TSTP Solution File: SET085-6 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET085-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:11:04 EDT 2024
% Result : Unsatisfiable 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 116
% Syntax : Number of formulae : 207 ( 85 unt; 0 def)
% Number of atoms : 401 ( 49 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 331 ( 137 ~; 138 |; 0 &)
% ( 56 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 67 ( 65 usr; 57 prp; 0-3 aty)
% Number of functors : 28 ( 28 usr; 11 con; 0-3 aty)
% Number of variables : 210 ( 210 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f481,plain,
$false,
inference(avatar_sat_refutation,[],[f173,f178,f183,f188,f193,f198,f202,f207,f211,f215,f219,f223,f228,f233,f237,f241,f246,f250,f254,f258,f262,f266,f270,f275,f280,f284,f288,f292,f296,f300,f304,f308,f312,f316,f332,f336,f340,f344,f349,f374,f379,f383,f391,f395,f399,f403,f407,f411,f415,f419,f448,f455,f460,f469,f473,f477,f480]) ).
fof(f480,plain,
( spl0_3
| spl0_2
| ~ spl0_35
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f422,f389,f329,f175,f180]) ).
fof(f180,plain,
( spl0_3
<=> z = x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f175,plain,
( spl0_2
<=> y = x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f329,plain,
( spl0_35
<=> member(x,unordered_pair(y,z)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f389,plain,
( spl0_43
<=> ! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f422,plain,
( y = x
| z = x
| ~ spl0_35
| ~ spl0_43 ),
inference(resolution,[],[f390,f331]) ).
fof(f331,plain,
( member(x,unordered_pair(y,z))
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f390,plain,
( ! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| X0 = X2
| X1 = X2 )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f477,plain,
spl0_56,
inference(avatar_split_clause,[],[f148,f475]) ).
fof(f475,plain,
( spl0_56
<=> ! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f148,plain,
! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ),
inference(forward_demodulation,[],[f112,f108]) ).
fof(f108,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(f112,plain,
! [X0] :
( ~ inductive(X0)
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
inference(definition_unfolding,[],[f48,f98]) ).
fof(f98,plain,
! [X0,X5] : image(X5,X0) = domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X5),universal_class)))),
inference(definition_unfolding,[],[f42,f97,f29]) ).
fof(f97,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(f42,axiom,
! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive2) ).
fof(f473,plain,
spl0_55,
inference(avatar_split_clause,[],[f122,f471]) ).
fof(f471,plain,
( spl0_55
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f122,plain,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
inference(definition_unfolding,[],[f84,f97]) ).
fof(f84,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible3) ).
fof(f469,plain,
spl0_54,
inference(avatar_split_clause,[],[f118,f467]) ).
fof(f467,plain,
( spl0_54
<=> ! [X0,X1] :
( member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f118,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(definition_unfolding,[],[f19,f100]) ).
fof(f100,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f19,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation2) ).
fof(f460,plain,
spl0_53,
inference(avatar_split_clause,[],[f121,f458]) ).
fof(f458,plain,
( spl0_53
<=> ! [X4,X0] :
( ~ member(X4,domain_of(X0))
| null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f121,plain,
! [X0,X4] :
( ~ member(X4,domain_of(X0))
| null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
inference(definition_unfolding,[],[f30,f29,f12]) ).
fof(f30,axiom,
! [X0,X4] :
( ~ member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f455,plain,
spl0_52,
inference(avatar_split_clause,[],[f113,f453]) ).
fof(f453,plain,
( spl0_52
<=> ! [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_52])]) ).
fof(f113,plain,
! [X8] :
( ~ operation(X8)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
inference(definition_unfolding,[],[f80,f97]) ).
fof(f80,axiom,
! [X8] :
( ~ operation(X8)
| subclass(range_of(X8),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation3) ).
fof(f448,plain,
spl0_51,
inference(avatar_split_clause,[],[f79,f446]) ).
fof(f446,plain,
( spl0_51
<=> ! [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_51])]) ).
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(f419,plain,
spl0_50,
inference(avatar_split_clause,[],[f150,f417]) ).
fof(f417,plain,
( spl0_50
<=> ! [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_50])]) ).
fof(f150,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(forward_demodulation,[],[f117,f108]) ).
fof(f117,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
inference(definition_unfolding,[],[f54,f96]) ).
fof(f96,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(f415,plain,
spl0_49,
inference(avatar_split_clause,[],[f115,f413]) ).
fof(f413,plain,
( spl0_49
<=> ! [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_49])]) ).
fof(f115,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(f411,plain,
( spl0_48
| ~ spl0_1
| ~ spl0_36 ),
inference(avatar_split_clause,[],[f350,f334,f170,f409]) ).
fof(f409,plain,
( spl0_48
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(x,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f170,plain,
( spl0_1
<=> member(x,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f334,plain,
( spl0_36
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f350,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(x,X0) )
| ~ spl0_1
| ~ spl0_36 ),
inference(resolution,[],[f335,f172]) ).
fof(f172,plain,
( member(x,universal_class)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f170]) ).
fof(f335,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) )
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f407,plain,
spl0_47,
inference(avatar_split_clause,[],[f114,f405]) ).
fof(f405,plain,
( spl0_47
<=> ! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f114,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(f403,plain,
spl0_46,
inference(avatar_split_clause,[],[f110,f401]) ).
fof(f401,plain,
( spl0_46
<=> ! [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_46])]) ).
fof(f110,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(f399,plain,
spl0_45,
inference(avatar_split_clause,[],[f108,f397]) ).
fof(f397,plain,
( spl0_45
<=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f395,plain,
spl0_44,
inference(avatar_split_clause,[],[f23,f393]) ).
fof(f393,plain,
( spl0_44
<=> ! [X4,X0,X1] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
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(f391,plain,
spl0_43,
inference(avatar_split_clause,[],[f8,f389]) ).
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(f383,plain,
spl0_42,
inference(avatar_split_clause,[],[f128,f381]) ).
fof(f381,plain,
( spl0_42
<=> ! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f128,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(f379,plain,
spl0_41,
inference(avatar_split_clause,[],[f83,f377]) ).
fof(f377,plain,
( spl0_41
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
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(f374,plain,
spl0_40,
inference(avatar_split_clause,[],[f25,f372]) ).
fof(f372,plain,
( spl0_40
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
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(f349,plain,
spl0_39,
inference(avatar_split_clause,[],[f107,f346]) ).
fof(f346,plain,
( spl0_39
<=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f107,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(f344,plain,
spl0_38,
inference(avatar_split_clause,[],[f67,f342]) ).
fof(f342,plain,
( spl0_38
<=> ! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f67,axiom,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f340,plain,
spl0_37,
inference(avatar_split_clause,[],[f7,f338]) ).
fof(f338,plain,
( spl0_37
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f336,plain,
spl0_36,
inference(avatar_split_clause,[],[f1,f334]) ).
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(f332,plain,
( ~ spl0_1
| spl0_35
| ~ spl0_4
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f320,f286,f185,f329,f170]) ).
fof(f185,plain,
( spl0_4
<=> unordered_pair(y,z) = unordered_pair(x,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f286,plain,
( spl0_27
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f320,plain,
( member(x,unordered_pair(y,z))
| ~ member(x,universal_class)
| ~ spl0_4
| ~ spl0_27 ),
inference(superposition,[],[f287,f187]) ).
fof(f187,plain,
( unordered_pair(y,z) = unordered_pair(x,x)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f287,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f316,plain,
spl0_34,
inference(avatar_split_clause,[],[f111,f314]) ).
fof(f314,plain,
( spl0_34
<=> ! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f111,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(f312,plain,
spl0_33,
inference(avatar_split_clause,[],[f88,f310]) ).
fof(f310,plain,
( spl0_33
<=> ! [X9,X11,X10] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f88,axiom,
! [X10,X11,X9] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).
fof(f308,plain,
spl0_32,
inference(avatar_split_clause,[],[f35,f306]) ).
fof(f306,plain,
( spl0_32
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
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(f304,plain,
spl0_31,
inference(avatar_split_clause,[],[f32,f302]) ).
fof(f302,plain,
( spl0_31
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
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(f300,plain,
spl0_30,
inference(avatar_split_clause,[],[f22,f298]) ).
fof(f298,plain,
( spl0_30
<=> ! [X4,X0,X1] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f296,plain,
spl0_29,
inference(avatar_split_clause,[],[f21,f294]) ).
fof(f294,plain,
( spl0_29
<=> ! [X4,X0,X1] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f292,plain,
spl0_28,
inference(avatar_split_clause,[],[f10,f290]) ).
fof(f290,plain,
( spl0_28
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
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(f288,plain,
spl0_27,
inference(avatar_split_clause,[],[f9,f286]) ).
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(f284,plain,
spl0_26,
inference(avatar_split_clause,[],[f3,f282]) ).
fof(f282,plain,
( spl0_26
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
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(f280,plain,
spl0_25,
inference(avatar_split_clause,[],[f2,f278]) ).
fof(f278,plain,
( spl0_25
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
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(f275,plain,
( spl0_24
| ~ spl0_15
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f271,f256,f235,f273]) ).
fof(f273,plain,
( spl0_24
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f235,plain,
( spl0_15
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f256,plain,
( spl0_20
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f271,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) )
| ~ spl0_15
| ~ spl0_20 ),
inference(resolution,[],[f257,f236]) ).
fof(f236,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f257,plain,
( ! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f270,plain,
spl0_23,
inference(avatar_split_clause,[],[f66,f268]) ).
fof(f268,plain,
( spl0_23
<=> ! [X0] :
( null_class = X0
| member(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f66,axiom,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f266,plain,
spl0_22,
inference(avatar_split_clause,[],[f62,f264]) ).
fof(f264,plain,
( spl0_22
<=> ! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f62,axiom,
! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).
fof(f262,plain,
spl0_21,
inference(avatar_split_clause,[],[f57,f260]) ).
fof(f260,plain,
( spl0_21
<=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f57,axiom,
! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).
fof(f258,plain,
spl0_20,
inference(avatar_split_clause,[],[f24,f256]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f254,plain,
spl0_19,
inference(avatar_split_clause,[],[f87,f252]) ).
fof(f252,plain,
( spl0_19
<=> ! [X9,X11,X10] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f87,axiom,
! [X10,X11,X9] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
fof(f250,plain,
spl0_18,
inference(avatar_split_clause,[],[f86,f248]) ).
fof(f248,plain,
( spl0_18
<=> ! [X9,X11,X10] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f86,axiom,
! [X10,X11,X9] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
fof(f246,plain,
spl0_17,
inference(avatar_split_clause,[],[f82,f244]) ).
fof(f244,plain,
( spl0_17
<=> ! [X9,X11,X10] :
( function(X9)
| ~ compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f82,axiom,
! [X10,X11,X9] :
( function(X9)
| ~ compatible(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible1) ).
fof(f241,plain,
spl0_16,
inference(avatar_split_clause,[],[f51,f239]) ).
fof(f239,plain,
( spl0_16
<=> ! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f51,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive2) ).
fof(f237,plain,
spl0_15,
inference(avatar_split_clause,[],[f47,f235]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
fof(f233,plain,
spl0_14,
inference(avatar_split_clause,[],[f44,f230]) ).
fof(f230,plain,
( spl0_14
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation1) ).
fof(f228,plain,
spl0_13,
inference(avatar_split_clause,[],[f18,f225]) ).
fof(f225,plain,
( spl0_13
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).
fof(f223,plain,
spl0_12,
inference(avatar_split_clause,[],[f11,f221]) ).
fof(f221,plain,
( spl0_12
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f219,plain,
spl0_11,
inference(avatar_split_clause,[],[f78,f217]) ).
fof(f217,plain,
( spl0_11
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation1) ).
fof(f215,plain,
spl0_10,
inference(avatar_split_clause,[],[f71,f213]) ).
fof(f213,plain,
( spl0_10
<=> ! [X8] :
( ~ one_to_one(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f71,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one1) ).
fof(f211,plain,
spl0_9,
inference(avatar_split_clause,[],[f145,f209]) ).
fof(f209,plain,
( spl0_9
<=> ! [X1] : subclass(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f145,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass2) ).
fof(f207,plain,
spl0_8,
inference(avatar_split_clause,[],[f52,f204]) ).
fof(f204,plain,
( spl0_8
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f202,plain,
spl0_7,
inference(avatar_split_clause,[],[f4,f200]) ).
fof(f200,plain,
( spl0_7
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f198,plain,
spl0_6,
inference(avatar_split_clause,[],[f69,f195]) ).
fof(f195,plain,
( spl0_6
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
fof(f193,plain,
spl0_5,
inference(avatar_split_clause,[],[f50,f190]) ).
fof(f190,plain,
( spl0_5
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f188,plain,
spl0_4,
inference(avatar_split_clause,[],[f106,f185]) ).
fof(f106,plain,
unordered_pair(y,z) = unordered_pair(x,x),
inference(definition_unfolding,[],[f92,f12]) ).
fof(f92,axiom,
unordered_pair(y,z) = singleton(x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_1) ).
fof(f183,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f95,f180]) ).
fof(f95,axiom,
z != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_4) ).
fof(f178,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f94,f175]) ).
fof(f94,axiom,
y != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_3) ).
fof(f173,plain,
spl0_1,
inference(avatar_split_clause,[],[f93,f170]) ).
fof(f93,axiom,
member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET085-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.03/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 16:39:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (4583)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (4586)WARNING: value z3 for option sas not known
% 0.22/0.38 % (4585)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (4584)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (4587)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (4586)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)
% 0.22/0.38 % (4588)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)
% 0.22/0.38 % (4589)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)
% 0.22/0.38 % (4590)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)
% 0.22/0.40 % (4588)First to succeed.
% 0.22/0.40 % (4589)Also succeeded, but the first one will report.
% 0.22/0.40 % (4588)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4583"
% 0.22/0.40 % (4588)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.22/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.40 % (4588)------------------------------
% 0.22/0.40 % (4588)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.40 % (4588)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (4588)Memory used [KB]: 1081
% 0.22/0.40 % (4588)Time elapsed: 0.017 s
% 0.22/0.40 % (4588)Instructions burned: 26 (million)
% 0.22/0.40 % (4583)Success in time 0.036 s
%------------------------------------------------------------------------------