TSTP Solution File: SEU395+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU395+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n026.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 : Thu Aug 31 17:58:43 EDT 2023
% Result : Theorem 0.22s 0.48s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 454
% Syntax : Number of formulae : 1735 ( 165 unt; 0 def)
% Number of atoms : 6765 ( 117 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 8036 (3006 ~;3341 |;1192 &)
% ( 331 <=>; 164 =>; 0 <=; 2 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 403 ( 401 usr; 320 prp; 0-8 aty)
% Number of functors : 37 ( 37 usr; 11 con; 0-4 aty)
% Number of variables : 1225 (;1099 !; 126 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3557,plain,
$false,
inference(avatar_sat_refutation,[],[f995,f996,f1031,f1036,f1041,f1046,f1052,f1058,f1060,f1065,f1070,f1075,f1080,f1085,f1090,f1095,f1101,f1106,f1112,f1117,f1151,f1157,f1174,f1178,f1184,f1189,f1193,f1201,f1205,f1209,f1215,f1220,f1225,f1230,f1234,f1255,f1259,f1268,f1273,f1292,f1385,f1431,f1453,f1469,f1517,f1518,f1519,f1520,f1525,f1526,f1527,f1528,f1533,f1534,f1535,f1536,f1541,f1542,f1543,f1548,f1559,f1564,f1566,f1568,f1575,f1576,f1577,f1578,f1583,f1588,f1625,f1638,f1651,f1656,f1665,f1674,f1695,f1700,f1705,f1706,f1707,f1708,f1713,f1718,f1723,f1728,f1733,f1734,f1739,f1771,f1784,f1797,f1802,f1811,f1820,f1841,f1846,f1851,f1852,f1853,f1854,f1859,f1864,f1869,f1874,f1879,f1880,f1885,f1919,f2042,f2052,f2057,f2058,f2059,f2060,f2065,f2066,f2067,f2068,f2091,f2093,f2095,f2108,f2112,f2119,f2137,f2138,f2139,f2140,f2185,f2190,f2194,f2226,f2243,f2252,f2253,f2262,f2272,f2277,f2282,f2287,f2292,f2297,f2298,f2299,f2304,f2309,f2318,f2323,f2332,f2337,f2342,f2347,f2352,f2355,f2360,f2372,f2374,f2376,f2386,f2394,f2400,f2402,f2407,f2424,f2426,f2435,f2438,f2439,f2446,f2447,f2448,f2449,f2455,f2456,f2457,f2462,f2472,f2474,f2483,f2490,f2491,f2492,f2493,f2498,f2503,f2516,f2525,f2551,f2571,f2593,f2632,f2636,f2640,f2645,f2650,f2654,f2658,f2662,f2666,f2670,f2674,f2678,f2682,f2686,f2724,f2754,f2785,f2787,f2806,f2820,f2823,f2826,f2873,f2878,f2914,f2925,f2929,f2933,f2943,f2948,f2949,f2950,f2951,f2967,f2971,f2975,f2976,f2981,f2982,f2983,f2984,f2993,f2994,f2995,f2996,f3012,f3020,f3024,f3025,f3030,f3031,f3032,f3037,f3041,f3050,f3051,f3052,f3053,f3058,f3063,f3073,f3084,f3085,f3086,f3087,f3093,f3094,f3095,f3096,f3103,f3104,f3105,f3106,f3112,f3113,f3114,f3119,f3122,f3130,f3131,f3132,f3133,f3138,f3143,f3156,f3161,f3166,f3171,f3184,f3189,f3193,f3199,f3231,f3240,f3253,f3258,f3267,f3276,f3293,f3298,f3303,f3304,f3305,f3306,f3311,f3316,f3321,f3326,f3331,f3332,f3337,f3383,f3387,f3391,f3396,f3401,f3405,f3409,f3413,f3417,f3421,f3425,f3429,f3433,f3437,f3451,f3485,f3489,f3493,f3494,f3544,f3548,f3549,f3553,f3556]) ).
fof(f3556,plain,
( ~ spl88_1
| ~ spl88_319
| spl88_2
| ~ spl88_270 ),
inference(avatar_split_clause,[],[f3555,f3164,f992,f3541,f988]) ).
fof(f988,plain,
( spl88_1
<=> in(sK35,sF83) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_1])]) ).
fof(f3541,plain,
( spl88_319
<=> element(sK35,sF84) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_319])]) ).
fof(f992,plain,
( spl88_2
<=> is_a_convergence_point_of_set(sK33,sK34,sK35) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_2])]) ).
fof(f3164,plain,
( spl88_270
<=> ! [X1] :
( ~ in(X1,sF83)
| ~ element(X1,sF84)
| is_a_convergence_point_of_set(sK33,sK34,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_270])]) ).
fof(f3555,plain,
( ~ element(sK35,sF84)
| ~ in(sK35,sF83)
| spl88_2
| ~ spl88_270 ),
inference(resolution,[],[f994,f3165]) ).
fof(f3165,plain,
( ! [X1] :
( is_a_convergence_point_of_set(sK33,sK34,X1)
| ~ element(X1,sF84)
| ~ in(X1,sF83) )
| ~ spl88_270 ),
inference(avatar_component_clause,[],[f3164]) ).
fof(f994,plain,
( ~ is_a_convergence_point_of_set(sK33,sK34,sK35)
| spl88_2 ),
inference(avatar_component_clause,[],[f992]) ).
fof(f3553,plain,
( ~ spl88_41
| ~ spl88_1 ),
inference(avatar_split_clause,[],[f3551,f988,f1289]) ).
fof(f1289,plain,
( spl88_41
<=> empty(sF83) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_41])]) ).
fof(f3551,plain,
( ~ empty(sF83)
| ~ spl88_1 ),
inference(resolution,[],[f989,f851]) ).
fof(f851,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f337]) ).
fof(f337,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f136]) ).
fof(f136,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',t7_boole) ).
fof(f989,plain,
( in(sK35,sF83)
| ~ spl88_1 ),
inference(avatar_component_clause,[],[f988]) ).
fof(f3549,plain,
( ~ spl88_1
| spl88_40 ),
inference(avatar_split_clause,[],[f1325,f1285,f988]) ).
fof(f1285,plain,
( spl88_40
<=> element(sK35,sF83) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_40])]) ).
fof(f1325,plain,
( ~ in(sK35,sF83)
| spl88_40 ),
inference(resolution,[],[f1287,f821]) ).
fof(f821,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f311]) ).
fof(f311,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f129]) ).
fof(f129,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',t1_subset) ).
fof(f1287,plain,
( ~ element(sK35,sF83)
| spl88_40 ),
inference(avatar_component_clause,[],[f1285]) ).
fof(f3548,plain,
spl88_319,
inference(avatar_contradiction_clause,[],[f3545]) ).
fof(f3545,plain,
( $false
| spl88_319 ),
inference(resolution,[],[f3543,f979]) ).
fof(f979,plain,
element(sK35,sF84),
inference(definition_folding,[],[f566,f978]) ).
fof(f978,plain,
the_carrier(sK33) = sF84,
introduced(function_definition,[]) ).
fof(f566,plain,
element(sK35,the_carrier(sK33)),
inference(cnf_transformation,[],[f426]) ).
fof(f426,plain,
( ( ~ is_a_convergence_point_of_set(sK33,sK34,sK35)
| ~ in(sK35,lim_points_of_net(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),sK34))) )
& ( is_a_convergence_point_of_set(sK33,sK34,sK35)
| in(sK35,lim_points_of_net(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),sK34))) )
& element(sK35,the_carrier(sK33))
& element(sK34,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33)))))
& proper_element(sK34,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33)))))
& upper_relstr_subset(sK34,boole_POSet(cast_as_carrier_subset(sK33)))
& filtered_subset(sK34,boole_POSet(cast_as_carrier_subset(sK33)))
& ~ empty(sK34)
& top_str(sK33)
& topological_space(sK33)
& ~ empty_carrier(sK33) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34,sK35])],[f422,f425,f424,f423]) ).
fof(f423,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(X0,X1,X2)
| ~ in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& ( is_a_convergence_point_of_set(X0,X1,X2)
| in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(sK33,X1,X2)
| ~ in(X2,lim_points_of_net(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1))) )
& ( is_a_convergence_point_of_set(sK33,X1,X2)
| in(X2,lim_points_of_net(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1))) )
& element(X2,the_carrier(sK33)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
& ~ empty(X1) )
& top_str(sK33)
& topological_space(sK33)
& ~ empty_carrier(sK33) ) ),
introduced(choice_axiom,[]) ).
fof(f424,plain,
( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(sK33,X1,X2)
| ~ in(X2,lim_points_of_net(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1))) )
& ( is_a_convergence_point_of_set(sK33,X1,X2)
| in(X2,lim_points_of_net(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1))) )
& element(X2,the_carrier(sK33)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
& ~ empty(X1) )
=> ( ? [X2] :
( ( ~ is_a_convergence_point_of_set(sK33,sK34,X2)
| ~ in(X2,lim_points_of_net(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),sK34))) )
& ( is_a_convergence_point_of_set(sK33,sK34,X2)
| in(X2,lim_points_of_net(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),sK34))) )
& element(X2,the_carrier(sK33)) )
& element(sK34,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33)))))
& proper_element(sK34,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33)))))
& upper_relstr_subset(sK34,boole_POSet(cast_as_carrier_subset(sK33)))
& filtered_subset(sK34,boole_POSet(cast_as_carrier_subset(sK33)))
& ~ empty(sK34) ) ),
introduced(choice_axiom,[]) ).
fof(f425,plain,
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(sK33,sK34,X2)
| ~ in(X2,lim_points_of_net(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),sK34))) )
& ( is_a_convergence_point_of_set(sK33,sK34,X2)
| in(X2,lim_points_of_net(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),sK34))) )
& element(X2,the_carrier(sK33)) )
=> ( ( ~ is_a_convergence_point_of_set(sK33,sK34,sK35)
| ~ in(sK35,lim_points_of_net(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),sK34))) )
& ( is_a_convergence_point_of_set(sK33,sK34,sK35)
| in(sK35,lim_points_of_net(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),sK34))) )
& element(sK35,the_carrier(sK33)) ) ),
introduced(choice_axiom,[]) ).
fof(f422,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(X0,X1,X2)
| ~ in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& ( is_a_convergence_point_of_set(X0,X1,X2)
| in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f421]) ).
fof(f421,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ is_a_convergence_point_of_set(X0,X1,X2)
| ~ in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& ( is_a_convergence_point_of_set(X0,X1,X2)
| in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1))) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(nnf_transformation,[],[f196]) ).
fof(f196,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)))
<~> is_a_convergence_point_of_set(X0,X1,X2) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f195]) ).
fof(f195,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)))
<~> is_a_convergence_point_of_set(X0,X1,X2) )
& element(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f128]) ).
fof(f128,negated_conjecture,
~ ! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)))
<=> is_a_convergence_point_of_set(X0,X1,X2) ) ) ) ),
inference(negated_conjecture,[],[f127]) ).
fof(f127,conjecture,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,lim_points_of_net(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)))
<=> is_a_convergence_point_of_set(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',t18_yellow19) ).
fof(f3543,plain,
( ~ element(sK35,sF84)
| spl88_319 ),
inference(avatar_component_clause,[],[f3541]) ).
fof(f3544,plain,
( spl88_1
| ~ spl88_319
| ~ spl88_2
| ~ spl88_271 ),
inference(avatar_split_clause,[],[f3537,f3169,f992,f3541,f988]) ).
fof(f3169,plain,
( spl88_271
<=> ! [X0] :
( in(X0,sF83)
| ~ element(X0,sF84)
| ~ is_a_convergence_point_of_set(sK33,sK34,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_271])]) ).
fof(f3537,plain,
( ~ element(sK35,sF84)
| in(sK35,sF83)
| ~ spl88_2
| ~ spl88_271 ),
inference(resolution,[],[f3170,f993]) ).
fof(f993,plain,
( is_a_convergence_point_of_set(sK33,sK34,sK35)
| ~ spl88_2 ),
inference(avatar_component_clause,[],[f992]) ).
fof(f3170,plain,
( ! [X0] :
( ~ is_a_convergence_point_of_set(sK33,sK34,X0)
| ~ element(X0,sF84)
| in(X0,sF83) )
| ~ spl88_271 ),
inference(avatar_component_clause,[],[f3169]) ).
fof(f3494,plain,
( ~ spl88_314
| spl88_317
| ~ spl88_316
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3473,f1434,f3482,f3487,f3475]) ).
fof(f3475,plain,
( spl88_314
<=> function(the_mapping(sK33,sF82)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_314])]) ).
fof(f3487,plain,
( spl88_317
<=> ! [X5] :
( ~ relation_of2_as_subset(X5,the_carrier(sF82),the_carrier(sF82))
| strict_net_str(net_str_of(sK33,the_carrier(sF82),X5,the_mapping(sK33,sF82)),sK33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_317])]) ).
fof(f3482,plain,
( spl88_316
<=> relation_of2_as_subset(the_mapping(sK33,sF82),the_carrier(sF82),sF84) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_316])]) ).
fof(f1434,plain,
( spl88_56
<=> net_str(sF82,sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_56])]) ).
fof(f3473,plain,
( ! [X7] :
( ~ relation_of2_as_subset(the_mapping(sK33,sF82),the_carrier(sF82),sF84)
| ~ relation_of2_as_subset(X7,the_carrier(sF82),the_carrier(sF82))
| ~ function(the_mapping(sK33,sF82))
| strict_net_str(net_str_of(sK33,the_carrier(sF82),X7,the_mapping(sK33,sF82)),sK33) )
| ~ spl88_56 ),
inference(resolution,[],[f3176,f1242]) ).
fof(f1242,plain,
! [X21,X22,X23] :
( ~ quasi_total(X21,X22,sF84)
| ~ relation_of2_as_subset(X21,X22,sF84)
| ~ relation_of2_as_subset(X23,X22,X22)
| ~ function(X21)
| strict_net_str(net_str_of(sK33,X22,X23,X21),sK33) ),
inference(forward_literal_rewriting,[],[f1241,f878]) ).
fof(f878,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f525]) ).
fof(f525,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f123]) ).
fof(f123,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',redefinition_m2_relset_1) ).
fof(f1241,plain,
! [X21,X22,X23] :
( ~ relation_of2_as_subset(X21,X22,sF84)
| ~ quasi_total(X21,X22,sF84)
| ~ function(X21)
| ~ relation_of2(X23,X22,X22)
| strict_net_str(net_str_of(sK33,X22,X23,X21),sK33) ),
inference(forward_literal_rewriting,[],[f1240,f878]) ).
fof(f1240,plain,
! [X21,X22,X23] :
( ~ quasi_total(X21,X22,sF84)
| ~ relation_of2(X21,X22,sF84)
| ~ function(X21)
| ~ relation_of2(X23,X22,X22)
| strict_net_str(net_str_of(sK33,X22,X23,X21),sK33) ),
inference(forward_demodulation,[],[f1239,f978]) ).
fof(f1239,plain,
! [X21,X22,X23] :
( ~ relation_of2(X21,X22,sF84)
| ~ quasi_total(X21,X22,the_carrier(sK33))
| ~ function(X21)
| ~ relation_of2(X23,X22,X22)
| strict_net_str(net_str_of(sK33,X22,X23,X21),sK33) ),
inference(forward_demodulation,[],[f1141,f978]) ).
fof(f1141,plain,
! [X21,X22,X23] :
( ~ relation_of2(X21,X22,the_carrier(sK33))
| ~ quasi_total(X21,X22,the_carrier(sK33))
| ~ function(X21)
| ~ relation_of2(X23,X22,X22)
| strict_net_str(net_str_of(sK33,X22,X23,X21),sK33) ),
inference(resolution,[],[f997,f883]) ).
fof(f883,plain,
! [X2,X3,X0,X1] :
( ~ one_sorted_str(X0)
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| strict_net_str(net_str_of(X0,X1,X2,X3),X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f353,plain,
! [X0,X1,X2,X3] :
( ( net_str(net_str_of(X0,X1,X2,X3),X0)
& strict_net_str(net_str_of(X0,X1,X2,X3),X0) )
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f352]) ).
fof(f352,plain,
! [X0,X1,X2,X3] :
( ( net_str(net_str_of(X0,X1,X2,X3),X0)
& strict_net_str(net_str_of(X0,X1,X2,X3),X0) )
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1,X2,X3] :
( ( relation_of2(X3,X1,the_carrier(X0))
& quasi_total(X3,X1,the_carrier(X0))
& function(X3)
& relation_of2(X2,X1,X1)
& one_sorted_str(X0) )
=> ( net_str(net_str_of(X0,X1,X2,X3),X0)
& strict_net_str(net_str_of(X0,X1,X2,X3),X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',dt_g1_waybel_0) ).
fof(f997,plain,
one_sorted_str(sK33),
inference(resolution,[],[f560,f642]) ).
fof(f642,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',dt_l1_pre_topc) ).
fof(f560,plain,
top_str(sK33),
inference(cnf_transformation,[],[f426]) ).
fof(f3176,plain,
( quasi_total(the_mapping(sK33,sF82),the_carrier(sF82),sF84)
| ~ spl88_56 ),
inference(resolution,[],[f1435,f1888]) ).
fof(f1888,plain,
! [X0] :
( ~ net_str(X0,sK33)
| quasi_total(the_mapping(sK33,X0),the_carrier(X0),sF84) ),
inference(forward_demodulation,[],[f1886,f978]) ).
fof(f1886,plain,
! [X0] :
( ~ net_str(X0,sK33)
| quasi_total(the_mapping(sK33,X0),the_carrier(X0),the_carrier(sK33)) ),
inference(resolution,[],[f1134,f842]) ).
fof(f842,plain,
! [X0,X1] :
( ~ sP26(X0,X1)
| quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0)) ),
inference(cnf_transformation,[],[f506]) ).
fof(f506,plain,
! [X0,X1] :
( ( relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1)) )
| ~ sP26(X0,X1) ),
inference(nnf_transformation,[],[f408]) ).
fof(f408,plain,
! [X0,X1] :
( ( relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1)) )
| ~ sP26(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP26])]) ).
fof(f1134,plain,
! [X8] :
( sP26(sK33,X8)
| ~ net_str(X8,sK33) ),
inference(resolution,[],[f997,f844]) ).
fof(f844,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| sP26(X0,X1) ),
inference(cnf_transformation,[],[f409]) ).
fof(f409,plain,
! [X0,X1] :
( sP26(X0,X1)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(definition_folding,[],[f329,f408]) ).
fof(f329,plain,
! [X0,X1] :
( ( relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1)) )
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f328]) ).
fof(f328,plain,
! [X0,X1] :
( ( relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1)) )
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& one_sorted_str(X0) )
=> ( relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',dt_u1_waybel_0) ).
fof(f1435,plain,
( net_str(sF82,sK33)
| ~ spl88_56 ),
inference(avatar_component_clause,[],[f1434]) ).
fof(f3493,plain,
( ~ spl88_314
| spl88_318
| ~ spl88_316
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3472,f1434,f3482,f3491,f3475]) ).
fof(f3491,plain,
( spl88_318
<=> ! [X6] :
( ~ relation_of2_as_subset(X6,the_carrier(sF82),the_carrier(sF82))
| net_str(net_str_of(sK33,the_carrier(sF82),X6,the_mapping(sK33,sF82)),sK33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_318])]) ).
fof(f3472,plain,
( ! [X6] :
( ~ relation_of2_as_subset(the_mapping(sK33,sF82),the_carrier(sF82),sF84)
| ~ relation_of2_as_subset(X6,the_carrier(sF82),the_carrier(sF82))
| ~ function(the_mapping(sK33,sF82))
| net_str(net_str_of(sK33,the_carrier(sF82),X6,the_mapping(sK33,sF82)),sK33) )
| ~ spl88_56 ),
inference(resolution,[],[f3176,f1246]) ).
fof(f1246,plain,
! [X26,X24,X25] :
( ~ quasi_total(X24,X25,sF84)
| ~ relation_of2_as_subset(X24,X25,sF84)
| ~ relation_of2_as_subset(X26,X25,X25)
| ~ function(X24)
| net_str(net_str_of(sK33,X25,X26,X24),sK33) ),
inference(forward_literal_rewriting,[],[f1245,f878]) ).
fof(f1245,plain,
! [X26,X24,X25] :
( ~ relation_of2_as_subset(X24,X25,sF84)
| ~ quasi_total(X24,X25,sF84)
| ~ function(X24)
| ~ relation_of2(X26,X25,X25)
| net_str(net_str_of(sK33,X25,X26,X24),sK33) ),
inference(forward_literal_rewriting,[],[f1244,f878]) ).
fof(f1244,plain,
! [X26,X24,X25] :
( ~ quasi_total(X24,X25,sF84)
| ~ relation_of2(X24,X25,sF84)
| ~ function(X24)
| ~ relation_of2(X26,X25,X25)
| net_str(net_str_of(sK33,X25,X26,X24),sK33) ),
inference(forward_demodulation,[],[f1243,f978]) ).
fof(f1243,plain,
! [X26,X24,X25] :
( ~ relation_of2(X24,X25,sF84)
| ~ quasi_total(X24,X25,the_carrier(sK33))
| ~ function(X24)
| ~ relation_of2(X26,X25,X25)
| net_str(net_str_of(sK33,X25,X26,X24),sK33) ),
inference(forward_demodulation,[],[f1142,f978]) ).
fof(f1142,plain,
! [X26,X24,X25] :
( ~ relation_of2(X24,X25,the_carrier(sK33))
| ~ quasi_total(X24,X25,the_carrier(sK33))
| ~ function(X24)
| ~ relation_of2(X26,X25,X25)
| net_str(net_str_of(sK33,X25,X26,X24),sK33) ),
inference(resolution,[],[f997,f884]) ).
fof(f884,plain,
! [X2,X3,X0,X1] :
( ~ one_sorted_str(X0)
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| net_str(net_str_of(X0,X1,X2,X3),X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f3489,plain,
( spl88_300
| ~ spl88_314
| spl88_317
| ~ spl88_316
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3471,f1434,f3482,f3487,f3475,f3380]) ).
fof(f3380,plain,
( spl88_300
<=> empty(the_carrier(sF82)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_300])]) ).
fof(f3471,plain,
( ! [X5] :
( ~ relation_of2_as_subset(the_mapping(sK33,sF82),the_carrier(sF82),sF84)
| ~ relation_of2_as_subset(X5,the_carrier(sF82),the_carrier(sF82))
| ~ function(the_mapping(sK33,sF82))
| empty(the_carrier(sF82))
| strict_net_str(net_str_of(sK33,the_carrier(sF82),X5,the_mapping(sK33,sF82)),sK33) )
| ~ spl88_56 ),
inference(resolution,[],[f3176,f1238]) ).
fof(f1238,plain,
! [X18,X19,X20] :
( ~ quasi_total(X18,X19,sF84)
| ~ relation_of2_as_subset(X18,X19,sF84)
| ~ relation_of2_as_subset(X20,X19,X19)
| ~ function(X18)
| empty(X19)
| strict_net_str(net_str_of(sK33,X19,X20,X18),sK33) ),
inference(forward_literal_rewriting,[],[f1237,f878]) ).
fof(f1237,plain,
! [X18,X19,X20] :
( ~ relation_of2_as_subset(X18,X19,sF84)
| ~ quasi_total(X18,X19,sF84)
| ~ function(X18)
| ~ relation_of2(X20,X19,X19)
| empty(X19)
| strict_net_str(net_str_of(sK33,X19,X20,X18),sK33) ),
inference(forward_literal_rewriting,[],[f1236,f878]) ).
fof(f1236,plain,
! [X18,X19,X20] :
( ~ quasi_total(X18,X19,sF84)
| ~ relation_of2(X18,X19,sF84)
| ~ function(X18)
| ~ relation_of2(X20,X19,X19)
| empty(X19)
| strict_net_str(net_str_of(sK33,X19,X20,X18),sK33) ),
inference(forward_demodulation,[],[f1235,f978]) ).
fof(f1235,plain,
! [X18,X19,X20] :
( ~ relation_of2(X18,X19,sF84)
| ~ quasi_total(X18,X19,the_carrier(sK33))
| ~ function(X18)
| ~ relation_of2(X20,X19,X19)
| empty(X19)
| strict_net_str(net_str_of(sK33,X19,X20,X18),sK33) ),
inference(forward_demodulation,[],[f1140,f978]) ).
fof(f1140,plain,
! [X18,X19,X20] :
( ~ relation_of2(X18,X19,the_carrier(sK33))
| ~ quasi_total(X18,X19,the_carrier(sK33))
| ~ function(X18)
| ~ relation_of2(X20,X19,X19)
| empty(X19)
| strict_net_str(net_str_of(sK33,X19,X20,X18),sK33) ),
inference(resolution,[],[f997,f882]) ).
fof(f882,plain,
! [X2,X3,X0,X1] :
( ~ one_sorted_str(X0)
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| empty(X1)
| strict_net_str(net_str_of(X0,X1,X2,X3),X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f351,plain,
! [X0,X1,X2,X3] :
( ( strict_net_str(net_str_of(X0,X1,X2,X3),X0)
& ~ empty_carrier(net_str_of(X0,X1,X2,X3)) )
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| empty(X1)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f350]) ).
fof(f350,plain,
! [X0,X1,X2,X3] :
( ( strict_net_str(net_str_of(X0,X1,X2,X3),X0)
& ~ empty_carrier(net_str_of(X0,X1,X2,X3)) )
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| empty(X1)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,axiom,
! [X0,X1,X2,X3] :
( ( relation_of2(X3,X1,the_carrier(X0))
& quasi_total(X3,X1,the_carrier(X0))
& function(X3)
& relation_of2(X2,X1,X1)
& ~ empty(X1)
& one_sorted_str(X0) )
=> ( strict_net_str(net_str_of(X0,X1,X2,X3),X0)
& ~ empty_carrier(net_str_of(X0,X1,X2,X3)) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc6_waybel_0) ).
fof(f3485,plain,
( ~ spl88_314
| spl88_315
| ~ spl88_316
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3470,f1434,f3482,f3479,f3475]) ).
fof(f3479,plain,
( spl88_315
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation_of2_as_subset(X0,the_carrier(sF82),the_carrier(sF82))
| sP32(X4,the_mapping(sK33,sF82),X3,X0,X2,the_carrier(sF82),X1,sK33)
| net_str_of(X1,X2,X3,X4) != net_str_of(sK33,the_carrier(sF82),X0,the_mapping(sK33,sF82)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_315])]) ).
fof(f3470,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(the_mapping(sK33,sF82),the_carrier(sF82),sF84)
| ~ relation_of2_as_subset(X0,the_carrier(sF82),the_carrier(sF82))
| net_str_of(X1,X2,X3,X4) != net_str_of(sK33,the_carrier(sF82),X0,the_mapping(sK33,sF82))
| ~ function(the_mapping(sK33,sF82))
| sP32(X4,the_mapping(sK33,sF82),X3,X0,X2,the_carrier(sF82),X1,sK33) )
| ~ spl88_56 ),
inference(resolution,[],[f3176,f1250]) ).
fof(f1250,plain,
! [X31,X28,X29,X27,X32,X30,X33] :
( ~ quasi_total(X29,X27,sF84)
| ~ relation_of2_as_subset(X29,X27,sF84)
| ~ relation_of2_as_subset(X28,X27,X27)
| net_str_of(sK33,X27,X28,X29) != net_str_of(X30,X31,X32,X33)
| ~ function(X29)
| sP32(X33,X29,X32,X28,X31,X27,X30,sK33) ),
inference(forward_literal_rewriting,[],[f1249,f878]) ).
fof(f1249,plain,
! [X31,X28,X29,X27,X32,X30,X33] :
( ~ relation_of2_as_subset(X29,X27,sF84)
| ~ quasi_total(X29,X27,sF84)
| net_str_of(sK33,X27,X28,X29) != net_str_of(X30,X31,X32,X33)
| ~ function(X29)
| ~ relation_of2(X28,X27,X27)
| sP32(X33,X29,X32,X28,X31,X27,X30,sK33) ),
inference(forward_literal_rewriting,[],[f1248,f878]) ).
fof(f1248,plain,
! [X31,X28,X29,X27,X32,X30,X33] :
( ~ quasi_total(X29,X27,sF84)
| ~ relation_of2(X29,X27,sF84)
| net_str_of(sK33,X27,X28,X29) != net_str_of(X30,X31,X32,X33)
| ~ function(X29)
| ~ relation_of2(X28,X27,X27)
| sP32(X33,X29,X32,X28,X31,X27,X30,sK33) ),
inference(forward_demodulation,[],[f1247,f978]) ).
fof(f1247,plain,
! [X31,X28,X29,X27,X32,X30,X33] :
( ~ relation_of2(X29,X27,sF84)
| net_str_of(sK33,X27,X28,X29) != net_str_of(X30,X31,X32,X33)
| ~ quasi_total(X29,X27,the_carrier(sK33))
| ~ function(X29)
| ~ relation_of2(X28,X27,X27)
| sP32(X33,X29,X32,X28,X31,X27,X30,sK33) ),
inference(forward_demodulation,[],[f1143,f978]) ).
fof(f1143,plain,
! [X31,X28,X29,X27,X32,X30,X33] :
( net_str_of(sK33,X27,X28,X29) != net_str_of(X30,X31,X32,X33)
| ~ relation_of2(X29,X27,the_carrier(sK33))
| ~ quasi_total(X29,X27,the_carrier(sK33))
| ~ function(X29)
| ~ relation_of2(X28,X27,X27)
| sP32(X33,X29,X32,X28,X31,X27,X30,sK33) ),
inference(resolution,[],[f997,f889]) ).
fof(f889,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ one_sorted_str(X0)
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7)
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| sP32(X7,X3,X6,X2,X5,X1,X4,X0) ),
inference(cnf_transformation,[],[f420]) ).
fof(f420,plain,
! [X0,X1,X2,X3] :
( ! [X4,X5,X6,X7] :
( sP32(X7,X3,X6,X2,X5,X1,X4,X0)
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7) )
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ),
inference(definition_folding,[],[f355,f419]) ).
fof(f419,plain,
! [X7,X3,X6,X2,X5,X1,X4,X0] :
( ( X3 = X7
& X2 = X6
& X1 = X5
& X0 = X4 )
| ~ sP32(X7,X3,X6,X2,X5,X1,X4,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP32])]) ).
fof(f355,plain,
! [X0,X1,X2,X3] :
( ! [X4,X5,X6,X7] :
( ( X3 = X7
& X2 = X6
& X1 = X5
& X0 = X4 )
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7) )
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f354]) ).
fof(f354,plain,
! [X0,X1,X2,X3] :
( ! [X4,X5,X6,X7] :
( ( X3 = X7
& X2 = X6
& X1 = X5
& X0 = X4 )
| net_str_of(X0,X1,X2,X3) != net_str_of(X4,X5,X6,X7) )
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0,X1,X2,X3] :
( ( relation_of2(X3,X1,the_carrier(X0))
& quasi_total(X3,X1,the_carrier(X0))
& function(X3)
& relation_of2(X2,X1,X1)
& one_sorted_str(X0) )
=> ! [X4,X5,X6,X7] :
( net_str_of(X0,X1,X2,X3) = net_str_of(X4,X5,X6,X7)
=> ( X3 = X7
& X2 = X6
& X1 = X5
& X0 = X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',free_g1_waybel_0) ).
fof(f3451,plain,
( ~ spl88_193
| spl88_281 ),
inference(avatar_contradiction_clause,[],[f3450]) ).
fof(f3450,plain,
( $false
| ~ spl88_193
| spl88_281 ),
inference(resolution,[],[f3248,f2821]) ).
fof(f2821,plain,
( reflexive_relstr(sF82)
| ~ spl88_193 ),
inference(forward_demodulation,[],[f2815,f974]) ).
fof(f974,plain,
net_of_bool_filter(sK33,sF81,sK34) = sF82,
introduced(function_definition,[]) ).
fof(f2815,plain,
( reflexive_relstr(net_of_bool_filter(sK33,sF81,sK34))
| ~ spl88_193 ),
inference(resolution,[],[f2570,f856]) ).
fof(f856,plain,
! [X2,X0,X1] :
( ~ sP27(X0,X1,X2)
| reflexive_relstr(net_of_bool_filter(X2,X1,X0)) ),
inference(cnf_transformation,[],[f515]) ).
fof(f515,plain,
! [X0,X1,X2] :
( ( directed_relstr(net_of_bool_filter(X2,X1,X0))
& strict_net_str(net_of_bool_filter(X2,X1,X0),X2)
& transitive_relstr(net_of_bool_filter(X2,X1,X0))
& reflexive_relstr(net_of_bool_filter(X2,X1,X0))
& ~ empty_carrier(net_of_bool_filter(X2,X1,X0)) )
| ~ sP27(X0,X1,X2) ),
inference(rectify,[],[f514]) ).
fof(f514,plain,
! [X2,X1,X0] :
( ( directed_relstr(net_of_bool_filter(X0,X1,X2))
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ sP27(X2,X1,X0) ),
inference(nnf_transformation,[],[f410]) ).
fof(f410,plain,
! [X2,X1,X0] :
( ( directed_relstr(net_of_bool_filter(X0,X1,X2))
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ sP27(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP27])]) ).
fof(f2570,plain,
( sP27(sK34,sF81,sK33)
| ~ spl88_193 ),
inference(avatar_component_clause,[],[f2568]) ).
fof(f2568,plain,
( spl88_193
<=> sP27(sK34,sF81,sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_193])]) ).
fof(f3248,plain,
( ~ reflexive_relstr(sF82)
| spl88_281 ),
inference(avatar_component_clause,[],[f3246]) ).
fof(f3246,plain,
( spl88_281
<=> reflexive_relstr(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_281])]) ).
fof(f3437,plain,
( spl88_59
| spl88_313
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3374,f1434,f3435,f1446]) ).
fof(f1446,plain,
( spl88_59
<=> empty_carrier(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_59])]) ).
fof(f3435,plain,
( spl88_313
<=> ! [X16,X17] :
( ~ net_str(X16,sF82)
| sP31(X17,sF82,X16)
| empty_carrier(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_313])]) ).
fof(f3374,plain,
( ! [X16,X17] :
( ~ net_str(X16,sF82)
| empty_carrier(X16)
| sP31(X17,sF82,X16)
| empty_carrier(sF82) )
| ~ spl88_56 ),
inference(resolution,[],[f3200,f876]) ).
fof(f876,plain,
! [X2,X0,X1] :
( ~ one_sorted_str(X1)
| ~ net_str(X2,X1)
| empty_carrier(X2)
| sP31(X0,X1,X2)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f418]) ).
fof(f418,plain,
! [X0,X1,X2] :
( sP31(X0,X1,X2)
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(definition_folding,[],[f346,f417,f416]) ).
fof(f416,plain,
! [X2,X1,X0] :
( sP30(X2,X1,X0)
<=> ? [X3] :
( is_eventually_in(X1,X2,X3)
& X0 = X3
& element(X3,powerset(the_carrier(X1))) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP30])]) ).
fof(f417,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_1_yellow19(X1,X2))
<=> sP30(X2,X1,X0) )
| ~ sP31(X0,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP31])]) ).
fof(f346,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_1_yellow19(X1,X2))
<=> ? [X3] :
( is_eventually_in(X1,X2,X3)
& X0 = X3
& element(X3,powerset(the_carrier(X1))) ) )
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(flattening,[],[f345]) ).
fof(f345,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_1_yellow19(X1,X2))
<=> ? [X3] :
( is_eventually_in(X1,X2,X3)
& X0 = X3
& element(X3,powerset(the_carrier(X1))) ) )
| ~ net_str(X2,X1)
| empty_carrier(X2)
| ~ one_sorted_str(X1)
| empty_carrier(X1) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0,X1,X2] :
( ( net_str(X2,X1)
& ~ empty_carrier(X2)
& one_sorted_str(X1)
& ~ empty_carrier(X1) )
=> ( in(X0,a_2_1_yellow19(X1,X2))
<=> ? [X3] :
( is_eventually_in(X1,X2,X3)
& X0 = X3
& element(X3,powerset(the_carrier(X1))) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fraenkel_a_2_1_yellow19) ).
fof(f3200,plain,
( one_sorted_str(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f666]) ).
fof(f666,plain,
! [X0] :
( ~ rel_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f212,plain,
! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0] :
( rel_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',dt_l1_orders_2) ).
fof(f3172,plain,
( rel_str(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f1435,f1120]) ).
fof(f1120,plain,
! [X0] :
( ~ net_str(X0,sK33)
| rel_str(X0) ),
inference(resolution,[],[f997,f649]) ).
fof(f649,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| rel_str(X1) ),
inference(cnf_transformation,[],[f206]) ).
fof(f206,plain,
! [X0] :
( ! [X1] :
( rel_str(X1)
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( net_str(X1,X0)
=> rel_str(X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',dt_l1_waybel_0) ).
fof(f3433,plain,
( spl88_59
| spl88_312
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3373,f1434,f3431,f1446]) ).
fof(f3431,plain,
( spl88_312
<=> ! [X14,X15] :
( ~ element(X14,powerset(the_carrier(boole_POSet(X15))))
| sP29(sF82,X14,X15)
| empty(X15)
| ~ element(X15,powerset(the_carrier(sF82)))
| empty(X14)
| ~ filtered_subset(X14,boole_POSet(X15))
| ~ upper_relstr_subset(X14,boole_POSet(X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_312])]) ).
fof(f3373,plain,
( ! [X14,X15] :
( ~ element(X14,powerset(the_carrier(boole_POSet(X15))))
| ~ upper_relstr_subset(X14,boole_POSet(X15))
| ~ filtered_subset(X14,boole_POSet(X15))
| empty(X14)
| ~ element(X15,powerset(the_carrier(sF82)))
| empty(X15)
| sP29(sF82,X14,X15)
| empty_carrier(sF82) )
| ~ spl88_56 ),
inference(resolution,[],[f3200,f869]) ).
fof(f869,plain,
! [X2,X0,X1] :
( ~ one_sorted_str(X0)
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| sP29(X0,X2,X1)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f415]) ).
fof(f415,plain,
! [X0,X1,X2] :
( sP29(X0,X2,X1)
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f344,f414]) ).
fof(f414,plain,
! [X0,X2,X1] :
( ( net_str(net_of_bool_filter(X0,X1,X2),X0)
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ sP29(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP29])]) ).
fof(f344,plain,
! [X0,X1,X2] :
( ( net_str(net_of_bool_filter(X0,X1,X2),X0)
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f343]) ).
fof(f343,plain,
! [X0,X1,X2] :
( ( net_str(net_of_bool_filter(X0,X1,X2),X0)
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(the_carrier(boole_POSet(X1))))
& upper_relstr_subset(X2,boole_POSet(X1))
& filtered_subset(X2,boole_POSet(X1))
& ~ empty(X2)
& element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( net_str(net_of_bool_filter(X0,X1,X2),X0)
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',dt_k3_yellow19) ).
fof(f3429,plain,
( spl88_59
| spl88_311
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3372,f1434,f3427,f1446]) ).
fof(f3427,plain,
( spl88_311
<=> ! [X13,X12] :
( ~ element(X12,powerset(the_carrier(boole_POSet(X13))))
| sP28(sF82,X12,X13)
| empty(X13)
| ~ element(X13,powerset(the_carrier(sF82)))
| empty(X12)
| ~ filtered_subset(X12,boole_POSet(X13))
| ~ upper_relstr_subset(X12,boole_POSet(X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_311])]) ).
fof(f3372,plain,
( ! [X12,X13] :
( ~ element(X12,powerset(the_carrier(boole_POSet(X13))))
| ~ upper_relstr_subset(X12,boole_POSet(X13))
| ~ filtered_subset(X12,boole_POSet(X13))
| empty(X12)
| ~ element(X13,powerset(the_carrier(sF82)))
| empty(X13)
| sP28(sF82,X12,X13)
| empty_carrier(sF82) )
| ~ spl88_56 ),
inference(resolution,[],[f3200,f865]) ).
fof(f865,plain,
! [X2,X0,X1] :
( ~ one_sorted_str(X0)
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| sP28(X0,X2,X1)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f413]) ).
fof(f413,plain,
! [X0,X1,X2] :
( sP28(X0,X2,X1)
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f342,f412]) ).
fof(f412,plain,
! [X0,X2,X1] :
( ( strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ sP28(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP28])]) ).
fof(f342,plain,
! [X0,X1,X2] :
( ( strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f341]) ).
fof(f341,plain,
! [X0,X1,X2] :
( ( strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(the_carrier(boole_POSet(X1))))
& upper_relstr_subset(X2,boole_POSet(X1))
& filtered_subset(X2,boole_POSet(X1))
& ~ empty(X2)
& element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc4_yellow19) ).
fof(f3425,plain,
( spl88_59
| spl88_310
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3371,f1434,f3423,f1446]) ).
fof(f3423,plain,
( spl88_310
<=> ! [X11,X10] :
( ~ element(X10,powerset(the_carrier(boole_POSet(X11))))
| sP27(X10,X11,sF82)
| empty(X11)
| ~ element(X11,powerset(the_carrier(sF82)))
| empty(X10)
| ~ filtered_subset(X10,boole_POSet(X11))
| ~ upper_relstr_subset(X10,boole_POSet(X11))
| ~ proper_element(X10,powerset(the_carrier(boole_POSet(X11)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_310])]) ).
fof(f3371,plain,
( ! [X10,X11] :
( ~ element(X10,powerset(the_carrier(boole_POSet(X11))))
| ~ proper_element(X10,powerset(the_carrier(boole_POSet(X11))))
| ~ upper_relstr_subset(X10,boole_POSet(X11))
| ~ filtered_subset(X10,boole_POSet(X11))
| empty(X10)
| ~ element(X11,powerset(the_carrier(sF82)))
| empty(X11)
| sP27(X10,X11,sF82)
| empty_carrier(sF82) )
| ~ spl88_56 ),
inference(resolution,[],[f3200,f860]) ).
fof(f860,plain,
! [X2,X0,X1] :
( ~ one_sorted_str(X0)
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| sP27(X2,X1,X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f411]) ).
fof(f411,plain,
! [X0,X1,X2] :
( sP27(X2,X1,X0)
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f340,f410]) ).
fof(f340,plain,
! [X0,X1,X2] :
( ( directed_relstr(net_of_bool_filter(X0,X1,X2))
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f339]) ).
fof(f339,plain,
! [X0,X1,X2] :
( ( directed_relstr(net_of_bool_filter(X0,X1,X2))
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
| ~ upper_relstr_subset(X2,boole_POSet(X1))
| ~ filtered_subset(X2,boole_POSet(X1))
| empty(X2)
| ~ element(X1,powerset(the_carrier(X0)))
| empty(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(the_carrier(boole_POSet(X1))))
& proper_element(X2,powerset(the_carrier(boole_POSet(X1))))
& upper_relstr_subset(X2,boole_POSet(X1))
& filtered_subset(X2,boole_POSet(X1))
& ~ empty(X2)
& element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( directed_relstr(net_of_bool_filter(X0,X1,X2))
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& transitive_relstr(net_of_bool_filter(X0,X1,X2))
& reflexive_relstr(net_of_bool_filter(X0,X1,X2))
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc5_yellow19) ).
fof(f3421,plain,
( spl88_59
| spl88_309
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3368,f1434,f3419,f1446]) ).
fof(f3419,plain,
( spl88_309
<=> ! [X7] :
( ~ net_str(X7,sF82)
| upper_relstr_subset(filter_of_net_str(sF82,X7),boole_POSet(cast_as_carrier_subset(sF82)))
| empty_carrier(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_309])]) ).
fof(f3368,plain,
( ! [X7] :
( ~ net_str(X7,sF82)
| empty_carrier(X7)
| upper_relstr_subset(filter_of_net_str(sF82,X7),boole_POSet(cast_as_carrier_subset(sF82)))
| empty_carrier(sF82) )
| ~ spl88_56 ),
inference(resolution,[],[f3200,f840]) ).
fof(f840,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| upper_relstr_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f327,plain,
! [X0,X1] :
( ( upper_relstr_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(filter_of_net_str(X0,X1)) )
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f326]) ).
fof(f326,plain,
! [X0,X1] :
( ( upper_relstr_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(filter_of_net_str(X0,X1)) )
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( upper_relstr_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(filter_of_net_str(X0,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc2_yellow19) ).
fof(f3417,plain,
( spl88_59
| spl88_308
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3367,f1434,f3415,f1446]) ).
fof(f3415,plain,
( spl88_308
<=> ! [X6] :
( ~ net_str(X6,sF82)
| ~ empty(filter_of_net_str(sF82,X6))
| empty_carrier(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_308])]) ).
fof(f3367,plain,
( ! [X6] :
( ~ net_str(X6,sF82)
| empty_carrier(X6)
| ~ empty(filter_of_net_str(sF82,X6))
| empty_carrier(sF82) )
| ~ spl88_56 ),
inference(resolution,[],[f3200,f839]) ).
fof(f839,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ empty(filter_of_net_str(X0,X1))
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f3413,plain,
( spl88_59
| spl88_307
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3366,f1434,f3411,f1446]) ).
fof(f3411,plain,
( spl88_307
<=> ! [X5] :
( ~ net_str(X5,sF82)
| sP25(sF82,X5)
| empty_carrier(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_307])]) ).
fof(f3366,plain,
( ! [X5] :
( ~ net_str(X5,sF82)
| empty_carrier(X5)
| sP25(sF82,X5)
| empty_carrier(sF82) )
| ~ spl88_56 ),
inference(resolution,[],[f3200,f838]) ).
fof(f838,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| sP25(X0,X1)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f407]) ).
fof(f407,plain,
! [X0,X1] :
( sP25(X0,X1)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f325,f406]) ).
fof(f406,plain,
! [X0,X1] :
( ( quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1))
& ~ empty(the_mapping(X0,X1)) )
| ~ sP25(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP25])]) ).
fof(f325,plain,
! [X0,X1] :
( ( quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1))
& ~ empty(the_mapping(X0,X1)) )
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f324]) ).
fof(f324,plain,
! [X0,X1] :
( ( quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1))
& ~ empty(the_mapping(X0,X1)) )
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f188]) ).
fof(f188,plain,
! [X0,X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1))
& ~ empty(the_mapping(X0,X1)) ) ),
inference(pure_predicate_removal,[],[f59]) ).
fof(f59,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1))
& relation(the_mapping(X0,X1))
& ~ empty(the_mapping(X0,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc15_yellow_6) ).
fof(f3409,plain,
( spl88_59
| spl88_306
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3365,f1434,f3407,f1446]) ).
fof(f3407,plain,
( spl88_306
<=> ! [X4] :
( ~ net_str(X4,sF82)
| element(filter_of_net_str(sF82,X4),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sF82)))))
| empty_carrier(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_306])]) ).
fof(f3365,plain,
( ! [X4] :
( ~ net_str(X4,sF82)
| empty_carrier(X4)
| element(filter_of_net_str(sF82,X4),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sF82)))))
| empty_carrier(sF82) )
| ~ spl88_56 ),
inference(resolution,[],[f3200,f834]) ).
fof(f834,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f323]) ).
fof(f323,plain,
! [X0,X1] :
( element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f322]) ).
fof(f322,plain,
! [X0,X1] :
( element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0))))) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',dt_k2_yellow19) ).
fof(f3405,plain,
( spl88_59
| spl88_305
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3364,f1434,f3403,f1446]) ).
fof(f3403,plain,
( spl88_305
<=> ! [X3] :
( ~ net_str(X3,sF82)
| sP24(sF82,X3)
| empty_carrier(X3)
| ~ transitive_relstr(X3)
| ~ directed_relstr(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_305])]) ).
fof(f3364,plain,
( ! [X3] :
( ~ net_str(X3,sF82)
| ~ directed_relstr(X3)
| ~ transitive_relstr(X3)
| empty_carrier(X3)
| sP24(sF82,X3)
| empty_carrier(sF82) )
| ~ spl88_56 ),
inference(resolution,[],[f3200,f833]) ).
fof(f833,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| sP24(X0,X1)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f405]) ).
fof(f405,plain,
! [X0,X1] :
( sP24(X0,X1)
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f321,f404]) ).
fof(f404,plain,
! [X0,X1] :
( ( proper_element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(filter_of_net_str(X0,X1)) )
| ~ sP24(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP24])]) ).
fof(f321,plain,
! [X0,X1] :
( ( proper_element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(filter_of_net_str(X0,X1)) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f320]) ).
fof(f320,plain,
! [X0,X1] :
( ( proper_element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(filter_of_net_str(X0,X1)) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ( proper_element(filter_of_net_str(X0,X1),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(filter_of_net_str(X0,X1),boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(filter_of_net_str(X0,X1)) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc3_yellow19) ).
fof(f3401,plain,
( spl88_59
| ~ spl88_304
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3363,f1434,f3398,f1446]) ).
fof(f3398,plain,
( spl88_304
<=> empty(sK49(sF82)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_304])]) ).
fof(f3363,plain,
( ~ empty(sK49(sF82))
| empty_carrier(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3200,f752]) ).
fof(f752,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ~ empty(sK49(X0))
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f472]) ).
fof(f472,plain,
! [X0] :
( ( ~ empty(sK49(X0))
& element(sK49(X0),powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49])],[f265,f471]) ).
fof(f471,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( ~ empty(sK49(X0))
& element(sK49(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f265,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f264]) ).
fof(f264,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f115]) ).
fof(f115,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc5_struct_0) ).
fof(f3396,plain,
( spl88_59
| spl88_303
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3362,f1434,f3393,f1446]) ).
fof(f3393,plain,
( spl88_303
<=> element(sK49(sF82),powerset(the_carrier(sF82))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_303])]) ).
fof(f3362,plain,
( element(sK49(sF82),powerset(the_carrier(sF82)))
| empty_carrier(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3200,f751]) ).
fof(f751,plain,
! [X0] :
( ~ one_sorted_str(X0)
| element(sK49(X0),powerset(the_carrier(X0)))
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f472]) ).
fof(f3391,plain,
( spl88_59
| spl88_302
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3361,f1434,f3389,f1446]) ).
fof(f3389,plain,
( spl88_302
<=> ! [X2] :
( ~ net_str(X2,sF82)
| filter_of_net_str(sF82,X2) = a_2_1_yellow19(sF82,X2)
| empty_carrier(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_302])]) ).
fof(f3361,plain,
( ! [X2] :
( ~ net_str(X2,sF82)
| empty_carrier(X2)
| filter_of_net_str(sF82,X2) = a_2_1_yellow19(sF82,X2)
| empty_carrier(sF82) )
| ~ spl88_56 ),
inference(resolution,[],[f3200,f750]) ).
fof(f750,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f263]) ).
fof(f263,plain,
! [X0] :
( ! [X1] :
( filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1)
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f262]) ).
fof(f262,plain,
! [X0] :
( ! [X1] :
( filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1)
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1) )
=> filter_of_net_str(X0,X1) = a_2_1_yellow19(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',d3_yellow19) ).
fof(f3387,plain,
( spl88_59
| spl88_301
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3360,f1434,f3385,f1446]) ).
fof(f3385,plain,
( spl88_301
<=> ! [X1] :
( ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sF82)))))
| filter_of_net_str(sF82,net_of_bool_filter(sF82,cast_as_carrier_subset(sF82),X1)) = X1
| empty(X1)
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sF82)))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sF82)))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sF82))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_301])]) ).
fof(f3360,plain,
( ! [X1] :
( ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sF82)))))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sF82)))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sF82)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sF82)))
| empty(X1)
| filter_of_net_str(sF82,net_of_bool_filter(sF82,cast_as_carrier_subset(sF82),X1)) = X1
| empty_carrier(sF82) )
| ~ spl88_56 ),
inference(resolution,[],[f3200,f749]) ).
fof(f749,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| empty(X1)
| filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) = X1
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f261]) ).
fof(f261,plain,
! [X0] :
( ! [X1] :
( filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) = X1
| ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| empty(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f260]) ).
fof(f260,plain,
! [X0] :
( ! [X1] :
( filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) = X1
| ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
| empty(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f126]) ).
fof(f126,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(X0)))))
& upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& filtered_subset(X1,boole_POSet(cast_as_carrier_subset(X0)))
& ~ empty(X1) )
=> filter_of_net_str(X0,net_of_bool_filter(X0,cast_as_carrier_subset(X0),X1)) = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',t15_yellow19) ).
fof(f3383,plain,
( spl88_59
| ~ spl88_300
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3359,f1434,f3380,f1446]) ).
fof(f3359,plain,
( ~ empty(the_carrier(sF82))
| empty_carrier(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3200,f748]) ).
fof(f748,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0))
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f259]) ).
fof(f259,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f258]) ).
fof(f258,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc1_struct_0) ).
fof(f3337,plain,
( ~ spl88_281
| ~ spl88_58
| ~ spl88_285
| ~ spl88_289
| ~ spl88_298
| spl88_299
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3222,f1434,f3334,f3328,f3282,f3264,f1442,f3246]) ).
fof(f1442,plain,
( spl88_58
<=> transitive_relstr(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_58])]) ).
fof(f3264,plain,
( spl88_285
<=> antisymmetric_relstr(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_285])]) ).
fof(f3282,plain,
( spl88_289
<=> with_suprema_relstr(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_289])]) ).
fof(f3328,plain,
( spl88_298
<=> with_infima_relstr(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_298])]) ).
fof(f3334,plain,
( spl88_299
<=> sP23(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_299])]) ).
fof(f3222,plain,
( sP23(sF82)
| ~ with_infima_relstr(sF82)
| ~ with_suprema_relstr(sF82)
| ~ antisymmetric_relstr(sF82)
| ~ transitive_relstr(sF82)
| ~ reflexive_relstr(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f812]) ).
fof(f812,plain,
! [X0] :
( ~ rel_str(X0)
| sP23(X0)
| ~ with_infima_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(cnf_transformation,[],[f403]) ).
fof(f403,plain,
! [X0] :
( sP23(X0)
| ~ rel_str(X0)
| ~ with_infima_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(definition_folding,[],[f309,f402]) ).
fof(f402,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP23(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).
fof(f309,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ with_infima_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(flattening,[],[f308]) ).
fof(f308,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ with_infima_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0) ),
inference(ennf_transformation,[],[f163]) ).
fof(f163,plain,
! [X0] :
( ( rel_str(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0) )
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f142]) ).
fof(f142,plain,
! [X0] :
( ( rel_str(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0) )
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f87]) ).
fof(f87,axiom,
! [X0] :
( ( rel_str(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0) )
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& directed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc11_waybel_0) ).
fof(f3332,plain,
( ~ spl88_289
| ~ spl88_293
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3221,f1434,f3300,f3282]) ).
fof(f3300,plain,
( spl88_293
<=> empty(cast_as_carrier_subset(sF82)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_293])]) ).
fof(f3221,plain,
( ~ empty(cast_as_carrier_subset(sF82))
| ~ with_suprema_relstr(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f807]) ).
fof(f807,plain,
! [X0] :
( ~ rel_str(X0)
| ~ empty(cast_as_carrier_subset(X0))
| ~ with_suprema_relstr(X0) ),
inference(cnf_transformation,[],[f307]) ).
fof(f307,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| ~ with_suprema_relstr(X0) ),
inference(flattening,[],[f306]) ).
fof(f306,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| ~ with_suprema_relstr(X0) ),
inference(ennf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0] :
( ( rel_str(X0)
& with_suprema_relstr(X0) )
=> ~ empty(cast_as_carrier_subset(X0)) ),
inference(pure_predicate_removal,[],[f64]) ).
fof(f64,axiom,
! [X0] :
( ( rel_str(X0)
& with_suprema_relstr(X0) )
=> ( directed_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc2_waybel_0) ).
fof(f3331,plain,
( ~ spl88_298
| ~ spl88_293
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3220,f1434,f3300,f3328]) ).
fof(f3220,plain,
( ~ empty(cast_as_carrier_subset(sF82))
| ~ with_infima_relstr(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f805]) ).
fof(f805,plain,
! [X0] :
( ~ rel_str(X0)
| ~ empty(cast_as_carrier_subset(X0))
| ~ with_infima_relstr(X0) ),
inference(cnf_transformation,[],[f305]) ).
fof(f305,plain,
! [X0] :
( ( filtered_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) )
| ~ rel_str(X0)
| ~ with_infima_relstr(X0) ),
inference(flattening,[],[f304]) ).
fof(f304,plain,
! [X0] :
( ( filtered_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) )
| ~ rel_str(X0)
| ~ with_infima_relstr(X0) ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,axiom,
! [X0] :
( ( rel_str(X0)
& with_infima_relstr(X0) )
=> ( filtered_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc4_waybel_0) ).
fof(f3326,plain,
( spl88_59
| ~ spl88_281
| ~ spl88_58
| spl88_297
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3219,f1434,f3323,f1442,f3246,f1446]) ).
fof(f3323,plain,
( spl88_297
<=> sP19(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_297])]) ).
fof(f3219,plain,
( sP19(sF82)
| ~ transitive_relstr(sF82)
| ~ reflexive_relstr(sF82)
| empty_carrier(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f774]) ).
fof(f774,plain,
! [X0] :
( ~ rel_str(X0)
| sP19(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f395]) ).
fof(f395,plain,
! [X0] :
( sP19(X0)
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f281,f394]) ).
fof(f394,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP19(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
fof(f281,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f280]) ).
fof(f280,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0] :
( ( rel_str(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc10_waybel_0) ).
fof(f3321,plain,
( spl88_59
| ~ spl88_281
| ~ spl88_58
| spl88_296
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3218,f1434,f3318,f1442,f3246,f1446]) ).
fof(f3318,plain,
( spl88_296
<=> element(sK52(sF82),powerset(the_carrier(sF82))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_296])]) ).
fof(f3218,plain,
( element(sK52(sF82),powerset(the_carrier(sF82)))
| ~ transitive_relstr(sF82)
| ~ reflexive_relstr(sF82)
| empty_carrier(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f768]) ).
fof(f768,plain,
! [X0] :
( ~ rel_str(X0)
| element(sK52(X0),powerset(the_carrier(X0)))
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f480]) ).
fof(f480,plain,
! [X0] :
( ( ~ empty(sK52(X0))
& element(sK52(X0),powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f279,f479]) ).
fof(f479,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( ~ empty(sK52(X0))
& element(sK52(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f279,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f278]) ).
fof(f278,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f167]) ).
fof(f167,plain,
! [X0] :
( ( rel_str(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f145]) ).
fof(f145,plain,
! [X0] :
( ( rel_str(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( lower_relstr_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f122]) ).
fof(f122,axiom,
! [X0] :
( ( rel_str(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( lower_relstr_subset(X1,X0)
& directed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc9_waybel_0) ).
fof(f3316,plain,
( spl88_59
| ~ spl88_281
| spl88_295
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3217,f1434,f3313,f3246,f1446]) ).
fof(f3313,plain,
( spl88_295
<=> sP18(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_295])]) ).
fof(f3217,plain,
( sP18(sF82)
| ~ reflexive_relstr(sF82)
| empty_carrier(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f767]) ).
fof(f767,plain,
! [X0] :
( ~ rel_str(X0)
| sP18(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f393]) ).
fof(f393,plain,
! [X0] :
( sP18(X0)
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f277,f392]) ).
fof(f392,plain,
! [X0] :
( ? [X1] :
( filtered_subset(X1,X0)
& finite(X1)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP18(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f277,plain,
! [X0] :
( ? [X1] :
( filtered_subset(X1,X0)
& finite(X1)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f276]) ).
fof(f276,plain,
! [X0] :
( ? [X1] :
( filtered_subset(X1,X0)
& finite(X1)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0] :
( ( rel_str(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( filtered_subset(X1,X0)
& finite(X1)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f102]) ).
fof(f102,axiom,
! [X0] :
( ( rel_str(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( filtered_subset(X1,X0)
& directed_subset(X1,X0)
& finite(X1)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc2_waybel_0) ).
fof(f3311,plain,
( spl88_59
| spl88_294
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3216,f1434,f3308,f1446]) ).
fof(f3308,plain,
( spl88_294
<=> sP17(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_294])]) ).
fof(f3216,plain,
( sP17(sF82)
| empty_carrier(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f762]) ).
fof(f762,plain,
! [X0] :
( ~ rel_str(X0)
| sP17(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f391]) ).
fof(f391,plain,
! [X0] :
( sP17(X0)
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f275,f390]) ).
fof(f390,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP17(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f275,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f274]) ).
fof(f274,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f166]) ).
fof(f166,plain,
! [X0] :
( ( rel_str(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f121]) ).
fof(f121,axiom,
! [X0] :
( ( rel_str(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc8_waybel_0) ).
fof(f3306,plain,
( spl88_59
| ~ spl88_293
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3215,f1434,f3300,f1446]) ).
fof(f3215,plain,
( ~ empty(cast_as_carrier_subset(sF82))
| empty_carrier(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f757]) ).
fof(f757,plain,
! [X0] :
( ~ rel_str(X0)
| ~ empty(cast_as_carrier_subset(X0))
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f273,plain,
! [X0] :
( ( upper_relstr_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) )
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f272]) ).
fof(f272,plain,
! [X0] :
( ( upper_relstr_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) )
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f165]) ).
fof(f165,plain,
! [X0] :
( ( rel_str(X0)
& ~ empty_carrier(X0) )
=> ( upper_relstr_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) ) ),
inference(pure_predicate_removal,[],[f58]) ).
fof(f58,axiom,
! [X0] :
( ( rel_str(X0)
& ~ empty_carrier(X0) )
=> ( upper_relstr_subset(cast_as_carrier_subset(X0),X0)
& lower_relstr_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc15_waybel_0) ).
fof(f3305,plain,
( spl88_59
| ~ spl88_293
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3214,f1434,f3300,f1446]) ).
fof(f3214,plain,
( ~ empty(cast_as_carrier_subset(sF82))
| empty_carrier(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f756]) ).
fof(f756,plain,
! [X0] :
( ~ rel_str(X0)
| ~ empty(cast_as_carrier_subset(X0))
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f271,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f270]) ).
fof(f270,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0] :
( ( rel_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(cast_as_carrier_subset(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc2_yellow_0) ).
fof(f3304,plain,
( spl88_59
| ~ spl88_287
| ~ spl88_293
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3213,f1434,f3300,f3273,f1446]) ).
fof(f3273,plain,
( spl88_287
<=> upper_bounded_relstr(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_287])]) ).
fof(f3213,plain,
( ~ empty(cast_as_carrier_subset(sF82))
| ~ upper_bounded_relstr(sF82)
| empty_carrier(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f755]) ).
fof(f755,plain,
! [X0] :
( ~ rel_str(X0)
| ~ empty(cast_as_carrier_subset(X0))
| ~ upper_bounded_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f269]) ).
fof(f269,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f268]) ).
fof(f268,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0] :
( ( rel_str(X0)
& upper_bounded_relstr(X0)
& ~ empty_carrier(X0) )
=> ~ empty(cast_as_carrier_subset(X0)) ),
inference(pure_predicate_removal,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( ( rel_str(X0)
& upper_bounded_relstr(X0)
& ~ empty_carrier(X0) )
=> ( directed_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc3_waybel_0) ).
fof(f3303,plain,
( spl88_59
| ~ spl88_290
| ~ spl88_293
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3212,f1434,f3300,f3286,f1446]) ).
fof(f3286,plain,
( spl88_290
<=> lower_bounded_relstr(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_290])]) ).
fof(f3212,plain,
( ~ empty(cast_as_carrier_subset(sF82))
| ~ lower_bounded_relstr(sF82)
| empty_carrier(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f753]) ).
fof(f753,plain,
! [X0] :
( ~ rel_str(X0)
| ~ empty(cast_as_carrier_subset(X0))
| ~ lower_bounded_relstr(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f267]) ).
fof(f267,plain,
! [X0] :
( ( filtered_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) )
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f266]) ).
fof(f266,plain,
! [X0] :
( ( filtered_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) )
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0] :
( ( rel_str(X0)
& lower_bounded_relstr(X0)
& ~ empty_carrier(X0) )
=> ( filtered_subset(cast_as_carrier_subset(X0),X0)
& ~ empty(cast_as_carrier_subset(X0)) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc5_waybel_0) ).
fof(f3298,plain,
( spl88_292
| ~ spl88_281
| ~ spl88_289
| ~ spl88_291
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3209,f1434,f3290,f3282,f3246,f3295]) ).
fof(f3295,plain,
( spl88_292
<=> sP13(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_292])]) ).
fof(f3290,plain,
( spl88_291
<=> up_complete_relstr(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_291])]) ).
fof(f3209,plain,
( ~ up_complete_relstr(sF82)
| ~ with_suprema_relstr(sF82)
| ~ reflexive_relstr(sF82)
| sP13(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f723]) ).
fof(f723,plain,
! [X0] :
( ~ rel_str(X0)
| ~ up_complete_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ reflexive_relstr(X0)
| sP13(X0) ),
inference(cnf_transformation,[],[f383]) ).
fof(f383,plain,
! [X0] :
( sP13(X0)
| ~ up_complete_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0) ),
inference(definition_folding,[],[f243,f382]) ).
fof(f382,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP13(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f243,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ up_complete_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f242]) ).
fof(f242,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ up_complete_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ reflexive_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( rel_str(X0)
=> ( ( up_complete_relstr(X0)
& with_suprema_relstr(X0)
& reflexive_relstr(X0) )
=> ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',cc9_waybel_0) ).
fof(f3293,plain,
( spl88_288
| spl88_59
| ~ spl88_281
| ~ spl88_58
| ~ spl88_285
| ~ spl88_289
| ~ spl88_290
| ~ spl88_291
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3208,f1434,f3290,f3286,f3282,f3264,f1442,f3246,f1446,f3278]) ).
fof(f3278,plain,
( spl88_288
<=> sP12(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_288])]) ).
fof(f3208,plain,
( ~ up_complete_relstr(sF82)
| ~ lower_bounded_relstr(sF82)
| ~ with_suprema_relstr(sF82)
| ~ antisymmetric_relstr(sF82)
| ~ transitive_relstr(sF82)
| ~ reflexive_relstr(sF82)
| empty_carrier(sF82)
| sP12(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f717]) ).
fof(f717,plain,
! [X0] :
( ~ rel_str(X0)
| ~ up_complete_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| sP12(X0) ),
inference(cnf_transformation,[],[f381]) ).
fof(f381,plain,
! [X0] :
( sP12(X0)
| ~ up_complete_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(definition_folding,[],[f239,f380]) ).
fof(f380,plain,
! [X0] :
( ( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP12(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f239,plain,
! [X0] :
( ( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ up_complete_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f238]) ).
fof(f238,plain,
! [X0] :
( ( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ up_complete_relstr(X0)
| ~ lower_bounded_relstr(X0)
| ~ with_suprema_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( rel_str(X0)
=> ( ( up_complete_relstr(X0)
& lower_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( bounded_relstr(X0)
& upper_bounded_relstr(X0)
& lower_bounded_relstr(X0)
& complete_relstr(X0)
& with_infima_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',cc12_waybel_0) ).
fof(f3276,plain,
( spl88_286
| spl88_59
| ~ spl88_281
| ~ spl88_285
| ~ spl88_287
| ~ spl88_282
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3207,f1434,f3250,f3273,f3264,f3246,f1446,f3269]) ).
fof(f3269,plain,
( spl88_286
<=> sP11(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_286])]) ).
fof(f3250,plain,
( spl88_282
<=> join_complete_relstr(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_282])]) ).
fof(f3207,plain,
( ~ join_complete_relstr(sF82)
| ~ upper_bounded_relstr(sF82)
| ~ antisymmetric_relstr(sF82)
| ~ reflexive_relstr(sF82)
| empty_carrier(sF82)
| sP11(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f706]) ).
fof(f706,plain,
! [X0] :
( ~ rel_str(X0)
| ~ join_complete_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| sP11(X0) ),
inference(cnf_transformation,[],[f379]) ).
fof(f379,plain,
! [X0] :
( sP11(X0)
| ~ join_complete_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(definition_folding,[],[f237,f378]) ).
fof(f378,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP11(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f237,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f236]) ).
fof(f236,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( rel_str(X0)
=> ( ( join_complete_relstr(X0)
& upper_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( upper_bounded_relstr(X0)
& with_suprema_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',cc14_waybel_0) ).
fof(f3267,plain,
( spl88_284
| spl88_59
| ~ spl88_281
| ~ spl88_285
| ~ spl88_282
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3206,f1434,f3250,f3264,f3246,f1446,f3260]) ).
fof(f3260,plain,
( spl88_284
<=> sP10(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_284])]) ).
fof(f3206,plain,
( ~ join_complete_relstr(sF82)
| ~ antisymmetric_relstr(sF82)
| ~ reflexive_relstr(sF82)
| empty_carrier(sF82)
| sP10(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f700]) ).
fof(f700,plain,
! [X0] :
( ~ rel_str(X0)
| ~ join_complete_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| sP10(X0) ),
inference(cnf_transformation,[],[f377]) ).
fof(f377,plain,
! [X0] :
( sP10(X0)
| ~ join_complete_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(definition_folding,[],[f235,f376]) ).
fof(f376,plain,
! [X0] :
( ( with_infima_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP10(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f235,plain,
! [X0] :
( ( with_infima_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f234]) ).
fof(f234,plain,
! [X0] :
( ( with_infima_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( rel_str(X0)
=> ( ( join_complete_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( with_infima_relstr(X0)
& antisymmetric_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',cc13_waybel_0) ).
fof(f3258,plain,
( spl88_283
| spl88_59
| ~ spl88_281
| ~ spl88_279
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3205,f1434,f3237,f3246,f1446,f3255]) ).
fof(f3255,plain,
( spl88_283
<=> sP9(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_283])]) ).
fof(f3237,plain,
( spl88_279
<=> complete_relstr(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_279])]) ).
fof(f3205,plain,
( ~ complete_relstr(sF82)
| ~ reflexive_relstr(sF82)
| empty_carrier(sF82)
| sP9(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f695]) ).
fof(f695,plain,
! [X0] :
( ~ rel_str(X0)
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| sP9(X0) ),
inference(cnf_transformation,[],[f375]) ).
fof(f375,plain,
! [X0] :
( sP9(X0)
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(definition_folding,[],[f233,f374]) ).
fof(f374,plain,
! [X0] :
( ( join_complete_relstr(X0)
& up_complete_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP9(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f233,plain,
! [X0] :
( ( join_complete_relstr(X0)
& up_complete_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f232]) ).
fof(f232,plain,
! [X0] :
( ( join_complete_relstr(X0)
& up_complete_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( rel_str(X0)
=> ( ( complete_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( join_complete_relstr(X0)
& up_complete_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',cc10_waybel_0) ).
fof(f3253,plain,
( spl88_280
| spl88_59
| ~ spl88_281
| ~ spl88_282
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3204,f1434,f3250,f3246,f1446,f3242]) ).
fof(f3242,plain,
( spl88_280
<=> sP8(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_280])]) ).
fof(f3204,plain,
( ~ join_complete_relstr(sF82)
| ~ reflexive_relstr(sF82)
| empty_carrier(sF82)
| sP8(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f690]) ).
fof(f690,plain,
! [X0] :
( ~ rel_str(X0)
| ~ join_complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| sP8(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f373,plain,
! [X0] :
( sP8(X0)
| ~ join_complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(definition_folding,[],[f231,f372]) ).
fof(f372,plain,
! [X0] :
( ( lower_bounded_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f231,plain,
! [X0] :
( ( lower_bounded_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f230]) ).
fof(f230,plain,
! [X0] :
( ( lower_bounded_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
| ~ join_complete_relstr(X0)
| ~ reflexive_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( rel_str(X0)
=> ( ( join_complete_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) )
=> ( lower_bounded_relstr(X0)
& reflexive_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',cc11_waybel_0) ).
fof(f3240,plain,
( spl88_278
| spl88_59
| ~ spl88_279
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3203,f1434,f3237,f1446,f3233]) ).
fof(f3233,plain,
( spl88_278
<=> sP6(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_278])]) ).
fof(f3203,plain,
( ~ complete_relstr(sF82)
| empty_carrier(sF82)
| sP6(sF82)
| ~ spl88_56 ),
inference(resolution,[],[f3172,f678]) ).
fof(f678,plain,
! [X0] :
( ~ rel_str(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| sP6(X0) ),
inference(cnf_transformation,[],[f369]) ).
fof(f369,plain,
! [X0] :
( sP6(X0)
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(definition_folding,[],[f225,f368]) ).
fof(f368,plain,
! [X0] :
( ( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& ~ empty_carrier(X0) )
| ~ sP6(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f225,plain,
! [X0] :
( ( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& ~ empty_carrier(X0) )
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f224]) ).
fof(f224,plain,
! [X0] :
( ( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& ~ empty_carrier(X0) )
| ~ complete_relstr(X0)
| empty_carrier(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( rel_str(X0)
=> ( ( complete_relstr(X0)
& ~ empty_carrier(X0) )
=> ( with_infima_relstr(X0)
& with_suprema_relstr(X0)
& ~ empty_carrier(X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',cc1_yellow_0) ).
fof(f3231,plain,
( spl88_276
| ~ spl88_277
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3202,f1434,f3228,f3224]) ).
fof(f3224,plain,
( spl88_276
<=> sF82 = rel_str_of(the_carrier(sF82),the_InternalRel(sF82)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_276])]) ).
fof(f3228,plain,
( spl88_277
<=> strict_rel_str(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_277])]) ).
fof(f3202,plain,
( ~ strict_rel_str(sF82)
| sF82 = rel_str_of(the_carrier(sF82),the_InternalRel(sF82))
| ~ spl88_56 ),
inference(resolution,[],[f3172,f671]) ).
fof(f671,plain,
! [X0] :
( ~ rel_str(X0)
| ~ strict_rel_str(X0)
| rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0 ),
inference(cnf_transformation,[],[f219]) ).
fof(f219,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f218]) ).
fof(f218,plain,
! [X0] :
( rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( rel_str(X0)
=> ( strict_rel_str(X0)
=> rel_str_of(the_carrier(X0),the_InternalRel(X0)) = X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',abstractness_v1_orders_2) ).
fof(f3199,plain,
( spl88_275
| spl88_59
| ~ spl88_30
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3178,f1434,f1203,f1446,f3196]) ).
fof(f3196,plain,
( spl88_275
<=> sP0(the_mapping(sK33,sF82)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_275])]) ).
fof(f1203,plain,
( spl88_30
<=> ! [X5] :
( ~ net_str(X5,sK33)
| sP25(sK33,X5)
| empty_carrier(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_30])]) ).
fof(f3178,plain,
( empty_carrier(sF82)
| sP0(the_mapping(sK33,sF82))
| ~ spl88_30
| ~ spl88_56 ),
inference(resolution,[],[f1435,f2450]) ).
fof(f2450,plain,
( ! [X0] :
( ~ net_str(X0,sK33)
| empty_carrier(X0)
| sP0(the_mapping(sK33,X0)) )
| ~ spl88_30 ),
inference(resolution,[],[f1935,f631]) ).
fof(f631,plain,
! [X0] :
( empty(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f357,plain,
! [X0] :
( sP0(X0)
| empty(X0) ),
inference(definition_folding,[],[f197,f356]) ).
fof(f356,plain,
! [X0] :
( ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f197,plain,
! [X0] :
( ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f162]) ).
fof(f162,plain,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(pure_predicate_removal,[],[f157]) ).
fof(f157,plain,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(pure_predicate_removal,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(pure_predicate_removal,[],[f152]) ).
fof(f152,plain,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(pure_predicate_removal,[],[f147]) ).
fof(f147,plain,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& complemented_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
inference(pure_predicate_removal,[],[f65]) ).
fof(f65,axiom,
! [X0] :
( ~ empty(X0)
=> ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& boolean_relstr(boole_POSet(X0))
& complemented_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc2_waybel_7) ).
fof(f1935,plain,
( ! [X0] :
( ~ empty(the_mapping(sK33,X0))
| empty_carrier(X0)
| ~ net_str(X0,sK33) )
| ~ spl88_30 ),
inference(resolution,[],[f1204,f835]) ).
fof(f835,plain,
! [X0,X1] :
( ~ sP25(X0,X1)
| ~ empty(the_mapping(X0,X1)) ),
inference(cnf_transformation,[],[f505]) ).
fof(f505,plain,
! [X0,X1] :
( ( quasi_total(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0))
& function(the_mapping(X0,X1))
& ~ empty(the_mapping(X0,X1)) )
| ~ sP25(X0,X1) ),
inference(nnf_transformation,[],[f406]) ).
fof(f1204,plain,
( ! [X5] :
( sP25(sK33,X5)
| ~ net_str(X5,sK33)
| empty_carrier(X5) )
| ~ spl88_30 ),
inference(avatar_component_clause,[],[f1203]) ).
fof(f3193,plain,
( spl88_59
| spl88_274
| ~ spl88_36
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3175,f1434,f1232,f3191,f1446]) ).
fof(f3191,plain,
( spl88_274
<=> ! [X0] : sP31(X0,sK33,sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_274])]) ).
fof(f1232,plain,
( spl88_36
<=> ! [X16,X17] :
( ~ net_str(X16,sK33)
| sP31(X17,sK33,X16)
| empty_carrier(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_36])]) ).
fof(f3175,plain,
( ! [X0] :
( sP31(X0,sK33,sF82)
| empty_carrier(sF82) )
| ~ spl88_36
| ~ spl88_56 ),
inference(resolution,[],[f1435,f1233]) ).
fof(f1233,plain,
( ! [X16,X17] :
( ~ net_str(X16,sK33)
| sP31(X17,sK33,X16)
| empty_carrier(X16) )
| ~ spl88_36 ),
inference(avatar_component_clause,[],[f1232]) ).
fof(f3189,plain,
( ~ spl88_57
| ~ spl88_58
| spl88_59
| spl88_273
| ~ spl88_28
| ~ spl88_56 ),
inference(avatar_split_clause,[],[f3174,f1434,f1191,f3186,f1446,f1442,f1438]) ).
fof(f1438,plain,
( spl88_57
<=> directed_relstr(sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_57])]) ).
fof(f3186,plain,
( spl88_273
<=> sP24(sK33,sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_273])]) ).
fof(f1191,plain,
( spl88_28
<=> ! [X3] :
( ~ net_str(X3,sK33)
| sP24(sK33,X3)
| empty_carrier(X3)
| ~ transitive_relstr(X3)
| ~ directed_relstr(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_28])]) ).
fof(f3174,plain,
( sP24(sK33,sF82)
| empty_carrier(sF82)
| ~ transitive_relstr(sF82)
| ~ directed_relstr(sF82)
| ~ spl88_28
| ~ spl88_56 ),
inference(resolution,[],[f1435,f1192]) ).
fof(f1192,plain,
( ! [X3] :
( ~ net_str(X3,sK33)
| sP24(sK33,X3)
| empty_carrier(X3)
| ~ transitive_relstr(X3)
| ~ directed_relstr(X3) )
| ~ spl88_28 ),
inference(avatar_component_clause,[],[f1191]) ).
fof(f3184,plain,
( spl88_59
| spl88_272
| ~ spl88_25
| ~ spl88_56
| ~ spl88_139 ),
inference(avatar_split_clause,[],[f3179,f2088,f1434,f1176,f3181,f1446]) ).
fof(f3181,plain,
( spl88_272
<=> sK34 = a_2_1_yellow19(sK33,sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_272])]) ).
fof(f1176,plain,
( spl88_25
<=> ! [X2] :
( ~ net_str(X2,sK33)
| filter_of_net_str(sK33,X2) = a_2_1_yellow19(sK33,X2)
| empty_carrier(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_25])]) ).
fof(f2088,plain,
( spl88_139
<=> sK34 = filter_of_net_str(sK33,sF82) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_139])]) ).
fof(f3179,plain,
( sK34 = a_2_1_yellow19(sK33,sF82)
| empty_carrier(sF82)
| ~ spl88_25
| ~ spl88_56
| ~ spl88_139 ),
inference(forward_demodulation,[],[f3173,f2090]) ).
fof(f2090,plain,
( sK34 = filter_of_net_str(sK33,sF82)
| ~ spl88_139 ),
inference(avatar_component_clause,[],[f2088]) ).
fof(f3173,plain,
( filter_of_net_str(sK33,sF82) = a_2_1_yellow19(sK33,sF82)
| empty_carrier(sF82)
| ~ spl88_25
| ~ spl88_56 ),
inference(resolution,[],[f1435,f1177]) ).
fof(f1177,plain,
( ! [X2] :
( ~ net_str(X2,sK33)
| filter_of_net_str(sK33,X2) = a_2_1_yellow19(sK33,X2)
| empty_carrier(X2) )
| ~ spl88_25 ),
inference(avatar_component_clause,[],[f1176]) ).
fof(f3171,plain,
( ~ spl88_56
| ~ spl88_57
| ~ spl88_58
| spl88_59
| spl88_271
| ~ spl88_6
| ~ spl88_139 ),
inference(avatar_split_clause,[],[f3167,f2088,f1034,f3169,f1446,f1442,f1438,f1434]) ).
fof(f1034,plain,
( spl88_6
<=> ! [X4,X3] :
( ~ element(X4,sF84)
| in(X4,lim_points_of_net(sK33,X3))
| empty_carrier(X3)
| ~ transitive_relstr(X3)
| ~ directed_relstr(X3)
| ~ net_str(X3,sK33)
| ~ is_a_convergence_point_of_set(sK33,filter_of_net_str(sK33,X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_6])]) ).
fof(f3167,plain,
( ! [X0] :
( in(X0,sF83)
| ~ is_a_convergence_point_of_set(sK33,sK34,X0)
| empty_carrier(sF82)
| ~ transitive_relstr(sF82)
| ~ directed_relstr(sF82)
| ~ net_str(sF82,sK33)
| ~ element(X0,sF84) )
| ~ spl88_6
| ~ spl88_139 ),
inference(forward_demodulation,[],[f2411,f975]) ).
fof(f975,plain,
lim_points_of_net(sK33,sF82) = sF83,
introduced(function_definition,[]) ).
fof(f2411,plain,
( ! [X0] :
( ~ is_a_convergence_point_of_set(sK33,sK34,X0)
| in(X0,lim_points_of_net(sK33,sF82))
| empty_carrier(sF82)
| ~ transitive_relstr(sF82)
| ~ directed_relstr(sF82)
| ~ net_str(sF82,sK33)
| ~ element(X0,sF84) )
| ~ spl88_6
| ~ spl88_139 ),
inference(superposition,[],[f1035,f2090]) ).
fof(f1035,plain,
( ! [X3,X4] :
( ~ is_a_convergence_point_of_set(sK33,filter_of_net_str(sK33,X3),X4)
| in(X4,lim_points_of_net(sK33,X3))
| empty_carrier(X3)
| ~ transitive_relstr(X3)
| ~ directed_relstr(X3)
| ~ net_str(X3,sK33)
| ~ element(X4,sF84) )
| ~ spl88_6 ),
inference(avatar_component_clause,[],[f1034]) ).
fof(f3166,plain,
( ~ spl88_56
| ~ spl88_57
| ~ spl88_58
| spl88_59
| spl88_270
| ~ spl88_5
| ~ spl88_139 ),
inference(avatar_split_clause,[],[f3162,f2088,f1029,f3164,f1446,f1442,f1438,f1434]) ).
fof(f1029,plain,
( spl88_5
<=> ! [X2,X1] :
( ~ element(X1,sF84)
| is_a_convergence_point_of_set(sK33,filter_of_net_str(sK33,X2),X1)
| empty_carrier(X2)
| ~ transitive_relstr(X2)
| ~ directed_relstr(X2)
| ~ net_str(X2,sK33)
| ~ in(X1,lim_points_of_net(sK33,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_5])]) ).
fof(f3162,plain,
( ! [X1] :
( ~ in(X1,sF83)
| is_a_convergence_point_of_set(sK33,sK34,X1)
| ~ element(X1,sF84)
| empty_carrier(sF82)
| ~ transitive_relstr(sF82)
| ~ directed_relstr(sF82)
| ~ net_str(sF82,sK33) )
| ~ spl88_5
| ~ spl88_139 ),
inference(forward_demodulation,[],[f2412,f975]) ).
fof(f2412,plain,
( ! [X1] :
( is_a_convergence_point_of_set(sK33,sK34,X1)
| ~ element(X1,sF84)
| empty_carrier(sF82)
| ~ transitive_relstr(sF82)
| ~ directed_relstr(sF82)
| ~ net_str(sF82,sK33)
| ~ in(X1,lim_points_of_net(sK33,sF82)) )
| ~ spl88_5
| ~ spl88_139 ),
inference(superposition,[],[f1030,f2090]) ).
fof(f1030,plain,
( ! [X2,X1] :
( is_a_convergence_point_of_set(sK33,filter_of_net_str(sK33,X2),X1)
| ~ element(X1,sF84)
| empty_carrier(X2)
| ~ transitive_relstr(X2)
| ~ directed_relstr(X2)
| ~ net_str(X2,sK33)
| ~ in(X1,lim_points_of_net(sK33,X2)) )
| ~ spl88_5 ),
inference(avatar_component_clause,[],[f1029]) ).
fof(f3161,plain,
( spl88_269
| ~ spl88_56
| ~ spl88_193 ),
inference(avatar_split_clause,[],[f2880,f2568,f1434,f3158]) ).
fof(f3158,plain,
( spl88_269
<=> sF82 = net_str_of(sK33,the_carrier(sF82),the_InternalRel(sF82),the_mapping(sK33,sF82)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_269])]) ).
fof(f2880,plain,
( ~ net_str(sF82,sK33)
| sF82 = net_str_of(sK33,the_carrier(sF82),the_InternalRel(sF82),the_mapping(sK33,sF82))
| ~ spl88_193 ),
inference(resolution,[],[f2824,f1135]) ).
fof(f1135,plain,
! [X9] :
( ~ strict_net_str(X9,sK33)
| ~ net_str(X9,sK33)
| net_str_of(sK33,the_carrier(X9),the_InternalRel(X9),the_mapping(sK33,X9)) = X9 ),
inference(resolution,[],[f997,f845]) ).
fof(f845,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ strict_net_str(X1,X0)
| ~ net_str(X1,X0)
| net_str_of(X0,the_carrier(X1),the_InternalRel(X1),the_mapping(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f331]) ).
fof(f331,plain,
! [X0,X1] :
( net_str_of(X0,the_carrier(X1),the_InternalRel(X1),the_mapping(X0,X1)) = X1
| ~ strict_net_str(X1,X0)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f330]) ).
fof(f330,plain,
! [X0,X1] :
( net_str_of(X0,the_carrier(X1),the_InternalRel(X1),the_mapping(X0,X1)) = X1
| ~ strict_net_str(X1,X0)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& one_sorted_str(X0) )
=> ( strict_net_str(X1,X0)
=> net_str_of(X0,the_carrier(X1),the_InternalRel(X1),the_mapping(X0,X1)) = X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',abstractness_v6_waybel_0) ).
fof(f2824,plain,
( strict_net_str(sF82,sK33)
| ~ spl88_193 ),
inference(forward_demodulation,[],[f2817,f974]) ).
fof(f2817,plain,
( strict_net_str(net_of_bool_filter(sK33,sF81,sK34),sK33)
| ~ spl88_193 ),
inference(resolution,[],[f2570,f858]) ).
fof(f858,plain,
! [X2,X0,X1] :
( ~ sP27(X0,X1,X2)
| strict_net_str(net_of_bool_filter(X2,X1,X0),X2) ),
inference(cnf_transformation,[],[f515]) ).
fof(f3156,plain,
( ~ spl88_135
| ~ spl88_137
| spl88_138
| spl88_56
| ~ spl88_136
| ~ spl88_177 ),
inference(avatar_split_clause,[],[f3155,f2398,f2076,f1434,f2084,f2080,f2072]) ).
fof(f2072,plain,
( spl88_135
<=> filtered_subset(sK34,sF85) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_135])]) ).
fof(f2080,plain,
( spl88_137
<=> element(sK34,sF87) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_137])]) ).
fof(f2084,plain,
( spl88_138
<=> empty(sK34) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_138])]) ).
fof(f2076,plain,
( spl88_136
<=> upper_relstr_subset(sK34,sF85) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_136])]) ).
fof(f2398,plain,
( spl88_177
<=> ! [X0] :
( ~ element(X0,sF87)
| ~ filtered_subset(X0,sF85)
| empty(X0)
| sP29(sK33,X0,sF81)
| ~ upper_relstr_subset(X0,sF85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_177])]) ).
fof(f3155,plain,
( net_str(sF82,sK33)
| empty(sK34)
| ~ element(sK34,sF87)
| ~ filtered_subset(sK34,sF85)
| ~ spl88_136
| ~ spl88_177 ),
inference(forward_demodulation,[],[f3152,f974]) ).
fof(f3152,plain,
( empty(sK34)
| ~ element(sK34,sF87)
| ~ filtered_subset(sK34,sF85)
| net_str(net_of_bool_filter(sK33,sF81,sK34),sK33)
| ~ spl88_136
| ~ spl88_177 ),
inference(resolution,[],[f2563,f2077]) ).
fof(f2077,plain,
( upper_relstr_subset(sK34,sF85)
| ~ spl88_136 ),
inference(avatar_component_clause,[],[f2076]) ).
fof(f2563,plain,
( ! [X2] :
( ~ upper_relstr_subset(X2,sF85)
| empty(X2)
| ~ element(X2,sF87)
| ~ filtered_subset(X2,sF85)
| net_str(net_of_bool_filter(sK33,sF81,X2),sK33) )
| ~ spl88_177 ),
inference(resolution,[],[f2399,f868]) ).
fof(f868,plain,
! [X2,X0,X1] :
( ~ sP29(X0,X1,X2)
| net_str(net_of_bool_filter(X0,X2,X1),X0) ),
inference(cnf_transformation,[],[f519]) ).
fof(f519,plain,
! [X0,X1,X2] :
( ( net_str(net_of_bool_filter(X0,X2,X1),X0)
& strict_net_str(net_of_bool_filter(X0,X2,X1),X0)
& ~ empty_carrier(net_of_bool_filter(X0,X2,X1)) )
| ~ sP29(X0,X1,X2) ),
inference(rectify,[],[f518]) ).
fof(f518,plain,
! [X0,X2,X1] :
( ( net_str(net_of_bool_filter(X0,X1,X2),X0)
& strict_net_str(net_of_bool_filter(X0,X1,X2),X0)
& ~ empty_carrier(net_of_bool_filter(X0,X1,X2)) )
| ~ sP29(X0,X2,X1) ),
inference(nnf_transformation,[],[f414]) ).
fof(f2399,plain,
( ! [X0] :
( sP29(sK33,X0,sF81)
| ~ filtered_subset(X0,sF85)
| empty(X0)
| ~ element(X0,sF87)
| ~ upper_relstr_subset(X0,sF85) )
| ~ spl88_177 ),
inference(avatar_component_clause,[],[f2398]) ).
fof(f3143,plain,
( ~ spl88_225
| ~ spl88_268
| ~ spl88_219 ),
inference(avatar_split_clause,[],[f3129,f2727,f3140,f2751]) ).
fof(f2751,plain,
( spl88_225
<=> rel_str(boole_POSet(sK47(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_225])]) ).
fof(f3140,plain,
( spl88_268
<=> with_infima_relstr(boole_POSet(sK47(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_268])]) ).
fof(f2727,plain,
( spl88_219
<=> empty_carrier(boole_POSet(sK47(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_219])]) ).
fof(f3129,plain,
( ~ with_infima_relstr(boole_POSet(sK47(sK33)))
| ~ rel_str(boole_POSet(sK47(sK33)))
| ~ spl88_219 ),
inference(resolution,[],[f2729,f670]) ).
fof(f670,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_infima_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_infima_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f216]) ).
fof(f216,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_infima_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( rel_str(X0)
=> ( with_infima_relstr(X0)
=> ~ empty_carrier(X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',cc2_lattice3) ).
fof(f2729,plain,
( empty_carrier(boole_POSet(sK47(sK33)))
| ~ spl88_219 ),
inference(avatar_component_clause,[],[f2727]) ).
fof(f3138,plain,
( ~ spl88_225
| ~ spl88_267
| ~ spl88_219 ),
inference(avatar_split_clause,[],[f3128,f2727,f3135,f2751]) ).
fof(f3135,plain,
( spl88_267
<=> with_suprema_relstr(boole_POSet(sK47(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_267])]) ).
fof(f3128,plain,
( ~ with_suprema_relstr(boole_POSet(sK47(sK33)))
| ~ rel_str(boole_POSet(sK47(sK33)))
| ~ spl88_219 ),
inference(resolution,[],[f2729,f672]) ).
fof(f672,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_suprema_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f221]) ).
fof(f221,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_suprema_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f220]) ).
fof(f220,plain,
! [X0] :
( ~ empty_carrier(X0)
| ~ with_suprema_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( rel_str(X0)
=> ( with_suprema_relstr(X0)
=> ~ empty_carrier(X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',cc1_lattice3) ).
fof(f3133,plain,
~ spl88_219,
inference(avatar_contradiction_clause,[],[f3124]) ).
fof(f3124,plain,
( $false
| ~ spl88_219 ),
inference(resolution,[],[f2729,f604]) ).
fof(f604,plain,
! [X0] : ~ empty_carrier(boole_POSet(X0)),
inference(cnf_transformation,[],[f80]) ).
fof(f80,axiom,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc8_yellow_1) ).
fof(f3132,plain,
~ spl88_219,
inference(avatar_contradiction_clause,[],[f3125]) ).
fof(f3125,plain,
( $false
| ~ spl88_219 ),
inference(resolution,[],[f2729,f591]) ).
fof(f591,plain,
! [X0] : ~ empty_carrier(boole_POSet(X0)),
inference(cnf_transformation,[],[f159]) ).
fof(f159,plain,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
inference(pure_predicate_removal,[],[f158]) ).
fof(f158,plain,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
inference(pure_predicate_removal,[],[f154]) ).
fof(f154,plain,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
inference(pure_predicate_removal,[],[f150]) ).
fof(f150,plain,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
inference(pure_predicate_removal,[],[f148]) ).
fof(f148,plain,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& complemented_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
inference(pure_predicate_removal,[],[f62]) ).
fof(f62,axiom,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& boolean_relstr(boole_POSet(X0))
& complemented_relstr(boole_POSet(X0))
& heyting_relstr(boole_POSet(X0))
& distributive_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc1_waybel_7) ).
fof(f3131,plain,
~ spl88_219,
inference(avatar_contradiction_clause,[],[f3126]) ).
fof(f3126,plain,
( $false
| ~ spl88_219 ),
inference(resolution,[],[f2729,f577]) ).
fof(f577,plain,
! [X0] : ~ empty_carrier(boole_POSet(X0)),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& directed_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
inference(pure_predicate_removal,[],[f81]) ).
fof(f81,axiom,
! [X0] :
( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& ~ v1_yellow_3(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& directed_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc8_yellow_6) ).
fof(f3130,plain,
~ spl88_219,
inference(avatar_contradiction_clause,[],[f3127]) ).
fof(f3127,plain,
( $false
| ~ spl88_219 ),
inference(resolution,[],[f2729,f572]) ).
fof(f572,plain,
! [X0] : ~ empty_carrier(boole_POSet(X0)),
inference(cnf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0] :
( antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc7_yellow_1) ).
fof(f3122,plain,
spl88_225,
inference(avatar_contradiction_clause,[],[f3121]) ).
fof(f3121,plain,
( $false
| spl88_225 ),
inference(resolution,[],[f2753,f616]) ).
fof(f616,plain,
! [X0] : rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( rel_str(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',dt_k3_yellow_1) ).
fof(f2753,plain,
( ~ rel_str(boole_POSet(sK47(sK33)))
| spl88_225 ),
inference(avatar_component_clause,[],[f2751]) ).
fof(f3119,plain,
( ~ spl88_225
| ~ spl88_266
| spl88_224 ),
inference(avatar_split_clause,[],[f3111,f2747,f3116,f2751]) ).
fof(f3116,plain,
( spl88_266
<=> bounded_relstr(boole_POSet(sK47(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_266])]) ).
fof(f2747,plain,
( spl88_224
<=> upper_bounded_relstr(boole_POSet(sK47(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_224])]) ).
fof(f3111,plain,
( ~ bounded_relstr(boole_POSet(sK47(sK33)))
| ~ rel_str(boole_POSet(sK47(sK33)))
| spl88_224 ),
inference(resolution,[],[f2749,f669]) ).
fof(f669,plain,
! [X0] :
( upper_bounded_relstr(X0)
| ~ bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f215]) ).
fof(f215,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& lower_bounded_relstr(X0) )
| ~ bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(flattening,[],[f214]) ).
fof(f214,plain,
! [X0] :
( ( upper_bounded_relstr(X0)
& lower_bounded_relstr(X0) )
| ~ bounded_relstr(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( rel_str(X0)
=> ( bounded_relstr(X0)
=> ( upper_bounded_relstr(X0)
& lower_bounded_relstr(X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',cc4_yellow_0) ).
fof(f2749,plain,
( ~ upper_bounded_relstr(boole_POSet(sK47(sK33)))
| spl88_224 ),
inference(avatar_component_clause,[],[f2747]) ).
fof(f3114,plain,
spl88_224,
inference(avatar_contradiction_clause,[],[f3108]) ).
fof(f3108,plain,
( $false
| spl88_224 ),
inference(resolution,[],[f2749,f610]) ).
fof(f610,plain,
! [X0] : upper_bounded_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f80]) ).
fof(f3113,plain,
spl88_224,
inference(avatar_contradiction_clause,[],[f3109]) ).
fof(f3109,plain,
( $false
| spl88_224 ),
inference(resolution,[],[f2749,f597]) ).
fof(f597,plain,
! [X0] : upper_bounded_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f159]) ).
fof(f3112,plain,
spl88_224,
inference(avatar_contradiction_clause,[],[f3110]) ).
fof(f3110,plain,
( $false
| spl88_224 ),
inference(resolution,[],[f2749,f583]) ).
fof(f583,plain,
! [X0] : upper_bounded_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f160]) ).
fof(f3106,plain,
spl88_223,
inference(avatar_contradiction_clause,[],[f3099]) ).
fof(f3099,plain,
( $false
| spl88_223 ),
inference(resolution,[],[f2745,f608]) ).
fof(f608,plain,
! [X0] : antisymmetric_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f80]) ).
fof(f2745,plain,
( ~ antisymmetric_relstr(boole_POSet(sK47(sK33)))
| spl88_223 ),
inference(avatar_component_clause,[],[f2743]) ).
fof(f2743,plain,
( spl88_223
<=> antisymmetric_relstr(boole_POSet(sK47(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_223])]) ).
fof(f3105,plain,
spl88_223,
inference(avatar_contradiction_clause,[],[f3100]) ).
fof(f3100,plain,
( $false
| spl88_223 ),
inference(resolution,[],[f2745,f595]) ).
fof(f595,plain,
! [X0] : antisymmetric_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f159]) ).
fof(f3104,plain,
spl88_223,
inference(avatar_contradiction_clause,[],[f3101]) ).
fof(f3101,plain,
( $false
| spl88_223 ),
inference(resolution,[],[f2745,f581]) ).
fof(f581,plain,
! [X0] : antisymmetric_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f160]) ).
fof(f3103,plain,
spl88_223,
inference(avatar_contradiction_clause,[],[f3102]) ).
fof(f3102,plain,
( $false
| spl88_223 ),
inference(resolution,[],[f2745,f576]) ).
fof(f576,plain,
! [X0] : antisymmetric_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f78]) ).
fof(f3096,plain,
spl88_222,
inference(avatar_contradiction_clause,[],[f3089]) ).
fof(f3089,plain,
( $false
| spl88_222 ),
inference(resolution,[],[f2741,f607]) ).
fof(f607,plain,
! [X0] : transitive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f80]) ).
fof(f2741,plain,
( ~ transitive_relstr(boole_POSet(sK47(sK33)))
| spl88_222 ),
inference(avatar_component_clause,[],[f2739]) ).
fof(f2739,plain,
( spl88_222
<=> transitive_relstr(boole_POSet(sK47(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_222])]) ).
fof(f3095,plain,
spl88_222,
inference(avatar_contradiction_clause,[],[f3090]) ).
fof(f3090,plain,
( $false
| spl88_222 ),
inference(resolution,[],[f2741,f594]) ).
fof(f594,plain,
! [X0] : transitive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f159]) ).
fof(f3094,plain,
spl88_222,
inference(avatar_contradiction_clause,[],[f3091]) ).
fof(f3091,plain,
( $false
| spl88_222 ),
inference(resolution,[],[f2741,f580]) ).
fof(f580,plain,
! [X0] : transitive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f160]) ).
fof(f3093,plain,
spl88_222,
inference(avatar_contradiction_clause,[],[f3092]) ).
fof(f3092,plain,
( $false
| spl88_222 ),
inference(resolution,[],[f2741,f575]) ).
fof(f575,plain,
! [X0] : transitive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f78]) ).
fof(f3087,plain,
spl88_221,
inference(avatar_contradiction_clause,[],[f3080]) ).
fof(f3080,plain,
( $false
| spl88_221 ),
inference(resolution,[],[f2737,f606]) ).
fof(f606,plain,
! [X0] : reflexive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f80]) ).
fof(f2737,plain,
( ~ reflexive_relstr(boole_POSet(sK47(sK33)))
| spl88_221 ),
inference(avatar_component_clause,[],[f2735]) ).
fof(f2735,plain,
( spl88_221
<=> reflexive_relstr(boole_POSet(sK47(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_221])]) ).
fof(f3086,plain,
spl88_221,
inference(avatar_contradiction_clause,[],[f3081]) ).
fof(f3081,plain,
( $false
| spl88_221 ),
inference(resolution,[],[f2737,f593]) ).
fof(f593,plain,
! [X0] : reflexive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f159]) ).
fof(f3085,plain,
spl88_221,
inference(avatar_contradiction_clause,[],[f3082]) ).
fof(f3082,plain,
( $false
| spl88_221 ),
inference(resolution,[],[f2737,f579]) ).
fof(f579,plain,
! [X0] : reflexive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f160]) ).
fof(f3084,plain,
spl88_221,
inference(avatar_contradiction_clause,[],[f3083]) ).
fof(f3083,plain,
( $false
| spl88_221 ),
inference(resolution,[],[f2737,f574]) ).
fof(f574,plain,
! [X0] : reflexive_relstr(boole_POSet(X0)),
inference(cnf_transformation,[],[f78]) ).
fof(f3073,plain,
( spl88_264
| ~ spl88_265
| spl88_40 ),
inference(avatar_split_clause,[],[f3064,f1285,f3070,f3066]) ).
fof(f3066,plain,
( spl88_264
<=> empty(powerset(sK35)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_264])]) ).
fof(f3070,plain,
( spl88_265
<=> element(powerset(sK35),powerset(sF83)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_265])]) ).
fof(f3064,plain,
( ~ element(powerset(sK35),powerset(sF83))
| empty(powerset(sK35))
| spl88_40 ),
inference(resolution,[],[f2418,f819]) ).
fof(f819,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f124]) ).
fof(f124,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',reflexivity_r1_tarski) ).
fof(f2418,plain,
( ! [X3] :
( ~ subset(sK35,X3)
| ~ element(powerset(X3),powerset(sF83))
| empty(powerset(X3)) )
| spl88_40 ),
inference(resolution,[],[f1920,f849]) ).
fof(f849,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f335]) ).
fof(f335,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f139]) ).
fof(f139,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f132]) ).
fof(f132,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',t3_subset) ).
fof(f1920,plain,
( ! [X0] :
( ~ element(sK35,X0)
| empty(X0)
| ~ element(X0,powerset(sF83)) )
| spl88_40 ),
inference(resolution,[],[f1324,f822]) ).
fof(f822,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f313]) ).
fof(f313,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f312]) ).
fof(f312,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f130]) ).
fof(f130,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',t2_subset) ).
fof(f1324,plain,
( ! [X0] :
( ~ in(sK35,X0)
| ~ element(X0,powerset(sF83)) )
| spl88_40 ),
inference(resolution,[],[f1287,f877]) ).
fof(f877,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f348]) ).
fof(f348,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f347]) ).
fof(f347,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f133]) ).
fof(f133,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',t4_subset) ).
fof(f3063,plain,
( ~ spl88_218
| ~ spl88_263
| ~ spl88_212 ),
inference(avatar_split_clause,[],[f3049,f2697,f3060,f2721]) ).
fof(f2721,plain,
( spl88_218
<=> rel_str(boole_POSet(sK49(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_218])]) ).
fof(f3060,plain,
( spl88_263
<=> with_infima_relstr(boole_POSet(sK49(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_263])]) ).
fof(f2697,plain,
( spl88_212
<=> empty_carrier(boole_POSet(sK49(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_212])]) ).
fof(f3049,plain,
( ~ with_infima_relstr(boole_POSet(sK49(sK33)))
| ~ rel_str(boole_POSet(sK49(sK33)))
| ~ spl88_212 ),
inference(resolution,[],[f2699,f670]) ).
fof(f2699,plain,
( empty_carrier(boole_POSet(sK49(sK33)))
| ~ spl88_212 ),
inference(avatar_component_clause,[],[f2697]) ).
fof(f3058,plain,
( ~ spl88_218
| ~ spl88_262
| ~ spl88_212 ),
inference(avatar_split_clause,[],[f3048,f2697,f3055,f2721]) ).
fof(f3055,plain,
( spl88_262
<=> with_suprema_relstr(boole_POSet(sK49(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_262])]) ).
fof(f3048,plain,
( ~ with_suprema_relstr(boole_POSet(sK49(sK33)))
| ~ rel_str(boole_POSet(sK49(sK33)))
| ~ spl88_212 ),
inference(resolution,[],[f2699,f672]) ).
fof(f3053,plain,
~ spl88_212,
inference(avatar_contradiction_clause,[],[f3044]) ).
fof(f3044,plain,
( $false
| ~ spl88_212 ),
inference(resolution,[],[f2699,f604]) ).
fof(f3052,plain,
~ spl88_212,
inference(avatar_contradiction_clause,[],[f3045]) ).
fof(f3045,plain,
( $false
| ~ spl88_212 ),
inference(resolution,[],[f2699,f591]) ).
fof(f3051,plain,
~ spl88_212,
inference(avatar_contradiction_clause,[],[f3046]) ).
fof(f3046,plain,
( $false
| ~ spl88_212 ),
inference(resolution,[],[f2699,f577]) ).
fof(f3050,plain,
~ spl88_212,
inference(avatar_contradiction_clause,[],[f3047]) ).
fof(f3047,plain,
( $false
| ~ spl88_212 ),
inference(resolution,[],[f2699,f572]) ).
fof(f3041,plain,
spl88_218,
inference(avatar_contradiction_clause,[],[f3040]) ).
fof(f3040,plain,
( $false
| spl88_218 ),
inference(resolution,[],[f2723,f616]) ).
fof(f2723,plain,
( ~ rel_str(boole_POSet(sK49(sK33)))
| spl88_218 ),
inference(avatar_component_clause,[],[f2721]) ).
fof(f3037,plain,
( ~ spl88_218
| ~ spl88_261
| spl88_217 ),
inference(avatar_split_clause,[],[f3029,f2717,f3034,f2721]) ).
fof(f3034,plain,
( spl88_261
<=> bounded_relstr(boole_POSet(sK49(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_261])]) ).
fof(f2717,plain,
( spl88_217
<=> upper_bounded_relstr(boole_POSet(sK49(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_217])]) ).
fof(f3029,plain,
( ~ bounded_relstr(boole_POSet(sK49(sK33)))
| ~ rel_str(boole_POSet(sK49(sK33)))
| spl88_217 ),
inference(resolution,[],[f2719,f669]) ).
fof(f2719,plain,
( ~ upper_bounded_relstr(boole_POSet(sK49(sK33)))
| spl88_217 ),
inference(avatar_component_clause,[],[f2717]) ).
fof(f3032,plain,
spl88_217,
inference(avatar_contradiction_clause,[],[f3026]) ).
fof(f3026,plain,
( $false
| spl88_217 ),
inference(resolution,[],[f2719,f610]) ).
fof(f3031,plain,
spl88_217,
inference(avatar_contradiction_clause,[],[f3027]) ).
fof(f3027,plain,
( $false
| spl88_217 ),
inference(resolution,[],[f2719,f597]) ).
fof(f3030,plain,
spl88_217,
inference(avatar_contradiction_clause,[],[f3028]) ).
fof(f3028,plain,
( $false
| spl88_217 ),
inference(resolution,[],[f2719,f583]) ).
fof(f3025,plain,
( ~ spl88_255
| spl88_259
| ~ spl88_257
| ~ spl88_181 ),
inference(avatar_split_clause,[],[f3000,f2480,f3009,f3018,f3002]) ).
fof(f3002,plain,
( spl88_255
<=> function(the_mapping(sK33,sK40(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_255])]) ).
fof(f3018,plain,
( spl88_259
<=> ! [X5] :
( ~ relation_of2_as_subset(X5,the_carrier(sK40(sK33)),the_carrier(sK40(sK33)))
| strict_net_str(net_str_of(sK33,the_carrier(sK40(sK33)),X5,the_mapping(sK33,sK40(sK33))),sK33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_259])]) ).
fof(f3009,plain,
( spl88_257
<=> relation_of2_as_subset(the_mapping(sK33,sK40(sK33)),the_carrier(sK40(sK33)),sF84) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_257])]) ).
fof(f2480,plain,
( spl88_181
<=> quasi_total(the_mapping(sK33,sK40(sK33)),the_carrier(sK40(sK33)),sF84) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_181])]) ).
fof(f3000,plain,
( ! [X7] :
( ~ relation_of2_as_subset(the_mapping(sK33,sK40(sK33)),the_carrier(sK40(sK33)),sF84)
| ~ relation_of2_as_subset(X7,the_carrier(sK40(sK33)),the_carrier(sK40(sK33)))
| ~ function(the_mapping(sK33,sK40(sK33)))
| strict_net_str(net_str_of(sK33,the_carrier(sK40(sK33)),X7,the_mapping(sK33,sK40(sK33))),sK33) )
| ~ spl88_181 ),
inference(resolution,[],[f2482,f1242]) ).
fof(f2482,plain,
( quasi_total(the_mapping(sK33,sK40(sK33)),the_carrier(sK40(sK33)),sF84)
| ~ spl88_181 ),
inference(avatar_component_clause,[],[f2480]) ).
fof(f3024,plain,
( ~ spl88_255
| spl88_260
| ~ spl88_257
| ~ spl88_181 ),
inference(avatar_split_clause,[],[f2999,f2480,f3009,f3022,f3002]) ).
fof(f3022,plain,
( spl88_260
<=> ! [X6] :
( ~ relation_of2_as_subset(X6,the_carrier(sK40(sK33)),the_carrier(sK40(sK33)))
| net_str(net_str_of(sK33,the_carrier(sK40(sK33)),X6,the_mapping(sK33,sK40(sK33))),sK33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_260])]) ).
fof(f2999,plain,
( ! [X6] :
( ~ relation_of2_as_subset(the_mapping(sK33,sK40(sK33)),the_carrier(sK40(sK33)),sF84)
| ~ relation_of2_as_subset(X6,the_carrier(sK40(sK33)),the_carrier(sK40(sK33)))
| ~ function(the_mapping(sK33,sK40(sK33)))
| net_str(net_str_of(sK33,the_carrier(sK40(sK33)),X6,the_mapping(sK33,sK40(sK33))),sK33) )
| ~ spl88_181 ),
inference(resolution,[],[f2482,f1246]) ).
fof(f3020,plain,
( spl88_258
| ~ spl88_255
| spl88_259
| ~ spl88_257
| ~ spl88_181 ),
inference(avatar_split_clause,[],[f2998,f2480,f3009,f3018,f3002,f3014]) ).
fof(f3014,plain,
( spl88_258
<=> empty(the_carrier(sK40(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_258])]) ).
fof(f2998,plain,
( ! [X5] :
( ~ relation_of2_as_subset(the_mapping(sK33,sK40(sK33)),the_carrier(sK40(sK33)),sF84)
| ~ relation_of2_as_subset(X5,the_carrier(sK40(sK33)),the_carrier(sK40(sK33)))
| ~ function(the_mapping(sK33,sK40(sK33)))
| empty(the_carrier(sK40(sK33)))
| strict_net_str(net_str_of(sK33,the_carrier(sK40(sK33)),X5,the_mapping(sK33,sK40(sK33))),sK33) )
| ~ spl88_181 ),
inference(resolution,[],[f2482,f1238]) ).
fof(f3012,plain,
( ~ spl88_255
| spl88_256
| ~ spl88_257
| ~ spl88_181 ),
inference(avatar_split_clause,[],[f2997,f2480,f3009,f3006,f3002]) ).
fof(f3006,plain,
( spl88_256
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation_of2_as_subset(X0,the_carrier(sK40(sK33)),the_carrier(sK40(sK33)))
| sP32(X4,the_mapping(sK33,sK40(sK33)),X3,X0,X2,the_carrier(sK40(sK33)),X1,sK33)
| net_str_of(X1,X2,X3,X4) != net_str_of(sK33,the_carrier(sK40(sK33)),X0,the_mapping(sK33,sK40(sK33))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_256])]) ).
fof(f2997,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(the_mapping(sK33,sK40(sK33)),the_carrier(sK40(sK33)),sF84)
| ~ relation_of2_as_subset(X0,the_carrier(sK40(sK33)),the_carrier(sK40(sK33)))
| net_str_of(X1,X2,X3,X4) != net_str_of(sK33,the_carrier(sK40(sK33)),X0,the_mapping(sK33,sK40(sK33)))
| ~ function(the_mapping(sK33,sK40(sK33)))
| sP32(X4,the_mapping(sK33,sK40(sK33)),X3,X0,X2,the_carrier(sK40(sK33)),X1,sK33) )
| ~ spl88_181 ),
inference(resolution,[],[f2482,f1250]) ).
fof(f2996,plain,
spl88_216,
inference(avatar_contradiction_clause,[],[f2989]) ).
fof(f2989,plain,
( $false
| spl88_216 ),
inference(resolution,[],[f2715,f608]) ).
fof(f2715,plain,
( ~ antisymmetric_relstr(boole_POSet(sK49(sK33)))
| spl88_216 ),
inference(avatar_component_clause,[],[f2713]) ).
fof(f2713,plain,
( spl88_216
<=> antisymmetric_relstr(boole_POSet(sK49(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_216])]) ).
fof(f2995,plain,
spl88_216,
inference(avatar_contradiction_clause,[],[f2990]) ).
fof(f2990,plain,
( $false
| spl88_216 ),
inference(resolution,[],[f2715,f595]) ).
fof(f2994,plain,
spl88_216,
inference(avatar_contradiction_clause,[],[f2991]) ).
fof(f2991,plain,
( $false
| spl88_216 ),
inference(resolution,[],[f2715,f581]) ).
fof(f2993,plain,
spl88_216,
inference(avatar_contradiction_clause,[],[f2992]) ).
fof(f2992,plain,
( $false
| spl88_216 ),
inference(resolution,[],[f2715,f576]) ).
fof(f2984,plain,
spl88_215,
inference(avatar_contradiction_clause,[],[f2977]) ).
fof(f2977,plain,
( $false
| spl88_215 ),
inference(resolution,[],[f2711,f607]) ).
fof(f2711,plain,
( ~ transitive_relstr(boole_POSet(sK49(sK33)))
| spl88_215 ),
inference(avatar_component_clause,[],[f2709]) ).
fof(f2709,plain,
( spl88_215
<=> transitive_relstr(boole_POSet(sK49(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_215])]) ).
fof(f2983,plain,
spl88_215,
inference(avatar_contradiction_clause,[],[f2978]) ).
fof(f2978,plain,
( $false
| spl88_215 ),
inference(resolution,[],[f2711,f594]) ).
fof(f2982,plain,
spl88_215,
inference(avatar_contradiction_clause,[],[f2979]) ).
fof(f2979,plain,
( $false
| spl88_215 ),
inference(resolution,[],[f2711,f580]) ).
fof(f2981,plain,
spl88_215,
inference(avatar_contradiction_clause,[],[f2980]) ).
fof(f2980,plain,
( $false
| spl88_215 ),
inference(resolution,[],[f2711,f575]) ).
fof(f2976,plain,
( ~ spl88_250
| spl88_253
| ~ spl88_252 ),
inference(avatar_split_clause,[],[f2955,f2964,f2969,f2957]) ).
fof(f2957,plain,
( spl88_250
<=> function(the_mapping(sK33,sK41(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_250])]) ).
fof(f2969,plain,
( spl88_253
<=> ! [X5] :
( ~ relation_of2_as_subset(X5,the_carrier(sK41(sK33)),the_carrier(sK41(sK33)))
| strict_net_str(net_str_of(sK33,the_carrier(sK41(sK33)),X5,the_mapping(sK33,sK41(sK33))),sK33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_253])]) ).
fof(f2964,plain,
( spl88_252
<=> relation_of2_as_subset(the_mapping(sK33,sK41(sK33)),the_carrier(sK41(sK33)),sF84) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_252])]) ).
fof(f2955,plain,
! [X7] :
( ~ relation_of2_as_subset(the_mapping(sK33,sK41(sK33)),the_carrier(sK41(sK33)),sF84)
| ~ relation_of2_as_subset(X7,the_carrier(sK41(sK33)),the_carrier(sK41(sK33)))
| ~ function(the_mapping(sK33,sK41(sK33)))
| strict_net_str(net_str_of(sK33,the_carrier(sK41(sK33)),X7,the_mapping(sK33,sK41(sK33))),sK33) ),
inference(resolution,[],[f2475,f1242]) ).
fof(f2475,plain,
quasi_total(the_mapping(sK33,sK41(sK33)),the_carrier(sK41(sK33)),sF84),
inference(resolution,[],[f1888,f1318]) ).
fof(f1318,plain,
net_str(sK41(sK33),sK33),
inference(resolution,[],[f1121,f651]) ).
fof(f651,plain,
! [X0] :
( ~ sP4(X0)
| net_str(sK41(X0),X0) ),
inference(cnf_transformation,[],[f443]) ).
fof(f443,plain,
! [X0] :
( ( directed_relstr(sK41(X0))
& strict_net_str(sK41(X0),X0)
& antisymmetric_relstr(sK41(X0))
& transitive_relstr(sK41(X0))
& reflexive_relstr(sK41(X0))
& ~ empty_carrier(sK41(X0))
& net_str(sK41(X0),X0) )
| ~ sP4(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f441,f442]) ).
fof(f442,plain,
! [X0] :
( ? [X1] :
( directed_relstr(X1)
& strict_net_str(X1,X0)
& antisymmetric_relstr(X1)
& transitive_relstr(X1)
& reflexive_relstr(X1)
& ~ empty_carrier(X1)
& net_str(X1,X0) )
=> ( directed_relstr(sK41(X0))
& strict_net_str(sK41(X0),X0)
& antisymmetric_relstr(sK41(X0))
& transitive_relstr(sK41(X0))
& reflexive_relstr(sK41(X0))
& ~ empty_carrier(sK41(X0))
& net_str(sK41(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f441,plain,
! [X0] :
( ? [X1] :
( directed_relstr(X1)
& strict_net_str(X1,X0)
& antisymmetric_relstr(X1)
& transitive_relstr(X1)
& reflexive_relstr(X1)
& ~ empty_carrier(X1)
& net_str(X1,X0) )
| ~ sP4(X0) ),
inference(nnf_transformation,[],[f364]) ).
fof(f364,plain,
! [X0] :
( ? [X1] :
( directed_relstr(X1)
& strict_net_str(X1,X0)
& antisymmetric_relstr(X1)
& transitive_relstr(X1)
& reflexive_relstr(X1)
& ~ empty_carrier(X1)
& net_str(X1,X0) )
| ~ sP4(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f1121,plain,
sP4(sK33),
inference(resolution,[],[f997,f658]) ).
fof(f658,plain,
! [X0] :
( ~ one_sorted_str(X0)
| sP4(X0) ),
inference(cnf_transformation,[],[f365]) ).
fof(f365,plain,
! [X0] :
( sP4(X0)
| ~ one_sorted_str(X0) ),
inference(definition_folding,[],[f208,f364]) ).
fof(f208,plain,
! [X0] :
( ? [X1] :
( directed_relstr(X1)
& strict_net_str(X1,X0)
& antisymmetric_relstr(X1)
& transitive_relstr(X1)
& reflexive_relstr(X1)
& ~ empty_carrier(X1)
& net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f117]) ).
fof(f117,axiom,
! [X0] :
( one_sorted_str(X0)
=> ? [X1] :
( directed_relstr(X1)
& strict_net_str(X1,X0)
& antisymmetric_relstr(X1)
& transitive_relstr(X1)
& reflexive_relstr(X1)
& ~ empty_carrier(X1)
& net_str(X1,X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc5_waybel_0) ).
fof(f2975,plain,
( ~ spl88_250
| spl88_254
| ~ spl88_252 ),
inference(avatar_split_clause,[],[f2954,f2964,f2973,f2957]) ).
fof(f2973,plain,
( spl88_254
<=> ! [X6] :
( ~ relation_of2_as_subset(X6,the_carrier(sK41(sK33)),the_carrier(sK41(sK33)))
| net_str(net_str_of(sK33,the_carrier(sK41(sK33)),X6,the_mapping(sK33,sK41(sK33))),sK33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_254])]) ).
fof(f2954,plain,
! [X6] :
( ~ relation_of2_as_subset(the_mapping(sK33,sK41(sK33)),the_carrier(sK41(sK33)),sF84)
| ~ relation_of2_as_subset(X6,the_carrier(sK41(sK33)),the_carrier(sK41(sK33)))
| ~ function(the_mapping(sK33,sK41(sK33)))
| net_str(net_str_of(sK33,the_carrier(sK41(sK33)),X6,the_mapping(sK33,sK41(sK33))),sK33) ),
inference(resolution,[],[f2475,f1246]) ).
fof(f2971,plain,
( spl88_198
| ~ spl88_250
| spl88_253
| ~ spl88_252 ),
inference(avatar_split_clause,[],[f2953,f2964,f2969,f2957,f2629]) ).
fof(f2629,plain,
( spl88_198
<=> empty(the_carrier(sK41(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_198])]) ).
fof(f2953,plain,
! [X5] :
( ~ relation_of2_as_subset(the_mapping(sK33,sK41(sK33)),the_carrier(sK41(sK33)),sF84)
| ~ relation_of2_as_subset(X5,the_carrier(sK41(sK33)),the_carrier(sK41(sK33)))
| ~ function(the_mapping(sK33,sK41(sK33)))
| empty(the_carrier(sK41(sK33)))
| strict_net_str(net_str_of(sK33,the_carrier(sK41(sK33)),X5,the_mapping(sK33,sK41(sK33))),sK33) ),
inference(resolution,[],[f2475,f1238]) ).
fof(f2967,plain,
( ~ spl88_250
| spl88_251
| ~ spl88_252 ),
inference(avatar_split_clause,[],[f2952,f2964,f2961,f2957]) ).
fof(f2961,plain,
( spl88_251
<=> ! [X4,X0,X3,X2,X1] :
( ~ relation_of2_as_subset(X0,the_carrier(sK41(sK33)),the_carrier(sK41(sK33)))
| sP32(X4,the_mapping(sK33,sK41(sK33)),X3,X0,X2,the_carrier(sK41(sK33)),X1,sK33)
| net_str_of(sK33,the_carrier(sK41(sK33)),X0,the_mapping(sK33,sK41(sK33))) != net_str_of(X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_251])]) ).
fof(f2952,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation_of2_as_subset(the_mapping(sK33,sK41(sK33)),the_carrier(sK41(sK33)),sF84)
| ~ relation_of2_as_subset(X0,the_carrier(sK41(sK33)),the_carrier(sK41(sK33)))
| net_str_of(sK33,the_carrier(sK41(sK33)),X0,the_mapping(sK33,sK41(sK33))) != net_str_of(X1,X2,X3,X4)
| ~ function(the_mapping(sK33,sK41(sK33)))
| sP32(X4,the_mapping(sK33,sK41(sK33)),X3,X0,X2,the_carrier(sK41(sK33)),X1,sK33) ),
inference(resolution,[],[f2475,f1250]) ).
fof(f2951,plain,
spl88_214,
inference(avatar_contradiction_clause,[],[f2944]) ).
fof(f2944,plain,
( $false
| spl88_214 ),
inference(resolution,[],[f2707,f606]) ).
fof(f2707,plain,
( ~ reflexive_relstr(boole_POSet(sK49(sK33)))
| spl88_214 ),
inference(avatar_component_clause,[],[f2705]) ).
fof(f2705,plain,
( spl88_214
<=> reflexive_relstr(boole_POSet(sK49(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_214])]) ).
fof(f2950,plain,
spl88_214,
inference(avatar_contradiction_clause,[],[f2945]) ).
fof(f2945,plain,
( $false
| spl88_214 ),
inference(resolution,[],[f2707,f593]) ).
fof(f2949,plain,
spl88_214,
inference(avatar_contradiction_clause,[],[f2946]) ).
fof(f2946,plain,
( $false
| spl88_214 ),
inference(resolution,[],[f2707,f579]) ).
fof(f2948,plain,
spl88_214,
inference(avatar_contradiction_clause,[],[f2947]) ).
fof(f2947,plain,
( $false
| spl88_214 ),
inference(resolution,[],[f2707,f574]) ).
fof(f2943,plain,
( spl88_249
| spl88_144
| ~ spl88_30 ),
inference(avatar_split_clause,[],[f2935,f1203,f2178,f2940]) ).
fof(f2940,plain,
( spl88_249
<=> sP0(the_mapping(sK33,sK41(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_249])]) ).
fof(f2178,plain,
( spl88_144
<=> empty_carrier(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_144])]) ).
fof(f2935,plain,
( empty_carrier(sK41(sK33))
| sP0(the_mapping(sK33,sK41(sK33)))
| ~ spl88_30 ),
inference(resolution,[],[f2450,f1318]) ).
fof(f2933,plain,
( ~ spl88_159
| ~ spl88_142
| ~ spl88_143
| spl88_144
| spl88_248
| ~ spl88_5
| ~ spl88_146 ),
inference(avatar_split_clause,[],[f2920,f2187,f1029,f2931,f2178,f2174,f2170,f2269]) ).
fof(f2269,plain,
( spl88_159
<=> net_str(sK41(sK33),sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_159])]) ).
fof(f2170,plain,
( spl88_142
<=> directed_relstr(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_142])]) ).
fof(f2174,plain,
( spl88_143
<=> transitive_relstr(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_143])]) ).
fof(f2931,plain,
( spl88_248
<=> ! [X1] :
( is_a_convergence_point_of_set(sK33,a_2_1_yellow19(sK33,sK41(sK33)),X1)
| ~ in(X1,lim_points_of_net(sK33,sK41(sK33)))
| ~ element(X1,sF84) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_248])]) ).
fof(f2187,plain,
( spl88_146
<=> filter_of_net_str(sK33,sK41(sK33)) = a_2_1_yellow19(sK33,sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_146])]) ).
fof(f2920,plain,
( ! [X1] :
( is_a_convergence_point_of_set(sK33,a_2_1_yellow19(sK33,sK41(sK33)),X1)
| ~ element(X1,sF84)
| empty_carrier(sK41(sK33))
| ~ transitive_relstr(sK41(sK33))
| ~ directed_relstr(sK41(sK33))
| ~ net_str(sK41(sK33),sK33)
| ~ in(X1,lim_points_of_net(sK33,sK41(sK33))) )
| ~ spl88_5
| ~ spl88_146 ),
inference(superposition,[],[f1030,f2189]) ).
fof(f2189,plain,
( filter_of_net_str(sK33,sK41(sK33)) = a_2_1_yellow19(sK33,sK41(sK33))
| ~ spl88_146 ),
inference(avatar_component_clause,[],[f2187]) ).
fof(f2929,plain,
( ~ spl88_159
| ~ spl88_142
| ~ spl88_143
| spl88_144
| spl88_247
| ~ spl88_6
| ~ spl88_146 ),
inference(avatar_split_clause,[],[f2919,f2187,f1034,f2927,f2178,f2174,f2170,f2269]) ).
fof(f2927,plain,
( spl88_247
<=> ! [X0] :
( ~ is_a_convergence_point_of_set(sK33,a_2_1_yellow19(sK33,sK41(sK33)),X0)
| ~ element(X0,sF84)
| in(X0,lim_points_of_net(sK33,sK41(sK33))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_247])]) ).
fof(f2919,plain,
( ! [X0] :
( ~ is_a_convergence_point_of_set(sK33,a_2_1_yellow19(sK33,sK41(sK33)),X0)
| in(X0,lim_points_of_net(sK33,sK41(sK33)))
| empty_carrier(sK41(sK33))
| ~ transitive_relstr(sK41(sK33))
| ~ directed_relstr(sK41(sK33))
| ~ net_str(sK41(sK33),sK33)
| ~ element(X0,sF84) )
| ~ spl88_6
| ~ spl88_146 ),
inference(superposition,[],[f1035,f2189]) ).
fof(f2925,plain,
( ~ spl88_159
| spl88_144
| spl88_246
| ~ spl88_29
| ~ spl88_146 ),
inference(avatar_split_clause,[],[f2917,f2187,f1199,f2922,f2178,f2269]) ).
fof(f2922,plain,
( spl88_246
<=> element(a_2_1_yellow19(sK33,sK41(sK33)),sF87) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_246])]) ).
fof(f1199,plain,
( spl88_29
<=> ! [X4] :
( element(filter_of_net_str(sK33,X4),sF87)
| empty_carrier(X4)
| ~ net_str(X4,sK33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_29])]) ).
fof(f2917,plain,
( element(a_2_1_yellow19(sK33,sK41(sK33)),sF87)
| empty_carrier(sK41(sK33))
| ~ net_str(sK41(sK33),sK33)
| ~ spl88_29
| ~ spl88_146 ),
inference(superposition,[],[f1200,f2189]) ).
fof(f1200,plain,
( ! [X4] :
( element(filter_of_net_str(sK33,X4),sF87)
| empty_carrier(X4)
| ~ net_str(X4,sK33) )
| ~ spl88_29 ),
inference(avatar_component_clause,[],[f1199]) ).
fof(f2914,plain,
( spl88_239
| spl88_240
| ~ spl88_241
| ~ spl88_242
| ~ spl88_243
| ~ spl88_244
| ~ spl88_245 ),
inference(avatar_split_clause,[],[f2885,f2911,f2907,f2903,f2899,f2895,f2891,f2887]) ).
fof(f2887,plain,
( spl88_239
<=> empty_carrier(boole_POSet(sK43(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_239])]) ).
fof(f2891,plain,
( spl88_240
<=> sP14(boole_POSet(sK43(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_240])]) ).
fof(f2895,plain,
( spl88_241
<=> reflexive_relstr(boole_POSet(sK43(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_241])]) ).
fof(f2899,plain,
( spl88_242
<=> transitive_relstr(boole_POSet(sK43(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_242])]) ).
fof(f2903,plain,
( spl88_243
<=> antisymmetric_relstr(boole_POSet(sK43(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_243])]) ).
fof(f2907,plain,
( spl88_244
<=> upper_bounded_relstr(boole_POSet(sK43(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_244])]) ).
fof(f2911,plain,
( spl88_245
<=> rel_str(boole_POSet(sK43(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_245])]) ).
fof(f2885,plain,
( ~ rel_str(boole_POSet(sK43(sK33)))
| ~ upper_bounded_relstr(boole_POSet(sK43(sK33)))
| ~ antisymmetric_relstr(boole_POSet(sK43(sK33)))
| ~ transitive_relstr(boole_POSet(sK43(sK33)))
| ~ reflexive_relstr(boole_POSet(sK43(sK33)))
| sP14(boole_POSet(sK43(sK33)))
| empty_carrier(boole_POSet(sK43(sK33))) ),
inference(resolution,[],[f1922,f735]) ).
fof(f735,plain,
! [X0] :
( trivial_carrier(X0)
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| sP14(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f385]) ).
fof(f385,plain,
! [X0] :
( sP14(X0)
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| trivial_carrier(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f249,f384]) ).
fof(f384,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP14(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f249,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| trivial_carrier(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f248]) ).
fof(f248,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0)
| ~ upper_bounded_relstr(X0)
| ~ antisymmetric_relstr(X0)
| ~ transitive_relstr(X0)
| ~ reflexive_relstr(X0)
| trivial_carrier(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f113]) ).
fof(f113,axiom,
! [X0] :
( ( rel_str(X0)
& upper_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& transitive_relstr(X0)
& reflexive_relstr(X0)
& ~ trivial_carrier(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc4_waybel_7) ).
fof(f1922,plain,
~ trivial_carrier(boole_POSet(sK43(sK33))),
inference(resolution,[],[f1470,f618]) ).
fof(f618,plain,
! [X0] :
( ~ sP0(X0)
| ~ trivial_carrier(boole_POSet(X0)) ),
inference(cnf_transformation,[],[f427]) ).
fof(f427,plain,
! [X0] :
( ( complete_relstr(boole_POSet(X0))
& with_infima_relstr(boole_POSet(X0))
& with_suprema_relstr(boole_POSet(X0))
& join_complete_relstr(boole_POSet(X0))
& up_complete_relstr(boole_POSet(X0))
& bounded_relstr(boole_POSet(X0))
& upper_bounded_relstr(boole_POSet(X0))
& lower_bounded_relstr(boole_POSet(X0))
& antisymmetric_relstr(boole_POSet(X0))
& transitive_relstr(boole_POSet(X0))
& reflexive_relstr(boole_POSet(X0))
& strict_rel_str(boole_POSet(X0))
& ~ trivial_carrier(boole_POSet(X0))
& ~ empty_carrier(boole_POSet(X0)) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f356]) ).
fof(f1470,plain,
sP0(sK43(sK33)),
inference(resolution,[],[f1321,f631]) ).
fof(f1321,plain,
~ empty(sK43(sK33)),
inference(resolution,[],[f1122,f662]) ).
fof(f662,plain,
! [X0] :
( ~ sP5(X0)
| ~ empty(sK43(X0)) ),
inference(cnf_transformation,[],[f448]) ).
fof(f448,plain,
! [X0] :
( ( finite(sK43(X0))
& ~ empty(sK43(X0))
& element(sK43(X0),powerset(powerset(the_carrier(X0)))) )
| ~ sP5(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f446,f447]) ).
fof(f447,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ( finite(sK43(X0))
& ~ empty(sK43(X0))
& element(sK43(X0),powerset(powerset(the_carrier(X0)))) ) ),
introduced(choice_axiom,[]) ).
fof(f446,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f366]) ).
fof(f366,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f1122,plain,
sP5(sK33),
inference(resolution,[],[f997,f664]) ).
fof(f664,plain,
! [X0] :
( ~ one_sorted_str(X0)
| sP5(X0) ),
inference(cnf_transformation,[],[f367]) ).
fof(f367,plain,
! [X0] :
( sP5(X0)
| ~ one_sorted_str(X0) ),
inference(definition_folding,[],[f210,f366]) ).
fof(f210,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f109]) ).
fof(f109,axiom,
! [X0] :
( one_sorted_str(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(powerset(the_carrier(X0)))) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc3_waybel_7) ).
fof(f2878,plain,
( ~ spl88_233
| ~ spl88_234
| ~ spl88_235
| spl88_236
| spl88_138
| spl88_238
| ~ spl88_34
| ~ spl88_50 ),
inference(avatar_split_clause,[],[f2852,f1408,f1223,f2875,f2084,f2866,f2862,f2858,f2854]) ).
fof(f2854,plain,
( spl88_233
<=> element(sK46(boole_POSet(sK34)),powerset(the_carrier(boole_POSet(sK34)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_233])]) ).
fof(f2858,plain,
( spl88_234
<=> element(sK34,powerset(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_234])]) ).
fof(f2862,plain,
( spl88_235
<=> filtered_subset(sK46(boole_POSet(sK34)),boole_POSet(sK34)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_235])]) ).
fof(f2866,plain,
( spl88_236
<=> empty(sK46(boole_POSet(sK34))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_236])]) ).
fof(f2875,plain,
( spl88_238
<=> sP28(sK33,sK46(boole_POSet(sK34)),sK34) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_238])]) ).
fof(f1223,plain,
( spl88_34
<=> ! [X13,X12] :
( ~ element(X13,powerset(sF84))
| sP28(sK33,X12,X13)
| empty(X13)
| empty(X12)
| ~ filtered_subset(X12,boole_POSet(X13))
| ~ upper_relstr_subset(X12,boole_POSet(X13))
| ~ element(X12,powerset(the_carrier(boole_POSet(X13)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_34])]) ).
fof(f1408,plain,
( spl88_50
<=> sP14(boole_POSet(sK34)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_50])]) ).
fof(f2852,plain,
( sP28(sK33,sK46(boole_POSet(sK34)),sK34)
| empty(sK34)
| empty(sK46(boole_POSet(sK34)))
| ~ filtered_subset(sK46(boole_POSet(sK34)),boole_POSet(sK34))
| ~ element(sK34,powerset(sF84))
| ~ element(sK46(boole_POSet(sK34)),powerset(the_carrier(boole_POSet(sK34))))
| ~ spl88_34
| ~ spl88_50 ),
inference(resolution,[],[f1593,f1224]) ).
fof(f1224,plain,
( ! [X12,X13] :
( ~ upper_relstr_subset(X12,boole_POSet(X13))
| sP28(sK33,X12,X13)
| empty(X13)
| empty(X12)
| ~ filtered_subset(X12,boole_POSet(X13))
| ~ element(X13,powerset(sF84))
| ~ element(X12,powerset(the_carrier(boole_POSet(X13)))) )
| ~ spl88_34 ),
inference(avatar_component_clause,[],[f1223]) ).
fof(f1593,plain,
( upper_relstr_subset(sK46(boole_POSet(sK34)),boole_POSet(sK34))
| ~ spl88_50 ),
inference(resolution,[],[f1410,f734]) ).
fof(f734,plain,
! [X0] :
( ~ sP14(X0)
| upper_relstr_subset(sK46(X0),X0) ),
inference(cnf_transformation,[],[f463]) ).
fof(f463,plain,
! [X0] :
( ( upper_relstr_subset(sK46(X0),X0)
& filtered_subset(sK46(X0),X0)
& proper_element(sK46(X0),powerset(the_carrier(X0)))
& ~ empty(sK46(X0))
& element(sK46(X0),powerset(the_carrier(X0))) )
| ~ sP14(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f461,f462]) ).
fof(f462,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( upper_relstr_subset(sK46(X0),X0)
& filtered_subset(sK46(X0),X0)
& proper_element(sK46(X0),powerset(the_carrier(X0)))
& ~ empty(sK46(X0))
& element(sK46(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f461,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& filtered_subset(X1,X0)
& proper_element(X1,powerset(the_carrier(X0)))
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP14(X0) ),
inference(nnf_transformation,[],[f384]) ).
fof(f1410,plain,
( sP14(boole_POSet(sK34))
| ~ spl88_50 ),
inference(avatar_component_clause,[],[f1408]) ).
fof(f2873,plain,
( ~ spl88_233
| ~ spl88_234
| ~ spl88_235
| spl88_236
| spl88_138
| spl88_237
| ~ spl88_35
| ~ spl88_50 ),
inference(avatar_split_clause,[],[f2851,f1408,f1228,f2870,f2084,f2866,f2862,f2858,f2854]) ).
fof(f2870,plain,
( spl88_237
<=> sP29(sK33,sK46(boole_POSet(sK34)),sK34) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_237])]) ).
fof(f1228,plain,
( spl88_35
<=> ! [X14,X15] :
( ~ element(X15,powerset(sF84))
| sP29(sK33,X14,X15)
| empty(X15)
| empty(X14)
| ~ filtered_subset(X14,boole_POSet(X15))
| ~ upper_relstr_subset(X14,boole_POSet(X15))
| ~ element(X14,powerset(the_carrier(boole_POSet(X15)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_35])]) ).
fof(f2851,plain,
( sP29(sK33,sK46(boole_POSet(sK34)),sK34)
| empty(sK34)
| empty(sK46(boole_POSet(sK34)))
| ~ filtered_subset(sK46(boole_POSet(sK34)),boole_POSet(sK34))
| ~ element(sK34,powerset(sF84))
| ~ element(sK46(boole_POSet(sK34)),powerset(the_carrier(boole_POSet(sK34))))
| ~ spl88_35
| ~ spl88_50 ),
inference(resolution,[],[f1593,f1229]) ).
fof(f1229,plain,
( ! [X14,X15] :
( ~ upper_relstr_subset(X14,boole_POSet(X15))
| sP29(sK33,X14,X15)
| empty(X15)
| empty(X14)
| ~ filtered_subset(X14,boole_POSet(X15))
| ~ element(X15,powerset(sF84))
| ~ element(X14,powerset(the_carrier(boole_POSet(X15)))) )
| ~ spl88_35 ),
inference(avatar_component_clause,[],[f1228]) ).
fof(f2826,plain,
( spl88_57
| ~ spl88_193 ),
inference(avatar_split_clause,[],[f2825,f2568,f1438]) ).
fof(f2825,plain,
( directed_relstr(sF82)
| ~ spl88_193 ),
inference(forward_demodulation,[],[f2818,f974]) ).
fof(f2818,plain,
( directed_relstr(net_of_bool_filter(sK33,sF81,sK34))
| ~ spl88_193 ),
inference(resolution,[],[f2570,f859]) ).
fof(f859,plain,
! [X2,X0,X1] :
( ~ sP27(X0,X1,X2)
| directed_relstr(net_of_bool_filter(X2,X1,X0)) ),
inference(cnf_transformation,[],[f515]) ).
fof(f2823,plain,
( spl88_58
| ~ spl88_193 ),
inference(avatar_split_clause,[],[f2822,f2568,f1442]) ).
fof(f2822,plain,
( transitive_relstr(sF82)
| ~ spl88_193 ),
inference(forward_demodulation,[],[f2816,f974]) ).
fof(f2816,plain,
( transitive_relstr(net_of_bool_filter(sK33,sF81,sK34))
| ~ spl88_193 ),
inference(resolution,[],[f2570,f857]) ).
fof(f857,plain,
! [X2,X0,X1] :
( ~ sP27(X0,X1,X2)
| transitive_relstr(net_of_bool_filter(X2,X1,X0)) ),
inference(cnf_transformation,[],[f515]) ).
fof(f2820,plain,
( ~ spl88_59
| ~ spl88_193 ),
inference(avatar_split_clause,[],[f2819,f2568,f1446]) ).
fof(f2819,plain,
( ~ empty_carrier(sF82)
| ~ spl88_193 ),
inference(forward_demodulation,[],[f2814,f974]) ).
fof(f2814,plain,
( ~ empty_carrier(net_of_bool_filter(sK33,sF81,sK34))
| ~ spl88_193 ),
inference(resolution,[],[f2570,f855]) ).
fof(f855,plain,
! [X2,X0,X1] :
( ~ sP27(X0,X1,X2)
| ~ empty_carrier(net_of_bool_filter(X2,X1,X0)) ),
inference(cnf_transformation,[],[f515]) ).
fof(f2806,plain,
spl88_159,
inference(avatar_contradiction_clause,[],[f2805]) ).
fof(f2805,plain,
( $false
| spl88_159 ),
inference(resolution,[],[f2271,f1318]) ).
fof(f2271,plain,
( ~ net_str(sK41(sK33),sK33)
| spl88_159 ),
inference(avatar_component_clause,[],[f2269]) ).
fof(f2787,plain,
spl88_151,
inference(avatar_contradiction_clause,[],[f2786]) ).
fof(f2786,plain,
( $false
| spl88_151 ),
inference(resolution,[],[f2755,f1121]) ).
fof(f2755,plain,
( ~ sP4(sK33)
| spl88_151 ),
inference(resolution,[],[f2234,f653]) ).
fof(f653,plain,
! [X0] :
( reflexive_relstr(sK41(X0))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f443]) ).
fof(f2234,plain,
( ~ reflexive_relstr(sK41(sK33))
| spl88_151 ),
inference(avatar_component_clause,[],[f2232]) ).
fof(f2232,plain,
( spl88_151
<=> reflexive_relstr(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_151])]) ).
fof(f2785,plain,
( spl88_226
| spl88_227
| ~ spl88_228
| ~ spl88_229
| ~ spl88_230
| ~ spl88_231
| ~ spl88_232
| ~ spl88_8 ),
inference(avatar_split_clause,[],[f2756,f1043,f2782,f2778,f2774,f2770,f2766,f2762,f2758]) ).
fof(f2758,plain,
( spl88_226
<=> empty_carrier(boole_POSet(sK48(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_226])]) ).
fof(f2762,plain,
( spl88_227
<=> sP14(boole_POSet(sK48(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_227])]) ).
fof(f2766,plain,
( spl88_228
<=> reflexive_relstr(boole_POSet(sK48(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_228])]) ).
fof(f2770,plain,
( spl88_229
<=> transitive_relstr(boole_POSet(sK48(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_229])]) ).
fof(f2774,plain,
( spl88_230
<=> antisymmetric_relstr(boole_POSet(sK48(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_230])]) ).
fof(f2778,plain,
( spl88_231
<=> upper_bounded_relstr(boole_POSet(sK48(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_231])]) ).
fof(f2782,plain,
( spl88_232
<=> rel_str(boole_POSet(sK48(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_232])]) ).
fof(f1043,plain,
( spl88_8
<=> sP16(sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_8])]) ).
fof(f2756,plain,
( ~ rel_str(boole_POSet(sK48(sK33)))
| ~ upper_bounded_relstr(boole_POSet(sK48(sK33)))
| ~ antisymmetric_relstr(boole_POSet(sK48(sK33)))
| ~ transitive_relstr(boole_POSet(sK48(sK33)))
| ~ reflexive_relstr(boole_POSet(sK48(sK33)))
| sP14(boole_POSet(sK48(sK33)))
| empty_carrier(boole_POSet(sK48(sK33)))
| ~ spl88_8 ),
inference(resolution,[],[f1500,f735]) ).
fof(f1500,plain,
( ~ trivial_carrier(boole_POSet(sK48(sK33)))
| ~ spl88_8 ),
inference(resolution,[],[f1388,f618]) ).
fof(f1388,plain,
( sP0(sK48(sK33))
| ~ spl88_8 ),
inference(resolution,[],[f1280,f631]) ).
fof(f1280,plain,
( ~ empty(sK48(sK33))
| ~ spl88_8 ),
inference(resolution,[],[f1045,f744]) ).
fof(f744,plain,
! [X0] :
( ~ sP16(X0)
| ~ empty(sK48(X0)) ),
inference(cnf_transformation,[],[f470]) ).
fof(f470,plain,
! [X0] :
( ( closed_subset(sK48(X0),X0)
& ~ empty(sK48(X0))
& element(sK48(X0),powerset(the_carrier(X0))) )
| ~ sP16(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48])],[f468,f469]) ).
fof(f469,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( closed_subset(sK48(X0),X0)
& ~ empty(sK48(X0))
& element(sK48(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f468,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP16(X0) ),
inference(nnf_transformation,[],[f388]) ).
fof(f388,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP16(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f1045,plain,
( sP16(sK33)
| ~ spl88_8 ),
inference(avatar_component_clause,[],[f1043]) ).
fof(f2754,plain,
( spl88_219
| spl88_220
| ~ spl88_221
| ~ spl88_222
| ~ spl88_223
| ~ spl88_224
| ~ spl88_225
| ~ spl88_7 ),
inference(avatar_split_clause,[],[f2725,f1038,f2751,f2747,f2743,f2739,f2735,f2731,f2727]) ).
fof(f2731,plain,
( spl88_220
<=> sP14(boole_POSet(sK47(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_220])]) ).
fof(f1038,plain,
( spl88_7
<=> sP15(sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_7])]) ).
fof(f2725,plain,
( ~ rel_str(boole_POSet(sK47(sK33)))
| ~ upper_bounded_relstr(boole_POSet(sK47(sK33)))
| ~ antisymmetric_relstr(boole_POSet(sK47(sK33)))
| ~ transitive_relstr(boole_POSet(sK47(sK33)))
| ~ reflexive_relstr(boole_POSet(sK47(sK33)))
| sP14(boole_POSet(sK47(sK33)))
| empty_carrier(boole_POSet(sK47(sK33)))
| ~ spl88_7 ),
inference(resolution,[],[f1486,f735]) ).
fof(f1486,plain,
( ~ trivial_carrier(boole_POSet(sK47(sK33)))
| ~ spl88_7 ),
inference(resolution,[],[f1387,f618]) ).
fof(f1387,plain,
( sP0(sK47(sK33))
| ~ spl88_7 ),
inference(resolution,[],[f1275,f631]) ).
fof(f1275,plain,
( ~ empty(sK47(sK33))
| ~ spl88_7 ),
inference(resolution,[],[f1040,f739]) ).
fof(f739,plain,
! [X0] :
( ~ sP15(X0)
| ~ empty(sK47(X0)) ),
inference(cnf_transformation,[],[f467]) ).
fof(f467,plain,
! [X0] :
( ( closed_subset(sK47(X0),X0)
& open_subset(sK47(X0),X0)
& ~ empty(sK47(X0))
& element(sK47(X0),powerset(the_carrier(X0))) )
| ~ sP15(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK47])],[f465,f466]) ).
fof(f466,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( closed_subset(sK47(X0),X0)
& open_subset(sK47(X0),X0)
& ~ empty(sK47(X0))
& element(sK47(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f465,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP15(X0) ),
inference(nnf_transformation,[],[f386]) ).
fof(f386,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP15(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f1040,plain,
( sP15(sK33)
| ~ spl88_7 ),
inference(avatar_component_clause,[],[f1038]) ).
fof(f2724,plain,
( spl88_212
| spl88_213
| ~ spl88_214
| ~ spl88_215
| ~ spl88_216
| ~ spl88_217
| ~ spl88_218
| spl88_27 ),
inference(avatar_split_clause,[],[f2695,f1186,f2721,f2717,f2713,f2709,f2705,f2701,f2697]) ).
fof(f2701,plain,
( spl88_213
<=> sP14(boole_POSet(sK49(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_213])]) ).
fof(f1186,plain,
( spl88_27
<=> empty(sK49(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_27])]) ).
fof(f2695,plain,
( ~ rel_str(boole_POSet(sK49(sK33)))
| ~ upper_bounded_relstr(boole_POSet(sK49(sK33)))
| ~ antisymmetric_relstr(boole_POSet(sK49(sK33)))
| ~ transitive_relstr(boole_POSet(sK49(sK33)))
| ~ reflexive_relstr(boole_POSet(sK49(sK33)))
| sP14(boole_POSet(sK49(sK33)))
| empty_carrier(boole_POSet(sK49(sK33)))
| spl88_27 ),
inference(resolution,[],[f1472,f735]) ).
fof(f1472,plain,
( ~ trivial_carrier(boole_POSet(sK49(sK33)))
| spl88_27 ),
inference(resolution,[],[f1386,f618]) ).
fof(f1386,plain,
( sP0(sK49(sK33))
| spl88_27 ),
inference(resolution,[],[f1188,f631]) ).
fof(f1188,plain,
( ~ empty(sK49(sK33))
| spl88_27 ),
inference(avatar_component_clause,[],[f1186]) ).
fof(f2686,plain,
( spl88_144
| spl88_211 ),
inference(avatar_split_clause,[],[f2623,f2684,f2178]) ).
fof(f2684,plain,
( spl88_211
<=> ! [X16,X17] :
( ~ net_str(X16,sK41(sK33))
| sP31(X17,sK41(sK33),X16)
| empty_carrier(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_211])]) ).
fof(f2623,plain,
! [X16,X17] :
( ~ net_str(X16,sK41(sK33))
| empty_carrier(X16)
| sP31(X17,sK41(sK33),X16)
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2195,f876]) ).
fof(f2195,plain,
one_sorted_str(sK41(sK33)),
inference(resolution,[],[f2168,f666]) ).
fof(f2168,plain,
rel_str(sK41(sK33)),
inference(resolution,[],[f1318,f1120]) ).
fof(f2682,plain,
( spl88_144
| spl88_210 ),
inference(avatar_split_clause,[],[f2622,f2680,f2178]) ).
fof(f2680,plain,
( spl88_210
<=> ! [X14,X15] :
( ~ element(X14,powerset(the_carrier(boole_POSet(X15))))
| sP29(sK41(sK33),X14,X15)
| empty(X15)
| ~ element(X15,powerset(the_carrier(sK41(sK33))))
| empty(X14)
| ~ filtered_subset(X14,boole_POSet(X15))
| ~ upper_relstr_subset(X14,boole_POSet(X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_210])]) ).
fof(f2622,plain,
! [X14,X15] :
( ~ element(X14,powerset(the_carrier(boole_POSet(X15))))
| ~ upper_relstr_subset(X14,boole_POSet(X15))
| ~ filtered_subset(X14,boole_POSet(X15))
| empty(X14)
| ~ element(X15,powerset(the_carrier(sK41(sK33))))
| empty(X15)
| sP29(sK41(sK33),X14,X15)
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2195,f869]) ).
fof(f2678,plain,
( spl88_144
| spl88_209 ),
inference(avatar_split_clause,[],[f2621,f2676,f2178]) ).
fof(f2676,plain,
( spl88_209
<=> ! [X13,X12] :
( ~ element(X12,powerset(the_carrier(boole_POSet(X13))))
| sP28(sK41(sK33),X12,X13)
| empty(X13)
| ~ element(X13,powerset(the_carrier(sK41(sK33))))
| empty(X12)
| ~ filtered_subset(X12,boole_POSet(X13))
| ~ upper_relstr_subset(X12,boole_POSet(X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_209])]) ).
fof(f2621,plain,
! [X12,X13] :
( ~ element(X12,powerset(the_carrier(boole_POSet(X13))))
| ~ upper_relstr_subset(X12,boole_POSet(X13))
| ~ filtered_subset(X12,boole_POSet(X13))
| empty(X12)
| ~ element(X13,powerset(the_carrier(sK41(sK33))))
| empty(X13)
| sP28(sK41(sK33),X12,X13)
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2195,f865]) ).
fof(f2674,plain,
( spl88_144
| spl88_208 ),
inference(avatar_split_clause,[],[f2620,f2672,f2178]) ).
fof(f2672,plain,
( spl88_208
<=> ! [X11,X10] :
( ~ element(X10,powerset(the_carrier(boole_POSet(X11))))
| sP27(X10,X11,sK41(sK33))
| empty(X11)
| ~ element(X11,powerset(the_carrier(sK41(sK33))))
| empty(X10)
| ~ filtered_subset(X10,boole_POSet(X11))
| ~ upper_relstr_subset(X10,boole_POSet(X11))
| ~ proper_element(X10,powerset(the_carrier(boole_POSet(X11)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_208])]) ).
fof(f2620,plain,
! [X10,X11] :
( ~ element(X10,powerset(the_carrier(boole_POSet(X11))))
| ~ proper_element(X10,powerset(the_carrier(boole_POSet(X11))))
| ~ upper_relstr_subset(X10,boole_POSet(X11))
| ~ filtered_subset(X10,boole_POSet(X11))
| empty(X10)
| ~ element(X11,powerset(the_carrier(sK41(sK33))))
| empty(X11)
| sP27(X10,X11,sK41(sK33))
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2195,f860]) ).
fof(f2670,plain,
( spl88_144
| spl88_207 ),
inference(avatar_split_clause,[],[f2617,f2668,f2178]) ).
fof(f2668,plain,
( spl88_207
<=> ! [X7] :
( ~ net_str(X7,sK41(sK33))
| upper_relstr_subset(filter_of_net_str(sK41(sK33),X7),boole_POSet(cast_as_carrier_subset(sK41(sK33))))
| empty_carrier(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_207])]) ).
fof(f2617,plain,
! [X7] :
( ~ net_str(X7,sK41(sK33))
| empty_carrier(X7)
| upper_relstr_subset(filter_of_net_str(sK41(sK33),X7),boole_POSet(cast_as_carrier_subset(sK41(sK33))))
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2195,f840]) ).
fof(f2666,plain,
( spl88_144
| spl88_206 ),
inference(avatar_split_clause,[],[f2616,f2664,f2178]) ).
fof(f2664,plain,
( spl88_206
<=> ! [X6] :
( ~ net_str(X6,sK41(sK33))
| ~ empty(filter_of_net_str(sK41(sK33),X6))
| empty_carrier(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_206])]) ).
fof(f2616,plain,
! [X6] :
( ~ net_str(X6,sK41(sK33))
| empty_carrier(X6)
| ~ empty(filter_of_net_str(sK41(sK33),X6))
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2195,f839]) ).
fof(f2662,plain,
( spl88_144
| spl88_205 ),
inference(avatar_split_clause,[],[f2615,f2660,f2178]) ).
fof(f2660,plain,
( spl88_205
<=> ! [X5] :
( ~ net_str(X5,sK41(sK33))
| sP25(sK41(sK33),X5)
| empty_carrier(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_205])]) ).
fof(f2615,plain,
! [X5] :
( ~ net_str(X5,sK41(sK33))
| empty_carrier(X5)
| sP25(sK41(sK33),X5)
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2195,f838]) ).
fof(f2658,plain,
( spl88_144
| spl88_204 ),
inference(avatar_split_clause,[],[f2614,f2656,f2178]) ).
fof(f2656,plain,
( spl88_204
<=> ! [X4] :
( ~ net_str(X4,sK41(sK33))
| element(filter_of_net_str(sK41(sK33),X4),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK41(sK33))))))
| empty_carrier(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_204])]) ).
fof(f2614,plain,
! [X4] :
( ~ net_str(X4,sK41(sK33))
| empty_carrier(X4)
| element(filter_of_net_str(sK41(sK33),X4),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK41(sK33))))))
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2195,f834]) ).
fof(f2654,plain,
( spl88_144
| spl88_203 ),
inference(avatar_split_clause,[],[f2613,f2652,f2178]) ).
fof(f2652,plain,
( spl88_203
<=> ! [X3] :
( ~ net_str(X3,sK41(sK33))
| sP24(sK41(sK33),X3)
| empty_carrier(X3)
| ~ transitive_relstr(X3)
| ~ directed_relstr(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_203])]) ).
fof(f2613,plain,
! [X3] :
( ~ net_str(X3,sK41(sK33))
| ~ directed_relstr(X3)
| ~ transitive_relstr(X3)
| empty_carrier(X3)
| sP24(sK41(sK33),X3)
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2195,f833]) ).
fof(f2650,plain,
( spl88_144
| ~ spl88_202 ),
inference(avatar_split_clause,[],[f2612,f2647,f2178]) ).
fof(f2647,plain,
( spl88_202
<=> empty(sK49(sK41(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_202])]) ).
fof(f2612,plain,
( ~ empty(sK49(sK41(sK33)))
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2195,f752]) ).
fof(f2645,plain,
( spl88_144
| spl88_201 ),
inference(avatar_split_clause,[],[f2611,f2642,f2178]) ).
fof(f2642,plain,
( spl88_201
<=> element(sK49(sK41(sK33)),powerset(the_carrier(sK41(sK33)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_201])]) ).
fof(f2611,plain,
( element(sK49(sK41(sK33)),powerset(the_carrier(sK41(sK33))))
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2195,f751]) ).
fof(f2640,plain,
( spl88_144
| spl88_200 ),
inference(avatar_split_clause,[],[f2610,f2638,f2178]) ).
fof(f2638,plain,
( spl88_200
<=> ! [X2] :
( ~ net_str(X2,sK41(sK33))
| filter_of_net_str(sK41(sK33),X2) = a_2_1_yellow19(sK41(sK33),X2)
| empty_carrier(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_200])]) ).
fof(f2610,plain,
! [X2] :
( ~ net_str(X2,sK41(sK33))
| empty_carrier(X2)
| filter_of_net_str(sK41(sK33),X2) = a_2_1_yellow19(sK41(sK33),X2)
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2195,f750]) ).
fof(f2636,plain,
( spl88_144
| spl88_199 ),
inference(avatar_split_clause,[],[f2609,f2634,f2178]) ).
fof(f2634,plain,
( spl88_199
<=> ! [X1] :
( ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK41(sK33))))))
| filter_of_net_str(sK41(sK33),net_of_bool_filter(sK41(sK33),cast_as_carrier_subset(sK41(sK33)),X1)) = X1
| empty(X1)
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK41(sK33))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK41(sK33))))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK41(sK33)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_199])]) ).
fof(f2609,plain,
! [X1] :
( ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK41(sK33))))))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK41(sK33))))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK41(sK33))))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK41(sK33))))
| empty(X1)
| filter_of_net_str(sK41(sK33),net_of_bool_filter(sK41(sK33),cast_as_carrier_subset(sK41(sK33)),X1)) = X1
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2195,f749]) ).
fof(f2632,plain,
( spl88_144
| ~ spl88_198 ),
inference(avatar_split_clause,[],[f2608,f2629,f2178]) ).
fof(f2608,plain,
( ~ empty(the_carrier(sK41(sK33)))
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2195,f748]) ).
fof(f2593,plain,
( ~ spl88_48
| ~ spl88_140
| spl88_194
| spl88_195
| spl88_22
| ~ spl88_196
| ~ spl88_197
| ~ spl88_34 ),
inference(avatar_split_clause,[],[f2576,f1223,f2590,f2586,f1148,f2582,f2578,f2102,f1382]) ).
fof(f1382,plain,
( spl88_48
<=> rel_str(sF85) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_48])]) ).
fof(f2102,plain,
( spl88_140
<=> element(sF81,powerset(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_140])]) ).
fof(f2578,plain,
( spl88_194
<=> sP28(sK33,sK44(sF85),sF81) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_194])]) ).
fof(f2582,plain,
( spl88_195
<=> empty(sK44(sF85)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_195])]) ).
fof(f1148,plain,
( spl88_22
<=> empty(sF81) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_22])]) ).
fof(f2586,plain,
( spl88_196
<=> filtered_subset(sK44(sF85),sF85) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_196])]) ).
fof(f2590,plain,
( spl88_197
<=> element(sK44(sF85),sF87) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_197])]) ).
fof(f2576,plain,
( ~ element(sK44(sF85),sF87)
| ~ filtered_subset(sK44(sF85),sF85)
| empty(sF81)
| empty(sK44(sF85))
| sP28(sK33,sK44(sF85),sF81)
| ~ element(sF81,powerset(sF84))
| ~ rel_str(sF85)
| ~ spl88_34 ),
inference(forward_demodulation,[],[f2575,f982]) ).
fof(f982,plain,
powerset(sF86) = sF87,
introduced(function_definition,[]) ).
fof(f2575,plain,
( ~ element(sK44(sF85),powerset(sF86))
| ~ filtered_subset(sK44(sF85),sF85)
| empty(sF81)
| empty(sK44(sF85))
| sP28(sK33,sK44(sF85),sF81)
| ~ element(sF81,powerset(sF84))
| ~ rel_str(sF85)
| ~ spl88_34 ),
inference(forward_demodulation,[],[f2574,f981]) ).
fof(f981,plain,
the_carrier(sF85) = sF86,
introduced(function_definition,[]) ).
fof(f2574,plain,
( ~ filtered_subset(sK44(sF85),sF85)
| empty(sF81)
| empty(sK44(sF85))
| sP28(sK33,sK44(sF85),sF81)
| ~ element(sF81,powerset(sF84))
| ~ element(sK44(sF85),powerset(the_carrier(sF85)))
| ~ rel_str(sF85)
| ~ spl88_34 ),
inference(superposition,[],[f2096,f980]) ).
fof(f980,plain,
boole_POSet(sF81) = sF85,
introduced(function_definition,[]) ).
fof(f2096,plain,
( ! [X0] :
( ~ filtered_subset(sK44(boole_POSet(X0)),boole_POSet(X0))
| empty(X0)
| empty(sK44(boole_POSet(X0)))
| sP28(sK33,sK44(boole_POSet(X0)),X0)
| ~ element(X0,powerset(sF84))
| ~ element(sK44(boole_POSet(X0)),powerset(the_carrier(boole_POSet(X0))))
| ~ rel_str(boole_POSet(X0)) )
| ~ spl88_34 ),
inference(resolution,[],[f1224,f725]) ).
fof(f725,plain,
! [X0] :
( upper_relstr_subset(sK44(X0),X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f458]) ).
fof(f458,plain,
! [X0] :
( ( upper_relstr_subset(sK44(X0),X0)
& element(sK44(X0),powerset(the_carrier(X0))) )
| ~ rel_str(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f244,f457]) ).
fof(f457,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
=> ( upper_relstr_subset(sK44(X0),X0)
& element(sK44(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f244,plain,
! [X0] :
( ? [X1] :
( upper_relstr_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f164]) ).
fof(f164,plain,
! [X0] :
( rel_str(X0)
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f120]) ).
fof(f120,axiom,
! [X0] :
( rel_str(X0)
=> ? [X1] :
( upper_relstr_subset(X1,X0)
& lower_relstr_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc7_waybel_0) ).
fof(f2571,plain,
( ~ spl88_137
| spl88_193
| spl88_138
| ~ spl88_135
| ~ spl88_136
| ~ spl88_176 ),
inference(avatar_split_clause,[],[f2566,f2392,f2076,f2072,f2084,f2568,f2080]) ).
fof(f2392,plain,
( spl88_176
<=> ! [X0] :
( ~ element(X0,sF87)
| ~ upper_relstr_subset(X0,sF85)
| ~ filtered_subset(X0,sF85)
| empty(X0)
| sP27(X0,sF81,sK33)
| ~ proper_element(X0,sF87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_176])]) ).
fof(f2566,plain,
( ~ upper_relstr_subset(sK34,sF85)
| ~ filtered_subset(sK34,sF85)
| empty(sK34)
| sP27(sK34,sF81,sK33)
| ~ element(sK34,sF87)
| ~ spl88_176 ),
inference(resolution,[],[f2393,f984]) ).
fof(f984,plain,
proper_element(sK34,sF87),
inference(definition_folding,[],[f564,f982,f981,f980,f973]) ).
fof(f973,plain,
cast_as_carrier_subset(sK33) = sF81,
introduced(function_definition,[]) ).
fof(f564,plain,
proper_element(sK34,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33))))),
inference(cnf_transformation,[],[f426]) ).
fof(f2393,plain,
( ! [X0] :
( ~ proper_element(X0,sF87)
| ~ upper_relstr_subset(X0,sF85)
| ~ filtered_subset(X0,sF85)
| empty(X0)
| sP27(X0,sF81,sK33)
| ~ element(X0,sF87) )
| ~ spl88_176 ),
inference(avatar_component_clause,[],[f2392]) ).
fof(f2551,plain,
( ~ spl88_65
| spl88_188
| ~ spl88_189
| ~ spl88_99
| ~ spl88_190
| ~ spl88_191
| ~ spl88_192
| ~ spl88_133 ),
inference(avatar_split_clause,[],[f2530,f2045,f2548,f2544,f2540,f1777,f2536,f2532,f1552]) ).
fof(f1552,plain,
( spl88_65
<=> one_sorted_str(sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_65])]) ).
fof(f2532,plain,
( spl88_188
<=> empty(the_carrier(sK42(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_188])]) ).
fof(f2536,plain,
( spl88_189
<=> function(the_mapping(sK33,sK42(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_189])]) ).
fof(f1777,plain,
( spl88_99
<=> empty_carrier(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_99])]) ).
fof(f2540,plain,
( spl88_190
<=> quasi_total(the_mapping(sK33,sK42(sK33)),the_carrier(sK42(sK33)),sF84) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_190])]) ).
fof(f2544,plain,
( spl88_191
<=> relation_of2_as_subset(the_mapping(sK33,sK42(sK33)),the_carrier(sK42(sK33)),sF84) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_191])]) ).
fof(f2548,plain,
( spl88_192
<=> relation_of2_as_subset(the_InternalRel(sK42(sK33)),the_carrier(sK42(sK33)),the_carrier(sK42(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_192])]) ).
fof(f2045,plain,
( spl88_133
<=> sK42(sK33) = net_str_of(sK33,the_carrier(sK42(sK33)),the_InternalRel(sK42(sK33)),the_mapping(sK33,sK42(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_133])]) ).
fof(f2530,plain,
( ~ relation_of2_as_subset(the_InternalRel(sK42(sK33)),the_carrier(sK42(sK33)),the_carrier(sK42(sK33)))
| ~ relation_of2_as_subset(the_mapping(sK33,sK42(sK33)),the_carrier(sK42(sK33)),sF84)
| ~ quasi_total(the_mapping(sK33,sK42(sK33)),the_carrier(sK42(sK33)),sF84)
| ~ empty_carrier(sK42(sK33))
| ~ function(the_mapping(sK33,sK42(sK33)))
| empty(the_carrier(sK42(sK33)))
| ~ one_sorted_str(sK33)
| ~ spl88_133 ),
inference(forward_literal_rewriting,[],[f2529,f878]) ).
fof(f2529,plain,
( ~ relation_of2_as_subset(the_mapping(sK33,sK42(sK33)),the_carrier(sK42(sK33)),sF84)
| ~ quasi_total(the_mapping(sK33,sK42(sK33)),the_carrier(sK42(sK33)),sF84)
| ~ empty_carrier(sK42(sK33))
| ~ function(the_mapping(sK33,sK42(sK33)))
| ~ relation_of2(the_InternalRel(sK42(sK33)),the_carrier(sK42(sK33)),the_carrier(sK42(sK33)))
| empty(the_carrier(sK42(sK33)))
| ~ one_sorted_str(sK33)
| ~ spl88_133 ),
inference(forward_literal_rewriting,[],[f2528,f878]) ).
fof(f2528,plain,
( ~ quasi_total(the_mapping(sK33,sK42(sK33)),the_carrier(sK42(sK33)),sF84)
| ~ relation_of2(the_mapping(sK33,sK42(sK33)),the_carrier(sK42(sK33)),sF84)
| ~ empty_carrier(sK42(sK33))
| ~ function(the_mapping(sK33,sK42(sK33)))
| ~ relation_of2(the_InternalRel(sK42(sK33)),the_carrier(sK42(sK33)),the_carrier(sK42(sK33)))
| empty(the_carrier(sK42(sK33)))
| ~ one_sorted_str(sK33)
| ~ spl88_133 ),
inference(forward_demodulation,[],[f2527,f978]) ).
fof(f2527,plain,
( ~ relation_of2(the_mapping(sK33,sK42(sK33)),the_carrier(sK42(sK33)),sF84)
| ~ empty_carrier(sK42(sK33))
| ~ quasi_total(the_mapping(sK33,sK42(sK33)),the_carrier(sK42(sK33)),the_carrier(sK33))
| ~ function(the_mapping(sK33,sK42(sK33)))
| ~ relation_of2(the_InternalRel(sK42(sK33)),the_carrier(sK42(sK33)),the_carrier(sK42(sK33)))
| empty(the_carrier(sK42(sK33)))
| ~ one_sorted_str(sK33)
| ~ spl88_133 ),
inference(forward_demodulation,[],[f2526,f978]) ).
fof(f2526,plain,
( ~ empty_carrier(sK42(sK33))
| ~ relation_of2(the_mapping(sK33,sK42(sK33)),the_carrier(sK42(sK33)),the_carrier(sK33))
| ~ quasi_total(the_mapping(sK33,sK42(sK33)),the_carrier(sK42(sK33)),the_carrier(sK33))
| ~ function(the_mapping(sK33,sK42(sK33)))
| ~ relation_of2(the_InternalRel(sK42(sK33)),the_carrier(sK42(sK33)),the_carrier(sK42(sK33)))
| empty(the_carrier(sK42(sK33)))
| ~ one_sorted_str(sK33)
| ~ spl88_133 ),
inference(superposition,[],[f881,f2047]) ).
fof(f2047,plain,
( sK42(sK33) = net_str_of(sK33,the_carrier(sK42(sK33)),the_InternalRel(sK42(sK33)),the_mapping(sK33,sK42(sK33)))
| ~ spl88_133 ),
inference(avatar_component_clause,[],[f2045]) ).
fof(f881,plain,
! [X2,X3,X0,X1] :
( ~ empty_carrier(net_str_of(X0,X1,X2,X3))
| ~ relation_of2(X3,X1,the_carrier(X0))
| ~ quasi_total(X3,X1,the_carrier(X0))
| ~ function(X3)
| ~ relation_of2(X2,X1,X1)
| empty(X1)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f2525,plain,
( ~ spl88_186
| spl88_187 ),
inference(avatar_split_clause,[],[f2506,f2522,f2518]) ).
fof(f2518,plain,
( spl88_186
<=> net_str(sK33,sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_186])]) ).
fof(f2522,plain,
( spl88_187
<=> relation_of2_as_subset(the_mapping(sK33,sK33),sF84,sF84) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_187])]) ).
fof(f2506,plain,
( relation_of2_as_subset(the_mapping(sK33,sK33),sF84,sF84)
| ~ net_str(sK33,sK33) ),
inference(superposition,[],[f1889,f978]) ).
fof(f1889,plain,
! [X1] :
( relation_of2_as_subset(the_mapping(sK33,X1),the_carrier(X1),sF84)
| ~ net_str(X1,sK33) ),
inference(forward_demodulation,[],[f1887,f978]) ).
fof(f1887,plain,
! [X1] :
( ~ net_str(X1,sK33)
| relation_of2_as_subset(the_mapping(sK33,X1),the_carrier(X1),the_carrier(sK33)) ),
inference(resolution,[],[f1134,f843]) ).
fof(f843,plain,
! [X0,X1] :
( ~ sP26(X0,X1)
| relation_of2_as_subset(the_mapping(X0,X1),the_carrier(X1),the_carrier(X0)) ),
inference(cnf_transformation,[],[f506]) ).
fof(f2516,plain,
( ~ spl88_184
| spl88_185 ),
inference(avatar_split_clause,[],[f2505,f2513,f2509]) ).
fof(f2509,plain,
( spl88_184
<=> net_str(sF85,sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_184])]) ).
fof(f2513,plain,
( spl88_185
<=> relation_of2_as_subset(the_mapping(sK33,sF85),sF86,sF84) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_185])]) ).
fof(f2505,plain,
( relation_of2_as_subset(the_mapping(sK33,sF85),sF86,sF84)
| ~ net_str(sF85,sK33) ),
inference(superposition,[],[f1889,f981]) ).
fof(f2503,plain,
( ~ spl88_128
| ~ spl88_183
| ~ spl88_122 ),
inference(avatar_split_clause,[],[f2489,f1892,f2500,f1916]) ).
fof(f1916,plain,
( spl88_128
<=> rel_str(boole_POSet(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_128])]) ).
fof(f2500,plain,
( spl88_183
<=> with_infima_relstr(boole_POSet(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_183])]) ).
fof(f1892,plain,
( spl88_122
<=> empty_carrier(boole_POSet(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_122])]) ).
fof(f2489,plain,
( ~ with_infima_relstr(boole_POSet(sF84))
| ~ rel_str(boole_POSet(sF84))
| ~ spl88_122 ),
inference(resolution,[],[f1894,f670]) ).
fof(f1894,plain,
( empty_carrier(boole_POSet(sF84))
| ~ spl88_122 ),
inference(avatar_component_clause,[],[f1892]) ).
fof(f2498,plain,
( ~ spl88_128
| ~ spl88_182
| ~ spl88_122 ),
inference(avatar_split_clause,[],[f2488,f1892,f2495,f1916]) ).
fof(f2495,plain,
( spl88_182
<=> with_suprema_relstr(boole_POSet(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_182])]) ).
fof(f2488,plain,
( ~ with_suprema_relstr(boole_POSet(sF84))
| ~ rel_str(boole_POSet(sF84))
| ~ spl88_122 ),
inference(resolution,[],[f1894,f672]) ).
fof(f2493,plain,
~ spl88_122,
inference(avatar_contradiction_clause,[],[f2484]) ).
fof(f2484,plain,
( $false
| ~ spl88_122 ),
inference(resolution,[],[f1894,f604]) ).
fof(f2492,plain,
~ spl88_122,
inference(avatar_contradiction_clause,[],[f2485]) ).
fof(f2485,plain,
( $false
| ~ spl88_122 ),
inference(resolution,[],[f1894,f591]) ).
fof(f2491,plain,
~ spl88_122,
inference(avatar_contradiction_clause,[],[f2486]) ).
fof(f2486,plain,
( $false
| ~ spl88_122 ),
inference(resolution,[],[f1894,f577]) ).
fof(f2490,plain,
~ spl88_122,
inference(avatar_contradiction_clause,[],[f2487]) ).
fof(f2487,plain,
( $false
| ~ spl88_122 ),
inference(resolution,[],[f1894,f572]) ).
fof(f2483,plain,
( ~ spl88_65
| spl88_181 ),
inference(avatar_split_clause,[],[f2477,f2480,f1552]) ).
fof(f2477,plain,
( quasi_total(the_mapping(sK33,sK40(sK33)),the_carrier(sK40(sK33)),sF84)
| ~ one_sorted_str(sK33) ),
inference(resolution,[],[f1888,f650]) ).
fof(f650,plain,
! [X0] :
( net_str(sK40(X0),X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f440]) ).
fof(f440,plain,
! [X0] :
( net_str(sK40(X0),X0)
| ~ one_sorted_str(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f207,f439]) ).
fof(f439,plain,
! [X0] :
( ? [X1] : net_str(X1,X0)
=> net_str(sK40(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f207,plain,
! [X0] :
( ? [X1] : net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( one_sorted_str(X0)
=> ? [X1] : net_str(X1,X0) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',existence_l1_waybel_0) ).
fof(f2474,plain,
spl88_128,
inference(avatar_contradiction_clause,[],[f2473]) ).
fof(f2473,plain,
( $false
| spl88_128 ),
inference(resolution,[],[f1918,f616]) ).
fof(f1918,plain,
( ~ rel_str(boole_POSet(sF84))
| spl88_128 ),
inference(avatar_component_clause,[],[f1916]) ).
fof(f2472,plain,
( spl88_144
| spl88_180
| ~ spl88_31
| ~ spl88_146 ),
inference(avatar_split_clause,[],[f2467,f2187,f1207,f2469,f2178]) ).
fof(f2469,plain,
( spl88_180
<=> sP0(a_2_1_yellow19(sK33,sK41(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_180])]) ).
fof(f1207,plain,
( spl88_31
<=> ! [X6] :
( ~ net_str(X6,sK33)
| ~ empty(filter_of_net_str(sK33,X6))
| empty_carrier(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_31])]) ).
fof(f2467,plain,
( sP0(a_2_1_yellow19(sK33,sK41(sK33)))
| empty_carrier(sK41(sK33))
| ~ spl88_31
| ~ spl88_146 ),
inference(forward_demodulation,[],[f2463,f2189]) ).
fof(f2463,plain,
( empty_carrier(sK41(sK33))
| sP0(filter_of_net_str(sK33,sK41(sK33)))
| ~ spl88_31 ),
inference(resolution,[],[f1971,f1318]) ).
fof(f1971,plain,
( ! [X0] :
( ~ net_str(X0,sK33)
| empty_carrier(X0)
| sP0(filter_of_net_str(sK33,X0)) )
| ~ spl88_31 ),
inference(resolution,[],[f1208,f631]) ).
fof(f1208,plain,
( ! [X6] :
( ~ empty(filter_of_net_str(sK33,X6))
| ~ net_str(X6,sK33)
| empty_carrier(X6) )
| ~ spl88_31 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f2462,plain,
( ~ spl88_128
| ~ spl88_179
| spl88_127 ),
inference(avatar_split_clause,[],[f2454,f1912,f2459,f1916]) ).
fof(f2459,plain,
( spl88_179
<=> bounded_relstr(boole_POSet(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_179])]) ).
fof(f1912,plain,
( spl88_127
<=> upper_bounded_relstr(boole_POSet(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_127])]) ).
fof(f2454,plain,
( ~ bounded_relstr(boole_POSet(sF84))
| ~ rel_str(boole_POSet(sF84))
| spl88_127 ),
inference(resolution,[],[f1914,f669]) ).
fof(f1914,plain,
( ~ upper_bounded_relstr(boole_POSet(sF84))
| spl88_127 ),
inference(avatar_component_clause,[],[f1912]) ).
fof(f2457,plain,
spl88_127,
inference(avatar_contradiction_clause,[],[f2451]) ).
fof(f2451,plain,
( $false
| spl88_127 ),
inference(resolution,[],[f1914,f610]) ).
fof(f2456,plain,
spl88_127,
inference(avatar_contradiction_clause,[],[f2452]) ).
fof(f2452,plain,
( $false
| spl88_127 ),
inference(resolution,[],[f1914,f597]) ).
fof(f2455,plain,
spl88_127,
inference(avatar_contradiction_clause,[],[f2453]) ).
fof(f2453,plain,
( $false
| spl88_127 ),
inference(resolution,[],[f1914,f583]) ).
fof(f2449,plain,
spl88_126,
inference(avatar_contradiction_clause,[],[f2442]) ).
fof(f2442,plain,
( $false
| spl88_126 ),
inference(resolution,[],[f1910,f608]) ).
fof(f1910,plain,
( ~ antisymmetric_relstr(boole_POSet(sF84))
| spl88_126 ),
inference(avatar_component_clause,[],[f1908]) ).
fof(f1908,plain,
( spl88_126
<=> antisymmetric_relstr(boole_POSet(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_126])]) ).
fof(f2448,plain,
spl88_126,
inference(avatar_contradiction_clause,[],[f2443]) ).
fof(f2443,plain,
( $false
| spl88_126 ),
inference(resolution,[],[f1910,f595]) ).
fof(f2447,plain,
spl88_126,
inference(avatar_contradiction_clause,[],[f2444]) ).
fof(f2444,plain,
( $false
| spl88_126 ),
inference(resolution,[],[f1910,f581]) ).
fof(f2446,plain,
spl88_126,
inference(avatar_contradiction_clause,[],[f2445]) ).
fof(f2445,plain,
( $false
| spl88_126 ),
inference(resolution,[],[f1910,f576]) ).
fof(f2439,plain,
( ~ spl88_174
| ~ spl88_61
| ~ spl88_13
| spl88_173 ),
inference(avatar_split_clause,[],[f2437,f2349,f1073,f1458,f2357]) ).
fof(f2357,plain,
( spl88_174
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_174])]) ).
fof(f1458,plain,
( spl88_61
<=> element(empty_set,powerset(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_61])]) ).
fof(f1073,plain,
( spl88_13
<=> ! [X7] :
( ~ element(X7,powerset(sF84))
| closed_subset(X7,sK33)
| ~ empty(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_13])]) ).
fof(f2349,plain,
( spl88_173
<=> closed_subset(empty_set,sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_173])]) ).
fof(f2437,plain,
( ~ element(empty_set,powerset(sF84))
| ~ empty(empty_set)
| ~ spl88_13
| spl88_173 ),
inference(resolution,[],[f2351,f1074]) ).
fof(f1074,plain,
( ! [X7] :
( closed_subset(X7,sK33)
| ~ element(X7,powerset(sF84))
| ~ empty(X7) )
| ~ spl88_13 ),
inference(avatar_component_clause,[],[f1073]) ).
fof(f2351,plain,
( ~ closed_subset(empty_set,sK33)
| spl88_173 ),
inference(avatar_component_clause,[],[f2349]) ).
fof(f2438,plain,
( ~ spl88_17
| spl88_173 ),
inference(avatar_contradiction_clause,[],[f2436]) ).
fof(f2436,plain,
( $false
| ~ spl88_17
| spl88_173 ),
inference(resolution,[],[f2351,f1395]) ).
fof(f1395,plain,
( closed_subset(empty_set,sK33)
| ~ spl88_17 ),
inference(backward_demodulation,[],[f1296,f1392]) ).
fof(f1392,plain,
( empty_set = sK54(sK33)
| ~ spl88_17 ),
inference(resolution,[],[f1294,f729]) ).
fof(f729,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f247]) ).
fof(f247,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f135]) ).
fof(f135,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',t6_boole) ).
fof(f1294,plain,
( empty(sK54(sK33))
| ~ spl88_17 ),
inference(resolution,[],[f1094,f791]) ).
fof(f791,plain,
! [X0] :
( ~ sP21(X0)
| empty(sK54(X0)) ),
inference(cnf_transformation,[],[f487]) ).
fof(f487,plain,
! [X0] :
( ( nowhere_dense(sK54(X0),X0)
& boundary_set(sK54(X0),X0)
& closed_subset(sK54(X0),X0)
& open_subset(sK54(X0),X0)
& empty(sK54(X0))
& element(sK54(X0),powerset(the_carrier(X0))) )
| ~ sP21(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54])],[f485,f486]) ).
fof(f486,plain,
! [X0] :
( ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( nowhere_dense(sK54(X0),X0)
& boundary_set(sK54(X0),X0)
& closed_subset(sK54(X0),X0)
& open_subset(sK54(X0),X0)
& empty(sK54(X0))
& element(sK54(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f485,plain,
! [X0] :
( ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP21(X0) ),
inference(nnf_transformation,[],[f398]) ).
fof(f398,plain,
! [X0] :
( ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP21(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).
fof(f1094,plain,
( sP21(sK33)
| ~ spl88_17 ),
inference(avatar_component_clause,[],[f1092]) ).
fof(f1092,plain,
( spl88_17
<=> sP21(sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_17])]) ).
fof(f1296,plain,
( closed_subset(sK54(sK33),sK33)
| ~ spl88_17 ),
inference(resolution,[],[f1094,f793]) ).
fof(f793,plain,
! [X0] :
( ~ sP21(X0)
| closed_subset(sK54(X0),X0) ),
inference(cnf_transformation,[],[f487]) ).
fof(f2435,plain,
( ~ spl88_173
| spl88_132
| ~ spl88_175 ),
inference(avatar_split_clause,[],[f2432,f2369,f2039,f2349]) ).
fof(f2039,plain,
( spl88_132
<=> closed_subset(sK39(sK33),sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_132])]) ).
fof(f2369,plain,
( spl88_175
<=> empty(sK39(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_175])]) ).
fof(f2432,plain,
( ~ closed_subset(empty_set,sK33)
| spl88_132
| ~ spl88_175 ),
inference(backward_demodulation,[],[f2041,f2428]) ).
fof(f2428,plain,
( empty_set = sK39(sK33)
| ~ spl88_175 ),
inference(resolution,[],[f2370,f729]) ).
fof(f2370,plain,
( empty(sK39(sK33))
| ~ spl88_175 ),
inference(avatar_component_clause,[],[f2369]) ).
fof(f2041,plain,
( ~ closed_subset(sK39(sK33),sK33)
| spl88_132 ),
inference(avatar_component_clause,[],[f2039]) ).
fof(f2426,plain,
spl88_175,
inference(avatar_contradiction_clause,[],[f2425]) ).
fof(f2425,plain,
( $false
| spl88_175 ),
inference(resolution,[],[f2413,f999]) ).
fof(f999,plain,
sP3(sK33),
inference(resolution,[],[f560,f647]) ).
fof(f647,plain,
! [X0] :
( ~ top_str(X0)
| sP3(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f363,plain,
! [X0] :
( sP3(X0)
| ~ top_str(X0) ),
inference(definition_folding,[],[f204,f362]) ).
fof(f362,plain,
! [X0] :
( ? [X1] :
( boundary_set(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP3(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f204,plain,
! [X0] :
( ? [X1] :
( boundary_set(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f184]) ).
fof(f184,plain,
! [X0] :
( top_str(X0)
=> ? [X1] :
( boundary_set(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f179]) ).
fof(f179,plain,
! [X0] :
( top_str(X0)
=> ? [X1] :
( boundary_set(X1,X0)
& v1_membered(X1)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f178]) ).
fof(f178,plain,
! [X0] :
( top_str(X0)
=> ? [X1] :
( boundary_set(X1,X0)
& v2_membered(X1)
& v1_membered(X1)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f173]) ).
fof(f173,plain,
! [X0] :
( top_str(X0)
=> ? [X1] :
( boundary_set(X1,X0)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f170]) ).
fof(f170,plain,
! [X0] :
( top_str(X0)
=> ? [X1] :
( boundary_set(X1,X0)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f111]) ).
fof(f111,axiom,
! [X0] :
( top_str(X0)
=> ? [X1] :
( boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc4_tops_1) ).
fof(f2413,plain,
( ~ sP3(sK33)
| spl88_175 ),
inference(resolution,[],[f2371,f645]) ).
fof(f645,plain,
! [X0] :
( empty(sK39(X0))
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f438]) ).
fof(f438,plain,
! [X0] :
( ( boundary_set(sK39(X0),X0)
& empty(sK39(X0))
& element(sK39(X0),powerset(the_carrier(X0))) )
| ~ sP3(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39])],[f436,f437]) ).
fof(f437,plain,
! [X0] :
( ? [X1] :
( boundary_set(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( boundary_set(sK39(X0),X0)
& empty(sK39(X0))
& element(sK39(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f436,plain,
! [X0] :
( ? [X1] :
( boundary_set(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP3(X0) ),
inference(nnf_transformation,[],[f362]) ).
fof(f2371,plain,
( ~ empty(sK39(sK33))
| spl88_175 ),
inference(avatar_component_clause,[],[f2369]) ).
fof(f2424,plain,
( ~ spl88_178
| spl88_23
| spl88_40 ),
inference(avatar_split_clause,[],[f2415,f1285,f1154,f2421]) ).
fof(f2421,plain,
( spl88_178
<=> element(sF84,powerset(sF83)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_178])]) ).
fof(f1154,plain,
( spl88_23
<=> empty(sF84) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_23])]) ).
fof(f2415,plain,
( empty(sF84)
| ~ element(sF84,powerset(sF83))
| spl88_40 ),
inference(resolution,[],[f1920,f979]) ).
fof(f2407,plain,
spl88_131,
inference(avatar_contradiction_clause,[],[f2403]) ).
fof(f2403,plain,
( $false
| spl88_131 ),
inference(resolution,[],[f2037,f1253]) ).
fof(f1253,plain,
element(sK39(sK33),powerset(sF84)),
inference(forward_demodulation,[],[f1251,f978]) ).
fof(f1251,plain,
element(sK39(sK33),powerset(the_carrier(sK33))),
inference(resolution,[],[f999,f644]) ).
fof(f644,plain,
! [X0] :
( ~ sP3(X0)
| element(sK39(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f438]) ).
fof(f2037,plain,
( ~ element(sK39(sK33),powerset(sF84))
| spl88_131 ),
inference(avatar_component_clause,[],[f2035]) ).
fof(f2035,plain,
( spl88_131
<=> element(sK39(sK33),powerset(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_131])]) ).
fof(f2402,plain,
spl88_143,
inference(avatar_contradiction_clause,[],[f2401]) ).
fof(f2401,plain,
( $false
| spl88_143 ),
inference(resolution,[],[f2381,f1121]) ).
fof(f2381,plain,
( ~ sP4(sK33)
| spl88_143 ),
inference(resolution,[],[f2176,f654]) ).
fof(f654,plain,
! [X0] :
( transitive_relstr(sK41(X0))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f443]) ).
fof(f2176,plain,
( ~ transitive_relstr(sK41(sK33))
| spl88_143 ),
inference(avatar_component_clause,[],[f2174]) ).
fof(f2400,plain,
( ~ spl88_140
| spl88_22
| spl88_177
| ~ spl88_35 ),
inference(avatar_split_clause,[],[f2396,f1228,f2398,f1148,f2102]) ).
fof(f2396,plain,
( ! [X0] :
( ~ element(X0,sF87)
| ~ upper_relstr_subset(X0,sF85)
| sP29(sK33,X0,sF81)
| empty(sF81)
| empty(X0)
| ~ filtered_subset(X0,sF85)
| ~ element(sF81,powerset(sF84)) )
| ~ spl88_35 ),
inference(forward_demodulation,[],[f2395,f982]) ).
fof(f2395,plain,
( ! [X0] :
( ~ element(X0,powerset(sF86))
| ~ upper_relstr_subset(X0,sF85)
| sP29(sK33,X0,sF81)
| empty(sF81)
| empty(X0)
| ~ filtered_subset(X0,sF85)
| ~ element(sF81,powerset(sF84)) )
| ~ spl88_35 ),
inference(forward_demodulation,[],[f2115,f981]) ).
fof(f2115,plain,
( ! [X0] :
( ~ upper_relstr_subset(X0,sF85)
| sP29(sK33,X0,sF81)
| empty(sF81)
| empty(X0)
| ~ filtered_subset(X0,sF85)
| ~ element(sF81,powerset(sF84))
| ~ element(X0,powerset(the_carrier(sF85))) )
| ~ spl88_35 ),
inference(superposition,[],[f1229,f980]) ).
fof(f2394,plain,
( ~ spl88_140
| spl88_22
| spl88_176
| ~ spl88_33 ),
inference(avatar_split_clause,[],[f2390,f1218,f2392,f1148,f2102]) ).
fof(f1218,plain,
( spl88_33
<=> ! [X11,X10] :
( ~ element(X11,powerset(sF84))
| sP27(X10,X11,sK33)
| empty(X11)
| empty(X10)
| ~ filtered_subset(X10,boole_POSet(X11))
| ~ upper_relstr_subset(X10,boole_POSet(X11))
| ~ proper_element(X10,powerset(the_carrier(boole_POSet(X11))))
| ~ element(X10,powerset(the_carrier(boole_POSet(X11)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_33])]) ).
fof(f2390,plain,
( ! [X0] :
( ~ element(X0,sF87)
| ~ proper_element(X0,sF87)
| sP27(X0,sF81,sK33)
| empty(sF81)
| empty(X0)
| ~ filtered_subset(X0,sF85)
| ~ upper_relstr_subset(X0,sF85)
| ~ element(sF81,powerset(sF84)) )
| ~ spl88_33 ),
inference(forward_demodulation,[],[f2389,f982]) ).
fof(f2389,plain,
( ! [X0] :
( ~ element(X0,powerset(sF86))
| ~ proper_element(X0,sF87)
| sP27(X0,sF81,sK33)
| empty(sF81)
| empty(X0)
| ~ filtered_subset(X0,sF85)
| ~ upper_relstr_subset(X0,sF85)
| ~ element(sF81,powerset(sF84)) )
| ~ spl88_33 ),
inference(forward_demodulation,[],[f2388,f981]) ).
fof(f2388,plain,
( ! [X0] :
( ~ proper_element(X0,sF87)
| sP27(X0,sF81,sK33)
| empty(sF81)
| empty(X0)
| ~ filtered_subset(X0,sF85)
| ~ upper_relstr_subset(X0,sF85)
| ~ element(sF81,powerset(sF84))
| ~ element(X0,powerset(the_carrier(sF85))) )
| ~ spl88_33 ),
inference(forward_demodulation,[],[f2387,f982]) ).
fof(f2387,plain,
( ! [X0] :
( ~ proper_element(X0,powerset(sF86))
| sP27(X0,sF81,sK33)
| empty(sF81)
| empty(X0)
| ~ filtered_subset(X0,sF85)
| ~ upper_relstr_subset(X0,sF85)
| ~ element(sF81,powerset(sF84))
| ~ element(X0,powerset(the_carrier(sF85))) )
| ~ spl88_33 ),
inference(forward_demodulation,[],[f2159,f981]) ).
fof(f2159,plain,
( ! [X0] :
( ~ proper_element(X0,powerset(the_carrier(sF85)))
| sP27(X0,sF81,sK33)
| empty(sF81)
| empty(X0)
| ~ filtered_subset(X0,sF85)
| ~ upper_relstr_subset(X0,sF85)
| ~ element(sF81,powerset(sF84))
| ~ element(X0,powerset(the_carrier(sF85))) )
| ~ spl88_33 ),
inference(superposition,[],[f1219,f980]) ).
fof(f1219,plain,
( ! [X10,X11] :
( ~ proper_element(X10,powerset(the_carrier(boole_POSet(X11))))
| sP27(X10,X11,sK33)
| empty(X11)
| empty(X10)
| ~ filtered_subset(X10,boole_POSet(X11))
| ~ upper_relstr_subset(X10,boole_POSet(X11))
| ~ element(X11,powerset(sF84))
| ~ element(X10,powerset(the_carrier(boole_POSet(X11)))) )
| ~ spl88_33 ),
inference(avatar_component_clause,[],[f1218]) ).
fof(f2386,plain,
spl88_140,
inference(avatar_contradiction_clause,[],[f2382]) ).
fof(f2382,plain,
( $false
| spl88_140 ),
inference(resolution,[],[f2104,f1145]) ).
fof(f1145,plain,
element(sF81,powerset(sF84)),
inference(forward_demodulation,[],[f1144,f973]) ).
fof(f1144,plain,
element(cast_as_carrier_subset(sK33),powerset(sF84)),
inference(forward_demodulation,[],[f1119,f978]) ).
fof(f1119,plain,
element(cast_as_carrier_subset(sK33),powerset(the_carrier(sK33))),
inference(resolution,[],[f997,f648]) ).
fof(f648,plain,
! [X0] :
( ~ one_sorted_str(X0)
| element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f205]) ).
fof(f205,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( one_sorted_str(X0)
=> element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',dt_k2_pre_topc) ).
fof(f2104,plain,
( ~ element(sF81,powerset(sF84))
| spl88_140 ),
inference(avatar_component_clause,[],[f2102]) ).
fof(f2376,plain,
( ~ spl88_65
| spl88_134 ),
inference(avatar_split_clause,[],[f2375,f2049,f1552]) ).
fof(f2049,plain,
( spl88_134
<=> net_str(sK42(sK33),sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_134])]) ).
fof(f2375,plain,
( ~ one_sorted_str(sK33)
| spl88_134 ),
inference(resolution,[],[f2051,f659]) ).
fof(f659,plain,
! [X0] :
( net_str(sK42(X0),X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f445]) ).
fof(f445,plain,
! [X0] :
( ( strict_net_str(sK42(X0),X0)
& net_str(sK42(X0),X0) )
| ~ one_sorted_str(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42])],[f209,f444]) ).
fof(f444,plain,
! [X0] :
( ? [X1] :
( strict_net_str(X1,X0)
& net_str(X1,X0) )
=> ( strict_net_str(sK42(X0),X0)
& net_str(sK42(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f209,plain,
! [X0] :
( ? [X1] :
( strict_net_str(X1,X0)
& net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f112]) ).
fof(f112,axiom,
! [X0] :
( one_sorted_str(X0)
=> ? [X1] :
( strict_net_str(X1,X0)
& net_str(X1,X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc4_waybel_0) ).
fof(f2051,plain,
( ~ net_str(sK42(sK33),sK33)
| spl88_134 ),
inference(avatar_component_clause,[],[f2049]) ).
fof(f2374,plain,
spl88_142,
inference(avatar_contradiction_clause,[],[f2373]) ).
fof(f2373,plain,
( $false
| spl88_142 ),
inference(resolution,[],[f2366,f1121]) ).
fof(f2366,plain,
( ~ sP4(sK33)
| spl88_142 ),
inference(resolution,[],[f2172,f657]) ).
fof(f657,plain,
! [X0] :
( directed_relstr(sK41(X0))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f443]) ).
fof(f2172,plain,
( ~ directed_relstr(sK41(sK33))
| spl88_142 ),
inference(avatar_component_clause,[],[f2170]) ).
fof(f2372,plain,
( ~ spl88_175
| ~ spl88_131
| ~ spl88_12
| spl88_129 ),
inference(avatar_split_clause,[],[f2367,f2027,f1068,f2035,f2369]) ).
fof(f1068,plain,
( spl88_12
<=> ! [X6] :
( ~ element(X6,powerset(sF84))
| open_subset(X6,sK33)
| ~ empty(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_12])]) ).
fof(f2027,plain,
( spl88_129
<=> open_subset(sK39(sK33),sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_129])]) ).
fof(f2367,plain,
( ~ element(sK39(sK33),powerset(sF84))
| ~ empty(sK39(sK33))
| ~ spl88_12
| spl88_129 ),
inference(resolution,[],[f2029,f1069]) ).
fof(f1069,plain,
( ! [X6] :
( open_subset(X6,sK33)
| ~ element(X6,powerset(sF84))
| ~ empty(X6) )
| ~ spl88_12 ),
inference(avatar_component_clause,[],[f1068]) ).
fof(f2029,plain,
( ~ open_subset(sK39(sK33),sK33)
| spl88_129 ),
inference(avatar_component_clause,[],[f2027]) ).
fof(f2360,plain,
( ~ spl88_174
| ~ spl88_61
| ~ spl88_12
| spl88_62 ),
inference(avatar_split_clause,[],[f2354,f1462,f1068,f1458,f2357]) ).
fof(f1462,plain,
( spl88_62
<=> open_subset(empty_set,sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_62])]) ).
fof(f2354,plain,
( ~ element(empty_set,powerset(sF84))
| ~ empty(empty_set)
| ~ spl88_12
| spl88_62 ),
inference(resolution,[],[f1464,f1069]) ).
fof(f1464,plain,
( ~ open_subset(empty_set,sK33)
| spl88_62 ),
inference(avatar_component_clause,[],[f1462]) ).
fof(f2355,plain,
( ~ spl88_17
| spl88_62 ),
inference(avatar_contradiction_clause,[],[f2353]) ).
fof(f2353,plain,
( $false
| ~ spl88_17
| spl88_62 ),
inference(resolution,[],[f1464,f1394]) ).
fof(f1394,plain,
( open_subset(empty_set,sK33)
| ~ spl88_17 ),
inference(backward_demodulation,[],[f1295,f1392]) ).
fof(f1295,plain,
( open_subset(sK54(sK33),sK33)
| ~ spl88_17 ),
inference(resolution,[],[f1094,f792]) ).
fof(f792,plain,
! [X0] :
( ~ sP21(X0)
| open_subset(sK54(X0),X0) ),
inference(cnf_transformation,[],[f487]) ).
fof(f2352,plain,
( ~ spl88_62
| spl88_63
| ~ spl88_61
| ~ spl88_173
| ~ spl88_15
| ~ spl88_16
| ~ spl88_17 ),
inference(avatar_split_clause,[],[f2022,f1092,f1088,f1083,f2349,f1458,f1466,f1462]) ).
fof(f1466,plain,
( spl88_63
<=> sP20(sK33,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_63])]) ).
fof(f1083,plain,
( spl88_15
<=> ! [X9] :
( ~ element(X9,powerset(sF84))
| sP20(sK33,X9)
| ~ open_subset(X9,sK33)
| ~ nowhere_dense(X9,sK33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_15])]) ).
fof(f1088,plain,
( spl88_16
<=> ! [X10] :
( ~ element(X10,powerset(sF84))
| nowhere_dense(X10,sK33)
| ~ closed_subset(X10,sK33)
| ~ boundary_set(X10,sK33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_16])]) ).
fof(f2022,plain,
( ~ closed_subset(empty_set,sK33)
| ~ element(empty_set,powerset(sF84))
| sP20(sK33,empty_set)
| ~ open_subset(empty_set,sK33)
| ~ spl88_15
| ~ spl88_16
| ~ spl88_17 ),
inference(resolution,[],[f1401,f1396]) ).
fof(f1396,plain,
( boundary_set(empty_set,sK33)
| ~ spl88_17 ),
inference(backward_demodulation,[],[f1297,f1392]) ).
fof(f1297,plain,
( boundary_set(sK54(sK33),sK33)
| ~ spl88_17 ),
inference(resolution,[],[f1094,f794]) ).
fof(f794,plain,
! [X0] :
( ~ sP21(X0)
| boundary_set(sK54(X0),X0) ),
inference(cnf_transformation,[],[f487]) ).
fof(f1401,plain,
( ! [X0] :
( ~ boundary_set(X0,sK33)
| ~ closed_subset(X0,sK33)
| ~ element(X0,powerset(sF84))
| sP20(sK33,X0)
| ~ open_subset(X0,sK33) )
| ~ spl88_15
| ~ spl88_16 ),
inference(duplicate_literal_removal,[],[f1400]) ).
fof(f1400,plain,
( ! [X0] :
( ~ element(X0,powerset(sF84))
| ~ closed_subset(X0,sK33)
| ~ boundary_set(X0,sK33)
| sP20(sK33,X0)
| ~ open_subset(X0,sK33)
| ~ element(X0,powerset(sF84)) )
| ~ spl88_15
| ~ spl88_16 ),
inference(resolution,[],[f1089,f1084]) ).
fof(f1084,plain,
( ! [X9] :
( ~ nowhere_dense(X9,sK33)
| sP20(sK33,X9)
| ~ open_subset(X9,sK33)
| ~ element(X9,powerset(sF84)) )
| ~ spl88_15 ),
inference(avatar_component_clause,[],[f1083]) ).
fof(f1089,plain,
( ! [X10] :
( nowhere_dense(X10,sK33)
| ~ element(X10,powerset(sF84))
| ~ closed_subset(X10,sK33)
| ~ boundary_set(X10,sK33) )
| ~ spl88_16 ),
inference(avatar_component_clause,[],[f1088]) ).
fof(f2347,plain,
( ~ spl88_17
| spl88_61 ),
inference(avatar_contradiction_clause,[],[f2343]) ).
fof(f2343,plain,
( $false
| ~ spl88_17
| spl88_61 ),
inference(resolution,[],[f1460,f1398]) ).
fof(f1398,plain,
( element(empty_set,powerset(sF84))
| ~ spl88_17 ),
inference(backward_demodulation,[],[f1299,f1392]) ).
fof(f1299,plain,
( element(sK54(sK33),powerset(sF84))
| ~ spl88_17 ),
inference(forward_demodulation,[],[f1293,f978]) ).
fof(f1293,plain,
( element(sK54(sK33),powerset(the_carrier(sK33)))
| ~ spl88_17 ),
inference(resolution,[],[f1094,f790]) ).
fof(f790,plain,
! [X0] :
( ~ sP21(X0)
| element(sK54(X0),powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f487]) ).
fof(f1460,plain,
( ~ element(empty_set,powerset(sF84))
| spl88_61 ),
inference(avatar_component_clause,[],[f1458]) ).
fof(f2342,plain,
( spl88_172
| spl88_144
| ~ spl88_170 ),
inference(avatar_split_clause,[],[f2198,f2329,f2178,f2339]) ).
fof(f2339,plain,
( spl88_172
<=> sP6(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_172])]) ).
fof(f2329,plain,
( spl88_170
<=> complete_relstr(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_170])]) ).
fof(f2198,plain,
( ~ complete_relstr(sK41(sK33))
| empty_carrier(sK41(sK33))
| sP6(sK41(sK33)) ),
inference(resolution,[],[f2168,f678]) ).
fof(f2337,plain,
( spl88_171
| spl88_144
| ~ spl88_151
| ~ spl88_167 ),
inference(avatar_split_clause,[],[f2199,f2315,f2232,f2178,f2334]) ).
fof(f2334,plain,
( spl88_171
<=> sP8(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_171])]) ).
fof(f2315,plain,
( spl88_167
<=> join_complete_relstr(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_167])]) ).
fof(f2199,plain,
( ~ join_complete_relstr(sK41(sK33))
| ~ reflexive_relstr(sK41(sK33))
| empty_carrier(sK41(sK33))
| sP8(sK41(sK33)) ),
inference(resolution,[],[f2168,f690]) ).
fof(f2332,plain,
( spl88_169
| spl88_144
| ~ spl88_151
| ~ spl88_170 ),
inference(avatar_split_clause,[],[f2200,f2329,f2232,f2178,f2325]) ).
fof(f2325,plain,
( spl88_169
<=> sP9(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_169])]) ).
fof(f2200,plain,
( ~ complete_relstr(sK41(sK33))
| ~ reflexive_relstr(sK41(sK33))
| empty_carrier(sK41(sK33))
| sP9(sK41(sK33)) ),
inference(resolution,[],[f2168,f695]) ).
fof(f2323,plain,
( spl88_168
| spl88_144
| ~ spl88_151
| ~ spl88_156
| ~ spl88_167 ),
inference(avatar_split_clause,[],[f2201,f2315,f2255,f2232,f2178,f2320]) ).
fof(f2320,plain,
( spl88_168
<=> sP10(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_168])]) ).
fof(f2255,plain,
( spl88_156
<=> antisymmetric_relstr(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_156])]) ).
fof(f2201,plain,
( ~ join_complete_relstr(sK41(sK33))
| ~ antisymmetric_relstr(sK41(sK33))
| ~ reflexive_relstr(sK41(sK33))
| empty_carrier(sK41(sK33))
| sP10(sK41(sK33)) ),
inference(resolution,[],[f2168,f700]) ).
fof(f2318,plain,
( spl88_166
| spl88_144
| ~ spl88_151
| ~ spl88_156
| ~ spl88_164
| ~ spl88_167 ),
inference(avatar_split_clause,[],[f2202,f2315,f2301,f2255,f2232,f2178,f2311]) ).
fof(f2311,plain,
( spl88_166
<=> sP11(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_166])]) ).
fof(f2301,plain,
( spl88_164
<=> upper_bounded_relstr(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_164])]) ).
fof(f2202,plain,
( ~ join_complete_relstr(sK41(sK33))
| ~ upper_bounded_relstr(sK41(sK33))
| ~ antisymmetric_relstr(sK41(sK33))
| ~ reflexive_relstr(sK41(sK33))
| empty_carrier(sK41(sK33))
| sP11(sK41(sK33)) ),
inference(resolution,[],[f2168,f706]) ).
fof(f2309,plain,
( spl88_144
| ~ spl88_165
| ~ spl88_155 ),
inference(avatar_split_clause,[],[f2207,f2249,f2306,f2178]) ).
fof(f2306,plain,
( spl88_165
<=> lower_bounded_relstr(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_165])]) ).
fof(f2249,plain,
( spl88_155
<=> empty(cast_as_carrier_subset(sK41(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_155])]) ).
fof(f2207,plain,
( ~ empty(cast_as_carrier_subset(sK41(sK33)))
| ~ lower_bounded_relstr(sK41(sK33))
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2168,f753]) ).
fof(f2304,plain,
( spl88_144
| ~ spl88_164
| ~ spl88_155 ),
inference(avatar_split_clause,[],[f2208,f2249,f2301,f2178]) ).
fof(f2208,plain,
( ~ empty(cast_as_carrier_subset(sK41(sK33)))
| ~ upper_bounded_relstr(sK41(sK33))
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2168,f755]) ).
fof(f2299,plain,
( spl88_144
| ~ spl88_155 ),
inference(avatar_split_clause,[],[f2209,f2249,f2178]) ).
fof(f2209,plain,
( ~ empty(cast_as_carrier_subset(sK41(sK33)))
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2168,f756]) ).
fof(f2298,plain,
( spl88_144
| ~ spl88_155 ),
inference(avatar_split_clause,[],[f2210,f2249,f2178]) ).
fof(f2210,plain,
( ~ empty(cast_as_carrier_subset(sK41(sK33)))
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2168,f757]) ).
fof(f2297,plain,
( spl88_144
| spl88_163 ),
inference(avatar_split_clause,[],[f2211,f2294,f2178]) ).
fof(f2294,plain,
( spl88_163
<=> sP17(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_163])]) ).
fof(f2211,plain,
( sP17(sK41(sK33))
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2168,f762]) ).
fof(f2292,plain,
( spl88_144
| ~ spl88_151
| spl88_162 ),
inference(avatar_split_clause,[],[f2212,f2289,f2232,f2178]) ).
fof(f2289,plain,
( spl88_162
<=> sP18(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_162])]) ).
fof(f2212,plain,
( sP18(sK41(sK33))
| ~ reflexive_relstr(sK41(sK33))
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2168,f767]) ).
fof(f2287,plain,
( spl88_144
| ~ spl88_151
| ~ spl88_143
| spl88_161 ),
inference(avatar_split_clause,[],[f2213,f2284,f2174,f2232,f2178]) ).
fof(f2284,plain,
( spl88_161
<=> element(sK52(sK41(sK33)),powerset(the_carrier(sK41(sK33)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_161])]) ).
fof(f2213,plain,
( element(sK52(sK41(sK33)),powerset(the_carrier(sK41(sK33))))
| ~ transitive_relstr(sK41(sK33))
| ~ reflexive_relstr(sK41(sK33))
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2168,f768]) ).
fof(f2282,plain,
( spl88_144
| ~ spl88_151
| ~ spl88_143
| spl88_160 ),
inference(avatar_split_clause,[],[f2214,f2279,f2174,f2232,f2178]) ).
fof(f2279,plain,
( spl88_160
<=> sP19(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_160])]) ).
fof(f2214,plain,
( sP19(sK41(sK33))
| ~ transitive_relstr(sK41(sK33))
| ~ reflexive_relstr(sK41(sK33))
| empty_carrier(sK41(sK33)) ),
inference(resolution,[],[f2168,f774]) ).
fof(f2277,plain,
~ spl88_144,
inference(avatar_contradiction_clause,[],[f2276]) ).
fof(f2276,plain,
( $false
| ~ spl88_144 ),
inference(resolution,[],[f2273,f1121]) ).
fof(f2273,plain,
( ~ sP4(sK33)
| ~ spl88_144 ),
inference(resolution,[],[f2180,f652]) ).
fof(f652,plain,
! [X0] :
( ~ empty_carrier(sK41(X0))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f443]) ).
fof(f2180,plain,
( empty_carrier(sK41(sK33))
| ~ spl88_144 ),
inference(avatar_component_clause,[],[f2178]) ).
fof(f2272,plain,
( spl88_158
| ~ spl88_159 ),
inference(avatar_split_clause,[],[f2263,f2269,f2265]) ).
fof(f2265,plain,
( spl88_158
<=> sK41(sK33) = net_str_of(sK33,the_carrier(sK41(sK33)),the_InternalRel(sK41(sK33)),the_mapping(sK33,sK41(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_158])]) ).
fof(f2263,plain,
( ~ net_str(sK41(sK33),sK33)
| sK41(sK33) = net_str_of(sK33,the_carrier(sK41(sK33)),the_InternalRel(sK41(sK33)),the_mapping(sK33,sK41(sK33))) ),
inference(resolution,[],[f1319,f1135]) ).
fof(f1319,plain,
strict_net_str(sK41(sK33),sK33),
inference(resolution,[],[f1121,f656]) ).
fof(f656,plain,
! [X0] :
( ~ sP4(X0)
| strict_net_str(sK41(X0),X0) ),
inference(cnf_transformation,[],[f443]) ).
fof(f2262,plain,
( ~ spl88_151
| ~ spl88_143
| ~ spl88_156
| ~ spl88_152
| ~ spl88_154
| spl88_157 ),
inference(avatar_split_clause,[],[f2217,f2259,f2245,f2236,f2255,f2174,f2232]) ).
fof(f2236,plain,
( spl88_152
<=> with_suprema_relstr(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_152])]) ).
fof(f2245,plain,
( spl88_154
<=> with_infima_relstr(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_154])]) ).
fof(f2259,plain,
( spl88_157
<=> sP23(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_157])]) ).
fof(f2217,plain,
( sP23(sK41(sK33))
| ~ with_infima_relstr(sK41(sK33))
| ~ with_suprema_relstr(sK41(sK33))
| ~ antisymmetric_relstr(sK41(sK33))
| ~ transitive_relstr(sK41(sK33))
| ~ reflexive_relstr(sK41(sK33)) ),
inference(resolution,[],[f2168,f812]) ).
fof(f2253,plain,
( ~ spl88_152
| ~ spl88_155 ),
inference(avatar_split_clause,[],[f2216,f2249,f2236]) ).
fof(f2216,plain,
( ~ empty(cast_as_carrier_subset(sK41(sK33)))
| ~ with_suprema_relstr(sK41(sK33)) ),
inference(resolution,[],[f2168,f807]) ).
fof(f2252,plain,
( ~ spl88_154
| ~ spl88_155 ),
inference(avatar_split_clause,[],[f2215,f2249,f2245]) ).
fof(f2215,plain,
( ~ empty(cast_as_carrier_subset(sK41(sK33)))
| ~ with_infima_relstr(sK41(sK33)) ),
inference(resolution,[],[f2168,f805]) ).
fof(f2243,plain,
( spl88_150
| ~ spl88_151
| ~ spl88_152
| ~ spl88_153 ),
inference(avatar_split_clause,[],[f2204,f2240,f2236,f2232,f2228]) ).
fof(f2228,plain,
( spl88_150
<=> sP13(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_150])]) ).
fof(f2240,plain,
( spl88_153
<=> up_complete_relstr(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_153])]) ).
fof(f2204,plain,
( ~ up_complete_relstr(sK41(sK33))
| ~ with_suprema_relstr(sK41(sK33))
| ~ reflexive_relstr(sK41(sK33))
| sP13(sK41(sK33)) ),
inference(resolution,[],[f2168,f723]) ).
fof(f2226,plain,
( spl88_148
| ~ spl88_149 ),
inference(avatar_split_clause,[],[f2197,f2223,f2219]) ).
fof(f2219,plain,
( spl88_148
<=> sK41(sK33) = rel_str_of(the_carrier(sK41(sK33)),the_InternalRel(sK41(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_148])]) ).
fof(f2223,plain,
( spl88_149
<=> strict_rel_str(sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_149])]) ).
fof(f2197,plain,
( ~ strict_rel_str(sK41(sK33))
| sK41(sK33) = rel_str_of(the_carrier(sK41(sK33)),the_InternalRel(sK41(sK33))) ),
inference(resolution,[],[f2168,f671]) ).
fof(f2194,plain,
( spl88_144
| spl88_147
| ~ spl88_36 ),
inference(avatar_split_clause,[],[f2167,f1232,f2192,f2178]) ).
fof(f2192,plain,
( spl88_147
<=> ! [X0] : sP31(X0,sK33,sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_147])]) ).
fof(f2167,plain,
( ! [X0] :
( sP31(X0,sK33,sK41(sK33))
| empty_carrier(sK41(sK33)) )
| ~ spl88_36 ),
inference(resolution,[],[f1318,f1233]) ).
fof(f2190,plain,
( spl88_144
| spl88_146
| ~ spl88_25 ),
inference(avatar_split_clause,[],[f2166,f1176,f2187,f2178]) ).
fof(f2166,plain,
( filter_of_net_str(sK33,sK41(sK33)) = a_2_1_yellow19(sK33,sK41(sK33))
| empty_carrier(sK41(sK33))
| ~ spl88_25 ),
inference(resolution,[],[f1318,f1177]) ).
fof(f2185,plain,
( ~ spl88_142
| ~ spl88_143
| spl88_144
| spl88_145
| ~ spl88_28 ),
inference(avatar_split_clause,[],[f2165,f1191,f2182,f2178,f2174,f2170]) ).
fof(f2182,plain,
( spl88_145
<=> sP24(sK33,sK41(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_145])]) ).
fof(f2165,plain,
( sP24(sK33,sK41(sK33))
| empty_carrier(sK41(sK33))
| ~ transitive_relstr(sK41(sK33))
| ~ directed_relstr(sK41(sK33))
| ~ spl88_28 ),
inference(resolution,[],[f1318,f1192]) ).
fof(f2140,plain,
~ spl88_138,
inference(avatar_split_clause,[],[f561,f2084]) ).
fof(f561,plain,
~ empty(sK34),
inference(cnf_transformation,[],[f426]) ).
fof(f2139,plain,
spl88_137,
inference(avatar_split_clause,[],[f983,f2080]) ).
fof(f983,plain,
element(sK34,sF87),
inference(definition_folding,[],[f565,f982,f981,f980,f973]) ).
fof(f565,plain,
element(sK34,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33))))),
inference(cnf_transformation,[],[f426]) ).
fof(f2138,plain,
spl88_136,
inference(avatar_split_clause,[],[f985,f2076]) ).
fof(f985,plain,
upper_relstr_subset(sK34,sF85),
inference(definition_folding,[],[f563,f980,f973]) ).
fof(f563,plain,
upper_relstr_subset(sK34,boole_POSet(cast_as_carrier_subset(sK33))),
inference(cnf_transformation,[],[f426]) ).
fof(f2137,plain,
spl88_135,
inference(avatar_split_clause,[],[f986,f2072]) ).
fof(f986,plain,
filtered_subset(sK34,sF85),
inference(definition_folding,[],[f562,f980,f973]) ).
fof(f562,plain,
filtered_subset(sK34,boole_POSet(cast_as_carrier_subset(sK33))),
inference(cnf_transformation,[],[f426]) ).
fof(f2119,plain,
~ spl88_138,
inference(avatar_contradiction_clause,[],[f2116]) ).
fof(f2116,plain,
( $false
| ~ spl88_138 ),
inference(resolution,[],[f2086,f561]) ).
fof(f2086,plain,
( empty(sK34)
| ~ spl88_138 ),
inference(avatar_component_clause,[],[f2084]) ).
fof(f2112,plain,
spl88_137,
inference(avatar_contradiction_clause,[],[f2109]) ).
fof(f2109,plain,
( $false
| spl88_137 ),
inference(resolution,[],[f2082,f983]) ).
fof(f2082,plain,
( ~ element(sK34,sF87)
| spl88_137 ),
inference(avatar_component_clause,[],[f2080]) ).
fof(f2108,plain,
( ~ spl88_140
| spl88_22
| spl88_141
| ~ spl88_34 ),
inference(avatar_split_clause,[],[f2100,f1223,f2106,f1148,f2102]) ).
fof(f2106,plain,
( spl88_141
<=> ! [X0] :
( ~ element(X0,sF87)
| ~ filtered_subset(X0,sF85)
| empty(X0)
| sP28(sK33,X0,sF81)
| ~ upper_relstr_subset(X0,sF85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_141])]) ).
fof(f2100,plain,
( ! [X0] :
( ~ element(X0,sF87)
| ~ upper_relstr_subset(X0,sF85)
| sP28(sK33,X0,sF81)
| empty(sF81)
| empty(X0)
| ~ filtered_subset(X0,sF85)
| ~ element(sF81,powerset(sF84)) )
| ~ spl88_34 ),
inference(forward_demodulation,[],[f2099,f982]) ).
fof(f2099,plain,
( ! [X0] :
( ~ element(X0,powerset(sF86))
| ~ upper_relstr_subset(X0,sF85)
| sP28(sK33,X0,sF81)
| empty(sF81)
| empty(X0)
| ~ filtered_subset(X0,sF85)
| ~ element(sF81,powerset(sF84)) )
| ~ spl88_34 ),
inference(forward_demodulation,[],[f2098,f981]) ).
fof(f2098,plain,
( ! [X0] :
( ~ upper_relstr_subset(X0,sF85)
| sP28(sK33,X0,sF81)
| empty(sF81)
| empty(X0)
| ~ filtered_subset(X0,sF85)
| ~ element(sF81,powerset(sF84))
| ~ element(X0,powerset(the_carrier(sF85))) )
| ~ spl88_34 ),
inference(superposition,[],[f1224,f980]) ).
fof(f2095,plain,
spl88_136,
inference(avatar_contradiction_clause,[],[f2094]) ).
fof(f2094,plain,
( $false
| spl88_136 ),
inference(resolution,[],[f2078,f985]) ).
fof(f2078,plain,
( ~ upper_relstr_subset(sK34,sF85)
| spl88_136 ),
inference(avatar_component_clause,[],[f2076]) ).
fof(f2093,plain,
spl88_135,
inference(avatar_contradiction_clause,[],[f2092]) ).
fof(f2092,plain,
( $false
| spl88_135 ),
inference(resolution,[],[f2074,f986]) ).
fof(f2074,plain,
( ~ filtered_subset(sK34,sF85)
| spl88_135 ),
inference(avatar_component_clause,[],[f2072]) ).
fof(f2091,plain,
( ~ spl88_135
| ~ spl88_136
| ~ spl88_137
| spl88_138
| spl88_139
| ~ spl88_24 ),
inference(avatar_split_clause,[],[f2070,f1172,f2088,f2084,f2080,f2076,f2072]) ).
fof(f1172,plain,
( spl88_24
<=> ! [X1] :
( filter_of_net_str(sK33,net_of_bool_filter(sK33,sF81,X1)) = X1
| empty(X1)
| ~ element(X1,sF87)
| ~ proper_element(X1,sF87)
| ~ upper_relstr_subset(X1,sF85)
| ~ filtered_subset(X1,sF85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_24])]) ).
fof(f2070,plain,
( sK34 = filter_of_net_str(sK33,sF82)
| empty(sK34)
| ~ element(sK34,sF87)
| ~ upper_relstr_subset(sK34,sF85)
| ~ filtered_subset(sK34,sF85)
| ~ spl88_24 ),
inference(forward_demodulation,[],[f2069,f974]) ).
fof(f2069,plain,
( empty(sK34)
| ~ element(sK34,sF87)
| sK34 = filter_of_net_str(sK33,net_of_bool_filter(sK33,sF81,sK34))
| ~ upper_relstr_subset(sK34,sF85)
| ~ filtered_subset(sK34,sF85)
| ~ spl88_24 ),
inference(resolution,[],[f1173,f984]) ).
fof(f1173,plain,
( ! [X1] :
( ~ proper_element(X1,sF87)
| empty(X1)
| ~ element(X1,sF87)
| filter_of_net_str(sK33,net_of_bool_filter(sK33,sF81,X1)) = X1
| ~ upper_relstr_subset(X1,sF85)
| ~ filtered_subset(X1,sF85) )
| ~ spl88_24 ),
inference(avatar_component_clause,[],[f1172]) ).
fof(f2068,plain,
spl88_125,
inference(avatar_contradiction_clause,[],[f2061]) ).
fof(f2061,plain,
( $false
| spl88_125 ),
inference(resolution,[],[f1906,f607]) ).
fof(f1906,plain,
( ~ transitive_relstr(boole_POSet(sF84))
| spl88_125 ),
inference(avatar_component_clause,[],[f1904]) ).
fof(f1904,plain,
( spl88_125
<=> transitive_relstr(boole_POSet(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_125])]) ).
fof(f2067,plain,
spl88_125,
inference(avatar_contradiction_clause,[],[f2062]) ).
fof(f2062,plain,
( $false
| spl88_125 ),
inference(resolution,[],[f1906,f594]) ).
fof(f2066,plain,
spl88_125,
inference(avatar_contradiction_clause,[],[f2063]) ).
fof(f2063,plain,
( $false
| spl88_125 ),
inference(resolution,[],[f1906,f580]) ).
fof(f2065,plain,
spl88_125,
inference(avatar_contradiction_clause,[],[f2064]) ).
fof(f2064,plain,
( $false
| spl88_125 ),
inference(resolution,[],[f1906,f575]) ).
fof(f2060,plain,
spl88_124,
inference(avatar_contradiction_clause,[],[f2053]) ).
fof(f2053,plain,
( $false
| spl88_124 ),
inference(resolution,[],[f1902,f606]) ).
fof(f1902,plain,
( ~ reflexive_relstr(boole_POSet(sF84))
| spl88_124 ),
inference(avatar_component_clause,[],[f1900]) ).
fof(f1900,plain,
( spl88_124
<=> reflexive_relstr(boole_POSet(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_124])]) ).
fof(f2059,plain,
spl88_124,
inference(avatar_contradiction_clause,[],[f2054]) ).
fof(f2054,plain,
( $false
| spl88_124 ),
inference(resolution,[],[f1902,f593]) ).
fof(f2058,plain,
spl88_124,
inference(avatar_contradiction_clause,[],[f2055]) ).
fof(f2055,plain,
( $false
| spl88_124 ),
inference(resolution,[],[f1902,f579]) ).
fof(f2057,plain,
spl88_124,
inference(avatar_contradiction_clause,[],[f2056]) ).
fof(f2056,plain,
( $false
| spl88_124 ),
inference(resolution,[],[f1902,f574]) ).
fof(f2052,plain,
( ~ spl88_65
| spl88_133
| ~ spl88_134 ),
inference(avatar_split_clause,[],[f2043,f2049,f2045,f1552]) ).
fof(f2043,plain,
( ~ net_str(sK42(sK33),sK33)
| sK42(sK33) = net_str_of(sK33,the_carrier(sK42(sK33)),the_InternalRel(sK42(sK33)),the_mapping(sK33,sK42(sK33)))
| ~ one_sorted_str(sK33) ),
inference(resolution,[],[f1135,f660]) ).
fof(f660,plain,
! [X0] :
( strict_net_str(sK42(X0),X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f445]) ).
fof(f2042,plain,
( ~ spl88_129
| spl88_130
| ~ spl88_131
| ~ spl88_132
| ~ spl88_15
| ~ spl88_16 ),
inference(avatar_split_clause,[],[f2023,f1088,f1083,f2039,f2035,f2031,f2027]) ).
fof(f2031,plain,
( spl88_130
<=> sP20(sK33,sK39(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_130])]) ).
fof(f2023,plain,
( ~ closed_subset(sK39(sK33),sK33)
| ~ element(sK39(sK33),powerset(sF84))
| sP20(sK33,sK39(sK33))
| ~ open_subset(sK39(sK33),sK33)
| ~ spl88_15
| ~ spl88_16 ),
inference(resolution,[],[f1401,f1252]) ).
fof(f1252,plain,
boundary_set(sK39(sK33),sK33),
inference(resolution,[],[f999,f646]) ).
fof(f646,plain,
! [X0] :
( ~ sP3(X0)
| boundary_set(sK39(X0),X0) ),
inference(cnf_transformation,[],[f438]) ).
fof(f1919,plain,
( spl88_122
| spl88_123
| ~ spl88_124
| ~ spl88_125
| ~ spl88_126
| ~ spl88_127
| ~ spl88_128
| spl88_23 ),
inference(avatar_split_clause,[],[f1890,f1154,f1916,f1912,f1908,f1904,f1900,f1896,f1892]) ).
fof(f1896,plain,
( spl88_123
<=> sP14(boole_POSet(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_123])]) ).
fof(f1890,plain,
( ~ rel_str(boole_POSet(sF84))
| ~ upper_bounded_relstr(boole_POSet(sF84))
| ~ antisymmetric_relstr(boole_POSet(sF84))
| ~ transitive_relstr(boole_POSet(sF84))
| ~ reflexive_relstr(boole_POSet(sF84))
| sP14(boole_POSet(sF84))
| empty_carrier(boole_POSet(sF84))
| spl88_23 ),
inference(resolution,[],[f1343,f735]) ).
fof(f1343,plain,
( ~ trivial_carrier(boole_POSet(sF84))
| spl88_23 ),
inference(resolution,[],[f1326,f618]) ).
fof(f1326,plain,
( sP0(sF84)
| spl88_23 ),
inference(resolution,[],[f1156,f631]) ).
fof(f1156,plain,
( ~ empty(sF84)
| spl88_23 ),
inference(avatar_component_clause,[],[f1154]) ).
fof(f1885,plain,
( ~ spl88_102
| ~ spl88_110
| ~ spl88_106
| ~ spl88_111
| ~ spl88_120
| spl88_121
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1762,f1561,f1882,f1876,f1830,f1808,f1826,f1790]) ).
fof(f1790,plain,
( spl88_102
<=> reflexive_relstr(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_102])]) ).
fof(f1826,plain,
( spl88_110
<=> transitive_relstr(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_110])]) ).
fof(f1808,plain,
( spl88_106
<=> antisymmetric_relstr(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_106])]) ).
fof(f1830,plain,
( spl88_111
<=> with_suprema_relstr(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_111])]) ).
fof(f1876,plain,
( spl88_120
<=> with_infima_relstr(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_120])]) ).
fof(f1882,plain,
( spl88_121
<=> sP23(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_121])]) ).
fof(f1561,plain,
( spl88_67
<=> rel_str(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_67])]) ).
fof(f1762,plain,
( sP23(sK42(sK33))
| ~ with_infima_relstr(sK42(sK33))
| ~ with_suprema_relstr(sK42(sK33))
| ~ antisymmetric_relstr(sK42(sK33))
| ~ transitive_relstr(sK42(sK33))
| ~ reflexive_relstr(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f812]) ).
fof(f1563,plain,
( rel_str(sK42(sK33))
| ~ spl88_67 ),
inference(avatar_component_clause,[],[f1561]) ).
fof(f1880,plain,
( ~ spl88_111
| ~ spl88_115
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1761,f1561,f1848,f1830]) ).
fof(f1848,plain,
( spl88_115
<=> empty(cast_as_carrier_subset(sK42(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_115])]) ).
fof(f1761,plain,
( ~ empty(cast_as_carrier_subset(sK42(sK33)))
| ~ with_suprema_relstr(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f807]) ).
fof(f1879,plain,
( ~ spl88_120
| ~ spl88_115
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1760,f1561,f1848,f1876]) ).
fof(f1760,plain,
( ~ empty(cast_as_carrier_subset(sK42(sK33)))
| ~ with_infima_relstr(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f805]) ).
fof(f1874,plain,
( spl88_99
| ~ spl88_102
| ~ spl88_110
| spl88_119
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1759,f1561,f1871,f1826,f1790,f1777]) ).
fof(f1871,plain,
( spl88_119
<=> sP19(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_119])]) ).
fof(f1759,plain,
( sP19(sK42(sK33))
| ~ transitive_relstr(sK42(sK33))
| ~ reflexive_relstr(sK42(sK33))
| empty_carrier(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f774]) ).
fof(f1869,plain,
( spl88_99
| ~ spl88_102
| ~ spl88_110
| spl88_118
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1758,f1561,f1866,f1826,f1790,f1777]) ).
fof(f1866,plain,
( spl88_118
<=> element(sK52(sK42(sK33)),powerset(the_carrier(sK42(sK33)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_118])]) ).
fof(f1758,plain,
( element(sK52(sK42(sK33)),powerset(the_carrier(sK42(sK33))))
| ~ transitive_relstr(sK42(sK33))
| ~ reflexive_relstr(sK42(sK33))
| empty_carrier(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f768]) ).
fof(f1864,plain,
( spl88_99
| ~ spl88_102
| spl88_117
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1757,f1561,f1861,f1790,f1777]) ).
fof(f1861,plain,
( spl88_117
<=> sP18(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_117])]) ).
fof(f1757,plain,
( sP18(sK42(sK33))
| ~ reflexive_relstr(sK42(sK33))
| empty_carrier(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f767]) ).
fof(f1859,plain,
( spl88_99
| spl88_116
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1756,f1561,f1856,f1777]) ).
fof(f1856,plain,
( spl88_116
<=> sP17(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_116])]) ).
fof(f1756,plain,
( sP17(sK42(sK33))
| empty_carrier(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f762]) ).
fof(f1854,plain,
( spl88_99
| ~ spl88_115
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1755,f1561,f1848,f1777]) ).
fof(f1755,plain,
( ~ empty(cast_as_carrier_subset(sK42(sK33)))
| empty_carrier(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f757]) ).
fof(f1853,plain,
( spl88_99
| ~ spl88_115
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1754,f1561,f1848,f1777]) ).
fof(f1754,plain,
( ~ empty(cast_as_carrier_subset(sK42(sK33)))
| empty_carrier(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f756]) ).
fof(f1852,plain,
( spl88_99
| ~ spl88_108
| ~ spl88_115
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1753,f1561,f1848,f1817,f1777]) ).
fof(f1817,plain,
( spl88_108
<=> upper_bounded_relstr(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_108])]) ).
fof(f1753,plain,
( ~ empty(cast_as_carrier_subset(sK42(sK33)))
| ~ upper_bounded_relstr(sK42(sK33))
| empty_carrier(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f755]) ).
fof(f1851,plain,
( spl88_99
| ~ spl88_112
| ~ spl88_115
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1752,f1561,f1848,f1834,f1777]) ).
fof(f1834,plain,
( spl88_112
<=> lower_bounded_relstr(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_112])]) ).
fof(f1752,plain,
( ~ empty(cast_as_carrier_subset(sK42(sK33)))
| ~ lower_bounded_relstr(sK42(sK33))
| empty_carrier(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f753]) ).
fof(f1846,plain,
( spl88_114
| ~ spl88_102
| ~ spl88_111
| ~ spl88_113
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1749,f1561,f1838,f1830,f1790,f1843]) ).
fof(f1843,plain,
( spl88_114
<=> sP13(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_114])]) ).
fof(f1838,plain,
( spl88_113
<=> up_complete_relstr(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_113])]) ).
fof(f1749,plain,
( ~ up_complete_relstr(sK42(sK33))
| ~ with_suprema_relstr(sK42(sK33))
| ~ reflexive_relstr(sK42(sK33))
| sP13(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f723]) ).
fof(f1841,plain,
( spl88_109
| spl88_99
| ~ spl88_102
| ~ spl88_110
| ~ spl88_106
| ~ spl88_111
| ~ spl88_112
| ~ spl88_113
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1748,f1561,f1838,f1834,f1830,f1808,f1826,f1790,f1777,f1822]) ).
fof(f1822,plain,
( spl88_109
<=> sP12(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_109])]) ).
fof(f1748,plain,
( ~ up_complete_relstr(sK42(sK33))
| ~ lower_bounded_relstr(sK42(sK33))
| ~ with_suprema_relstr(sK42(sK33))
| ~ antisymmetric_relstr(sK42(sK33))
| ~ transitive_relstr(sK42(sK33))
| ~ reflexive_relstr(sK42(sK33))
| empty_carrier(sK42(sK33))
| sP12(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f717]) ).
fof(f1820,plain,
( spl88_107
| spl88_99
| ~ spl88_102
| ~ spl88_106
| ~ spl88_108
| ~ spl88_103
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1747,f1561,f1794,f1817,f1808,f1790,f1777,f1813]) ).
fof(f1813,plain,
( spl88_107
<=> sP11(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_107])]) ).
fof(f1794,plain,
( spl88_103
<=> join_complete_relstr(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_103])]) ).
fof(f1747,plain,
( ~ join_complete_relstr(sK42(sK33))
| ~ upper_bounded_relstr(sK42(sK33))
| ~ antisymmetric_relstr(sK42(sK33))
| ~ reflexive_relstr(sK42(sK33))
| empty_carrier(sK42(sK33))
| sP11(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f706]) ).
fof(f1811,plain,
( spl88_105
| spl88_99
| ~ spl88_102
| ~ spl88_106
| ~ spl88_103
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1746,f1561,f1794,f1808,f1790,f1777,f1804]) ).
fof(f1804,plain,
( spl88_105
<=> sP10(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_105])]) ).
fof(f1746,plain,
( ~ join_complete_relstr(sK42(sK33))
| ~ antisymmetric_relstr(sK42(sK33))
| ~ reflexive_relstr(sK42(sK33))
| empty_carrier(sK42(sK33))
| sP10(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f700]) ).
fof(f1802,plain,
( spl88_104
| spl88_99
| ~ spl88_102
| ~ spl88_100
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1745,f1561,f1781,f1790,f1777,f1799]) ).
fof(f1799,plain,
( spl88_104
<=> sP9(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_104])]) ).
fof(f1781,plain,
( spl88_100
<=> complete_relstr(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_100])]) ).
fof(f1745,plain,
( ~ complete_relstr(sK42(sK33))
| ~ reflexive_relstr(sK42(sK33))
| empty_carrier(sK42(sK33))
| sP9(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f695]) ).
fof(f1797,plain,
( spl88_101
| spl88_99
| ~ spl88_102
| ~ spl88_103
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1744,f1561,f1794,f1790,f1777,f1786]) ).
fof(f1786,plain,
( spl88_101
<=> sP8(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_101])]) ).
fof(f1744,plain,
( ~ join_complete_relstr(sK42(sK33))
| ~ reflexive_relstr(sK42(sK33))
| empty_carrier(sK42(sK33))
| sP8(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f690]) ).
fof(f1784,plain,
( spl88_98
| spl88_99
| ~ spl88_100
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1743,f1561,f1781,f1777,f1773]) ).
fof(f1773,plain,
( spl88_98
<=> sP6(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_98])]) ).
fof(f1743,plain,
( ~ complete_relstr(sK42(sK33))
| empty_carrier(sK42(sK33))
| sP6(sK42(sK33))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f678]) ).
fof(f1771,plain,
( spl88_96
| ~ spl88_97
| ~ spl88_67 ),
inference(avatar_split_clause,[],[f1742,f1561,f1768,f1764]) ).
fof(f1764,plain,
( spl88_96
<=> sK42(sK33) = rel_str_of(the_carrier(sK42(sK33)),the_InternalRel(sK42(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_96])]) ).
fof(f1768,plain,
( spl88_97
<=> strict_rel_str(sK42(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_97])]) ).
fof(f1742,plain,
( ~ strict_rel_str(sK42(sK33))
| sK42(sK33) = rel_str_of(the_carrier(sK42(sK33)),the_InternalRel(sK42(sK33)))
| ~ spl88_67 ),
inference(resolution,[],[f1563,f671]) ).
fof(f1739,plain,
( ~ spl88_76
| ~ spl88_84
| ~ spl88_80
| ~ spl88_85
| ~ spl88_94
| spl88_95
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1616,f1556,f1736,f1730,f1684,f1662,f1680,f1644]) ).
fof(f1644,plain,
( spl88_76
<=> reflexive_relstr(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_76])]) ).
fof(f1680,plain,
( spl88_84
<=> transitive_relstr(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_84])]) ).
fof(f1662,plain,
( spl88_80
<=> antisymmetric_relstr(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_80])]) ).
fof(f1684,plain,
( spl88_85
<=> with_suprema_relstr(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_85])]) ).
fof(f1730,plain,
( spl88_94
<=> with_infima_relstr(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_94])]) ).
fof(f1736,plain,
( spl88_95
<=> sP23(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_95])]) ).
fof(f1556,plain,
( spl88_66
<=> rel_str(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_66])]) ).
fof(f1616,plain,
( sP23(sK40(sK33))
| ~ with_infima_relstr(sK40(sK33))
| ~ with_suprema_relstr(sK40(sK33))
| ~ antisymmetric_relstr(sK40(sK33))
| ~ transitive_relstr(sK40(sK33))
| ~ reflexive_relstr(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f812]) ).
fof(f1558,plain,
( rel_str(sK40(sK33))
| ~ spl88_66 ),
inference(avatar_component_clause,[],[f1556]) ).
fof(f1734,plain,
( ~ spl88_85
| ~ spl88_89
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1615,f1556,f1702,f1684]) ).
fof(f1702,plain,
( spl88_89
<=> empty(cast_as_carrier_subset(sK40(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_89])]) ).
fof(f1615,plain,
( ~ empty(cast_as_carrier_subset(sK40(sK33)))
| ~ with_suprema_relstr(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f807]) ).
fof(f1733,plain,
( ~ spl88_94
| ~ spl88_89
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1614,f1556,f1702,f1730]) ).
fof(f1614,plain,
( ~ empty(cast_as_carrier_subset(sK40(sK33)))
| ~ with_infima_relstr(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f805]) ).
fof(f1728,plain,
( spl88_73
| ~ spl88_76
| ~ spl88_84
| spl88_93
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1613,f1556,f1725,f1680,f1644,f1631]) ).
fof(f1631,plain,
( spl88_73
<=> empty_carrier(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_73])]) ).
fof(f1725,plain,
( spl88_93
<=> sP19(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_93])]) ).
fof(f1613,plain,
( sP19(sK40(sK33))
| ~ transitive_relstr(sK40(sK33))
| ~ reflexive_relstr(sK40(sK33))
| empty_carrier(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f774]) ).
fof(f1723,plain,
( spl88_73
| ~ spl88_76
| ~ spl88_84
| spl88_92
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1612,f1556,f1720,f1680,f1644,f1631]) ).
fof(f1720,plain,
( spl88_92
<=> element(sK52(sK40(sK33)),powerset(the_carrier(sK40(sK33)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_92])]) ).
fof(f1612,plain,
( element(sK52(sK40(sK33)),powerset(the_carrier(sK40(sK33))))
| ~ transitive_relstr(sK40(sK33))
| ~ reflexive_relstr(sK40(sK33))
| empty_carrier(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f768]) ).
fof(f1718,plain,
( spl88_73
| ~ spl88_76
| spl88_91
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1611,f1556,f1715,f1644,f1631]) ).
fof(f1715,plain,
( spl88_91
<=> sP18(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_91])]) ).
fof(f1611,plain,
( sP18(sK40(sK33))
| ~ reflexive_relstr(sK40(sK33))
| empty_carrier(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f767]) ).
fof(f1713,plain,
( spl88_73
| spl88_90
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1610,f1556,f1710,f1631]) ).
fof(f1710,plain,
( spl88_90
<=> sP17(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_90])]) ).
fof(f1610,plain,
( sP17(sK40(sK33))
| empty_carrier(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f762]) ).
fof(f1708,plain,
( spl88_73
| ~ spl88_89
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1609,f1556,f1702,f1631]) ).
fof(f1609,plain,
( ~ empty(cast_as_carrier_subset(sK40(sK33)))
| empty_carrier(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f757]) ).
fof(f1707,plain,
( spl88_73
| ~ spl88_89
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1608,f1556,f1702,f1631]) ).
fof(f1608,plain,
( ~ empty(cast_as_carrier_subset(sK40(sK33)))
| empty_carrier(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f756]) ).
fof(f1706,plain,
( spl88_73
| ~ spl88_82
| ~ spl88_89
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1607,f1556,f1702,f1671,f1631]) ).
fof(f1671,plain,
( spl88_82
<=> upper_bounded_relstr(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_82])]) ).
fof(f1607,plain,
( ~ empty(cast_as_carrier_subset(sK40(sK33)))
| ~ upper_bounded_relstr(sK40(sK33))
| empty_carrier(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f755]) ).
fof(f1705,plain,
( spl88_73
| ~ spl88_86
| ~ spl88_89
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1606,f1556,f1702,f1688,f1631]) ).
fof(f1688,plain,
( spl88_86
<=> lower_bounded_relstr(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_86])]) ).
fof(f1606,plain,
( ~ empty(cast_as_carrier_subset(sK40(sK33)))
| ~ lower_bounded_relstr(sK40(sK33))
| empty_carrier(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f753]) ).
fof(f1700,plain,
( spl88_88
| ~ spl88_76
| ~ spl88_85
| ~ spl88_87
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1603,f1556,f1692,f1684,f1644,f1697]) ).
fof(f1697,plain,
( spl88_88
<=> sP13(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_88])]) ).
fof(f1692,plain,
( spl88_87
<=> up_complete_relstr(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_87])]) ).
fof(f1603,plain,
( ~ up_complete_relstr(sK40(sK33))
| ~ with_suprema_relstr(sK40(sK33))
| ~ reflexive_relstr(sK40(sK33))
| sP13(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f723]) ).
fof(f1695,plain,
( spl88_83
| spl88_73
| ~ spl88_76
| ~ spl88_84
| ~ spl88_80
| ~ spl88_85
| ~ spl88_86
| ~ spl88_87
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1602,f1556,f1692,f1688,f1684,f1662,f1680,f1644,f1631,f1676]) ).
fof(f1676,plain,
( spl88_83
<=> sP12(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_83])]) ).
fof(f1602,plain,
( ~ up_complete_relstr(sK40(sK33))
| ~ lower_bounded_relstr(sK40(sK33))
| ~ with_suprema_relstr(sK40(sK33))
| ~ antisymmetric_relstr(sK40(sK33))
| ~ transitive_relstr(sK40(sK33))
| ~ reflexive_relstr(sK40(sK33))
| empty_carrier(sK40(sK33))
| sP12(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f717]) ).
fof(f1674,plain,
( spl88_81
| spl88_73
| ~ spl88_76
| ~ spl88_80
| ~ spl88_82
| ~ spl88_77
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1601,f1556,f1648,f1671,f1662,f1644,f1631,f1667]) ).
fof(f1667,plain,
( spl88_81
<=> sP11(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_81])]) ).
fof(f1648,plain,
( spl88_77
<=> join_complete_relstr(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_77])]) ).
fof(f1601,plain,
( ~ join_complete_relstr(sK40(sK33))
| ~ upper_bounded_relstr(sK40(sK33))
| ~ antisymmetric_relstr(sK40(sK33))
| ~ reflexive_relstr(sK40(sK33))
| empty_carrier(sK40(sK33))
| sP11(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f706]) ).
fof(f1665,plain,
( spl88_79
| spl88_73
| ~ spl88_76
| ~ spl88_80
| ~ spl88_77
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1600,f1556,f1648,f1662,f1644,f1631,f1658]) ).
fof(f1658,plain,
( spl88_79
<=> sP10(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_79])]) ).
fof(f1600,plain,
( ~ join_complete_relstr(sK40(sK33))
| ~ antisymmetric_relstr(sK40(sK33))
| ~ reflexive_relstr(sK40(sK33))
| empty_carrier(sK40(sK33))
| sP10(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f700]) ).
fof(f1656,plain,
( spl88_78
| spl88_73
| ~ spl88_76
| ~ spl88_74
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1599,f1556,f1635,f1644,f1631,f1653]) ).
fof(f1653,plain,
( spl88_78
<=> sP9(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_78])]) ).
fof(f1635,plain,
( spl88_74
<=> complete_relstr(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_74])]) ).
fof(f1599,plain,
( ~ complete_relstr(sK40(sK33))
| ~ reflexive_relstr(sK40(sK33))
| empty_carrier(sK40(sK33))
| sP9(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f695]) ).
fof(f1651,plain,
( spl88_75
| spl88_73
| ~ spl88_76
| ~ spl88_77
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1598,f1556,f1648,f1644,f1631,f1640]) ).
fof(f1640,plain,
( spl88_75
<=> sP8(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_75])]) ).
fof(f1598,plain,
( ~ join_complete_relstr(sK40(sK33))
| ~ reflexive_relstr(sK40(sK33))
| empty_carrier(sK40(sK33))
| sP8(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f690]) ).
fof(f1638,plain,
( spl88_72
| spl88_73
| ~ spl88_74
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1597,f1556,f1635,f1631,f1627]) ).
fof(f1627,plain,
( spl88_72
<=> sP6(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_72])]) ).
fof(f1597,plain,
( ~ complete_relstr(sK40(sK33))
| empty_carrier(sK40(sK33))
| sP6(sK40(sK33))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f678]) ).
fof(f1625,plain,
( spl88_70
| ~ spl88_71
| ~ spl88_66 ),
inference(avatar_split_clause,[],[f1596,f1556,f1622,f1618]) ).
fof(f1618,plain,
( spl88_70
<=> sK40(sK33) = rel_str_of(the_carrier(sK40(sK33)),the_InternalRel(sK40(sK33))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_70])]) ).
fof(f1622,plain,
( spl88_71
<=> strict_rel_str(sK40(sK33)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_71])]) ).
fof(f1596,plain,
( ~ strict_rel_str(sK40(sK33))
| sK40(sK33) = rel_str_of(the_carrier(sK40(sK33)),the_InternalRel(sK40(sK33)))
| ~ spl88_66 ),
inference(resolution,[],[f1558,f671]) ).
fof(f1588,plain,
( ~ spl88_55
| ~ spl88_69
| ~ spl88_49 ),
inference(avatar_split_clause,[],[f1574,f1404,f1585,f1428]) ).
fof(f1428,plain,
( spl88_55
<=> rel_str(boole_POSet(sK34)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_55])]) ).
fof(f1585,plain,
( spl88_69
<=> with_infima_relstr(boole_POSet(sK34)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_69])]) ).
fof(f1404,plain,
( spl88_49
<=> empty_carrier(boole_POSet(sK34)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_49])]) ).
fof(f1574,plain,
( ~ with_infima_relstr(boole_POSet(sK34))
| ~ rel_str(boole_POSet(sK34))
| ~ spl88_49 ),
inference(resolution,[],[f1406,f670]) ).
fof(f1406,plain,
( empty_carrier(boole_POSet(sK34))
| ~ spl88_49 ),
inference(avatar_component_clause,[],[f1404]) ).
fof(f1583,plain,
( ~ spl88_55
| ~ spl88_68
| ~ spl88_49 ),
inference(avatar_split_clause,[],[f1573,f1404,f1580,f1428]) ).
fof(f1580,plain,
( spl88_68
<=> with_suprema_relstr(boole_POSet(sK34)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_68])]) ).
fof(f1573,plain,
( ~ with_suprema_relstr(boole_POSet(sK34))
| ~ rel_str(boole_POSet(sK34))
| ~ spl88_49 ),
inference(resolution,[],[f1406,f672]) ).
fof(f1578,plain,
~ spl88_49,
inference(avatar_contradiction_clause,[],[f1569]) ).
fof(f1569,plain,
( $false
| ~ spl88_49 ),
inference(resolution,[],[f1406,f604]) ).
fof(f1577,plain,
~ spl88_49,
inference(avatar_contradiction_clause,[],[f1570]) ).
fof(f1570,plain,
( $false
| ~ spl88_49 ),
inference(resolution,[],[f1406,f591]) ).
fof(f1576,plain,
~ spl88_49,
inference(avatar_contradiction_clause,[],[f1571]) ).
fof(f1571,plain,
( $false
| ~ spl88_49 ),
inference(resolution,[],[f1406,f577]) ).
fof(f1575,plain,
~ spl88_49,
inference(avatar_contradiction_clause,[],[f1572]) ).
fof(f1572,plain,
( $false
| ~ spl88_49 ),
inference(resolution,[],[f1406,f572]) ).
fof(f1568,plain,
spl88_55,
inference(avatar_contradiction_clause,[],[f1567]) ).
fof(f1567,plain,
( $false
| spl88_55 ),
inference(resolution,[],[f1430,f616]) ).
fof(f1430,plain,
( ~ rel_str(boole_POSet(sK34))
| spl88_55 ),
inference(avatar_component_clause,[],[f1428]) ).
fof(f1566,plain,
spl88_65,
inference(avatar_contradiction_clause,[],[f1565]) ).
fof(f1565,plain,
( $false
| spl88_65 ),
inference(resolution,[],[f1554,f997]) ).
fof(f1554,plain,
( ~ one_sorted_str(sK33)
| spl88_65 ),
inference(avatar_component_clause,[],[f1552]) ).
fof(f1564,plain,
( ~ spl88_65
| spl88_67 ),
inference(avatar_split_clause,[],[f1550,f1561,f1552]) ).
fof(f1550,plain,
( rel_str(sK42(sK33))
| ~ one_sorted_str(sK33) ),
inference(resolution,[],[f1120,f659]) ).
fof(f1559,plain,
( ~ spl88_65
| spl88_66 ),
inference(avatar_split_clause,[],[f1549,f1556,f1552]) ).
fof(f1549,plain,
( rel_str(sK40(sK33))
| ~ one_sorted_str(sK33) ),
inference(resolution,[],[f1120,f650]) ).
fof(f1548,plain,
( ~ spl88_55
| ~ spl88_64
| spl88_54 ),
inference(avatar_split_clause,[],[f1540,f1424,f1545,f1428]) ).
fof(f1545,plain,
( spl88_64
<=> bounded_relstr(boole_POSet(sK34)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_64])]) ).
fof(f1424,plain,
( spl88_54
<=> upper_bounded_relstr(boole_POSet(sK34)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_54])]) ).
fof(f1540,plain,
( ~ bounded_relstr(boole_POSet(sK34))
| ~ rel_str(boole_POSet(sK34))
| spl88_54 ),
inference(resolution,[],[f1426,f669]) ).
fof(f1426,plain,
( ~ upper_bounded_relstr(boole_POSet(sK34))
| spl88_54 ),
inference(avatar_component_clause,[],[f1424]) ).
fof(f1543,plain,
spl88_54,
inference(avatar_contradiction_clause,[],[f1537]) ).
fof(f1537,plain,
( $false
| spl88_54 ),
inference(resolution,[],[f1426,f610]) ).
fof(f1542,plain,
spl88_54,
inference(avatar_contradiction_clause,[],[f1538]) ).
fof(f1538,plain,
( $false
| spl88_54 ),
inference(resolution,[],[f1426,f597]) ).
fof(f1541,plain,
spl88_54,
inference(avatar_contradiction_clause,[],[f1539]) ).
fof(f1539,plain,
( $false
| spl88_54 ),
inference(resolution,[],[f1426,f583]) ).
fof(f1536,plain,
spl88_53,
inference(avatar_contradiction_clause,[],[f1529]) ).
fof(f1529,plain,
( $false
| spl88_53 ),
inference(resolution,[],[f1422,f608]) ).
fof(f1422,plain,
( ~ antisymmetric_relstr(boole_POSet(sK34))
| spl88_53 ),
inference(avatar_component_clause,[],[f1420]) ).
fof(f1420,plain,
( spl88_53
<=> antisymmetric_relstr(boole_POSet(sK34)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_53])]) ).
fof(f1535,plain,
spl88_53,
inference(avatar_contradiction_clause,[],[f1530]) ).
fof(f1530,plain,
( $false
| spl88_53 ),
inference(resolution,[],[f1422,f595]) ).
fof(f1534,plain,
spl88_53,
inference(avatar_contradiction_clause,[],[f1531]) ).
fof(f1531,plain,
( $false
| spl88_53 ),
inference(resolution,[],[f1422,f581]) ).
fof(f1533,plain,
spl88_53,
inference(avatar_contradiction_clause,[],[f1532]) ).
fof(f1532,plain,
( $false
| spl88_53 ),
inference(resolution,[],[f1422,f576]) ).
fof(f1528,plain,
spl88_52,
inference(avatar_contradiction_clause,[],[f1521]) ).
fof(f1521,plain,
( $false
| spl88_52 ),
inference(resolution,[],[f1418,f607]) ).
fof(f1418,plain,
( ~ transitive_relstr(boole_POSet(sK34))
| spl88_52 ),
inference(avatar_component_clause,[],[f1416]) ).
fof(f1416,plain,
( spl88_52
<=> transitive_relstr(boole_POSet(sK34)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_52])]) ).
fof(f1527,plain,
spl88_52,
inference(avatar_contradiction_clause,[],[f1522]) ).
fof(f1522,plain,
( $false
| spl88_52 ),
inference(resolution,[],[f1418,f594]) ).
fof(f1526,plain,
spl88_52,
inference(avatar_contradiction_clause,[],[f1523]) ).
fof(f1523,plain,
( $false
| spl88_52 ),
inference(resolution,[],[f1418,f580]) ).
fof(f1525,plain,
spl88_52,
inference(avatar_contradiction_clause,[],[f1524]) ).
fof(f1524,plain,
( $false
| spl88_52 ),
inference(resolution,[],[f1418,f575]) ).
fof(f1520,plain,
spl88_51,
inference(avatar_contradiction_clause,[],[f1513]) ).
fof(f1513,plain,
( $false
| spl88_51 ),
inference(resolution,[],[f1414,f606]) ).
fof(f1414,plain,
( ~ reflexive_relstr(boole_POSet(sK34))
| spl88_51 ),
inference(avatar_component_clause,[],[f1412]) ).
fof(f1412,plain,
( spl88_51
<=> reflexive_relstr(boole_POSet(sK34)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_51])]) ).
fof(f1519,plain,
spl88_51,
inference(avatar_contradiction_clause,[],[f1514]) ).
fof(f1514,plain,
( $false
| spl88_51 ),
inference(resolution,[],[f1414,f593]) ).
fof(f1518,plain,
spl88_51,
inference(avatar_contradiction_clause,[],[f1515]) ).
fof(f1515,plain,
( $false
| spl88_51 ),
inference(resolution,[],[f1414,f579]) ).
fof(f1517,plain,
spl88_51,
inference(avatar_contradiction_clause,[],[f1516]) ).
fof(f1516,plain,
( $false
| spl88_51 ),
inference(resolution,[],[f1414,f574]) ).
fof(f1469,plain,
( ~ spl88_61
| ~ spl88_62
| spl88_63
| ~ spl88_15
| ~ spl88_17 ),
inference(avatar_split_clause,[],[f1456,f1092,f1083,f1466,f1462,f1458]) ).
fof(f1456,plain,
( sP20(sK33,empty_set)
| ~ open_subset(empty_set,sK33)
| ~ element(empty_set,powerset(sF84))
| ~ spl88_15
| ~ spl88_17 ),
inference(resolution,[],[f1397,f1084]) ).
fof(f1397,plain,
( nowhere_dense(empty_set,sK33)
| ~ spl88_17 ),
inference(backward_demodulation,[],[f1298,f1392]) ).
fof(f1298,plain,
( nowhere_dense(sK54(sK33),sK33)
| ~ spl88_17 ),
inference(resolution,[],[f1094,f795]) ).
fof(f795,plain,
! [X0] :
( ~ sP21(X0)
| nowhere_dense(sK54(X0),X0) ),
inference(cnf_transformation,[],[f487]) ).
fof(f1453,plain,
( ~ spl88_56
| ~ spl88_57
| ~ spl88_58
| spl88_59
| spl88_60
| ~ spl88_21 ),
inference(avatar_split_clause,[],[f1432,f1115,f1450,f1446,f1442,f1438,f1434]) ).
fof(f1450,plain,
( spl88_60
<=> element(sF83,powerset(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_60])]) ).
fof(f1115,plain,
( spl88_21
<=> ! [X11] :
( element(lim_points_of_net(sK33,X11),powerset(sF84))
| empty_carrier(X11)
| ~ transitive_relstr(X11)
| ~ directed_relstr(X11)
| ~ net_str(X11,sK33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_21])]) ).
fof(f1432,plain,
( element(sF83,powerset(sF84))
| empty_carrier(sF82)
| ~ transitive_relstr(sF82)
| ~ directed_relstr(sF82)
| ~ net_str(sF82,sK33)
| ~ spl88_21 ),
inference(superposition,[],[f1116,f975]) ).
fof(f1116,plain,
( ! [X11] :
( element(lim_points_of_net(sK33,X11),powerset(sF84))
| empty_carrier(X11)
| ~ transitive_relstr(X11)
| ~ directed_relstr(X11)
| ~ net_str(X11,sK33) )
| ~ spl88_21 ),
inference(avatar_component_clause,[],[f1115]) ).
fof(f1431,plain,
( spl88_49
| spl88_50
| ~ spl88_51
| ~ spl88_52
| ~ spl88_53
| ~ spl88_54
| ~ spl88_55 ),
inference(avatar_split_clause,[],[f1402,f1428,f1424,f1420,f1416,f1412,f1408,f1404]) ).
fof(f1402,plain,
( ~ rel_str(boole_POSet(sK34))
| ~ upper_bounded_relstr(boole_POSet(sK34))
| ~ antisymmetric_relstr(boole_POSet(sK34))
| ~ transitive_relstr(boole_POSet(sK34))
| ~ reflexive_relstr(boole_POSet(sK34))
| sP14(boole_POSet(sK34))
| empty_carrier(boole_POSet(sK34)) ),
inference(resolution,[],[f1305,f735]) ).
fof(f1305,plain,
~ trivial_carrier(boole_POSet(sK34)),
inference(resolution,[],[f1118,f618]) ).
fof(f1118,plain,
sP0(sK34),
inference(resolution,[],[f561,f631]) ).
fof(f1385,plain,
( spl88_42
| spl88_43
| ~ spl88_44
| ~ spl88_45
| ~ spl88_46
| ~ spl88_47
| ~ spl88_48
| spl88_22 ),
inference(avatar_split_clause,[],[f1356,f1148,f1382,f1378,f1374,f1370,f1366,f1362,f1358]) ).
fof(f1358,plain,
( spl88_42
<=> empty_carrier(sF85) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_42])]) ).
fof(f1362,plain,
( spl88_43
<=> sP14(sF85) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_43])]) ).
fof(f1366,plain,
( spl88_44
<=> reflexive_relstr(sF85) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_44])]) ).
fof(f1370,plain,
( spl88_45
<=> transitive_relstr(sF85) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_45])]) ).
fof(f1374,plain,
( spl88_46
<=> antisymmetric_relstr(sF85) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_46])]) ).
fof(f1378,plain,
( spl88_47
<=> upper_bounded_relstr(sF85) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_47])]) ).
fof(f1356,plain,
( ~ rel_str(sF85)
| ~ upper_bounded_relstr(sF85)
| ~ antisymmetric_relstr(sF85)
| ~ transitive_relstr(sF85)
| ~ reflexive_relstr(sF85)
| sP14(sF85)
| empty_carrier(sF85)
| spl88_22 ),
inference(resolution,[],[f1341,f735]) ).
fof(f1341,plain,
( ~ trivial_carrier(sF85)
| spl88_22 ),
inference(forward_demodulation,[],[f1328,f980]) ).
fof(f1328,plain,
( ~ trivial_carrier(boole_POSet(sF81))
| spl88_22 ),
inference(resolution,[],[f1323,f618]) ).
fof(f1323,plain,
( sP0(sF81)
| spl88_22 ),
inference(resolution,[],[f1150,f631]) ).
fof(f1150,plain,
( ~ empty(sF81)
| spl88_22 ),
inference(avatar_component_clause,[],[f1148]) ).
fof(f1292,plain,
( ~ spl88_40
| spl88_41
| spl88_1 ),
inference(avatar_split_clause,[],[f1283,f988,f1289,f1285]) ).
fof(f1283,plain,
( empty(sF83)
| ~ element(sK35,sF83)
| spl88_1 ),
inference(resolution,[],[f990,f822]) ).
fof(f990,plain,
( ~ in(sK35,sF83)
| spl88_1 ),
inference(avatar_component_clause,[],[f988]) ).
fof(f1273,plain,
( ~ spl88_37
| ~ spl88_39
| ~ spl88_3 ),
inference(avatar_split_clause,[],[f1258,f1021,f1270,f1261]) ).
fof(f1261,plain,
( spl88_37
<=> rel_str(sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_37])]) ).
fof(f1270,plain,
( spl88_39
<=> with_infima_relstr(sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_39])]) ).
fof(f1021,plain,
( spl88_3
<=> empty_carrier(sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_3])]) ).
fof(f1258,plain,
( ~ with_infima_relstr(sK33)
| ~ rel_str(sK33)
| ~ spl88_3 ),
inference(resolution,[],[f1023,f670]) ).
fof(f1023,plain,
( empty_carrier(sK33)
| ~ spl88_3 ),
inference(avatar_component_clause,[],[f1021]) ).
fof(f1268,plain,
( ~ spl88_37
| ~ spl88_38
| ~ spl88_3 ),
inference(avatar_split_clause,[],[f1257,f1021,f1265,f1261]) ).
fof(f1265,plain,
( spl88_38
<=> with_suprema_relstr(sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_38])]) ).
fof(f1257,plain,
( ~ with_suprema_relstr(sK33)
| ~ rel_str(sK33)
| ~ spl88_3 ),
inference(resolution,[],[f1023,f672]) ).
fof(f1259,plain,
~ spl88_3,
inference(avatar_contradiction_clause,[],[f1256]) ).
fof(f1256,plain,
( $false
| ~ spl88_3 ),
inference(resolution,[],[f1023,f558]) ).
fof(f558,plain,
~ empty_carrier(sK33),
inference(cnf_transformation,[],[f426]) ).
fof(f1255,plain,
spl88_4,
inference(avatar_contradiction_clause,[],[f1254]) ).
fof(f1254,plain,
( $false
| spl88_4 ),
inference(resolution,[],[f1027,f559]) ).
fof(f559,plain,
topological_space(sK33),
inference(cnf_transformation,[],[f426]) ).
fof(f1027,plain,
( ~ topological_space(sK33)
| spl88_4 ),
inference(avatar_component_clause,[],[f1025]) ).
fof(f1025,plain,
( spl88_4
<=> topological_space(sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_4])]) ).
fof(f1234,plain,
( spl88_3
| spl88_36 ),
inference(avatar_split_clause,[],[f1139,f1232,f1021]) ).
fof(f1139,plain,
! [X16,X17] :
( ~ net_str(X16,sK33)
| empty_carrier(X16)
| sP31(X17,sK33,X16)
| empty_carrier(sK33) ),
inference(resolution,[],[f997,f876]) ).
fof(f1230,plain,
( spl88_3
| spl88_35 ),
inference(avatar_split_clause,[],[f1226,f1228,f1021]) ).
fof(f1226,plain,
! [X14,X15] :
( ~ element(X15,powerset(sF84))
| ~ element(X14,powerset(the_carrier(boole_POSet(X15))))
| ~ upper_relstr_subset(X14,boole_POSet(X15))
| ~ filtered_subset(X14,boole_POSet(X15))
| empty(X14)
| empty(X15)
| sP29(sK33,X14,X15)
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1138,f978]) ).
fof(f1138,plain,
! [X14,X15] :
( ~ element(X14,powerset(the_carrier(boole_POSet(X15))))
| ~ upper_relstr_subset(X14,boole_POSet(X15))
| ~ filtered_subset(X14,boole_POSet(X15))
| empty(X14)
| ~ element(X15,powerset(the_carrier(sK33)))
| empty(X15)
| sP29(sK33,X14,X15)
| empty_carrier(sK33) ),
inference(resolution,[],[f997,f869]) ).
fof(f1225,plain,
( spl88_3
| spl88_34 ),
inference(avatar_split_clause,[],[f1221,f1223,f1021]) ).
fof(f1221,plain,
! [X12,X13] :
( ~ element(X13,powerset(sF84))
| ~ element(X12,powerset(the_carrier(boole_POSet(X13))))
| ~ upper_relstr_subset(X12,boole_POSet(X13))
| ~ filtered_subset(X12,boole_POSet(X13))
| empty(X12)
| empty(X13)
| sP28(sK33,X12,X13)
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1137,f978]) ).
fof(f1137,plain,
! [X12,X13] :
( ~ element(X12,powerset(the_carrier(boole_POSet(X13))))
| ~ upper_relstr_subset(X12,boole_POSet(X13))
| ~ filtered_subset(X12,boole_POSet(X13))
| empty(X12)
| ~ element(X13,powerset(the_carrier(sK33)))
| empty(X13)
| sP28(sK33,X12,X13)
| empty_carrier(sK33) ),
inference(resolution,[],[f997,f865]) ).
fof(f1220,plain,
( spl88_3
| spl88_33 ),
inference(avatar_split_clause,[],[f1216,f1218,f1021]) ).
fof(f1216,plain,
! [X10,X11] :
( ~ element(X11,powerset(sF84))
| ~ element(X10,powerset(the_carrier(boole_POSet(X11))))
| ~ proper_element(X10,powerset(the_carrier(boole_POSet(X11))))
| ~ upper_relstr_subset(X10,boole_POSet(X11))
| ~ filtered_subset(X10,boole_POSet(X11))
| empty(X10)
| empty(X11)
| sP27(X10,X11,sK33)
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1136,f978]) ).
fof(f1136,plain,
! [X10,X11] :
( ~ element(X10,powerset(the_carrier(boole_POSet(X11))))
| ~ proper_element(X10,powerset(the_carrier(boole_POSet(X11))))
| ~ upper_relstr_subset(X10,boole_POSet(X11))
| ~ filtered_subset(X10,boole_POSet(X11))
| empty(X10)
| ~ element(X11,powerset(the_carrier(sK33)))
| empty(X11)
| sP27(X10,X11,sK33)
| empty_carrier(sK33) ),
inference(resolution,[],[f997,f860]) ).
fof(f1215,plain,
( spl88_3
| spl88_32 ),
inference(avatar_split_clause,[],[f1211,f1213,f1021]) ).
fof(f1213,plain,
( spl88_32
<=> ! [X7] :
( upper_relstr_subset(filter_of_net_str(sK33,X7),sF85)
| empty_carrier(X7)
| ~ net_str(X7,sK33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_32])]) ).
fof(f1211,plain,
! [X7] :
( upper_relstr_subset(filter_of_net_str(sK33,X7),sF85)
| ~ net_str(X7,sK33)
| empty_carrier(X7)
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1210,f980]) ).
fof(f1210,plain,
! [X7] :
( upper_relstr_subset(filter_of_net_str(sK33,X7),boole_POSet(sF81))
| ~ net_str(X7,sK33)
| empty_carrier(X7)
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1133,f973]) ).
fof(f1133,plain,
! [X7] :
( ~ net_str(X7,sK33)
| empty_carrier(X7)
| upper_relstr_subset(filter_of_net_str(sK33,X7),boole_POSet(cast_as_carrier_subset(sK33)))
| empty_carrier(sK33) ),
inference(resolution,[],[f997,f840]) ).
fof(f1209,plain,
( spl88_3
| spl88_31 ),
inference(avatar_split_clause,[],[f1132,f1207,f1021]) ).
fof(f1132,plain,
! [X6] :
( ~ net_str(X6,sK33)
| empty_carrier(X6)
| ~ empty(filter_of_net_str(sK33,X6))
| empty_carrier(sK33) ),
inference(resolution,[],[f997,f839]) ).
fof(f1205,plain,
( spl88_3
| spl88_30 ),
inference(avatar_split_clause,[],[f1131,f1203,f1021]) ).
fof(f1131,plain,
! [X5] :
( ~ net_str(X5,sK33)
| empty_carrier(X5)
| sP25(sK33,X5)
| empty_carrier(sK33) ),
inference(resolution,[],[f997,f838]) ).
fof(f1201,plain,
( spl88_3
| spl88_29 ),
inference(avatar_split_clause,[],[f1197,f1199,f1021]) ).
fof(f1197,plain,
! [X4] :
( element(filter_of_net_str(sK33,X4),sF87)
| ~ net_str(X4,sK33)
| empty_carrier(X4)
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1196,f982]) ).
fof(f1196,plain,
! [X4] :
( element(filter_of_net_str(sK33,X4),powerset(sF86))
| ~ net_str(X4,sK33)
| empty_carrier(X4)
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1195,f981]) ).
fof(f1195,plain,
! [X4] :
( element(filter_of_net_str(sK33,X4),powerset(the_carrier(sF85)))
| ~ net_str(X4,sK33)
| empty_carrier(X4)
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1194,f980]) ).
fof(f1194,plain,
! [X4] :
( element(filter_of_net_str(sK33,X4),powerset(the_carrier(boole_POSet(sF81))))
| ~ net_str(X4,sK33)
| empty_carrier(X4)
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1130,f973]) ).
fof(f1130,plain,
! [X4] :
( ~ net_str(X4,sK33)
| empty_carrier(X4)
| element(filter_of_net_str(sK33,X4),powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33)))))
| empty_carrier(sK33) ),
inference(resolution,[],[f997,f834]) ).
fof(f1193,plain,
( spl88_3
| spl88_28 ),
inference(avatar_split_clause,[],[f1129,f1191,f1021]) ).
fof(f1129,plain,
! [X3] :
( ~ net_str(X3,sK33)
| ~ directed_relstr(X3)
| ~ transitive_relstr(X3)
| empty_carrier(X3)
| sP24(sK33,X3)
| empty_carrier(sK33) ),
inference(resolution,[],[f997,f833]) ).
fof(f1189,plain,
( spl88_3
| ~ spl88_27 ),
inference(avatar_split_clause,[],[f1128,f1186,f1021]) ).
fof(f1128,plain,
( ~ empty(sK49(sK33))
| empty_carrier(sK33) ),
inference(resolution,[],[f997,f752]) ).
fof(f1184,plain,
( spl88_3
| spl88_26 ),
inference(avatar_split_clause,[],[f1179,f1181,f1021]) ).
fof(f1181,plain,
( spl88_26
<=> element(sK49(sK33),powerset(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_26])]) ).
fof(f1179,plain,
( element(sK49(sK33),powerset(sF84))
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1127,f978]) ).
fof(f1127,plain,
( element(sK49(sK33),powerset(the_carrier(sK33)))
| empty_carrier(sK33) ),
inference(resolution,[],[f997,f751]) ).
fof(f1178,plain,
( spl88_3
| spl88_25 ),
inference(avatar_split_clause,[],[f1126,f1176,f1021]) ).
fof(f1126,plain,
! [X2] :
( ~ net_str(X2,sK33)
| empty_carrier(X2)
| filter_of_net_str(sK33,X2) = a_2_1_yellow19(sK33,X2)
| empty_carrier(sK33) ),
inference(resolution,[],[f997,f750]) ).
fof(f1174,plain,
( spl88_3
| spl88_24 ),
inference(avatar_split_clause,[],[f1170,f1172,f1021]) ).
fof(f1170,plain,
! [X1] :
( filter_of_net_str(sK33,net_of_bool_filter(sK33,sF81,X1)) = X1
| ~ filtered_subset(X1,sF85)
| ~ upper_relstr_subset(X1,sF85)
| ~ proper_element(X1,sF87)
| ~ element(X1,sF87)
| empty(X1)
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1169,f973]) ).
fof(f1169,plain,
! [X1] :
( ~ filtered_subset(X1,sF85)
| ~ upper_relstr_subset(X1,sF85)
| ~ proper_element(X1,sF87)
| ~ element(X1,sF87)
| empty(X1)
| filter_of_net_str(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1)) = X1
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1168,f980]) ).
fof(f1168,plain,
! [X1] :
( ~ filtered_subset(X1,boole_POSet(sF81))
| ~ upper_relstr_subset(X1,sF85)
| ~ proper_element(X1,sF87)
| ~ element(X1,sF87)
| empty(X1)
| filter_of_net_str(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1)) = X1
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1167,f973]) ).
fof(f1167,plain,
! [X1] :
( ~ upper_relstr_subset(X1,sF85)
| ~ proper_element(X1,sF87)
| ~ element(X1,sF87)
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| empty(X1)
| filter_of_net_str(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1)) = X1
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1166,f980]) ).
fof(f1166,plain,
! [X1] :
( ~ upper_relstr_subset(X1,boole_POSet(sF81))
| ~ proper_element(X1,sF87)
| ~ element(X1,sF87)
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| empty(X1)
| filter_of_net_str(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1)) = X1
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1165,f973]) ).
fof(f1165,plain,
! [X1] :
( ~ proper_element(X1,sF87)
| ~ element(X1,sF87)
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| empty(X1)
| filter_of_net_str(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1)) = X1
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1164,f982]) ).
fof(f1164,plain,
! [X1] :
( ~ proper_element(X1,powerset(sF86))
| ~ element(X1,sF87)
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| empty(X1)
| filter_of_net_str(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1)) = X1
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1163,f981]) ).
fof(f1163,plain,
! [X1] :
( ~ proper_element(X1,powerset(the_carrier(sF85)))
| ~ element(X1,sF87)
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| empty(X1)
| filter_of_net_str(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1)) = X1
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1162,f980]) ).
fof(f1162,plain,
! [X1] :
( ~ proper_element(X1,powerset(the_carrier(boole_POSet(sF81))))
| ~ element(X1,sF87)
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| empty(X1)
| filter_of_net_str(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1)) = X1
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1161,f973]) ).
fof(f1161,plain,
! [X1] :
( ~ element(X1,sF87)
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33)))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| empty(X1)
| filter_of_net_str(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1)) = X1
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1160,f982]) ).
fof(f1160,plain,
! [X1] :
( ~ element(X1,powerset(sF86))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33)))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| empty(X1)
| filter_of_net_str(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1)) = X1
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1159,f981]) ).
fof(f1159,plain,
! [X1] :
( ~ element(X1,powerset(the_carrier(sF85)))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33)))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| empty(X1)
| filter_of_net_str(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1)) = X1
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1158,f980]) ).
fof(f1158,plain,
! [X1] :
( ~ element(X1,powerset(the_carrier(boole_POSet(sF81))))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33)))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| empty(X1)
| filter_of_net_str(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1)) = X1
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1125,f973]) ).
fof(f1125,plain,
! [X1] :
( ~ element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33)))))
| ~ proper_element(X1,powerset(the_carrier(boole_POSet(cast_as_carrier_subset(sK33)))))
| ~ upper_relstr_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| ~ filtered_subset(X1,boole_POSet(cast_as_carrier_subset(sK33)))
| empty(X1)
| filter_of_net_str(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),X1)) = X1
| empty_carrier(sK33) ),
inference(resolution,[],[f997,f749]) ).
fof(f1157,plain,
( spl88_3
| ~ spl88_23 ),
inference(avatar_split_clause,[],[f1152,f1154,f1021]) ).
fof(f1152,plain,
( ~ empty(sF84)
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1124,f978]) ).
fof(f1124,plain,
( ~ empty(the_carrier(sK33))
| empty_carrier(sK33) ),
inference(resolution,[],[f997,f748]) ).
fof(f1151,plain,
( spl88_3
| ~ spl88_22 ),
inference(avatar_split_clause,[],[f1146,f1148,f1021]) ).
fof(f1146,plain,
( ~ empty(sF81)
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1123,f973]) ).
fof(f1123,plain,
( ~ empty(cast_as_carrier_subset(sK33))
| empty_carrier(sK33) ),
inference(resolution,[],[f997,f747]) ).
fof(f747,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ~ empty(cast_as_carrier_subset(X0))
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f257]) ).
fof(f257,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f256]) ).
fof(f256,plain,
! [X0] :
( ~ empty(cast_as_carrier_subset(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(cast_as_carrier_subset(X0)) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc2_pre_topc) ).
fof(f1117,plain,
( spl88_3
| ~ spl88_4
| spl88_21 ),
inference(avatar_split_clause,[],[f1113,f1115,f1025,f1021]) ).
fof(f1113,plain,
! [X11] :
( element(lim_points_of_net(sK33,X11),powerset(sF84))
| ~ net_str(X11,sK33)
| ~ directed_relstr(X11)
| ~ transitive_relstr(X11)
| empty_carrier(X11)
| ~ topological_space(sK33)
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1017,f978]) ).
fof(f1017,plain,
! [X11] :
( ~ net_str(X11,sK33)
| ~ directed_relstr(X11)
| ~ transitive_relstr(X11)
| empty_carrier(X11)
| element(lim_points_of_net(sK33,X11),powerset(the_carrier(sK33)))
| ~ topological_space(sK33)
| empty_carrier(sK33) ),
inference(resolution,[],[f560,f828]) ).
fof(f828,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f319,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f318]) ).
fof(f318,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> element(lim_points_of_net(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',dt_k11_yellow_6) ).
fof(f1112,plain,
( ~ spl88_4
| spl88_20 ),
inference(avatar_split_clause,[],[f1107,f1109,f1025]) ).
fof(f1109,plain,
( spl88_20
<=> element(sK57(sK33),powerset(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_20])]) ).
fof(f1107,plain,
( element(sK57(sK33),powerset(sF84))
| ~ topological_space(sK33) ),
inference(forward_demodulation,[],[f1016,f978]) ).
fof(f1016,plain,
( element(sK57(sK33),powerset(the_carrier(sK33)))
| ~ topological_space(sK33) ),
inference(resolution,[],[f560,f803]) ).
fof(f803,plain,
! [X0] :
( ~ top_str(X0)
| element(sK57(X0),powerset(the_carrier(X0)))
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f494]) ).
fof(f494,plain,
! [X0] :
( ( closed_subset(sK57(X0),X0)
& element(sK57(X0),powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f303,f493]) ).
fof(f493,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
=> ( closed_subset(sK57(X0),X0)
& element(sK57(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f303,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f302]) ).
fof(f302,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f118]) ).
fof(f118,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc6_pre_topc) ).
fof(f1106,plain,
( ~ spl88_4
| spl88_19 ),
inference(avatar_split_clause,[],[f1015,f1103,f1025]) ).
fof(f1103,plain,
( spl88_19
<=> sP22(sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_19])]) ).
fof(f1015,plain,
( sP22(sK33)
| ~ topological_space(sK33) ),
inference(resolution,[],[f560,f802]) ).
fof(f802,plain,
! [X0] :
( ~ top_str(X0)
| sP22(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f401]) ).
fof(f401,plain,
! [X0] :
( sP22(X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(definition_folding,[],[f301,f400]) ).
fof(f400,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ sP22(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).
fof(f301,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f300]) ).
fof(f300,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f101]) ).
fof(f101,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc2_tops_1) ).
fof(f1101,plain,
( ~ spl88_4
| spl88_18 ),
inference(avatar_split_clause,[],[f1096,f1098,f1025]) ).
fof(f1098,plain,
( spl88_18
<=> element(sK55(sK33),powerset(sF84)) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_18])]) ).
fof(f1096,plain,
( element(sK55(sK33),powerset(sF84))
| ~ topological_space(sK33) ),
inference(forward_demodulation,[],[f1014,f978]) ).
fof(f1014,plain,
( element(sK55(sK33),powerset(the_carrier(sK33)))
| ~ topological_space(sK33) ),
inference(resolution,[],[f560,f797]) ).
fof(f797,plain,
! [X0] :
( ~ top_str(X0)
| element(sK55(X0),powerset(the_carrier(X0)))
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f489]) ).
fof(f489,plain,
! [X0] :
( ( open_subset(sK55(X0),X0)
& element(sK55(X0),powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55])],[f299,f488]) ).
fof(f488,plain,
! [X0] :
( ? [X1] :
( open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
=> ( open_subset(sK55(X0),X0)
& element(sK55(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f299,plain,
! [X0] :
( ? [X1] :
( open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f298]) ).
fof(f298,plain,
! [X0] :
( ? [X1] :
( open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( open_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc1_tops_1) ).
fof(f1095,plain,
( ~ spl88_4
| spl88_17 ),
inference(avatar_split_clause,[],[f1013,f1092,f1025]) ).
fof(f1013,plain,
( sP21(sK33)
| ~ topological_space(sK33) ),
inference(resolution,[],[f560,f796]) ).
fof(f796,plain,
! [X0] :
( ~ top_str(X0)
| sP21(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f399]) ).
fof(f399,plain,
! [X0] :
( sP21(X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(definition_folding,[],[f297,f398]) ).
fof(f297,plain,
! [X0] :
( ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f296]) ).
fof(f296,plain,
! [X0] :
( ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f180]) ).
fof(f180,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f174]) ).
fof(f174,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f171]) ).
fof(f171,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
inference(pure_predicate_removal,[],[f116]) ).
fof(f116,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc5_tops_1) ).
fof(f1090,plain,
( ~ spl88_4
| spl88_16 ),
inference(avatar_split_clause,[],[f1086,f1088,f1025]) ).
fof(f1086,plain,
! [X10] :
( ~ element(X10,powerset(sF84))
| ~ boundary_set(X10,sK33)
| ~ closed_subset(X10,sK33)
| nowhere_dense(X10,sK33)
| ~ topological_space(sK33) ),
inference(forward_demodulation,[],[f1012,f978]) ).
fof(f1012,plain,
! [X10] :
( ~ boundary_set(X10,sK33)
| ~ closed_subset(X10,sK33)
| ~ element(X10,powerset(the_carrier(sK33)))
| nowhere_dense(X10,sK33)
| ~ topological_space(sK33) ),
inference(resolution,[],[f560,f789]) ).
fof(f789,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ boundary_set(X1,X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| nowhere_dense(X1,X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f295]) ).
fof(f295,plain,
! [X0] :
( ! [X1] :
( ( nowhere_dense(X1,X0)
& boundary_set(X1,X0) )
| ~ boundary_set(X1,X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f294]) ).
fof(f294,plain,
! [X0] :
( ! [X1] :
( ( nowhere_dense(X1,X0)
& boundary_set(X1,X0) )
| ~ boundary_set(X1,X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( boundary_set(X1,X0)
& closed_subset(X1,X0) )
=> ( nowhere_dense(X1,X0)
& boundary_set(X1,X0) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',cc5_tops_1) ).
fof(f1085,plain,
( ~ spl88_4
| spl88_15 ),
inference(avatar_split_clause,[],[f1081,f1083,f1025]) ).
fof(f1081,plain,
! [X9] :
( ~ element(X9,powerset(sF84))
| ~ nowhere_dense(X9,sK33)
| ~ open_subset(X9,sK33)
| sP20(sK33,X9)
| ~ topological_space(sK33) ),
inference(forward_demodulation,[],[f1011,f978]) ).
fof(f1011,plain,
! [X9] :
( ~ nowhere_dense(X9,sK33)
| ~ open_subset(X9,sK33)
| ~ element(X9,powerset(the_carrier(sK33)))
| sP20(sK33,X9)
| ~ topological_space(sK33) ),
inference(resolution,[],[f560,f787]) ).
fof(f787,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| sP20(X0,X1)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f397]) ).
fof(f397,plain,
! [X0] :
( ! [X1] :
( sP20(X0,X1)
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(definition_folding,[],[f293,f396]) ).
fof(f396,plain,
! [X0,X1] :
( ( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1) )
| ~ sP20(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).
fof(f293,plain,
! [X0] :
( ! [X1] :
( ( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1) )
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f292]) ).
fof(f292,plain,
! [X0] :
( ! [X1] :
( ( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1) )
| ~ nowhere_dense(X1,X0)
| ~ open_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f183]) ).
fof(f183,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( nowhere_dense(X1,X0)
& open_subset(X1,X0) )
=> ( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1) ) ) ) ),
inference(pure_predicate_removal,[],[f181]) ).
fof(f181,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( nowhere_dense(X1,X0)
& open_subset(X1,X0) )
=> ( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1) ) ) ) ),
inference(pure_predicate_removal,[],[f177]) ).
fof(f177,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( nowhere_dense(X1,X0)
& open_subset(X1,X0) )
=> ( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1) ) ) ) ),
inference(pure_predicate_removal,[],[f175]) ).
fof(f175,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( nowhere_dense(X1,X0)
& open_subset(X1,X0) )
=> ( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1) ) ) ) ),
inference(pure_predicate_removal,[],[f172]) ).
fof(f172,plain,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( nowhere_dense(X1,X0)
& open_subset(X1,X0) )
=> ( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1) ) ) ) ),
inference(pure_predicate_removal,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( nowhere_dense(X1,X0)
& open_subset(X1,X0) )
=> ( nowhere_dense(X1,X0)
& boundary_set(X1,X0)
& v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1)
& closed_subset(X1,X0)
& open_subset(X1,X0)
& empty(X1) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',cc6_tops_1) ).
fof(f1080,plain,
( ~ spl88_4
| spl88_14 ),
inference(avatar_split_clause,[],[f1076,f1078,f1025]) ).
fof(f1078,plain,
( spl88_14
<=> ! [X8] :
( ~ element(X8,powerset(sF84))
| boundary_set(X8,sK33)
| ~ nowhere_dense(X8,sK33) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_14])]) ).
fof(f1076,plain,
! [X8] :
( ~ element(X8,powerset(sF84))
| ~ nowhere_dense(X8,sK33)
| boundary_set(X8,sK33)
| ~ topological_space(sK33) ),
inference(forward_demodulation,[],[f1010,f978]) ).
fof(f1010,plain,
! [X8] :
( ~ nowhere_dense(X8,sK33)
| ~ element(X8,powerset(the_carrier(sK33)))
| boundary_set(X8,sK33)
| ~ topological_space(sK33) ),
inference(resolution,[],[f560,f781]) ).
fof(f781,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ nowhere_dense(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| boundary_set(X1,X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f291]) ).
fof(f291,plain,
! [X0] :
( ! [X1] :
( boundary_set(X1,X0)
| ~ nowhere_dense(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f290]) ).
fof(f290,plain,
! [X0] :
( ! [X1] :
( boundary_set(X1,X0)
| ~ nowhere_dense(X1,X0)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( nowhere_dense(X1,X0)
=> boundary_set(X1,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',cc4_tops_1) ).
fof(f1075,plain,
( ~ spl88_4
| spl88_13 ),
inference(avatar_split_clause,[],[f1071,f1073,f1025]) ).
fof(f1071,plain,
! [X7] :
( ~ element(X7,powerset(sF84))
| ~ empty(X7)
| closed_subset(X7,sK33)
| ~ topological_space(sK33) ),
inference(forward_demodulation,[],[f1009,f978]) ).
fof(f1009,plain,
! [X7] :
( ~ empty(X7)
| ~ element(X7,powerset(the_carrier(sK33)))
| closed_subset(X7,sK33)
| ~ topological_space(sK33) ),
inference(resolution,[],[f560,f780]) ).
fof(f780,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0)))
| closed_subset(X1,X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f289,plain,
! [X0] :
( ! [X1] :
( ( closed_subset(X1,X0)
& open_subset(X1,X0) )
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f288]) ).
fof(f288,plain,
! [X0] :
( ! [X1] :
( ( closed_subset(X1,X0)
& open_subset(X1,X0) )
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( empty(X1)
=> ( closed_subset(X1,X0)
& open_subset(X1,X0) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',cc1_tops_1) ).
fof(f1070,plain,
( ~ spl88_4
| spl88_12 ),
inference(avatar_split_clause,[],[f1066,f1068,f1025]) ).
fof(f1066,plain,
! [X6] :
( ~ element(X6,powerset(sF84))
| ~ empty(X6)
| open_subset(X6,sK33)
| ~ topological_space(sK33) ),
inference(forward_demodulation,[],[f1008,f978]) ).
fof(f1008,plain,
! [X6] :
( ~ empty(X6)
| ~ element(X6,powerset(the_carrier(sK33)))
| open_subset(X6,sK33)
| ~ topological_space(sK33) ),
inference(resolution,[],[f560,f779]) ).
fof(f779,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0)))
| open_subset(X1,X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f1065,plain,
( ~ spl88_4
| spl88_11 ),
inference(avatar_split_clause,[],[f1061,f1063,f1025]) ).
fof(f1063,plain,
( spl88_11
<=> ! [X5] :
( ~ element(X5,powerset(sF84))
| nowhere_dense(X5,sK33)
| ~ empty(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_11])]) ).
fof(f1061,plain,
! [X5] :
( ~ element(X5,powerset(sF84))
| ~ empty(X5)
| nowhere_dense(X5,sK33)
| ~ topological_space(sK33) ),
inference(forward_demodulation,[],[f1007,f978]) ).
fof(f1007,plain,
! [X5] :
( ~ empty(X5)
| ~ element(X5,powerset(the_carrier(sK33)))
| nowhere_dense(X5,sK33)
| ~ topological_space(sK33) ),
inference(resolution,[],[f560,f778]) ).
fof(f778,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0)))
| nowhere_dense(X1,X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f287,plain,
! [X0] :
( ! [X1] :
( nowhere_dense(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f286]) ).
fof(f286,plain,
! [X0] :
( ! [X1] :
( nowhere_dense(X1,X0)
| ~ empty(X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( empty(X1)
=> nowhere_dense(X1,X0) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',cc3_tops_1) ).
fof(f1060,plain,
( ~ spl88_4
| spl88_9 ),
inference(avatar_split_clause,[],[f1059,f1049,f1025]) ).
fof(f1049,plain,
( spl88_9
<=> closed_subset(sF81,sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_9])]) ).
fof(f1059,plain,
( closed_subset(sF81,sK33)
| ~ topological_space(sK33) ),
inference(forward_demodulation,[],[f1006,f973]) ).
fof(f1006,plain,
( closed_subset(cast_as_carrier_subset(sK33),sK33)
| ~ topological_space(sK33) ),
inference(resolution,[],[f560,f777]) ).
fof(f777,plain,
! [X0] :
( ~ top_str(X0)
| closed_subset(cast_as_carrier_subset(X0),X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f285,plain,
! [X0] :
( ( closed_subset(cast_as_carrier_subset(X0),X0)
& open_subset(cast_as_carrier_subset(X0),X0) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f284]) ).
fof(f284,plain,
! [X0] :
( ( closed_subset(cast_as_carrier_subset(X0),X0)
& open_subset(cast_as_carrier_subset(X0),X0) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ( closed_subset(cast_as_carrier_subset(X0),X0)
& open_subset(cast_as_carrier_subset(X0),X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc8_tops_1) ).
fof(f1058,plain,
( ~ spl88_4
| spl88_10 ),
inference(avatar_split_clause,[],[f1053,f1055,f1025]) ).
fof(f1055,plain,
( spl88_10
<=> open_subset(sF81,sK33) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_10])]) ).
fof(f1053,plain,
( open_subset(sF81,sK33)
| ~ topological_space(sK33) ),
inference(forward_demodulation,[],[f1005,f973]) ).
fof(f1005,plain,
( open_subset(cast_as_carrier_subset(sK33),sK33)
| ~ topological_space(sK33) ),
inference(resolution,[],[f560,f776]) ).
fof(f776,plain,
! [X0] :
( ~ top_str(X0)
| open_subset(cast_as_carrier_subset(X0),X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f1052,plain,
( ~ spl88_4
| spl88_9 ),
inference(avatar_split_clause,[],[f1047,f1049,f1025]) ).
fof(f1047,plain,
( closed_subset(sF81,sK33)
| ~ topological_space(sK33) ),
inference(forward_demodulation,[],[f1004,f973]) ).
fof(f1004,plain,
( closed_subset(cast_as_carrier_subset(sK33),sK33)
| ~ topological_space(sK33) ),
inference(resolution,[],[f560,f775]) ).
fof(f775,plain,
! [X0] :
( ~ top_str(X0)
| closed_subset(cast_as_carrier_subset(X0),X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f283,plain,
! [X0] :
( closed_subset(cast_as_carrier_subset(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f282]) ).
fof(f282,plain,
! [X0] :
( closed_subset(cast_as_carrier_subset(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f74]) ).
fof(f74,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> closed_subset(cast_as_carrier_subset(X0),X0) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',fc5_pre_topc) ).
fof(f1046,plain,
( spl88_3
| ~ spl88_4
| spl88_8 ),
inference(avatar_split_clause,[],[f1003,f1043,f1025,f1021]) ).
fof(f1003,plain,
( sP16(sK33)
| ~ topological_space(sK33)
| empty_carrier(sK33) ),
inference(resolution,[],[f560,f746]) ).
fof(f746,plain,
! [X0] :
( ~ top_str(X0)
| sP16(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f389]) ).
fof(f389,plain,
! [X0] :
( sP16(X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f255,f388]) ).
fof(f255,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f254]) ).
fof(f254,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f119]) ).
fof(f119,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( closed_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc7_pre_topc) ).
fof(f1041,plain,
( spl88_3
| ~ spl88_4
| spl88_7 ),
inference(avatar_split_clause,[],[f1002,f1038,f1025,f1021]) ).
fof(f1002,plain,
( sP15(sK33)
| ~ topological_space(sK33)
| empty_carrier(sK33) ),
inference(resolution,[],[f560,f742]) ).
fof(f742,plain,
! [X0] :
( ~ top_str(X0)
| sP15(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f387]) ).
fof(f387,plain,
! [X0] :
( sP15(X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(definition_folding,[],[f253,f386]) ).
fof(f253,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f252]) ).
fof(f252,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f108]) ).
fof(f108,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( closed_subset(X1,X0)
& open_subset(X1,X0)
& ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',rc3_tops_1) ).
fof(f1036,plain,
( spl88_3
| ~ spl88_4
| spl88_6 ),
inference(avatar_split_clause,[],[f1032,f1034,f1025,f1021]) ).
fof(f1032,plain,
! [X3,X4] :
( ~ element(X4,sF84)
| ~ is_a_convergence_point_of_set(sK33,filter_of_net_str(sK33,X3),X4)
| ~ net_str(X3,sK33)
| ~ directed_relstr(X3)
| ~ transitive_relstr(X3)
| empty_carrier(X3)
| in(X4,lim_points_of_net(sK33,X3))
| ~ topological_space(sK33)
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1001,f978]) ).
fof(f1001,plain,
! [X3,X4] :
( ~ is_a_convergence_point_of_set(sK33,filter_of_net_str(sK33,X3),X4)
| ~ element(X4,the_carrier(sK33))
| ~ net_str(X3,sK33)
| ~ directed_relstr(X3)
| ~ transitive_relstr(X3)
| empty_carrier(X3)
| in(X4,lim_points_of_net(sK33,X3))
| ~ topological_space(sK33)
| empty_carrier(sK33) ),
inference(resolution,[],[f560,f737]) ).
fof(f737,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| in(X2,lim_points_of_net(X0,X1))
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f464]) ).
fof(f464,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( in(X2,lim_points_of_net(X0,X1))
| ~ is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) )
& ( is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| ~ in(X2,lim_points_of_net(X0,X1)) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f251]) ).
fof(f251,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,lim_points_of_net(X0,X1))
<=> is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) )
| ~ element(X2,the_carrier(X0)) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f250]) ).
fof(f250,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,lim_points_of_net(X0,X1))
<=> is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) )
| ~ element(X2,the_carrier(X0)) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f125]) ).
fof(f125,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,lim_points_of_net(X0,X1))
<=> is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982',t13_yellow19) ).
fof(f1031,plain,
( spl88_3
| ~ spl88_4
| spl88_5 ),
inference(avatar_split_clause,[],[f1019,f1029,f1025,f1021]) ).
fof(f1019,plain,
! [X2,X1] :
( ~ element(X1,sF84)
| ~ in(X1,lim_points_of_net(sK33,X2))
| ~ net_str(X2,sK33)
| ~ directed_relstr(X2)
| ~ transitive_relstr(X2)
| empty_carrier(X2)
| is_a_convergence_point_of_set(sK33,filter_of_net_str(sK33,X2),X1)
| ~ topological_space(sK33)
| empty_carrier(sK33) ),
inference(forward_demodulation,[],[f1000,f978]) ).
fof(f1000,plain,
! [X2,X1] :
( ~ in(X1,lim_points_of_net(sK33,X2))
| ~ element(X1,the_carrier(sK33))
| ~ net_str(X2,sK33)
| ~ directed_relstr(X2)
| ~ transitive_relstr(X2)
| empty_carrier(X2)
| is_a_convergence_point_of_set(sK33,filter_of_net_str(sK33,X2),X1)
| ~ topological_space(sK33)
| empty_carrier(sK33) ),
inference(resolution,[],[f560,f736]) ).
fof(f736,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ in(X2,lim_points_of_net(X0,X1))
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| is_a_convergence_point_of_set(X0,filter_of_net_str(X0,X1),X2)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f464]) ).
fof(f996,plain,
( spl88_1
| spl88_2 ),
inference(avatar_split_clause,[],[f977,f992,f988]) ).
fof(f977,plain,
( is_a_convergence_point_of_set(sK33,sK34,sK35)
| in(sK35,sF83) ),
inference(definition_folding,[],[f567,f975,f974,f973]) ).
fof(f567,plain,
( is_a_convergence_point_of_set(sK33,sK34,sK35)
| in(sK35,lim_points_of_net(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),sK34))) ),
inference(cnf_transformation,[],[f426]) ).
fof(f995,plain,
( ~ spl88_1
| ~ spl88_2 ),
inference(avatar_split_clause,[],[f976,f992,f988]) ).
fof(f976,plain,
( ~ is_a_convergence_point_of_set(sK33,sK34,sK35)
| ~ in(sK35,sF83) ),
inference(definition_folding,[],[f568,f975,f974,f973]) ).
fof(f568,plain,
( ~ is_a_convergence_point_of_set(sK33,sK34,sK35)
| ~ in(sK35,lim_points_of_net(sK33,net_of_bool_filter(sK33,cast_as_carrier_subset(sK33),sK34))) ),
inference(cnf_transformation,[],[f426]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU395+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.36 % Computer : n026.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Wed Aug 23 21:08:16 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.16/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.R6WEWm3Q2c/Vampire---4.8_15982
% 0.16/0.37 % (16125)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (16126)lrs+1011_1_bd=preordered:flr=on:fsd=off:fsr=off:irw=on:lcm=reverse:msp=off:nm=2:nwc=10.0:sos=on:sp=reverse_weighted_frequency:tgt=full:stl=62_562 on Vampire---4 for (562ds/0Mi)
% 0.22/0.43 % (16127)lrs-1004_3_av=off:ep=RSTC:fsd=off:fsr=off:urr=ec_only:stl=62_525 on Vampire---4 for (525ds/0Mi)
% 0.22/0.43 % (16129)ott+1011_4_er=known:fsd=off:nm=4:tgt=ground_499 on Vampire---4 for (499ds/0Mi)
% 0.22/0.43 % (16128)lrs+10_4:5_amm=off:bsr=on:bce=on:flr=on:fsd=off:fde=unused:gs=on:gsem=on:lcm=predicate:sos=all:tgt=ground:stl=62_514 on Vampire---4 for (514ds/0Mi)
% 0.22/0.43 % (16131)lrs+10_1024_av=off:bsr=on:br=off:ep=RSTC:fsd=off:irw=on:nm=4:nwc=1.1:sims=off:urr=on:stl=125_440 on Vampire---4 for (440ds/0Mi)
% 0.22/0.43 % (16130)ott+11_8:1_aac=none:amm=sco:anc=none:er=known:flr=on:fde=unused:irw=on:nm=0:nwc=1.2:nicw=on:sims=off:sos=all:sac=on_470 on Vampire---4 for (470ds/0Mi)
% 0.22/0.43 % (16132)ott+1010_2:5_bd=off:fsd=off:fde=none:nm=16:sos=on_419 on Vampire---4 for (419ds/0Mi)
% 0.22/0.45 % (16132)Refutation not found, incomplete strategy% (16132)------------------------------
% 0.22/0.45 % (16132)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.45 % (16132)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.45 % (16132)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.45
% 0.22/0.45 % (16132)Memory used [KB]: 6140
% 0.22/0.45 % (16132)Time elapsed: 0.012 s
% 0.22/0.45 % (16132)------------------------------
% 0.22/0.45 % (16132)------------------------------
% 0.22/0.47 % (16126)First to succeed.
% 0.22/0.48 % (16126)Refutation found. Thanks to Tanya!
% 0.22/0.48 % SZS status Theorem for Vampire---4
% 0.22/0.48 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.49 % (16126)------------------------------
% 0.22/0.49 % (16126)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.49 % (16126)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.49 % (16126)Termination reason: Refutation
% 0.22/0.49
% 0.22/0.49 % (16126)Memory used [KB]: 8059
% 0.22/0.49 % (16126)Time elapsed: 0.048 s
% 0.22/0.49 % (16126)------------------------------
% 0.22/0.49 % (16126)------------------------------
% 0.22/0.49 % (16125)Success in time 0.118 s
% 0.22/0.49 % Vampire---4.8 exiting
%------------------------------------------------------------------------------