_0(X1)
& X0 != X1
& v1_xboole_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f258,plain,
spl10_26,
inference(avatar_split_clause,[],[f123,f256]) ).
fof(f123,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
=> m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(unused_predicate_definition_removal,[],[f38]) ).
fof(f38,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(f254,plain,
spl10_25,
inference(avatar_split_clause,[],[f113,f252]) ).
fof(f113,plain,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : k3_xboole_0(X0,X1) = k3_xboole_0(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f250,plain,
( ~ spl10_24
| ~ spl10_3
| ~ spl10_19 ),
inference(avatar_split_clause,[],[f227,f222,f147,f247]) ).
fof(f247,plain,
( spl10_24
<=> v1_xboole_0(u1_struct_0(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_24])]) ).
fof(f227,plain,
( ~ v1_xboole_0(u1_struct_0(sK0))
| ~ spl10_3
| ~ spl10_19 ),
inference(resolution,[],[f223,f149]) ).
fof(f243,plain,
spl10_23,
inference(avatar_split_clause,[],[f127,f241]) ).
fof(f127,plain,
! [X0,X1] : m2_relset_1(sK6(X0,X1),X0,X1),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] : m2_relset_1(sK6(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f26,f84]) ).
fof(f84,plain,
! [X0,X1] :
( ? [X2] : m2_relset_1(X2,X0,X1)
=> m2_relset_1(sK6(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
! [X0,X1] :
? [X2] : m2_relset_1(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(f239,plain,
spl10_22,
inference(avatar_split_clause,[],[f126,f237]) ).
fof(f126,plain,
! [X0,X1] : m1_relset_1(sK5(X0,X1),X0,X1),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1] : m1_relset_1(sK5(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f24,f82]) ).
fof(f82,plain,
! [X0,X1] :
( ? [X2] : m1_relset_1(X2,X0,X1)
=> m1_relset_1(sK5(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
! [X0,X1] :
? [X2] : m1_relset_1(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(f235,plain,
spl10_21,
inference(avatar_split_clause,[],[f115,f233]) ).
fof(f115,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f231,plain,
spl10_20,
inference(avatar_split_clause,[],[f114,f229]) ).
fof(f114,plain,
! [X0,X1] :
( ~ r2_hidden(X1,X0)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( ~ r2_hidden(X1,X0)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> ~ r2_hidden(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f224,plain,
spl10_19,
inference(avatar_split_clause,[],[f125,f222]) ).
fof(f125,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
~ ( v1_xboole_0(X1)
& r2_hidden(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f220,plain,
spl10_18,
inference(avatar_split_clause,[],[f112,f218]) ).
fof(f112,plain,
! [X0] : k3_xboole_0(X0,X0) = X0,
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] : k3_xboole_0(X0,X0) = X0,
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] : k3_xboole_0(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f216,plain,
spl10_17,
inference(avatar_split_clause,[],[f104,f214]) ).
fof(f104,plain,
! [X0] :
( k1_xboole_0 = X0
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( k1_xboole_0 = X0
| ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( v1_xboole_0(X0)
=> k1_xboole_0 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f212,plain,
spl10_16,
inference(avatar_split_clause,[],[f103,f210]) ).
fof(f103,plain,
! [X0] : k1_xboole_0 = k3_xboole_0(X0,k1_xboole_0),
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] : k1_xboole_0 = k3_xboole_0(X0,k1_xboole_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
fof(f208,plain,
spl10_15,
inference(avatar_split_clause,[],[f110,f206]) ).
fof(f110,plain,
! [X0] : m1_subset_1(sK4(X0),X0),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] : m1_subset_1(sK4(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f25,f80]) ).
fof(f80,plain,
! [X0] :
( ? [X1] : m1_subset_1(X1,X0)
=> m1_subset_1(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
! [X0] :
? [X1] : m1_subset_1(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f204,plain,
spl10_14,
inference(avatar_split_clause,[],[f111,f202]) ).
fof(f202,plain,
( spl10_14
<=> ! [X0] : r1_tarski(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_14])]) ).
fof(f111,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f200,plain,
spl10_13,
inference(avatar_split_clause,[],[f98,f197]) ).
fof(f98,plain,
m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1))),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
( ~ r2_hidden(sK2,u1_struct_0(sK0))
& r2_hidden(sK3,u1_struct_0(sK0))
& r1_orders_2(k1_latsum_1(sK0,sK1),sK2,sK3)
& m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1)
& m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1)))
& m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1)))
& l1_orders_2(sK1)
& l1_orders_2(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f51,f77,f76,f75,f74]) ).
fof(f74,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ r2_hidden(X2,u1_struct_0(X0))
& r2_hidden(X3,u1_struct_0(X0))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1))) )
& m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1))) )
& l1_orders_2(X1) )
& l1_orders_2(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ r2_hidden(X2,u1_struct_0(sK0))
& r2_hidden(X3,u1_struct_0(sK0))
& r1_orders_2(k1_latsum_1(sK0,X1),X2,X3)
& m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(X1)),X1)
& m1_subset_1(X3,u1_struct_0(k1_latsum_1(sK0,X1))) )
& m1_subset_1(X2,u1_struct_0(k1_latsum_1(sK0,X1))) )
& l1_orders_2(X1) )
& l1_orders_2(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ r2_hidden(X2,u1_struct_0(sK0))
& r2_hidden(X3,u1_struct_0(sK0))
& r1_orders_2(k1_latsum_1(sK0,X1),X2,X3)
& m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(X1)),X1)
& m1_subset_1(X3,u1_struct_0(k1_latsum_1(sK0,X1))) )
& m1_subset_1(X2,u1_struct_0(k1_latsum_1(sK0,X1))) )
& l1_orders_2(X1) )
=> ( ? [X2] :
( ? [X3] :
( ~ r2_hidden(X2,u1_struct_0(sK0))
& r2_hidden(X3,u1_struct_0(sK0))
& r1_orders_2(k1_latsum_1(sK0,sK1),X2,X3)
& m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1)
& m1_subset_1(X3,u1_struct_0(k1_latsum_1(sK0,sK1))) )
& m1_subset_1(X2,u1_struct_0(k1_latsum_1(sK0,sK1))) )
& l1_orders_2(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
( ? [X2] :
( ? [X3] :
( ~ r2_hidden(X2,u1_struct_0(sK0))
& r2_hidden(X3,u1_struct_0(sK0))
& r1_orders_2(k1_latsum_1(sK0,sK1),X2,X3)
& m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1)
& m1_subset_1(X3,u1_struct_0(k1_latsum_1(sK0,sK1))) )
& m1_subset_1(X2,u1_struct_0(k1_latsum_1(sK0,sK1))) )
=> ( ? [X3] :
( ~ r2_hidden(sK2,u1_struct_0(sK0))
& r2_hidden(X3,u1_struct_0(sK0))
& r1_orders_2(k1_latsum_1(sK0,sK1),sK2,X3)
& m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1)
& m1_subset_1(X3,u1_struct_0(k1_latsum_1(sK0,sK1))) )
& m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
( ? [X3] :
( ~ r2_hidden(sK2,u1_struct_0(sK0))
& r2_hidden(X3,u1_struct_0(sK0))
& r1_orders_2(k1_latsum_1(sK0,sK1),sK2,X3)
& m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1)
& m1_subset_1(X3,u1_struct_0(k1_latsum_1(sK0,sK1))) )
=> ( ~ r2_hidden(sK2,u1_struct_0(sK0))
& r2_hidden(sK3,u1_struct_0(sK0))
& r1_orders_2(k1_latsum_1(sK0,sK1),sK2,sK3)
& m1_subset_1(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),k1_zfmisc_1(u1_struct_0(sK1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1)
& m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1))) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ r2_hidden(X2,u1_struct_0(X0))
& r2_hidden(X3,u1_struct_0(X0))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1))) )
& m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1))) )
& l1_orders_2(X1) )
& l1_orders_2(X0) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ r2_hidden(X2,u1_struct_0(X0))
& r2_hidden(X3,u1_struct_0(X0))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1)
& m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1))) )
& m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1))) )
& l1_orders_2(X1) )
& l1_orders_2(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1)))
=> ( ( r2_hidden(X3,u1_struct_0(X0))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1) )
=> r2_hidden(X2,u1_struct_0(X0)) ) ) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0] :
( l1_orders_2(X0)
=> ! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(k1_latsum_1(X0,X1)))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X0,X1)))
=> ( ( r2_hidden(X3,u1_struct_0(X0))
& r1_orders_2(k1_latsum_1(X0,X1),X2,X3)
& m1_subset_1(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),k1_zfmisc_1(u1_struct_0(X1)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(X0),u1_struct_0(X1)),X1) )
=> r2_hidden(X2,u1_struct_0(X0)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_latsum_1) ).
fof(f195,plain,
spl10_12,
inference(avatar_split_clause,[],[f135,f192]) ).
fof(f192,plain,
( spl10_12
<=> l1_orders_2(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_12])]) ).
fof(f135,plain,
l1_orders_2(sK9),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
l1_orders_2(sK9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f22,f91]) ).
fof(f91,plain,
( ? [X0] : l1_orders_2(X0)
=> l1_orders_2(sK9) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] : l1_orders_2(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_orders_2) ).
fof(f190,plain,
spl10_11,
inference(avatar_split_clause,[],[f134,f187]) ).
fof(f134,plain,
v1_xboole_0(sK8),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
v1_xboole_0(sK8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f30,f89]) ).
fof(f89,plain,
( ? [X0] : v1_xboole_0(X0)
=> v1_xboole_0(sK8) ),
introduced(choice_axiom,[]) ).
fof(f30,axiom,
? [X0] : v1_xboole_0(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f185,plain,
~ spl10_10,
inference(avatar_split_clause,[],[f133,f182]) ).
fof(f182,plain,
( spl10_10
<=> v1_xboole_0(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_10])]) ).
fof(f133,plain,
~ v1_xboole_0(sK7),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
~ v1_xboole_0(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f31,f87]) ).
fof(f87,plain,
( ? [X0] : ~ v1_xboole_0(X0)
=> ~ v1_xboole_0(sK7) ),
introduced(choice_axiom,[]) ).
fof(f31,axiom,
? [X0] : ~ v1_xboole_0(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f180,plain,
spl10_9,
inference(avatar_split_clause,[],[f102,f177]) ).
fof(f177,plain,
( spl10_9
<=> v1_xboole_0(k1_xboole_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_9])]) ).
fof(f102,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f175,plain,
spl10_8,
inference(avatar_split_clause,[],[f97,f172]) ).
fof(f97,plain,
v12_waybel_0(k3_xboole_0(u1_struct_0(sK0),u1_struct_0(sK1)),sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f170,plain,
spl10_7,
inference(avatar_split_clause,[],[f99,f167]) ).
fof(f99,plain,
r1_orders_2(k1_latsum_1(sK0,sK1),sK2,sK3),
inference(cnf_transformation,[],[f78]) ).
fof(f165,plain,
spl10_6,
inference(avatar_split_clause,[],[f96,f162]) ).
fof(f96,plain,
m1_subset_1(sK3,u1_struct_0(k1_latsum_1(sK0,sK1))),
inference(cnf_transformation,[],[f78]) ).
fof(f160,plain,
spl10_5,
inference(avatar_split_clause,[],[f95,f157]) ).
fof(f95,plain,
m1_subset_1(sK2,u1_struct_0(k1_latsum_1(sK0,sK1))),
inference(cnf_transformation,[],[f78]) ).
fof(f155,plain,
~ spl10_4,
inference(avatar_split_clause,[],[f101,f152]) ).
fof(f101,plain,
~ r2_hidden(sK2,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f78]) ).
fof(f150,plain,
spl10_3,
inference(avatar_split_clause,[],[f100,f147]) ).
fof(f100,plain,
r2_hidden(sK3,u1_struct_0(sK0)),
inference(cnf_transformation,[],[f78]) ).
fof(f145,plain,
spl10_2,
inference(avatar_split_clause,[],[f94,f142]) ).
fof(f94,plain,
l1_orders_2(sK1),
inference(cnf_transformation,[],[f78]) ).
fof(f140,plain,
spl10_1,
inference(avatar_split_clause,[],[f93,f137]) ).
fof(f93,plain,
l1_orders_2(sK0),
inference(cnf_transformation,[],[f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SEU413+1 : TPTP v8.1.2. Released v3.4.0.
% 0.02/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Apr 29 20:37:33 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (18040)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (18045)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)
% 0.11/0.34 % (18047)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)
% 0.11/0.34 % (18044)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.34 % (18046)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)
% 0.11/0.35 TRYING [1]
% 0.11/0.35 TRYING [2]
% 0.11/0.35 TRYING [3]
% 0.11/0.36 % (18045)First to succeed.
% 0.11/0.36 TRYING [4]
% 0.11/0.36 % (18043)WARNING: value z3 for option sas not known
% 0.11/0.36 % (18045)Refutation found. Thanks to Tanya!
% 0.11/0.36 % SZS status Theorem for theBenchmark
% 0.11/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.37 % (18045)------------------------------
% 0.11/0.37 % (18045)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.11/0.37 % (18045)Termination reason: Refutation
% 0.11/0.37
% 0.11/0.37 % (18045)Memory used [KB]: 1174
% 0.11/0.37 % (18045)Time elapsed: 0.020 s
% 0.11/0.37 % (18045)Instructions burned: 35 (million)
% 0.11/0.37 % (18045)------------------------------
% 0.11/0.37 % (18045)------------------------------
% 0.11/0.37 % (18040)Success in time 0.037 s
%------------------------------------------------------------------------------