TSTP Solution File: SET563-6 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET563-6 : 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 : n014.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 09:14:11 EDT 2024
% Result : Unsatisfiable 0.16s 0.36s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 148
% Syntax : Number of formulae : 268 ( 104 unt; 0 def)
% Number of atoms : 523 ( 56 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 435 ( 180 ~; 182 |; 0 &)
% ( 73 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 85 ( 83 usr; 74 prp; 0-3 aty)
% Number of functors : 35 ( 35 usr; 17 con; 0-3 aty)
% Number of variables : 289 ( 289 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f615,plain,
$false,
inference(avatar_sat_refutation,[],[f210,f215,f220,f225,f230,f234,f239,f243,f247,f251,f255,f260,f265,f269,f273,f278,f282,f286,f290,f294,f298,f304,f308,f312,f317,f321,f326,f331,f337,f342,f346,f350,f354,f358,f362,f366,f370,f374,f378,f382,f395,f399,f403,f408,f413,f441,f447,f451,f455,f465,f469,f473,f478,f482,f486,f490,f494,f521,f526,f530,f534,f539,f547,f553,f557,f565,f569,f578,f584,f588,f592,f596,f613,f614]) ).
fof(f614,plain,
( spl0_5
| ~ spl0_1
| ~ spl0_58
| ~ spl0_64 ),
inference(avatar_split_clause,[],[f560,f551,f518,f207,f227]) ).
fof(f227,plain,
( spl0_5
<=> subclass(domain_of(domain_of(flip(cross_product(xh1,universal_class)))),domain_of(xh2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f207,plain,
( spl0_1
<=> compatible(xh1,xf1,xf2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f518,plain,
( spl0_58
<=> domain_of(xh2) = domain_of(domain_of(xf2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f551,plain,
( spl0_64
<=> ! [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_64])]) ).
fof(f560,plain,
( subclass(domain_of(domain_of(flip(cross_product(xh1,universal_class)))),domain_of(xh2))
| ~ spl0_1
| ~ spl0_58
| ~ spl0_64 ),
inference(forward_demodulation,[],[f558,f520]) ).
fof(f520,plain,
( domain_of(xh2) = domain_of(domain_of(xf2))
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f558,plain,
( subclass(domain_of(domain_of(flip(cross_product(xh1,universal_class)))),domain_of(domain_of(xf2)))
| ~ spl0_1
| ~ spl0_64 ),
inference(resolution,[],[f552,f209]) ).
fof(f209,plain,
( compatible(xh1,xf1,xf2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f552,plain,
( ! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f613,plain,
spl0_73,
inference(avatar_split_clause,[],[f153,f611]) ).
fof(f611,plain,
( spl0_73
<=> ! [X4,X0,X1] :
( compose(X0,X1) = X4
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f153,plain,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose_class(X0)) ),
inference(definition_unfolding,[],[f93,f120]) ).
fof(f120,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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f93,axiom,
! [X0,X1,X4] :
( compose(X0,X1) = X4
| ~ member(ordered_pair(X1,X4),compose_class(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition2) ).
fof(f596,plain,
spl0_72,
inference(avatar_split_clause,[],[f165,f594]) ).
fof(f594,plain,
( spl0_72
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f165,plain,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
inference(definition_unfolding,[],[f31,f29,f12]) ).
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(f31,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f592,plain,
spl0_71,
inference(avatar_split_clause,[],[f163,f590]) ).
fof(f590,plain,
( spl0_71
<=> ! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f163,plain,
! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f64,f38]) ).
fof(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f64,axiom,
! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function3) ).
fof(f588,plain,
spl0_70,
inference(avatar_split_clause,[],[f144,f586]) ).
fof(f586,plain,
( spl0_70
<=> ! [X0,X3,X2,X1] :
( member(X3,X1)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f15,f120]) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f584,plain,
spl0_69,
inference(avatar_split_clause,[],[f143,f582]) ).
fof(f582,plain,
( spl0_69
<=> ! [X0,X3,X2,X1] :
( member(X2,X0)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f14,f120]) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f578,plain,
spl0_68,
inference(avatar_split_clause,[],[f141,f576]) ).
fof(f576,plain,
( spl0_68
<=> ! [X0] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f141,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(domain_of(X0),domain_of(X0)))),domain_relation) ),
inference(definition_unfolding,[],[f100,f120]) ).
fof(f100,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(ordered_pair(X0,domain_of(X0)),domain_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation3) ).
fof(f569,plain,
spl0_67,
inference(avatar_split_clause,[],[f161,f567]) ).
fof(f567,plain,
( spl0_67
<=> ! [X1,X8] :
( ~ function(X8)
| ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
| maps(X8,domain_of(X8),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f161,plain,
! [X1,X8] :
( ~ function(X8)
| ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),X1)
| maps(X8,domain_of(X8),X1) ),
inference(definition_unfolding,[],[f112,f117]) ).
fof(f117,plain,
! [X4] : range_of(X4) = domain_of(domain_of(flip(cross_product(X4,universal_class)))),
inference(definition_unfolding,[],[f39,f38]) ).
fof(f39,axiom,
! [X4] : domain_of(inverse(X4)) = range_of(X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).
fof(f112,axiom,
! [X1,X8] :
( ~ function(X8)
| ~ subclass(range_of(X8),X1)
| maps(X8,domain_of(X8),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps4) ).
fof(f565,plain,
spl0_66,
inference(avatar_split_clause,[],[f149,f563]) ).
fof(f563,plain,
( spl0_66
<=> ! [X0,X1] :
( domain_of(X0) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f149,plain,
! [X0,X1] :
( domain_of(X0) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_relation) ),
inference(definition_unfolding,[],[f99,f120]) ).
fof(f99,axiom,
! [X0,X1] :
( domain_of(X0) = X1
| ~ member(ordered_pair(X0,X1),domain_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation2) ).
fof(f557,plain,
spl0_65,
inference(avatar_split_clause,[],[f183,f555]) ).
fof(f555,plain,
( spl0_65
<=> ! [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_65])]) ).
fof(f183,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,[],[f135,f131]) ).
fof(f131,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/sandbox2/benchmark/theBenchmark.p',restriction1) ).
fof(f135,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,f118]) ).
fof(f118,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,f117,f29]) ).
fof(f42,axiom,
! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive2) ).
fof(f553,plain,
spl0_64,
inference(avatar_split_clause,[],[f147,f551]) ).
fof(f147,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,f117]) ).
fof(f84,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible3) ).
fof(f547,plain,
spl0_63,
inference(avatar_split_clause,[],[f142,f545]) ).
fof(f545,plain,
( spl0_63
<=> ! [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_63])]) ).
fof(f142,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,f120]) ).
fof(f19,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation2) ).
fof(f539,plain,
spl0_62,
inference(avatar_split_clause,[],[f145,f537]) ).
fof(f537,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(f145,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/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f534,plain,
spl0_61,
inference(avatar_split_clause,[],[f146,f532]) ).
fof(f532,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(f146,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(f111,axiom,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| subclass(range_of(X8),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps3) ).
fof(f530,plain,
spl0_60,
inference(avatar_split_clause,[],[f136,f528]) ).
fof(f528,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(f136,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/sandbox2/benchmark/theBenchmark.p',operation3) ).
fof(f526,plain,
spl0_59,
inference(avatar_split_clause,[],[f79,f524]) ).
fof(f524,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(f79,axiom,
! [X8] :
( ~ operation(X8)
| domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation2) ).
fof(f521,plain,
( spl0_58
| ~ spl0_2
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f460,f449,f212,f518]) ).
fof(f212,plain,
( spl0_2
<=> compatible(xh2,xf2,xf3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f449,plain,
( spl0_48
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f460,plain,
( domain_of(xh2) = domain_of(domain_of(xf2))
| ~ spl0_2
| ~ spl0_48 ),
inference(resolution,[],[f450,f214]) ).
fof(f214,plain,
( compatible(xh2,xf2,xf3)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f450,plain,
( ! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f494,plain,
spl0_57,
inference(avatar_split_clause,[],[f185,f492]) ).
fof(f492,plain,
( spl0_57
<=> ! [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_57])]) ).
fof(f185,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(forward_demodulation,[],[f140,f131]) ).
fof(f140,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/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(f490,plain,
spl0_56,
inference(avatar_split_clause,[],[f138,f488]) ).
fof(f488,plain,
( spl0_56
<=> ! [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_56])]) ).
fof(f138,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/sandbox2/benchmark/theBenchmark.p',single_valued_class2) ).
fof(f486,plain,
spl0_55,
inference(avatar_split_clause,[],[f137,f484]) ).
fof(f484,plain,
( spl0_55
<=> ! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f137,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(f482,plain,
spl0_54,
inference(avatar_split_clause,[],[f133,f480]) ).
fof(f480,plain,
( spl0_54
<=> ! [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_54])]) ).
fof(f133,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(f478,plain,
( spl0_53
| ~ spl0_1
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f459,f449,f207,f475]) ).
fof(f475,plain,
( spl0_53
<=> domain_of(domain_of(xf1)) = domain_of(xh1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f459,plain,
( domain_of(domain_of(xf1)) = domain_of(xh1)
| ~ spl0_1
| ~ spl0_48 ),
inference(resolution,[],[f450,f209]) ).
fof(f473,plain,
spl0_52,
inference(avatar_split_clause,[],[f131,f471]) ).
fof(f471,plain,
( spl0_52
<=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f469,plain,
spl0_51,
inference(avatar_split_clause,[],[f23,f467]) ).
fof(f467,plain,
( spl0_51
<=> ! [X4,X0,X1] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
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(f465,plain,
spl0_50,
inference(avatar_split_clause,[],[f8,f463]) ).
fof(f463,plain,
( spl0_50
<=> ! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
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(f455,plain,
spl0_49,
inference(avatar_split_clause,[],[f159,f453]) ).
fof(f453,plain,
( spl0_49
<=> ! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f159,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(f451,plain,
spl0_48,
inference(avatar_split_clause,[],[f83,f449]) ).
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(f447,plain,
spl0_47,
inference(avatar_split_clause,[],[f25,f445]) ).
fof(f445,plain,
( spl0_47
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
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(f441,plain,
( spl0_46
| ~ spl0_14
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f332,f302,f267,f439]) ).
fof(f439,plain,
( spl0_46
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f267,plain,
( spl0_14
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f302,plain,
( spl0_22
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f332,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) )
| ~ spl0_14
| ~ spl0_22 ),
inference(resolution,[],[f303,f268]) ).
fof(f268,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f303,plain,
( ! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f413,plain,
spl0_45,
inference(avatar_split_clause,[],[f130,f410]) ).
fof(f410,plain,
( spl0_45
<=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f130,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(f408,plain,
spl0_44,
inference(avatar_split_clause,[],[f104,f405]) ).
fof(f405,plain,
( spl0_44
<=> intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f104,axiom,
intersection(complement(compose(element_relation,complement(identity_relation))),element_relation) = singleton_relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_can_define_singleton) ).
fof(f403,plain,
spl0_43,
inference(avatar_split_clause,[],[f67,f401]) ).
fof(f401,plain,
( spl0_43
<=> ! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f67,axiom,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).
fof(f399,plain,
spl0_42,
inference(avatar_split_clause,[],[f7,f397]) ).
fof(f397,plain,
( spl0_42
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f395,plain,
spl0_41,
inference(avatar_split_clause,[],[f1,f393]) ).
fof(f393,plain,
( spl0_41
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
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(f382,plain,
spl0_40,
inference(avatar_split_clause,[],[f134,f380]) ).
fof(f380,plain,
( spl0_40
<=> ! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f134,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(f378,plain,
spl0_39,
inference(avatar_split_clause,[],[f110,f376]) ).
fof(f376,plain,
( spl0_39
<=> ! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| domain_of(X8) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f110,axiom,
! [X0,X1,X8] :
( ~ maps(X8,X0,X1)
| domain_of(X8) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps2) ).
fof(f374,plain,
spl0_38,
inference(avatar_split_clause,[],[f88,f372]) ).
fof(f372,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/sandbox2/benchmark/theBenchmark.p',homomorphism3) ).
fof(f370,plain,
spl0_37,
inference(avatar_split_clause,[],[f35,f368]) ).
fof(f368,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/sandbox2/benchmark/theBenchmark.p',flip1) ).
fof(f366,plain,
spl0_36,
inference(avatar_split_clause,[],[f32,f364]) ).
fof(f364,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/sandbox2/benchmark/theBenchmark.p',rotate1) ).
fof(f362,plain,
spl0_35,
inference(avatar_split_clause,[],[f22,f360]) ).
fof(f360,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/sandbox2/benchmark/theBenchmark.p',intersection2) ).
fof(f358,plain,
spl0_34,
inference(avatar_split_clause,[],[f21,f356]) ).
fof(f356,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/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f354,plain,
spl0_33,
inference(avatar_split_clause,[],[f10,f352]) ).
fof(f352,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/sandbox2/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f350,plain,
spl0_32,
inference(avatar_split_clause,[],[f9,f348]) ).
fof(f348,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/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f346,plain,
spl0_31,
inference(avatar_split_clause,[],[f3,f344]) ).
fof(f344,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/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f342,plain,
( spl0_30
| ~ spl0_2
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f300,f280,f212,f339]) ).
fof(f339,plain,
( spl0_30
<=> function(xh2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f280,plain,
( spl0_17
<=> ! [X9,X11,X10] :
( function(X9)
| ~ compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f300,plain,
( function(xh2)
| ~ spl0_2
| ~ spl0_17 ),
inference(resolution,[],[f281,f214]) ).
fof(f281,plain,
( ! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| function(X9) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f337,plain,
spl0_29,
inference(avatar_split_clause,[],[f2,f335]) ).
fof(f335,plain,
( spl0_29
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
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(f331,plain,
spl0_28,
inference(avatar_split_clause,[],[f105,f328]) ).
fof(f328,plain,
( spl0_28
<=> subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f105,axiom,
subclass(application_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',application_function_defn1) ).
fof(f326,plain,
spl0_27,
inference(avatar_split_clause,[],[f95,f323]) ).
fof(f323,plain,
( spl0_27
<=> subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f95,axiom,
subclass(composition_function,cross_product(universal_class,cross_product(universal_class,universal_class))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_composition_function1) ).
fof(f321,plain,
spl0_26,
inference(avatar_split_clause,[],[f66,f319]) ).
fof(f319,plain,
( spl0_26
<=> ! [X0] :
( null_class = X0
| member(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f66,axiom,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
fof(f317,plain,
( spl0_25
| ~ spl0_1
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f299,f280,f207,f314]) ).
fof(f314,plain,
( spl0_25
<=> function(xh1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f299,plain,
( function(xh1)
| ~ spl0_1
| ~ spl0_17 ),
inference(resolution,[],[f281,f209]) ).
fof(f312,plain,
spl0_24,
inference(avatar_split_clause,[],[f62,f310]) ).
fof(f310,plain,
( spl0_24
<=> ! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f62,axiom,
! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).
fof(f308,plain,
spl0_23,
inference(avatar_split_clause,[],[f57,f306]) ).
fof(f306,plain,
( spl0_23
<=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f57,axiom,
! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).
fof(f304,plain,
spl0_22,
inference(avatar_split_clause,[],[f24,f302]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f298,plain,
spl0_21,
inference(avatar_split_clause,[],[f109,f296]) ).
fof(f296,plain,
( spl0_21
<=> ! [X0,X1,X8] :
( function(X8)
| ~ maps(X8,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f109,axiom,
! [X0,X1,X8] :
( function(X8)
| ~ maps(X8,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maps1) ).
fof(f294,plain,
spl0_20,
inference(avatar_split_clause,[],[f92,f292]) ).
fof(f292,plain,
( spl0_20
<=> ! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f92,axiom,
! [X0] : subclass(compose_class(X0),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_class_definition1) ).
fof(f290,plain,
spl0_19,
inference(avatar_split_clause,[],[f87,f288]) ).
fof(f288,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/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
fof(f286,plain,
spl0_18,
inference(avatar_split_clause,[],[f86,f284]) ).
fof(f284,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/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
fof(f282,plain,
spl0_17,
inference(avatar_split_clause,[],[f82,f280]) ).
fof(f82,axiom,
! [X10,X11,X9] :
( function(X9)
| ~ compatible(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible1) ).
fof(f278,plain,
spl0_16,
inference(avatar_split_clause,[],[f98,f275]) ).
fof(f275,plain,
( spl0_16
<=> subclass(domain_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f98,axiom,
subclass(domain_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_domain_relation1) ).
fof(f273,plain,
spl0_15,
inference(avatar_split_clause,[],[f51,f271]) ).
fof(f271,plain,
( spl0_15
<=> ! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f51,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).
fof(f269,plain,
spl0_14,
inference(avatar_split_clause,[],[f47,f267]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f251,plain,
spl0_10,
inference(avatar_split_clause,[],[f78,f249]) ).
fof(f249,plain,
( spl0_10
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).
fof(f247,plain,
spl0_9,
inference(avatar_split_clause,[],[f71,f245]) ).
fof(f245,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/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).
fof(f243,plain,
spl0_8,
inference(avatar_split_clause,[],[f179,f241]) ).
fof(f241,plain,
( spl0_8
<=> ! [X1] : subclass(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f179,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_implies_subclass2) ).
fof(f239,plain,
spl0_7,
inference(avatar_split_clause,[],[f52,f236]) ).
fof(f236,plain,
( spl0_7
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f234,plain,
spl0_6,
inference(avatar_split_clause,[],[f4,f232]) ).
fof(f232,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/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f230,plain,
~ spl0_5,
inference(avatar_split_clause,[],[f129,f227]) ).
fof(f129,plain,
~ subclass(domain_of(domain_of(flip(cross_product(xh1,universal_class)))),domain_of(xh2)),
inference(definition_unfolding,[],[f115,f117]) ).
fof(f115,axiom,
~ subclass(range_of(xh1),domain_of(xh2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_compatible_function_property3_3) ).
fof(f225,plain,
spl0_4,
inference(avatar_split_clause,[],[f69,f222]) ).
fof(f222,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(f220,plain,
spl0_3,
inference(avatar_split_clause,[],[f50,f217]) ).
fof(f217,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(f215,plain,
spl0_2,
inference(avatar_split_clause,[],[f114,f212]) ).
fof(f114,axiom,
compatible(xh2,xf2,xf3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_compatible_function_property3_2) ).
fof(f210,plain,
spl0_1,
inference(avatar_split_clause,[],[f113,f207]) ).
fof(f113,axiom,
compatible(xh1,xf1,xf2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_compatible_function_property3_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET563-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.03/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri May 3 16:59:38 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (21549)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (21552)WARNING: value z3 for option sas not known
% 0.11/0.34 % (21550)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.34 % (21556)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)
% 0.11/0.34 % (21553)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.34 % (21552)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)
% 0.11/0.34 % (21551)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.34 % (21555)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)
% 0.11/0.34 % (21554)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)
% 0.16/0.36 % (21554)First to succeed.
% 0.16/0.36 % (21555)Also succeeded, but the first one will report.
% 0.16/0.36 % (21554)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-21549"
% 0.16/0.36 % (21554)Refutation found. Thanks to Tanya!
% 0.16/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.36 % (21554)------------------------------
% 0.16/0.36 % (21554)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.36 % (21554)Termination reason: Refutation
% 0.16/0.36
% 0.16/0.36 % (21554)Memory used [KB]: 1265
% 0.16/0.36 % (21554)Time elapsed: 0.019 s
% 0.16/0.36 % (21554)Instructions burned: 32 (million)
% 0.16/0.36 % (21549)Success in time 0.036 s
%------------------------------------------------------------------------------