TSTP Solution File: SET114-7 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET114-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n018.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 15:05:44 EDT 2024
% Result : Unsatisfiable 0.21s 0.54s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 314
% Syntax : Number of formulae : 734 ( 192 unt; 0 def)
% Number of atoms : 2314 ( 365 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 2679 (1099 ~;1413 |; 0 &)
% ( 167 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 25 ( 4 avg)
% Number of predicates : 178 ( 176 usr; 168 prp; 0-3 aty)
% Number of functors : 36 ( 36 usr; 9 con; 0-3 aty)
% Number of variables : 1141 (1141 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2922,plain,
$false,
inference(avatar_sat_refutation,[],[f288,f293,f298,f302,f307,f311,f315,f319,f324,f328,f332,f337,f341,f346,f351,f355,f359,f364,f370,f374,f378,f382,f386,f390,f398,f402,f406,f410,f414,f418,f422,f427,f440,f444,f448,f452,f456,f460,f464,f468,f472,f476,f480,f484,f488,f492,f496,f500,f504,f508,f512,f532,f555,f559,f563,f567,f572,f576,f580,f584,f651,f655,f659,f663,f667,f671,f675,f689,f693,f697,f701,f705,f709,f713,f717,f721,f725,f729,f733,f737,f807,f832,f836,f842,f846,f850,f854,f860,f864,f937,f941,f946,f950,f954,f958,f988,f1003,f1007,f1011,f1015,f1019,f1023,f1027,f1031,f1061,f1108,f1112,f1116,f1126,f1137,f1141,f1145,f1172,f1176,f1181,f1205,f1209,f1213,f1269,f1273,f1282,f1286,f1320,f1324,f1328,f1383,f1387,f1449,f1453,f1457,f1461,f1465,f1491,f1496,f1567,f1804,f1813,f1817,f1977,f2002,f2010,f2015,f2023,f2042,f2060,f2068,f2134,f2199,f2331,f2553,f2643,f2651,f2667,f2675,f2704,f2712,f2740,f2748,f2774,f2784,f2812,f2823,f2827,f2853,f2867,f2898,f2920,f2921]) ).
fof(f2921,plain,
( spl0_1
| spl0_12
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1343,f1322,f334,f285]) ).
fof(f285,plain,
( spl0_1
<=> x = second(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f334,plain,
( spl0_12
<=> member(unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1322,plain,
( spl0_125
<=> ! [X0] :
( second(X0) = X0
| member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1343,plain,
( x = second(x)
| spl0_12
| ~ spl0_125 ),
inference(resolution,[],[f1323,f336]) ).
fof(f336,plain,
( ~ member(unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))),cross_product(universal_class,universal_class))
| spl0_12 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f1323,plain,
( ! [X0] :
( member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class))
| second(X0) = X0 )
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1322]) ).
fof(f2920,plain,
( spl0_167
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2916,f2896,f1322,f1279,f669,f412,f334,f2918]) ).
fof(f2918,plain,
( spl0_167
<=> ! [X9,X11,X10] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(x,unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f412,plain,
( spl0_29
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f669,plain,
( spl0_66
<=> ! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1279,plain,
( spl0_122
<=> member(second(x),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f2896,plain,
( spl0_166
<=> ! [X9,X11,X10] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f2916,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(x,unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2915,f413]) ).
fof(f413,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f2915,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11)))),x),universal_class)),universal_class)))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2914,f1476]) ).
fof(f1476,plain,
( ! [X0] : unordered_pair(X0,X0) = unordered_pair(X0,x)
| spl0_12
| ~ spl0_66
| spl0_122
| ~ spl0_125 ),
inference(forward_demodulation,[],[f1468,f1343]) ).
fof(f1468,plain,
( ! [X0] : unordered_pair(X0,X0) = unordered_pair(X0,second(x))
| ~ spl0_66
| spl0_122 ),
inference(resolution,[],[f1281,f670]) ).
fof(f670,plain,
( ! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X0,X0) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f1281,plain,
( ~ member(second(x),universal_class)
| spl0_122 ),
inference(avatar_component_clause,[],[f1279]) ).
fof(f2914,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2913,f413]) ).
fof(f2913,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),x),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2912,f1476]) ).
fof(f2912,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2911,f413]) ).
fof(f2911,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),x),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2910,f413]) ).
fof(f2910,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),x),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),x),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),x),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),x),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),x),universal_class)),universal_class))))))),x),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),x),universal_class)),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(x,not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2909,f413]) ).
fof(f2909,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),x),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),x),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),x),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),x),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x)))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),x),universal_class)),universal_class))))))),x),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),x),universal_class)),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),x),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2908,f413]) ).
fof(f2908,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),x),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),x),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),x),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),x),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x)))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),x),universal_class)),universal_class))))))),x),unordered_pair(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),x),universal_class)),universal_class)))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),x),universal_class)),universal_class)))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2907,f1476]) ).
fof(f2907,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x)))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),x),unordered_pair(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),x),universal_class)),universal_class)))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2906,f413]) ).
fof(f2906,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x)))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),x),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),x),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2905,f413]) ).
fof(f2905,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x)))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),x),universal_class)),universal_class))))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),x))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2904,f1476]) ).
fof(f2904,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x)))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),x),universal_class)),universal_class))))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2903,f413]) ).
fof(f2903,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x)))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x)))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),x),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2902,f1476]) ).
fof(f2902,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2901,f413]) ).
fof(f2901,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),x)))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2900,f1476]) ).
fof(f2900,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(x,unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2899,f413]) ).
fof(f2899,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),x),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_166 ),
inference(forward_demodulation,[],[f2897,f1476]) ).
fof(f2897,plain,
( ! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f2896]) ).
fof(f2898,plain,
spl0_166,
inference(avatar_split_clause,[],[f283,f2896]) ).
fof(f283,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class)),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f282,f183]) ).
fof(f183,plain,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
inference(definition_unfolding,[],[f28,f29]) ).
fof(f29,axiom,
! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).
fof(f28,axiom,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).
fof(f282,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f281,f183]) ).
fof(f281,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class)),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f280,f183]) ).
fof(f280,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f279,f183]) ).
fof(f279,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X11,cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f278,f183]) ).
fof(f278,plain,
! [X10,X11,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class))))))) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f277,f183]) ).
fof(f277,plain,
! [X10,X11,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X10,cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class)),universal_class)))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f276,f183]) ).
fof(f276,plain,
! [X10,X11,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class)))))))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f275,f183]) ).
fof(f275,plain,
! [X10,X11,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(X9,cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class)),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f274,f183]) ).
fof(f274,plain,
! [X10,X11,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class)))))))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ),
inference(forward_demodulation,[],[f259,f183]) ).
fof(f259,plain,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) != domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11))))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
inference(definition_unfolding,[],[f91,f165,f166,f165,f165,f165,f165,f166]) ).
fof(f166,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(f165,plain,
! [X1,X8] : apply(X8,X1) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X8),universal_class))))),element_relation)),
inference(definition_unfolding,[],[f68,f162,f164,f12]) ).
fof(f164,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,f163,f29]) ).
fof(f163,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/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f39,axiom,
! [X4] : domain_of(inverse(X4)) = range_of(X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).
fof(f42,axiom,
! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image) ).
fof(f162,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(f68,axiom,
! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply) ).
fof(f91,axiom,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| apply(X11,ordered_pair(apply(X9,not_homomorphism1(X9,X10,X11)),apply(X9,not_homomorphism2(X9,X10,X11)))) != apply(X9,apply(X10,ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism6) ).
fof(f2867,plain,
( spl0_165
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2863,f2851,f1322,f1279,f669,f412,f334,f2865]) ).
fof(f2865,plain,
( spl0_165
<=> ! [X10,X11,X0,X9,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(x,unordered_pair(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(x,unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f2851,plain,
( spl0_164
<=> ! [X10,X11,X0,X9,X1] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f2863,plain,
( ! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(x,unordered_pair(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(x,unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_164 ),
inference(forward_demodulation,[],[f2862,f413]) ).
fof(f2862,plain,
( ! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(x,unordered_pair(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),x),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_164 ),
inference(forward_demodulation,[],[f2861,f1476]) ).
fof(f2861,plain,
( ! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(x,unordered_pair(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_164 ),
inference(forward_demodulation,[],[f2860,f413]) ).
fof(f2860,plain,
( ! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(x,unordered_pair(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),x),universal_class),X9),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_164 ),
inference(forward_demodulation,[],[f2859,f1476]) ).
fof(f2859,plain,
( ! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(x,unordered_pair(unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_164 ),
inference(forward_demodulation,[],[f2858,f413]) ).
fof(f2858,plain,
( ! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(x,unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),x),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_164 ),
inference(forward_demodulation,[],[f2857,f1476]) ).
fof(f2857,plain,
( ! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(x,unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(x,domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_164 ),
inference(forward_demodulation,[],[f2856,f413]) ).
fof(f2856,plain,
( ! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(x,unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),x)))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_164 ),
inference(forward_demodulation,[],[f2855,f1476]) ).
fof(f2855,plain,
( ! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(x,unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_164 ),
inference(forward_demodulation,[],[f2854,f413]) ).
fof(f2854,plain,
( ! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),x),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) )
| spl0_12
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_164 ),
inference(forward_demodulation,[],[f2852,f1476]) ).
fof(f2852,plain,
( ! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) )
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f2851]) ).
fof(f2853,plain,
spl0_164,
inference(avatar_split_clause,[],[f273,f2851]) ).
fof(f273,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class)))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))))),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
inference(forward_demodulation,[],[f272,f183]) ).
fof(f272,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class)))))))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))))))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
inference(forward_demodulation,[],[f271,f183]) ).
fof(f271,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class))))))) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
inference(forward_demodulation,[],[f270,f183]) ).
fof(f270,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))))),domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class)))))))),universal_class),X9),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
inference(forward_demodulation,[],[f269,f183]) ).
fof(f269,plain,
! [X10,X0,X11,X1,X9] :
( domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class)))))))
| ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10)) ),
inference(forward_demodulation,[],[f251,f183]) ).
fof(f251,plain,
! [X10,X0,X11,X1,X9] :
( ~ homomorphism(X9,X10,X11)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),domain_of(X10))
| domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation))))),unordered_pair(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation))),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X0,X0),universal_class),X9),universal_class))))),element_relation)),unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X9),universal_class))))),element_relation)))))),universal_class),X11),universal_class))))),element_relation)) = domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation)),domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),universal_class),X10),universal_class))))),element_relation))),universal_class),X9),universal_class))))),element_relation)) ),
inference(definition_unfolding,[],[f89,f166,f165,f166,f165,f165,f165,f165,f166]) ).
fof(f89,axiom,
! [X10,X0,X11,X1,X9] :
( ~ homomorphism(X9,X10,X11)
| ~ member(ordered_pair(X0,X1),domain_of(X10))
| apply(X11,ordered_pair(apply(X9,X0),apply(X9,X1))) = apply(X9,apply(X10,ordered_pair(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism4) ).
fof(f2827,plain,
( spl0_163
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2818,f2810,f1322,f1279,f669,f412,f334,f2825]) ).
fof(f2825,plain,
( spl0_163
<=> ! [X3,X0,X6,X2] :
( ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f2810,plain,
( spl0_161
<=> ! [X3,X0,X6,X2] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f2818,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_161 ),
inference(forward_demodulation,[],[f2817,f413]) ).
fof(f2817,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),x),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_161 ),
inference(forward_demodulation,[],[f2816,f1476]) ).
fof(f2816,plain,
( ! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_161 ),
inference(forward_demodulation,[],[f2815,f413]) ).
fof(f2815,plain,
( ! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),x),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_161 ),
inference(forward_demodulation,[],[f2814,f1476]) ).
fof(f2814,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_161 ),
inference(forward_demodulation,[],[f2813,f413]) ).
fof(f2813,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),x),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| spl0_12
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_161 ),
inference(forward_demodulation,[],[f2811,f1476]) ).
fof(f2811,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f2810]) ).
fof(f2823,plain,
( spl0_162
| spl0_12
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1329,f1318,f334,f2820]) ).
fof(f2820,plain,
( spl0_162
<=> x = first(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1318,plain,
( spl0_124
<=> ! [X0] :
( first(X0) = X0
| member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1329,plain,
( x = first(x)
| spl0_12
| ~ spl0_124 ),
inference(resolution,[],[f1319,f336]) ).
fof(f1319,plain,
( ! [X0] :
( member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class))
| first(X0) = X0 )
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1318]) ).
fof(f2812,plain,
spl0_161,
inference(avatar_split_clause,[],[f254,f2810]) ).
fof(f254,plain,
! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition_unfolding,[],[f37,f166,f166,f166,f166,f166,f166]) ).
fof(f37,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip3) ).
fof(f2784,plain,
( spl0_160
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f2780,f2772,f1322,f1279,f669,f412,f334,f2782]) ).
fof(f2782,plain,
( spl0_160
<=> ! [X3,X0,X6,X2] :
( ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f2772,plain,
( spl0_159
<=> ! [X3,X0,X6,X2] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f2780,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_159 ),
inference(forward_demodulation,[],[f2779,f413]) ).
fof(f2779,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),x),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class))
| member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_159 ),
inference(forward_demodulation,[],[f2778,f1476]) ).
fof(f2778,plain,
( ! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_159 ),
inference(forward_demodulation,[],[f2777,f413]) ).
fof(f2777,plain,
( ! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),x),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_159 ),
inference(forward_demodulation,[],[f2776,f1476]) ).
fof(f2776,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_159 ),
inference(forward_demodulation,[],[f2775,f413]) ).
fof(f2775,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),x),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| spl0_12
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_159 ),
inference(forward_demodulation,[],[f2773,f1476]) ).
fof(f2773,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f2772]) ).
fof(f2774,plain,
spl0_159,
inference(avatar_split_clause,[],[f253,f2772]) ).
fof(f253,plain,
! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition_unfolding,[],[f34,f166,f166,f166,f166,f166,f166]) ).
fof(f34,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate3) ).
fof(f2748,plain,
( spl0_158
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f2744,f2738,f1322,f1279,f669,f412,f334,f2746]) ).
fof(f2746,plain,
( spl0_158
<=> ! [X3,X0,X6,X2] :
( ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f2738,plain,
( spl0_157
<=> ! [X3,X0,X6,X2] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f2744,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_157 ),
inference(forward_demodulation,[],[f2743,f413]) ).
fof(f2743,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),x),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0))
| member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_157 ),
inference(forward_demodulation,[],[f2742,f1476]) ).
fof(f2742,plain,
( ! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_157 ),
inference(forward_demodulation,[],[f2741,f413]) ).
fof(f2741,plain,
( ! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),x),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) )
| spl0_12
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_157 ),
inference(forward_demodulation,[],[f2739,f1476]) ).
fof(f2739,plain,
( ! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f2738]) ).
fof(f2740,plain,
spl0_157,
inference(avatar_split_clause,[],[f228,f2738]) ).
fof(f228,plain,
! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X2,X2))),unordered_pair(X6,X6))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),flip(X0)) ),
inference(definition_unfolding,[],[f36,f166,f166,f166,f166]) ).
fof(f36,axiom,
! [X2,X3,X0,X6] :
( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip2) ).
fof(f2712,plain,
( spl0_156
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f2708,f2702,f1322,f1279,f669,f412,f334,f2710]) ).
fof(f2710,plain,
( spl0_156
<=> ! [X3,X0,X6,X2] :
( ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f2702,plain,
( spl0_155
<=> ! [X3,X0,X6,X2] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f2708,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_155 ),
inference(forward_demodulation,[],[f2707,f413]) ).
fof(f2707,plain,
( ! [X2,X3,X0,X6] :
( ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),x),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0))
| member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_155 ),
inference(forward_demodulation,[],[f2706,f1476]) ).
fof(f2706,plain,
( ! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(x,unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_155 ),
inference(forward_demodulation,[],[f2705,f413]) ).
fof(f2705,plain,
( ! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),x),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) )
| spl0_12
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_155 ),
inference(forward_demodulation,[],[f2703,f1476]) ).
fof(f2703,plain,
( ! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) )
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f2702]) ).
fof(f2704,plain,
spl0_155,
inference(avatar_split_clause,[],[f227,f2702]) ).
fof(f227,plain,
! [X2,X3,X0,X6] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6)))),unordered_pair(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,unordered_pair(X6,X6))),unordered_pair(X2,X2))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X6,X6))),rotate(X0)) ),
inference(definition_unfolding,[],[f33,f166,f166,f166,f166]) ).
fof(f33,axiom,
! [X2,X3,X0,X6] :
( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate2) ).
fof(f2675,plain,
( spl0_154
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2671,f2665,f1322,f1279,f669,f412,f334,f2673]) ).
fof(f2673,plain,
( spl0_154
<=> ! [X4,X1] :
( member(unordered_pair(unordered_pair(x,first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))))),unordered_pair(first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),unordered_pair(x,second(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))))))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f2665,plain,
( spl0_153
<=> ! [X4,X1] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))))),unordered_pair(first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),unordered_pair(second(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),second(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f2671,plain,
( ! [X1,X4] :
( member(unordered_pair(unordered_pair(x,first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))))),unordered_pair(first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),unordered_pair(x,second(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))))))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_153 ),
inference(forward_demodulation,[],[f2670,f413]) ).
fof(f2670,plain,
( ! [X1,X4] :
( member(unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),x),unordered_pair(first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),unordered_pair(x,second(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))))))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_153 ),
inference(forward_demodulation,[],[f2669,f1476]) ).
fof(f2669,plain,
( ! [X1,X4] :
( member(unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))))),unordered_pair(first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),unordered_pair(x,second(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))))))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_153 ),
inference(forward_demodulation,[],[f2668,f413]) ).
fof(f2668,plain,
( ! [X1,X4] :
( member(unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))))),unordered_pair(first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),unordered_pair(second(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),x))),cross_product(universal_class,universal_class))
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) )
| spl0_12
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_153 ),
inference(forward_demodulation,[],[f2666,f1476]) ).
fof(f2666,plain,
( ! [X1,X4] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))))),unordered_pair(first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),unordered_pair(second(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),second(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f2665]) ).
fof(f2667,plain,
spl0_153,
inference(avatar_split_clause,[],[f225,f2665]) ).
fof(f225,plain,
! [X1,X4] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))))),unordered_pair(first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),unordered_pair(second(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4)))),second(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))))))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f153,f166,f166,f166,f166]) ).
fof(f153,axiom,
! [X1,X4] :
( ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class))
| member(ordered_pair(first(ordered_pair(X1,X4)),second(ordered_pair(X1,X4))),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_1) ).
fof(f2651,plain,
( spl0_152
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f2647,f2641,f1322,f1279,f669,f412,f334,f2649]) ).
fof(f2649,plain,
( spl0_152
<=> ! [X0] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f2641,plain,
( spl0_151
<=> ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f2647,plain,
( ! [X0] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_151 ),
inference(forward_demodulation,[],[f2646,f413]) ).
fof(f2646,plain,
( ! [X0] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),x))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_151 ),
inference(forward_demodulation,[],[f2645,f1476]) ).
fof(f2645,plain,
( ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(x,complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_151 ),
inference(forward_demodulation,[],[f2644,f413]) ).
fof(f2644,plain,
( ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),x))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) )
| spl0_12
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_151 ),
inference(forward_demodulation,[],[f2642,f1476]) ).
fof(f2642,plain,
( ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) )
| ~ spl0_151 ),
inference(avatar_component_clause,[],[f2641]) ).
fof(f2643,plain,
spl0_151,
inference(avatar_split_clause,[],[f262,f2641]) ).
fof(f262,plain,
! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),complement(intersection(complement(X0),complement(unordered_pair(X0,X0))))))),cross_product(universal_class,universal_class)) ),
inference(equality_resolution,[],[f250]) ).
fof(f250,plain,
! [X0,X1] :
( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) != X1
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f46,f169,f166,f166]) ).
fof(f169,plain,
! [X0] : successor(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),
inference(definition_unfolding,[],[f43,f26,f12]) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f43,axiom,
! [X0] : union(X0,singleton(X0)) = successor(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor) ).
fof(f46,axiom,
! [X0,X1] :
( successor(X0) != X1
| member(ordered_pair(X0,X1),successor_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation3) ).
fof(f2553,plain,
spl0_150,
inference(avatar_split_clause,[],[f252,f2551]) ).
fof(f2551,plain,
( spl0_150
<=> ! [X4,X7,X5,X1] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f252,plain,
! [X1,X7,X4,X5] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class))
| member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| ~ member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
inference(definition_unfolding,[],[f59,f166,f166,f164,f164,f12]) ).
fof(f59,axiom,
! [X1,X7,X4,X5] :
( ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X4),compose(X7,X5))
| ~ member(X4,image(X7,image(X5,singleton(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose3) ).
fof(f2331,plain,
( ~ spl0_138
| spl0_12
| spl0_122
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f2129,f1322,f1279,f334,f1810]) ).
fof(f1810,plain,
( spl0_138
<=> member(x,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f2129,plain,
( ~ member(x,universal_class)
| spl0_12
| spl0_122
| ~ spl0_125 ),
inference(forward_demodulation,[],[f1281,f1343]) ).
fof(f2199,plain,
( spl0_149
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2152,f2000,f1318,f1275,f669,f412,f334,f2197]) ).
fof(f2197,plain,
( spl0_149
<=> ! [X0] :
( unordered_pair(x,not_subclass_element(X0,null_class)) = X0
| null_class = X0
| not_subclass_element(X0,null_class) != not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1275,plain,
( spl0_121
<=> member(first(x),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f2000,plain,
( spl0_141
<=> ! [X0] :
( null_class = X0
| unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class)) = X0
| not_subclass_element(X0,null_class) != not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f2152,plain,
( ! [X0] :
( unordered_pair(x,not_subclass_element(X0,null_class)) = X0
| null_class = X0
| not_subclass_element(X0,null_class) != not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_141 ),
inference(forward_demodulation,[],[f2003,f413]) ).
fof(f2003,plain,
( ! [X0] :
( unordered_pair(not_subclass_element(X0,null_class),x) = X0
| null_class = X0
| not_subclass_element(X0,null_class) != not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class) )
| spl0_12
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_141 ),
inference(forward_demodulation,[],[f2001,f1368]) ).
fof(f1368,plain,
( ! [X0] : unordered_pair(X0,X0) = unordered_pair(X0,x)
| spl0_12
| ~ spl0_66
| spl0_121
| ~ spl0_124 ),
inference(forward_demodulation,[],[f1360,f1329]) ).
fof(f1360,plain,
( ! [X0] : unordered_pair(X0,X0) = unordered_pair(X0,first(x))
| ~ spl0_66
| spl0_121 ),
inference(resolution,[],[f1277,f670]) ).
fof(f1277,plain,
( ~ member(first(x),universal_class)
| spl0_121 ),
inference(avatar_component_clause,[],[f1275]) ).
fof(f2001,plain,
( ! [X0] :
( not_subclass_element(X0,null_class) != not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class)
| unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class)) = X0
| null_class = X0 )
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f2000]) ).
fof(f2134,plain,
( spl0_148
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f2080,f1802,f1322,f1279,f669,f412,f334,f2132]) ).
fof(f2132,plain,
( spl0_148
<=> ! [X0] :
( unordered_pair(x,not_subclass_element(X0,null_class)) = X0
| null_class = X0
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1802,plain,
( spl0_137
<=> ! [X0] :
( null_class = X0
| unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class)) = X0
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f2080,plain,
( ! [X0] :
( unordered_pair(x,not_subclass_element(X0,null_class)) = X0
| null_class = X0
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class),X0) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_137 ),
inference(forward_demodulation,[],[f1805,f413]) ).
fof(f1805,plain,
( ! [X0] :
( unordered_pair(not_subclass_element(X0,null_class),x) = X0
| null_class = X0
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class),X0) )
| spl0_12
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_137 ),
inference(forward_demodulation,[],[f1803,f1476]) ).
fof(f1803,plain,
( ! [X0] :
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class),X0)
| unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class)) = X0
| null_class = X0 )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1802]) ).
fof(f2068,plain,
( spl0_147
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f2064,f2058,f1318,f1275,f669,f412,f334,f2066]) ).
fof(f2066,plain,
( spl0_147
<=> ! [X9,X11,X10] :
( member(unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11)))),domain_of(X10))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f2058,plain,
( spl0_146
<=> ! [X9,X11,X10] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f2064,plain,
( ! [X10,X11,X9] :
( member(unordered_pair(unordered_pair(x,not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11)))),domain_of(X10))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_146 ),
inference(forward_demodulation,[],[f2063,f413]) ).
fof(f2063,plain,
( ! [X10,X11,X9] :
( member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),x),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11)))),domain_of(X10))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_146 ),
inference(forward_demodulation,[],[f2062,f1368]) ).
fof(f2062,plain,
( ! [X10,X11,X9] :
( member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(x,not_homomorphism2(X9,X10,X11)))),domain_of(X10))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_146 ),
inference(forward_demodulation,[],[f2061,f413]) ).
fof(f2061,plain,
( ! [X10,X11,X9] :
( member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),x))),domain_of(X10))
| ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11) )
| spl0_12
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_146 ),
inference(forward_demodulation,[],[f2059,f1368]) ).
fof(f2059,plain,
( ! [X10,X11,X9] :
( member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10))
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| ~ operation(X10) )
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f2058]) ).
fof(f2060,plain,
spl0_146,
inference(avatar_split_clause,[],[f258,f2058]) ).
fof(f258,plain,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(unordered_pair(unordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism1(X9,X10,X11)),unordered_pair(not_homomorphism1(X9,X10,X11),unordered_pair(not_homomorphism2(X9,X10,X11),not_homomorphism2(X9,X10,X11)))),domain_of(X10)) ),
inference(definition_unfolding,[],[f90,f166]) ).
fof(f90,axiom,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)),domain_of(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism5) ).
fof(f2042,plain,
spl0_145,
inference(avatar_split_clause,[],[f226,f2040]) ).
fof(f2040,plain,
( spl0_145
<=> ! [X4,X7,X5,X1] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f226,plain,
! [X1,X7,X4,X5] :
( ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),compose(X7,X5))
| member(X4,domain_of(domain_of(flip(cross_product(intersection(cross_product(domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),X5),universal_class)))),universal_class),X7),universal_class))))) ),
inference(definition_unfolding,[],[f58,f166,f164,f164,f12]) ).
fof(f58,axiom,
! [X1,X7,X4,X5] :
( ~ member(ordered_pair(X1,X4),compose(X7,X5))
| member(X4,image(X7,image(X5,singleton(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose2) ).
fof(f2023,plain,
( spl0_144
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f2019,f2013,f1318,f1275,f669,f412,f334,f2021]) ).
fof(f2021,plain,
( spl0_144
<=> ! [X0] :
( member(not_subclass_element(intersection(complement(unordered_pair(x,not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(unordered_pair(x,not_subclass_element(X0,null_class))),X0))
| unordered_pair(x,not_subclass_element(X0,null_class)) = X0
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f2013,plain,
( spl0_143
<=> ! [X0] :
( null_class = X0
| unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class)) = X0
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f2019,plain,
( ! [X0] :
( member(not_subclass_element(intersection(complement(unordered_pair(x,not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(unordered_pair(x,not_subclass_element(X0,null_class))),X0))
| unordered_pair(x,not_subclass_element(X0,null_class)) = X0
| null_class = X0 )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_143 ),
inference(forward_demodulation,[],[f2018,f413]) ).
fof(f2018,plain,
( ! [X0] :
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),x)),X0),null_class),intersection(complement(unordered_pair(not_subclass_element(X0,null_class),x)),X0))
| unordered_pair(x,not_subclass_element(X0,null_class)) = X0
| null_class = X0 )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_143 ),
inference(forward_demodulation,[],[f2017,f1368]) ).
fof(f2017,plain,
( ! [X0] :
( unordered_pair(x,not_subclass_element(X0,null_class)) = X0
| null_class = X0
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0)) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_143 ),
inference(forward_demodulation,[],[f2016,f413]) ).
fof(f2016,plain,
( ! [X0] :
( unordered_pair(not_subclass_element(X0,null_class),x) = X0
| null_class = X0
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0)) )
| spl0_12
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_143 ),
inference(forward_demodulation,[],[f2014,f1368]) ).
fof(f2014,plain,
( ! [X0] :
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0))
| unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class)) = X0
| null_class = X0 )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f2013]) ).
fof(f2015,plain,
spl0_143,
inference(avatar_split_clause,[],[f248,f2013]) ).
fof(f248,plain,
! [X0] :
( null_class = X0
| unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class)) = X0
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0)) ),
inference(definition_unfolding,[],[f141,f12,f12,f12]) ).
fof(f141,axiom,
! [X0] :
( null_class = X0
| singleton(not_subclass_element(X0,null_class)) = X0
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(singleton(not_subclass_element(X0,null_class))),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',number_of_elements_in_class) ).
fof(f2010,plain,
( spl0_142
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_141 ),
inference(avatar_split_clause,[],[f2006,f2000,f1318,f1275,f669,f412,f334,f2008]) ).
fof(f2008,plain,
( spl0_142
<=> ! [X0] :
( not_subclass_element(X0,null_class) != not_subclass_element(intersection(complement(unordered_pair(x,not_subclass_element(X0,null_class))),X0),null_class)
| unordered_pair(x,not_subclass_element(X0,null_class)) = X0
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f2006,plain,
( ! [X0] :
( not_subclass_element(X0,null_class) != not_subclass_element(intersection(complement(unordered_pair(x,not_subclass_element(X0,null_class))),X0),null_class)
| unordered_pair(x,not_subclass_element(X0,null_class)) = X0
| null_class = X0 )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_141 ),
inference(forward_demodulation,[],[f2005,f413]) ).
fof(f2005,plain,
( ! [X0] :
( not_subclass_element(X0,null_class) != not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),x)),X0),null_class)
| unordered_pair(x,not_subclass_element(X0,null_class)) = X0
| null_class = X0 )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_141 ),
inference(forward_demodulation,[],[f2004,f1368]) ).
fof(f2004,plain,
( ! [X0] :
( unordered_pair(x,not_subclass_element(X0,null_class)) = X0
| null_class = X0
| not_subclass_element(X0,null_class) != not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_121
| ~ spl0_124
| ~ spl0_141 ),
inference(forward_demodulation,[],[f2003,f413]) ).
fof(f2002,plain,
spl0_141,
inference(avatar_split_clause,[],[f247,f2000]) ).
fof(f247,plain,
! [X0] :
( null_class = X0
| unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class)) = X0
| not_subclass_element(X0,null_class) != not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class) ),
inference(definition_unfolding,[],[f143,f12,f12]) ).
fof(f143,axiom,
! [X0] :
( null_class = X0
| singleton(not_subclass_element(X0,null_class)) = X0
| not_subclass_element(X0,null_class) != not_subclass_element(intersection(complement(singleton(not_subclass_element(X0,null_class))),X0),null_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_1_to_number_of_elements_in_class) ).
fof(f1977,plain,
spl0_140,
inference(avatar_split_clause,[],[f235,f1975]) ).
fof(f1975,plain,
( spl0_140
<=> ! [X0,X1] :
( ~ member(X0,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f235,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f20,f166,f166]) ).
fof(f20,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| member(ordered_pair(X0,X1),element_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation3) ).
fof(f1817,plain,
( spl0_139
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1808,f1802,f1322,f1279,f669,f412,f334,f1815]) ).
fof(f1815,plain,
( spl0_139
<=> ! [X0] :
( member(not_subclass_element(intersection(complement(unordered_pair(x,not_subclass_element(X0,null_class))),X0),null_class),X0)
| unordered_pair(x,not_subclass_element(X0,null_class)) = X0
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1808,plain,
( ! [X0] :
( member(not_subclass_element(intersection(complement(unordered_pair(x,not_subclass_element(X0,null_class))),X0),null_class),X0)
| unordered_pair(x,not_subclass_element(X0,null_class)) = X0
| null_class = X0 )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_137 ),
inference(forward_demodulation,[],[f1807,f413]) ).
fof(f1807,plain,
( ! [X0] :
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),x)),X0),null_class),X0)
| unordered_pair(x,not_subclass_element(X0,null_class)) = X0
| null_class = X0 )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_137 ),
inference(forward_demodulation,[],[f1806,f1476]) ).
fof(f1806,plain,
( ! [X0] :
( unordered_pair(x,not_subclass_element(X0,null_class)) = X0
| null_class = X0
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class),X0) )
| spl0_12
| ~ spl0_29
| ~ spl0_66
| spl0_122
| ~ spl0_125
| ~ spl0_137 ),
inference(forward_demodulation,[],[f1805,f413]) ).
fof(f1813,plain,
( spl0_138
| spl0_12
| ~ spl0_121
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1563,f1318,f1275,f334,f1810]) ).
fof(f1563,plain,
( member(x,universal_class)
| spl0_12
| ~ spl0_121
| ~ spl0_124 ),
inference(forward_demodulation,[],[f1276,f1329]) ).
fof(f1276,plain,
( member(first(x),universal_class)
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1275]) ).
fof(f1804,plain,
spl0_137,
inference(avatar_split_clause,[],[f246,f1802]) ).
fof(f246,plain,
! [X0] :
( null_class = X0
| unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class)) = X0
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(X0,null_class),not_subclass_element(X0,null_class))),X0),null_class),X0) ),
inference(definition_unfolding,[],[f142,f12,f12]) ).
fof(f142,axiom,
! [X0] :
( null_class = X0
| singleton(not_subclass_element(X0,null_class)) = X0
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X0,null_class))),X0),null_class),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_number_of_elements_in_class) ).
fof(f1567,plain,
spl0_136,
inference(avatar_split_clause,[],[f268,f1565]) ).
fof(f1565,plain,
( spl0_136
<=> ! [X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
| ~ member(X1,universal_class)
| null_class = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f268,plain,
! [X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(choice,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))))),X1)
| ~ member(X1,universal_class)
| null_class = X1 ),
inference(forward_demodulation,[],[f267,f183]) ).
fof(f267,plain,
! [X1] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))))),X1)
| ~ member(X1,universal_class)
| null_class = X1 ),
inference(forward_demodulation,[],[f240,f183]) ).
fof(f240,plain,
! [X1] :
( ~ member(X1,universal_class)
| null_class = X1
| member(domain_of(intersection(cross_product(universal_class,domain_of(domain_of(flip(cross_product(intersection(cross_product(unordered_pair(X1,X1),universal_class),choice),universal_class))))),element_relation)),X1) ),
inference(definition_unfolding,[],[f70,f165]) ).
fof(f70,axiom,
! [X1] :
( ~ member(X1,universal_class)
| null_class = X1
| member(apply(choice,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice2) ).
fof(f1496,plain,
( spl0_135
| spl0_12
| ~ spl0_65
| spl0_121
| ~ spl0_124
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1492,f1489,f1318,f1275,f665,f334,f1494]) ).
fof(f1494,plain,
( spl0_135
<=> ! [X0,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(null_class,unordered_pair(x,unordered_pair(X1,X1)))
| ~ member(X1,universal_class)
| member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f665,plain,
( spl0_65
<=> ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1489,plain,
( spl0_134
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(null_class,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1492,plain,
( ! [X0,X1] :
( unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(null_class,unordered_pair(x,unordered_pair(X1,X1)))
| ~ member(X1,universal_class)
| member(X0,universal_class) )
| spl0_12
| ~ spl0_65
| spl0_121
| ~ spl0_124
| ~ spl0_134 ),
inference(forward_demodulation,[],[f1490,f1367]) ).
fof(f1367,plain,
( ! [X0] : unordered_pair(X0,X0) = unordered_pair(x,X0)
| spl0_12
| ~ spl0_65
| spl0_121
| ~ spl0_124 ),
inference(forward_demodulation,[],[f1359,f1329]) ).
fof(f1359,plain,
( ! [X0] : unordered_pair(X0,X0) = unordered_pair(first(x),X0)
| ~ spl0_65
| spl0_121 ),
inference(resolution,[],[f1277,f666]) ).
fof(f666,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X1,X1) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f665]) ).
fof(f1490,plain,
( ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(null_class,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X1))) )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1489]) ).
fof(f1491,plain,
spl0_134,
inference(avatar_split_clause,[],[f241,f1489]) ).
fof(f241,plain,
! [X0,X1] :
( ~ member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(null_class,unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X1))) ),
inference(definition_unfolding,[],[f149,f166,f12,f12]) ).
fof(f149,axiom,
! [X0,X1] :
( ~ member(X1,universal_class)
| member(X0,universal_class)
| ordered_pair(X0,X1) = unordered_pair(null_class,singleton(singleton(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_2_of_ordered_pair) ).
fof(f1465,plain,
spl0_133,
inference(avatar_split_clause,[],[f239,f1463]) ).
fof(f1463,plain,
( spl0_133
<=> ! [X4,X0,X6,X1] :
( ~ member(X0,universal_class)
| X0 = X4
| unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))) != unordered_pair(unordered_pair(X6,X6),unordered_pair(X6,unordered_pair(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f239,plain,
! [X0,X1,X6,X4] :
( ~ member(X0,universal_class)
| X0 = X4
| unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))) != unordered_pair(unordered_pair(X6,X6),unordered_pair(X6,unordered_pair(X0,X0))) ),
inference(definition_unfolding,[],[f152,f166,f166]) ).
fof(f152,axiom,
! [X0,X1,X6,X4] :
( ~ member(X0,universal_class)
| X0 = X4
| ordered_pair(X1,X4) != ordered_pair(X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_determines_components2) ).
fof(f1461,plain,
spl0_132,
inference(avatar_split_clause,[],[f238,f1459]) ).
fof(f1459,plain,
( spl0_132
<=> ! [X4,X0,X6,X1] :
( ~ member(X6,universal_class)
| X1 = X6
| unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))) != unordered_pair(unordered_pair(X6,X6),unordered_pair(X6,unordered_pair(X0,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f238,plain,
! [X0,X1,X6,X4] :
( ~ member(X6,universal_class)
| X1 = X6
| unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))) != unordered_pair(unordered_pair(X6,X6),unordered_pair(X6,unordered_pair(X0,X0))) ),
inference(definition_unfolding,[],[f151,f166,f166]) ).
fof(f151,axiom,
! [X0,X1,X6,X4] :
( ~ member(X6,universal_class)
| X1 = X6
| ordered_pair(X1,X4) != ordered_pair(X6,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_determines_components1) ).
fof(f1457,plain,
spl0_131,
inference(avatar_split_clause,[],[f224,f1455]) ).
fof(f1455,plain,
( spl0_131
<=> ! [X2,X3] :
( second(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))) = X3
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f224,plain,
! [X2,X3] :
( second(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))) = X3
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f159,f166,f166]) ).
fof(f159,axiom,
! [X2,X3] :
( second(ordered_pair(X2,X3)) = X3
| ~ member(ordered_pair(X2,X3),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_1st_and_2nd_in_pair_of_sets2) ).
fof(f1453,plain,
spl0_130,
inference(avatar_split_clause,[],[f223,f1451]) ).
fof(f1451,plain,
( spl0_130
<=> ! [X2,X3] :
( first(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))) = X2
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f223,plain,
! [X2,X3] :
( first(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))) = X2
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f158,f166,f166]) ).
fof(f158,axiom,
! [X2,X3] :
( first(ordered_pair(X2,X3)) = X2
| ~ member(ordered_pair(X2,X3),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_1st_and_2nd_in_pair_of_sets1) ).
fof(f1449,plain,
spl0_129,
inference(avatar_split_clause,[],[f255,f1447]) ).
fof(f1447,plain,
( spl0_129
<=> ! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f255,plain,
! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
inference(definition_unfolding,[],[f81,f163]) ).
fof(f81,axiom,
! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(range_of(X8),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation4) ).
fof(f1387,plain,
spl0_128,
inference(avatar_split_clause,[],[f244,f1385]) ).
fof(f1385,plain,
( spl0_128
<=> ! [X4,X0,X1] :
( X1 = X4
| unordered_pair(X0,X1) != unordered_pair(X0,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f244,plain,
! [X0,X1,X4] :
( X1 = X4
| unordered_pair(X0,X1) != unordered_pair(X0,X4)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X4,X4))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f114,f166]) ).
fof(f114,axiom,
! [X0,X1,X4] :
( X1 = X4
| unordered_pair(X0,X1) != unordered_pair(X0,X4)
| ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_cancellation) ).
fof(f1383,plain,
spl0_127,
inference(avatar_split_clause,[],[f243,f1381]) ).
fof(f1381,plain,
( spl0_127
<=> ! [X4,X0,X1] :
( X0 = X1
| unordered_pair(X0,X4) != unordered_pair(X1,X4)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f243,plain,
! [X0,X1,X4] :
( X0 = X1
| unordered_pair(X0,X4) != unordered_pair(X1,X4)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f115,f166]) ).
fof(f115,axiom,
! [X0,X1,X4] :
( X0 = X1
| unordered_pair(X0,X4) != unordered_pair(X1,X4)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_cancellation) ).
fof(f1328,plain,
spl0_126,
inference(avatar_split_clause,[],[f256,f1326]) ).
fof(f1326,plain,
( spl0_126
<=> ! [X9,X11,X10] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f256,plain,
! [X10,X11,X9] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
inference(definition_unfolding,[],[f85,f163]) ).
fof(f85,axiom,
! [X10,X11,X9] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible4) ).
fof(f1324,plain,
spl0_125,
inference(avatar_split_clause,[],[f218,f1322]) ).
fof(f218,plain,
! [X0] :
( second(X0) = X0
| member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f155,f166]) ).
fof(f155,axiom,
! [X0] :
( second(X0) = X0
| member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_3) ).
fof(f1320,plain,
spl0_124,
inference(avatar_split_clause,[],[f214,f1318]) ).
fof(f214,plain,
! [X0] :
( first(X0) = X0
| member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f154,f166]) ).
fof(f154,axiom,
! [X0] :
( first(X0) = X0
| member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_2) ).
fof(f1286,plain,
spl0_123,
inference(avatar_split_clause,[],[f249,f1284]) ).
fof(f1284,plain,
( spl0_123
<=> ! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(null_class,unordered_pair(null_class,null_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f249,plain,
! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(null_class,unordered_pair(null_class,null_class)) ),
inference(definition_unfolding,[],[f150,f166,f12]) ).
fof(f150,axiom,
! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| ordered_pair(X0,X1) = unordered_pair(null_class,singleton(null_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_3_of_ordered_pair) ).
fof(f1282,plain,
( ~ spl0_121
| ~ spl0_122
| spl0_12
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1186,f1174,f334,f1279,f1275]) ).
fof(f1174,plain,
( spl0_114
<=> ! [X0,X3,X2,X1] :
( ~ member(X2,X0)
| ~ 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_114])]) ).
fof(f1186,plain,
( ~ member(second(x),universal_class)
| ~ member(first(x),universal_class)
| spl0_12
| ~ spl0_114 ),
inference(resolution,[],[f1175,f336]) ).
fof(f1175,plain,
( ! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1))
| ~ member(X3,X1)
| ~ member(X2,X0) )
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1174]) ).
fof(f1273,plain,
spl0_120,
inference(avatar_split_clause,[],[f220,f1271]) ).
fof(f1271,plain,
( spl0_120
<=> ! [X4,X0,X1] :
( ~ member(X4,cross_product(X0,X1))
| unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f220,plain,
! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ),
inference(definition_unfolding,[],[f17,f166]) ).
fof(f17,axiom,
! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| ordered_pair(first(X4),second(X4)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f1269,plain,
spl0_119,
inference(avatar_split_clause,[],[f212,f1267]) ).
fof(f1267,plain,
( spl0_119
<=> ! [X0,X1] :
( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f212,plain,
! [X0,X1] :
( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f45,f169,f166]) ).
fof(f45,axiom,
! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation2) ).
fof(f1213,plain,
spl0_118,
inference(avatar_split_clause,[],[f217,f1211]) ).
fof(f1211,plain,
( spl0_118
<=> ! [X0] :
( second(X0) = X0
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f217,plain,
! [X0] :
( second(X0) = X0
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(definition_unfolding,[],[f157,f166]) ).
fof(f157,axiom,
! [X0] :
( second(X0) = X0
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_5) ).
fof(f1209,plain,
spl0_117,
inference(avatar_split_clause,[],[f213,f1207]) ).
fof(f1207,plain,
( spl0_117
<=> ! [X0] :
( first(X0) = X0
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f213,plain,
! [X0] :
( first(X0) = X0
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(definition_unfolding,[],[f156,f166]) ).
fof(f156,axiom,
! [X0] :
( first(X0) = X0
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_4) ).
fof(f1205,plain,
spl0_116,
inference(avatar_split_clause,[],[f209,f1203]) ).
fof(f1203,plain,
( spl0_116
<=> ! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,null_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f209,plain,
! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,null_class)) ),
inference(definition_unfolding,[],[f148,f166,f12]) ).
fof(f148,axiom,
! [X0,X1] :
( member(X1,universal_class)
| ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,null_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_1_of_ordered_pair) ).
fof(f1181,plain,
( ~ spl0_9
| spl0_115
| ~ spl0_4
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1132,f1114,f300,f1178,f321]) ).
fof(f321,plain,
( spl0_9
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1178,plain,
( spl0_115
<=> inductive(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f300,plain,
( spl0_4
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1114,plain,
( spl0_108
<=> ! [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_108])]) ).
fof(f1132,plain,
( inductive(universal_class)
| ~ member(null_class,universal_class)
| ~ spl0_4
| ~ spl0_108 ),
inference(resolution,[],[f1115,f301]) ).
fof(f301,plain,
( ! [X0] : subclass(X0,universal_class)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f1115,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) )
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f1114]) ).
fof(f1176,plain,
spl0_114,
inference(avatar_split_clause,[],[f233,f1174]) ).
fof(f233,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f16,f166]) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f1172,plain,
spl0_113,
inference(avatar_split_clause,[],[f184,f1169]) ).
fof(f1169,plain,
( spl0_113
<=> subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f184,plain,
subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
inference(definition_unfolding,[],[f74,f38]) ).
fof(f74,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_relation) ).
fof(f1145,plain,
spl0_112,
inference(avatar_split_clause,[],[f222,f1143]) ).
fof(f1143,plain,
( spl0_112
<=> ! [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_112])]) ).
fof(f222,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,f166]) ).
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/sandbox2/benchmark/theBenchmark.p',corollary_1_to_unordered_pair) ).
fof(f1141,plain,
spl0_111,
inference(avatar_split_clause,[],[f221,f1139]) ).
fof(f1139,plain,
( spl0_111
<=> ! [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_111])]) ).
fof(f221,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,f166]) ).
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/sandbox2/benchmark/theBenchmark.p',corollary_2_to_unordered_pair) ).
fof(f1137,plain,
spl0_110,
inference(avatar_split_clause,[],[f219,f1135]) ).
fof(f1135,plain,
( spl0_110
<=> ! [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_110])]) ).
fof(f219,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,f166]) ).
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/sandbox2/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom3) ).
fof(f1126,plain,
( spl0_109
| ~ spl0_38
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f630,f569,f458,f1124]) ).
fof(f1124,plain,
( spl0_109
<=> ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f458,plain,
( spl0_38
<=> ! [X4,X0,X1] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f569,plain,
( spl0_57
<=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f630,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) )
| ~ spl0_38
| ~ spl0_57 ),
inference(superposition,[],[f459,f571]) ).
fof(f571,plain,
( identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f459,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X1) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f1116,plain,
spl0_108,
inference(avatar_split_clause,[],[f266,f1114]) ).
fof(f266,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,[],[f231,f183]) ).
fof(f231,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,f164]) ).
fof(f49,axiom,
! [X0] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive3) ).
fof(f1112,plain,
spl0_107,
inference(avatar_split_clause,[],[f264,f1110]) ).
fof(f1110,plain,
( spl0_107
<=> ! [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_107])]) ).
fof(f264,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,[],[f194,f183]) ).
fof(f194,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,f170]) ).
fof(f170,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,f164]) ).
fof(f55,axiom,
! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_definition) ).
fof(f56,axiom,
! [X2] :
( ~ member(X2,universal_class)
| member(power_class(X2),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class2) ).
fof(f1108,plain,
spl0_106,
inference(avatar_split_clause,[],[f230,f1106]) ).
fof(f1106,plain,
( spl0_106
<=> ! [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_106])]) ).
fof(f230,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,f164]) ).
fof(f65,axiom,
! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(image(X8,X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).
fof(f1061,plain,
( spl0_105
| ~ spl0_8
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f624,f565,f317,f1059]) ).
fof(f1059,plain,
( spl0_105
<=> ! [X0,X1] :
( ~ subclass(X0,null_class)
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f317,plain,
( spl0_8
<=> ! [X0] : subclass(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f565,plain,
( spl0_56
<=> ! [X4,X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X4)
| subclass(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f624,plain,
( ! [X0,X1] :
( ~ subclass(X0,null_class)
| subclass(X0,X1) )
| ~ spl0_8
| ~ spl0_56 ),
inference(resolution,[],[f566,f318]) ).
fof(f318,plain,
( ! [X0] : subclass(null_class,X0)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f566,plain,
( ! [X0,X1,X4] :
( ~ subclass(X1,X4)
| ~ subclass(X0,X1)
| subclass(X0,X4) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f1031,plain,
spl0_104,
inference(avatar_split_clause,[],[f257,f1029]) ).
fof(f1029,plain,
( spl0_104
<=> ! [X4,X0,X1] :
( ~ member(X0,universal_class)
| X0 = X4
| X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f257,plain,
! [X0,X1,X4] :
( ~ member(X0,universal_class)
| X0 = X4
| X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X4) ),
inference(definition_unfolding,[],[f129,f12]) ).
fof(f129,axiom,
! [X0,X1,X4] :
( ~ member(X0,universal_class)
| X0 = X4
| X0 = X1
| singleton(X0) != unordered_pair(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_in_unordered_pair3) ).
fof(f1027,plain,
spl0_103,
inference(avatar_split_clause,[],[f242,f1025]) ).
fof(f1025,plain,
( spl0_103
<=> ! [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_103])]) ).
fof(f242,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/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f1023,plain,
spl0_102,
inference(avatar_split_clause,[],[f232,f1021]) ).
fof(f1021,plain,
( spl0_102
<=> ! [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_102])]) ).
fof(f232,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/sandbox2/benchmark/theBenchmark.p',function3) ).
fof(f1019,plain,
spl0_101,
inference(avatar_split_clause,[],[f208,f1017]) ).
fof(f1017,plain,
( spl0_101
<=> ! [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_101])]) ).
fof(f208,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,f166]) ).
fof(f95,axiom,
! [X2,X3,X0,X1] :
( member(X3,universal_class)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
fof(f1015,plain,
spl0_100,
inference(avatar_split_clause,[],[f207,f1013]) ).
fof(f1013,plain,
( spl0_100
<=> ! [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_100])]) ).
fof(f207,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,f166]) ).
fof(f94,axiom,
! [X2,X3,X0,X1] :
( member(X2,universal_class)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).
fof(f1011,plain,
spl0_99,
inference(avatar_split_clause,[],[f202,f1009]) ).
fof(f1009,plain,
( spl0_99
<=> ! [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_99])]) ).
fof(f202,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,f166]) ).
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(f1007,plain,
spl0_98,
inference(avatar_split_clause,[],[f201,f1005]) ).
fof(f1005,plain,
( spl0_98
<=> ! [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_98])]) ).
fof(f201,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,f166]) ).
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(f1003,plain,
spl0_97,
inference(avatar_split_clause,[],[f198,f1001]) ).
fof(f1001,plain,
( spl0_97
<=> ! [X1] :
( ~ member(X1,universal_class)
| unordered_pair(X1,X1) = unordered_pair(member_of(unordered_pair(X1,X1)),member_of(unordered_pair(X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f198,plain,
! [X1] :
( ~ member(X1,universal_class)
| unordered_pair(X1,X1) = unordered_pair(member_of(unordered_pair(X1,X1)),member_of(unordered_pair(X1,X1))) ),
inference(definition_unfolding,[],[f131,f12,f12,f12]) ).
fof(f131,axiom,
! [X1] :
( ~ member(X1,universal_class)
| singleton(X1) = singleton(member_of(singleton(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_exists2) ).
fof(f988,plain,
spl0_96,
inference(avatar_split_clause,[],[f182,f986]) ).
fof(f986,plain,
( spl0_96
<=> ! [X0,X1] : member(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f182,plain,
! [X0,X1] : member(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),
inference(definition_unfolding,[],[f147,f12,f166]) ).
fof(f147,axiom,
! [X0,X1] : member(unordered_pair(X0,singleton(X1)),ordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member_of_ordered_pair) ).
fof(f958,plain,
spl0_95,
inference(avatar_split_clause,[],[f263,f956]) ).
fof(f956,plain,
( spl0_95
<=> ! [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_95])]) ).
fof(f263,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,[],[f187,f183]) ).
fof(f187,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,f164]) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive2) ).
fof(f954,plain,
spl0_94,
inference(avatar_split_clause,[],[f234,f952]) ).
fof(f952,plain,
( spl0_94
<=> ! [X0,X1] :
( ~ member(X1,X0)
| member_of(X0) = X1
| unordered_pair(member_of(X0),member_of(X0)) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f234,plain,
! [X0,X1] :
( ~ member(X1,X0)
| member_of(X0) = X1
| unordered_pair(member_of(X0),member_of(X0)) != X0 ),
inference(definition_unfolding,[],[f138,f12]) ).
fof(f138,axiom,
! [X0,X1] :
( ~ member(X1,X0)
| member_of(X0) = X1
| singleton(member_of(X0)) != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_singletons1) ).
fof(f950,plain,
spl0_93,
inference(avatar_split_clause,[],[f211,f948]) ).
fof(f948,plain,
( spl0_93
<=> ! [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_93])]) ).
fof(f211,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,f163]) ).
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(f946,plain,
( spl0_92
| ~ spl0_3
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f855,f805,f295,f943]) ).
fof(f943,plain,
( spl0_92
<=> single_valued_class(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f295,plain,
( spl0_3
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f805,plain,
( spl0_81
<=> ! [X0] :
( single_valued_class(X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f855,plain,
( single_valued_class(choice)
| ~ spl0_3
| ~ spl0_81 ),
inference(resolution,[],[f806,f297]) ).
fof(f297,plain,
( function(choice)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f806,plain,
( ! [X0] :
( ~ function(X0)
| single_valued_class(X0) )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f805]) ).
fof(f941,plain,
spl0_91,
inference(avatar_split_clause,[],[f200,f939]) ).
fof(f939,plain,
( spl0_91
<=> ! [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_91])]) ).
fof(f200,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,f166]) ).
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(f937,plain,
spl0_90,
inference(avatar_split_clause,[],[f172,f935]) ).
fof(f935,plain,
( spl0_90
<=> ! [X0,X1] : unordered_pair(X0,X1) = complement(intersection(complement(unordered_pair(X0,X0)),complement(unordered_pair(X1,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f172,plain,
! [X0,X1] : unordered_pair(X0,X1) = complement(intersection(complement(unordered_pair(X0,X0)),complement(unordered_pair(X1,X1)))),
inference(definition_unfolding,[],[f144,f26,f12,f12]) ).
fof(f144,axiom,
! [X0,X1] : unordered_pair(X0,X1) = union(singleton(X0),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_and_singletons) ).
fof(f864,plain,
spl0_89,
inference(avatar_split_clause,[],[f245,f862]) ).
fof(f862,plain,
( spl0_89
<=> ! [X0,X1] :
( null_class = X0
| ~ subclass(X0,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f245,plain,
! [X0,X1] :
( null_class = X0
| ~ subclass(X0,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = X0 ),
inference(definition_unfolding,[],[f140,f12,f12]) ).
fof(f140,axiom,
! [X0,X1] :
( null_class = X0
| ~ subclass(X0,singleton(X1))
| singleton(X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_subsets_of_singleton) ).
fof(f860,plain,
spl0_88,
inference(avatar_split_clause,[],[f236,f858]) ).
fof(f858,plain,
( spl0_88
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f236,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/sandbox2/benchmark/theBenchmark.p',singleton_identified_by_element1) ).
fof(f854,plain,
spl0_87,
inference(avatar_split_clause,[],[f210,f852]) ).
fof(f852,plain,
( spl0_87
<=> ! [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_87])]) ).
fof(f210,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(f850,plain,
spl0_86,
inference(avatar_split_clause,[],[f101,f848]) ).
fof(f848,plain,
( spl0_86
<=> ! [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_86])]) ).
fof(f101,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X1,X0),X0)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality4) ).
fof(f846,plain,
spl0_85,
inference(avatar_split_clause,[],[f100,f844]) ).
fof(f844,plain,
( spl0_85
<=> ! [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_85])]) ).
fof(f100,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X1,X0),X0)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality3) ).
fof(f842,plain,
spl0_84,
inference(avatar_split_clause,[],[f98,f840]) ).
fof(f840,plain,
( spl0_84
<=> ! [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_84])]) ).
fof(f98,axiom,
! [X0,X1] :
( X0 = X1
| member(not_subclass_element(X1,X0),X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality1) ).
fof(f836,plain,
spl0_83,
inference(avatar_split_clause,[],[f188,f834]) ).
fof(f834,plain,
( spl0_83
<=> ! [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_83])]) ).
fof(f188,plain,
! [X8] :
( ~ operation(X8)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
inference(definition_unfolding,[],[f80,f163]) ).
fof(f80,axiom,
! [X8] :
( ~ operation(X8)
| subclass(range_of(X8),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation3) ).
fof(f832,plain,
spl0_82,
inference(avatar_split_clause,[],[f79,f830]) ).
fof(f830,plain,
( spl0_82
<=> ! [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_82])]) ).
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(f807,plain,
( spl0_81
| ~ spl0_75
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f785,f719,f715,f805]) ).
fof(f715,plain,
( spl0_75
<=> ! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f719,plain,
( spl0_76
<=> ! [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_76])]) ).
fof(f785,plain,
( ! [X0] :
( single_valued_class(X0)
| ~ function(X0) )
| ~ spl0_75
| ~ spl0_76 ),
inference(resolution,[],[f720,f716]) ).
fof(f716,plain,
( ! [X8] :
( subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
| ~ function(X8) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f715]) ).
fof(f720,plain,
( ! [X0] :
( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| single_valued_class(X0) )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f719]) ).
fof(f737,plain,
spl0_80,
inference(avatar_split_clause,[],[f265,f735]) ).
fof(f735,plain,
( spl0_80
<=> ! [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_80])]) ).
fof(f265,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(forward_demodulation,[],[f195,f183]) ).
fof(f195,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
inference(definition_unfolding,[],[f54,f162]) ).
fof(f54,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class2) ).
fof(f733,plain,
( spl0_79
| ~ spl0_4
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f602,f557,f300,f731]) ).
fof(f731,plain,
( spl0_79
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f557,plain,
( spl0_54
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f602,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 )
| ~ spl0_4
| ~ spl0_54 ),
inference(resolution,[],[f558,f301]) ).
fof(f558,plain,
( ! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f729,plain,
spl0_78,
inference(avatar_split_clause,[],[f216,f727]) ).
fof(f727,plain,
( spl0_78
<=> ! [X0] :
( member_of(X0) = X0
| unordered_pair(member_of(X0),member_of(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f216,plain,
! [X0] :
( member_of(X0) = X0
| unordered_pair(member_of(X0),member_of(X0)) = X0 ),
inference(definition_unfolding,[],[f133,f12]) ).
fof(f133,axiom,
! [X0] :
( member_of(X0) = X0
| singleton(member_of(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_exists4) ).
fof(f725,plain,
spl0_77,
inference(avatar_split_clause,[],[f215,f723]) ).
fof(f723,plain,
( spl0_77
<=> ! [X0] :
( member_of(X0) = X0
| unordered_pair(member_of1(X0),member_of1(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f215,plain,
! [X0] :
( member_of(X0) = X0
| unordered_pair(member_of1(X0),member_of1(X0)) = X0 ),
inference(definition_unfolding,[],[f136,f12]) ).
fof(f136,axiom,
! [X0] :
( member_of(X0) = X0
| singleton(member_of1(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_non_singleton_unique2) ).
fof(f721,plain,
spl0_76,
inference(avatar_split_clause,[],[f190,f719]) ).
fof(f190,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(f717,plain,
spl0_75,
inference(avatar_split_clause,[],[f189,f715]) ).
fof(f189,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(f713,plain,
spl0_74,
inference(avatar_split_clause,[],[f185,f711]) ).
fof(f711,plain,
( spl0_74
<=> ! [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_74])]) ).
fof(f185,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(f709,plain,
spl0_73,
inference(avatar_split_clause,[],[f183,f707]) ).
fof(f707,plain,
( spl0_73
<=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f705,plain,
spl0_72,
inference(avatar_split_clause,[],[f119,f703]) ).
fof(f703,plain,
( spl0_72
<=> ! [X4,X0,X1] :
( ~ member(X0,X4)
| ~ member(X1,X4)
| subclass(unordered_pair(X0,X1),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f119,axiom,
! [X0,X1,X4] :
( ~ member(X0,X4)
| ~ member(X1,X4)
| subclass(unordered_pair(X0,X1),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_is_subset) ).
fof(f701,plain,
spl0_71,
inference(avatar_split_clause,[],[f113,f699]) ).
fof(f699,plain,
( spl0_71
<=> ! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f113,axiom,
! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(X0,X1) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_unordered_pair) ).
fof(f697,plain,
spl0_70,
inference(avatar_split_clause,[],[f23,f695]) ).
fof(f695,plain,
( spl0_70
<=> ! [X4,X0,X1] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
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(f693,plain,
spl0_69,
inference(avatar_split_clause,[],[f8,f691]) ).
fof(f691,plain,
( spl0_69
<=> ! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
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(f689,plain,
( spl0_68
| ~ spl0_5
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f592,f553,f304,f687]) ).
fof(f687,plain,
( spl0_68
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(omega,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f304,plain,
( spl0_5
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f553,plain,
( spl0_53
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f592,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(omega,X0) )
| ~ spl0_5
| ~ spl0_53 ),
inference(resolution,[],[f554,f306]) ).
fof(f306,plain,
( member(omega,universal_class)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f554,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f675,plain,
spl0_67,
inference(avatar_split_clause,[],[f229,f673]) ).
fof(f673,plain,
( spl0_67
<=> ! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f229,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(f671,plain,
spl0_66,
inference(avatar_split_clause,[],[f206,f669]) ).
fof(f206,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/sandbox2/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
fof(f667,plain,
spl0_65,
inference(avatar_split_clause,[],[f205,f665]) ).
fof(f205,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/sandbox2/benchmark/theBenchmark.p',unordered_pair_equals_singleton2) ).
fof(f663,plain,
spl0_64,
inference(avatar_split_clause,[],[f204,f661]) ).
fof(f661,plain,
( spl0_64
<=> ! [X0] :
( member(X0,universal_class)
| unordered_pair(member_of(X0),member_of(X0)) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f204,plain,
! [X0] :
( member(X0,universal_class)
| unordered_pair(member_of(X0),member_of(X0)) != X0 ),
inference(definition_unfolding,[],[f137,f12]) ).
fof(f137,axiom,
! [X0] :
( member(X0,universal_class)
| singleton(member_of(X0)) != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_singletons_are_sets) ).
fof(f659,plain,
( spl0_63
| ~ spl0_9
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f591,f553,f321,f657]) ).
fof(f657,plain,
( spl0_63
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f591,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(null_class,X0) )
| ~ spl0_9
| ~ spl0_53 ),
inference(resolution,[],[f554,f323]) ).
fof(f323,plain,
( member(null_class,universal_class)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f655,plain,
spl0_62,
inference(avatar_split_clause,[],[f83,f653]) ).
fof(f653,plain,
( spl0_62
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
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(f651,plain,
spl0_61,
inference(avatar_split_clause,[],[f25,f649]) ).
fof(f649,plain,
( spl0_61
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
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(f584,plain,
spl0_60,
inference(avatar_split_clause,[],[f197,f582]) ).
fof(f582,plain,
( spl0_60
<=> ! [X1] :
( ~ member(X1,universal_class)
| member(member_of(unordered_pair(X1,X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f197,plain,
! [X1] :
( ~ member(X1,universal_class)
| member(member_of(unordered_pair(X1,X1)),universal_class) ),
inference(definition_unfolding,[],[f130,f12]) ).
fof(f130,axiom,
! [X1] :
( ~ member(X1,universal_class)
| member(member_of(singleton(X1)),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_exists1) ).
fof(f580,plain,
spl0_59,
inference(avatar_split_clause,[],[f196,f578]) ).
fof(f578,plain,
( spl0_59
<=> ! [X2] :
( ~ member(X2,universal_class)
| member_of(unordered_pair(X2,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f196,plain,
! [X2] :
( ~ member(X2,universal_class)
| member_of(unordered_pair(X2,X2)) = X2 ),
inference(definition_unfolding,[],[f134,f12]) ).
fof(f134,axiom,
! [X2] :
( ~ member(X2,universal_class)
| member_of(singleton(X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_singleton_is_unique) ).
fof(f576,plain,
spl0_58,
inference(avatar_split_clause,[],[f181,f574]) ).
fof(f574,plain,
( spl0_58
<=> ! [X0,X1] : member(unordered_pair(X1,X1),unordered_pair(X0,unordered_pair(X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f181,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/sandbox2/benchmark/theBenchmark.p',corollary_1_to_singletons_are_sets) ).
fof(f572,plain,
spl0_57,
inference(avatar_split_clause,[],[f177,f569]) ).
fof(f177,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(f567,plain,
spl0_56,
inference(avatar_split_clause,[],[f97,f565]) ).
fof(f97,axiom,
! [X0,X1,X4] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X4)
| subclass(X0,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_subclass) ).
fof(f563,plain,
spl0_55,
inference(avatar_split_clause,[],[f67,f561]) ).
fof(f561,plain,
( spl0_55
<=> ! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f67,axiom,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).
fof(f559,plain,
spl0_54,
inference(avatar_split_clause,[],[f7,f557]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f555,plain,
spl0_53,
inference(avatar_split_clause,[],[f1,f553]) ).
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(f532,plain,
( spl0_52
| ~ spl0_23
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f429,f408,f384,f530]) ).
fof(f530,plain,
( spl0_52
<=> ! [X0] : null_class = intersection(complement(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f384,plain,
( spl0_23
<=> ! [X0,X1] : ~ member(X1,intersection(complement(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f408,plain,
( spl0_28
<=> ! [X0] :
( null_class = X0
| member(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f429,plain,
( ! [X0] : null_class = intersection(complement(X0),X0)
| ~ spl0_23
| ~ spl0_28 ),
inference(resolution,[],[f409,f385]) ).
fof(f385,plain,
( ! [X0,X1] : ~ member(X1,intersection(complement(X0),X0))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f409,plain,
( ! [X0] :
( member(regular(X0),X0)
| null_class = X0 )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f512,plain,
spl0_51,
inference(avatar_split_clause,[],[f203,f510]) ).
fof(f510,plain,
( spl0_51
<=> ! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f203,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/sandbox2/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f508,plain,
spl0_50,
inference(avatar_split_clause,[],[f199,f506]) ).
fof(f506,plain,
( spl0_50
<=> ! [X0,X1] :
( X0 = X1
| ~ member(X1,unordered_pair(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f199,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/sandbox2/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f504,plain,
spl0_49,
inference(avatar_split_clause,[],[f191,f502]) ).
fof(f502,plain,
( spl0_49
<=> ! [X0,X1] :
( ~ member(X0,X1)
| subclass(unordered_pair(X0,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f191,plain,
! [X0,X1] :
( ~ member(X0,X1)
| subclass(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f139,f12]) ).
fof(f139,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| subclass(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_singletons2) ).
fof(f500,plain,
spl0_48,
inference(avatar_split_clause,[],[f186,f498]) ).
fof(f498,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(f186,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(f496,plain,
( spl0_47
| ~ spl0_16
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f423,f396,f353,f494]) ).
fof(f494,plain,
( spl0_47
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f353,plain,
( spl0_16
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f396,plain,
( spl0_25
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f423,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) )
| ~ spl0_16
| ~ spl0_25 ),
inference(resolution,[],[f397,f354]) ).
fof(f354,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f397,plain,
( ! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f396]) ).
fof(f492,plain,
spl0_46,
inference(avatar_split_clause,[],[f135,f490]) ).
fof(f490,plain,
( spl0_46
<=> ! [X0] :
( member_of(X0) = X0
| member(member_of1(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f135,axiom,
! [X0] :
( member_of(X0) = X0
| member(member_of1(X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_non_singleton_unique1) ).
fof(f488,plain,
spl0_45,
inference(avatar_split_clause,[],[f132,f486]) ).
fof(f486,plain,
( spl0_45
<=> ! [X0] :
( member_of(X0) = X0
| member(member_of(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f132,axiom,
! [X0] :
( member_of(X0) = X0
| member(member_of(X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_exists3) ).
fof(f484,plain,
spl0_44,
inference(avatar_split_clause,[],[f117,f482]) ).
fof(f482,plain,
( spl0_44
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| unordered_pair(X0,X1) != null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f117,axiom,
! [X0,X1] :
( ~ member(X1,universal_class)
| unordered_pair(X0,X1) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom2) ).
fof(f480,plain,
spl0_43,
inference(avatar_split_clause,[],[f116,f478]) ).
fof(f478,plain,
( spl0_43
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| unordered_pair(X0,X1) != null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f116,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| unordered_pair(X0,X1) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom1) ).
fof(f476,plain,
spl0_42,
inference(avatar_split_clause,[],[f106,f474]) ).
fof(f474,plain,
( spl0_42
<=> ! [X4] :
( null_class = X4
| member(not_subclass_element(X4,null_class),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f106,axiom,
! [X4] :
( null_class = X4
| member(not_subclass_element(X4,null_class),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_unique) ).
fof(f472,plain,
spl0_41,
inference(avatar_split_clause,[],[f88,f470]) ).
fof(f470,plain,
( spl0_41
<=> ! [X9,X11,X10] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f88,axiom,
! [X10,X11,X9] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism3) ).
fof(f468,plain,
spl0_40,
inference(avatar_split_clause,[],[f35,f466]) ).
fof(f466,plain,
( spl0_40
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
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(f464,plain,
spl0_39,
inference(avatar_split_clause,[],[f32,f462]) ).
fof(f462,plain,
( spl0_39
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
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(f460,plain,
spl0_38,
inference(avatar_split_clause,[],[f22,f458]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
fof(f456,plain,
spl0_37,
inference(avatar_split_clause,[],[f21,f454]) ).
fof(f454,plain,
( spl0_37
<=> ! [X4,X0,X1] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f452,plain,
spl0_36,
inference(avatar_split_clause,[],[f10,f450]) ).
fof(f450,plain,
( spl0_36
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
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(f448,plain,
spl0_35,
inference(avatar_split_clause,[],[f9,f446]) ).
fof(f446,plain,
( spl0_35
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
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(f444,plain,
spl0_34,
inference(avatar_split_clause,[],[f3,f442]) ).
fof(f442,plain,
( spl0_34
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
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(f440,plain,
spl0_33,
inference(avatar_split_clause,[],[f2,f438]) ).
fof(f438,plain,
( spl0_33
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
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(f427,plain,
( spl0_32
| ~ spl0_16
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f391,f384,f353,f425]) ).
fof(f425,plain,
( spl0_32
<=> ! [X0] : ~ inductive(intersection(complement(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f391,plain,
( ! [X0] : ~ inductive(intersection(complement(X0),X0))
| ~ spl0_16
| ~ spl0_23 ),
inference(resolution,[],[f385,f354]) ).
fof(f422,plain,
spl0_31,
inference(avatar_split_clause,[],[f179,f420]) ).
fof(f420,plain,
( spl0_31
<=> ! [X0,X1] : subclass(unordered_pair(X0,X0),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f179,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/sandbox2/benchmark/theBenchmark.p',singleton_in_unordered_pair1) ).
fof(f418,plain,
spl0_30,
inference(avatar_split_clause,[],[f178,f416]) ).
fof(f416,plain,
( spl0_30
<=> ! [X0,X1] : subclass(unordered_pair(X1,X1),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f178,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/sandbox2/benchmark/theBenchmark.p',singleton_in_unordered_pair2) ).
fof(f414,plain,
spl0_29,
inference(avatar_split_clause,[],[f108,f412]) ).
fof(f108,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f410,plain,
spl0_28,
inference(avatar_split_clause,[],[f66,f408]) ).
fof(f66,axiom,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
fof(f406,plain,
spl0_27,
inference(avatar_split_clause,[],[f62,f404]) ).
fof(f404,plain,
( spl0_27
<=> ! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f62,axiom,
! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).
fof(f402,plain,
spl0_26,
inference(avatar_split_clause,[],[f57,f400]) ).
fof(f400,plain,
( spl0_26
<=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f57,axiom,
! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).
fof(f398,plain,
spl0_25,
inference(avatar_split_clause,[],[f24,f396]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f390,plain,
spl0_24,
inference(avatar_split_clause,[],[f105,f388]) ).
fof(f388,plain,
( spl0_24
<=> ! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f105,axiom,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_of_null_class_is_subclass) ).
fof(f386,plain,
spl0_23,
inference(avatar_split_clause,[],[f102,f384]) ).
fof(f102,axiom,
! [X0,X1] : ~ member(X1,intersection(complement(X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',special_classes_lemma) ).
fof(f382,plain,
spl0_22,
inference(avatar_split_clause,[],[f87,f380]) ).
fof(f380,plain,
( spl0_22
<=> ! [X9,X11,X10] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f87,axiom,
! [X10,X11,X9] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
fof(f378,plain,
spl0_21,
inference(avatar_split_clause,[],[f86,f376]) ).
fof(f376,plain,
( spl0_21
<=> ! [X9,X11,X10] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f86,axiom,
! [X10,X11,X9] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
fof(f374,plain,
spl0_20,
inference(avatar_split_clause,[],[f82,f372]) ).
fof(f372,plain,
( spl0_20
<=> ! [X9,X11,X10] :
( function(X9)
| ~ compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f82,axiom,
! [X10,X11,X9] :
( function(X9)
| ~ compatible(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible1) ).
fof(f370,plain,
( ~ spl0_19
| ~ spl0_7
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f365,f353,f313,f367]) ).
fof(f367,plain,
( spl0_19
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f313,plain,
( spl0_7
<=> ! [X4] : ~ member(X4,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f365,plain,
( ~ inductive(null_class)
| ~ spl0_7
| ~ spl0_16 ),
inference(resolution,[],[f354,f314]) ).
fof(f314,plain,
( ! [X4] : ~ member(X4,null_class)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f364,plain,
spl0_18,
inference(avatar_split_clause,[],[f174,f361]) ).
fof(f361,plain,
( spl0_18
<=> member(null_class,unordered_pair(null_class,null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f174,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/sandbox2/benchmark/theBenchmark.p',null_class_in_its_singleton) ).
fof(f359,plain,
spl0_17,
inference(avatar_split_clause,[],[f51,f357]) ).
fof(f357,plain,
( spl0_17
<=> ! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f51,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).
fof(f355,plain,
spl0_16,
inference(avatar_split_clause,[],[f47,f353]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).
fof(f351,plain,
spl0_15,
inference(avatar_split_clause,[],[f44,f348]) ).
fof(f348,plain,
( spl0_15
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation1) ).
fof(f346,plain,
spl0_14,
inference(avatar_split_clause,[],[f18,f343]) ).
fof(f343,plain,
( spl0_14
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).
fof(f341,plain,
spl0_13,
inference(avatar_split_clause,[],[f11,f339]) ).
fof(f339,plain,
( spl0_13
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f337,plain,
~ spl0_12,
inference(avatar_split_clause,[],[f173,f334]) ).
fof(f173,plain,
~ member(unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))),cross_product(universal_class,universal_class)),
inference(definition_unfolding,[],[f160,f166]) ).
fof(f160,axiom,
~ member(ordered_pair(first(x),second(x)),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_non_sets2_1) ).
fof(f332,plain,
spl0_11,
inference(avatar_split_clause,[],[f78,f330]) ).
fof(f330,plain,
( spl0_11
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).
fof(f328,plain,
spl0_10,
inference(avatar_split_clause,[],[f71,f326]) ).
fof(f326,plain,
( spl0_10
<=> ! [X8] :
( ~ one_to_one(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f71,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).
fof(f324,plain,
spl0_9,
inference(avatar_split_clause,[],[f107,f321]) ).
fof(f107,axiom,
member(null_class,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_a_set) ).
fof(f319,plain,
spl0_8,
inference(avatar_split_clause,[],[f104,f317]) ).
fof(f104,axiom,
! [X0] : subclass(null_class,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_subclass) ).
fof(f315,plain,
spl0_7,
inference(avatar_split_clause,[],[f103,f313]) ).
fof(f103,axiom,
! [X4] : ~ member(X4,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f311,plain,
spl0_6,
inference(avatar_split_clause,[],[f96,f309]) ).
fof(f309,plain,
( spl0_6
<=> ! [X0] : subclass(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f96,axiom,
! [X0] : subclass(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_is_reflexive) ).
fof(f307,plain,
spl0_5,
inference(avatar_split_clause,[],[f52,f304]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f302,plain,
spl0_4,
inference(avatar_split_clause,[],[f4,f300]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f298,plain,
spl0_3,
inference(avatar_split_clause,[],[f69,f295]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).
fof(f293,plain,
spl0_2,
inference(avatar_split_clause,[],[f50,f290]) ).
fof(f290,plain,
( spl0_2
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f288,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f161,f285]) ).
fof(f161,axiom,
x != second(x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_2nd_in_pair_of_non_sets) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET114-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 30 01:28:28 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (31186)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (31195)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (31194)WARNING: value z3 for option sas not known
% 0.14/0.38 % (31191)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (31193)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (31196)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (31194)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (31198)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 % (31197)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)
% 0.21/0.43 TRYING [1]
% 0.21/0.44 TRYING [1]
% 0.21/0.44 TRYING [2]
% 0.21/0.44 TRYING [2]
% 0.21/0.46 TRYING [3]
% 0.21/0.52 TRYING [3]
% 0.21/0.52 TRYING [1]
% 0.21/0.52 TRYING [4]
% 0.21/0.53 % (31196)First to succeed.
% 0.21/0.53 TRYING [2]
% 0.21/0.54 % (31194)Also succeeded, but the first one will report.
% 0.21/0.54 % (31196)Refutation found. Thanks to Tanya!
% 0.21/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.55 % (31196)------------------------------
% 0.21/0.55 % (31196)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.55 % (31196)Termination reason: Refutation
% 0.21/0.55
% 0.21/0.55 % (31196)Memory used [KB]: 2561
% 0.21/0.55 % (31196)Time elapsed: 0.158 s
% 0.21/0.55 % (31196)Instructions burned: 380 (million)
% 0.21/0.55 % (31196)------------------------------
% 0.21/0.55 % (31196)------------------------------
% 0.21/0.55 % (31186)Success in time 0.181 s
%------------------------------------------------------------------------------