TSTP Solution File: SET980+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET980+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n017.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 : Sun May 5 09:19:51 EDT 2024
% Result : Theorem 0.18s 0.38s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 24
% Syntax : Number of formulae : 163 ( 12 unt; 0 def)
% Number of atoms : 448 ( 122 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 519 ( 234 ~; 225 |; 33 &)
% ( 19 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 16 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 133 ( 115 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f437,plain,
$false,
inference(avatar_sat_refutation,[],[f67,f114,f155,f162,f164,f166,f182,f197,f204,f212,f214,f216,f235,f272,f337,f366,f369,f371,f392,f394,f396,f411,f418,f420,f422,f426,f436]) ).
fof(f436,plain,
( ~ spl8_2
| ~ spl8_3 ),
inference(avatar_contradiction_clause,[],[f435]) ).
fof(f435,plain,
( $false
| ~ spl8_2
| ~ spl8_3 ),
inference(subsumption_resolution,[],[f434,f37]) ).
fof(f37,plain,
empty_set != sK1,
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
( ( sK1 != sK3
| sK0 != sK2 )
& empty_set != sK1
& empty_set != sK0
& cartesian_product2(sK2,sK3) = cartesian_product2(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f15,f18]) ).
fof(f18,plain,
( ? [X0,X1,X2,X3] :
( ( X1 != X3
| X0 != X2 )
& empty_set != X1
& empty_set != X0
& cartesian_product2(X2,X3) = cartesian_product2(X0,X1) )
=> ( ( sK1 != sK3
| sK0 != sK2 )
& empty_set != sK1
& empty_set != sK0
& cartesian_product2(sK2,sK3) = cartesian_product2(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
? [X0,X1,X2,X3] :
( ( X1 != X3
| X0 != X2 )
& empty_set != X1
& empty_set != X0
& cartesian_product2(X2,X3) = cartesian_product2(X0,X1) ),
inference(flattening,[],[f14]) ).
fof(f14,plain,
? [X0,X1,X2,X3] :
( ( X1 != X3
| X0 != X2 )
& empty_set != X1
& empty_set != X0
& cartesian_product2(X2,X3) = cartesian_product2(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
=> ( ( X1 = X3
& X0 = X2 )
| empty_set = X1
| empty_set = X0 ) ),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X0,X1,X2,X3] :
( cartesian_product2(X2,X3) = cartesian_product2(X0,X1)
=> ( ( X1 = X3
& X0 = X2 )
| empty_set = X1
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t134_zfmisc_1) ).
fof(f434,plain,
( empty_set = sK1
| ~ spl8_2
| ~ spl8_3 ),
inference(forward_demodulation,[],[f65,f105]) ).
fof(f105,plain,
( empty_set = sK3
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f103,plain,
( spl8_3
<=> empty_set = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
fof(f65,plain,
( sK1 = sK3
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f64,plain,
( spl8_2
<=> sK1 = sK3 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f426,plain,
( ~ spl8_3
| ~ spl8_7
| ~ spl8_13 ),
inference(avatar_contradiction_clause,[],[f425]) ).
fof(f425,plain,
( $false
| ~ spl8_3
| ~ spl8_7
| ~ spl8_13 ),
inference(subsumption_resolution,[],[f424,f37]) ).
fof(f424,plain,
( empty_set = sK1
| ~ spl8_3
| ~ spl8_7
| ~ spl8_13 ),
inference(forward_demodulation,[],[f273,f105]) ).
fof(f273,plain,
( sK1 = sK3
| ~ spl8_7
| ~ spl8_13 ),
inference(subsumption_resolution,[],[f262,f168]) ).
fof(f168,plain,
( ! [X0] :
( ~ in(sK5(X0,sK3),sK1)
| sK3 = X0
| ~ in(sK5(X0,sK3),X0) )
| ~ spl8_7 ),
inference(resolution,[],[f154,f47]) ).
fof(f47,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X1)
| X0 = X1
| ~ in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),X0) )
& ( in(sK5(X0,X1),X1)
| in(sK5(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f24,f25]) ).
fof(f25,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK5(X0,X1),X1)
| ~ in(sK5(X0,X1),X0) )
& ( in(sK5(X0,X1),X1)
| in(sK5(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f154,plain,
( ! [X0] :
( in(X0,sK3)
| ~ in(X0,sK1) )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f153,plain,
( spl8_7
<=> ! [X0] :
( ~ in(X0,sK1)
| in(X0,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
fof(f262,plain,
( in(sK5(sK1,sK3),sK1)
| sK1 = sK3
| ~ spl8_13 ),
inference(factoring,[],[f219]) ).
fof(f219,plain,
( ! [X0] :
( in(sK5(X0,sK3),sK1)
| in(sK5(X0,sK3),X0)
| sK3 = X0 )
| ~ spl8_13 ),
inference(resolution,[],[f203,f46]) ).
fof(f46,plain,
! [X0,X1] :
( in(sK5(X0,X1),X1)
| in(sK5(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f26]) ).
fof(f203,plain,
( ! [X0] :
( ~ in(X0,sK3)
| in(X0,sK1) )
| ~ spl8_13 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f202,plain,
( spl8_13
<=> ! [X0] :
( ~ in(X0,sK3)
| in(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).
fof(f422,plain,
~ spl8_9,
inference(avatar_contradiction_clause,[],[f421]) ).
fof(f421,plain,
( $false
| ~ spl8_9 ),
inference(subsumption_resolution,[],[f416,f37]) ).
fof(f416,plain,
( empty_set = sK1
| ~ spl8_9 ),
inference(resolution,[],[f181,f126]) ).
fof(f126,plain,
! [X0] :
( in(sK5(empty_set,X0),X0)
| empty_set = X0 ),
inference(resolution,[],[f46,f56]) ).
fof(f56,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f40]) ).
fof(f40,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0] :
( ( empty_set = X0
| in(sK4(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f21,f22]) ).
fof(f22,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f181,plain,
( ! [X0] : ~ in(X0,sK1)
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f180,plain,
( spl8_9
<=> ! [X0] : ~ in(X0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
fof(f420,plain,
~ spl8_9,
inference(avatar_contradiction_clause,[],[f419]) ).
fof(f419,plain,
( $false
| ~ spl8_9 ),
inference(subsumption_resolution,[],[f415,f37]) ).
fof(f415,plain,
( empty_set = sK1
| ~ spl8_9 ),
inference(resolution,[],[f181,f124]) ).
fof(f124,plain,
! [X0] :
( in(sK5(X0,empty_set),X0)
| empty_set = X0 ),
inference(resolution,[],[f46,f56]) ).
fof(f418,plain,
~ spl8_9,
inference(avatar_contradiction_clause,[],[f417]) ).
fof(f417,plain,
( $false
| ~ spl8_9 ),
inference(subsumption_resolution,[],[f412,f37]) ).
fof(f412,plain,
( empty_set = sK1
| ~ spl8_9 ),
inference(resolution,[],[f181,f41]) ).
fof(f41,plain,
! [X0] :
( in(sK4(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f23]) ).
fof(f411,plain,
( spl8_6
| ~ spl8_8
| ~ spl8_12 ),
inference(avatar_split_clause,[],[f205,f199,f177,f150]) ).
fof(f150,plain,
( spl8_6
<=> ! [X1] : ~ in(X1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
fof(f177,plain,
( spl8_8
<=> ! [X1] :
( ~ in(X1,sK0)
| in(X1,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
fof(f199,plain,
( spl8_12
<=> ! [X1] : ~ in(X1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).
fof(f205,plain,
( ! [X0] : ~ in(X0,sK0)
| ~ spl8_8
| ~ spl8_12 ),
inference(resolution,[],[f200,f178]) ).
fof(f178,plain,
( ! [X1] :
( in(X1,sK2)
| ~ in(X1,sK0) )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f200,plain,
( ! [X1] : ~ in(X1,sK2)
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f396,plain,
( spl8_3
| ~ spl8_15 ),
inference(avatar_contradiction_clause,[],[f395]) ).
fof(f395,plain,
( $false
| spl8_3
| ~ spl8_15 ),
inference(subsumption_resolution,[],[f390,f104]) ).
fof(f104,plain,
( empty_set != sK3
| spl8_3 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f390,plain,
( empty_set = sK3
| ~ spl8_15 ),
inference(resolution,[],[f234,f126]) ).
fof(f234,plain,
( ! [X0] : ~ in(X0,sK3)
| ~ spl8_15 ),
inference(avatar_component_clause,[],[f233]) ).
fof(f233,plain,
( spl8_15
<=> ! [X0] : ~ in(X0,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).
fof(f394,plain,
( spl8_3
| ~ spl8_15 ),
inference(avatar_contradiction_clause,[],[f393]) ).
fof(f393,plain,
( $false
| spl8_3
| ~ spl8_15 ),
inference(subsumption_resolution,[],[f389,f104]) ).
fof(f389,plain,
( empty_set = sK3
| ~ spl8_15 ),
inference(resolution,[],[f234,f124]) ).
fof(f392,plain,
( spl8_3
| ~ spl8_15 ),
inference(avatar_contradiction_clause,[],[f391]) ).
fof(f391,plain,
( $false
| spl8_3
| ~ spl8_15 ),
inference(subsumption_resolution,[],[f386,f104]) ).
fof(f386,plain,
( empty_set = sK3
| ~ spl8_15 ),
inference(resolution,[],[f234,f41]) ).
fof(f371,plain,
( ~ spl8_1
| ~ spl8_4 ),
inference(avatar_contradiction_clause,[],[f370]) ).
fof(f370,plain,
( $false
| ~ spl8_1
| ~ spl8_4 ),
inference(subsumption_resolution,[],[f356,f36]) ).
fof(f36,plain,
empty_set != sK0,
inference(cnf_transformation,[],[f19]) ).
fof(f356,plain,
( empty_set = sK0
| ~ spl8_1
| ~ spl8_4 ),
inference(superposition,[],[f61,f109]) ).
fof(f109,plain,
( empty_set = sK2
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f107,plain,
( spl8_4
<=> empty_set = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
fof(f61,plain,
( sK0 = sK2
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f60,plain,
( spl8_1
<=> sK0 = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
fof(f369,plain,
( ~ spl8_4
| spl8_5 ),
inference(avatar_contradiction_clause,[],[f368]) ).
fof(f368,plain,
( $false
| ~ spl8_4
| spl8_5 ),
inference(subsumption_resolution,[],[f367,f113]) ).
fof(f113,plain,
( empty_set != cartesian_product2(sK0,sK1)
| spl8_5 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f111,plain,
( spl8_5
<=> empty_set = cartesian_product2(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
fof(f367,plain,
( empty_set = cartesian_product2(sK0,sK1)
| ~ spl8_4 ),
inference(forward_demodulation,[],[f355,f58]) ).
fof(f58,plain,
! [X1] : empty_set = cartesian_product2(empty_set,X1),
inference(equality_resolution,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( empty_set = cartesian_product2(X0,X1)
| empty_set != X0 ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( empty_set = cartesian_product2(X0,X1)
| ( empty_set != X1
& empty_set != X0 ) )
& ( empty_set = X1
| empty_set = X0
| empty_set != cartesian_product2(X0,X1) ) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( empty_set = cartesian_product2(X0,X1)
| ( empty_set != X1
& empty_set != X0 ) )
& ( empty_set = X1
| empty_set = X0
| empty_set != cartesian_product2(X0,X1) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( empty_set = cartesian_product2(X0,X1)
<=> ( empty_set = X1
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(f355,plain,
( cartesian_product2(sK0,sK1) = cartesian_product2(empty_set,sK3)
| ~ spl8_4 ),
inference(superposition,[],[f35,f109]) ).
fof(f35,plain,
cartesian_product2(sK2,sK3) = cartesian_product2(sK0,sK1),
inference(cnf_transformation,[],[f19]) ).
fof(f366,plain,
( ~ spl8_1
| ~ spl8_4 ),
inference(avatar_contradiction_clause,[],[f365]) ).
fof(f365,plain,
( $false
| ~ spl8_1
| ~ spl8_4 ),
inference(subsumption_resolution,[],[f354,f36]) ).
fof(f354,plain,
( empty_set = sK0
| ~ spl8_1
| ~ spl8_4 ),
inference(superposition,[],[f109,f61]) ).
fof(f337,plain,
( spl8_1
| ~ spl8_8
| ~ spl8_14 ),
inference(avatar_contradiction_clause,[],[f336]) ).
fof(f336,plain,
( $false
| spl8_1
| ~ spl8_8
| ~ spl8_14 ),
inference(subsumption_resolution,[],[f335,f332]) ).
fof(f332,plain,
( in(sK5(sK0,sK2),sK0)
| spl8_1
| ~ spl8_14 ),
inference(subsumption_resolution,[],[f324,f62]) ).
fof(f62,plain,
( sK0 != sK2
| spl8_1 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f324,plain,
( in(sK5(sK0,sK2),sK0)
| sK0 = sK2
| ~ spl8_14 ),
inference(factoring,[],[f238]) ).
fof(f238,plain,
( ! [X0] :
( in(sK5(X0,sK2),sK0)
| in(sK5(X0,sK2),X0)
| sK2 = X0 )
| ~ spl8_14 ),
inference(resolution,[],[f231,f46]) ).
fof(f231,plain,
( ! [X1] :
( ~ in(X1,sK2)
| in(X1,sK0) )
| ~ spl8_14 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f230,plain,
( spl8_14
<=> ! [X1] :
( ~ in(X1,sK2)
| in(X1,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).
fof(f335,plain,
( ~ in(sK5(sK0,sK2),sK0)
| spl8_1
| ~ spl8_8
| ~ spl8_14 ),
inference(subsumption_resolution,[],[f333,f62]) ).
fof(f333,plain,
( sK0 = sK2
| ~ in(sK5(sK0,sK2),sK0)
| spl8_1
| ~ spl8_8
| ~ spl8_14 ),
inference(resolution,[],[f332,f185]) ).
fof(f185,plain,
( ! [X0] :
( ~ in(sK5(X0,sK2),sK0)
| sK2 = X0
| ~ in(sK5(X0,sK2),X0) )
| ~ spl8_8 ),
inference(resolution,[],[f178,f47]) ).
fof(f272,plain,
( spl8_2
| ~ spl8_7
| ~ spl8_13 ),
inference(avatar_contradiction_clause,[],[f271]) ).
fof(f271,plain,
( $false
| spl8_2
| ~ spl8_7
| ~ spl8_13 ),
inference(subsumption_resolution,[],[f270,f267]) ).
fof(f267,plain,
( in(sK5(sK1,sK3),sK1)
| spl8_2
| ~ spl8_13 ),
inference(subsumption_resolution,[],[f262,f66]) ).
fof(f66,plain,
( sK1 != sK3
| spl8_2 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f270,plain,
( ~ in(sK5(sK1,sK3),sK1)
| spl8_2
| ~ spl8_7
| ~ spl8_13 ),
inference(subsumption_resolution,[],[f268,f66]) ).
fof(f268,plain,
( sK1 = sK3
| ~ in(sK5(sK1,sK3),sK1)
| spl8_2
| ~ spl8_7
| ~ spl8_13 ),
inference(resolution,[],[f267,f168]) ).
fof(f235,plain,
( spl8_14
| spl8_15 ),
inference(avatar_split_clause,[],[f172,f233,f230]) ).
fof(f172,plain,
! [X0,X1] :
( ~ in(X0,sK3)
| ~ in(X1,sK2)
| in(X1,sK0) ),
inference(resolution,[],[f148,f51]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(f148,plain,
! [X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(sK0,sK1))
| ~ in(X1,sK3)
| ~ in(X0,sK2) ),
inference(superposition,[],[f53,f35]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f216,plain,
( spl8_4
| ~ spl8_12 ),
inference(avatar_contradiction_clause,[],[f215]) ).
fof(f215,plain,
( $false
| spl8_4
| ~ spl8_12 ),
inference(subsumption_resolution,[],[f210,f108]) ).
fof(f108,plain,
( empty_set != sK2
| spl8_4 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f210,plain,
( empty_set = sK2
| ~ spl8_12 ),
inference(resolution,[],[f200,f126]) ).
fof(f214,plain,
( spl8_4
| ~ spl8_12 ),
inference(avatar_contradiction_clause,[],[f213]) ).
fof(f213,plain,
( $false
| spl8_4
| ~ spl8_12 ),
inference(subsumption_resolution,[],[f209,f108]) ).
fof(f209,plain,
( empty_set = sK2
| ~ spl8_12 ),
inference(resolution,[],[f200,f124]) ).
fof(f212,plain,
( spl8_4
| ~ spl8_12 ),
inference(avatar_contradiction_clause,[],[f211]) ).
fof(f211,plain,
( $false
| spl8_4
| ~ spl8_12 ),
inference(subsumption_resolution,[],[f206,f108]) ).
fof(f206,plain,
( empty_set = sK2
| ~ spl8_12 ),
inference(resolution,[],[f200,f41]) ).
fof(f204,plain,
( spl8_12
| spl8_13 ),
inference(avatar_split_clause,[],[f171,f202,f199]) ).
fof(f171,plain,
! [X0,X1] :
( ~ in(X0,sK3)
| ~ in(X1,sK2)
| in(X0,sK1) ),
inference(resolution,[],[f148,f52]) ).
fof(f52,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f30]) ).
fof(f197,plain,
( ~ spl8_10
| ~ spl8_11
| ~ spl8_7
| ~ spl8_8 ),
inference(avatar_split_clause,[],[f184,f177,f153,f194,f190]) ).
fof(f190,plain,
( spl8_10
<=> in(sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
fof(f194,plain,
( spl8_11
<=> in(sK3,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
fof(f184,plain,
( ~ in(sK3,sK0)
| ~ in(sK2,sK1)
| ~ spl8_7
| ~ spl8_8 ),
inference(resolution,[],[f178,f167]) ).
fof(f167,plain,
( ! [X0] :
( ~ in(sK3,X0)
| ~ in(X0,sK1) )
| ~ spl8_7 ),
inference(resolution,[],[f154,f45]) ).
fof(f45,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f182,plain,
( spl8_8
| spl8_9 ),
inference(avatar_split_clause,[],[f144,f180,f177]) ).
fof(f144,plain,
! [X0,X1] :
( ~ in(X0,sK1)
| ~ in(X1,sK0)
| in(X1,sK2) ),
inference(resolution,[],[f53,f79]) ).
fof(f79,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(sK0,sK1))
| in(X0,sK2) ),
inference(superposition,[],[f51,f35]) ).
fof(f166,plain,
~ spl8_6,
inference(avatar_contradiction_clause,[],[f165]) ).
fof(f165,plain,
( $false
| ~ spl8_6 ),
inference(subsumption_resolution,[],[f160,f36]) ).
fof(f160,plain,
( empty_set = sK0
| ~ spl8_6 ),
inference(resolution,[],[f151,f126]) ).
fof(f151,plain,
( ! [X1] : ~ in(X1,sK0)
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f164,plain,
~ spl8_6,
inference(avatar_contradiction_clause,[],[f163]) ).
fof(f163,plain,
( $false
| ~ spl8_6 ),
inference(subsumption_resolution,[],[f159,f36]) ).
fof(f159,plain,
( empty_set = sK0
| ~ spl8_6 ),
inference(resolution,[],[f151,f124]) ).
fof(f162,plain,
~ spl8_6,
inference(avatar_contradiction_clause,[],[f161]) ).
fof(f161,plain,
( $false
| ~ spl8_6 ),
inference(subsumption_resolution,[],[f156,f36]) ).
fof(f156,plain,
( empty_set = sK0
| ~ spl8_6 ),
inference(resolution,[],[f151,f41]) ).
fof(f155,plain,
( spl8_6
| spl8_7 ),
inference(avatar_split_clause,[],[f143,f153,f150]) ).
fof(f143,plain,
! [X0,X1] :
( ~ in(X0,sK1)
| ~ in(X1,sK0)
| in(X0,sK3) ),
inference(resolution,[],[f53,f82]) ).
fof(f82,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(sK0,sK1))
| in(X1,sK3) ),
inference(superposition,[],[f52,f35]) ).
fof(f114,plain,
( spl8_3
| spl8_4
| ~ spl8_5 ),
inference(avatar_split_clause,[],[f101,f111,f107,f103]) ).
fof(f101,plain,
( empty_set != cartesian_product2(sK0,sK1)
| empty_set = sK2
| empty_set = sK3 ),
inference(superposition,[],[f48,f35]) ).
fof(f48,plain,
! [X0,X1] :
( empty_set != cartesian_product2(X0,X1)
| empty_set = X0
| empty_set = X1 ),
inference(cnf_transformation,[],[f28]) ).
fof(f67,plain,
( ~ spl8_1
| ~ spl8_2 ),
inference(avatar_split_clause,[],[f38,f64,f60]) ).
fof(f38,plain,
( sK1 != sK3
| sK0 != sK2 ),
inference(cnf_transformation,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET980+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.12/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34 % Computer : n017.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri May 3 16:50:23 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % (13011)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.35 % (13013)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.35 % (13012)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.36 TRYING [1]
% 0.18/0.36 TRYING [2]
% 0.18/0.36 % (13014)WARNING: value z3 for option sas not known
% 0.18/0.36 % (13015)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.18/0.36 % (13014)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)
% 0.18/0.36 % (13016)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)
% 0.18/0.36 % (13018)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)
% 0.18/0.36 TRYING [3]
% 0.18/0.36 TRYING [1]
% 0.18/0.36 TRYING [2]
% 0.18/0.36 % (13017)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)
% 0.18/0.36 TRYING [3]
% 0.18/0.37 TRYING [4]
% 0.18/0.37 TRYING [4]
% 0.18/0.38 % (13014)First to succeed.
% 0.18/0.38 % (13014)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13011"
% 0.18/0.38 % (13014)Refutation found. Thanks to Tanya!
% 0.18/0.38 % SZS status Theorem for theBenchmark
% 0.18/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.38 % (13014)------------------------------
% 0.18/0.38 % (13014)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.18/0.38 % (13014)Termination reason: Refutation
% 0.18/0.38
% 0.18/0.38 % (13014)Memory used [KB]: 930
% 0.18/0.38 % (13014)Time elapsed: 0.021 s
% 0.18/0.38 % (13014)Instructions burned: 24 (million)
% 0.18/0.38 % (13011)Success in time 0.037 s
%------------------------------------------------------------------------------