TSTP Solution File: SET081-6 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET081-6 : 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 : n003.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 09:11:02 EDT 2024
% Result : Unsatisfiable 0.14s 0.32s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 97
% Syntax : Number of formulae : 170 ( 69 unt; 0 def)
% Number of atoms : 337 ( 33 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 281 ( 114 ~; 119 |; 0 &)
% ( 48 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 59 ( 57 usr; 49 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 10 con; 0-3 aty)
% Number of variables : 175 ( 175 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f417,plain,
$false,
inference(avatar_sat_refutation,[],[f171,f176,f181,f186,f190,f195,f199,f203,f207,f211,f216,f221,f225,f229,f233,f237,f241,f245,f249,f253,f257,f263,f267,f271,f275,f279,f283,f287,f291,f295,f299,f303,f316,f320,f324,f328,f333,f358,f362,f366,f373,f378,f382,f386,f390,f394,f398,f402,f416]) ).
fof(f416,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f409,f376,f173,f168]) ).
fof(f168,plain,
( spl0_1
<=> y = x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f173,plain,
( spl0_2
<=> member(y,unordered_pair(x,x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f376,plain,
( spl0_42
<=> ! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f409,plain,
( y = x
| ~ spl0_2
| ~ spl0_42 ),
inference(duplicate_literal_removal,[],[f408]) ).
fof(f408,plain,
( y = x
| y = x
| ~ spl0_2
| ~ spl0_42 ),
inference(resolution,[],[f377,f175]) ).
fof(f175,plain,
( member(y,unordered_pair(x,x))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f377,plain,
( ! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| X0 = X2
| X1 = X2 )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f402,plain,
spl0_48,
inference(avatar_split_clause,[],[f148,f400]) ).
fof(f400,plain,
( spl0_48
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f148,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(forward_demodulation,[],[f115,f106]) ).
fof(f106,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/sandbox2/benchmark/theBenchmark.p',restriction2) ).
fof(f28,axiom,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).
fof(f115,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
inference(definition_unfolding,[],[f54,f94]) ).
fof(f94,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/sandbox2/benchmark/theBenchmark.p',sum_class_definition) ).
fof(f54,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class2) ).
fof(f398,plain,
spl0_47,
inference(avatar_split_clause,[],[f113,f396]) ).
fof(f396,plain,
( spl0_47
<=> ! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f113,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(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f61,axiom,
! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class2) ).
fof(f394,plain,
spl0_46,
inference(avatar_split_clause,[],[f112,f392]) ).
fof(f392,plain,
( spl0_46
<=> ! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f112,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/sandbox2/benchmark/theBenchmark.p',function2) ).
fof(f390,plain,
spl0_45,
inference(avatar_split_clause,[],[f108,f388]) ).
fof(f388,plain,
( spl0_45
<=> ! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f108,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/sandbox2/benchmark/theBenchmark.p',single_valued_class1) ).
fof(f386,plain,
spl0_44,
inference(avatar_split_clause,[],[f106,f384]) ).
fof(f384,plain,
( spl0_44
<=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f382,plain,
spl0_43,
inference(avatar_split_clause,[],[f23,f380]) ).
fof(f380,plain,
( spl0_43
<=> ! [X4,X0,X1] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f23,axiom,
! [X0,X1,X4] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
fof(f378,plain,
spl0_42,
inference(avatar_split_clause,[],[f8,f376]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f373,plain,
( spl0_41
| ~ spl0_2
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f341,f314,f173,f371]) ).
fof(f371,plain,
( spl0_41
<=> ! [X0] :
( ~ subclass(unordered_pair(x,x),X0)
| member(y,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f314,plain,
( spl0_33
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f341,plain,
( ! [X0] :
( ~ subclass(unordered_pair(x,x),X0)
| member(y,X0) )
| ~ spl0_2
| ~ spl0_33 ),
inference(resolution,[],[f315,f175]) ).
fof(f315,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f366,plain,
spl0_40,
inference(avatar_split_clause,[],[f126,f364]) ).
fof(f364,plain,
( spl0_40
<=> ! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f126,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/sandbox2/benchmark/theBenchmark.p',one_to_one3) ).
fof(f362,plain,
spl0_39,
inference(avatar_split_clause,[],[f83,f360]) ).
fof(f360,plain,
( spl0_39
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f83,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible2) ).
fof(f358,plain,
spl0_38,
inference(avatar_split_clause,[],[f25,f356]) ).
fof(f356,plain,
( spl0_38
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f25,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
fof(f333,plain,
spl0_37,
inference(avatar_split_clause,[],[f105,f330]) ).
fof(f330,plain,
( spl0_37
<=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f105,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/sandbox2/benchmark/theBenchmark.p',identity_relation) ).
fof(f328,plain,
( spl0_36
| ~ spl0_13
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f308,f281,f223,f326]) ).
fof(f326,plain,
( spl0_36
<=> ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f223,plain,
( spl0_13
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f281,plain,
( spl0_27
<=> ! [X4,X0,X1] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f308,plain,
( ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X0,X1)) )
| ~ spl0_13
| ~ spl0_27 ),
inference(resolution,[],[f282,f224]) ).
fof(f224,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f282,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X0) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f324,plain,
spl0_35,
inference(avatar_split_clause,[],[f67,f322]) ).
fof(f322,plain,
( spl0_35
<=> ! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f67,axiom,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).
fof(f320,plain,
spl0_34,
inference(avatar_split_clause,[],[f7,f318]) ).
fof(f318,plain,
( spl0_34
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f316,plain,
spl0_33,
inference(avatar_split_clause,[],[f1,f314]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f303,plain,
spl0_32,
inference(avatar_split_clause,[],[f109,f301]) ).
fof(f301,plain,
( spl0_32
<=> ! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f109,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/sandbox2/benchmark/theBenchmark.p',one_to_one2) ).
fof(f299,plain,
spl0_31,
inference(avatar_split_clause,[],[f88,f297]) ).
fof(f297,plain,
( spl0_31
<=> ! [X9,X11,X10] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f88,axiom,
! [X10,X11,X9] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism3) ).
fof(f295,plain,
spl0_30,
inference(avatar_split_clause,[],[f35,f293]) ).
fof(f293,plain,
( spl0_30
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f35,axiom,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip1) ).
fof(f291,plain,
spl0_29,
inference(avatar_split_clause,[],[f32,f289]) ).
fof(f289,plain,
( spl0_29
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f32,axiom,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate1) ).
fof(f287,plain,
spl0_28,
inference(avatar_split_clause,[],[f22,f285]) ).
fof(f285,plain,
( spl0_28
<=> ! [X4,X0,X1] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
fof(f283,plain,
spl0_27,
inference(avatar_split_clause,[],[f21,f281]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f279,plain,
spl0_26,
inference(avatar_split_clause,[],[f10,f277]) ).
fof(f277,plain,
( spl0_26
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f10,axiom,
! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f275,plain,
( spl0_25
| ~ spl0_13
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f258,f243,f223,f273]) ).
fof(f273,plain,
( spl0_25
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f243,plain,
( spl0_18
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f258,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) )
| ~ spl0_13
| ~ spl0_18 ),
inference(resolution,[],[f244,f224]) ).
fof(f244,plain,
( ! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f271,plain,
spl0_24,
inference(avatar_split_clause,[],[f9,f269]) ).
fof(f269,plain,
( spl0_24
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f9,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f267,plain,
spl0_23,
inference(avatar_split_clause,[],[f3,f265]) ).
fof(f265,plain,
( spl0_23
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f263,plain,
spl0_22,
inference(avatar_split_clause,[],[f2,f261]) ).
fof(f261,plain,
( spl0_22
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f257,plain,
spl0_21,
inference(avatar_split_clause,[],[f66,f255]) ).
fof(f255,plain,
( spl0_21
<=> ! [X0] :
( null_class = X0
| member(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f66,axiom,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
fof(f253,plain,
spl0_20,
inference(avatar_split_clause,[],[f62,f251]) ).
fof(f251,plain,
( spl0_20
<=> ! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f62,axiom,
! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).
fof(f249,plain,
spl0_19,
inference(avatar_split_clause,[],[f57,f247]) ).
fof(f247,plain,
( spl0_19
<=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f57,axiom,
! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).
fof(f245,plain,
spl0_18,
inference(avatar_split_clause,[],[f24,f243]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f241,plain,
spl0_17,
inference(avatar_split_clause,[],[f87,f239]) ).
fof(f239,plain,
( spl0_17
<=> ! [X9,X11,X10] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f87,axiom,
! [X10,X11,X9] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
fof(f237,plain,
spl0_16,
inference(avatar_split_clause,[],[f86,f235]) ).
fof(f235,plain,
( spl0_16
<=> ! [X9,X11,X10] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f86,axiom,
! [X10,X11,X9] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
fof(f233,plain,
spl0_15,
inference(avatar_split_clause,[],[f82,f231]) ).
fof(f231,plain,
( spl0_15
<=> ! [X9,X11,X10] :
( function(X9)
| ~ compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f82,axiom,
! [X10,X11,X9] :
( function(X9)
| ~ compatible(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible1) ).
fof(f229,plain,
spl0_14,
inference(avatar_split_clause,[],[f51,f227]) ).
fof(f227,plain,
( spl0_14
<=> ! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f51,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).
fof(f225,plain,
spl0_13,
inference(avatar_split_clause,[],[f47,f223]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).
fof(f221,plain,
spl0_12,
inference(avatar_split_clause,[],[f44,f218]) ).
fof(f218,plain,
( spl0_12
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation1) ).
fof(f216,plain,
spl0_11,
inference(avatar_split_clause,[],[f18,f213]) ).
fof(f213,plain,
( spl0_11
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).
fof(f211,plain,
spl0_10,
inference(avatar_split_clause,[],[f11,f209]) ).
fof(f209,plain,
( spl0_10
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f207,plain,
spl0_9,
inference(avatar_split_clause,[],[f78,f205]) ).
fof(f205,plain,
( spl0_9
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).
fof(f203,plain,
spl0_8,
inference(avatar_split_clause,[],[f71,f201]) ).
fof(f201,plain,
( spl0_8
<=> ! [X8] :
( ~ one_to_one(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f71,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).
fof(f199,plain,
spl0_7,
inference(avatar_split_clause,[],[f143,f197]) ).
fof(f197,plain,
( spl0_7
<=> ! [X1] : subclass(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f143,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass1) ).
fof(f195,plain,
spl0_6,
inference(avatar_split_clause,[],[f52,f192]) ).
fof(f192,plain,
( spl0_6
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f190,plain,
spl0_5,
inference(avatar_split_clause,[],[f4,f188]) ).
fof(f188,plain,
( spl0_5
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f186,plain,
spl0_4,
inference(avatar_split_clause,[],[f69,f183]) ).
fof(f183,plain,
( spl0_4
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).
fof(f181,plain,
spl0_3,
inference(avatar_split_clause,[],[f50,f178]) ).
fof(f178,plain,
( spl0_3
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f176,plain,
spl0_2,
inference(avatar_split_clause,[],[f104,f173]) ).
fof(f104,plain,
member(y,unordered_pair(x,x)),
inference(definition_unfolding,[],[f92,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f92,axiom,
member(y,singleton(x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_only_member_in_singleton_1) ).
fof(f171,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f93,f168]) ).
fof(f93,axiom,
y != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_only_member_in_singleton_2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET081-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.09/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.29 % Computer : n003.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Fri May 3 17:05:37 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.09/0.30 % (13020)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.31 % (13023)WARNING: value z3 for option sas not known
% 0.14/0.31 % (13021)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.31 % (13023)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)
% 0.14/0.31 % (13022)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.31 % (13025)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)
% 0.14/0.31 % (13026)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)
% 0.14/0.31 % (13024)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.31 % (13027)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)
% 0.14/0.32 % (13025)First to succeed.
% 0.14/0.32 % (13026)Also succeeded, but the first one will report.
% 0.14/0.32 % (13025)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13020"
% 0.14/0.32 % (13025)Refutation found. Thanks to Tanya!
% 0.14/0.32 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.33 % (13025)------------------------------
% 0.14/0.33 % (13025)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.33 % (13025)Termination reason: Refutation
% 0.14/0.33
% 0.14/0.33 % (13025)Memory used [KB]: 1049
% 0.14/0.33 % (13025)Time elapsed: 0.012 s
% 0.14/0.33 % (13025)Instructions burned: 22 (million)
% 0.14/0.33 % (13020)Success in time 0.028 s
%------------------------------------------------------------------------------