TSTP Solution File: SEU177+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU177+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n010.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 15:23:15 EDT 2024
% Result : Theorem 0.16s 0.55s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 53
% Syntax : Number of formulae : 201 ( 27 unt; 0 def)
% Number of atoms : 679 ( 131 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 769 ( 291 ~; 287 |; 116 &)
% ( 46 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 15 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 4 con; 0-3 aty)
% Number of variables : 374 ( 320 !; 54 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8562,plain,
$false,
inference(avatar_sat_refutation,[],[f746,f2414,f4148,f4229,f4334,f4367,f7907,f8492,f8561]) ).
fof(f8561,plain,
spl52_1,
inference(avatar_contradiction_clause,[],[f8560]) ).
fof(f8560,plain,
( $false
| spl52_1 ),
inference(subsumption_resolution,[],[f8559,f396]) ).
fof(f396,plain,
relation(sK12),
inference(cnf_transformation,[],[f263]) ).
fof(f263,plain,
( ( ~ in(sK11,relation_rng(sK12))
| ~ in(sK10,relation_dom(sK12)) )
& in(ordered_pair(sK10,sK11),sK12)
& relation(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f156,f262]) ).
fof(f262,plain,
( ? [X0,X1,X2] :
( ( ~ in(X1,relation_rng(X2))
| ~ in(X0,relation_dom(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) )
=> ( ( ~ in(sK11,relation_rng(sK12))
| ~ in(sK10,relation_dom(sK12)) )
& in(ordered_pair(sK10,sK11),sK12)
& relation(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f156,plain,
? [X0,X1,X2] :
( ( ~ in(X1,relation_rng(X2))
| ~ in(X0,relation_dom(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
? [X0,X1,X2] :
( ( ~ in(X1,relation_rng(X2))
| ~ in(X0,relation_dom(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
inference(negated_conjecture,[],[f94]) ).
fof(f94,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f8559,plain,
( ~ relation(sK12)
| spl52_1 ),
inference(subsumption_resolution,[],[f8533,f741]) ).
fof(f741,plain,
( ~ in(sK10,relation_dom(sK12))
| spl52_1 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f739,plain,
( spl52_1
<=> in(sK10,relation_dom(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_1])]) ).
fof(f8533,plain,
( in(sK10,relation_dom(sK12))
| ~ relation(sK12) ),
inference(resolution,[],[f647,f397]) ).
fof(f397,plain,
in(ordered_pair(sK10,sK11),sK12),
inference(cnf_transformation,[],[f263]) ).
fof(f647,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f498]) ).
fof(f498,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f303]) ).
fof(f303,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK21(X0,X1),X3),X0)
| ~ in(sK21(X0,X1),X1) )
& ( in(ordered_pair(sK21(X0,X1),sK22(X0,X1)),X0)
| in(sK21(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK23(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22,sK23])],[f299,f302,f301,f300]) ).
fof(f300,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(sK21(X0,X1),X3),X0)
| ~ in(sK21(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK21(X0,X1),X4),X0)
| in(sK21(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f301,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK21(X0,X1),X4),X0)
=> in(ordered_pair(sK21(X0,X1),sK22(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f302,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK23(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f299,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f298]) ).
fof(f298,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f8492,plain,
spl52_2,
inference(avatar_contradiction_clause,[],[f8491]) ).
fof(f8491,plain,
( $false
| spl52_2 ),
inference(subsumption_resolution,[],[f8490,f396]) ).
fof(f8490,plain,
( ~ relation(sK12)
| spl52_2 ),
inference(subsumption_resolution,[],[f8464,f745]) ).
fof(f745,plain,
( ~ in(sK11,relation_rng(sK12))
| spl52_2 ),
inference(avatar_component_clause,[],[f743]) ).
fof(f743,plain,
( spl52_2
<=> in(sK11,relation_rng(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_2])]) ).
fof(f8464,plain,
( in(sK11,relation_rng(sK12))
| ~ relation(sK12) ),
inference(resolution,[],[f645,f397]) ).
fof(f645,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X6,X5),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f494]) ).
fof(f494,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f297,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK18(X0,X1)),X0)
| ~ in(sK18(X0,X1),X1) )
& ( in(ordered_pair(sK19(X0,X1),sK18(X0,X1)),X0)
| in(sK18(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK20(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20])],[f293,f296,f295,f294]) ).
fof(f294,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(X3,sK18(X0,X1)),X0)
| ~ in(sK18(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK18(X0,X1)),X0)
| in(sK18(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f295,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK18(X0,X1)),X0)
=> in(ordered_pair(sK19(X0,X1),sK18(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f296,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK20(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f293,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f292]) ).
fof(f292,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f206]) ).
fof(f206,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f7907,plain,
( ~ spl52_13
| ~ spl52_14 ),
inference(avatar_split_clause,[],[f7897,f7904,f7900]) ).
fof(f7900,plain,
( spl52_13
<=> subset(singleton(sK10),empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_13])]) ).
fof(f7904,plain,
( spl52_14
<=> in(empty_set,singleton(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_14])]) ).
fof(f7897,plain,
( ~ in(empty_set,singleton(sK12))
| ~ subset(singleton(sK10),empty_set) ),
inference(resolution,[],[f7760,f937]) ).
fof(f937,plain,
! [X0] :
( in(X0,singleton(empty_set))
| ~ subset(X0,empty_set) ),
inference(superposition,[],[f662,f399]) ).
fof(f399,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[],[f93]) ).
fof(f93,axiom,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f662,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f584]) ).
fof(f584,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f357]) ).
fof(f357,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ( ( ~ subset(sK39(X0,X1),X0)
| ~ in(sK39(X0,X1),X1) )
& ( subset(sK39(X0,X1),X0)
| in(sK39(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39])],[f355,f356]) ).
fof(f356,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ subset(sK39(X0,X1),X0)
| ~ in(sK39(X0,X1),X1) )
& ( subset(sK39(X0,X1),X0)
| in(sK39(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f355,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f354]) ).
fof(f354,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( powerset(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f7760,plain,
! [X0] :
( ~ in(singleton(sK10),singleton(X0))
| ~ in(X0,singleton(sK12)) ),
inference(resolution,[],[f7743,f446]) ).
fof(f446,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f279]) ).
fof(f279,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f106]) ).
fof(f106,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(f7743,plain,
! [X0] :
( ~ subset(X0,singleton(sK12))
| ~ in(singleton(sK10),X0) ),
inference(resolution,[],[f7506,f456]) ).
fof(f456,plain,
! [X0,X1] :
( ~ disjoint(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f183]) ).
fof(f183,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f7506,plain,
! [X0] :
( disjoint(singleton(singleton(sK10)),X0)
| ~ subset(X0,singleton(sK12)) ),
inference(resolution,[],[f7307,f539]) ).
fof(f539,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f216]) ).
fof(f216,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f7307,plain,
! [X0] :
( disjoint(X0,singleton(singleton(sK10)))
| ~ subset(X0,singleton(sK12)) ),
inference(resolution,[],[f7303,f465]) ).
fof(f465,plain,
! [X2,X0,X1] :
( ~ disjoint(X1,X2)
| disjoint(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f193]) ).
fof(f193,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f129]) ).
fof(f129,axiom,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X1) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(f7303,plain,
disjoint(singleton(sK12),singleton(singleton(sK10))),
inference(trivial_inequality_removal,[],[f7281]) ).
fof(f7281,plain,
( singleton(sK12) != singleton(sK12)
| disjoint(singleton(sK12),singleton(singleton(sK10))) ),
inference(superposition,[],[f438,f7041]) ).
fof(f7041,plain,
singleton(sK12) = set_difference(singleton(sK12),singleton(singleton(sK10))),
inference(resolution,[],[f7031,f454]) ).
fof(f454,plain,
! [X0,X1] :
( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ),
inference(cnf_transformation,[],[f283]) ).
fof(f283,plain,
! [X0,X1] :
( ( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) )
& ( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ) ),
inference(nnf_transformation,[],[f130]) ).
fof(f130,axiom,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f7031,plain,
~ in(singleton(sK10),singleton(sK12)),
inference(resolution,[],[f6732,f5557]) ).
fof(f5557,plain,
! [X0,X1] : in(singleton(X0),ordered_pair(X0,X1)),
inference(superposition,[],[f973,f520]) ).
fof(f520,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f973,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(resolution,[],[f666,f668]) ).
fof(f668,plain,
! [X0,X1] : sP6(X1,X0,unordered_pair(X0,X1)),
inference(equality_resolution,[],[f610]) ).
fof(f610,plain,
! [X2,X0,X1] :
( sP6(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f371]) ).
fof(f371,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ~ sP6(X1,X0,X2) )
& ( sP6(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> sP6(X1,X0,X2) ),
inference(definition_folding,[],[f12,f254]) ).
fof(f254,plain,
! [X1,X0,X2] :
( sP6(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f12,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f666,plain,
! [X2,X1,X4] :
( ~ sP6(X4,X1,X2)
| in(X4,X2) ),
inference(equality_resolution,[],[f606]) ).
fof(f606,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f370]) ).
fof(f370,plain,
! [X0,X1,X2] :
( ( sP6(X0,X1,X2)
| ( ( ( sK45(X0,X1,X2) != X0
& sK45(X0,X1,X2) != X1 )
| ~ in(sK45(X0,X1,X2),X2) )
& ( sK45(X0,X1,X2) = X0
| sK45(X0,X1,X2) = X1
| in(sK45(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP6(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f368,f369]) ).
fof(f369,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) )
=> ( ( ( sK45(X0,X1,X2) != X0
& sK45(X0,X1,X2) != X1 )
| ~ in(sK45(X0,X1,X2),X2) )
& ( sK45(X0,X1,X2) = X0
| sK45(X0,X1,X2) = X1
| in(sK45(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f368,plain,
! [X0,X1,X2] :
( ( sP6(X0,X1,X2)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP6(X0,X1,X2) ) ),
inference(rectify,[],[f367]) ).
fof(f367,plain,
! [X1,X0,X2] :
( ( sP6(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| ~ sP6(X1,X0,X2) ) ),
inference(flattening,[],[f366]) ).
fof(f366,plain,
! [X1,X0,X2] :
( ( sP6(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| ~ sP6(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f254]) ).
fof(f6732,plain,
! [X0] :
( ~ in(X0,ordered_pair(sK10,sK11))
| ~ in(X0,singleton(sK12)) ),
inference(resolution,[],[f6727,f419]) ).
fof(f419,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f270]) ).
fof(f270,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ( in(sK15(X0,X1),X1)
& in(sK15(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f163,f269]) ).
fof(f269,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
=> ( in(sK15(X0,X1),X1)
& in(sK15(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f163,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X3] :
~ ( in(X3,X1)
& in(X3,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f112]) ).
fof(f112,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f6727,plain,
disjoint(ordered_pair(sK10,sK11),singleton(sK12)),
inference(trivial_inequality_removal,[],[f6705]) ).
fof(f6705,plain,
( ordered_pair(sK10,sK11) != ordered_pair(sK10,sK11)
| disjoint(ordered_pair(sK10,sK11),singleton(sK12)) ),
inference(superposition,[],[f438,f3449]) ).
fof(f3449,plain,
ordered_pair(sK10,sK11) = set_difference(ordered_pair(sK10,sK11),singleton(sK12)),
inference(resolution,[],[f454,f726]) ).
fof(f726,plain,
~ in(sK12,ordered_pair(sK10,sK11)),
inference(resolution,[],[f541,f397]) ).
fof(f541,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f219]) ).
fof(f219,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(f438,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f274]) ).
fof(f274,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_difference(X0,X1) != X0 )
& ( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f136]) ).
fof(f136,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f4367,plain,
( ~ spl52_11
| ~ spl52_12
| spl52_2 ),
inference(avatar_split_clause,[],[f4356,f743,f4364,f4360]) ).
fof(f4360,plain,
( spl52_11
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_11])]) ).
fof(f4364,plain,
( spl52_12
<=> in(empty_set,relation_rng(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_12])]) ).
fof(f4356,plain,
( ~ in(empty_set,relation_rng(sK12))
| ~ empty(sK11)
| spl52_2 ),
inference(resolution,[],[f4092,f3047]) ).
fof(f3047,plain,
! [X0] :
( in(X0,singleton(empty_set))
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f3045,f483]) ).
fof(f483,plain,
! [X0] : ~ empty(singleton(X0)),
inference(cnf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] : ~ empty(singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(f3045,plain,
! [X0] :
( ~ empty(X0)
| in(X0,singleton(empty_set))
| empty(singleton(empty_set)) ),
inference(resolution,[],[f3042,f521]) ).
fof(f521,plain,
! [X0,X1] :
( ~ element(X1,X0)
| in(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f316]) ).
fof(f316,plain,
! [X0,X1] :
( ( ( ( element(X1,X0)
| ~ empty(X1) )
& ( empty(X1)
| ~ element(X1,X0) ) )
| ~ empty(X0) )
& ( ( ( element(X1,X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ element(X1,X0) ) )
| empty(X0) ) ),
inference(nnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) )
& ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f3042,plain,
! [X0] :
( element(X0,singleton(empty_set))
| ~ empty(X0) ),
inference(superposition,[],[f3030,f399]) ).
fof(f3030,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ empty(X0) ),
inference(resolution,[],[f435,f590]) ).
fof(f590,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f236,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f134]) ).
fof(f134,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f435,plain,
! [X0,X1] :
( in(sK16(X0,X1),X0)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f273]) ).
fof(f273,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ( ~ in(sK16(X0,X1),X1)
& in(sK16(X0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f181,f272]) ).
fof(f272,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK16(X0,X1),X1)
& in(sK16(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f181,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f4092,plain,
( ! [X0] :
( ~ in(sK11,singleton(X0))
| ~ in(X0,relation_rng(sK12)) )
| spl52_2 ),
inference(resolution,[],[f4078,f446]) ).
fof(f4078,plain,
( ! [X0] :
( ~ subset(X0,relation_rng(sK12))
| ~ in(sK11,X0) )
| spl52_2 ),
inference(resolution,[],[f3938,f456]) ).
fof(f3938,plain,
( ! [X0] :
( disjoint(singleton(sK11),X0)
| ~ subset(X0,relation_rng(sK12)) )
| spl52_2 ),
inference(resolution,[],[f3747,f539]) ).
fof(f3747,plain,
( ! [X0] :
( disjoint(X0,singleton(sK11))
| ~ subset(X0,relation_rng(sK12)) )
| spl52_2 ),
inference(resolution,[],[f465,f3586]) ).
fof(f3586,plain,
( disjoint(relation_rng(sK12),singleton(sK11))
| spl52_2 ),
inference(trivial_inequality_removal,[],[f3567]) ).
fof(f3567,plain,
( relation_rng(sK12) != relation_rng(sK12)
| disjoint(relation_rng(sK12),singleton(sK11))
| spl52_2 ),
inference(superposition,[],[f438,f3448]) ).
fof(f3448,plain,
( relation_rng(sK12) = set_difference(relation_rng(sK12),singleton(sK11))
| spl52_2 ),
inference(resolution,[],[f454,f745]) ).
fof(f4334,plain,
( ~ spl52_9
| ~ spl52_10
| spl52_1 ),
inference(avatar_split_clause,[],[f4323,f739,f4331,f4327]) ).
fof(f4327,plain,
( spl52_9
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_9])]) ).
fof(f4331,plain,
( spl52_10
<=> in(empty_set,relation_dom(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_10])]) ).
fof(f4323,plain,
( ~ in(empty_set,relation_dom(sK12))
| ~ empty(sK10)
| spl52_1 ),
inference(resolution,[],[f4014,f3047]) ).
fof(f4014,plain,
( ! [X0] :
( ~ in(sK10,singleton(X0))
| ~ in(X0,relation_dom(sK12)) )
| spl52_1 ),
inference(resolution,[],[f4000,f446]) ).
fof(f4000,plain,
( ! [X0] :
( ~ subset(X0,relation_dom(sK12))
| ~ in(sK10,X0) )
| spl52_1 ),
inference(resolution,[],[f3878,f456]) ).
fof(f3878,plain,
( ! [X0] :
( disjoint(singleton(sK10),X0)
| ~ subset(X0,relation_dom(sK12)) )
| spl52_1 ),
inference(resolution,[],[f3746,f539]) ).
fof(f3746,plain,
( ! [X0] :
( disjoint(X0,singleton(sK10))
| ~ subset(X0,relation_dom(sK12)) )
| spl52_1 ),
inference(resolution,[],[f465,f3479]) ).
fof(f3479,plain,
( disjoint(relation_dom(sK12),singleton(sK10))
| spl52_1 ),
inference(trivial_inequality_removal,[],[f3460]) ).
fof(f3460,plain,
( relation_dom(sK12) != relation_dom(sK12)
| disjoint(relation_dom(sK12),singleton(sK10))
| spl52_1 ),
inference(superposition,[],[f438,f3447]) ).
fof(f3447,plain,
( relation_dom(sK12) = set_difference(relation_dom(sK12),singleton(sK10))
| spl52_1 ),
inference(resolution,[],[f454,f741]) ).
fof(f4229,plain,
( spl52_7
| ~ spl52_8
| spl52_2 ),
inference(avatar_split_clause,[],[f3985,f743,f4226,f4222]) ).
fof(f4222,plain,
( spl52_7
<=> empty(relation_rng(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_7])]) ).
fof(f4226,plain,
( spl52_8
<=> subset(relation_rng(sK12),singleton(sK11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_8])]) ).
fof(f3985,plain,
( ~ subset(relation_rng(sK12),singleton(sK11))
| empty(relation_rng(sK12))
| spl52_2 ),
inference(resolution,[],[f3745,f2027]) ).
fof(f2027,plain,
! [X0] :
( ~ disjoint(X0,X0)
| empty(X0) ),
inference(superposition,[],[f1992,f515]) ).
fof(f515,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f56]) ).
fof(f56,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f1992,plain,
! [X0,X1] :
( empty(set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ),
inference(resolution,[],[f1967,f416]) ).
fof(f416,plain,
! [X2,X0,X1] :
( ~ in(X2,set_intersection2(X0,X1))
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f268]) ).
fof(f268,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( in(sK14(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f162,f267]) ).
fof(f267,plain,
! [X0,X1] :
( ? [X3] : in(X3,set_intersection2(X0,X1))
=> in(sK14(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f162,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( ? [X3] : in(X3,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f124]) ).
fof(f124,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f1967,plain,
! [X0] :
( in(sK25(X0),X0)
| empty(X0) ),
inference(resolution,[],[f521,f504]) ).
fof(f504,plain,
! [X0] : element(sK25(X0),X0),
inference(cnf_transformation,[],[f309]) ).
fof(f309,plain,
! [X0] : element(sK25(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f47,f308]) ).
fof(f308,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK25(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f47,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f3745,plain,
( ! [X0] :
( disjoint(X0,relation_rng(sK12))
| ~ subset(X0,singleton(sK11)) )
| spl52_2 ),
inference(resolution,[],[f465,f3593]) ).
fof(f3593,plain,
( disjoint(singleton(sK11),relation_rng(sK12))
| spl52_2 ),
inference(resolution,[],[f3586,f539]) ).
fof(f4148,plain,
( spl52_5
| ~ spl52_6
| spl52_1 ),
inference(avatar_split_clause,[],[f3972,f739,f4145,f4141]) ).
fof(f4141,plain,
( spl52_5
<=> empty(relation_dom(sK12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_5])]) ).
fof(f4145,plain,
( spl52_6
<=> subset(relation_dom(sK12),singleton(sK10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_6])]) ).
fof(f3972,plain,
( ~ subset(relation_dom(sK12),singleton(sK10))
| empty(relation_dom(sK12))
| spl52_1 ),
inference(resolution,[],[f3744,f2027]) ).
fof(f3744,plain,
( ! [X0] :
( disjoint(X0,relation_dom(sK12))
| ~ subset(X0,singleton(sK10)) )
| spl52_1 ),
inference(resolution,[],[f465,f3486]) ).
fof(f3486,plain,
( disjoint(singleton(sK10),relation_dom(sK12))
| spl52_1 ),
inference(resolution,[],[f3479,f539]) ).
fof(f2414,plain,
( ~ spl52_3
| spl52_4 ),
inference(avatar_split_clause,[],[f2405,f2411,f2407]) ).
fof(f2407,plain,
( spl52_3
<=> sP1(empty_set,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_3])]) ).
fof(f2411,plain,
( spl52_4
<=> sP0(empty_set,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl52_4])]) ).
fof(f2405,plain,
( sP0(empty_set,empty_set)
| ~ sP1(empty_set,empty_set) ),
inference(forward_demodulation,[],[f2404,f652]) ).
fof(f652,plain,
empty_set = set_meet(empty_set),
inference(equality_resolution,[],[f651]) ).
fof(f651,plain,
! [X0] :
( empty_set = set_meet(X0)
| empty_set != X0 ),
inference(equality_resolution,[],[f535]) ).
fof(f535,plain,
! [X0,X1] :
( set_meet(X0) = X1
| empty_set != X1
| empty_set != X0 ),
inference(cnf_transformation,[],[f325]) ).
fof(f325,plain,
! [X0,X1] :
( ( ( ( set_meet(X0) = X1
| empty_set != X1 )
& ( empty_set = X1
| set_meet(X0) != X1 ) )
| empty_set != X0 )
& ( sP1(X1,X0)
| empty_set = X0 ) ),
inference(nnf_transformation,[],[f246]) ).
fof(f246,plain,
! [X0,X1] :
( ( ( set_meet(X0) = X1
<=> empty_set = X1 )
| empty_set != X0 )
& ( sP1(X1,X0)
| empty_set = X0 ) ),
inference(definition_folding,[],[f212,f245,f244]) ).
fof(f244,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f245,plain,
! [X1,X0] :
( ( set_meet(X0) = X1
<=> sP0(X0,X1) )
| ~ sP1(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f212,plain,
! [X0,X1] :
( ( ( set_meet(X0) = X1
<=> empty_set = X1 )
| empty_set != X0 )
& ( ( set_meet(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) ) ) )
| empty_set = X0 ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( ( empty_set = X0
=> ( set_meet(X0) = X1
<=> empty_set = X1 ) )
& ( empty_set != X0
=> ( set_meet(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X3,X0)
=> in(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setfam_1) ).
fof(f2404,plain,
( ~ sP1(empty_set,empty_set)
| sP0(empty_set,set_meet(empty_set)) ),
inference(superposition,[],[f650,f652]) ).
fof(f650,plain,
! [X1] :
( ~ sP1(set_meet(X1),X1)
| sP0(X1,set_meet(X1)) ),
inference(equality_resolution,[],[f525]) ).
fof(f525,plain,
! [X0,X1] :
( sP0(X1,X0)
| set_meet(X1) != X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f318]) ).
fof(f318,plain,
! [X0,X1] :
( ( ( set_meet(X1) = X0
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| set_meet(X1) != X0 ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f317]) ).
fof(f317,plain,
! [X1,X0] :
( ( ( set_meet(X0) = X1
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| set_meet(X0) != X1 ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f245]) ).
fof(f746,plain,
( ~ spl52_1
| ~ spl52_2 ),
inference(avatar_split_clause,[],[f398,f743,f739]) ).
fof(f398,plain,
( ~ in(sK11,relation_rng(sK12))
| ~ in(sK10,relation_dom(sK12)) ),
inference(cnf_transformation,[],[f263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU177+2 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Apr 29 20:53:20 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (15826)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (15829)WARNING: value z3 for option sas not known
% 0.11/0.34 % (15829)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)
% 0.11/0.34 % (15833)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.11/0.34 % (15830)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.34 % (15831)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.11/0.34 % (15832)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.11/0.35 % (15828)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.36 TRYING [1]
% 0.11/0.36 TRYING [2]
% 0.11/0.36 % (15827)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.37 TRYING [3]
% 0.16/0.45 TRYING [4]
% 0.16/0.47 TRYING [1]
% 0.16/0.47 TRYING [2]
% 0.16/0.49 TRYING [3]
% 0.16/0.51 TRYING [1]
% 0.16/0.53 TRYING [2]
% 0.16/0.54 % (15829)First to succeed.
% 0.16/0.55 % (15829)Refutation found. Thanks to Tanya!
% 0.16/0.55 % SZS status Theorem for theBenchmark
% 0.16/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.55 % (15829)------------------------------
% 0.16/0.55 % (15829)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.55 % (15829)Termination reason: Refutation
% 0.16/0.55
% 0.16/0.55 % (15829)Memory used [KB]: 3802
% 0.16/0.55 % (15829)Time elapsed: 0.209 s
% 0.16/0.55 % (15829)Instructions burned: 397 (million)
% 0.16/0.55 % (15829)------------------------------
% 0.16/0.55 % (15829)------------------------------
% 0.16/0.55 % (15826)Success in time 0.228 s
%------------------------------------------------------------------------------