TSTP Solution File: SET101-7 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET101-7 : 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 : n029.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 09:11:13 EDT 2024
% Result : Unsatisfiable 0.15s 0.40s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 101
% Syntax : Number of formulae : 176 ( 76 unt; 0 def)
% Number of atoms : 317 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 239 ( 98 ~; 90 |; 0 &)
% ( 51 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 61 ( 59 usr; 52 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 8 con; 0-2 aty)
% Number of variables : 162 ( 162 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f523,plain,
$false,
inference(avatar_sat_refutation,[],[f259,f264,f268,f273,f277,f281,f285,f290,f295,f299,f303,f307,f312,f317,f321,f325,f330,f336,f340,f344,f348,f352,f356,f364,f368,f372,f376,f380,f384,f388,f393,f406,f410,f414,f418,f422,f426,f430,f434,f438,f442,f446,f450,f454,f458,f462,f466,f470,f474,f478,f500,f522]) ).
fof(f522,plain,
( ~ spl0_12
| spl0_51 ),
inference(avatar_contradiction_clause,[],[f520]) ).
fof(f520,plain,
( $false
| ~ spl0_12
| spl0_51 ),
inference(resolution,[],[f499,f306]) ).
fof(f306,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f305,plain,
( spl0_12
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f499,plain,
( ~ member(unordered_pair(x,x),universal_class)
| spl0_51 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f497,plain,
( spl0_51
<=> member(unordered_pair(x,x),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f500,plain,
( ~ spl0_51
| spl0_9
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f485,f412,f292,f497]) ).
fof(f292,plain,
( spl0_9
<=> member(unordered_pair(x,x),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f412,plain,
( spl0_34
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f485,plain,
( ~ member(unordered_pair(x,x),universal_class)
| spl0_9
| ~ spl0_34 ),
inference(resolution,[],[f413,f294]) ).
fof(f294,plain,
( ~ member(unordered_pair(x,x),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))))
| spl0_9 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f413,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f478,plain,
spl0_50,
inference(avatar_split_clause,[],[f186,f476]) ).
fof(f476,plain,
( spl0_50
<=> ! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f186,plain,
! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ),
inference(definition_unfolding,[],[f126,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f126,axiom,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f474,plain,
spl0_49,
inference(avatar_split_clause,[],[f182,f472]) ).
fof(f472,plain,
( spl0_49
<=> ! [X0,X1] :
( X0 = X1
| ~ member(X1,unordered_pair(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f182,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X1,unordered_pair(X0,X0)) ),
inference(definition_unfolding,[],[f125,f12]) ).
fof(f125,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(X1,singleton(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f470,plain,
( spl0_48
| ~ spl0_15
| ~ spl0_24 ),
inference(avatar_split_clause,[],[f389,f362,f319,f468]) ).
fof(f468,plain,
( spl0_48
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f319,plain,
( spl0_15
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f362,plain,
( spl0_24
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f389,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) )
| ~ spl0_15
| ~ spl0_24 ),
inference(resolution,[],[f363,f320]) ).
fof(f320,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f363,plain,
( ! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f466,plain,
spl0_47,
inference(avatar_split_clause,[],[f174,f464]) ).
fof(f464,plain,
( spl0_47
<=> ! [X0,X1] :
( ~ member(X0,X1)
| subclass(unordered_pair(X0,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f174,plain,
! [X0,X1] :
( ~ member(X0,X1)
| subclass(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f139,f12]) ).
fof(f139,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| subclass(singleton(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_singletons2) ).
fof(f462,plain,
spl0_46,
inference(avatar_split_clause,[],[f169,f460]) ).
fof(f460,plain,
( spl0_46
<=> ! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f169,plain,
! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ),
inference(definition_unfolding,[],[f72,f38]) ).
fof(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f72,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(inverse(X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one2) ).
fof(f458,plain,
spl0_45,
inference(avatar_split_clause,[],[f135,f456]) ).
fof(f456,plain,
( spl0_45
<=> ! [X0] :
( member_of(X0) = X0
| member(member_of1(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f135,axiom,
! [X0] :
( member_of(X0) = X0
| member(member_of1(X0),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_non_singleton_unique1) ).
fof(f454,plain,
spl0_44,
inference(avatar_split_clause,[],[f132,f452]) ).
fof(f452,plain,
( spl0_44
<=> ! [X0] :
( member_of(X0) = X0
| member(member_of(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f132,axiom,
! [X0] :
( member_of(X0) = X0
| member(member_of(X0),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_exists3) ).
fof(f450,plain,
spl0_43,
inference(avatar_split_clause,[],[f117,f448]) ).
fof(f448,plain,
( spl0_43
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| unordered_pair(X0,X1) != null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f117,axiom,
! [X0,X1] :
( ~ member(X1,universal_class)
| unordered_pair(X0,X1) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom2) ).
fof(f446,plain,
spl0_42,
inference(avatar_split_clause,[],[f116,f444]) ).
fof(f444,plain,
( spl0_42
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| unordered_pair(X0,X1) != null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f116,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| unordered_pair(X0,X1) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom1) ).
fof(f442,plain,
spl0_41,
inference(avatar_split_clause,[],[f106,f440]) ).
fof(f440,plain,
( spl0_41
<=> ! [X4] :
( null_class = X4
| member(not_subclass_element(X4,null_class),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f106,axiom,
! [X4] :
( null_class = X4
| member(not_subclass_element(X4,null_class),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_unique) ).
fof(f438,plain,
spl0_40,
inference(avatar_split_clause,[],[f88,f436]) ).
fof(f436,plain,
( spl0_40
<=> ! [X9,X11,X10] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f88,axiom,
! [X10,X11,X9] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).
fof(f434,plain,
spl0_39,
inference(avatar_split_clause,[],[f35,f432]) ).
fof(f432,plain,
( spl0_39
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
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(f430,plain,
spl0_38,
inference(avatar_split_clause,[],[f32,f428]) ).
fof(f428,plain,
( spl0_38
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
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(f426,plain,
spl0_37,
inference(avatar_split_clause,[],[f22,f424]) ).
fof(f424,plain,
( spl0_37
<=> ! [X4,X0,X1] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f422,plain,
spl0_36,
inference(avatar_split_clause,[],[f21,f420]) ).
fof(f420,plain,
( spl0_36
<=> ! [X4,X0,X1] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f418,plain,
spl0_35,
inference(avatar_split_clause,[],[f10,f416]) ).
fof(f416,plain,
( spl0_35
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
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(f414,plain,
spl0_34,
inference(avatar_split_clause,[],[f9,f412]) ).
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(f410,plain,
spl0_33,
inference(avatar_split_clause,[],[f3,f408]) ).
fof(f408,plain,
( spl0_33
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
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(f406,plain,
spl0_32,
inference(avatar_split_clause,[],[f2,f404]) ).
fof(f404,plain,
( spl0_32
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
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(f393,plain,
( spl0_31
| ~ spl0_15
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f357,f350,f319,f391]) ).
fof(f391,plain,
( spl0_31
<=> ! [X0] : ~ inductive(intersection(complement(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f350,plain,
( spl0_22
<=> ! [X0,X1] : ~ member(X1,intersection(complement(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f357,plain,
( ! [X0] : ~ inductive(intersection(complement(X0),X0))
| ~ spl0_15
| ~ spl0_22 ),
inference(resolution,[],[f351,f320]) ).
fof(f351,plain,
( ! [X0,X1] : ~ member(X1,intersection(complement(X0),X0))
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f388,plain,
spl0_30,
inference(avatar_split_clause,[],[f164,f386]) ).
fof(f386,plain,
( spl0_30
<=> ! [X0,X1] : subclass(unordered_pair(X1,X1),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f164,plain,
! [X0,X1] : subclass(unordered_pair(X1,X1),unordered_pair(X0,X1)),
inference(definition_unfolding,[],[f110,f12]) ).
fof(f110,axiom,
! [X0,X1] : subclass(singleton(X1),unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_in_unordered_pair2) ).
fof(f384,plain,
spl0_29,
inference(avatar_split_clause,[],[f163,f382]) ).
fof(f382,plain,
( spl0_29
<=> ! [X0,X1] : subclass(unordered_pair(X0,X0),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f163,plain,
! [X0,X1] : subclass(unordered_pair(X0,X0),unordered_pair(X0,X1)),
inference(definition_unfolding,[],[f109,f12]) ).
fof(f109,axiom,
! [X0,X1] : subclass(singleton(X0),unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_in_unordered_pair1) ).
fof(f380,plain,
spl0_28,
inference(avatar_split_clause,[],[f108,f378]) ).
fof(f378,plain,
( spl0_28
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f108,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f376,plain,
spl0_27,
inference(avatar_split_clause,[],[f66,f374]) ).
fof(f374,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(f372,plain,
spl0_26,
inference(avatar_split_clause,[],[f62,f370]) ).
fof(f370,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(f368,plain,
spl0_25,
inference(avatar_split_clause,[],[f57,f366]) ).
fof(f366,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(f364,plain,
spl0_24,
inference(avatar_split_clause,[],[f24,f362]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f356,plain,
spl0_23,
inference(avatar_split_clause,[],[f105,f354]) ).
fof(f354,plain,
( spl0_23
<=> ! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f105,axiom,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_of_null_class_is_subclass) ).
fof(f352,plain,
spl0_22,
inference(avatar_split_clause,[],[f102,f350]) ).
fof(f102,axiom,
! [X0,X1] : ~ member(X1,intersection(complement(X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',special_classes_lemma) ).
fof(f348,plain,
spl0_21,
inference(avatar_split_clause,[],[f87,f346]) ).
fof(f346,plain,
( spl0_21
<=> ! [X9,X11,X10] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f87,axiom,
! [X10,X11,X9] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
fof(f344,plain,
spl0_20,
inference(avatar_split_clause,[],[f86,f342]) ).
fof(f342,plain,
( spl0_20
<=> ! [X9,X11,X10] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f86,axiom,
! [X10,X11,X9] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
fof(f340,plain,
spl0_19,
inference(avatar_split_clause,[],[f82,f338]) ).
fof(f338,plain,
( spl0_19
<=> ! [X9,X11,X10] :
( function(X9)
| ~ compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f82,axiom,
! [X10,X11,X9] :
( function(X9)
| ~ compatible(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible1) ).
fof(f336,plain,
( ~ spl0_18
| ~ spl0_6
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f331,f319,f279,f333]) ).
fof(f333,plain,
( spl0_18
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f279,plain,
( spl0_6
<=> ! [X4] : ~ member(X4,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f331,plain,
( ~ inductive(null_class)
| ~ spl0_6
| ~ spl0_15 ),
inference(resolution,[],[f320,f280]) ).
fof(f280,plain,
( ! [X4] : ~ member(X4,null_class)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f330,plain,
spl0_17,
inference(avatar_split_clause,[],[f159,f327]) ).
fof(f327,plain,
( spl0_17
<=> member(null_class,unordered_pair(null_class,null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f159,plain,
member(null_class,unordered_pair(null_class,null_class)),
inference(definition_unfolding,[],[f124,f12]) ).
fof(f124,axiom,
member(null_class,singleton(null_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_in_its_singleton) ).
fof(f325,plain,
spl0_16,
inference(avatar_split_clause,[],[f51,f323]) ).
fof(f323,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(f321,plain,
spl0_15,
inference(avatar_split_clause,[],[f47,f319]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
fof(f317,plain,
spl0_14,
inference(avatar_split_clause,[],[f44,f314]) ).
fof(f314,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(f312,plain,
spl0_13,
inference(avatar_split_clause,[],[f18,f309]) ).
fof(f309,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(f307,plain,
spl0_12,
inference(avatar_split_clause,[],[f11,f305]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f303,plain,
spl0_11,
inference(avatar_split_clause,[],[f78,f301]) ).
fof(f301,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(f299,plain,
spl0_10,
inference(avatar_split_clause,[],[f71,f297]) ).
fof(f297,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(f295,plain,
~ spl0_9,
inference(avatar_split_clause,[],[f158,f292]) ).
fof(f158,plain,
~ member(unordered_pair(x,x),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))),
inference(definition_unfolding,[],[f146,f12,f151]) ).
fof(f151,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(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(f146,axiom,
~ member(singleton(x),ordered_pair(x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_member_of_ordered_pair_1) ).
fof(f290,plain,
spl0_8,
inference(avatar_split_clause,[],[f107,f287]) ).
fof(f287,plain,
( spl0_8
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f107,axiom,
member(null_class,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_a_set) ).
fof(f285,plain,
spl0_7,
inference(avatar_split_clause,[],[f104,f283]) ).
fof(f283,plain,
( spl0_7
<=> ! [X0] : subclass(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f104,axiom,
! [X0] : subclass(null_class,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_subclass) ).
fof(f281,plain,
spl0_6,
inference(avatar_split_clause,[],[f103,f279]) ).
fof(f103,axiom,
! [X4] : ~ member(X4,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f277,plain,
spl0_5,
inference(avatar_split_clause,[],[f96,f275]) ).
fof(f275,plain,
( spl0_5
<=> ! [X0] : subclass(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f96,axiom,
! [X0] : subclass(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_is_reflexive) ).
fof(f273,plain,
spl0_4,
inference(avatar_split_clause,[],[f52,f270]) ).
fof(f270,plain,
( spl0_4
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f268,plain,
spl0_3,
inference(avatar_split_clause,[],[f4,f266]) ).
fof(f266,plain,
( spl0_3
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f264,plain,
spl0_2,
inference(avatar_split_clause,[],[f69,f261]) ).
fof(f261,plain,
( spl0_2
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
fof(f259,plain,
spl0_1,
inference(avatar_split_clause,[],[f50,f256]) ).
fof(f256,plain,
( spl0_1
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET101-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n029.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 : Fri May 3 16:19:08 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (11345)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (11348)WARNING: value z3 for option sas not known
% 0.15/0.38 % (11346)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (11349)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (11348)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.39 % (11350)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.39 % (11347)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39 % (11351)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.39 % (11352)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.40 % (11350)First to succeed.
% 0.15/0.40 % (11350)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-11345"
% 0.15/0.40 % (11350)Refutation found. Thanks to Tanya!
% 0.15/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.40 % (11350)------------------------------
% 0.26/0.40 % (11350)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.26/0.40 % (11350)Termination reason: Refutation
% 0.26/0.40
% 0.26/0.40 % (11350)Memory used [KB]: 1085
% 0.26/0.40 % (11350)Time elapsed: 0.017 s
% 0.26/0.40 % (11350)Instructions burned: 26 (million)
% 0.26/0.40 % (11345)Success in time 0.037 s
%------------------------------------------------------------------------------