TSTP Solution File: SET060-7 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET060-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.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 03:15:44 EDT 2024
% Result : Unsatisfiable 0.13s 0.39s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 103
% Syntax : Number of formulae : 178 ( 71 unt; 0 def)
% Number of atoms : 350 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 286 ( 114 ~; 121 |; 0 &)
% ( 51 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 62 ( 60 usr; 52 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 10 con; 0-3 aty)
% Number of variables : 180 ( 180 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f469,plain,
$false,
inference(avatar_sat_refutation,[],[f183,f188,f193,f197,f202,f206,f210,f214,f218,f223,f228,f232,f236,f240,f244,f248,f252,f256,f260,f264,f270,f274,f278,f282,f286,f290,f294,f298,f302,f306,f310,f322,f330,f334,f338,f342,f347,f352,f386,f390,f394,f403,f407,f411,f415,f419,f423,f427,f457,f461,f467,f468]) ).
fof(f468,plain,
( ~ spl0_38
| ~ spl0_17
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f439,f319,f250,f349]) ).
fof(f349,plain,
( spl0_38
<=> member(y,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f250,plain,
( spl0_17
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f319,plain,
( spl0_32
<=> member(y,complement(x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f439,plain,
( ~ member(y,x)
| ~ spl0_17
| ~ spl0_32 ),
inference(resolution,[],[f321,f251]) ).
fof(f251,plain,
( ! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f321,plain,
( member(y,complement(x))
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f467,plain,
spl0_51,
inference(avatar_split_clause,[],[f98,f465]) ).
fof(f465,plain,
( spl0_51
<=> ! [X0,X1] :
( X0 = X1
| member(not_subclass_element(X1,X0),X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f98,axiom,
! [X0,X1] :
( X0 = X1
| member(not_subclass_element(X1,X0),X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality1) ).
fof(f461,plain,
spl0_50,
inference(avatar_split_clause,[],[f119,f459]) ).
fof(f459,plain,
( spl0_50
<=> ! [X8] :
( ~ operation(X8)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f119,plain,
! [X8] :
( ~ operation(X8)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
inference(definition_unfolding,[],[f80,f104]) ).
fof(f104,plain,
! [X4] : range_of(X4) = domain_of(domain_of(flip(cross_product(X4,universal_class)))),
inference(definition_unfolding,[],[f39,f38]) ).
fof(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f39,axiom,
! [X4] : domain_of(inverse(X4)) = range_of(X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of) ).
fof(f80,axiom,
! [X8] :
( ~ operation(X8)
| subclass(range_of(X8),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation3) ).
fof(f457,plain,
spl0_49,
inference(avatar_split_clause,[],[f79,f455]) ).
fof(f455,plain,
( spl0_49
<=> ! [X8] :
( ~ operation(X8)
| domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f79,axiom,
! [X8] :
( ~ operation(X8)
| domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation2) ).
fof(f427,plain,
spl0_48,
inference(avatar_split_clause,[],[f160,f425]) ).
fof(f425,plain,
( spl0_48
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f160,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(forward_demodulation,[],[f123,f114]) ).
fof(f114,plain,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
inference(definition_unfolding,[],[f28,f29]) ).
fof(f29,axiom,
! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction2) ).
fof(f28,axiom,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction1) ).
fof(f123,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
inference(definition_unfolding,[],[f54,f103]) ).
fof(f103,plain,
! [X0] : sum_class(X0) = domain_of(intersection(cross_product(universal_class,X0),element_relation)),
inference(definition_unfolding,[],[f53,f29]) ).
fof(f53,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_definition) ).
fof(f54,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class2) ).
fof(f423,plain,
spl0_47,
inference(avatar_split_clause,[],[f121,f421]) ).
fof(f421,plain,
( spl0_47
<=> ! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f121,plain,
! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f61,f38]) ).
fof(f61,axiom,
! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_class2) ).
fof(f419,plain,
spl0_46,
inference(avatar_split_clause,[],[f120,f417]) ).
fof(f417,plain,
( spl0_46
<=> ! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f120,plain,
! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f63,f38]) ).
fof(f63,axiom,
! [X8] :
( ~ function(X8)
| subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function2) ).
fof(f415,plain,
spl0_45,
inference(avatar_split_clause,[],[f116,f413]) ).
fof(f413,plain,
( spl0_45
<=> ! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f116,plain,
! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f60,f38]) ).
fof(f60,axiom,
! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,inverse(X0)),identity_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_class1) ).
fof(f411,plain,
spl0_44,
inference(avatar_split_clause,[],[f114,f409]) ).
fof(f409,plain,
( spl0_44
<=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f407,plain,
spl0_43,
inference(avatar_split_clause,[],[f23,f405]) ).
fof(f405,plain,
( spl0_43
<=> ! [X4,X0,X1] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f23,axiom,
! [X0,X1,X4] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f403,plain,
spl0_42,
inference(avatar_split_clause,[],[f8,f401]) ).
fof(f401,plain,
( spl0_42
<=> ! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f394,plain,
spl0_41,
inference(avatar_split_clause,[],[f138,f392]) ).
fof(f392,plain,
( spl0_41
<=> ! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f138,plain,
! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ),
inference(definition_unfolding,[],[f73,f38]) ).
fof(f73,axiom,
! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(inverse(X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one3) ).
fof(f390,plain,
spl0_40,
inference(avatar_split_clause,[],[f83,f388]) ).
fof(f388,plain,
( spl0_40
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f83,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible2) ).
fof(f386,plain,
spl0_39,
inference(avatar_split_clause,[],[f25,f384]) ).
fof(f384,plain,
( spl0_39
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f25,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f352,plain,
( spl0_38
| ~ spl0_1
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f326,f292,f180,f349]) ).
fof(f180,plain,
( spl0_1
<=> member(y,intersection(complement(x),x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f292,plain,
( spl0_27
<=> ! [X4,X0,X1] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f326,plain,
( member(y,x)
| ~ spl0_1
| ~ spl0_27 ),
inference(resolution,[],[f293,f182]) ).
fof(f182,plain,
( member(y,intersection(complement(x),x))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f293,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X1) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f347,plain,
spl0_37,
inference(avatar_split_clause,[],[f113,f344]) ).
fof(f344,plain,
( spl0_37
<=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f113,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/benchmark/theBenchmark.p',identity_relation) ).
fof(f342,plain,
spl0_36,
inference(avatar_split_clause,[],[f97,f340]) ).
fof(f340,plain,
( spl0_36
<=> ! [X4,X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X4)
| subclass(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f97,axiom,
! [X0,X1,X4] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X4)
| subclass(X0,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_subclass) ).
fof(f338,plain,
spl0_35,
inference(avatar_split_clause,[],[f67,f336]) ).
fof(f336,plain,
( spl0_35
<=> ! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f67,axiom,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f334,plain,
spl0_34,
inference(avatar_split_clause,[],[f7,f332]) ).
fof(f332,plain,
( spl0_34
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f330,plain,
spl0_33,
inference(avatar_split_clause,[],[f1,f328]) ).
fof(f328,plain,
( spl0_33
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f322,plain,
( spl0_32
| ~ spl0_1
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f317,f284,f180,f319]) ).
fof(f284,plain,
( spl0_25
<=> ! [X4,X0,X1] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f317,plain,
( member(y,complement(x))
| ~ spl0_1
| ~ spl0_25 ),
inference(resolution,[],[f285,f182]) ).
fof(f285,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X0) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f310,plain,
spl0_31,
inference(avatar_split_clause,[],[f117,f308]) ).
fof(f308,plain,
( spl0_31
<=> ! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f117,plain,
! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ),
inference(definition_unfolding,[],[f72,f38]) ).
fof(f72,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(inverse(X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one2) ).
fof(f306,plain,
spl0_30,
inference(avatar_split_clause,[],[f88,f304]) ).
fof(f304,plain,
( spl0_30
<=> ! [X9,X11,X10] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f88,axiom,
! [X10,X11,X9] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).
fof(f302,plain,
spl0_29,
inference(avatar_split_clause,[],[f35,f300]) ).
fof(f300,plain,
( spl0_29
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f35,axiom,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip1) ).
fof(f298,plain,
spl0_28,
inference(avatar_split_clause,[],[f32,f296]) ).
fof(f296,plain,
( spl0_28
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f32,axiom,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate1) ).
fof(f294,plain,
spl0_27,
inference(avatar_split_clause,[],[f22,f292]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f290,plain,
( spl0_26
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f265,f250,f230,f288]) ).
fof(f288,plain,
( spl0_26
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f230,plain,
( spl0_12
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f265,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) )
| ~ spl0_12
| ~ spl0_17 ),
inference(resolution,[],[f251,f231]) ).
fof(f231,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f230]) ).
fof(f286,plain,
spl0_25,
inference(avatar_split_clause,[],[f21,f284]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f282,plain,
spl0_24,
inference(avatar_split_clause,[],[f10,f280]) ).
fof(f280,plain,
( spl0_24
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f10,axiom,
! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f278,plain,
spl0_23,
inference(avatar_split_clause,[],[f9,f276]) ).
fof(f276,plain,
( spl0_23
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f9,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f274,plain,
spl0_22,
inference(avatar_split_clause,[],[f3,f272]) ).
fof(f272,plain,
( spl0_22
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f270,plain,
spl0_21,
inference(avatar_split_clause,[],[f2,f268]) ).
fof(f268,plain,
( spl0_21
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f264,plain,
spl0_20,
inference(avatar_split_clause,[],[f66,f262]) ).
fof(f262,plain,
( spl0_20
<=> ! [X0] :
( null_class = X0
| member(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f66,axiom,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f260,plain,
spl0_19,
inference(avatar_split_clause,[],[f62,f258]) ).
fof(f258,plain,
( spl0_19
<=> ! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f62,axiom,
! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).
fof(f256,plain,
spl0_18,
inference(avatar_split_clause,[],[f57,f254]) ).
fof(f254,plain,
( spl0_18
<=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f57,axiom,
! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).
fof(f252,plain,
spl0_17,
inference(avatar_split_clause,[],[f24,f250]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f248,plain,
spl0_16,
inference(avatar_split_clause,[],[f87,f246]) ).
fof(f246,plain,
( spl0_16
<=> ! [X9,X11,X10] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f87,axiom,
! [X10,X11,X9] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
fof(f244,plain,
spl0_15,
inference(avatar_split_clause,[],[f86,f242]) ).
fof(f242,plain,
( spl0_15
<=> ! [X9,X11,X10] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f86,axiom,
! [X10,X11,X9] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
fof(f240,plain,
spl0_14,
inference(avatar_split_clause,[],[f82,f238]) ).
fof(f238,plain,
( spl0_14
<=> ! [X9,X11,X10] :
( function(X9)
| ~ compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f82,axiom,
! [X10,X11,X9] :
( function(X9)
| ~ compatible(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible1) ).
fof(f236,plain,
spl0_13,
inference(avatar_split_clause,[],[f51,f234]) ).
fof(f234,plain,
( spl0_13
<=> ! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f51,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive2) ).
fof(f232,plain,
spl0_12,
inference(avatar_split_clause,[],[f47,f230]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
fof(f228,plain,
spl0_11,
inference(avatar_split_clause,[],[f44,f225]) ).
fof(f225,plain,
( spl0_11
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation1) ).
fof(f223,plain,
spl0_10,
inference(avatar_split_clause,[],[f18,f220]) ).
fof(f220,plain,
( spl0_10
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).
fof(f218,plain,
spl0_9,
inference(avatar_split_clause,[],[f11,f216]) ).
fof(f216,plain,
( spl0_9
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f214,plain,
spl0_8,
inference(avatar_split_clause,[],[f78,f212]) ).
fof(f212,plain,
( spl0_8
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation1) ).
fof(f210,plain,
spl0_7,
inference(avatar_split_clause,[],[f71,f208]) ).
fof(f208,plain,
( spl0_7
<=> ! [X8] :
( ~ one_to_one(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f71,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one1) ).
fof(f206,plain,
spl0_6,
inference(avatar_split_clause,[],[f96,f204]) ).
fof(f204,plain,
( spl0_6
<=> ! [X0] : subclass(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f96,axiom,
! [X0] : subclass(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_is_reflexive) ).
fof(f202,plain,
spl0_5,
inference(avatar_split_clause,[],[f52,f199]) ).
fof(f199,plain,
( spl0_5
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f197,plain,
spl0_4,
inference(avatar_split_clause,[],[f4,f195]) ).
fof(f195,plain,
( spl0_4
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f193,plain,
spl0_3,
inference(avatar_split_clause,[],[f69,f190]) ).
fof(f190,plain,
( spl0_3
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
fof(f188,plain,
spl0_2,
inference(avatar_split_clause,[],[f50,f185]) ).
fof(f185,plain,
( spl0_2
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f183,plain,
spl0_1,
inference(avatar_split_clause,[],[f102,f180]) ).
fof(f102,axiom,
member(y,intersection(complement(x),x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_special_classes_lemma_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET060-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.12/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 11:41:08 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % (23185)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (23190)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)
% 0.13/0.38 % (23192)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)
% 0.13/0.38 % (23187)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38 % (23186)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38 % (23190)First to succeed.
% 0.13/0.39 % (23191)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)
% 0.13/0.39 % (23190)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-23185"
% 0.13/0.39 % (23189)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.39 % (23190)Refutation found. Thanks to Tanya!
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.39 % (23190)------------------------------
% 0.13/0.39 % (23190)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.39 % (23190)Termination reason: Refutation
% 0.13/0.39
% 0.13/0.39 % (23190)Memory used [KB]: 1064
% 0.13/0.39 % (23190)Time elapsed: 0.014 s
% 0.13/0.39 % (23190)Instructions burned: 25 (million)
% 0.13/0.39 % (23185)Success in time 0.041 s
%------------------------------------------------------------------------------