TSTP Solution File: SEU435+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU435+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 : n007.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 15:34:34 EDT 2024
% Result : Theorem 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 124
% Syntax : Number of formulae : 337 ( 94 unt; 0 def)
% Number of atoms : 810 ( 50 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 778 ( 305 ~; 279 |; 74 &)
% ( 73 <=>; 46 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 80 ( 78 usr; 68 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 10 con; 0-6 aty)
% Number of variables : 618 ( 568 !; 50 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f612,plain,
$false,
inference(avatar_sat_refutation,[],[f190,f195,f200,f205,f210,f215,f220,f225,f230,f235,f239,f243,f247,f251,f255,f259,f263,f267,f271,f278,f282,f286,f290,f294,f302,f306,f310,f314,f318,f322,f327,f331,f335,f339,f349,f353,f357,f361,f365,f369,f373,f395,f402,f414,f418,f434,f443,f449,f453,f467,f478,f483,f487,f504,f514,f526,f534,f538,f543,f559,f565,f571,f588,f592,f599,f603,f611]) ).
fof(f611,plain,
( ~ spl18_2
| ~ spl18_1
| spl18_10
| ~ spl18_56 ),
inference(avatar_split_clause,[],[f527,f524,f232,f187,f192]) ).
fof(f192,plain,
( spl18_2
<=> m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).
fof(f187,plain,
( spl18_1
<=> m1_subset_1(sK5,k1_zfmisc_1(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).
fof(f232,plain,
( spl18_10
<=> m1_subset_1(a_6_0_relset_2(sK0,sK1,sK2,sK3,sK4,sK5),k1_zfmisc_1(k1_zfmisc_1(sK4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_10])]) ).
fof(f524,plain,
( spl18_56
<=> ! [X3,X4,X0,X5,X2,X1] :
( m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
| ~ m1_subset_1(X5,k1_zfmisc_1(X3))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_56])]) ).
fof(f527,plain,
( ~ m1_subset_1(sK5,k1_zfmisc_1(sK3))
| ~ m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))))
| spl18_10
| ~ spl18_56 ),
inference(resolution,[],[f525,f234]) ).
fof(f234,plain,
( ~ m1_subset_1(a_6_0_relset_2(sK0,sK1,sK2,sK3,sK4,sK5),k1_zfmisc_1(k1_zfmisc_1(sK4)))
| spl18_10 ),
inference(avatar_component_clause,[],[f232]) ).
fof(f525,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
| ~ m1_subset_1(X5,k1_zfmisc_1(X3))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1)))) )
| ~ spl18_56 ),
inference(avatar_component_clause,[],[f524]) ).
fof(f603,plain,
( spl18_67
| ~ spl18_2
| ~ spl18_46 ),
inference(avatar_split_clause,[],[f425,f416,f192,f601]) ).
fof(f601,plain,
( spl18_67
<=> ! [X0] :
( m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ r2_hidden(X0,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_67])]) ).
fof(f416,plain,
( spl18_46
<=> ! [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,[spl18_46])]) ).
fof(f425,plain,
( ! [X0] :
( m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))
| ~ r2_hidden(X0,sK2) )
| ~ spl18_2
| ~ spl18_46 ),
inference(resolution,[],[f417,f194]) ).
fof(f194,plain,
( m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(sK0,sK1))))
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f417,plain,
( ! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| m1_subset_1(X0,X2)
| ~ r2_hidden(X0,X1) )
| ~ spl18_46 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f599,plain,
( ~ spl18_66
| spl18_10
| ~ spl18_36 ),
inference(avatar_split_clause,[],[f374,f351,f232,f596]) ).
fof(f596,plain,
( spl18_66
<=> m1_eqrel_1(a_6_0_relset_2(sK0,sK1,sK2,sK3,sK4,sK5),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_66])]) ).
fof(f351,plain,
( spl18_36
<=> ! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
| ~ m1_eqrel_1(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_36])]) ).
fof(f374,plain,
( ~ m1_eqrel_1(a_6_0_relset_2(sK0,sK1,sK2,sK3,sK4,sK5),sK4)
| spl18_10
| ~ spl18_36 ),
inference(resolution,[],[f352,f234]) ).
fof(f352,plain,
( ! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
| ~ m1_eqrel_1(X1,X0) )
| ~ spl18_36 ),
inference(avatar_component_clause,[],[f351]) ).
fof(f592,plain,
( spl18_65
| ~ spl18_1
| ~ spl18_46 ),
inference(avatar_split_clause,[],[f426,f416,f187,f590]) ).
fof(f590,plain,
( spl18_65
<=> ! [X0] :
( m1_subset_1(X0,sK3)
| ~ r2_hidden(X0,sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_65])]) ).
fof(f426,plain,
( ! [X0] :
( m1_subset_1(X0,sK3)
| ~ r2_hidden(X0,sK5) )
| ~ spl18_1
| ~ spl18_46 ),
inference(resolution,[],[f417,f189]) ).
fof(f189,plain,
( m1_subset_1(sK5,k1_zfmisc_1(sK3))
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f588,plain,
( spl18_63
| ~ spl18_64
| ~ spl18_1
| ~ spl18_44 ),
inference(avatar_split_clause,[],[f406,f400,f187,f585,f582]) ).
fof(f582,plain,
( spl18_63
<=> ! [X0] : ~ r2_hidden(X0,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_63])]) ).
fof(f585,plain,
( spl18_64
<=> v1_xboole_0(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_64])]) ).
fof(f400,plain,
( spl18_44
<=> ! [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,[spl18_44])]) ).
fof(f406,plain,
( ! [X0] :
( ~ v1_xboole_0(sK3)
| ~ r2_hidden(X0,sK5) )
| ~ spl18_1
| ~ spl18_44 ),
inference(resolution,[],[f401,f189]) ).
fof(f401,plain,
( ! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ v1_xboole_0(X2)
| ~ r2_hidden(X0,X1) )
| ~ spl18_44 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f571,plain,
spl18_62,
inference(avatar_split_clause,[],[f185,f569]) ).
fof(f569,plain,
( spl18_62
<=> ! [X5,X4,X2,X7,X6,X3,X1] :
( r2_hidden(k8_relset_2(X4,X5,X6,X7),a_6_0_relset_2(X1,X2,X3,X4,X5,X6))
| ~ r2_hidden(X7,X3)
| ~ m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X4,X5)))
| ~ m1_subset_1(X6,k1_zfmisc_1(X4))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_62])]) ).
fof(f185,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( r2_hidden(k8_relset_2(X4,X5,X6,X7),a_6_0_relset_2(X1,X2,X3,X4,X5,X6))
| ~ r2_hidden(X7,X3)
| ~ m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X4,X5)))
| ~ m1_subset_1(X6,k1_zfmisc_1(X4))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))) ),
inference(equality_resolution,[],[f179]) ).
fof(f179,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( r2_hidden(X0,a_6_0_relset_2(X1,X2,X3,X4,X5,X6))
| ~ r2_hidden(X7,X3)
| k8_relset_2(X4,X5,X6,X7) != X0
| ~ m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X4,X5)))
| ~ m1_subset_1(X6,k1_zfmisc_1(X4))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( r2_hidden(X0,a_6_0_relset_2(X1,X2,X3,X4,X5,X6))
| ! [X7] :
( ~ r2_hidden(X7,X3)
| k8_relset_2(X4,X5,X6,X7) != X0
| ~ m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X4,X5))) ) )
& ( ( r2_hidden(sK14(X0,X3,X4,X5,X6),X3)
& k8_relset_2(X4,X5,X6,sK14(X0,X3,X4,X5,X6)) = X0
& m1_subset_1(sK14(X0,X3,X4,X5,X6),k1_zfmisc_1(k2_zfmisc_1(X4,X5))) )
| ~ r2_hidden(X0,a_6_0_relset_2(X1,X2,X3,X4,X5,X6)) ) )
| ~ m1_subset_1(X6,k1_zfmisc_1(X4))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f118,f119]) ).
fof(f119,plain,
! [X0,X3,X4,X5,X6] :
( ? [X8] :
( r2_hidden(X8,X3)
& k8_relset_2(X4,X5,X6,X8) = X0
& m1_subset_1(X8,k1_zfmisc_1(k2_zfmisc_1(X4,X5))) )
=> ( r2_hidden(sK14(X0,X3,X4,X5,X6),X3)
& k8_relset_2(X4,X5,X6,sK14(X0,X3,X4,X5,X6)) = X0
& m1_subset_1(sK14(X0,X3,X4,X5,X6),k1_zfmisc_1(k2_zfmisc_1(X4,X5))) ) ),
introduced(choice_axiom,[]) ).
fof(f118,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( r2_hidden(X0,a_6_0_relset_2(X1,X2,X3,X4,X5,X6))
| ! [X7] :
( ~ r2_hidden(X7,X3)
| k8_relset_2(X4,X5,X6,X7) != X0
| ~ m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X4,X5))) ) )
& ( ? [X8] :
( r2_hidden(X8,X3)
& k8_relset_2(X4,X5,X6,X8) = X0
& m1_subset_1(X8,k1_zfmisc_1(k2_zfmisc_1(X4,X5))) )
| ~ r2_hidden(X0,a_6_0_relset_2(X1,X2,X3,X4,X5,X6)) ) )
| ~ m1_subset_1(X6,k1_zfmisc_1(X4))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))) ),
inference(rectify,[],[f117]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( ( r2_hidden(X0,a_6_0_relset_2(X1,X2,X3,X4,X5,X6))
| ! [X7] :
( ~ r2_hidden(X7,X3)
| k8_relset_2(X4,X5,X6,X7) != X0
| ~ m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X4,X5))) ) )
& ( ? [X7] :
( r2_hidden(X7,X3)
& k8_relset_2(X4,X5,X6,X7) = X0
& m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X4,X5))) )
| ~ r2_hidden(X0,a_6_0_relset_2(X1,X2,X3,X4,X5,X6)) ) )
| ~ m1_subset_1(X6,k1_zfmisc_1(X4))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))) ),
inference(nnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( r2_hidden(X0,a_6_0_relset_2(X1,X2,X3,X4,X5,X6))
<=> ? [X7] :
( r2_hidden(X7,X3)
& k8_relset_2(X4,X5,X6,X7) = X0
& m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X4,X5))) ) )
| ~ m1_subset_1(X6,k1_zfmisc_1(X4))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))) ),
inference(flattening,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( r2_hidden(X0,a_6_0_relset_2(X1,X2,X3,X4,X5,X6))
<=> ? [X7] :
( r2_hidden(X7,X3)
& k8_relset_2(X4,X5,X6,X7) = X0
& m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X4,X5))) ) )
| ~ m1_subset_1(X6,k1_zfmisc_1(X4))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( m1_subset_1(X6,k1_zfmisc_1(X4))
& m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))) )
=> ( r2_hidden(X0,a_6_0_relset_2(X1,X2,X3,X4,X5,X6))
<=> ? [X7] :
( r2_hidden(X7,X3)
& k8_relset_2(X4,X5,X6,X7) = X0
& m1_subset_1(X7,k1_zfmisc_1(k2_zfmisc_1(X4,X5))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_6_0_relset_2) ).
fof(f565,plain,
spl18_61,
inference(avatar_split_clause,[],[f177,f563]) ).
fof(f563,plain,
( spl18_61
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( k8_relset_2(X4,X5,X6,sK14(X0,X3,X4,X5,X6)) = X0
| ~ r2_hidden(X0,a_6_0_relset_2(X1,X2,X3,X4,X5,X6))
| ~ m1_subset_1(X6,k1_zfmisc_1(X4))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_61])]) ).
fof(f177,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( k8_relset_2(X4,X5,X6,sK14(X0,X3,X4,X5,X6)) = X0
| ~ r2_hidden(X0,a_6_0_relset_2(X1,X2,X3,X4,X5,X6))
| ~ m1_subset_1(X6,k1_zfmisc_1(X4))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))) ),
inference(cnf_transformation,[],[f120]) ).
fof(f559,plain,
spl18_60,
inference(avatar_split_clause,[],[f176,f557]) ).
fof(f557,plain,
( spl18_60
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( m1_subset_1(sK14(X0,X3,X4,X5,X6),k1_zfmisc_1(k2_zfmisc_1(X4,X5)))
| ~ r2_hidden(X0,a_6_0_relset_2(X1,X2,X3,X4,X5,X6))
| ~ m1_subset_1(X6,k1_zfmisc_1(X4))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_60])]) ).
fof(f176,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( m1_subset_1(sK14(X0,X3,X4,X5,X6),k1_zfmisc_1(k2_zfmisc_1(X4,X5)))
| ~ r2_hidden(X0,a_6_0_relset_2(X1,X2,X3,X4,X5,X6))
| ~ m1_subset_1(X6,k1_zfmisc_1(X4))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))) ),
inference(cnf_transformation,[],[f120]) ).
fof(f543,plain,
( ~ spl18_59
| ~ spl18_26
| ~ spl18_42 ),
inference(avatar_split_clause,[],[f489,f388,f304,f540]) ).
fof(f540,plain,
( spl18_59
<=> r2_hidden(k1_zfmisc_1(sK3),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_59])]) ).
fof(f304,plain,
( spl18_26
<=> ! [X0,X1] :
( ~ r2_hidden(X1,X0)
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_26])]) ).
fof(f388,plain,
( spl18_42
<=> r2_hidden(sK5,k1_zfmisc_1(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_42])]) ).
fof(f489,plain,
( ~ r2_hidden(k1_zfmisc_1(sK3),sK5)
| ~ spl18_26
| ~ spl18_42 ),
inference(resolution,[],[f390,f305]) ).
fof(f305,plain,
( ! [X0,X1] :
( ~ r2_hidden(X1,X0)
| ~ r2_hidden(X0,X1) )
| ~ spl18_26 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f390,plain,
( r2_hidden(sK5,k1_zfmisc_1(sK3))
| ~ spl18_42 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f538,plain,
spl18_58,
inference(avatar_split_clause,[],[f178,f536]) ).
fof(f536,plain,
( spl18_58
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( r2_hidden(sK14(X0,X3,X4,X5,X6),X3)
| ~ r2_hidden(X0,a_6_0_relset_2(X1,X2,X3,X4,X5,X6))
| ~ m1_subset_1(X6,k1_zfmisc_1(X4))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_58])]) ).
fof(f178,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( r2_hidden(sK14(X0,X3,X4,X5,X6),X3)
| ~ r2_hidden(X0,a_6_0_relset_2(X1,X2,X3,X4,X5,X6))
| ~ m1_subset_1(X6,k1_zfmisc_1(X4))
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X1,X2)))) ),
inference(cnf_transformation,[],[f120]) ).
fof(f534,plain,
spl18_57,
inference(avatar_split_clause,[],[f162,f532]) ).
fof(f532,plain,
( spl18_57
<=> ! [X0,X3,X2,X1] :
( k7_relset_2(X0,X1,X2,X3) = k8_setfam_1(X1,k4_relset_2(k1_zfmisc_1(X0),X1,k6_relset_2(X1,X0,X3),k3_pua2mss1(X2)))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_57])]) ).
fof(f162,plain,
! [X2,X3,X0,X1] :
( k7_relset_2(X0,X1,X2,X3) = k8_setfam_1(X1,k4_relset_2(k1_zfmisc_1(X0),X1,k6_relset_2(X1,X0,X3),k3_pua2mss1(X2)))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ! [X3] :
( k7_relset_2(X0,X1,X2,X3) = k8_setfam_1(X1,k4_relset_2(k1_zfmisc_1(X0),X1,k6_relset_2(X1,X0,X3),k3_pua2mss1(X2)))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) )
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> k7_relset_2(X0,X1,X2,X3) = k8_setfam_1(X1,k4_relset_2(k1_zfmisc_1(X0),X1,k6_relset_2(X1,X0,X3),k3_pua2mss1(X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relset_2) ).
fof(f526,plain,
spl18_56,
inference(avatar_split_clause,[],[f175,f524]) ).
fof(f175,plain,
! [X2,X3,X0,X1,X4,X5] :
( m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
| ~ m1_subset_1(X5,k1_zfmisc_1(X3))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1)))) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4,X5] :
( m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
| ~ m1_subset_1(X5,k1_zfmisc_1(X3))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1)))) ),
inference(flattening,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2,X3,X4,X5] :
( m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
| ~ m1_subset_1(X5,k1_zfmisc_1(X3))
| ~ m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1)))) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( m1_subset_1(X5,k1_zfmisc_1(X3))
& m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1)))) )
=> m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s8_domain_1__e1_46__relset_2) ).
fof(f514,plain,
spl18_55,
inference(avatar_split_clause,[],[f174,f512]) ).
fof(f512,plain,
( spl18_55
<=> ! [X0,X3,X2,X1] :
( k7_relset_2(X0,X1,X2,X3) = k8_relset_2(X0,X1,X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_55])]) ).
fof(f174,plain,
! [X2,X3,X0,X1] :
( k7_relset_2(X0,X1,X2,X3) = k8_relset_2(X0,X1,X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( k7_relset_2(X0,X1,X2,X3) = k8_relset_2(X0,X1,X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( k7_relset_2(X0,X1,X2,X3) = k8_relset_2(X0,X1,X2,X3)
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1,X2,X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
& m1_subset_1(X2,k1_zfmisc_1(X0)) )
=> k7_relset_2(X0,X1,X2,X3) = k8_relset_2(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k8_relset_2) ).
fof(f504,plain,
spl18_54,
inference(avatar_split_clause,[],[f173,f502]) ).
fof(f502,plain,
( spl18_54
<=> ! [X0,X3,X2,X1] :
( m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_54])]) ).
fof(f173,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(flattening,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( ( m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
& m1_subset_1(X2,k1_zfmisc_1(X0)) )
=> m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relset_2) ).
fof(f487,plain,
spl18_53,
inference(avatar_split_clause,[],[f172,f485]) ).
fof(f485,plain,
( spl18_53
<=> ! [X0,X3,X2,X1] :
( m1_subset_1(k4_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,k1_zfmisc_1(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_53])]) ).
fof(f172,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(k4_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,k1_zfmisc_1(X1)))) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(k4_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,k1_zfmisc_1(X1)))) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1,X2,X3] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,k1_zfmisc_1(X1))))
=> m1_subset_1(k4_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_relset_2) ).
fof(f483,plain,
spl18_52,
inference(avatar_split_clause,[],[f171,f481]) ).
fof(f481,plain,
( spl18_52
<=> ! [X0,X3,X2,X1] :
( k4_relset_2(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,k1_zfmisc_1(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_52])]) ).
fof(f171,plain,
! [X2,X3,X0,X1] :
( k4_relset_2(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,k1_zfmisc_1(X1)))) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( k4_relset_2(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,k1_zfmisc_1(X1)))) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1,X2,X3] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,k1_zfmisc_1(X1))))
=> k4_relset_2(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_relset_2) ).
fof(f478,plain,
spl18_51,
inference(avatar_split_clause,[],[f166,f476]) ).
fof(f476,plain,
( spl18_51
<=> ! [X2,X0,X1] :
( m2_relset_1(k6_relset_2(X0,X1,X2),k1_zfmisc_1(X1),k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_51])]) ).
fof(f166,plain,
! [X2,X0,X1] :
( m2_relset_1(k6_relset_2(X0,X1,X2),k1_zfmisc_1(X1),k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X0))) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( m2_relset_1(k6_relset_2(X0,X1,X2),k1_zfmisc_1(X1),k1_zfmisc_1(X0))
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X0))) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X0)))
=> m2_relset_1(k6_relset_2(X0,X1,X2),k1_zfmisc_1(X1),k1_zfmisc_1(X0)) ),
inference(pure_predicate_removal,[],[f57]) ).
fof(f57,plain,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X0)))
=> ( m2_relset_1(k6_relset_2(X0,X1,X2),k1_zfmisc_1(X1),k1_zfmisc_1(X0))
& v1_funct_1(k6_relset_2(X0,X1,X2)) ) ),
inference(pure_predicate_removal,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X0)))
=> ( m2_relset_1(k6_relset_2(X0,X1,X2),k1_zfmisc_1(X1),k1_zfmisc_1(X0))
& v1_funct_2(k6_relset_2(X0,X1,X2),k1_zfmisc_1(X1),k1_zfmisc_1(X0))
& v1_funct_1(k6_relset_2(X0,X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relset_2) ).
fof(f467,plain,
spl18_50,
inference(avatar_split_clause,[],[f165,f465]) ).
fof(f465,plain,
( spl18_50
<=> ! [X2,X0,X1] :
( k6_relset_2(X0,X1,X2) = k5_relset_2(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_50])]) ).
fof(f165,plain,
! [X2,X0,X1] :
( k6_relset_2(X0,X1,X2) = k5_relset_2(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X0))) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( k6_relset_2(X0,X1,X2) = k5_relset_2(X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X0))) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X0)))
=> k6_relset_2(X0,X1,X2) = k5_relset_2(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_relset_2) ).
fof(f453,plain,
spl18_49,
inference(avatar_split_clause,[],[f154,f451]) ).
fof(f451,plain,
( spl18_49
<=> ! [X0,X1] :
( X0 = X1
| ~ r2_hidden(sK10(X0,X1),X1)
| ~ r2_hidden(sK10(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_49])]) ).
fof(f154,plain,
! [X0,X1] :
( X0 = X1
| ~ r2_hidden(sK10(X0,X1),X1)
| ~ r2_hidden(sK10(X0,X1),X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ r2_hidden(sK10(X0,X1),X1)
| ~ r2_hidden(sK10(X0,X1),X0) )
& ( r2_hidden(sK10(X0,X1),X1)
| r2_hidden(sK10(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f107,f108]) ).
fof(f108,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) )
& ( r2_hidden(X2,X1)
| r2_hidden(X2,X0) ) )
=> ( ( ~ r2_hidden(sK10(X0,X1),X1)
| ~ r2_hidden(sK10(X0,X1),X0) )
& ( r2_hidden(sK10(X0,X1),X1)
| r2_hidden(sK10(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f107,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) )
& ( r2_hidden(X2,X1)
| r2_hidden(X2,X0) ) ) ),
inference(nnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( r2_hidden(X2,X0)
<~> r2_hidden(X2,X1) ) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0,X1] :
( ! [X2] :
( r2_hidden(X2,X0)
<=> r2_hidden(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f449,plain,
spl18_48,
inference(avatar_split_clause,[],[f153,f447]) ).
fof(f447,plain,
( spl18_48
<=> ! [X0,X1] :
( X0 = X1
| r2_hidden(sK10(X0,X1),X1)
| r2_hidden(sK10(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_48])]) ).
fof(f153,plain,
! [X0,X1] :
( X0 = X1
| r2_hidden(sK10(X0,X1),X1)
| r2_hidden(sK10(X0,X1),X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f443,plain,
( ~ spl18_11
| ~ spl18_43 ),
inference(avatar_contradiction_clause,[],[f439]) ).
fof(f439,plain,
( $false
| ~ spl18_11
| ~ spl18_43 ),
inference(resolution,[],[f394,f238]) ).
fof(f238,plain,
( ! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0))
| ~ spl18_11 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f237,plain,
( spl18_11
<=> ! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_11])]) ).
fof(f394,plain,
( v1_xboole_0(k1_zfmisc_1(sK3))
| ~ spl18_43 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f392,plain,
( spl18_43
<=> v1_xboole_0(k1_zfmisc_1(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_43])]) ).
fof(f434,plain,
spl18_47,
inference(avatar_split_clause,[],[f151,f432]) ).
fof(f432,plain,
( spl18_47
<=> ! [X0,X1] :
( m1_subset_1(k8_setfam_1(X0,X1),k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_47])]) ).
fof(f151,plain,
! [X0,X1] :
( m1_subset_1(k8_setfam_1(X0,X1),k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0))) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( m1_subset_1(k8_setfam_1(X0,X1),k1_zfmisc_1(X0))
| ~ m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0))) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
=> m1_subset_1(k8_setfam_1(X0,X1),k1_zfmisc_1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_setfam_1) ).
fof(f418,plain,
spl18_46,
inference(avatar_split_clause,[],[f167,f416]) ).
fof(f167,plain,
! [X2,X0,X1] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,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(f414,plain,
spl18_45,
inference(avatar_split_clause,[],[f163,f412]) ).
fof(f412,plain,
( spl18_45
<=> ! [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,[spl18_45])]) ).
fof(f163,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,[],[f79]) ).
fof(f79,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,[],[f21]) ).
fof(f21,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(f402,plain,
spl18_44,
inference(avatar_split_clause,[],[f170,f400]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,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(f395,plain,
( spl18_42
| spl18_43
| ~ spl18_1
| ~ spl18_37 ),
inference(avatar_split_clause,[],[f378,f355,f187,f392,f388]) ).
fof(f355,plain,
( spl18_37
<=> ! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_37])]) ).
fof(f378,plain,
( v1_xboole_0(k1_zfmisc_1(sK3))
| r2_hidden(sK5,k1_zfmisc_1(sK3))
| ~ spl18_1
| ~ spl18_37 ),
inference(resolution,[],[f356,f189]) ).
fof(f356,plain,
( ! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| v1_xboole_0(X1)
| r2_hidden(X0,X1) )
| ~ spl18_37 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f373,plain,
spl18_41,
inference(avatar_split_clause,[],[f169,f371]) ).
fof(f371,plain,
( spl18_41
<=> ! [X2,X0,X1] :
( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_41])]) ).
fof(f169,plain,
! [X2,X0,X1] :
( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,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,[],[f41]) ).
fof(f41,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(f369,plain,
spl18_40,
inference(avatar_split_clause,[],[f168,f367]) ).
fof(f367,plain,
( spl18_40
<=> ! [X2,X0,X1] :
( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_40])]) ).
fof(f168,plain,
! [X2,X0,X1] :
( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f365,plain,
spl18_39,
inference(avatar_split_clause,[],[f164,f363]) ).
fof(f363,plain,
( spl18_39
<=> ! [X2,X0,X1] :
( v1_relat_1(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_39])]) ).
fof(f164,plain,
! [X2,X0,X1] :
( v1_relat_1(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( v1_relat_1(X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1))) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
=> v1_relat_1(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f361,plain,
spl18_38,
inference(avatar_split_clause,[],[f152,f359]) ).
fof(f359,plain,
( spl18_38
<=> ! [X0,X1] :
( ~ v1_xboole_0(k2_zfmisc_1(X0,X1))
| v1_xboole_0(X1)
| v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_38])]) ).
fof(f152,plain,
! [X0,X1] :
( ~ v1_xboole_0(k2_zfmisc_1(X0,X1))
| v1_xboole_0(X1)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ~ v1_xboole_0(k2_zfmisc_1(X0,X1))
| v1_xboole_0(X1)
| v1_xboole_0(X0) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ~ v1_xboole_0(k2_zfmisc_1(X0,X1))
| v1_xboole_0(X1)
| v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( ( ~ v1_xboole_0(X1)
& ~ v1_xboole_0(X0) )
=> ~ v1_xboole_0(k2_zfmisc_1(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f357,plain,
spl18_37,
inference(avatar_split_clause,[],[f150,f355]) ).
fof(f150,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,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(f353,plain,
spl18_36,
inference(avatar_split_clause,[],[f149,f351]) ).
fof(f149,plain,
! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
| ~ m1_eqrel_1(X1,X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
| ~ m1_eqrel_1(X1,X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( m1_eqrel_1(X1,X0)
=> m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_eqrel_1) ).
fof(f349,plain,
( ~ spl18_35
| spl18_10
| ~ spl18_33 ),
inference(avatar_split_clause,[],[f340,f333,f232,f346]) ).
fof(f346,plain,
( spl18_35
<=> r1_tarski(a_6_0_relset_2(sK0,sK1,sK2,sK3,sK4,sK5),k1_zfmisc_1(sK4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_35])]) ).
fof(f333,plain,
( spl18_33
<=> ! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_33])]) ).
fof(f340,plain,
( ~ r1_tarski(a_6_0_relset_2(sK0,sK1,sK2,sK3,sK4,sK5),k1_zfmisc_1(sK4))
| spl18_10
| ~ spl18_33 ),
inference(resolution,[],[f334,f234]) ).
fof(f334,plain,
( ! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) )
| ~ spl18_33 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f339,plain,
spl18_34,
inference(avatar_split_clause,[],[f156,f337]) ).
fof(f337,plain,
( spl18_34
<=> ! [X0,X1] :
( ~ v1_xboole_0(X1)
| X0 = X1
| ~ v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_34])]) ).
fof(f156,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| X0 = X1
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| X0 = X1
| ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0,X1] :
~ ( v1_xboole_0(X1)
& X0 != X1
& v1_xboole_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f335,plain,
spl18_33,
inference(avatar_split_clause,[],[f155,f333]) ).
fof(f155,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( r1_tarski(X0,X1)
=> m1_subset_1(X0,k1_zfmisc_1(X1)) ),
inference(unused_predicate_definition_removal,[],[f47]) ).
fof(f47,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(f331,plain,
spl18_32,
inference(avatar_split_clause,[],[f136,f329]) ).
fof(f329,plain,
( spl18_32
<=> ! [X0] :
( m1_subset_1(sK6(X0),k1_zfmisc_1(X0))
| v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_32])]) ).
fof(f136,plain,
! [X0] :
( m1_subset_1(sK6(X0),k1_zfmisc_1(X0))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0] :
( ( ~ v1_xboole_0(sK6(X0))
& m1_subset_1(sK6(X0),k1_zfmisc_1(X0)) )
| v1_xboole_0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f62,f99]) ).
fof(f99,plain,
! [X0] :
( ? [X1] :
( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(X0)) )
=> ( ~ v1_xboole_0(sK6(X0))
& m1_subset_1(sK6(X0),k1_zfmisc_1(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
! [X0] :
( ? [X1] :
( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(X0)) )
| v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,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(f327,plain,
( spl18_31
| ~ spl18_7
| ~ spl18_22 ),
inference(avatar_split_clause,[],[f296,f284,f217,f324]) ).
fof(f324,plain,
( spl18_31
<=> k1_xboole_0 = sK16 ),
introduced(avatar_definition,[new_symbols(naming,[spl18_31])]) ).
fof(f217,plain,
( spl18_7
<=> v1_xboole_0(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_7])]) ).
fof(f284,plain,
( spl18_22
<=> ! [X0] :
( k1_xboole_0 = X0
| ~ v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_22])]) ).
fof(f296,plain,
( k1_xboole_0 = sK16
| ~ spl18_7
| ~ spl18_22 ),
inference(resolution,[],[f285,f219]) ).
fof(f219,plain,
( v1_xboole_0(sK16)
| ~ spl18_7 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f285,plain,
( ! [X0] :
( ~ v1_xboole_0(X0)
| k1_xboole_0 = X0 )
| ~ spl18_22 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f322,plain,
spl18_30,
inference(avatar_split_clause,[],[f160,f320]) ).
fof(f320,plain,
( spl18_30
<=> ! [X0,X1] : m1_relset_1(sK13(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_30])]) ).
fof(f160,plain,
! [X0,X1] : m1_relset_1(sK13(X0,X1),X0,X1),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( v1_relat_1(sK13(X0,X1))
& m1_relset_1(sK13(X0,X1),X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f59,f114]) ).
fof(f114,plain,
! [X0,X1] :
( ? [X2] :
( v1_relat_1(X2)
& m1_relset_1(X2,X0,X1) )
=> ( v1_relat_1(sK13(X0,X1))
& m1_relset_1(sK13(X0,X1),X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0,X1] :
? [X2] :
( v1_relat_1(X2)
& m1_relset_1(X2,X0,X1) ),
inference(pure_predicate_removal,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
? [X2] :
( v1_funct_1(X2)
& v1_relat_1(X2)
& m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_partfun1) ).
fof(f318,plain,
spl18_29,
inference(avatar_split_clause,[],[f159,f316]) ).
fof(f316,plain,
( spl18_29
<=> ! [X0,X1] : m2_relset_1(sK12(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_29])]) ).
fof(f159,plain,
! [X0,X1] : m2_relset_1(sK12(X0,X1),X0,X1),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1] : m2_relset_1(sK12(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f25,f112]) ).
fof(f112,plain,
! [X0,X1] :
( ? [X2] : m2_relset_1(X2,X0,X1)
=> m2_relset_1(sK12(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
! [X0,X1] :
? [X2] : m2_relset_1(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(f314,plain,
spl18_28,
inference(avatar_split_clause,[],[f158,f312]) ).
fof(f312,plain,
( spl18_28
<=> ! [X0,X1] : m1_relset_1(sK11(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_28])]) ).
fof(f158,plain,
! [X0,X1] : m1_relset_1(sK11(X0,X1),X0,X1),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1] : m1_relset_1(sK11(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f23,f110]) ).
fof(f110,plain,
! [X0,X1] :
( ? [X2] : m1_relset_1(X2,X0,X1)
=> m1_relset_1(sK11(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
! [X0,X1] :
? [X2] : m1_relset_1(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(f310,plain,
spl18_27,
inference(avatar_split_clause,[],[f148,f308]) ).
fof(f308,plain,
( spl18_27
<=> ! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_27])]) ).
fof(f148,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f306,plain,
spl18_26,
inference(avatar_split_clause,[],[f147,f304]) ).
fof(f147,plain,
! [X0,X1] :
( ~ r2_hidden(X1,X0)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,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(f302,plain,
spl18_25,
inference(avatar_split_clause,[],[f146,f300]) ).
fof(f300,plain,
( spl18_25
<=> ! [X0,X1] :
( v1_relat_1(k5_relset_2(X0,X1))
| ~ v1_relat_1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_25])]) ).
fof(f146,plain,
! [X0,X1] :
( v1_relat_1(k5_relset_2(X0,X1))
| ~ v1_relat_1(X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( v1_relat_1(k5_relset_2(X0,X1))
| ~ v1_relat_1(X1) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( v1_relat_1(X1)
=> v1_relat_1(k5_relset_2(X0,X1)) ),
inference(pure_predicate_removal,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( v1_relat_1(X1)
=> ( v1_funct_1(k5_relset_2(X0,X1))
& v1_relat_1(k5_relset_2(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relset_2) ).
fof(f294,plain,
spl18_24,
inference(avatar_split_clause,[],[f157,f292]) ).
fof(f292,plain,
( spl18_24
<=> ! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_24])]) ).
fof(f157,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0,X1] :
~ ( v1_xboole_0(X1)
& r2_hidden(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f290,plain,
spl18_23,
inference(avatar_split_clause,[],[f142,f288]) ).
fof(f288,plain,
( spl18_23
<=> ! [X0] : m1_subset_1(sK9(X0),k1_zfmisc_1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_23])]) ).
fof(f142,plain,
! [X0] : m1_subset_1(sK9(X0),k1_zfmisc_1(X0)),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0] :
( v1_xboole_0(sK9(X0))
& m1_subset_1(sK9(X0),k1_zfmisc_1(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f36,f105]) ).
fof(f105,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(f36,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(f286,plain,
spl18_22,
inference(avatar_split_clause,[],[f139,f284]) ).
fof(f139,plain,
! [X0] :
( k1_xboole_0 = X0
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( k1_xboole_0 = X0
| ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] :
( v1_xboole_0(X0)
=> k1_xboole_0 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f282,plain,
spl18_21,
inference(avatar_split_clause,[],[f137,f280]) ).
fof(f280,plain,
( spl18_21
<=> ! [X0] :
( ~ v1_xboole_0(sK6(X0))
| v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_21])]) ).
fof(f137,plain,
! [X0] :
( ~ v1_xboole_0(sK6(X0))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f278,plain,
( spl18_20
| ~ spl18_12
| ~ spl18_15 ),
inference(avatar_split_clause,[],[f274,f253,f241,f276]) ).
fof(f276,plain,
( spl18_20
<=> ! [X0] : v1_relat_1(sK9(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_20])]) ).
fof(f241,plain,
( spl18_12
<=> ! [X0] : v1_xboole_0(sK9(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_12])]) ).
fof(f253,plain,
( spl18_15
<=> ! [X0] :
( v1_relat_1(X0)
| ~ v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_15])]) ).
fof(f274,plain,
( ! [X0] : v1_relat_1(sK9(X0))
| ~ spl18_12
| ~ spl18_15 ),
inference(resolution,[],[f254,f242]) ).
fof(f242,plain,
( ! [X0] : v1_xboole_0(sK9(X0))
| ~ spl18_12 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f254,plain,
( ! [X0] :
( ~ v1_xboole_0(X0)
| v1_relat_1(X0) )
| ~ spl18_15 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f271,plain,
spl18_19,
inference(avatar_split_clause,[],[f161,f269]) ).
fof(f269,plain,
( spl18_19
<=> ! [X0,X1] : v1_relat_1(sK13(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_19])]) ).
fof(f161,plain,
! [X0,X1] : v1_relat_1(sK13(X0,X1)),
inference(cnf_transformation,[],[f115]) ).
fof(f267,plain,
spl18_18,
inference(avatar_split_clause,[],[f145,f265]) ).
fof(f265,plain,
( spl18_18
<=> ! [X0,X1] : v1_relat_1(k2_zfmisc_1(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_18])]) ).
fof(f145,plain,
! [X0,X1] : v1_relat_1(k2_zfmisc_1(X0,X1)),
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] : v1_relat_1(k2_zfmisc_1(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_sysrel) ).
fof(f263,plain,
spl18_17,
inference(avatar_split_clause,[],[f141,f261]) ).
fof(f261,plain,
( spl18_17
<=> ! [X0] : m1_subset_1(sK8(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_17])]) ).
fof(f141,plain,
! [X0] : m1_subset_1(sK8(X0),X0),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] : m1_subset_1(sK8(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f24,f103]) ).
fof(f103,plain,
! [X0] :
( ? [X1] : m1_subset_1(X1,X0)
=> m1_subset_1(sK8(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
! [X0] :
? [X1] : m1_subset_1(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f259,plain,
spl18_16,
inference(avatar_split_clause,[],[f140,f257]) ).
fof(f257,plain,
( spl18_16
<=> ! [X0] : m1_eqrel_1(sK7(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_16])]) ).
fof(f140,plain,
! [X0] : m1_eqrel_1(sK7(X0),X0),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] : m1_eqrel_1(sK7(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f22,f101]) ).
fof(f101,plain,
! [X0] :
( ? [X1] : m1_eqrel_1(X1,X0)
=> m1_eqrel_1(sK7(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
! [X0] :
? [X1] : m1_eqrel_1(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_eqrel_1) ).
fof(f255,plain,
spl18_15,
inference(avatar_split_clause,[],[f138,f253]) ).
fof(f138,plain,
! [X0] :
( v1_relat_1(X0)
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( v1_relat_1(X0)
| ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( v1_xboole_0(X0)
=> v1_relat_1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f251,plain,
spl18_14,
inference(avatar_split_clause,[],[f135,f249]) ).
fof(f249,plain,
( spl18_14
<=> ! [X0] : m1_eqrel_1(k3_pua2mss1(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_14])]) ).
fof(f135,plain,
! [X0] : m1_eqrel_1(k3_pua2mss1(X0),X0),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : m1_eqrel_1(k3_pua2mss1(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_pua2mss1) ).
fof(f247,plain,
spl18_13,
inference(avatar_split_clause,[],[f144,f245]) ).
fof(f245,plain,
( spl18_13
<=> ! [X0] : r1_tarski(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_13])]) ).
fof(f144,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f243,plain,
spl18_12,
inference(avatar_split_clause,[],[f143,f241]) ).
fof(f143,plain,
! [X0] : v1_xboole_0(sK9(X0)),
inference(cnf_transformation,[],[f106]) ).
fof(f239,plain,
spl18_11,
inference(avatar_split_clause,[],[f134,f237]) ).
fof(f134,plain,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f235,plain,
~ spl18_10,
inference(avatar_split_clause,[],[f129,f232]) ).
fof(f129,plain,
~ m1_subset_1(a_6_0_relset_2(sK0,sK1,sK2,sK3,sK4,sK5),k1_zfmisc_1(k1_zfmisc_1(sK4))),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
( ~ m1_subset_1(a_6_0_relset_2(sK0,sK1,sK2,sK3,sK4,sK5),k1_zfmisc_1(k1_zfmisc_1(sK4)))
& m1_subset_1(sK5,k1_zfmisc_1(sK3))
& m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f61,f97,f96]) ).
fof(f96,plain,
( ? [X0,X1,X2] :
( ? [X3,X4,X5] :
( ~ m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
& m1_subset_1(X5,k1_zfmisc_1(X3)) )
& m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1)))) )
=> ( ? [X5,X4,X3] :
( ~ m1_subset_1(a_6_0_relset_2(sK0,sK1,sK2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
& m1_subset_1(X5,k1_zfmisc_1(X3)) )
& m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))) ) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
( ? [X5,X4,X3] :
( ~ m1_subset_1(a_6_0_relset_2(sK0,sK1,sK2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
& m1_subset_1(X5,k1_zfmisc_1(X3)) )
=> ( ~ m1_subset_1(a_6_0_relset_2(sK0,sK1,sK2,sK3,sK4,sK5),k1_zfmisc_1(k1_zfmisc_1(sK4)))
& m1_subset_1(sK5,k1_zfmisc_1(sK3)) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
? [X0,X1,X2] :
( ? [X3,X4,X5] :
( ~ m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4)))
& m1_subset_1(X5,k1_zfmisc_1(X3)) )
& m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1)))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1))))
=> ! [X3,X4,X5] :
( m1_subset_1(X5,k1_zfmisc_1(X3))
=> m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4))) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0,X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(X0,X1))))
=> ! [X3,X4,X5] :
( m1_subset_1(X5,k1_zfmisc_1(X3))
=> m1_subset_1(a_6_0_relset_2(X0,X1,X2,X3,X4,X5),k1_zfmisc_1(k1_zfmisc_1(X4))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_relset_2) ).
fof(f230,plain,
spl18_9,
inference(avatar_split_clause,[],[f184,f227]) ).
fof(f227,plain,
( spl18_9
<=> v1_relat_1(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_9])]) ).
fof(f184,plain,
v1_relat_1(sK17),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
v1_relat_1(sK17),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f55,f125]) ).
fof(f125,plain,
( ? [X0] : v1_relat_1(X0)
=> v1_relat_1(sK17) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
? [X0] : v1_relat_1(X0),
inference(pure_predicate_removal,[],[f37]) ).
fof(f37,axiom,
? [X0] :
( v3_relat_1(X0)
& v1_relat_1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f225,plain,
spl18_8,
inference(avatar_split_clause,[],[f183,f222]) ).
fof(f222,plain,
( spl18_8
<=> v1_relat_1(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_8])]) ).
fof(f183,plain,
v1_relat_1(sK16),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
( v1_relat_1(sK16)
& v1_xboole_0(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f32,f123]) ).
fof(f123,plain,
( ? [X0] :
( v1_relat_1(X0)
& v1_xboole_0(X0) )
=> ( v1_relat_1(sK16)
& v1_xboole_0(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f32,axiom,
? [X0] :
( v1_relat_1(X0)
& v1_xboole_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f220,plain,
spl18_7,
inference(avatar_split_clause,[],[f182,f217]) ).
fof(f182,plain,
v1_xboole_0(sK16),
inference(cnf_transformation,[],[f124]) ).
fof(f215,plain,
spl18_6,
inference(avatar_split_clause,[],[f181,f212]) ).
fof(f212,plain,
( spl18_6
<=> v1_relat_1(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_6])]) ).
fof(f181,plain,
v1_relat_1(sK15),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
( v1_relat_1(sK15)
& ~ v1_xboole_0(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f35,f121]) ).
fof(f121,plain,
( ? [X0] :
( v1_relat_1(X0)
& ~ v1_xboole_0(X0) )
=> ( v1_relat_1(sK15)
& ~ v1_xboole_0(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f35,axiom,
? [X0] :
( v1_relat_1(X0)
& ~ v1_xboole_0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f210,plain,
~ spl18_5,
inference(avatar_split_clause,[],[f180,f207]) ).
fof(f207,plain,
( spl18_5
<=> v1_xboole_0(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_5])]) ).
fof(f180,plain,
~ v1_xboole_0(sK15),
inference(cnf_transformation,[],[f122]) ).
fof(f205,plain,
spl18_4,
inference(avatar_split_clause,[],[f131,f202]) ).
fof(f202,plain,
( spl18_4
<=> v1_relat_1(k1_xboole_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_4])]) ).
fof(f131,plain,
v1_relat_1(k1_xboole_0),
inference(cnf_transformation,[],[f29]) ).
fof(f29,axiom,
( v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f200,plain,
spl18_3,
inference(avatar_split_clause,[],[f130,f197]) ).
fof(f197,plain,
( spl18_3
<=> v1_xboole_0(k1_xboole_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_3])]) ).
fof(f130,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f29]) ).
fof(f195,plain,
spl18_2,
inference(avatar_split_clause,[],[f127,f192]) ).
fof(f127,plain,
m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(sK0,sK1)))),
inference(cnf_transformation,[],[f98]) ).
fof(f190,plain,
spl18_1,
inference(avatar_split_clause,[],[f128,f187]) ).
fof(f128,plain,
m1_subset_1(sK5,k1_zfmisc_1(sK3)),
inference(cnf_transformation,[],[f98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU435+1 : TPTP v8.1.2. Released v3.4.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Apr 29 20:36:47 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (1182)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (1185)WARNING: value z3 for option sas not known
% 0.15/0.38 % (1183)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (1186)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (1184)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (1185)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (1187)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (1188)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 % (1189)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 % (1187)First to succeed.
% 0.15/0.39 TRYING [1]
% 0.15/0.40 TRYING [2]
% 0.15/0.40 TRYING [3]
% 0.15/0.40 % (1187)Refutation found. Thanks to Tanya!
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40 % (1187)------------------------------
% 0.15/0.40 % (1187)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.40 % (1187)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (1187)Memory used [KB]: 1047
% 0.15/0.40 % (1187)Time elapsed: 0.019 s
% 0.15/0.40 % (1187)Instructions burned: 27 (million)
% 0.15/0.40 % (1187)------------------------------
% 0.15/0.40 % (1187)------------------------------
% 0.15/0.40 % (1182)Success in time 0.036 s
%------------------------------------------------------------------------------