TSTP Solution File: SET077+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET077+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.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 May 21 03:15:55 EDT 2024
% Result : Theorem 0.15s 0.33s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 26
% Syntax : Number of formulae : 71 ( 35 unt; 0 def)
% Number of atoms : 156 ( 15 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 126 ( 41 ~; 38 |; 27 &)
% ( 14 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 57 ( 47 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f324,plain,
$false,
inference(avatar_sat_refutation,[],[f271,f276,f281,f285,f289,f294,f298,f303,f308,f312,f316,f320,f323]) ).
fof(f323,plain,
( spl7_1
| ~ spl7_11 ),
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f322,plain,
( $false
| spl7_1
| ~ spl7_11 ),
inference(resolution,[],[f315,f270]) ).
fof(f270,plain,
( ~ member(unordered_pair(sK0,sK0),universal_class)
| spl7_1 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f268,plain,
( spl7_1
<=> member(unordered_pair(sK0,sK0),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
fof(f315,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
| ~ spl7_11 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f314,plain,
( spl7_11
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_11])]) ).
fof(f320,plain,
spl7_12,
inference(avatar_split_clause,[],[f222,f318]) ).
fof(f318,plain,
( spl7_12
<=> ! [X1] :
( subclass(sK6,X1)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_12])]) ).
fof(f222,plain,
! [X1] :
( subclass(sK6,X1)
| ~ inductive(X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
( ! [X1] :
( subclass(sK6,X1)
| ~ inductive(X1) )
& inductive(sK6)
& member(sK6,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f84,f133]) ).
fof(f133,plain,
( ? [X0] :
( ! [X1] :
( subclass(X0,X1)
| ~ inductive(X1) )
& inductive(X0)
& member(X0,universal_class) )
=> ( ! [X1] :
( subclass(sK6,X1)
| ~ inductive(X1) )
& inductive(sK6)
& member(sK6,universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
? [X0] :
( ! [X1] :
( subclass(X0,X1)
| ~ inductive(X1) )
& inductive(X0)
& member(X0,universal_class) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
? [X0] :
( ! [X1] :
( inductive(X1)
=> subclass(X0,X1) )
& inductive(X0)
& member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity) ).
fof(f316,plain,
spl7_11,
inference(avatar_split_clause,[],[f160,f314]) ).
fof(f160,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
fof(f312,plain,
spl7_10,
inference(avatar_split_clause,[],[f151,f310]) ).
fof(f310,plain,
( spl7_10
<=> ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_10])]) ).
fof(f151,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) )
& ( ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) )
| ~ inductive(X0) ) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) )
& ( ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) )
| ~ inductive(X0) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( inductive(X0)
<=> ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive_defn) ).
fof(f308,plain,
spl7_9,
inference(avatar_split_clause,[],[f137,f305]) ).
fof(f305,plain,
( spl7_9
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_9])]) ).
fof(f137,plain,
subclass(successor_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation_defn1) ).
fof(f303,plain,
spl7_8,
inference(avatar_split_clause,[],[f136,f300]) ).
fof(f300,plain,
( spl7_8
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_8])]) ).
fof(f136,plain,
subclass(element_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation) ).
fof(f298,plain,
spl7_7,
inference(avatar_split_clause,[],[f262,f296]) ).
fof(f296,plain,
( spl7_7
<=> ! [X1] : subclass(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_7])]) ).
fof(f262,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f169]) ).
fof(f169,plain,
! [X0,X1] :
( subclass(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) )
& ( ( subclass(X1,X0)
& subclass(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) )
& ( ( subclass(X1,X0)
& subclass(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X1,X0)
& subclass(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality) ).
fof(f294,plain,
spl7_6,
inference(avatar_split_clause,[],[f220,f291]) ).
fof(f291,plain,
( spl7_6
<=> member(sK6,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).
fof(f220,plain,
member(sK6,universal_class),
inference(cnf_transformation,[],[f134]) ).
fof(f289,plain,
spl7_5,
inference(avatar_split_clause,[],[f139,f287]) ).
fof(f287,plain,
( spl7_5
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).
fof(f139,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f285,plain,
spl7_4,
inference(avatar_split_clause,[],[f138,f283]) ).
fof(f283,plain,
( spl7_4
<=> ! [X0] : ~ member(X0,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).
fof(f138,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_defn) ).
fof(f281,plain,
spl7_3,
inference(avatar_split_clause,[],[f221,f278]) ).
fof(f278,plain,
( spl7_3
<=> inductive(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).
fof(f221,plain,
inductive(sK6),
inference(cnf_transformation,[],[f134]) ).
fof(f276,plain,
spl7_2,
inference(avatar_split_clause,[],[f218,f273]) ).
fof(f273,plain,
( spl7_2
<=> function(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
fof(f218,plain,
function(sK5),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
( ! [X1] :
( member(apply(sK5,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f83,f131]) ).
fof(f131,plain,
( ? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) )
=> ( ! [X1] :
( member(apply(sK5,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,plain,
? [X0] :
( ! [X1] :
( member(X1,universal_class)
=> ( member(apply(X0,X1),X1)
| null_class = X1 ) )
& function(X0) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
? [X8] :
( ! [X1] :
( member(X1,universal_class)
=> ( member(apply(X8,X1),X1)
| null_class = X1 ) )
& function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice) ).
fof(f271,plain,
~ spl7_1,
inference(avatar_split_clause,[],[f228,f268]) ).
fof(f228,plain,
~ member(unordered_pair(sK0,sK0),universal_class),
inference(definition_unfolding,[],[f135,f141]) ).
fof(f141,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f135,plain,
~ member(singleton(sK0),universal_class),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
~ member(singleton(sK0),universal_class),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f71,f85]) ).
fof(f85,plain,
( ? [X0] : ~ member(singleton(X0),universal_class)
=> ~ member(singleton(sK0),universal_class) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
? [X0] : ~ member(singleton(X0),universal_class),
inference(ennf_transformation,[],[f45]) ).
fof(f45,negated_conjecture,
~ ! [X0] : member(singleton(X0),universal_class),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
! [X0] : member(singleton(X0),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletons_are_sets) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET077+1 : TPTP v8.2.0. Bugfixed v5.4.0.
% 0.00/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.30 % Computer : n019.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon May 20 12:59:38 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.31 % (9412)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.32 % (9416)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.32 % (9417)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.32 % (9415)WARNING: value z3 for option sas not known
% 0.15/0.32 % (9413)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.32 % (9414)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.32 % (9415)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.32 % (9418)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.32 % (9419)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.32 % (9417)First to succeed.
% 0.15/0.33 % (9417)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9412"
% 0.15/0.33 % (9418)Also succeeded, but the first one will report.
% 0.15/0.33 % (9417)Refutation found. Thanks to Tanya!
% 0.15/0.33 % SZS status Theorem for theBenchmark
% 0.15/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.33 % (9417)------------------------------
% 0.15/0.33 % (9417)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.33 % (9417)Termination reason: Refutation
% 0.15/0.33
% 0.15/0.33 % (9417)Memory used [KB]: 969
% 0.15/0.33 % (9417)Time elapsed: 0.006 s
% 0.15/0.33 % (9417)Instructions burned: 10 (million)
% 0.15/0.33 % (9412)Success in time 0.02 s
%------------------------------------------------------------------------------