TSTP Solution File: SEU429+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU429+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 : n012.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 15:34:33 EDT 2024
% Result : Theorem 0.19s 0.37s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 122
% Syntax : Number of formulae : 327 ( 96 unt; 0 def)
% Number of atoms : 808 ( 47 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 769 ( 288 ~; 277 |; 84 &)
% ( 70 <=>; 49 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 77 ( 75 usr; 65 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 8 con; 0-5 aty)
% Number of variables : 563 ( 515 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f599,plain,
$false,
inference(avatar_sat_refutation,[],[f192,f197,f202,f207,f212,f217,f222,f227,f232,f237,f242,f246,f250,f254,f258,f262,f266,f270,f274,f278,f285,f289,f293,f297,f301,f309,f313,f317,f321,f325,f329,f333,f337,f341,f347,f355,f359,f363,f367,f371,f375,f388,f400,f411,f415,f430,f435,f443,f447,f461,f472,f477,f482,f496,f506,f514,f526,f533,f544,f559,f566,f575,f587,f592,f598]) ).
fof(f598,plain,
( spl16_1
| ~ spl16_3
| ~ spl16_2
| spl16_11
| ~ spl16_55 ),
inference(avatar_split_clause,[],[f507,f504,f239,f194,f199,f189]) ).
fof(f189,plain,
( spl16_1
<=> v1_xboole_0(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_1])]) ).
fof(f199,plain,
( spl16_3
<=> m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_3])]) ).
fof(f194,plain,
( spl16_2
<=> m2_relset_1(sK3,sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_2])]) ).
fof(f239,plain,
( spl16_11
<=> m1_subset_1(a_4_1_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_11])]) ).
fof(f504,plain,
( spl16_55
<=> ! [X0,X3,X2,X1] :
( m1_subset_1(a_4_1_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(k1_zfmisc_1(X0)))
| v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_55])]) ).
fof(f507,plain,
( ~ m2_relset_1(sK3,sK0,sK1)
| ~ m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(sK0)))
| v1_xboole_0(sK0)
| spl16_11
| ~ spl16_55 ),
inference(resolution,[],[f505,f241]) ).
fof(f241,plain,
( ~ m1_subset_1(a_4_1_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK1)))
| spl16_11 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f505,plain,
( ! [X2,X3,X0,X1] :
( m1_subset_1(a_4_1_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(k1_zfmisc_1(X0)))
| v1_xboole_0(X0) )
| ~ spl16_55 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f592,plain,
( ~ spl16_12
| ~ spl16_64 ),
inference(avatar_contradiction_clause,[],[f588]) ).
fof(f588,plain,
( $false
| ~ spl16_12
| ~ spl16_64 ),
inference(resolution,[],[f586,f245]) ).
fof(f245,plain,
( ! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0))
| ~ spl16_12 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f244,plain,
( spl16_12
<=> ! [X0] : ~ v1_xboole_0(k1_zfmisc_1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_12])]) ).
fof(f586,plain,
( v1_xboole_0(k1_zfmisc_1(k1_zfmisc_1(sK0)))
| ~ spl16_64 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f584,plain,
( spl16_64
<=> v1_xboole_0(k1_zfmisc_1(k1_zfmisc_1(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_64])]) ).
fof(f587,plain,
( spl16_63
| spl16_64
| ~ spl16_3
| ~ spl16_37 ),
inference(avatar_split_clause,[],[f379,f357,f199,f584,f580]) ).
fof(f580,plain,
( spl16_63
<=> r2_hidden(sK2,k1_zfmisc_1(k1_zfmisc_1(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_63])]) ).
fof(f357,plain,
( spl16_37
<=> ! [X0,X1] :
( r2_hidden(X0,X1)
| v1_xboole_0(X1)
| ~ m1_subset_1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_37])]) ).
fof(f379,plain,
( v1_xboole_0(k1_zfmisc_1(k1_zfmisc_1(sK0)))
| r2_hidden(sK2,k1_zfmisc_1(k1_zfmisc_1(sK0)))
| ~ spl16_3
| ~ spl16_37 ),
inference(resolution,[],[f358,f201]) ).
fof(f201,plain,
( m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(sK0)))
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f358,plain,
( ! [X0,X1] :
( ~ m1_subset_1(X0,X1)
| v1_xboole_0(X1)
| r2_hidden(X0,X1) )
| ~ spl16_37 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f575,plain,
( spl16_62
| ~ spl16_3
| ~ spl16_45 ),
inference(avatar_split_clause,[],[f422,f413,f199,f573]) ).
fof(f573,plain,
( spl16_62
<=> ! [X0] :
( m1_subset_1(X0,k1_zfmisc_1(sK0))
| ~ r2_hidden(X0,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_62])]) ).
fof(f413,plain,
( spl16_45
<=> ! [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,[spl16_45])]) ).
fof(f422,plain,
( ! [X0] :
( m1_subset_1(X0,k1_zfmisc_1(sK0))
| ~ r2_hidden(X0,sK2) )
| ~ spl16_3
| ~ spl16_45 ),
inference(resolution,[],[f414,f201]) ).
fof(f414,plain,
( ! [X2,X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| m1_subset_1(X0,X2)
| ~ r2_hidden(X0,X1) )
| ~ spl16_45 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f566,plain,
spl16_61,
inference(avatar_split_clause,[],[f179,f564]) ).
fof(f564,plain,
( spl16_61
<=> ! [X4,X0,X3,X2,X1] :
( k8_relset_2(X1,X2,sK12(X0,X1,X2,X3,X4),X4) = X0
| ~ r2_hidden(X0,a_4_1_relset_2(X1,X2,X3,X4))
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_61])]) ).
fof(f179,plain,
! [X2,X3,X0,X1,X4] :
( k8_relset_2(X1,X2,sK12(X0,X1,X2,X3,X4),X4) = X0
| ~ r2_hidden(X0,a_4_1_relset_2(X1,X2,X3,X4))
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0,X1,X2,X3,X4] :
( ( ( r2_hidden(X0,a_4_1_relset_2(X1,X2,X3,X4))
| ! [X5] :
( ~ r2_hidden(X5,X3)
| k8_relset_2(X1,X2,X5,X4) != X0
| ~ m1_subset_1(X5,k1_zfmisc_1(X1)) ) )
& ( ( r2_hidden(sK12(X0,X1,X2,X3,X4),X3)
& k8_relset_2(X1,X2,sK12(X0,X1,X2,X3,X4),X4) = X0
& m1_subset_1(sK12(X0,X1,X2,X3,X4),k1_zfmisc_1(X1)) )
| ~ r2_hidden(X0,a_4_1_relset_2(X1,X2,X3,X4)) ) )
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f119,f120]) ).
fof(f120,plain,
! [X0,X1,X2,X3,X4] :
( ? [X6] :
( r2_hidden(X6,X3)
& k8_relset_2(X1,X2,X6,X4) = X0
& m1_subset_1(X6,k1_zfmisc_1(X1)) )
=> ( r2_hidden(sK12(X0,X1,X2,X3,X4),X3)
& k8_relset_2(X1,X2,sK12(X0,X1,X2,X3,X4),X4) = X0
& m1_subset_1(sK12(X0,X1,X2,X3,X4),k1_zfmisc_1(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
! [X0,X1,X2,X3,X4] :
( ( ( r2_hidden(X0,a_4_1_relset_2(X1,X2,X3,X4))
| ! [X5] :
( ~ r2_hidden(X5,X3)
| k8_relset_2(X1,X2,X5,X4) != X0
| ~ m1_subset_1(X5,k1_zfmisc_1(X1)) ) )
& ( ? [X6] :
( r2_hidden(X6,X3)
& k8_relset_2(X1,X2,X6,X4) = X0
& m1_subset_1(X6,k1_zfmisc_1(X1)) )
| ~ r2_hidden(X0,a_4_1_relset_2(X1,X2,X3,X4)) ) )
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X1) ),
inference(rectify,[],[f118]) ).
fof(f118,plain,
! [X0,X1,X2,X3,X4] :
( ( ( r2_hidden(X0,a_4_1_relset_2(X1,X2,X3,X4))
| ! [X5] :
( ~ r2_hidden(X5,X3)
| k8_relset_2(X1,X2,X5,X4) != X0
| ~ m1_subset_1(X5,k1_zfmisc_1(X1)) ) )
& ( ? [X5] :
( r2_hidden(X5,X3)
& k8_relset_2(X1,X2,X5,X4) = X0
& m1_subset_1(X5,k1_zfmisc_1(X1)) )
| ~ r2_hidden(X0,a_4_1_relset_2(X1,X2,X3,X4)) ) )
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X1) ),
inference(nnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2,X3,X4] :
( ( r2_hidden(X0,a_4_1_relset_2(X1,X2,X3,X4))
<=> ? [X5] :
( r2_hidden(X5,X3)
& k8_relset_2(X1,X2,X5,X4) = X0
& m1_subset_1(X5,k1_zfmisc_1(X1)) ) )
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X1) ),
inference(flattening,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2,X3,X4] :
( ( r2_hidden(X0,a_4_1_relset_2(X1,X2,X3,X4))
<=> ? [X5] :
( r2_hidden(X5,X3)
& k8_relset_2(X1,X2,X5,X4) = X0
& m1_subset_1(X5,k1_zfmisc_1(X1)) ) )
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1,X2,X3,X4] :
( ( m2_relset_1(X4,X1,X2)
& m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
& ~ v1_xboole_0(X1) )
=> ( r2_hidden(X0,a_4_1_relset_2(X1,X2,X3,X4))
<=> ? [X5] :
( r2_hidden(X5,X3)
& k8_relset_2(X1,X2,X5,X4) = X0
& m1_subset_1(X5,k1_zfmisc_1(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fraenkel_a_4_1_relset_2) ).
fof(f559,plain,
spl16_60,
inference(avatar_split_clause,[],[f187,f557]) ).
fof(f557,plain,
( spl16_60
<=> ! [X5,X4,X3,X2,X1] :
( r2_hidden(k8_relset_2(X1,X2,X5,X4),a_4_1_relset_2(X1,X2,X3,X4))
| ~ r2_hidden(X5,X3)
| ~ m1_subset_1(X5,k1_zfmisc_1(X1))
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_60])]) ).
fof(f187,plain,
! [X2,X3,X1,X4,X5] :
( r2_hidden(k8_relset_2(X1,X2,X5,X4),a_4_1_relset_2(X1,X2,X3,X4))
| ~ r2_hidden(X5,X3)
| ~ m1_subset_1(X5,k1_zfmisc_1(X1))
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X1) ),
inference(equality_resolution,[],[f181]) ).
fof(f181,plain,
! [X2,X3,X0,X1,X4,X5] :
( r2_hidden(X0,a_4_1_relset_2(X1,X2,X3,X4))
| ~ r2_hidden(X5,X3)
| k8_relset_2(X1,X2,X5,X4) != X0
| ~ m1_subset_1(X5,k1_zfmisc_1(X1))
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f544,plain,
spl16_59,
inference(avatar_split_clause,[],[f164,f542]) ).
fof(f542,plain,
( spl16_59
<=> ! [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,[spl16_59])]) ).
fof(f164,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(f533,plain,
spl16_58,
inference(avatar_split_clause,[],[f178,f531]) ).
fof(f531,plain,
( spl16_58
<=> ! [X4,X0,X3,X2,X1] :
( m1_subset_1(sK12(X0,X1,X2,X3,X4),k1_zfmisc_1(X1))
| ~ r2_hidden(X0,a_4_1_relset_2(X1,X2,X3,X4))
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_58])]) ).
fof(f178,plain,
! [X2,X3,X0,X1,X4] :
( m1_subset_1(sK12(X0,X1,X2,X3,X4),k1_zfmisc_1(X1))
| ~ r2_hidden(X0,a_4_1_relset_2(X1,X2,X3,X4))
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f526,plain,
spl16_57,
inference(avatar_split_clause,[],[f180,f524]) ).
fof(f524,plain,
( spl16_57
<=> ! [X4,X0,X3,X2,X1] :
( r2_hidden(sK12(X0,X1,X2,X3,X4),X3)
| ~ r2_hidden(X0,a_4_1_relset_2(X1,X2,X3,X4))
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_57])]) ).
fof(f180,plain,
! [X2,X3,X0,X1,X4] :
( r2_hidden(sK12(X0,X1,X2,X3,X4),X3)
| ~ r2_hidden(X0,a_4_1_relset_2(X1,X2,X3,X4))
| ~ m2_relset_1(X4,X1,X2)
| ~ m1_subset_1(X3,k1_zfmisc_1(k1_zfmisc_1(X1)))
| v1_xboole_0(X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f514,plain,
spl16_56,
inference(avatar_split_clause,[],[f177,f512]) ).
fof(f512,plain,
( spl16_56
<=> ! [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,[spl16_56])]) ).
fof(f177,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,[],[f93]) ).
fof(f93,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,[],[f92]) ).
fof(f92,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(f506,plain,
spl16_55,
inference(avatar_split_clause,[],[f175,f504]) ).
fof(f175,plain,
! [X2,X3,X0,X1] :
( m1_subset_1(a_4_1_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(k1_zfmisc_1(X0)))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(a_4_1_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(k1_zfmisc_1(X0)))
| v1_xboole_0(X0) ),
inference(flattening,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( m1_subset_1(a_4_1_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(k1_zfmisc_1(X0)))
| v1_xboole_0(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1,X2,X3] :
( ( m2_relset_1(X3,X0,X1)
& m1_subset_1(X2,k1_zfmisc_1(k1_zfmisc_1(X0)))
& ~ v1_xboole_0(X0) )
=> m1_subset_1(a_4_1_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s8_domain_1__e1_38__relset_2) ).
fof(f496,plain,
spl16_54,
inference(avatar_split_clause,[],[f176,f494]) ).
fof(f494,plain,
( spl16_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,[spl16_54])]) ).
fof(f176,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,[],[f91]) ).
fof(f91,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,[],[f90]) ).
fof(f90,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(f482,plain,
spl16_53,
inference(avatar_split_clause,[],[f174,f480]) ).
fof(f480,plain,
( spl16_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,[spl16_53])]) ).
fof(f174,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(f477,plain,
spl16_52,
inference(avatar_split_clause,[],[f173,f475]) ).
fof(f475,plain,
( spl16_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,[spl16_52])]) ).
fof(f173,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(f472,plain,
spl16_51,
inference(avatar_split_clause,[],[f168,f470]) ).
fof(f470,plain,
( spl16_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,[spl16_51])]) ).
fof(f168,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(f461,plain,
spl16_50,
inference(avatar_split_clause,[],[f167,f459]) ).
fof(f459,plain,
( spl16_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,[spl16_50])]) ).
fof(f167,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(f447,plain,
spl16_49,
inference(avatar_split_clause,[],[f156,f445]) ).
fof(f445,plain,
( spl16_49
<=> ! [X0,X1] :
( X0 = X1
| ~ r2_hidden(sK8(X0,X1),X1)
| ~ r2_hidden(sK8(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_49])]) ).
fof(f156,plain,
! [X0,X1] :
( X0 = X1
| ~ r2_hidden(sK8(X0,X1),X1)
| ~ r2_hidden(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ r2_hidden(sK8(X0,X1),X1)
| ~ r2_hidden(sK8(X0,X1),X0) )
& ( r2_hidden(sK8(X0,X1),X1)
| r2_hidden(sK8(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f108,f109]) ).
fof(f109,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ r2_hidden(X2,X1)
| ~ r2_hidden(X2,X0) )
& ( r2_hidden(X2,X1)
| r2_hidden(X2,X0) ) )
=> ( ( ~ r2_hidden(sK8(X0,X1),X1)
| ~ r2_hidden(sK8(X0,X1),X0) )
& ( r2_hidden(sK8(X0,X1),X1)
| r2_hidden(sK8(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f108,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(f443,plain,
spl16_48,
inference(avatar_split_clause,[],[f155,f441]) ).
fof(f441,plain,
( spl16_48
<=> ! [X0,X1] :
( X0 = X1
| r2_hidden(sK8(X0,X1),X1)
| r2_hidden(sK8(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_48])]) ).
fof(f155,plain,
! [X0,X1] :
( X0 = X1
| r2_hidden(sK8(X0,X1),X1)
| r2_hidden(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f435,plain,
( spl16_47
| ~ spl16_2
| ~ spl16_40 ),
inference(avatar_split_clause,[],[f393,f369,f194,f432]) ).
fof(f432,plain,
( spl16_47
<=> m1_relset_1(sK3,sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_47])]) ).
fof(f369,plain,
( spl16_40
<=> ! [X2,X0,X1] :
( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_40])]) ).
fof(f393,plain,
( m1_relset_1(sK3,sK0,sK1)
| ~ spl16_2
| ~ spl16_40 ),
inference(resolution,[],[f370,f196]) ).
fof(f196,plain,
( m2_relset_1(sK3,sK0,sK1)
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f370,plain,
( ! [X2,X0,X1] :
( ~ m2_relset_1(X2,X0,X1)
| m1_relset_1(X2,X0,X1) )
| ~ spl16_40 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f430,plain,
spl16_46,
inference(avatar_split_clause,[],[f153,f428]) ).
fof(f428,plain,
( spl16_46
<=> ! [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,[spl16_46])]) ).
fof(f153,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(f415,plain,
spl16_45,
inference(avatar_split_clause,[],[f169,f413]) ).
fof(f169,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(f411,plain,
spl16_44,
inference(avatar_split_clause,[],[f165,f409]) ).
fof(f409,plain,
( spl16_44
<=> ! [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,[spl16_44])]) ).
fof(f165,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(f400,plain,
spl16_43,
inference(avatar_split_clause,[],[f172,f398]) ).
fof(f398,plain,
( spl16_43
<=> ! [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,[spl16_43])]) ).
fof(f172,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(f388,plain,
( ~ spl16_42
| spl16_11
| ~ spl16_36 ),
inference(avatar_split_clause,[],[f376,f353,f239,f385]) ).
fof(f385,plain,
( spl16_42
<=> m1_eqrel_1(a_4_1_relset_2(sK0,sK1,sK2,sK3),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_42])]) ).
fof(f353,plain,
( spl16_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,[spl16_36])]) ).
fof(f376,plain,
( ~ m1_eqrel_1(a_4_1_relset_2(sK0,sK1,sK2,sK3),sK1)
| spl16_11
| ~ spl16_36 ),
inference(resolution,[],[f354,f241]) ).
fof(f354,plain,
( ! [X0,X1] :
( m1_subset_1(X1,k1_zfmisc_1(k1_zfmisc_1(X0)))
| ~ m1_eqrel_1(X1,X0) )
| ~ spl16_36 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f375,plain,
spl16_41,
inference(avatar_split_clause,[],[f171,f373]) ).
fof(f373,plain,
( spl16_41
<=> ! [X2,X0,X1] :
( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_41])]) ).
fof(f171,plain,
! [X2,X0,X1] :
( m2_relset_1(X2,X0,X1)
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,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(f371,plain,
spl16_40,
inference(avatar_split_clause,[],[f170,f369]) ).
fof(f170,plain,
! [X2,X0,X1] :
( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f367,plain,
spl16_39,
inference(avatar_split_clause,[],[f166,f365]) ).
fof(f365,plain,
( spl16_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,[spl16_39])]) ).
fof(f166,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(f363,plain,
spl16_38,
inference(avatar_split_clause,[],[f154,f361]) ).
fof(f361,plain,
( spl16_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,[spl16_38])]) ).
fof(f154,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(f359,plain,
spl16_37,
inference(avatar_split_clause,[],[f152,f357]) ).
fof(f152,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(f355,plain,
spl16_36,
inference(avatar_split_clause,[],[f151,f353]) ).
fof(f151,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(f347,plain,
( ~ spl16_35
| spl16_11
| ~ spl16_33 ),
inference(avatar_split_clause,[],[f342,f335,f239,f344]) ).
fof(f344,plain,
( spl16_35
<=> r1_tarski(a_4_1_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_35])]) ).
fof(f335,plain,
( spl16_33
<=> ! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_33])]) ).
fof(f342,plain,
( ~ r1_tarski(a_4_1_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(sK1))
| spl16_11
| ~ spl16_33 ),
inference(resolution,[],[f336,f241]) ).
fof(f336,plain,
( ! [X0,X1] :
( m1_subset_1(X0,k1_zfmisc_1(X1))
| ~ r1_tarski(X0,X1) )
| ~ spl16_33 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f341,plain,
spl16_34,
inference(avatar_split_clause,[],[f158,f339]) ).
fof(f339,plain,
( spl16_34
<=> ! [X0,X1] :
( ~ v1_xboole_0(X1)
| X0 = X1
| ~ v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_34])]) ).
fof(f158,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(f337,plain,
spl16_33,
inference(avatar_split_clause,[],[f157,f335]) ).
fof(f157,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(f333,plain,
spl16_32,
inference(avatar_split_clause,[],[f138,f331]) ).
fof(f331,plain,
( spl16_32
<=> ! [X0] :
( m1_subset_1(sK4(X0),k1_zfmisc_1(X0))
| v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_32])]) ).
fof(f138,plain,
! [X0] :
( m1_subset_1(sK4(X0),k1_zfmisc_1(X0))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,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])],[f62,f100]) ).
fof(f100,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(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(f329,plain,
spl16_31,
inference(avatar_split_clause,[],[f162,f327]) ).
fof(f327,plain,
( spl16_31
<=> ! [X0,X1] : m1_relset_1(sK11(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_31])]) ).
fof(f162,plain,
! [X0,X1] : m1_relset_1(sK11(X0,X1),X0,X1),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( v1_relat_1(sK11(X0,X1))
& m1_relset_1(sK11(X0,X1),X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f59,f115]) ).
fof(f115,plain,
! [X0,X1] :
( ? [X2] :
( v1_relat_1(X2)
& m1_relset_1(X2,X0,X1) )
=> ( v1_relat_1(sK11(X0,X1))
& m1_relset_1(sK11(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(f325,plain,
spl16_30,
inference(avatar_split_clause,[],[f161,f323]) ).
fof(f323,plain,
( spl16_30
<=> ! [X0,X1] : m2_relset_1(sK10(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_30])]) ).
fof(f161,plain,
! [X0,X1] : m2_relset_1(sK10(X0,X1),X0,X1),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1] : m2_relset_1(sK10(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f25,f113]) ).
fof(f113,plain,
! [X0,X1] :
( ? [X2] : m2_relset_1(X2,X0,X1)
=> m2_relset_1(sK10(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(f321,plain,
spl16_29,
inference(avatar_split_clause,[],[f160,f319]) ).
fof(f319,plain,
( spl16_29
<=> ! [X0,X1] : m1_relset_1(sK9(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_29])]) ).
fof(f160,plain,
! [X0,X1] : m1_relset_1(sK9(X0,X1),X0,X1),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1] : m1_relset_1(sK9(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f23,f111]) ).
fof(f111,plain,
! [X0,X1] :
( ? [X2] : m1_relset_1(X2,X0,X1)
=> m1_relset_1(sK9(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(f317,plain,
spl16_28,
inference(avatar_split_clause,[],[f150,f315]) ).
fof(f315,plain,
( spl16_28
<=> ! [X0,X1] :
( m1_subset_1(X0,X1)
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_28])]) ).
fof(f150,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(f313,plain,
spl16_27,
inference(avatar_split_clause,[],[f149,f311]) ).
fof(f311,plain,
( spl16_27
<=> ! [X0,X1] :
( ~ r2_hidden(X1,X0)
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_27])]) ).
fof(f149,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(f309,plain,
spl16_26,
inference(avatar_split_clause,[],[f148,f307]) ).
fof(f307,plain,
( spl16_26
<=> ! [X0,X1] :
( v1_relat_1(k5_relset_2(X0,X1))
| ~ v1_relat_1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_26])]) ).
fof(f148,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(f301,plain,
( spl16_25
| ~ spl16_13
| ~ spl16_16 ),
inference(avatar_split_clause,[],[f281,f260,f248,f299]) ).
fof(f299,plain,
( spl16_25
<=> ! [X0] : v1_relat_1(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_25])]) ).
fof(f248,plain,
( spl16_13
<=> ! [X0] : v1_xboole_0(sK7(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_13])]) ).
fof(f260,plain,
( spl16_16
<=> ! [X0] :
( v1_relat_1(X0)
| ~ v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_16])]) ).
fof(f281,plain,
( ! [X0] : v1_relat_1(sK7(X0))
| ~ spl16_13
| ~ spl16_16 ),
inference(resolution,[],[f261,f249]) ).
fof(f249,plain,
( ! [X0] : v1_xboole_0(sK7(X0))
| ~ spl16_13 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f261,plain,
( ! [X0] :
( ~ v1_xboole_0(X0)
| v1_relat_1(X0) )
| ~ spl16_16 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f297,plain,
spl16_24,
inference(avatar_split_clause,[],[f159,f295]) ).
fof(f295,plain,
( spl16_24
<=> ! [X0,X1] :
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_24])]) ).
fof(f159,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(f293,plain,
spl16_23,
inference(avatar_split_clause,[],[f144,f291]) ).
fof(f291,plain,
( spl16_23
<=> ! [X0] : m1_subset_1(sK7(X0),k1_zfmisc_1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_23])]) ).
fof(f144,plain,
! [X0] : m1_subset_1(sK7(X0),k1_zfmisc_1(X0)),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( v1_xboole_0(sK7(X0))
& m1_subset_1(sK7(X0),k1_zfmisc_1(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f36,f106]) ).
fof(f106,plain,
! [X0] :
( ? [X1] :
( v1_xboole_0(X1)
& m1_subset_1(X1,k1_zfmisc_1(X0)) )
=> ( v1_xboole_0(sK7(X0))
& m1_subset_1(sK7(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(f289,plain,
spl16_22,
inference(avatar_split_clause,[],[f141,f287]) ).
fof(f287,plain,
( spl16_22
<=> ! [X0] :
( k1_xboole_0 = X0
| ~ v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_22])]) ).
fof(f141,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(f285,plain,
spl16_21,
inference(avatar_split_clause,[],[f139,f283]) ).
fof(f283,plain,
( spl16_21
<=> ! [X0] :
( ~ v1_xboole_0(sK4(X0))
| v1_xboole_0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_21])]) ).
fof(f139,plain,
! [X0] :
( ~ v1_xboole_0(sK4(X0))
| v1_xboole_0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f278,plain,
spl16_20,
inference(avatar_split_clause,[],[f163,f276]) ).
fof(f276,plain,
( spl16_20
<=> ! [X0,X1] : v1_relat_1(sK11(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_20])]) ).
fof(f163,plain,
! [X0,X1] : v1_relat_1(sK11(X0,X1)),
inference(cnf_transformation,[],[f116]) ).
fof(f274,plain,
spl16_19,
inference(avatar_split_clause,[],[f147,f272]) ).
fof(f272,plain,
( spl16_19
<=> ! [X0,X1] : v1_relat_1(k2_zfmisc_1(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_19])]) ).
fof(f147,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(f270,plain,
spl16_18,
inference(avatar_split_clause,[],[f143,f268]) ).
fof(f268,plain,
( spl16_18
<=> ! [X0] : m1_subset_1(sK6(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_18])]) ).
fof(f143,plain,
! [X0] : m1_subset_1(sK6(X0),X0),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] : m1_subset_1(sK6(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f24,f104]) ).
fof(f104,plain,
! [X0] :
( ? [X1] : m1_subset_1(X1,X0)
=> m1_subset_1(sK6(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(f266,plain,
spl16_17,
inference(avatar_split_clause,[],[f142,f264]) ).
fof(f264,plain,
( spl16_17
<=> ! [X0] : m1_eqrel_1(sK5(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_17])]) ).
fof(f142,plain,
! [X0] : m1_eqrel_1(sK5(X0),X0),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] : m1_eqrel_1(sK5(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f22,f102]) ).
fof(f102,plain,
! [X0] :
( ? [X1] : m1_eqrel_1(X1,X0)
=> m1_eqrel_1(sK5(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(f262,plain,
spl16_16,
inference(avatar_split_clause,[],[f140,f260]) ).
fof(f140,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(f258,plain,
spl16_15,
inference(avatar_split_clause,[],[f137,f256]) ).
fof(f256,plain,
( spl16_15
<=> ! [X0] : m1_eqrel_1(k3_pua2mss1(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_15])]) ).
fof(f137,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(f254,plain,
spl16_14,
inference(avatar_split_clause,[],[f146,f252]) ).
fof(f252,plain,
( spl16_14
<=> ! [X0] : r1_tarski(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_14])]) ).
fof(f146,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(f250,plain,
spl16_13,
inference(avatar_split_clause,[],[f145,f248]) ).
fof(f145,plain,
! [X0] : v1_xboole_0(sK7(X0)),
inference(cnf_transformation,[],[f107]) ).
fof(f246,plain,
spl16_12,
inference(avatar_split_clause,[],[f136,f244]) ).
fof(f136,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(f242,plain,
~ spl16_11,
inference(avatar_split_clause,[],[f131,f239]) ).
fof(f131,plain,
~ m1_subset_1(a_4_1_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK1))),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
( ~ m1_subset_1(a_4_1_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(k1_zfmisc_1(sK0)))
& ~ v1_xboole_0(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f61,f98,f97,f96]) ).
fof(f96,plain,
( ? [X0] :
( ? [X1,X2] :
( ? [X3] :
( ~ m1_subset_1(a_4_1_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(k1_zfmisc_1(X0))) )
& ~ v1_xboole_0(X0) )
=> ( ? [X2,X1] :
( ? [X3] :
( ~ m1_subset_1(a_4_1_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(k1_zfmisc_1(sK0))) )
& ~ v1_xboole_0(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
( ? [X2,X1] :
( ? [X3] :
( ~ m1_subset_1(a_4_1_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(k1_zfmisc_1(sK0))) )
=> ( ? [X3] :
( ~ m1_subset_1(a_4_1_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(k1_zfmisc_1(sK0))) ) ),
introduced(choice_axiom,[]) ).
fof(f98,plain,
( ? [X3] :
( ~ m1_subset_1(a_4_1_relset_2(sK0,sK1,sK2,X3),k1_zfmisc_1(k1_zfmisc_1(sK1)))
& m2_relset_1(X3,sK0,sK1) )
=> ( ~ m1_subset_1(a_4_1_relset_2(sK0,sK1,sK2,sK3),k1_zfmisc_1(k1_zfmisc_1(sK1)))
& m2_relset_1(sK3,sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
? [X0] :
( ? [X1,X2] :
( ? [X3] :
( ~ m1_subset_1(a_4_1_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(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(k1_zfmisc_1(X0)))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> m1_subset_1(a_4_1_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(k1_zfmisc_1(X0)))
=> ! [X3] :
( m2_relset_1(X3,X0,X1)
=> m1_subset_1(a_4_1_relset_2(X0,X1,X2,X3),k1_zfmisc_1(k1_zfmisc_1(X1))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_relset_2) ).
fof(f237,plain,
spl16_10,
inference(avatar_split_clause,[],[f186,f234]) ).
fof(f234,plain,
( spl16_10
<=> v1_relat_1(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_10])]) ).
fof(f186,plain,
v1_relat_1(sK15),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
( v1_relat_1(sK15)
& v1_xboole_0(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f32,f126]) ).
fof(f126,plain,
( ? [X0] :
( v1_relat_1(X0)
& v1_xboole_0(X0) )
=> ( v1_relat_1(sK15)
& v1_xboole_0(sK15) ) ),
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(f232,plain,
spl16_9,
inference(avatar_split_clause,[],[f185,f229]) ).
fof(f229,plain,
( spl16_9
<=> v1_xboole_0(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_9])]) ).
fof(f185,plain,
v1_xboole_0(sK15),
inference(cnf_transformation,[],[f127]) ).
fof(f227,plain,
spl16_8,
inference(avatar_split_clause,[],[f184,f224]) ).
fof(f224,plain,
( spl16_8
<=> v1_relat_1(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_8])]) ).
fof(f184,plain,
v1_relat_1(sK14),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
v1_relat_1(sK14),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f55,f124]) ).
fof(f124,plain,
( ? [X0] : v1_relat_1(X0)
=> v1_relat_1(sK14) ),
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(f222,plain,
spl16_7,
inference(avatar_split_clause,[],[f183,f219]) ).
fof(f219,plain,
( spl16_7
<=> v1_relat_1(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_7])]) ).
fof(f183,plain,
v1_relat_1(sK13),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
( v1_relat_1(sK13)
& ~ v1_xboole_0(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f35,f122]) ).
fof(f122,plain,
( ? [X0] :
( v1_relat_1(X0)
& ~ v1_xboole_0(X0) )
=> ( v1_relat_1(sK13)
& ~ v1_xboole_0(sK13) ) ),
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(f217,plain,
~ spl16_6,
inference(avatar_split_clause,[],[f182,f214]) ).
fof(f214,plain,
( spl16_6
<=> v1_xboole_0(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_6])]) ).
fof(f182,plain,
~ v1_xboole_0(sK13),
inference(cnf_transformation,[],[f123]) ).
fof(f212,plain,
spl16_5,
inference(avatar_split_clause,[],[f133,f209]) ).
fof(f209,plain,
( spl16_5
<=> v1_relat_1(k1_xboole_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_5])]) ).
fof(f133,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(f207,plain,
spl16_4,
inference(avatar_split_clause,[],[f132,f204]) ).
fof(f204,plain,
( spl16_4
<=> v1_xboole_0(k1_xboole_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).
fof(f132,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[],[f29]) ).
fof(f202,plain,
spl16_3,
inference(avatar_split_clause,[],[f129,f199]) ).
fof(f129,plain,
m1_subset_1(sK2,k1_zfmisc_1(k1_zfmisc_1(sK0))),
inference(cnf_transformation,[],[f99]) ).
fof(f197,plain,
spl16_2,
inference(avatar_split_clause,[],[f130,f194]) ).
fof(f130,plain,
m2_relset_1(sK3,sK0,sK1),
inference(cnf_transformation,[],[f99]) ).
fof(f192,plain,
~ spl16_1,
inference(avatar_split_clause,[],[f128,f189]) ).
fof(f128,plain,
~ v1_xboole_0(sK0),
inference(cnf_transformation,[],[f99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU429+1 : TPTP v8.1.2. Released v3.4.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Apr 29 20:53:42 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % (14528)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.36 % (14533)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)
% 0.19/0.36 % (14531)WARNING: value z3 for option sas not known
% 0.19/0.36 % (14529)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.36 % (14532)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.36 % (14534)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)
% 0.19/0.36 % (14531)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)
% 0.19/0.36 % (14535)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)
% 0.19/0.36 % (14530)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.37 TRYING [1]
% 0.19/0.37 % (14533)First to succeed.
% 0.19/0.37 TRYING [2]
% 0.19/0.37 % (14533)Refutation found. Thanks to Tanya!
% 0.19/0.37 % SZS status Theorem for theBenchmark
% 0.19/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.37 % (14533)------------------------------
% 0.19/0.37 % (14533)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.37 % (14533)Termination reason: Refutation
% 0.19/0.37
% 0.19/0.37 % (14533)Memory used [KB]: 1033
% 0.19/0.37 % (14533)Time elapsed: 0.015 s
% 0.19/0.37 % (14533)Instructions burned: 26 (million)
% 0.19/0.37 % (14533)------------------------------
% 0.19/0.37 % (14533)------------------------------
% 0.19/0.37 % (14528)Success in time 0.028 s
%------------------------------------------------------------------------------