TSTP Solution File: SET085-7 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET085-7 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:05:32 EDT 2024
% Result : Unsatisfiable 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 193
% Syntax : Number of formulae : 353 ( 136 unt; 0 def)
% Number of atoms : 704 ( 92 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 592 ( 241 ~; 255 |; 0 &)
% ( 96 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 107 ( 105 usr; 97 prp; 0-3 aty)
% Number of functors : 29 ( 29 usr; 11 con; 0-3 aty)
% Number of variables : 421 ( 421 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f906,plain,
$false,
inference(avatar_sat_refutation,[],[f230,f235,f240,f245,f250,f255,f259,f264,f268,f272,f276,f281,f285,f289,f293,f298,f303,f307,f311,f316,f322,f326,f330,f334,f338,f343,f351,f355,f359,f363,f367,f371,f375,f393,f397,f401,f405,f409,f413,f417,f421,f425,f429,f433,f437,f441,f445,f449,f453,f457,f503,f510,f514,f518,f523,f527,f575,f584,f588,f592,f596,f600,f615,f619,f623,f627,f631,f635,f639,f643,f647,f656,f706,f710,f716,f720,f724,f728,f732,f791,f795,f799,f812,f817,f821,f825,f829,f833,f837,f876,f880,f884,f896,f900,f904,f905]) ).
fof(f905,plain,
( spl0_3
| spl0_2
| ~ spl0_63
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f864,f814,f613,f232,f237]) ).
fof(f237,plain,
( spl0_3
<=> z = x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f232,plain,
( spl0_2
<=> y = x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f613,plain,
( spl0_63
<=> ! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f814,plain,
( spl0_85
<=> member(x,unordered_pair(y,z)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f864,plain,
( y = x
| z = x
| ~ spl0_63
| ~ spl0_85 ),
inference(resolution,[],[f816,f614]) ).
fof(f614,plain,
( ! [X2,X0,X1] :
( ~ member(X2,unordered_pair(X0,X1))
| X0 = X2
| X1 = X2 )
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f816,plain,
( member(x,unordered_pair(y,z))
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f814]) ).
fof(f904,plain,
spl0_96,
inference(avatar_split_clause,[],[f177,f902]) ).
fof(f902,plain,
( spl0_96
<=> ! [X0,X3,X2,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f177,plain,
! [X2,X3,X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f92,f137]) ).
fof(f137,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f92,axiom,
! [X2,X3,X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_unordered_pair) ).
fof(f900,plain,
spl0_95,
inference(avatar_split_clause,[],[f176,f898]) ).
fof(f898,plain,
( spl0_95
<=> ! [X0,X3,X2,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f176,plain,
! [X2,X3,X0,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f93,f137]) ).
fof(f93,axiom,
! [X2,X3,X0,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_unordered_pair) ).
fof(f896,plain,
spl0_94,
inference(avatar_split_clause,[],[f174,f894]) ).
fof(f894,plain,
( spl0_94
<=> ! [X0,X3,X2,X1] :
( unordered_pair(X0,X1) != null_class
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f174,plain,
! [X2,X3,X0,X1] :
( unordered_pair(X0,X1) != null_class
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f118,f137]) ).
fof(f118,axiom,
! [X2,X3,X0,X1] :
( unordered_pair(X0,X1) != null_class
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom3) ).
fof(f884,plain,
spl0_93,
inference(avatar_split_clause,[],[f208,f882]) ).
fof(f882,plain,
( spl0_93
<=> ! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f208,plain,
! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(null_class,X0) ),
inference(forward_demodulation,[],[f183,f150]) ).
fof(f150,plain,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
inference(definition_unfolding,[],[f28,f29]) ).
fof(f29,axiom,
! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction2) ).
fof(f28,axiom,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction1) ).
fof(f183,plain,
! [X0] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
inference(definition_unfolding,[],[f49,f135]) ).
fof(f135,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,f134,f29]) ).
fof(f134,plain,
! [X4] : range_of(X4) = domain_of(domain_of(flip(cross_product(X4,universal_class)))),
inference(definition_unfolding,[],[f39,f38]) ).
fof(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f39,axiom,
! [X4] : domain_of(inverse(X4)) = range_of(X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of) ).
fof(f42,axiom,
! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image) ).
fof(f49,axiom,
! [X0] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive3) ).
fof(f880,plain,
spl0_92,
inference(avatar_split_clause,[],[f206,f878]) ).
fof(f878,plain,
( spl0_92
<=> ! [X2] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f206,plain,
! [X2] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
| ~ member(X2,universal_class) ),
inference(forward_demodulation,[],[f160,f150]) ).
fof(f160,plain,
! [X2] :
( ~ member(X2,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X2),universal_class),element_relation),universal_class))))),universal_class) ),
inference(definition_unfolding,[],[f56,f141]) ).
fof(f141,plain,
! [X0] : power_class(X0) = complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X0),universal_class),element_relation),universal_class))))),
inference(definition_unfolding,[],[f55,f135]) ).
fof(f55,axiom,
! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_definition) ).
fof(f56,axiom,
! [X2] :
( ~ member(X2,universal_class)
| member(power_class(X2),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class2) ).
fof(f876,plain,
spl0_91,
inference(avatar_split_clause,[],[f182,f874]) ).
fof(f874,plain,
( spl0_91
<=> ! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f182,plain,
! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ),
inference(definition_unfolding,[],[f65,f135]) ).
fof(f65,axiom,
! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(image(X8,X0),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replacement) ).
fof(f837,plain,
spl0_90,
inference(avatar_split_clause,[],[f190,f835]) ).
fof(f835,plain,
( spl0_90
<=> ! [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_90])]) ).
fof(f190,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(f31,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f833,plain,
spl0_89,
inference(avatar_split_clause,[],[f184,f831]) ).
fof(f831,plain,
( spl0_89
<=> ! [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_89])]) ).
fof(f184,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(f64,axiom,
! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function3) ).
fof(f829,plain,
spl0_88,
inference(avatar_split_clause,[],[f170,f827]) ).
fof(f827,plain,
( spl0_88
<=> ! [X0,X3,X2,X1] :
( member(X3,universal_class)
| ~ 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_88])]) ).
fof(f170,plain,
! [X2,X3,X0,X1] :
( member(X3,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f95,f137]) ).
fof(f95,axiom,
! [X2,X3,X0,X1] :
( member(X3,universal_class)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
fof(f825,plain,
spl0_87,
inference(avatar_split_clause,[],[f169,f823]) ).
fof(f823,plain,
( spl0_87
<=> ! [X0,X3,X2,X1] :
( member(X2,universal_class)
| ~ 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_87])]) ).
fof(f169,plain,
! [X2,X3,X0,X1] :
( member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f94,f137]) ).
fof(f94,axiom,
! [X2,X3,X0,X1] :
( member(X2,universal_class)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).
fof(f821,plain,
spl0_86,
inference(avatar_split_clause,[],[f165,f819]) ).
fof(f819,plain,
( spl0_86
<=> ! [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_86])]) ).
fof(f165,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,f137]) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f817,plain,
( ~ spl0_1
| spl0_85
| ~ spl0_4
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f464,f403,f242,f814,f227]) ).
fof(f227,plain,
( spl0_1
<=> member(x,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f242,plain,
( spl0_4
<=> unordered_pair(y,z) = unordered_pair(x,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f403,plain,
( spl0_37
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f464,plain,
( member(x,unordered_pair(y,z))
| ~ member(x,universal_class)
| ~ spl0_4
| ~ spl0_37 ),
inference(superposition,[],[f404,f244]) ).
fof(f244,plain,
( unordered_pair(y,z) = unordered_pair(x,x)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f404,plain,
( ! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f812,plain,
spl0_84,
inference(avatar_split_clause,[],[f164,f810]) ).
fof(f810,plain,
( spl0_84
<=> ! [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_84])]) ).
fof(f164,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,f137]) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f799,plain,
spl0_83,
inference(avatar_split_clause,[],[f205,f797]) ).
fof(f797,plain,
( spl0_83
<=> ! [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_83])]) ).
fof(f205,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,[],[f154,f150]) ).
fof(f154,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,f135]) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive2) ).
fof(f795,plain,
spl0_82,
inference(avatar_split_clause,[],[f172,f793]) ).
fof(f793,plain,
( spl0_82
<=> ! [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_82])]) ).
fof(f172,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,f134]) ).
fof(f84,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible3) ).
fof(f791,plain,
spl0_81,
inference(avatar_split_clause,[],[f163,f789]) ).
fof(f789,plain,
( spl0_81
<=> ! [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_81])]) ).
fof(f163,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,f137]) ).
fof(f19,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation2) ).
fof(f732,plain,
spl0_80,
inference(avatar_split_clause,[],[f187,f730]) ).
fof(f730,plain,
( spl0_80
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f187,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X1) ),
inference(definition_unfolding,[],[f127,f12,f12]) ).
fof(f127,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| X0 = X1
| singleton(X0) != singleton(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_identified_by_element1) ).
fof(f728,plain,
spl0_79,
inference(avatar_split_clause,[],[f171,f726]) ).
fof(f726,plain,
( spl0_79
<=> ! [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_79])]) ).
fof(f171,plain,
! [X0,X4] :
( ~ member(X4,domain_of(X0))
| null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
inference(definition_unfolding,[],[f30,f29,f12]) ).
fof(f30,axiom,
! [X0,X4] :
( ~ member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f724,plain,
spl0_78,
inference(avatar_split_clause,[],[f101,f722]) ).
fof(f722,plain,
( spl0_78
<=> ! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X1,X0),X0)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f101,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X1,X0),X0)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality4) ).
fof(f720,plain,
spl0_77,
inference(avatar_split_clause,[],[f100,f718]) ).
fof(f718,plain,
( spl0_77
<=> ! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X1,X0),X0)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f100,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X1,X0),X0)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality3) ).
fof(f716,plain,
spl0_76,
inference(avatar_split_clause,[],[f98,f714]) ).
fof(f714,plain,
( spl0_76
<=> ! [X0,X1] :
( X0 = X1
| member(not_subclass_element(X1,X0),X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f98,axiom,
! [X0,X1] :
( X0 = X1
| member(not_subclass_element(X1,X0),X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality1) ).
fof(f710,plain,
spl0_75,
inference(avatar_split_clause,[],[f155,f708]) ).
fof(f708,plain,
( spl0_75
<=> ! [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_75])]) ).
fof(f155,plain,
! [X8] :
( ~ operation(X8)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
inference(definition_unfolding,[],[f80,f134]) ).
fof(f80,axiom,
! [X8] :
( ~ operation(X8)
| subclass(range_of(X8),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation3) ).
fof(f706,plain,
spl0_74,
inference(avatar_split_clause,[],[f79,f704]) ).
fof(f704,plain,
( spl0_74
<=> ! [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_74])]) ).
fof(f79,axiom,
! [X8] :
( ~ operation(X8)
| domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation2) ).
fof(f656,plain,
( ~ spl0_72
| spl0_73
| ~ spl0_29
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f610,f573,f357,f653,f649]) ).
fof(f649,plain,
( spl0_72
<=> function(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f653,plain,
( spl0_73
<=> member(x,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f357,plain,
( spl0_29
<=> ! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f573,plain,
( spl0_57
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(x,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f610,plain,
( member(x,cross_product(universal_class,universal_class))
| ~ function(universal_class)
| ~ spl0_29
| ~ spl0_57 ),
inference(resolution,[],[f574,f358]) ).
fof(f358,plain,
( ! [X8] :
( subclass(X8,cross_product(universal_class,universal_class))
| ~ function(X8) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f574,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(x,X0) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f573]) ).
fof(f647,plain,
spl0_71,
inference(avatar_split_clause,[],[f207,f645]) ).
fof(f645,plain,
( spl0_71
<=> ! [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_71])]) ).
fof(f207,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(forward_demodulation,[],[f161,f150]) ).
fof(f161,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
inference(definition_unfolding,[],[f54,f133]) ).
fof(f133,plain,
! [X0] : sum_class(X0) = domain_of(intersection(cross_product(universal_class,X0),element_relation)),
inference(definition_unfolding,[],[f53,f29]) ).
fof(f53,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_definition) ).
fof(f54,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class2) ).
fof(f643,plain,
spl0_70,
inference(avatar_split_clause,[],[f157,f641]) ).
fof(f641,plain,
( spl0_70
<=> ! [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_70])]) ).
fof(f157,plain,
! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f61,f38]) ).
fof(f61,axiom,
! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_class2) ).
fof(f639,plain,
spl0_69,
inference(avatar_split_clause,[],[f156,f637]) ).
fof(f637,plain,
( spl0_69
<=> ! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f156,plain,
! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f63,f38]) ).
fof(f63,axiom,
! [X8] :
( ~ function(X8)
| subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function2) ).
fof(f635,plain,
spl0_68,
inference(avatar_split_clause,[],[f152,f633]) ).
fof(f633,plain,
( spl0_68
<=> ! [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_68])]) ).
fof(f152,plain,
! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f60,f38]) ).
fof(f60,axiom,
! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,inverse(X0)),identity_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_valued_class1) ).
fof(f631,plain,
spl0_67,
inference(avatar_split_clause,[],[f150,f629]) ).
fof(f629,plain,
( spl0_67
<=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f627,plain,
spl0_66,
inference(avatar_split_clause,[],[f119,f625]) ).
fof(f625,plain,
( spl0_66
<=> ! [X4,X0,X1] :
( ~ member(X0,X4)
| ~ member(X1,X4)
| subclass(unordered_pair(X0,X1),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f119,axiom,
! [X0,X1,X4] :
( ~ member(X0,X4)
| ~ member(X1,X4)
| subclass(unordered_pair(X0,X1),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_is_subset) ).
fof(f623,plain,
spl0_65,
inference(avatar_split_clause,[],[f113,f621]) ).
fof(f621,plain,
( spl0_65
<=> ! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f113,axiom,
! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(X0,X1) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_unordered_pair) ).
fof(f619,plain,
spl0_64,
inference(avatar_split_clause,[],[f23,f617]) ).
fof(f617,plain,
( spl0_64
<=> ! [X4,X0,X1] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f23,axiom,
! [X0,X1,X4] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f615,plain,
spl0_63,
inference(avatar_split_clause,[],[f8,f613]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f600,plain,
spl0_62,
inference(avatar_split_clause,[],[f181,f598]) ).
fof(f598,plain,
( spl0_62
<=> ! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f181,plain,
! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ),
inference(definition_unfolding,[],[f73,f38]) ).
fof(f73,axiom,
! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(inverse(X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one3) ).
fof(f596,plain,
spl0_61,
inference(avatar_split_clause,[],[f168,f594]) ).
fof(f594,plain,
( spl0_61
<=> ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f168,plain,
! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X1,X1) ),
inference(definition_unfolding,[],[f112,f12]) ).
fof(f112,axiom,
! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = singleton(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton2) ).
fof(f592,plain,
spl0_60,
inference(avatar_split_clause,[],[f167,f590]) ).
fof(f590,plain,
( spl0_60
<=> ! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f167,plain,
! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X0,X0) ),
inference(definition_unfolding,[],[f111,f12]) ).
fof(f111,axiom,
! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = singleton(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
fof(f588,plain,
spl0_59,
inference(avatar_split_clause,[],[f83,f586]) ).
fof(f586,plain,
( spl0_59
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f83,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible2) ).
fof(f584,plain,
spl0_58,
inference(avatar_split_clause,[],[f25,f582]) ).
fof(f582,plain,
( spl0_58
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f25,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f575,plain,
( spl0_57
| ~ spl0_1
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f532,f501,f227,f573]) ).
fof(f501,plain,
( spl0_51
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f532,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(x,X0) )
| ~ spl0_1
| ~ spl0_51 ),
inference(resolution,[],[f502,f229]) ).
fof(f229,plain,
( member(x,universal_class)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f502,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f527,plain,
spl0_56,
inference(avatar_split_clause,[],[f149,f525]) ).
fof(f525,plain,
( spl0_56
<=> ! [X0,X1] : member(unordered_pair(X1,X1),unordered_pair(X0,unordered_pair(X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f149,plain,
! [X0,X1] : member(unordered_pair(X1,X1),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f121,f12,f12]) ).
fof(f121,axiom,
! [X0,X1] : member(singleton(X1),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_singletons_are_sets) ).
fof(f523,plain,
spl0_55,
inference(avatar_split_clause,[],[f146,f520]) ).
fof(f520,plain,
( spl0_55
<=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f146,plain,
identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),
inference(definition_unfolding,[],[f75,f38]) ).
fof(f75,axiom,
identity_relation = intersection(inverse(subset_relation),subset_relation),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).
fof(f518,plain,
spl0_54,
inference(avatar_split_clause,[],[f97,f516]) ).
fof(f516,plain,
( spl0_54
<=> ! [X4,X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X4)
| subclass(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f97,axiom,
! [X0,X1,X4] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X4)
| subclass(X0,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_subclass) ).
fof(f514,plain,
spl0_53,
inference(avatar_split_clause,[],[f67,f512]) ).
fof(f512,plain,
( spl0_53
<=> ! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f67,axiom,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f510,plain,
spl0_52,
inference(avatar_split_clause,[],[f7,f508]) ).
fof(f508,plain,
( spl0_52
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f503,plain,
spl0_51,
inference(avatar_split_clause,[],[f1,f501]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f457,plain,
spl0_50,
inference(avatar_split_clause,[],[f166,f455]) ).
fof(f455,plain,
( spl0_50
<=> ! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f166,plain,
! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ),
inference(definition_unfolding,[],[f126,f12]) ).
fof(f126,axiom,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f453,plain,
spl0_49,
inference(avatar_split_clause,[],[f162,f451]) ).
fof(f451,plain,
( spl0_49
<=> ! [X0,X1] :
( X0 = X1
| ~ member(X1,unordered_pair(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f162,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(f449,plain,
spl0_48,
inference(avatar_split_clause,[],[f153,f447]) ).
fof(f447,plain,
( spl0_48
<=> ! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f153,plain,
! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ),
inference(definition_unfolding,[],[f72,f38]) ).
fof(f72,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(inverse(X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one2) ).
fof(f445,plain,
spl0_47,
inference(avatar_split_clause,[],[f117,f443]) ).
fof(f443,plain,
( spl0_47
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| unordered_pair(X0,X1) != null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
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(f441,plain,
( spl0_46
| ~ spl0_4
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f386,f373,f242,f439]) ).
fof(f439,plain,
( spl0_46
<=> ! [X0] : subclass(unordered_pair(y,z),unordered_pair(x,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f373,plain,
( spl0_33
<=> ! [X0,X1] : subclass(unordered_pair(X0,X0),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f386,plain,
( ! [X0] : subclass(unordered_pair(y,z),unordered_pair(x,X0))
| ~ spl0_4
| ~ spl0_33 ),
inference(superposition,[],[f374,f244]) ).
fof(f374,plain,
( ! [X0,X1] : subclass(unordered_pair(X0,X0),unordered_pair(X0,X1))
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f437,plain,
spl0_45,
inference(avatar_split_clause,[],[f116,f435]) ).
fof(f435,plain,
( spl0_45
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| unordered_pair(X0,X1) != null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
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(f433,plain,
spl0_44,
inference(avatar_split_clause,[],[f106,f431]) ).
fof(f431,plain,
( spl0_44
<=> ! [X4] :
( null_class = X4
| member(not_subclass_element(X4,null_class),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
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(f429,plain,
spl0_43,
inference(avatar_split_clause,[],[f88,f427]) ).
fof(f427,plain,
( spl0_43
<=> ! [X9,X11,X10] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f88,axiom,
! [X10,X11,X9] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism3) ).
fof(f425,plain,
spl0_42,
inference(avatar_split_clause,[],[f35,f423]) ).
fof(f423,plain,
( spl0_42
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
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(f421,plain,
spl0_41,
inference(avatar_split_clause,[],[f32,f419]) ).
fof(f419,plain,
( spl0_41
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
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(f417,plain,
spl0_40,
inference(avatar_split_clause,[],[f22,f415]) ).
fof(f415,plain,
( spl0_40
<=> ! [X4,X0,X1] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f413,plain,
spl0_39,
inference(avatar_split_clause,[],[f21,f411]) ).
fof(f411,plain,
( spl0_39
<=> ! [X4,X0,X1] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f409,plain,
spl0_38,
inference(avatar_split_clause,[],[f10,f407]) ).
fof(f407,plain,
( spl0_38
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
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(f405,plain,
spl0_37,
inference(avatar_split_clause,[],[f9,f403]) ).
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(f401,plain,
spl0_36,
inference(avatar_split_clause,[],[f3,f399]) ).
fof(f399,plain,
( spl0_36
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
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(f397,plain,
( spl0_35
| ~ spl0_4
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f382,f369,f242,f395]) ).
fof(f395,plain,
( spl0_35
<=> ! [X0] : subclass(unordered_pair(y,z),unordered_pair(X0,x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f369,plain,
( spl0_32
<=> ! [X0,X1] : subclass(unordered_pair(X1,X1),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f382,plain,
( ! [X0] : subclass(unordered_pair(y,z),unordered_pair(X0,x))
| ~ spl0_4
| ~ spl0_32 ),
inference(superposition,[],[f370,f244]) ).
fof(f370,plain,
( ! [X0,X1] : subclass(unordered_pair(X1,X1),unordered_pair(X0,X1))
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f393,plain,
spl0_34,
inference(avatar_split_clause,[],[f2,f391]) ).
fof(f391,plain,
( spl0_34
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
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(f375,plain,
spl0_33,
inference(avatar_split_clause,[],[f148,f373]) ).
fof(f148,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(f371,plain,
spl0_32,
inference(avatar_split_clause,[],[f147,f369]) ).
fof(f147,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(f367,plain,
spl0_31,
inference(avatar_split_clause,[],[f108,f365]) ).
fof(f365,plain,
( spl0_31
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
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(f363,plain,
spl0_30,
inference(avatar_split_clause,[],[f66,f361]) ).
fof(f361,plain,
( spl0_30
<=> ! [X0] :
( null_class = X0
| member(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f66,axiom,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f359,plain,
spl0_29,
inference(avatar_split_clause,[],[f62,f357]) ).
fof(f62,axiom,
! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).
fof(f355,plain,
spl0_28,
inference(avatar_split_clause,[],[f57,f353]) ).
fof(f353,plain,
( spl0_28
<=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f57,axiom,
! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).
fof(f351,plain,
spl0_27,
inference(avatar_split_clause,[],[f24,f349]) ).
fof(f349,plain,
( spl0_27
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f343,plain,
( ~ spl0_26
| ~ spl0_10
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f318,f305,f270,f340]) ).
fof(f340,plain,
( spl0_26
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f270,plain,
( spl0_10
<=> ! [X4] : ~ member(X4,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f305,plain,
( spl0_18
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f318,plain,
( ~ inductive(null_class)
| ~ spl0_10
| ~ spl0_18 ),
inference(resolution,[],[f306,f271]) ).
fof(f271,plain,
( ! [X4] : ~ member(X4,null_class)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f306,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f338,plain,
spl0_25,
inference(avatar_split_clause,[],[f105,f336]) ).
fof(f336,plain,
( spl0_25
<=> ! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
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(f334,plain,
spl0_24,
inference(avatar_split_clause,[],[f102,f332]) ).
fof(f332,plain,
( spl0_24
<=> ! [X0,X1] : ~ member(X1,intersection(complement(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f102,axiom,
! [X0,X1] : ~ member(X1,intersection(complement(X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',special_classes_lemma) ).
fof(f330,plain,
spl0_23,
inference(avatar_split_clause,[],[f87,f328]) ).
fof(f328,plain,
( spl0_23
<=> ! [X9,X11,X10] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f87,axiom,
! [X10,X11,X9] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
fof(f326,plain,
spl0_22,
inference(avatar_split_clause,[],[f86,f324]) ).
fof(f324,plain,
( spl0_22
<=> ! [X9,X11,X10] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f86,axiom,
! [X10,X11,X9] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
fof(f322,plain,
spl0_21,
inference(avatar_split_clause,[],[f82,f320]) ).
fof(f320,plain,
( spl0_21
<=> ! [X9,X11,X10] :
( function(X9)
| ~ compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f82,axiom,
! [X10,X11,X9] :
( function(X9)
| ~ compatible(X9,X10,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible1) ).
fof(f316,plain,
spl0_20,
inference(avatar_split_clause,[],[f144,f313]) ).
fof(f313,plain,
( spl0_20
<=> member(null_class,unordered_pair(null_class,null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f144,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(f311,plain,
spl0_19,
inference(avatar_split_clause,[],[f51,f309]) ).
fof(f309,plain,
( spl0_19
<=> ! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f51,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive2) ).
fof(f307,plain,
spl0_18,
inference(avatar_split_clause,[],[f47,f305]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
fof(f303,plain,
spl0_17,
inference(avatar_split_clause,[],[f44,f300]) ).
fof(f300,plain,
( spl0_17
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation1) ).
fof(f298,plain,
spl0_16,
inference(avatar_split_clause,[],[f18,f295]) ).
fof(f295,plain,
( spl0_16
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).
fof(f293,plain,
spl0_15,
inference(avatar_split_clause,[],[f11,f291]) ).
fof(f291,plain,
( spl0_15
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f289,plain,
spl0_14,
inference(avatar_split_clause,[],[f78,f287]) ).
fof(f287,plain,
( spl0_14
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation1) ).
fof(f285,plain,
spl0_13,
inference(avatar_split_clause,[],[f71,f283]) ).
fof(f283,plain,
( spl0_13
<=> ! [X8] :
( ~ one_to_one(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f71,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one1) ).
fof(f281,plain,
spl0_12,
inference(avatar_split_clause,[],[f107,f278]) ).
fof(f278,plain,
( spl0_12
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f107,axiom,
member(null_class,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_a_set) ).
fof(f276,plain,
spl0_11,
inference(avatar_split_clause,[],[f104,f274]) ).
fof(f274,plain,
( spl0_11
<=> ! [X0] : subclass(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f104,axiom,
! [X0] : subclass(null_class,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_subclass) ).
fof(f272,plain,
spl0_10,
inference(avatar_split_clause,[],[f103,f270]) ).
fof(f103,axiom,
! [X4] : ~ member(X4,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f268,plain,
spl0_9,
inference(avatar_split_clause,[],[f96,f266]) ).
fof(f266,plain,
( spl0_9
<=> ! [X0] : subclass(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f96,axiom,
! [X0] : subclass(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_is_reflexive) ).
fof(f264,plain,
spl0_8,
inference(avatar_split_clause,[],[f52,f261]) ).
fof(f261,plain,
( spl0_8
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f259,plain,
spl0_7,
inference(avatar_split_clause,[],[f4,f257]) ).
fof(f257,plain,
( spl0_7
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f255,plain,
spl0_6,
inference(avatar_split_clause,[],[f69,f252]) ).
fof(f252,plain,
( spl0_6
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
fof(f250,plain,
spl0_5,
inference(avatar_split_clause,[],[f50,f247]) ).
fof(f247,plain,
( spl0_5
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f245,plain,
spl0_4,
inference(avatar_split_clause,[],[f143,f242]) ).
fof(f143,plain,
unordered_pair(y,z) = unordered_pair(x,x),
inference(definition_unfolding,[],[f129,f12]) ).
fof(f129,axiom,
unordered_pair(y,z) = singleton(x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_1) ).
fof(f240,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f132,f237]) ).
fof(f132,axiom,
z != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_4) ).
fof(f235,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f131,f232]) ).
fof(f131,axiom,
y != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_3) ).
fof(f230,plain,
spl0_1,
inference(avatar_split_clause,[],[f130,f227]) ).
fof(f130,axiom,
member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_singleton_in_unordered_pair3_2) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET085-7 : 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 : n020.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 01:15:32 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (16678)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (16686)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)
% 0.15/0.38 % (16684)WARNING: value z3 for option sas not known
% 0.15/0.38 % (16682)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (16683)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (16685)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (16688)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)
% 0.15/0.38 % (16689)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)
% 0.15/0.38 % (16684)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 % (16686)First to succeed.
% 0.15/0.40 % (16686)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
% 0.15/0.40 % (16686)------------------------------
% 0.15/0.40 % (16686)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.40 % (16686)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (16686)Memory used [KB]: 1317
% 0.15/0.40 % (16686)Time elapsed: 0.018 s
% 0.15/0.40 % (16686)Instructions burned: 48 (million)
% 0.15/0.40 % (16686)------------------------------
% 0.15/0.40 % (16686)------------------------------
% 0.15/0.40 % (16678)Success in time 0.032 s
%------------------------------------------------------------------------------