TSTP Solution File: SET558-6 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET558-6 : 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 : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:08:34 EDT 2024
% Result : Unsatisfiable 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 124
% Syntax : Number of formulae : 221 ( 88 unt; 0 def)
% Number of atoms : 430 ( 46 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 356 ( 147 ~; 147 |; 0 &)
% ( 62 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 74 ( 72 usr; 63 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 15 con; 0-3 aty)
% Number of variables : 209 ( 209 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f542,plain,
$false,
inference(avatar_sat_refutation,[],[f209,f214,f219,f224,f229,f233,f238,f242,f246,f250,f255,f260,f265,f270,f274,f278,f283,f287,f291,f295,f299,f303,f308,f313,f317,f321,f325,f330,f335,f341,f345,f349,f353,f357,f361,f365,f369,f373,f377,f381,f385,f398,f402,f406,f411,f416,f440,f450,f454,f458,f467,f472,f476,f480,f484,f488,f492,f496,f523,f527,f531,f540,f541]) ).
fof(f541,plain,
( spl0_3
| ~ spl0_1
| ~ spl0_52
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f533,f521,f469,f206,f216]) ).
fof(f216,plain,
( spl0_3
<=> cross_product(domain_of(xh),domain_of(xh)) = domain_of(xf1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f206,plain,
( spl0_1
<=> operation(xf1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f469,plain,
( spl0_52
<=> domain_of(xh) = domain_of(domain_of(xf1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f521,plain,
( spl0_59
<=> ! [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_59])]) ).
fof(f533,plain,
( cross_product(domain_of(xh),domain_of(xh)) = domain_of(xf1)
| ~ spl0_1
| ~ spl0_52
| ~ spl0_59 ),
inference(forward_demodulation,[],[f532,f471]) ).
fof(f471,plain,
( domain_of(xh) = domain_of(domain_of(xf1))
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f532,plain,
( domain_of(xf1) = cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1)))
| ~ spl0_1
| ~ spl0_59 ),
inference(resolution,[],[f522,f208]) ).
fof(f208,plain,
( operation(xf1)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f522,plain,
( ! [X8] :
( ~ operation(X8)
| domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) )
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f521]) ).
fof(f540,plain,
spl0_62,
inference(avatar_split_clause,[],[f144,f538]) ).
fof(f538,plain,
( spl0_62
<=> ! [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_62])]) ).
fof(f144,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(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
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(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(f531,plain,
spl0_61,
inference(avatar_split_clause,[],[f145,f529]) ).
fof(f529,plain,
( spl0_61
<=> ! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f145,plain,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1) ),
inference(definition_unfolding,[],[f111,f117]) ).
fof(f117,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(f111,axiom,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| subclass(range_of(X8),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps3) ).
fof(f527,plain,
spl0_60,
inference(avatar_split_clause,[],[f135,f525]) ).
fof(f525,plain,
( spl0_60
<=> ! [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_60])]) ).
fof(f135,plain,
! [X8] :
( ~ operation(X8)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
inference(definition_unfolding,[],[f80,f117]) ).
fof(f80,axiom,
! [X8] :
( ~ operation(X8)
| subclass(range_of(X8),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation3) ).
fof(f523,plain,
spl0_59,
inference(avatar_split_clause,[],[f79,f521]) ).
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(f496,plain,
spl0_58,
inference(avatar_split_clause,[],[f184,f494]) ).
fof(f494,plain,
( spl0_58
<=> ! [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_58])]) ).
fof(f184,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(forward_demodulation,[],[f139,f130]) ).
fof(f130,plain,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
inference(definition_unfolding,[],[f28,f29]) ).
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(f139,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
inference(definition_unfolding,[],[f54,f116]) ).
fof(f116,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(f492,plain,
spl0_57,
inference(avatar_split_clause,[],[f137,f490]) ).
fof(f490,plain,
( spl0_57
<=> ! [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_57])]) ).
fof(f137,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(f488,plain,
spl0_56,
inference(avatar_split_clause,[],[f136,f486]) ).
fof(f486,plain,
( spl0_56
<=> ! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f136,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(f484,plain,
spl0_55,
inference(avatar_split_clause,[],[f132,f482]) ).
fof(f482,plain,
( spl0_55
<=> ! [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_55])]) ).
fof(f132,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(f480,plain,
spl0_54,
inference(avatar_split_clause,[],[f130,f478]) ).
fof(f478,plain,
( spl0_54
<=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f476,plain,
spl0_53,
inference(avatar_split_clause,[],[f23,f474]) ).
fof(f474,plain,
( spl0_53
<=> ! [X4,X0,X1] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
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(f472,plain,
( spl0_52
| ~ spl0_2
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f462,f452,f211,f469]) ).
fof(f211,plain,
( spl0_2
<=> compatible(xh,xf1,xf2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f452,plain,
( spl0_49
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f462,plain,
( domain_of(xh) = domain_of(domain_of(xf1))
| ~ spl0_2
| ~ spl0_49 ),
inference(resolution,[],[f453,f213]) ).
fof(f213,plain,
( compatible(xh,xf1,xf2)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f453,plain,
( ! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) )
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f452]) ).
fof(f467,plain,
spl0_51,
inference(avatar_split_clause,[],[f8,f465]) ).
fof(f465,plain,
( spl0_51
<=> ! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
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(f458,plain,
spl0_50,
inference(avatar_split_clause,[],[f158,f456]) ).
fof(f456,plain,
( spl0_50
<=> ! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f158,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(f454,plain,
spl0_49,
inference(avatar_split_clause,[],[f83,f452]) ).
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(f450,plain,
spl0_48,
inference(avatar_split_clause,[],[f25,f448]) ).
fof(f448,plain,
( spl0_48
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
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(f440,plain,
( spl0_47
| ~ spl0_7
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f417,f396,f235,f438]) ).
fof(f438,plain,
( spl0_47
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(omega,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f235,plain,
( spl0_7
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f396,plain,
( spl0_42
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f417,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(omega,X0) )
| ~ spl0_7
| ~ spl0_42 ),
inference(resolution,[],[f397,f237]) ).
fof(f237,plain,
( member(omega,universal_class)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f397,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f396]) ).
fof(f416,plain,
spl0_46,
inference(avatar_split_clause,[],[f129,f413]) ).
fof(f413,plain,
( spl0_46
<=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f129,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(f411,plain,
spl0_45,
inference(avatar_split_clause,[],[f104,f408]) ).
fof(f408,plain,
( spl0_45
<=> intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f104,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_can_define_singleton) ).
fof(f406,plain,
spl0_44,
inference(avatar_split_clause,[],[f67,f404]) ).
fof(f404,plain,
( spl0_44
<=> ! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f67,axiom,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f402,plain,
spl0_43,
inference(avatar_split_clause,[],[f7,f400]) ).
fof(f400,plain,
( spl0_43
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f398,plain,
spl0_42,
inference(avatar_split_clause,[],[f1,f396]) ).
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(f385,plain,
spl0_41,
inference(avatar_split_clause,[],[f133,f383]) ).
fof(f383,plain,
( spl0_41
<=> ! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f133,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(f381,plain,
spl0_40,
inference(avatar_split_clause,[],[f110,f379]) ).
fof(f379,plain,
( spl0_40
<=> ! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| domain_of(X8) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f110,axiom,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| domain_of(X8) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps2) ).
fof(f377,plain,
( spl0_39
| ~ spl0_15
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f336,f306,f272,f375]) ).
fof(f375,plain,
( spl0_39
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f272,plain,
( spl0_15
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f306,plain,
( spl0_23
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f336,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) )
| ~ spl0_15
| ~ spl0_23 ),
inference(resolution,[],[f307,f273]) ).
fof(f273,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f307,plain,
( ! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f373,plain,
spl0_38,
inference(avatar_split_clause,[],[f88,f371]) ).
fof(f371,plain,
( spl0_38
<=> ! [X9,X11,X10] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f88,axiom,
! [X10,X11,X9] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).
fof(f369,plain,
spl0_37,
inference(avatar_split_clause,[],[f35,f367]) ).
fof(f367,plain,
( spl0_37
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
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(f365,plain,
spl0_36,
inference(avatar_split_clause,[],[f32,f363]) ).
fof(f363,plain,
( spl0_36
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
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(f361,plain,
spl0_35,
inference(avatar_split_clause,[],[f22,f359]) ).
fof(f359,plain,
( spl0_35
<=> ! [X4,X0,X1] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f357,plain,
spl0_34,
inference(avatar_split_clause,[],[f21,f355]) ).
fof(f355,plain,
( spl0_34
<=> ! [X4,X0,X1] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f353,plain,
spl0_33,
inference(avatar_split_clause,[],[f10,f351]) ).
fof(f351,plain,
( spl0_33
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
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(f349,plain,
spl0_32,
inference(avatar_split_clause,[],[f9,f347]) ).
fof(f347,plain,
( spl0_32
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
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(f345,plain,
spl0_31,
inference(avatar_split_clause,[],[f3,f343]) ).
fof(f343,plain,
( spl0_31
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
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(f341,plain,
spl0_30,
inference(avatar_split_clause,[],[f2,f339]) ).
fof(f339,plain,
( spl0_30
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
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(f335,plain,
spl0_29,
inference(avatar_split_clause,[],[f105,f332]) ).
fof(f332,plain,
( spl0_29
<=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f105,axiom,
subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',application_function_defn1) ).
fof(f330,plain,
spl0_28,
inference(avatar_split_clause,[],[f95,f327]) ).
fof(f327,plain,
( spl0_28
<=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f95,axiom,
subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_composition_function1) ).
fof(f325,plain,
spl0_27,
inference(avatar_split_clause,[],[f66,f323]) ).
fof(f323,plain,
( spl0_27
<=> ! [X0] :
( null_class = X0
| member(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f66,axiom,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f321,plain,
spl0_26,
inference(avatar_split_clause,[],[f62,f319]) ).
fof(f319,plain,
( spl0_26
<=> ! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f62,axiom,
! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).
fof(f317,plain,
spl0_25,
inference(avatar_split_clause,[],[f57,f315]) ).
fof(f315,plain,
( spl0_25
<=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f57,axiom,
! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).
fof(f313,plain,
( spl0_24
| ~ spl0_2
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f304,f285,f211,f310]) ).
fof(f310,plain,
( spl0_24
<=> function(xh) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f285,plain,
( spl0_18
<=> ! [X9,X11,X10] :
( function(X9)
| ~ compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f304,plain,
( function(xh)
| ~ spl0_2
| ~ spl0_18 ),
inference(resolution,[],[f286,f213]) ).
fof(f286,plain,
( ! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| function(X9) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f308,plain,
spl0_23,
inference(avatar_split_clause,[],[f24,f306]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f303,plain,
spl0_22,
inference(avatar_split_clause,[],[f109,f301]) ).
fof(f301,plain,
( spl0_22
<=> ! [X0,X1,X8] :
( function(X8)
| ~ maps(X8,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f109,axiom,
! [X0,X1,X8] :
( function(X8)
| ~ maps(X8,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps1) ).
fof(f299,plain,
spl0_21,
inference(avatar_split_clause,[],[f92,f297]) ).
fof(f297,plain,
( spl0_21
<=> ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f92,axiom,
! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_class_definition1) ).
fof(f295,plain,
spl0_20,
inference(avatar_split_clause,[],[f87,f293]) ).
fof(f293,plain,
( spl0_20
<=> ! [X9,X11,X10] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f87,axiom,
! [X10,X11,X9] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
fof(f291,plain,
spl0_19,
inference(avatar_split_clause,[],[f86,f289]) ).
fof(f289,plain,
( spl0_19
<=> ! [X9,X11,X10] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f86,axiom,
! [X10,X11,X9] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
fof(f287,plain,
spl0_18,
inference(avatar_split_clause,[],[f82,f285]) ).
fof(f82,axiom,
! [X10,X11,X9] :
( function(X9)
| ~ compatible(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible1) ).
fof(f283,plain,
spl0_17,
inference(avatar_split_clause,[],[f98,f280]) ).
fof(f280,plain,
( spl0_17
<=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f98,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_domain_relation1) ).
fof(f278,plain,
spl0_16,
inference(avatar_split_clause,[],[f51,f276]) ).
fof(f276,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(f274,plain,
spl0_15,
inference(avatar_split_clause,[],[f47,f272]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
fof(f270,plain,
( spl0_14
| ~ spl0_1
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f251,f248,f206,f267]) ).
fof(f267,plain,
( spl0_14
<=> function(xf1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f248,plain,
( spl0_10
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f251,plain,
( function(xf1)
| ~ spl0_1
| ~ spl0_10 ),
inference(resolution,[],[f249,f208]) ).
fof(f249,plain,
( ! [X8] :
( ~ operation(X8)
| function(X8) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f265,plain,
spl0_13,
inference(avatar_split_clause,[],[f44,f262]) ).
fof(f262,plain,
( spl0_13
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation1) ).
fof(f260,plain,
spl0_12,
inference(avatar_split_clause,[],[f18,f257]) ).
fof(f257,plain,
( spl0_12
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).
fof(f255,plain,
spl0_11,
inference(avatar_split_clause,[],[f11,f253]) ).
fof(f253,plain,
( spl0_11
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f250,plain,
spl0_10,
inference(avatar_split_clause,[],[f78,f248]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation1) ).
fof(f246,plain,
spl0_9,
inference(avatar_split_clause,[],[f71,f244]) ).
fof(f244,plain,
( spl0_9
<=> ! [X8] :
( ~ one_to_one(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f71,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one1) ).
fof(f242,plain,
spl0_8,
inference(avatar_split_clause,[],[f178,f240]) ).
fof(f240,plain,
( spl0_8
<=> ! [X1] : subclass(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f178,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(f238,plain,
spl0_7,
inference(avatar_split_clause,[],[f52,f235]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f233,plain,
spl0_6,
inference(avatar_split_clause,[],[f4,f231]) ).
fof(f231,plain,
( spl0_6
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f229,plain,
spl0_5,
inference(avatar_split_clause,[],[f69,f226]) ).
fof(f226,plain,
( spl0_5
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
fof(f224,plain,
spl0_4,
inference(avatar_split_clause,[],[f50,f221]) ).
fof(f221,plain,
( spl0_4
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f219,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f115,f216]) ).
fof(f115,axiom,
cross_product(domain_of(xh),domain_of(xh)) != domain_of(xf1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_compatible_functions_alternate_defn1_3) ).
fof(f214,plain,
spl0_2,
inference(avatar_split_clause,[],[f114,f211]) ).
fof(f114,axiom,
compatible(xh,xf1,xf2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_compatible_functions_alternate_defn1_2) ).
fof(f209,plain,
spl0_1,
inference(avatar_split_clause,[],[f113,f206]) ).
fof(f113,axiom,
operation(xf1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_compatible_functions_alternate_defn1_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET558-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n021.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 : Tue Apr 30 01:33:25 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (7854)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (7857)WARNING: value z3 for option sas not known
% 0.22/0.38 % (7855)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (7856)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 % (7858)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (7860)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 % (7859)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 % (7857)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 % (7861)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 % (7859)First to succeed.
% 0.22/0.40 % (7859)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 % (7859)------------------------------
% 0.22/0.40 % (7859)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.40 % (7859)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (7859)Memory used [KB]: 1170
% 0.22/0.40 % (7859)Time elapsed: 0.018 s
% 0.22/0.40 % (7859)Instructions burned: 28 (million)
% 0.22/0.40 % (7859)------------------------------
% 0.22/0.40 % (7859)------------------------------
% 0.22/0.40 % (7854)Success in time 0.037 s
%------------------------------------------------------------------------------