TSTP Solution File: SET166-6 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET166-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n005.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 : Thu Aug 31 15:38:25 EDT 2023
% Result : Unsatisfiable 0.22s 0.50s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 57
% Syntax : Number of formulae : 128 ( 38 unt; 0 def)
% Number of atoms : 251 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 208 ( 85 ~; 89 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 40 ( 38 usr; 34 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 14 con; 0-2 aty)
% Number of variables : 25 (; 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f396,plain,
$false,
inference(avatar_smt_refutation,[],[f213,f217,f221,f225,f229,f233,f237,f241,f245,f249,f253,f257,f261,f265,f272,f298,f305,f325,f332,f339,f346,f353,f364,f369,f374,f386,f390,f395]) ).
fof(f395,plain,
( spl1_1
| ~ spl1_16
| spl1_33 ),
inference(avatar_contradiction_clause,[],[f394]) ).
fof(f394,plain,
( $false
| spl1_1
| ~ spl1_16
| spl1_33 ),
inference(subsumption_resolution,[],[f393,f297]) ).
fof(f297,plain,
( member(x,universal_class)
| ~ spl1_16 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f296,plain,
( spl1_16
<=> member(x,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
fof(f393,plain,
( ~ member(x,universal_class)
| spl1_1
| spl1_33 ),
inference(subsumption_resolution,[],[f392,f212]) ).
fof(f212,plain,
( ~ member(x,z)
| spl1_1 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f211,plain,
( spl1_1
<=> member(x,z) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
fof(f392,plain,
( member(x,z)
| ~ member(x,universal_class)
| spl1_33 ),
inference(resolution,[],[f385,f25]) ).
fof(f25,axiom,
! [X0,X4] :
( member(X4,complement(X0))
| member(X4,X0)
| ~ member(X4,universal_class) ),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',complement2) ).
fof(f385,plain,
( ~ member(x,complement(z))
| spl1_33 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f384,plain,
( spl1_33
<=> member(x,complement(z)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_33])]) ).
fof(f390,plain,
( spl1_2
| ~ spl1_16
| spl1_32 ),
inference(avatar_contradiction_clause,[],[f389]) ).
fof(f389,plain,
( $false
| spl1_2
| ~ spl1_16
| spl1_32 ),
inference(subsumption_resolution,[],[f388,f297]) ).
fof(f388,plain,
( ~ member(x,universal_class)
| spl1_2
| spl1_32 ),
inference(subsumption_resolution,[],[f387,f216]) ).
fof(f216,plain,
( ~ member(x,y)
| spl1_2 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f215,plain,
( spl1_2
<=> member(x,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
fof(f387,plain,
( member(x,y)
| ~ member(x,universal_class)
| spl1_32 ),
inference(resolution,[],[f382,f25]) ).
fof(f382,plain,
( ~ member(x,complement(y))
| spl1_32 ),
inference(avatar_component_clause,[],[f381]) ).
fof(f381,plain,
( spl1_32
<=> member(x,complement(y)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_32])]) ).
fof(f386,plain,
( ~ spl1_32
| ~ spl1_33
| spl1_15 ),
inference(avatar_split_clause,[],[f375,f270,f384,f381]) ).
fof(f270,plain,
( spl1_15
<=> member(x,intersection(complement(y),complement(z))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
fof(f375,plain,
( ~ member(x,complement(z))
| ~ member(x,complement(y))
| spl1_15 ),
inference(resolution,[],[f23,f271]) ).
fof(f271,plain,
( ~ member(x,intersection(complement(y),complement(z)))
| spl1_15 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f23,axiom,
! [X0,X1,X4] :
( member(X4,intersection(X0,X1))
| ~ member(X4,X1)
| ~ member(X4,X0) ),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',intersection3) ).
fof(f374,plain,
( spl1_31
| ~ spl1_13 ),
inference(avatar_split_clause,[],[f370,f259,f372]) ).
fof(f372,plain,
( spl1_31
<=> sQ0_eqProxy(singleton_relation,intersection(complement(compose(element_relation,complement(identity_relation))),element_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_31])]) ).
fof(f259,plain,
( spl1_13
<=> sQ0_eqProxy(intersection(complement(compose(element_relation,complement(identity_relation))),element_relation),singleton_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
fof(f370,plain,
( sQ0_eqProxy(singleton_relation,intersection(complement(compose(element_relation,complement(identity_relation))),element_relation))
| ~ spl1_13 ),
inference(resolution,[],[f260,f209]) ).
fof(f209,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(X0,X1)
| sQ0_eqProxy(X1,X0) ),
inference(equality_proxy_axiom,[],[f183]) ).
fof(f183,plain,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ0_eqProxy])]) ).
fof(f260,plain,
( sQ0_eqProxy(intersection(complement(compose(element_relation,complement(identity_relation))),element_relation),singleton_relation)
| ~ spl1_13 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f369,plain,
( spl1_30
| ~ spl1_10 ),
inference(avatar_split_clause,[],[f365,f247,f367]) ).
fof(f367,plain,
( spl1_30
<=> sQ0_eqProxy(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_30])]) ).
fof(f247,plain,
( spl1_10
<=> sQ0_eqProxy(identity_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
fof(f365,plain,
( sQ0_eqProxy(intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),identity_relation)
| ~ spl1_10 ),
inference(resolution,[],[f248,f209]) ).
fof(f248,plain,
( sQ0_eqProxy(identity_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation))
| ~ spl1_10 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f364,plain,
( ~ spl1_29
| spl1_18
| ~ spl1_16 ),
inference(avatar_split_clause,[],[f360,f296,f303,f362]) ).
fof(f362,plain,
( spl1_29
<=> function(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_29])]) ).
fof(f303,plain,
( spl1_18
<=> member(x,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
fof(f360,plain,
( member(x,cross_product(universal_class,universal_class))
| ~ function(universal_class)
| ~ spl1_16 ),
inference(resolution,[],[f354,f62]) ).
fof(f62,axiom,
! [X8] :
( subclass(X8,cross_product(universal_class,universal_class))
| ~ function(X8) ),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',function1) ).
fof(f354,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(x,X0) )
| ~ spl1_16 ),
inference(resolution,[],[f297,f1]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',subclass_members) ).
fof(f353,plain,
( spl1_27
| ~ spl1_28
| ~ spl1_12 ),
inference(avatar_split_clause,[],[f318,f255,f351,f348]) ).
fof(f348,plain,
( spl1_27
<=> sQ0_eqProxy(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_27])]) ).
fof(f351,plain,
( spl1_28
<=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_28])]) ).
fof(f255,plain,
( spl1_12
<=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
fof(f318,plain,
( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
| sQ0_eqProxy(cross_product(universal_class,cross_product(universal_class,universal_class)),application_function)
| ~ spl1_12 ),
inference(resolution,[],[f202,f256]) ).
fof(f256,plain,
( subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ spl1_12 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f202,plain,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| sQ0_eqProxy(X0,X1) ),
inference(equality_proxy_replacement,[],[f7,f183]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',subclass_implies_equal) ).
fof(f346,plain,
( spl1_25
| ~ spl1_26
| ~ spl1_7 ),
inference(avatar_split_clause,[],[f317,f235,f344,f341]) ).
fof(f341,plain,
( spl1_25
<=> sQ0_eqProxy(cross_product(universal_class,universal_class),domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_25])]) ).
fof(f344,plain,
( spl1_26
<=> subclass(cross_product(universal_class,universal_class),domain_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_26])]) ).
fof(f235,plain,
( spl1_7
<=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
fof(f317,plain,
( ~ subclass(cross_product(universal_class,universal_class),domain_relation)
| sQ0_eqProxy(cross_product(universal_class,universal_class),domain_relation)
| ~ spl1_7 ),
inference(resolution,[],[f202,f236]) ).
fof(f236,plain,
( subclass(domain_relation,cross_product(universal_class,universal_class))
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f339,plain,
( spl1_23
| ~ spl1_24
| ~ spl1_11 ),
inference(avatar_split_clause,[],[f316,f251,f337,f334]) ).
fof(f334,plain,
( spl1_23
<=> sQ0_eqProxy(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_23])]) ).
fof(f337,plain,
( spl1_24
<=> subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_24])]) ).
fof(f251,plain,
( spl1_11
<=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
fof(f316,plain,
( ~ subclass(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
| sQ0_eqProxy(cross_product(universal_class,cross_product(universal_class,universal_class)),composition_function)
| ~ spl1_11 ),
inference(resolution,[],[f202,f252]) ).
fof(f252,plain,
( subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class)))
| ~ spl1_11 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f332,plain,
( spl1_21
| ~ spl1_22
| ~ spl1_8 ),
inference(avatar_split_clause,[],[f312,f239,f330,f327]) ).
fof(f327,plain,
( spl1_21
<=> sQ0_eqProxy(cross_product(universal_class,universal_class),successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_21])]) ).
fof(f330,plain,
( spl1_22
<=> subclass(cross_product(universal_class,universal_class),successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_22])]) ).
fof(f239,plain,
( spl1_8
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
fof(f312,plain,
( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
| sQ0_eqProxy(cross_product(universal_class,universal_class),successor_relation)
| ~ spl1_8 ),
inference(resolution,[],[f202,f240]) ).
fof(f240,plain,
( subclass(successor_relation,cross_product(universal_class,universal_class))
| ~ spl1_8 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f325,plain,
( spl1_19
| ~ spl1_20
| ~ spl1_9 ),
inference(avatar_split_clause,[],[f309,f243,f323,f320]) ).
fof(f320,plain,
( spl1_19
<=> sQ0_eqProxy(cross_product(universal_class,universal_class),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_19])]) ).
fof(f323,plain,
( spl1_20
<=> subclass(cross_product(universal_class,universal_class),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_20])]) ).
fof(f243,plain,
( spl1_9
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
fof(f309,plain,
( ~ subclass(cross_product(universal_class,universal_class),element_relation)
| sQ0_eqProxy(cross_product(universal_class,universal_class),element_relation)
| ~ spl1_9 ),
inference(resolution,[],[f202,f244]) ).
fof(f244,plain,
( subclass(element_relation,cross_product(universal_class,universal_class))
| ~ spl1_9 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f305,plain,
( ~ spl1_17
| spl1_18
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f294,f219,f303,f300]) ).
fof(f300,plain,
( spl1_17
<=> function(complement(intersection(complement(y),complement(z)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
fof(f219,plain,
( spl1_3
<=> member(x,complement(intersection(complement(y),complement(z)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
fof(f294,plain,
( member(x,cross_product(universal_class,universal_class))
| ~ function(complement(intersection(complement(y),complement(z))))
| ~ spl1_3 ),
inference(resolution,[],[f290,f62]) ).
fof(f290,plain,
( ! [X17] :
( ~ subclass(complement(intersection(complement(y),complement(z))),X17)
| member(x,X17) )
| ~ spl1_3 ),
inference(resolution,[],[f1,f220]) ).
fof(f220,plain,
( member(x,complement(intersection(complement(y),complement(z))))
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f298,plain,
( spl1_16
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f292,f219,f296]) ).
fof(f292,plain,
( member(x,universal_class)
| ~ spl1_3 ),
inference(resolution,[],[f290,f4]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',class_elements_are_sets) ).
fof(f272,plain,
( ~ spl1_15
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f268,f219,f270]) ).
fof(f268,plain,
( ~ member(x,intersection(complement(y),complement(z)))
| ~ spl1_3 ),
inference(resolution,[],[f24,f220]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) ),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',complement1) ).
fof(f265,plain,
spl1_14,
inference(avatar_split_clause,[],[f187,f263]) ).
fof(f263,plain,
( spl1_14
<=> sQ0_eqProxy(subset_relation,intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
fof(f187,plain,
sQ0_eqProxy(subset_relation,intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class)))))))),
inference(equality_proxy_replacement,[],[f132,f183]) ).
fof(f132,plain,
subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
inference(definition_unfolding,[],[f74,f38]) ).
fof(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',inverse) ).
fof(f74,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',subset_relation) ).
fof(f261,plain,
spl1_13,
inference(avatar_split_clause,[],[f185,f259]) ).
fof(f185,plain,
sQ0_eqProxy(intersection(complement(compose(element_relation,complement(identity_relation))),element_relation),singleton_relation),
inference(equality_proxy_replacement,[],[f104,f183]) ).
fof(f104,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',compose_can_define_singleton) ).
fof(f257,plain,
spl1_12,
inference(avatar_split_clause,[],[f105,f255]) ).
fof(f105,axiom,
subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',application_function_defn1) ).
fof(f253,plain,
spl1_11,
inference(avatar_split_clause,[],[f95,f251]) ).
fof(f95,axiom,
subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',definition_of_composition_function1) ).
fof(f249,plain,
spl1_10,
inference(avatar_split_clause,[],[f184,f247]) ).
fof(f184,plain,
sQ0_eqProxy(identity_relation,intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)),
inference(equality_proxy_replacement,[],[f130,f183]) ).
fof(f130,plain,
identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),
inference(definition_unfolding,[],[f75,f38]) ).
fof(f75,axiom,
identity_relation = intersection(inverse(subset_relation),subset_relation),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',identity_relation) ).
fof(f245,plain,
spl1_9,
inference(avatar_split_clause,[],[f18,f243]) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',element_relation1) ).
fof(f241,plain,
spl1_8,
inference(avatar_split_clause,[],[f44,f239]) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',successor_relation1) ).
fof(f237,plain,
spl1_7,
inference(avatar_split_clause,[],[f98,f235]) ).
fof(f98,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',definition_of_domain_relation1) ).
fof(f233,plain,
spl1_6,
inference(avatar_split_clause,[],[f52,f231]) ).
fof(f231,plain,
( spl1_6
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',omega_in_universal) ).
fof(f229,plain,
spl1_5,
inference(avatar_split_clause,[],[f69,f227]) ).
fof(f227,plain,
( spl1_5
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',choice1) ).
fof(f225,plain,
spl1_4,
inference(avatar_split_clause,[],[f50,f223]) ).
fof(f223,plain,
( spl1_4
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',omega_is_inductive1) ).
fof(f221,plain,
spl1_3,
inference(avatar_split_clause,[],[f129,f219]) ).
fof(f129,plain,
member(x,complement(intersection(complement(y),complement(z)))),
inference(definition_unfolding,[],[f113,f26]) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',union) ).
fof(f113,axiom,
member(x,union(y,z)),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',prove_members_of_union1_1) ).
fof(f217,plain,
~ spl1_2,
inference(avatar_split_clause,[],[f114,f215]) ).
fof(f114,axiom,
~ member(x,y),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',prove_members_of_union1_2) ).
fof(f213,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f115,f211]) ).
fof(f115,axiom,
~ member(x,z),
file('/export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674',prove_members_of_union1_3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET166-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.14/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 15:56:53 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.n8h04usSTY/Vampire---4.8_26674
% 0.15/0.37 % (26782)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (26784)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.22/0.43 % (26783)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.22/0.43 % (26787)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.43 % (26786)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.22/0.43 % (26788)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.22/0.43 % (26789)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.22/0.43 % (26785)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.22/0.50 % (26789)First to succeed.
% 0.22/0.50 % (26789)Refutation found. Thanks to Tanya!
% 0.22/0.50 % SZS status Unsatisfiable for Vampire---4
% 0.22/0.50 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.51 % (26789)------------------------------
% 0.22/0.51 % (26789)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.51 % (26789)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.51 % (26789)Termination reason: Refutation
% 0.22/0.51
% 0.22/0.51 % (26789)Memory used [KB]: 1407
% 0.22/0.51 % (26789)Time elapsed: 0.074 s
% 0.22/0.51 % (26789)------------------------------
% 0.22/0.51 % (26789)------------------------------
% 0.22/0.51 % (26782)Success in time 0.136 s
% 0.22/0.51 % Vampire---4.8 exiting
%------------------------------------------------------------------------------