TSTP Solution File: SEU424+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU424+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 : n028.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 15:34:21 EDT 2024
% Result : Theorem 0.10s 0.29s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 90
% Syntax : Number of formulae : 246 ( 72 unt; 0 def)
% Number of atoms : 643 ( 41 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 654 ( 257 ~; 242 |; 66 &)
% ( 53 <=>; 35 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 56 ( 54 usr; 48 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-5 aty)
% Number of variables : 433 ( 391 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f438,plain,
$false,
inference(avatar_sat_refutation,[],[f156,f161,f166,f171,f176,f181,f186,f190,f194,f198,f202,f206,f210,f214,f218,f222,f230,f234,f239,f243,f247,f251,f255,f259,f269,f273,f277,f281,f295,f299,f309,f313,f326,f333,f337,f342,f358,f365,f369,f380,f384,f388,f399,f406,f423,f427,f436,f437]) ).
fof(f437,plain,
( spl13_1
| ~ spl13_2
| ~ spl13_3
| spl13_7
| ~ spl13_39 ),
inference(avatar_split_clause,[],[f373,f367,f183,f163,f158,f153]) ).
fof(f153,plain,
( spl13_1
<=> v1_xboole_0(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_1])]) ).
fof(f158,plain,
( spl13_2
<=> m1_subset_1(sK2,k1_zfmisc_1(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_2])]) ).
fof(f163,plain,
( spl13_3
<=> m2_relset_1(sK3,sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_3])]) ).
fof(f183,plain,
( spl13_7
<=> m1_subset_1(a_4_0_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_7])]) ).
fof(f367,plain,
( spl13_39
<=> ! [X0,X3,X2,X1] :
( m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| ~ m2_relset_1(X3,X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_39])]) ).
fof(f373,plain,
( ~ m2_relset_1(sK3,sK0,sK1)
| ~ m1_subset_1(sK2,k1_zfmisc_1(sK0))
| v1_xboole_0(sK0)
| spl13_7
| ~ spl13_39 ),
inference(resolution,[],[f368,f185]) ).
fof(f185,plain,
( ~ m1_subset_1(a_4_0_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK1)))
| spl13_7 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f368,plain,
( ! [X2,X3,X0,X1] :
( m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| ~ m2_relset_1(X3,X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| v1_xboole_0(X0) )
| ~ spl13_39 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f436,plain,
( ~ spl13_47
| spl13_7
| ~ spl13_23 ),
inference(avatar_split_clause,[],[f261,f253,f183,f433]) ).
fof(f433,plain,
( spl13_47
<=> r1_tarski(a_4_0_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_47])]) ).
fof(f253,plain,
( spl13_23
<=> ! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_23])]) ).
fof(f261,plain,
( ~ r1_tarski(a_4_0_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(sK1))
| spl13_7
| ~ spl13_23 ),
inference(resolution,[],[f254,f185]) ).
fof(f254,plain,
( ! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) )
| ~ spl13_23 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f427,plain,
( ~ spl13_9
| ~ spl13_46 ),
inference(avatar_contradiction_clause,[],[f424]) ).
fof(f424,plain,
( $false
| ~ spl13_9
| ~ spl13_46 ),
inference(resolution,[],[f422,f193]) ).
fof(f193,plain,
( ! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0))
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f192,plain,
( spl13_9
<=> ! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_9])]) ).
fof(f422,plain,
( v1_xboole_0(k1_zfmisc_1(sK0))
| ~ spl13_46 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f420,plain,
( spl13_46
<=> v1_xboole_0(k1_zfmisc_1(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_46])]) ).
fof(f423,plain,
( spl13_45
| spl13_46
| ~ spl13_2
| ~ spl13_25 ),
inference(avatar_split_clause,[],[f283,f267,f158,f420,f416]) ).
fof(f416,plain,
( spl13_45
<=> r2_hidden(sK2,k1_zfmisc_1(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_45])]) ).
fof(f267,plain,
( spl13_25
<=> ! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_25])]) ).
fof(f283,plain,
( v1_xboole_0(k1_zfmisc_1(sK0))
| r2_hidden(sK2,k1_zfmisc_1(sK0))
| ~ spl13_2
| ~ spl13_25 ),
inference(resolution,[],[f268,f160]) ).
fof(f160,plain,
( m1_subset_1(sK2,k1_zfmisc_1(sK0))
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f268,plain,
( ! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| v1_xboole_0(X1)
| r2_hidden(X0,X1) )
| ~ spl13_25 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f406,plain,
spl13_44,
inference(avatar_split_clause,[],[f146,f404]) ).
fof(f404,plain,
( spl13_44
<=> ! [X4,X0,X3,X2,X1] :
( k2_relset_2(X1,X2,X4,sK10(X0,X1,X2,X3,X4)) = X0
| ~ r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| v1_xboole_0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_44])]) ).
fof(f146,plain,
! [X2,X3,X0,X1,X4] :
( k2_relset_2(X1,X2,X4,sK10(X0,X1,X2,X3,X4)) = X0
| ~ r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2,X3,X4] :
( ( ( r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
| ! [X5] :
( ~ r2_hidden(X5,X3)
| k2_relset_2(X1,X2,X4,X5) != X0
| ~ m1_subset_1(X5,X1) ) )
& ( ( r2_hidden(sK10(X0,X1,X2,X3,X4),X3)
& k2_relset_2(X1,X2,X4,sK10(X0,X1,X2,X3,X4)) = X0
& m1_subset_1(sK10(X0,X1,X2,X3,X4),X1) )
| ~ r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4)) ) )
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| v1_xboole_0(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f102,f103]) ).
fof(f103,plain,
! [X0,X1,X2,X3,X4] :
( ? [X6] :
( r2_hidden(X6,X3)
& k2_relset_2(X1,X2,X4,X6) = X0
& m1_subset_1(X6,X1) )
=> ( r2_hidden(sK10(X0,X1,X2,X3,X4),X3)
& k2_relset_2(X1,X2,X4,sK10(X0,X1,X2,X3,X4)) = X0
& m1_subset_1(sK10(X0,X1,X2,X3,X4),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X1,X2,X3,X4] :
( ( ( r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
| ! [X5] :
( ~ r2_hidden(X5,X3)
| k2_relset_2(X1,X2,X4,X5) != X0
| ~ m1_subset_1(X5,X1) ) )
& ( ? [X6] :
( r2_hidden(X6,X3)
& k2_relset_2(X1,X2,X4,X6) = X0
& m1_subset_1(X6,X1) )
| ~ r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4)) ) )
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| v1_xboole_0(X1) ),
inference(rectify,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2,X3,X4] :
( ( ( r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
| ! [X5] :
( ~ r2_hidden(X5,X3)
| k2_relset_2(X1,X2,X4,X5) != X0
| ~ m1_subset_1(X5,X1) ) )
& ( ? [X5] :
( r2_hidden(X5,X3)
& k2_relset_2(X1,X2,X4,X5) = X0
& m1_subset_1(X5,X1) )
| ~ r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4)) ) )
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| v1_xboole_0(X1) ),
inference(nnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2,X3,X4] :
( ( r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
<=> ? [X5] :
( r2_hidden(X5,X3)
& k2_relset_2(X1,X2,X4,X5) = X0
& m1_subset_1(X5,X1) ) )
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| v1_xboole_0(X1) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2,X3,X4] :
( ( r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
<=> ? [X5] :
( r2_hidden(X5,X3)
& k2_relset_2(X1,X2,X4,X5) = X0
& m1_subset_1(X5,X1) ) )
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0,X1,X2,X3,X4] :
( ( m2_relset_1(X4,X1,X2)
& m1_subset_1(X3,k1_zfmisc_1(X1))
& ~ v1_xboole_0(X1) )
=> ( r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
<=> ? [X5] :
( r2_hidden(X5,X3)
& k2_relset_2(X1,X2,X4,X5) = X0
& m1_subset_1(X5,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_4_0_relset_2) ).
fof(f399,plain,
spl13_43,
inference(avatar_split_clause,[],[f151,f397]) ).
fof(f397,plain,
( spl13_43
<=> ! [X5,X4,X3,X2,X1] :
( r2_hidden(k2_relset_2(X1,X2,X4,X5),a_4_0_relset_2(X1,X2,X3,X4))
| ~ r2_hidden(X5,X3)
| ~ m1_subset_1(X5,X1)
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| v1_xboole_0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_43])]) ).
fof(f151,plain,
! [X2,X3,X1,X4,X5] :
( r2_hidden(k2_relset_2(X1,X2,X4,X5),a_4_0_relset_2(X1,X2,X3,X4))
| ~ r2_hidden(X5,X3)
| ~ m1_subset_1(X5,X1)
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| v1_xboole_0(X1) ),
inference(equality_resolution,[],[f148]) ).
fof(f148,plain,
! [X2,X3,X0,X1,X4,X5] :
( r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
| ~ r2_hidden(X5,X3)
| k2_relset_2(X1,X2,X4,X5) != X0
| ~ m1_subset_1(X5,X1)
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f388,plain,
spl13_42,
inference(avatar_split_clause,[],[f147,f386]) ).
fof(f386,plain,
( spl13_42
<=> ! [X4,X0,X3,X2,X1] :
( r2_hidden(sK10(X0,X1,X2,X3,X4),X3)
| ~ r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| v1_xboole_0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_42])]) ).
fof(f147,plain,
! [X2,X3,X0,X1,X4] :
( r2_hidden(sK10(X0,X1,X2,X3,X4),X3)
| ~ r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f384,plain,
spl13_41,
inference(avatar_split_clause,[],[f145,f382]) ).
fof(f382,plain,
( spl13_41
<=> ! [X4,X0,X3,X2,X1] :
( m1_subset_1(sK10(X0,X1,X2,X3,X4),X1)
| ~ r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| v1_xboole_0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_41])]) ).
fof(f145,plain,
! [X2,X3,X0,X1,X4] :
( m1_subset_1(sK10(X0,X1,X2,X3,X4),X1)
| ~ r2_hidden(X0,a_4_0_relset_2(X1,X2,X3,X4))
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f380,plain,
( spl13_40
| ~ spl13_2
| ~ spl13_32 ),
inference(avatar_split_clause,[],[f318,f311,f158,f378]) ).
fof(f378,plain,
( spl13_40
<=> ! [X0] :
( m1_subset_1(X0,sK0)
| ~ r2_hidden(X0,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_40])]) ).
fof(f311,plain,
( spl13_32
<=> ! [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,[spl13_32])]) ).
fof(f318,plain,
( ! [X0] :
( m1_subset_1(X0,sK0)
| ~ r2_hidden(X0,sK2) )
| ~ spl13_2
| ~ spl13_32 ),
inference(resolution,[],[f312,f160]) ).
fof(f312,plain,
( ! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| m1_subset_1(X0,X2)
| ~ r2_hidden(X0,X1) )
| ~ spl13_32 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f369,plain,
spl13_39,
inference(avatar_split_clause,[],[f143,f367]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| ~ m2_relset_1(X3,X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| ~ m2_relset_1(X3,X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| v1_xboole_0(X0) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
| ~ m2_relset_1(X3,X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(X0))
| v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1,X2,X3] :
( ( m2_relset_1(X3,X0,X1)
& m1_subset_1(X2,k1_zfmisc_1(X0))
& ~ v1_xboole_0(X0) )
=> m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s8_domain_1__e1_22__relset_2) ).
fof(f365,plain,
spl13_38,
inference(avatar_split_clause,[],[f136,f363]) ).
fof(f363,plain,
( spl13_38
<=> ! [X0,X3,X2,X1] :
( k2_relset_2(X0,X1,X2,X3) = k10_relset_1(X0,X1,X2,k1_tarski(X3))
| ~ m1_subset_1(X3,X0)
| ~ m2_relset_1(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_38])]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( k2_relset_2(X0,X1,X2,X3) = k10_relset_1(X0,X1,X2,k1_tarski(X3))
| ~ m1_subset_1(X3,X0)
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ! [X3] :
( k2_relset_2(X0,X1,X2,X3) = k10_relset_1(X0,X1,X2,k1_tarski(X3))
| ~ m1_subset_1(X3,X0) )
| ~ m2_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
=> ! [X3] :
( m1_subset_1(X3,X0)
=> k2_relset_2(X0,X1,X2,X3) = k10_relset_1(X0,X1,X2,k1_tarski(X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relset_2) ).
fof(f358,plain,
spl13_37,
inference(avatar_split_clause,[],[f144,f356]) ).
fof(f356,plain,
( spl13_37
<=> ! [X0,X3,X2,X1] :
( m1_subset_1(k2_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,X0)
| ~ m1_relset_1(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_37])]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(k2_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,X0)
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(k2_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,X0)
| ~ m1_relset_1(X2,X0,X1) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(k2_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,X0)
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1,X2,X3] :
( ( m1_subset_1(X3,X0)
& m1_relset_1(X2,X0,X1) )
=> m1_subset_1(k2_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_relset_2) ).
fof(f342,plain,
spl13_36,
inference(avatar_split_clause,[],[f142,f340]) ).
fof(f340,plain,
( spl13_36
<=> ! [X0,X3,X2,X1] :
( k10_relset_1(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ m1_relset_1(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_36])]) ).
fof(f142,plain,
! [X2,X3,X0,X1] :
( k10_relset_1(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2,X3] :
( k10_relset_1(X0,X1,X2,X3) = k9_relat_1(X2,X3)
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1,X2,X3] :
( m1_relset_1(X2,X0,X1)
=> k10_relset_1(X0,X1,X2,X3) = k9_relat_1(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k10_relset_1) ).
fof(f337,plain,
spl13_35,
inference(avatar_split_clause,[],[f129,f335]) ).
fof(f335,plain,
( spl13_35
<=> ! [X0,X1] :
( X0 = X1
| ~ r2_hidden(sK7(X0,X1),X1)
| ~ r2_hidden(sK7(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_35])]) ).
fof(f129,plain,
! [X0,X1] :
( X0 = X1
| ~ r2_hidden(sK7(X0,X1),X1)
| ~ r2_hidden(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ r2_hidden(sK7(X0,X1),X1)
| ~ r2_hidden(sK7(X0,X1),X0) )
& ( r2_hidden(sK7(X0,X1),X1)
| r2_hidden(sK7(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f93,f94]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) )
& ( r2_hidden(X2,X1)
| r2_hidden(X2,X0) ) )
=> ( ( ~ r2_hidden(sK7(X0,X1),X1)
| ~ r2_hidden(sK7(X0,X1),X0) )
& ( r2_hidden(sK7(X0,X1),X1)
| r2_hidden(sK7(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f93,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,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( r2_hidden(X2,X0)
<~> r2_hidden(X2,X1) ) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
( ! [X2] :
( r2_hidden(X2,X0)
<=> r2_hidden(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f333,plain,
spl13_34,
inference(avatar_split_clause,[],[f128,f331]) ).
fof(f331,plain,
( spl13_34
<=> ! [X0,X1] :
( X0 = X1
| r2_hidden(sK7(X0,X1),X1)
| r2_hidden(sK7(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_34])]) ).
fof(f128,plain,
! [X0,X1] :
( X0 = X1
| r2_hidden(sK7(X0,X1),X1)
| r2_hidden(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f326,plain,
spl13_33,
inference(avatar_split_clause,[],[f141,f324]) ).
fof(f324,plain,
( spl13_33
<=> ! [X0,X3,X2,X1] :
( m1_subset_1(k10_relset_1(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_relset_1(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_33])]) ).
fof(f141,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(k10_relset_1(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(k10_relset_1(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_relset_1(X2,X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( m1_relset_1(X2,X0,X1)
=> m1_subset_1(k10_relset_1(X0,X1,X2,X3),k1_zfmisc_1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k10_relset_1) ).
fof(f313,plain,
spl13_32,
inference(avatar_split_clause,[],[f137,f311]) ).
fof(f137,plain,
! [X2,X0,X1] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2] :
( m1_subset_1(X0,X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(flattening,[],[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(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( m1_subset_1(X1,k1_zfmisc_1(X2))
& r2_hidden(X0,X1) )
=> m1_subset_1(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f309,plain,
spl13_31,
inference(avatar_split_clause,[],[f135,f307]) ).
fof(f307,plain,
( spl13_31
<=> ! [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,[spl13_31])]) ).
fof(f135,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,[],[f16]) ).
fof(f16,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/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f299,plain,
spl13_30,
inference(avatar_split_clause,[],[f140,f297]) ).
fof(f297,plain,
( spl13_30
<=> ! [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,[spl13_30])]) ).
fof(f140,plain,
! [X2,X0,X1] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1,X2] :
~ ( v1_xboole_0(X2)
& m1_subset_1(X1,k1_zfmisc_1(X2))
& r2_hidden(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f295,plain,
( spl13_29
| ~ spl13_3
| ~ spl13_27 ),
inference(avatar_split_clause,[],[f288,f275,f163,f292]) ).
fof(f292,plain,
( spl13_29
<=> m1_relset_1(sK3,sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_29])]) ).
fof(f275,plain,
( spl13_27
<=> ! [X2,X0,X1] :
( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_27])]) ).
fof(f288,plain,
( m1_relset_1(sK3,sK0,sK1)
| ~ spl13_3
| ~ spl13_27 ),
inference(resolution,[],[f276,f165]) ).
fof(f165,plain,
( m2_relset_1(sK3,sK0,sK1)
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f276,plain,
( ! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) )
| ~ spl13_27 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f281,plain,
spl13_28,
inference(avatar_split_clause,[],[f139,f279]) ).
fof(f279,plain,
( spl13_28
<=> ! [X2,X0,X1] :
( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_28])]) ).
fof(f139,plain,
! [X2,X0,X1] :
( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,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,[],[f33]) ).
fof(f33,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X0,X1)
<=> m1_relset_1(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f277,plain,
spl13_27,
inference(avatar_split_clause,[],[f138,f275]) ).
fof(f138,plain,
! [X2,X0,X1] :
( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f273,plain,
spl13_26,
inference(avatar_split_clause,[],[f127,f271]) ).
fof(f271,plain,
( spl13_26
<=> ! [X0,X1] :
( ~ v1_xboole_0(k2_zfmisc_1(X0,X1))
| v1_xboole_0(X1)
| v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_26])]) ).
fof(f127,plain,
! [X0,X1] :
( ~ v1_xboole_0(k2_zfmisc_1(X0,X1))
| v1_xboole_0(X1)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ~ v1_xboole_0(k2_zfmisc_1(X0,X1))
| v1_xboole_0(X1)
| v1_xboole_0(X0) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( ~ v1_xboole_0(k2_zfmisc_1(X0,X1))
| v1_xboole_0(X1)
| v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] :
( ( ~ v1_xboole_0(X1)
& ~ v1_xboole_0(X0) )
=> ~ v1_xboole_0(k2_zfmisc_1(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f269,plain,
spl13_25,
inference(avatar_split_clause,[],[f126,f267]) ).
fof(f126,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ),
inference(flattening,[],[f62]) ).
fof(f62,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/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f259,plain,
spl13_24,
inference(avatar_split_clause,[],[f131,f257]) ).
fof(f257,plain,
( spl13_24
<=> ! [X0,X1] :
( ~ v1_xboole_0(X1)
| X0 = X1
| ~ v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_24])]) ).
fof(f131,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,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
~ ( v1_xboole_0(X1)
& X0 != X1
& v1_xboole_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f255,plain,
spl13_23,
inference(avatar_split_clause,[],[f130,f253]) ).
fof(f130,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,[],[f39]) ).
fof(f39,axiom,
! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
<=> r1_tarski(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f251,plain,
spl13_22,
inference(avatar_split_clause,[],[f117,f249]) ).
fof(f249,plain,
( spl13_22
<=> ! [X0] :
( m1_subset_1(sK4(X0),k1_zfmisc_1(X0))
| v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_22])]) ).
fof(f117,plain,
! [X0] :
( m1_subset_1(sK4(X0),k1_zfmisc_1(X0))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ( ~ v1_xboole_0(sK4(X0))
& m1_subset_1(sK4(X0),k1_zfmisc_1(X0)) )
| v1_xboole_0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f58,f87]) ).
fof(f87,plain,
! [X0] :
( ? [X1] :
( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(X0)) )
=> ( ~ v1_xboole_0(sK4(X0))
& m1_subset_1(sK4(X0),k1_zfmisc_1(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f58,plain,
! [X0] :
( ? [X1] :
( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(X0)) )
| v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ~ v1_xboole_0(X0)
=> ? [X1] :
( ~ v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f247,plain,
spl13_21,
inference(avatar_split_clause,[],[f134,f245]) ).
fof(f245,plain,
( spl13_21
<=> ! [X0,X1] : m2_relset_1(sK9(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_21])]) ).
fof(f134,plain,
! [X0,X1] : m2_relset_1(sK9(X0,X1),X0,X1),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1] : m2_relset_1(sK9(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f19,f98]) ).
fof(f98,plain,
! [X0,X1] :
( ? [X2] : m2_relset_1(X2,X0,X1)
=> m2_relset_1(sK9(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
! [X0,X1] :
? [X2] : m2_relset_1(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(f243,plain,
spl13_20,
inference(avatar_split_clause,[],[f133,f241]) ).
fof(f241,plain,
( spl13_20
<=> ! [X0,X1] : m1_relset_1(sK8(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_20])]) ).
fof(f133,plain,
! [X0,X1] : m1_relset_1(sK8(X0,X1),X0,X1),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1] : m1_relset_1(sK8(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f17,f96]) ).
fof(f96,plain,
! [X0,X1] :
( ? [X2] : m1_relset_1(X2,X0,X1)
=> m1_relset_1(sK8(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f17,axiom,
! [X0,X1] :
? [X2] : m1_relset_1(X2,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(f239,plain,
( spl13_19
| ~ spl13_6
| ~ spl13_14 ),
inference(avatar_split_clause,[],[f224,f212,f178,f236]) ).
fof(f236,plain,
( spl13_19
<=> k1_xboole_0 = sK12 ),
introduced(avatar_definition,[new_symbols(naming,[spl13_19])]) ).
fof(f178,plain,
( spl13_6
<=> v1_xboole_0(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_6])]) ).
fof(f212,plain,
( spl13_14
<=> ! [X0] :
( k1_xboole_0 = X0
| ~ v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_14])]) ).
fof(f224,plain,
( k1_xboole_0 = sK12
| ~ spl13_6
| ~ spl13_14 ),
inference(resolution,[],[f213,f180]) ).
fof(f180,plain,
( v1_xboole_0(sK12)
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f213,plain,
( ! [X0] :
( ~ v1_xboole_0(X0)
| k1_xboole_0 = X0 )
| ~ spl13_14 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f234,plain,
spl13_18,
inference(avatar_split_clause,[],[f125,f232]) ).
fof(f232,plain,
( spl13_18
<=> ! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_18])]) ).
fof(f125,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
( r2_hidden(X0,X1)
=> m1_subset_1(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f230,plain,
spl13_17,
inference(avatar_split_clause,[],[f124,f228]) ).
fof(f228,plain,
( spl13_17
<=> ! [X0,X1] :
( ~ r2_hidden(X1,X0)
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_17])]) ).
fof(f124,plain,
! [X0,X1] :
( ~ r2_hidden(X1,X0)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,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/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f222,plain,
spl13_16,
inference(avatar_split_clause,[],[f132,f220]) ).
fof(f220,plain,
( spl13_16
<=> ! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_16])]) ).
fof(f132,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,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] :
~ ( v1_xboole_0(X1)
& r2_hidden(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f218,plain,
spl13_15,
inference(avatar_split_clause,[],[f121,f216]) ).
fof(f216,plain,
( spl13_15
<=> ! [X0] : m1_subset_1(sK6(X0),k1_zfmisc_1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_15])]) ).
fof(f121,plain,
! [X0] : m1_subset_1(sK6(X0),k1_zfmisc_1(X0)),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( v1_xboole_0(sK6(X0))
& m1_subset_1(sK6(X0),k1_zfmisc_1(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f30,f91]) ).
fof(f91,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(f30,axiom,
! [X0] :
? [X1] :
( v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f214,plain,
spl13_14,
inference(avatar_split_clause,[],[f119,f212]) ).
fof(f119,plain,
! [X0] :
( k1_xboole_0 = X0
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( k1_xboole_0 = X0
| ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( v1_xboole_0(X0)
=> k1_xboole_0 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f210,plain,
spl13_13,
inference(avatar_split_clause,[],[f118,f208]) ).
fof(f208,plain,
( spl13_13
<=> ! [X0] :
( ~ v1_xboole_0(sK4(X0))
| v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_13])]) ).
fof(f118,plain,
! [X0] :
( ~ v1_xboole_0(sK4(X0))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f206,plain,
spl13_12,
inference(avatar_split_clause,[],[f120,f204]) ).
fof(f204,plain,
( spl13_12
<=> ! [X0] : m1_subset_1(sK5(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_12])]) ).
fof(f120,plain,
! [X0] : m1_subset_1(sK5(X0),X0),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] : m1_subset_1(sK5(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f18,f89]) ).
fof(f89,plain,
! [X0] :
( ? [X1] : m1_subset_1(X1,X0)
=> m1_subset_1(sK5(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f18,axiom,
! [X0] :
? [X1] : m1_subset_1(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f202,plain,
spl13_11,
inference(avatar_split_clause,[],[f123,f200]) ).
fof(f200,plain,
( spl13_11
<=> ! [X0] : r1_tarski(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_11])]) ).
fof(f123,plain,
! [X0] : r1_tarski(X0,X0),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] : r1_tarski(X0,X0),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] : r1_tarski(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f198,plain,
spl13_10,
inference(avatar_split_clause,[],[f122,f196]) ).
fof(f196,plain,
( spl13_10
<=> ! [X0] : v1_xboole_0(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_10])]) ).
fof(f122,plain,
! [X0] : v1_xboole_0(sK6(X0)),
inference(cnf_transformation,[],[f92]) ).
fof(f194,plain,
spl13_9,
inference(avatar_split_clause,[],[f116,f192]) ).
fof(f116,plain,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f190,plain,
spl13_8,
inference(avatar_split_clause,[],[f115,f188]) ).
fof(f188,plain,
( spl13_8
<=> ! [X0] : ~ v1_xboole_0(k1_tarski(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_8])]) ).
fof(f115,plain,
! [X0] : ~ v1_xboole_0(k1_tarski(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] : ~ v1_xboole_0(k1_tarski(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f186,plain,
~ spl13_7,
inference(avatar_split_clause,[],[f112,f183]) ).
fof(f112,plain,
~ m1_subset_1(a_4_0_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK1))),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
( ~ m1_subset_1(a_4_0_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK1)))
& m2_relset_1(sK3,sK0,sK1)
& m1_subset_1(sK2,k1_zfmisc_1(sK0))
& ~ v1_xboole_0(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f57,f85,f84,f83]) ).
fof(f83,plain,
( ? [X0] :
( ? [X1,X2] :
( ? [X3] :
( ~ m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
& m2_relset_1(X3,X0,X1) )
& m1_subset_1(X2,k1_zfmisc_1(X0)) )
& ~ v1_xboole_0(X0) )
=> ( ? [X2,X1] :
( ? [X3] :
( ~ m1_subset_1(a_4_0_relset_2(sK0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
& m2_relset_1(X3,sK0,X1) )
& m1_subset_1(X2,k1_zfmisc_1(sK0)) )
& ~ v1_xboole_0(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
( ? [X2,X1] :
( ? [X3] :
( ~ m1_subset_1(a_4_0_relset_2(sK0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
& m2_relset_1(X3,sK0,X1) )
& m1_subset_1(X2,k1_zfmisc_1(sK0)) )
=> ( ? [X3] :
( ~ m1_subset_1(a_4_0_relset_2(sK0,sK1,sK2,X3),k1_zfmisc_1(k1_zfmisc_1(sK1)))
& m2_relset_1(X3,sK0,sK1) )
& m1_subset_1(sK2,k1_zfmisc_1(sK0)) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
( ? [X3] :
( ~ m1_subset_1(a_4_0_relset_2(sK0,sK1,sK2,X3),k1_zfmisc_1(k1_zfmisc_1(sK1)))
& m2_relset_1(X3,sK0,sK1) )
=> ( ~ m1_subset_1(a_4_0_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK1)))
& m2_relset_1(sK3,sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
? [X0] :
( ? [X1,X2] :
( ? [X3] :
( ~ m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1)))
& m2_relset_1(X3,X0,X1) )
& m1_subset_1(X2,k1_zfmisc_1(X0)) )
& ~ v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0] :
( ~ v1_xboole_0(X0)
=> ! [X1,X2] :
( m1_subset_1(X2,k1_zfmisc_1(X0))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> m1_subset_1(a_4_0_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_relset_2) ).
fof(f181,plain,
spl13_6,
inference(avatar_split_clause,[],[f150,f178]) ).
fof(f150,plain,
v1_xboole_0(sK12),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
v1_xboole_0(sK12),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f52,f107]) ).
fof(f107,plain,
( ? [X0] : v1_xboole_0(X0)
=> v1_xboole_0(sK12) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
? [X0] : v1_xboole_0(X0),
inference(pure_predicate_removal,[],[f27]) ).
fof(f27,axiom,
? [X0] :
( v1_relat_1(X0)
& v1_xboole_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f176,plain,
~ spl13_5,
inference(avatar_split_clause,[],[f149,f173]) ).
fof(f173,plain,
( spl13_5
<=> v1_xboole_0(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_5])]) ).
fof(f149,plain,
~ v1_xboole_0(sK11),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
~ v1_xboole_0(sK11),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f50,f105]) ).
fof(f105,plain,
( ? [X0] : ~ v1_xboole_0(X0)
=> ~ v1_xboole_0(sK11) ),
introduced(choice_axiom,[]) ).
fof(f50,plain,
? [X0] : ~ v1_xboole_0(X0),
inference(pure_predicate_removal,[],[f29]) ).
fof(f29,axiom,
? [X0] :
( v1_relat_1(X0)
& ~ v1_xboole_0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f171,plain,
spl13_4,
inference(avatar_split_clause,[],[f113,f168]) ).
fof(f168,plain,
( spl13_4
<=> v1_xboole_0(k1_xboole_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl13_4])]) ).
fof(f113,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
v1_xboole_0(k1_xboole_0),
inference(pure_predicate_removal,[],[f24]) ).
fof(f24,axiom,
( v1_relat_1(k1_xboole_0)
& v1_xboole_0(k1_xboole_0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f166,plain,
spl13_3,
inference(avatar_split_clause,[],[f111,f163]) ).
fof(f111,plain,
m2_relset_1(sK3,sK0,sK1),
inference(cnf_transformation,[],[f86]) ).
fof(f161,plain,
spl13_2,
inference(avatar_split_clause,[],[f110,f158]) ).
fof(f110,plain,
m1_subset_1(sK2,k1_zfmisc_1(sK0)),
inference(cnf_transformation,[],[f86]) ).
fof(f156,plain,
~ spl13_1,
inference(avatar_split_clause,[],[f109,f153]) ).
fof(f109,plain,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SEU424+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.09 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.27 % Computer : n028.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Mon Apr 29 23:40:14 EDT 2024
% 0.07/0.27 % CPUTime :
% 0.07/0.27 % (18443)Running in auto input_syntax mode. Trying TPTP
% 0.07/0.28 % (18449)WARNING: value z3 for option sas not known
% 0.07/0.28 % (18450)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.07/0.28 % (18448)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.07/0.28 % (18447)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.07/0.28 % (18449)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)
% 0.07/0.28 % (18452)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)
% 0.07/0.28 % (18451)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)
% 0.07/0.28 % (18453)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)
% 0.07/0.28 TRYING [1]
% 0.07/0.28 TRYING [2]
% 0.10/0.29 TRYING [1]
% 0.10/0.29 TRYING [3]
% 0.10/0.29 % (18451)First to succeed.
% 0.10/0.29 TRYING [2]
% 0.10/0.29 TRYING [3]
% 0.10/0.29 % (18451)Refutation found. Thanks to Tanya!
% 0.10/0.29 % SZS status Theorem for theBenchmark
% 0.10/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.29 % (18451)------------------------------
% 0.10/0.29 % (18451)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.10/0.29 % (18451)Termination reason: Refutation
% 0.10/0.29
% 0.10/0.29 % (18451)Memory used [KB]: 997
% 0.10/0.29 % (18451)Time elapsed: 0.008 s
% 0.10/0.29 % (18451)Instructions burned: 18 (million)
% 0.10/0.29 % (18451)------------------------------
% 0.10/0.29 % (18451)------------------------------
% 0.10/0.29 % (18443)Success in time 0.017 s
%------------------------------------------------------------------------------